Search for $\boldsymbol{B\to h\nu\bar{\nu}}$ decays with semileptonic   tagging at Belle

The Belle Collaboration: J. Grygier; P. Goldenzweig; M. Heck; I.; Adachi; H. Aihara; S. Al Said; D. M. Asner; T. Aushev; R. Ayad; T. Aziz; V.; Babu; I. Badhrees; S. Bahinipati; A. M. Bakich; V. Bansal; E. Barberio; P.; Behera; B. Bhuyan; J. Biswal; A. Bobrov; A. Bondar; G. Bonvicini; A. Bozek,; M. Bra\v{c}ko; T. E. Browder; D. Cervenkov; P. Chang; V. Chekelian; A. Chen,; B. G. Cheon; K. Chilikin; R. Chistov; K. Cho; Y. Choi; D. Cinabro; N. Dash,; S. Di Carlo; Z. Dole\v{z}al; Z. Dr\'asal; D. Dutta; S. Eidelman; H. Farhat,; J. E. Fast; T. Ferber; B. G. Fulsom; V. Gaur; N. Gabyshev; A. Garmash; M.; Gelb; R. Gillard; B. Golob; O. Grzymkowska; E. Guido; J. Haba; T. Hara; K.; Hayasaka; H. Hayashii; M. T. Hedges; C.-L. Hsu; T. Iijima; K. Inami; G.; Inguglia; A. Ishikawa; R. Itoh; Y. Iwasaki; W. W. Jacobs; I. Jaegle; H. B.; Jeon; Y. Jin; D. Joffe; K. K. Joo; T. Julius; J. Kahn; A. B. Kaliyar; K. H.; Kang; G. Karyan; P. Katrenko; T. Kawasaki; T. Keck; H. Kichimi; C. Kiesling,; D. Y. Kim; H. J. Kim; J. B. Kim; K. T. Kim; M. J. Kim; S. H. Kim; K.; Kinoshita; P. Kody\v{s}; S. Korpar; D. Kotchetkov; P. Kri\v{z}an; P.; Krokovny; T. Kuhr; R. Kulasiri; T. Kumita; A. Kuzmin; Y.-J. Kwon; J. S.; Lange; C. H. Li; L. Li; Y. Li; L. Li Gioi; J. Libby; D. Liventsev; M. Lubej,; T. Luo; M. Masuda; T. Matsuda; D. Matvienko; F. Metzner; K. Miyabayashi; H.; Miyake; H. Miyata; R. Mizuk; G. B. Mohanty; H. K. Moon; T. Mori; R. Mussa; E.; Nakano; M. Nakao; T. Nanut; K. J. Nath; Z. Natkaniec; M. Nayak; N. K. Nisar,; S. Nishida; S. Ogawa; S. Okuno; H. Ono; Y. Onuki; G. Pakhlova; B. Pal; C.-S.; Park; C. W. Park; H. Park; S. Paul; T. K. Pedlar; L. Pes\'antez; L. E.; Piilonen; M. Prim; C. Pulvermacher; M. Ritter; A. Rostomyan; Y. Sakai; S.; Sandilya; L. Santelj; T. Sanuki; Y. Sato; V. Savinov; T. Schl\"uter; O.; Schneider; G. Schnell; C. Schwanda; Y. Seino; K. Senyo; I. S. Seong; M. E.; Sevior; V. Shebalin; C. P. Shen; T.-A. Shibata; J.-G. Shiu; B. Shwartz; F.; Simon; E. Solovieva; M. Stari\v{c}; J. F. Strube; T. Sumiyoshi; M. Takizawa,; U. Tamponi; F. Tenchini; K. Trabelsi; T. Tsuboyama; M. Uchida; T. Uglov; Y.; Unno; S. Uno; P. Urquijo; Y. Ushiroda; C. Van Hulse; G. Varner; V. Vorobyev,; A. Vossen; E. Waheed; B. Wang; C. H. Wang; M.-Z. Wang; P. Wang; M. Watanabe,; Y. Watanabe; S. Wehle; K. M. Williams; E. Won; H. Yamamoto; Y. Yamashita; H.; Ye; Y. Yook; C. Z. Yuan; Y. Yusa; Z. P. Zhang; V. Zhilich; V. Zhukova; V.; Zhulanov; M. Ziegler; and A. Zupanc

arXiv:1702.03224·hep-ex·December 6, 2017

Search for $\boldsymbol{B\to h\nu\bar{\nu}}$ decays with semileptonic tagging at Belle

The Belle Collaboration: J. Grygier, P. Goldenzweig, M. Heck, I., Adachi, H. Aihara, S. Al Said, D. M. Asner, T. Aushev, R. Ayad, T. Aziz, V., Babu, I. Badhrees, S. Bahinipati, A. M. Bakich, V. Bansal, E. Barberio, P., Behera, B. Bhuyan, J. Biswal, A. Bobrov, A. Bondar

PDF

TL;DR

This study searches for rare B meson decays involving neutrinos using semileptonic tagging at Belle, setting the most stringent upper limits to date due to no significant signals observed.

Contribution

First search for B→hνν̄ decays with semileptonic tagging at Belle, providing the most restrictive upper limits on these branching fractions.

Findings

01

No significant signals observed in any decay channel.

02

Set the world's most stringent upper limits on branching fractions.

03

Enhanced sensitivity compared to previous searches.

Abstract

We present the results of a search for the rare decays $B \to h ν \overline{ν}$ , where $h$ stands for $K^{+}, K_{S}^{0}, K^{*+}, K^{* 0}, π^{+}, π^{0}, ρ^{+}$ and $ρ^{0}$ . The results are obtained with $772 \times 1 0^{6}$ $B \overline{B}$ pairs collected with the Belle detector at the KEKB $e^{+} e^{-}$ collider. We reconstruct one $B$ meson in a semileptonic decay and require a single $h$ meson but nothing else on the signal side. We observe no significant signal and set upper limits on the branching fractions. The limits set on the $B \to K_{S}^{0} ν \overline{ν}$ , $B^{0} \to K^{* 0} ν \overline{ν}$ , $B \to π^{+} ν \overline{ν}$ , $B^{0} \to π^{0} ν \overline{ν}$ , $B^{+} \to ρ^{+} ν \overline{ν}$ , and $B^{0} \to ρ^{0} ν \overline{ν}$ channels are the world's most stringent.

Tables4

Table 1. Table 1 : Results

Channel						Significance
\IfEqCase321 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]	$17.7$	$\pm$	$9.1$	$\pm$	$3.4$	$1.9 σ$
\IfEqCase310 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]	$0.6$	$\pm$	$4.2$	$\pm$	$1.4$	$0.0 σ$
\IfEqCase323 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]	$16.2$	$\pm$	$7.4$	$\pm$	$1.8$	$2.3 σ$
\IfEqCase313 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]	$- 2.0$	$\pm$	$3.6$	$\pm$	$1.8$	$0.0 σ$
\IfEqCase211 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]	$5.6$	$\pm$	$15.1$	$\pm$	$5.9$	$0.0 σ$
\IfEqCase111 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]	$0.2$	$\pm$	$5.6$	$\pm$	$1.6$	$0.0 σ$
\IfEqCase213 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]	$6.2$	$\pm$	$12.3$	$\pm$	$2.4$	$0.3 σ$
\IfEqCase113 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]	$11.9$	$\pm$	$9.0$	$\pm$	$3.6$	$1.2 σ$

Table 2. (a) Observed signal yield (corrected for fitting bias) in each channel. The first error is statistical and the second is systematic.

