Measurement of the mass difference between neutral charm-meson eigenstates

TL;DR

This paper presents a highly precise measurement of the mass difference between neutral charm-meson eigenstates using a large dataset from the LHCb experiment, providing evidence for their mass difference and testing CP symmetry.

Contribution

It introduces a novel approach to measure the mass difference with unprecedented precision, confirming the mass eigenstates differ in mass.

Findings

Measured the normalized mass difference x_CP with high precision.

Found results consistent with CP symmetry.

Provided the first evidence of mass difference between charm-meson eigenstates.

Abstract

We report a measurement of the mass difference between neutral charm-meson eigenstates using a novel approach that enhances sensitivity to this parameter. We use $2.3\times 10^6$ $D^0\to K_S^0\pi^+\pi^-$ decays reconstructed in proton-proton collisions collected by the \lhcb experiment in 2011 and 2012. Allowing for $CP$ violation in mixing and in the interference between mixing and decay, we measure the $CP$-averaged normalized mass difference $x_{CP} = \left[2.7\pm1.6\text{(stat)}\pm0.4\text{(syst)}\right]\times10^{-3}$ and the $CP$-violating parameter $\Delta x = \left[-0.53\pm0.70\text{(stat)}\pm0.22\text{(syst)}\right]\times10^{-3}$. The results are consistent with $CP$ symmetry. These determinations are the most precise from a single experiment and, combined with current world-average results, yield the first evidence that the masses of the neutral charm-meson eigenstates differ.

Figures

Tables

Table 1. Table 1: Fit results. The first contribution to the uncertainty is statistical, and the second is systematic.

Parameter	Value	Stat. correlations			Syst. correlations
	[${10}^{-3}$]	$y_{CP}$	$\Delta x$	$\Delta y$	$y_{CP}$	$\Delta x$	$\Delta y$
$x_{CP}$	$2.7\pm 1.6\pm 0.4$	$-0.17$	$0.04$	$-0.02$	$0.15$	$0.01$	$-0.02$
$y_{CP}$	$7.4\pm 3.6\pm 1.1$		$-0.03$	$0.01$		$-0.05$	$-0.03$
$\Delta x$	$-0.53\pm 0.70\pm 0.22$			$-0.13$			$0.14$
$\Delta y$	$0.6\pm 1.6\pm 0.3$

Table 2. Table 2: Point estimates and 95.5% confidence-level (CL) intervals for the derived parameters. Uncertainties include statistical and systematic contributions.

Parameter	Value	95.5% CL interval
$x$ [${10}^{-2}$]	${0.27}_{-\mathrm{\hspace{0.17em}0.15}}^{+\mathrm{\hspace{0.17em}0.17}}$	$[-0.05,0.60]$
$y$ [${10}^{-2}$]	$\mathrm{\hspace{0.17em}\hspace{0.17em}0.74}\pm 0.37$	$[0.00,1.50]$
$\left|q/p\right|$	${1.05}_{-\mathrm{\hspace{0.17em}0.17}}^{+\mathrm{\hspace{0.17em}0.22}}$	$[0.55,2.15]$
$\varphi$	$-{0.09}_{-\mathrm{\hspace{0.17em}0.16}}^{+\mathrm{\hspace{0.17em}0.11}}$	$[-0.73,0.29]$

Table 3. Table 3: Results of the fit to the prompt data sample. The first contribution to the uncertainty is statistical, the second systematic.

Parameter	Value	Stat. correlations			Syst. correlations
	[${10}^{-3}$]	$y_{CP}$	$\Delta x$	$\Delta y$	$y_{CP}$	$\Delta x$	$\Delta y$
$x_{CP}$	$3.0\pm 1.9\pm 0.5$	$-0.14$	$0.05$	$-0.04$	$0.22$	$0.00$	$-0.01$
$y_{CP}$	$6.5\pm 4.3\pm 1.5$		$-0.03$	$0.02$		$-0.05$	$-0.05$
$\Delta x$	$-0.41\pm 0.78\pm 0.24$			$-0.12$			$0.17$
$\Delta y$	$0.3