Channel						Significance
\IfEqCase321 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]	$17.7$	$\pm$	$9.1$	$\pm$	$3.4$	$1.9 σ$
\IfEqCase310 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]	$0.6$	$\pm$	$4.2$	$\pm$	$1.4$	$0.0 σ$
\IfEqCase323 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]	$16.2$	$\pm$	$7.4$	$\pm$	$1.8$	$2.3 σ$
\IfEqCase313 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]	$- 2.0$	$\pm$	$3.6$	$\pm$	$1.8$	$0.0 σ$
\IfEqCase211 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]	$5.6$	$\pm$	$15.1$	$\pm$	$5.9$	$0.0 σ$
\IfEqCase111 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]	$0.2$	$\pm$	$5.6$	$\pm$	$1.6$	$0.0 σ$
\IfEqCase213 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]	$6.2$	$\pm$	$12.3$	$\pm$	$2.4$	$0.3 σ$
\IfEqCase113 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]	$11.9$	$\pm$	$9.0$	$\pm$	$3.6$	$1.2 σ$

Table 3. (b) Expected (median) and observed upper limits on the branching fraction at 90 % percent 90 90\,\mathrm{\%} C.L. The observed limits include the systematic uncertainties.

Channel	Efficiency	Expected limit	Observed limit
$\IfEqCase 321321 K^{+} ν bar ν 310 K_{S}^{0} ν bar ν 323 K^{}^{+} ν bar ν 3321 K^{}^{+} ({}^{+}π^{0}) ν bar ν 3310 K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν 313 K^{}^{0} ν bar ν 211 π^{+} ν bar ν 111 π^{0} ν bar ν 213 ρ^{+} ν bar ν 113 ρ^{0} ν bar ν [h ν bar ν]$	$2.16 \times 10^{- 3}$	$0.8 \times 10^{- 5}$	$1.9 \times 10^{- 5}$
$\IfEqCase 310321 K^{+} ν bar ν 310 K_{S}^{0} ν bar ν 323 K^{}^{+} ν bar ν 3321 K^{}^{+} ({}^{+}π^{0}) ν bar ν 3310 K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν 313 K^{}^{0} ν bar ν 211 π^{+} ν bar ν 111 π^{0} ν bar ν 213 ρ^{+} ν bar ν 113 ρ^{0} ν bar ν [h ν bar ν]$	$0.91 \times 10^{- 3}$	$1.2 \times 10^{- 5}$	$1.3 \times 10^{- 5}$
$\IfEqCase 323321 K^{+} ν bar ν 310 K_{S}^{0} ν bar ν 323 K^{}^{+} ν bar ν 3321 K^{}^{+} ({}^{+}π^{0}) ν bar ν 3310 K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν 313 K^{}^{0} ν bar ν 211 π^{+} ν bar ν 111 π^{0} ν bar ν 213 ρ^{+} ν bar ν 113 ρ^{0} ν bar ν [h ν bar ν]$	$0.57 \times 10^{- 3}$	$2.4 \times 10^{- 5}$	$6.1 \times 10^{- 5}$
$\IfEqCase 313321 K^{+} ν bar ν 310 K_{S}^{0} ν bar ν 323 K^{}^{+} ν bar ν 3321 K^{}^{+} ({}^{+}π^{0}) ν bar ν 3310 K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν 313 K^{}^{0} ν bar ν 211 π^{+} ν bar ν 111 π^{0} ν bar ν 213 ρ^{+} ν bar ν 113 ρ^{0} ν bar ν [h ν bar ν]$	$0.51 \times 10^{- 3}$	$2.4 \times 10^{- 5}$	$1.8 \times 10^{- 5}$
$\IfEqCase 211321 K^{+} ν bar ν 310 K_{S}^{0} ν bar ν 323 K^{}^{+} ν bar ν 3321 K^{}^{+} ({}^{+}π^{0}) ν bar ν 3310 K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν 313 K^{}^{0} ν bar ν 211 π^{+} ν bar ν 111 π^{0} ν bar ν 213 ρ^{+} ν bar ν 113 ρ^{0} ν bar ν [h ν bar ν]$	$2.92 \times 10^{- 3}$	$1.3 \times 10^{- 5}$	$1.4 \times 10^{- 5}$
$\IfEqCase 111321 K^{+} ν bar ν 310 K_{S}^{0} ν bar ν 323 K^{}^{+} ν bar ν 3321 K^{}^{+} ({}^{+}π^{0}) ν bar ν 3310 K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν 313 K^{}^{0} ν bar ν 211 π^{+} ν bar ν 111 π^{0} ν bar ν 213 ρ^{+} ν bar ν 113 ρ^{0} ν bar ν [h ν bar ν]$	$1.42 \times 10^{- 3}$	$1.0 \times 10^{- 5}$	$0.9 \times 10^{- 5}$
$\IfEqCase 213321 K^{+} ν bar ν 310 K_{S}^{0} ν bar ν 323 K^{}^{+} ν bar ν 3321 K^{}^{+} ({}^{+}π^{0}) ν bar ν 3310 K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν 313 K^{}^{0} ν bar ν 211 π^{+} ν bar ν 111 π^{0} ν bar ν 213 ρ^{+} ν bar ν 113 ρ^{0} ν bar ν [h ν bar ν]$	$1.11 \times 10^{- 3}$	$2.5 \times 10^{- 5}$	$3.0 \times 10^{- 5}$
$\IfEqCase 113321 K^{+} ν bar ν 310 K_{S}^{0} ν bar ν 323 K^{}^{+} ν bar ν 3321 K^{}^{+} ({}^{+}π^{0}) ν bar ν 3310 K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν 313 K^{}^{0} ν bar ν 211 π^{+} ν bar ν 111 π^{0} ν bar ν 213 ρ^{+} ν bar ν 113 ρ^{0} ν bar ν [h ν bar ν]$	$0.82 \times 10^{- 3}$	$2.2 \times 10^{- 5}$	$4.0 \times 10^{- 5}$

Table 4. Table 2 : Additive systematic uncertainties. All values are event yields.

	\IfEqCase321 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]	\IfEqCase310 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]	\IfEqCase323 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]	\IfEqCase313 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]	\IfEqCase211 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]	\IfEqCase111 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]	\IfEqCase213 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]	\IfEqCase113 321 $K^{+} ν bar ν$ 310 $K_{S}^{0} ν bar ν$ 323 $K^{}^{+} ν bar ν$ 3321 $K^{}^{+} ({}^{+}π^{0}) ν bar ν$ 3310 $K^{}^{+} (\to K_{S}^{0} π^{+}) ν bar ν$ 313 $K^{}^{0} ν bar ν$ 211 $π^{+} ν bar ν$ 111 $π^{0} ν bar ν$ 213 $ρ^{+} ν bar ν$ 113 $ρ^{0} ν bar ν$ [ $h ν bar ν$ ]
$K_{L}^{0}$ veto	0.2	0.2	0.1	0.2	0.6	0.4	0.6	0.0
Fixed fractions	0.4	0.3	0.1	0.2	1.3	0.1	0.1	1.0
Continuum scaling	2.0	0.0	0.0	0.0	3.1	0.0	0.0	0.0
Tag efficiency correction	0.5	0.2	0.1	0.1	1.9	0.1	0.2	0.5
Shape uncertainty	2.6	1.3	1.8	1.7	4.5	1.5	2.3	3.4
Fit bias	0.2	0.1	0.2	0.1	0.2	0.1	0.2	0.2
Total	3.4	1.4	1.8	1.8	5.9	1.6	2.4	3.6

Equations5

B (B \to K ν \overline{ν})

B (B \to K ν \overline{ν})

B (B \to K^{*} ν \overline{ν})

B (B \to π ν \overline{ν})

B (B \to ρ ν \overline{ν})

Peer Reviews

No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.

Videos

No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.

Full text

The Belle Collaboration

Belle Preprint 2017-10

KEK Preprint 2017-6

Search for $\boldsymbol{\IfEqCase{0}{{321}{\mbox{$ \boldsymbol{B^{+}\to K^{+}\nu\mathrm{bar}{\nu}} $}}{310}{\mbox{$ \boldsymbol{B^{0}{\phantom{+}}\to K{\text{S}}^{0}>\nu\mathrm{bar}{\nu}} $}}{323}{\mbox{$ \boldsymbol{B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}} $}}{3321}{\mbox{$ \boldsymbol{B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}} $}}{3310}{\mbox{$ \boldsymbol{B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}>\pi^{+}\right)\nu\mathrm{bar}{\nu}} $}}{313}{\mbox{$ \boldsymbol{B^{0}{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}} $}}{211}{\mbox{$ \boldsymbol{B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}} $}}{111}{\mbox{$ \boldsymbol{B^{0}{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}} $}}{213}{\mbox{$ \boldsymbol{B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}} $}}{113}{\mbox{$ \boldsymbol{B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}} $}}}[B\to h\nu\mathrm{bar}{\nu}]}$ decays with semileptonic tagging at Belle

J. Grygier

Institut für Experimentelle Kernphysik, Karlsruher Institut für Technologie, 76131 Karlsruhe

P. Goldenzweig

Institut für Experimentelle Kernphysik, Karlsruher Institut für Technologie, 76131 Karlsruhe

M. Heck

Institut für Experimentelle Kernphysik, Karlsruher Institut für Technologie, 76131 Karlsruhe

I. Adachi

High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801

SOKENDAI (The Graduate University for Advanced Studies), Hayama 240-0193

H. Aihara

Department of Physics, University of Tokyo, Tokyo 113-0033

S. Al Said

Department of Physics, Faculty of Science, University of Tabuk, Tabuk 71451

Department of Physics, Faculty of Science, King Abdulaziz University, Jeddah 21589

D. M. Asner

Pacific Northwest National Laboratory, Richland, Washington 99352

T. Aushev

Moscow Institute of Physics and Technology, Moscow Region 141700

R. Ayad

Department of Physics, Faculty of Science, University of Tabuk, Tabuk 71451

T. Aziz

Tata Institute of Fundamental Research, Mumbai 400005

V. Babu

Tata Institute of Fundamental Research, Mumbai 400005

I. Badhrees

Department of Physics, Faculty of Science, University of Tabuk, Tabuk 71451

King Abdulaziz City for Science and Technology, Riyadh 11442

S. Bahinipati

Indian Institute of Technology Bhubaneswar, Satya Nagar 751007

A. M. Bakich

School of Physics, University of Sydney, New South Wales 2006

V. Bansal

Pacific Northwest National Laboratory, Richland, Washington 99352

E. Barberio

School of Physics, University of Melbourne, Victoria 3010

P. Behera

Indian Institute of Technology Madras, Chennai 600036

B. Bhuyan

Indian Institute of Technology Guwahati, Assam 781039

J. Biswal

J. Stefan Institute, 1000 Ljubljana

A. Bobrov

Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090

Novosibirsk State University, Novosibirsk 630090

A. Bondar

Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090

Novosibirsk State University, Novosibirsk 630090

G. Bonvicini

Wayne State University, Detroit, Michigan 48202

A. Bozek

H. Niewodniczanski Institute of Nuclear Physics, Krakow 31-342

M. Bračko

University of Maribor, 2000 Maribor

J. Stefan Institute, 1000 Ljubljana

T. E. Browder

University of Hawaii, Honolulu, Hawaii 96822

D. Červenkov

Faculty of Mathematics and Physics, Charles University, 121 16 Prague

P. Chang

Department of Physics, National Taiwan University, Taipei 10617

V. Chekelian

Max-Planck-Institut für Physik, 80805 München

A. Chen

National Central University, Chung-li 32054

B. G. Cheon

Hanyang University, Seoul 133-791

K. Chilikin

P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow 119991

Moscow Physical Engineering Institute, Moscow 115409

R. Chistov

P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow 119991

Moscow Physical Engineering Institute, Moscow 115409

K. Cho

Korea Institute of Science and Technology Information, Daejeon 305-806

Y. Choi

Sungkyunkwan University, Suwon 440-746

D. Cinabro

Wayne State University, Detroit, Michigan 48202

N. Dash

Indian Institute of Technology Bhubaneswar, Satya Nagar 751007

S. Di Carlo

Wayne State University, Detroit, Michigan 48202

Z. Doležal

Faculty of Mathematics and Physics, Charles University, 121 16 Prague

Z. Drásal

Faculty of Mathematics and Physics, Charles University, 121 16 Prague

D. Dutta

Tata Institute of Fundamental Research, Mumbai 400005

S. Eidelman

Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090

Novosibirsk State University, Novosibirsk 630090

H. Farhat

Wayne State University, Detroit, Michigan 48202

J. E. Fast

Pacific Northwest National Laboratory, Richland, Washington 99352

T. Ferber

Deutsches Elektronen–Synchrotron, 22607 Hamburg

B. G. Fulsom

Pacific Northwest National Laboratory, Richland, Washington 99352

V. Gaur

Tata Institute of Fundamental Research, Mumbai 400005

N. Gabyshev

Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090

Novosibirsk State University, Novosibirsk 630090

A. Garmash

Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090

Novosibirsk State University, Novosibirsk 630090

M. Gelb

Institut für Experimentelle Kernphysik, Karlsruher Institut für Technologie, 76131 Karlsruhe

R. Gillard

Wayne State University, Detroit, Michigan 48202

B. Golob

Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana

J. Stefan Institute, 1000 Ljubljana

O. Grzymkowska

H. Niewodniczanski Institute of Nuclear Physics, Krakow 31-342

E. Guido

INFN - Sezione di Torino, 10125 Torino

J. Haba

High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801

SOKENDAI (The Graduate University for Advanced Studies), Hayama 240-0193

T. Hara

High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801

SOKENDAI (The Graduate University for Advanced Studies), Hayama 240-0193

K. Hayasaka

Niigata University, Niigata 950-2181

H. Hayashii

Nara Women’s University, Nara 630-8506

M. T. Hedges

University of Hawaii, Honolulu, Hawaii 96822

C.-L. Hsu

School of Physics, University of Melbourne, Victoria 3010

T. Iijima

Kobayashi-Maskawa Institute, Nagoya University, Nagoya 464-8602

Graduate School of Science, Nagoya University, Nagoya 464-8602

K. Inami

Graduate School of Science, Nagoya University, Nagoya 464-8602

G. Inguglia

Deutsches Elektronen–Synchrotron, 22607 Hamburg

A. Ishikawa

Department of Physics, Tohoku University, Sendai 980-8578

R. Itoh

High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801

SOKENDAI (The Graduate University for Advanced Studies), Hayama 240-0193

Y. Iwasaki

High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801

W. W. Jacobs

Indiana University, Bloomington, Indiana 47408

I. Jaegle

University of Florida, Gainesville, Florida 32611

H. B. Jeon

Kyungpook National University, Daegu 702-701

Y. Jin

Department of Physics, University of Tokyo, Tokyo 113-0033

D. Joffe

Kennesaw State University, Kennesaw, Georgia 30144

K. K. Joo

Chonnam National University, Kwangju 660-701

T. Julius

School of Physics, University of Melbourne, Victoria 3010

J. Kahn

Ludwig Maximilians University, 80539 Munich

A. B. Kaliyar

Indian Institute of Technology Madras, Chennai 600036

K. H. Kang

Kyungpook National University, Daegu 702-701

G. Karyan

Deutsches Elektronen–Synchrotron, 22607 Hamburg

P. Katrenko

Moscow Institute of Physics and Technology, Moscow Region 141700

P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow 119991

T. Kawasaki

Niigata University, Niigata 950-2181

T. Keck

Institut für Experimentelle Kernphysik, Karlsruher Institut für Technologie, 76131 Karlsruhe

H. Kichimi

High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801

C. Kiesling

Max-Planck-Institut für Physik, 80805 München

D. Y. Kim

Soongsil University, Seoul 156-743

H. J. Kim

Kyungpook National University, Daegu 702-701

J. B. Kim

Korea University, Seoul 136-713

K. T. Kim

Korea University, Seoul 136-713

M. J. Kim

Kyungpook National University, Daegu 702-701

S. H. Kim

Hanyang University, Seoul 133-791

K. Kinoshita

University of Cincinnati, Cincinnati, Ohio 45221

P. Kodyš

Faculty of Mathematics and Physics, Charles University, 121 16 Prague

S. Korpar

University of Maribor, 2000 Maribor

J. Stefan Institute, 1000 Ljubljana

D. Kotchetkov

University of Hawaii, Honolulu, Hawaii 96822

P. Križan

Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana

J. Stefan Institute, 1000 Ljubljana

P. Krokovny

Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090

Novosibirsk State University, Novosibirsk 630090

T. Kuhr

Ludwig Maximilians University, 80539 Munich

R. Kulasiri

Kennesaw State University, Kennesaw, Georgia 30144

T. Kumita

Tokyo Metropolitan University, Tokyo 192-0397

A. Kuzmin

Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090

Novosibirsk State University, Novosibirsk 630090

Y.-J. Kwon

Yonsei University, Seoul 120-749

J. S. Lange

Justus-Liebig-Universität Gießen, 35392 Gießen

C. H. Li

School of Physics, University of Melbourne, Victoria 3010

L. Li

University of Science and Technology of China, Hefei 230026

Y. Li

Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061

L. Li Gioi

Max-Planck-Institut für Physik, 80805 München

J. Libby

Indian Institute of Technology Madras, Chennai 600036

D. Liventsev

Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061

High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801

M. Lubej

J. Stefan Institute, 1000 Ljubljana

T. Luo

University of Pittsburgh, Pittsburgh, Pennsylvania 15260

M. Masuda

Earthquake Research Institute, University of Tokyo, Tokyo 113-0032

T. Matsuda

University of Miyazaki, Miyazaki 889-2192

D. Matvienko

Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090

Novosibirsk State University, Novosibirsk 630090

F. Metzner

Institut für Experimentelle Kernphysik, Karlsruher Institut für Technologie, 76131 Karlsruhe

K. Miyabayashi

Nara Women’s University, Nara 630-8506

H. Miyake

High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801

SOKENDAI (The Graduate University for Advanced Studies), Hayama 240-0193

H. Miyata

Niigata University, Niigata 950-2181

R. Mizuk

P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow 119991

Moscow Physical Engineering Institute, Moscow 115409

Moscow Institute of Physics and Technology, Moscow Region 141700

G. B. Mohanty

Tata Institute of Fundamental Research, Mumbai 400005

H. K. Moon

Korea University, Seoul 136-713

T. Mori

Graduate School of Science, Nagoya University, Nagoya 464-8602

R. Mussa

INFN - Sezione di Torino, 10125 Torino

E. Nakano

Osaka City University, Osaka 558-8585

M. Nakao

High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801

SOKENDAI (The Graduate University for Advanced Studies), Hayama 240-0193

T. Nanut

J. Stefan Institute, 1000 Ljubljana

K. J. Nath

Indian Institute of Technology Guwahati, Assam 781039

Z. Natkaniec

H. Niewodniczanski Institute of Nuclear Physics, Krakow 31-342

M. Nayak

Wayne State University, Detroit, Michigan 48202

High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801

N. K. Nisar

University of Pittsburgh, Pittsburgh, Pennsylvania 15260

S. Nishida

High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801

SOKENDAI (The Graduate University for Advanced Studies), Hayama 240-0193

S. Ogawa

Toho University, Funabashi 274-8510

S. Okuno

Kanagawa University, Yokohama 221-8686

H. Ono

Nippon Dental University, Niigata 951-8580

Niigata University, Niigata 950-2181

Y. Onuki

Department of Physics, University of Tokyo, Tokyo 113-0033

G. Pakhlova

P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow 119991

Moscow Institute of Physics and Technology, Moscow Region 141700

B. Pal

University of Cincinnati, Cincinnati, Ohio 45221

C.-S. Park

Yonsei University, Seoul 120-749

C. W. Park

Sungkyunkwan University, Suwon 440-746

H. Park

Kyungpook National University, Daegu 702-701

S. Paul

Department of Physics, Technische Universität München, 85748 Garching

T. K. Pedlar

Luther College, Decorah, Iowa 52101

L. Pesántez

University of Bonn, 53115 Bonn

L. E. Piilonen

Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061

M. Prim

Institut für Experimentelle Kernphysik, Karlsruher Institut für Technologie, 76131 Karlsruhe

C. Pulvermacher

High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801

M. Ritter

Ludwig Maximilians University, 80539 Munich

A. Rostomyan

Deutsches Elektronen–Synchrotron, 22607 Hamburg

Y. Sakai

High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801

SOKENDAI (The Graduate University for Advanced Studies), Hayama 240-0193

S. Sandilya

University of Cincinnati, Cincinnati, Ohio 45221

L. Santelj

High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801

T. Sanuki

Department of Physics, Tohoku University, Sendai 980-8578

Y. Sato

Graduate School of Science, Nagoya University, Nagoya 464-8602

V. Savinov

University of Pittsburgh, Pittsburgh, Pennsylvania 15260

T. Schlüter

Ludwig Maximilians University, 80539 Munich

O. Schneider

École Polytechnique Fédérale de Lausanne (EPFL), Lausanne 1015

G. Schnell

University of the Basque Country UPV/EHU, 48080 Bilbao

IKERBASQUE, Basque Foundation for Science, 48013 Bilbao

C. Schwanda

Institute of High Energy Physics, Vienna 1050

A. J. Schwartz

University of Cincinnati, Cincinnati, Ohio 45221

Y. Seino

Niigata University, Niigata 950-2181

K. Senyo

Yamagata University, Yamagata 990-8560

I. S. Seong

University of Hawaii, Honolulu, Hawaii 96822

M. E. Sevior

School of Physics, University of Melbourne, Victoria 3010

V. Shebalin

Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090

Novosibirsk State University, Novosibirsk 630090

C. P. Shen

Beihang University, Beijing 100191

T.-A. Shibata

Tokyo Institute of Technology, Tokyo 152-8550

J.-G. Shiu

Department of Physics, National Taiwan University, Taipei 10617

B. Shwartz

Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090

Novosibirsk State University, Novosibirsk 630090

F. Simon

Max-Planck-Institut für Physik, 80805 München

Excellence Cluster Universe, Technische Universität München, 85748 Garching

E. Solovieva

P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow 119991

Moscow Institute of Physics and Technology, Moscow Region 141700

M. Starič

J. Stefan Institute, 1000 Ljubljana

J. F. Strube

Pacific Northwest National Laboratory, Richland, Washington 99352

T. Sumiyoshi

Tokyo Metropolitan University, Tokyo 192-0397

M. Takizawa

Showa Pharmaceutical University, Tokyo 194-8543

J-PARC Branch, KEK Theory Center, High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801

Theoretical Research Division, Nishina Center, RIKEN, Saitama 351-0198

U. Tamponi

INFN - Sezione di Torino, 10125 Torino

University of Torino, 10124 Torino

F. Tenchini

School of Physics, University of Melbourne, Victoria 3010

K. Trabelsi

High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801

SOKENDAI (The Graduate University for Advanced Studies), Hayama 240-0193

T. Tsuboyama

High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801

SOKENDAI (The Graduate University for Advanced Studies), Hayama 240-0193

M. Uchida

Tokyo Institute of Technology, Tokyo 152-8550

T. Uglov

P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow 119991

Moscow Institute of Physics and Technology, Moscow Region 141700

Y. Unno

Hanyang University, Seoul 133-791

S. Uno

High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801

SOKENDAI (The Graduate University for Advanced Studies), Hayama 240-0193

P. Urquijo

School of Physics, University of Melbourne, Victoria 3010

Y. Ushiroda

High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801

SOKENDAI (The Graduate University for Advanced Studies), Hayama 240-0193

C. Van Hulse

University of the Basque Country UPV/EHU, 48080 Bilbao

G. Varner

University of Hawaii, Honolulu, Hawaii 96822

V. Vorobyev

Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090

Novosibirsk State University, Novosibirsk 630090

A. Vossen

Indiana University, Bloomington, Indiana 47408

E. Waheed

School of Physics, University of Melbourne, Victoria 3010

B. Wang

University of Cincinnati, Cincinnati, Ohio 45221

C. H. Wang

National United University, Miao Li 36003

M.-Z. Wang

Department of Physics, National Taiwan University, Taipei 10617

P. Wang

Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049

M. Watanabe

Niigata University, Niigata 950-2181

Y. Watanabe

Kanagawa University, Yokohama 221-8686

S. Wehle

Deutsches Elektronen–Synchrotron, 22607 Hamburg

K. M. Williams

Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061

E. Won

Korea University, Seoul 136-713

H. Yamamoto

Department of Physics, Tohoku University, Sendai 980-8578

Y. Yamashita

Nippon Dental University, Niigata 951-8580

H. Ye

Deutsches Elektronen–Synchrotron, 22607 Hamburg

Y. Yook

Yonsei University, Seoul 120-749

C. Z. Yuan

Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049

Y. Yusa

Niigata University, Niigata 950-2181

Z. P. Zhang

University of Science and Technology of China, Hefei 230026

V. Zhilich

Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090

Novosibirsk State University, Novosibirsk 630090

V. Zhukova

Moscow Physical Engineering Institute, Moscow 115409

V. Zhulanov

Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090

Novosibirsk State University, Novosibirsk 630090

M. Ziegler

Institut für Experimentelle Kernphysik, Karlsruher Institut für Technologie, 76131 Karlsruhe

A. Zupanc

Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana

J. Stefan Institute, 1000 Ljubljana

Abstract

We present the results of a search for the rare decays \IfEqCase0 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] , where h stands for $K^{+},\>K_{\text{S}}^{0}\>,\>{K^{\ast}}^{+},\>{K^{\ast}}^{0},\>\pi^{+},\>\pi^{0},\>\rho^{+}$ and $\rho^{0}$ . The results are obtained with $772\times 10^{6}$ $B\overline{B}$ pairs collected with the Belle detector at the KEKB $e^{+}e^{-}$ collider. We reconstruct one $B$ meson in a semileptonic decay and require a single $h$ meson but nothing else on the signal side. We observe no significant signal and set upper limits on the branching fractions. The limits set on the \IfEqCase310 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] , \IfEqCase313 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] , \IfEqCase211 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] , \IfEqCase111 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] , \IfEqCase213 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] , and \IfEqCase113 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] channels are the world’s most stringent.

pacs:

13.25.Hw, 12.15.Mm, 14.40.Nd

The decays \IfEqCase0 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] [1] can proceed only via a penguin or a box diagram at leading order in the standard model (SM), as shown in Fig. 1, and are thus highly suppressed [2]. Theoretical calculations for the branching fractions cover the range from $1.2\times 10^{-7}$ [3] ( \IfEqCase111 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] ) to $9.2\times 10^{-6}$ [2] ( \IfEqCase323 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] ). Recent results by LHCb [4, 5] show evidence for a deviation of experimental data from expected values in the angular observable $P_{5}^{\prime}$ in $B^{0}\to K^{\ast 0}\mu^{+}\mu^{-}$ decays, and in the ratio of the $B^{+}\to K^{+}\mu^{+}\mu^{-}$ to $B^{+}\to K^{+}e^{+}e^{-}$ branching fractions. A measurement of $P_{5}^{\prime}$ by Belle [6] is compatible with both, the SM prediction and the LHCb result. Different new physics models proposed to explain these observations can also influence $B\to K^{(\ast)}\nu\overline{\nu}$ decays. Therefore, \IfEqCase0 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] channels provide an important test for any model proposed to solve these tensions. Additionally, \IfEqCase0 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] channels are theoretically clean due to the mediation of the transition by a $Z$ boson alone, in contrast to $B\to K^{(\ast)}l^{+}l^{-}$ decays [2] where the photon contributes.

\IfEqCase

0 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] decays have been studied previously by Belle with a hadronic tagging algorithm [7], and by BaBar utilizing both hadronic [8] and semileptonic tagging [9]. Recent results by Belle [10] have shown that the usage of semileptonic tagging enhances the sensitivity of some analyses significantly. The semileptonically tagged sample provides a statistically independent and more efficiently tagged data set of reconstructed $B\overline{B}$ events as compared to the hadronically tagged sample.

We search for \IfEqCase0 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] decays with the full Belle data sample produced by the KEKB collider [11] at the $\Upsilon\!\left(\mathrm{4S}\right)$ center-of-mass (CM) energy with an integrated luminosity of $711\,\mathrm{fb^{-1}}$ , corresponding to $(772\pm 11)\times 10^{6}$ $B\overline{B}$ pairs. A data set of $89\,\mathrm{fb^{-1}}$ taken at an energy $60\,\mathrm{MeV/c^{2}}$ below the resonance energy is used to study background from $e^{+}e^{-}\to q\overline{q}$ processes (continuum), where $q\in u,d,s,c$ . We refer to this data set as the off-resonance sample. We model the decays with the EVTGEN package [12] and simulate the detector response with the GEANT3 package [13]. We include a randomly-triggered sample to account for beam-related background. The signal process is modeled according to three-body phase space.

The Belle detector [14] is a large-solid-angle magnetic spectrometer that consists of a silicon vertex detector (SVD), a 50-layer central drift chamber (CDC), an array of aerogel threshold Cherenkov counters (ACC), a barrel-like arrangement of time-of-flight scintillation counters (TOF), and an electromagnetic calorimeter comprised of CsI(Tl) crystals (ECL) located inside a super-conducting solenoid coil that provides a 1.5 T magnetic field. An iron flux-return located outside of the coil is instrumented to detect $K_{\text{L}}^{0}$ mesons and to identify muons (KLM). The detector is described in detail elsewhere [14]. Two inner detector configurations were used. A 2.0 cm beampipe and a 3-layer silicon vertex detector were used for the first sample of $152\times 10^{6}B\overline{B}$ pairs, while a 1.5 cm beampipe, a 4-layer silicon detector and a small-cell inner drift chamber were used to record the remaining $620\times 10^{6}B\overline{B}$ pairs [15].

The three-body \IfEqCase0 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] decay, with two invisible particles in the final state, does not convey sufficient kinematic information to isolate the signal. Thus, we first reconstruct the accompanying $B$ meson $\left(B_{\text{tag}}\>\!\right)$ in the semileptonic decay channels $B\to D^{(\ast)}l\nu_{l}$ ( $l=e,\mu$ ), where neutral (charged) $D$ candidates are reconstructed in 10 (7) different decay channels. This amounts to 108 different decay channels. The tagging algorithm, described elsewhere [16, 17], uses multiple instances of neural network classifiers built using the NeuroBayes package [18] in a hierarchical approach to find $B_{\text{tag}}$ candidates. The output of the neural network used to identify real $B_{\text{tag}}$ candidates transformed into the interval $\left[0,1\right]$ is referred to as $\mathscr{N}_{\text{tag}}$ and can be interpreted as the probability of the $B_{\text{tag}}$ meson to be a true $B$ in a generic sample. We combine $B_{\text{tag}}$ candidates with our signal selection to form signal event candidates. We separate charged pion and kaon candidates based on particle identification (PID) selection criteria utilizing CDC, ACC and TOF information. We combine the PID information in a likelihood ratio $\mathcal{P}_{K\pi}=\mathcal{L}_{K}/\left(\mathcal{L}_{K}+\mathcal{L}_{\pi}\right)$ , where $\mathcal{P}_{K\pi}$ is a function of the polar angle and the momentum of the track in the laboratory system. We require $\mathcal{P}_{K\pi}>0.6$ $(<0.4)$ for $K^{\pm}$ $(\pi^{\pm})$ candidates. The kaon (pion) identification efficiency is $88\,\%-93\,\%$ $(86\,\%-93\,\%)$ with a $\pi$ $(K)$ misidentification probability of $10\,\%-12\,\%$ $(8\,\%-11\,\%)$ .

We reduce the number of poor quality tracks by requiring that $dz\left(dr\right)<4\left(2\right)\,\mathrm{cm}$ , where $dz$ ( $dr$ ) is the distances of closest approach of a track to the interaction point along (transverse to) the $z$ axis, which is antiparallel to the positron beam. Signal $B$ daughter candidates are reconstructed through the decays $K^{*0}\to K^{+}\pi^{-}$ , $K^{*+}\to K^{+}\pi^{0}$ and $K_{\text{S}}^{0}\>\pi^{+}$ , $\rho^{+}\to\pi^{+}\pi^{0}$ , $\rho^{0}\to\pi^{+}\pi^{-}$ , $K_{\text{S}}^{0}\>\to\pi^{+}\pi^{-}$ , and $\pi^{0}\to\gamma\gamma$ . $K_{\text{S}}^{0}$ candidates are selected following Ref. [19]. Photons used for $\pi^{0}$ reconstruction are required to have a minimal energy of $50\,\mathrm{MeV/c^{2}},\>100\,\mathrm{MeV/c^{2}},\>150\,\mathrm{MeV/c^{2}}$ for the barrel ( $\theta\in\left[32^{\circ},129^{\circ}\right]$ ), forward ( $\left[17^{\circ},32^{\circ}\right]$ ), and backward ( $\left[129^{\circ},150^{\circ}\right]$ ) region of the ECL, respectively, where $\theta$ is taken with respect to the $z$ axis. The invariant mass of the two $\gamma$ candidates is required to fulfill $M_{\gamma\gamma}\in\left[118,150\right]\mathrm{MeV/c^{2}}$ , while the invariant mass of the $K^{\ast}$ ( $\rho$ ) candidates is required to be within $150\,\mathrm{MeV/c^{2}}$ $(250\,\mathrm{MeV/c^{2}})$ of the nominal mass from Ref. [20]. The mass requirements are subsequently optimized using Monte Carlo (MC) simulations by maximizing the figure of merit $N_{R}/\sqrt{N_{R}+N_{F}}$ , where $N_{R}$ is the number of correctly reconstructed mesons and $N_{F}$ the number of fake candidates, both passing the requirement. We combine a $B_{\text{tag}}$ candidate with the reconstructed signal- $B$ decay product ( $h_{\text{sig}}$ ) to form an $\Upsilon\!\left(\mathrm{4S}\right)$ candidate.

Events with additional charged tracks or $\pi^{0}$ candidates that satisfy our selection criteria are rejected. Furthermore, we remove events with two or more tracks not fulfilling our requirement on $dr$ or $dz$ “raw tracks.” We veto events with reconstructed $K_{\text{L}}^{0}$ candidates and weight our background simulations to account for known data–MC differences, as described in Ref. [21]. An important variable to identify correctly–reconstructed signal events is the extra energy, $E_{\text{ECL}}$ . We sum all ECL clusters not used in the reconstruction of the $\Upsilon\!\left(\mathrm{4S}\right)$ candidate, not associated with a track, and fulfilling the same energy requirements as the clusters used to form $\pi^{0}$ candidates. We require $E_{\text{ECL}}\><1.2\,\mathrm{GeV/c^{2}}$ . We also require the momentum of the $h_{\text{sig}}$ candidate in the CM system to fulfill $p_{\text{cms}}\>\!\in\left[0.5,2.96\right]\,\mathrm{GeV}/\mathrm{c}^{2}$ , the missing energy in the CM system $E_{\text{miss}}\>>2.5\,\mathrm{GeV/c^{2}}$ , the momentum of the $B_{\text{tag}}$ lepton candidate in the CM system $p_{l_{\text{tag}}}\><2.5\,\mathrm{GeV/c^{2}}$ , and a minimal tag quality of $\mathscr{N}_{\text{tag}}\>>0.005$ . These requirements are motivated by kinematic boundaries, data–MC differences in case of low–momentum $h_{\text{sig}}$ , and badly reconstructed tag candidates. To suppress pions from $D$ decays misreconstructed as muons, we veto events where the invariant mass of the $K$ ( ${K^{\ast}}^{0}$ ) candidate and the tag–side lepton fulfill $M_{Kl}\in\left[1.85,1.87\right]\mathrm{GeV/c^{2}}$ . The channel–dependent fraction of events with more than one $\Upsilon\!\left(\mathrm{4S}\right)$ candidate can be as large as $20\,\mathrm{\%}$ , dominated by candidate exchange between signal– and tag–side. In such cases, we select the candidate with the highest $\mathscr{N}_{\text{tag}}$ value, *i.e.*, the candidate with the highest probability of being correctly reconstructed. In MC studies, we find that the efficiency of this selection is between $65\,\mathrm{\%}$ ( \IfEqCase213 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] ) and $92\,\mathrm{\%}$ ( \IfEqCase310 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] ).

We reconstruct tagged $B^{+}\to\overline{D^{0}}\left(K^{+}\pi^{-}\right)\pi^{+}$ and $B^{0}\to D^{-}\left(K^{+}\pi^{-}\pi^{-}\right)\pi^{+}$ decays to correct for experimental data–MC efficiency differences. Both channels can be reconstructed with negligible background and are well described in MC. We bin $\mathscr{N}_{\text{tag}}$ equally in 4 (3) bins for charged (neutral) $B$ mesons and calculate the number of reconstructed events in data and MC. We assign the ratio as a weight in each bin of $\mathscr{N}_{\text{tag}}$ . This calibration includes a correction of the tagging efficiency $\times$ the number of $B\overline{B}$ pairs produced ( $N_{B\overline{B}}$ ) $\times$ the branching fraction of $\Upsilon\!\left(\mathrm{4S}\right)$ to charged and neutral $B$ meson pairs, as we have a separate calibration for $B^{+}$ and $B^{0}$ . We train one neural network per channel to suppress continuum events. We use 16 modified Fox-Wolfram moments [22], nine CLEO cones [23], the cosine of the angle of the thrust axis relative to the $z$ axis, and the angle of the momentum of the $B_{\text{tag}}$ candidate with respect to the $z$ axis. We refer to the output of this neural network as $\mathscr{N}_{\text{CS}}$ .

To optimally separate signal from background, another neural network is trained for each reconstructed channel. We optimize the requirement on the network output ( $\mathscr{N}_{\mathrm{sel}}$ ) by maximizing a figure-of-merit $\varepsilon/(\frac{n_{\sigma}}{2}+\sqrt{N_{B}})$ , which is independent of the signal-to-background ratio and optimized for searches [24]. Here, $\varepsilon$ is the signal efficiency while $N_{B}$ denotes the number of background events passing the requirement on $\mathscr{N}_{\mathrm{sel}}$ . Both values are determined from MC. We choose a desired significance $n_{\sigma}=3$ . The most powerful variables to identify the signal are $p_{\text{cms}}$ , $\mathscr{N}_{\text{CS}}$ , the cosine between the momentum of the $D^{(\ast)}l$ system and the momentum of the $B_{\text{tag}}$ in the CM system [25], the cosine of the angle of the missing momentum relative to the $z$ axis, the cosine of the angle of the thrust axis, $p_{l_{\text{tag}}}$ , and, for the $\rho$ and $K^{\ast}$ channels, the reconstructed invariant mass. The number of input variables varies for each channel, spanning a range from 17 to 31.

We evaluate the description of the data by our MC by looking into an $E_{\text{ECL}}$ sideband ( $E_{\text{ECL}}\>>0.3\,\mathrm{GeV/c^{2}}$ ), by reconstructing tagged $B\to D^{\ast}l\nu_{l}$ decays, and by utilizing the off-resonance sample. We find good agreement between data and MC in the $E_{\text{ECL}}$ sidebands for six of the eight channels. However, we find an underestimation of continuum background in MC in the \IfEqCase321 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] and the \IfEqCase211 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] channels, which we correct by scaling the continuum component in the background model by the observed data–MC ratio in the off-resonance sample.

To extract the signal yield in each channel, we perform an extended binned maximum likelihood (ML) fit to the $E_{\text{ECL}}$ distribution. We use histogram templates to model signal as well as backgrounds from charm $B$ -decay ( $b\to c$ ), charmless $B$ -decay ( $b\to s,u,d$ ), and continuum. We fix the relative fractions of the background components to MC expectations and leave only the signal and the overall background yields as freely floating parameters. We perform extensive toy MC studies to estimate the sensitivity of our procedure. For this purpose, we simulate 1000 background-only samples for each channel and calculate an expected limit on the signal yield by integrating the profile likelihood up to the point where it includes $90\,\mathrm{\%}$ of the positive region. We also simulate samples with various numbers of signal events to test for a possible bias. We find a non-negligible but modest bias in almost all investigated channels. We fit this bias with a linear function, whose slope is consistent with 1.0 and whose intercept lies between [math] and $-2$ events. We correct for this bias in our fit to data.

The fit results are listed in Table 1(a); Fig. 2 shows the distributions of the data together with the fitted signal and background models. The fit yields no significant signal in any channel. The largest signal contribution is observed in the \IfEqCase323 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] channel with a significance of $2.3\,\mathrm{\sigma}$ . The significance is defined by evaluating the likelihood of the complete model $\mathcal{L}_{\mathrm{max}}$ and the background-only likelihood $\mathcal{L}_{0}$ : $S=\sqrt{2\log{\left(\mathcal{L}_{\mathrm{max}}/\mathcal{L}_{0}\right)}}$ . Both are evaluated at their respective best fitting point. We calculate the branching fraction of the $i$ -th mode by $\mathscr{B}^{i}=N^{i}_{\mathrm{sig}}/\left(\varepsilon^{i}_{\mathrm{rec}}\times N_{B\overline{B}}\right)$ , where the reconstruction efficiency $\varepsilon_{\mathrm{rec}}^{i}$ includes all daughter branching fractions. These efficiencies, along with the expected and measured $90\,\mathrm{\%}$ confidence level (C.L.) upper limit [26] for each channel, are displayed in Table 1(b).

We estimate the uncertainty on the fixed fractions, the $K_{\text{L}}^{0}$ veto efficiency, the continuum scaling, the tagging efficiency, and the fit bias correction by refitting the data with each of these quantities varied by $\pm 1\,\sigma$ . We estimate the shape uncertainty by simulating 1000 toy templates obtained by drawing a random number from a Gaussian distribution with the mean and error of the respective bin of our fit model as the central value and deviation. The $\pm 1\,\mathrm{\sigma}$ quantiles of the resulting distribution are used as estimators of the uncertainty. We estimate the uncertainty on the $\pi^{0}$ and charged track vetoes by comparing the respective efficiency differences between data and MC for the $B\to D\pi$ sample with and without the veto applied. We obtain a value of $4\,\%$ in both cases for charged and neutral channels alike. We evaluate the influence of the requirement on the number of raw tracks via the same sample by setting it to two and zero, respectively. We subsequently average the contributions and obtain a value of $1\,\%$ . The uncertainty on the calibration (9.6%) includes the uncertainty on the correction of $N_{B\overline{B}}$ (1.4%) and the uncertainty on $\mathcal{B}\left(B\to D\pi\right)$ . Based on studies using dedicated control samples, we assign $2.0\,\mathrm{\%}$ , $4.0\,\mathrm{\%}$ , and $2.2\,\mathrm{\%}$ for the uncertainties on PID efficiency, $\pi^{0}$ efficiency and $K_{\text{S}}^{0}$ efficiency, respectively. The systematic uncertainty is included by convolving the likelihood function with a Gaussian with zero mean and a width equal to the square root of the quadratic sum of the additive and multiplicative error. The additive uncertainty is defined as the uncertainty on the signal yield, and contributions are summarized in Table 2. A comparison of our results with previous ones is presented in Fig. 3.

The systematic uncertainties are evaluated using independent samples of MC and data control samples for charged and neutral modes. They can therefore be considered uncorrelated. Thus, we combine charged and neutral modes by adding the negative log likelihoods. We scale the branching fraction of the neutral modes by a factor of $\tau_{B^{+}}/\tau_{B^{0}}$ since the lifetime difference is the only factor distinguishing charged from neutral \IfEqCase0 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] decays in the SM. We subsequently repeat the calculation of the limit and obtain the following values at $90\,\%$ C.L.:

[TABLE]

Based on the values and theoretical uncertainties from Ref. [2], we also give a limit on the ratios between the measured branching fractions of $B\to K\nu\overline{\nu}$ and of $B\to K^{\ast}\nu\overline{\nu}$ and the respective SM prediction $\mathcal{R}_{K^{\ast}}$ . We obtain values of $\mathcal{R}_{K}<3.9$ and $\mathcal{R}_{K^{\ast}}<2.7$ , respectively, where we included the theoretical uncertainty. Both values are quoted at $90\,\mathrm{\%}$ C.L.

In summary, we report the results of a search for eight different $B$ decay channels with a pair of neutrinos in the final state, where the second $B$ is reconstructed in one of 108 semileptonic decay channels. No significant signal is observed and limits are set on the respective branching fractions at a confidence level of $90\,\mathrm{\%}$ . The limits on the branching fraction for the \IfEqCase310 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] , \IfEqCase313 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] , \IfEqCase211 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] , \IfEqCase111 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] , \IfEqCase213 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] , and \IfEqCase113 321 $B^{+}\to K^{+}\nu\mathrm{bar}{\nu}$ 310 $B^{0}_{\phantom{+}}\to K_{\text{S}}^{0}\>\nu\mathrm{bar}{\nu}$ 323 $B^{+}\to{K^{\ast}}^{+}\nu\mathrm{bar}{\nu}$ 3321 $B^{+}\to{K^{\ast}}^{+}\left(\to K^{+}\pi^{0}\right)\nu\mathrm{bar}{\nu}$ 3310 $B^{+}\to{K^{\ast}}^{+}\left(\to K_{\text{S}}^{0}\>\pi^{+}\right)\nu\mathrm{bar}{\nu}$ 313 $B^{0}_{\phantom{+}}\to{K^{\ast}}^{0}\nu\mathrm{bar}{\nu}$ 211 $B^{+}\to\pi^{+}\nu\mathrm{bar}{\nu}$ 111 $B^{0}_{\phantom{+}}\to\pi^{0}\nu\mathrm{bar}{\nu}$ 213 $B^{+}\to\rho^{+}\nu\mathrm{bar}{\nu}$ 113 $B^{0}_{\phantom{+}}\to\rho^{0}\nu\mathrm{bar}{\nu}$ [ $B\to h\nu\mathrm{bar}{\nu}$ ] channels are the most stringent to date. Although our analysis yields important improvements, none of these limits excludes SM predictions and all of them leave room for contributions from new physics.

We thank the KEKB group for the excellent operation of the accelerator; the KEK cryogenics group for the efficient operation of the solenoid; and the KEK computer group, the National Institute of Informatics, and the PNNL/EMSL computing group for valuable computing and SINET5 network support. We acknowledge support from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan, the Japan Society for the Promotion of Science (JSPS), and the Tau-Lepton Physics Research Center of Nagoya University; the Australian Research Council; Austrian Science Fund under Grant No. P 26794-N20; the National Natural Science Foundation of China under Contracts No. 10575109, No. 10775142, No. 10875115, No. 11175187, No. 11475187, No. 11521505 and No. 11575017; the Chinese Academy of Science Center for Excellence in Particle Physics; the Ministry of Education, Youth and Sports of the Czech Republic under Contract No. LTT17020; the Carl Zeiss Foundation, the Deutsche Forschungsgemeinschaft, the Excellence Cluster Universe, and the VolkswagenStiftung; the Department of Science and Technology of India; the Istituto Nazionale di Fisica Nucleare of Italy; the WCU program of the Ministry of Education, National Research Foundation (NRF) of Korea Grants No. 2011-0029457, No. 2012-0008143, No. 2014R1A2A2A01005286, No. 2014R1A2A2A01002734, No. 2015R1A2A2A01003280, No. 2015H1A2A1033649, No. 2016R1D1A1B01010135, No. 2016K1A3A7A09005603, No. 2016K1A3A7A09005604, No. 2016R1D1A1B02012900, No. 2016K1A3A7A09005606, No. NRF-2013K1A3A7A06056592; the Brain Korea 21-Plus program, Radiation Science Research Institute, Foreign Large-size Research Facility Application Supporting project and the Global Science Experimental Data Hub Center of the Korea Institute of Science and Technology Information; the Polish Ministry of Science and Higher Education and the National Science Center; the Ministry of Education and Science of the Russian Federation and the Russian Foundation for Basic Research; the Slovenian Research Agency; Ikerbasque, Basque Foundation for Science and MINECO (Juan de la Cierva), Spain; the Swiss National Science Foundation; the Ministry of Education and the Ministry of Science and Technology of Taiwan; and the U.S. Department of Energy and the National Science Foundation.

Bibliography26

The reference list from the paper itself. Each links out to its DOI / PubMed record.

1[1] Throughout this letter, h ℎ h refers to one of the following charmless states: K + superscript 𝐾 K^{+} , K S 0 superscript subscript 𝐾 S 0 K_{\text{S}}^{0}\> , K ∗ + superscript 𝐾 ∗ absent K^{\ast+} , K ∗ 0 superscript 𝐾 ∗ absent 0 K^{\ast 0} , π + superscript 𝜋 \pi^{+} , π 0 superscript 𝜋 0 \pi^{0} , ρ + superscript 𝜌 \rho^{+} , ρ 0 superscript 𝜌 0 \rho^{0} . Charge-conjugate channels are implied throughout this paper unless explicitly stated otherwise.
2[2] A. Buras, J. Girrbach-Noe, C. Niehoff, and D. Straub, JHEP 02 , 184 (2015).
3[3] C. Hambrock, A. Khodjamirian, Alexander, and A. Rusov, Phys. Rev. D 92 , 074020 (2015).
4[4] R. Aaij et al. (LH Cb Collaboration), JHEP 02 , 104 (2016).
5[5] R. Aaij et al. (LH Cb Collaboration), Phys. Rev. Lett. 113 , 151601 (2014).
6[6] S. Wehle et al. (Belle Collaboration), Phys. Rev. Lett. 118 , 111801 (2017).
7[7] O. Lutz et al. (Belle Collaboration), Phys. Rev. D 87 , 111103 (2013).
8[8] J.P. Lees et al. (Ba Bar Collaboration), Phys. Rev. D 87 , 112005 (2013).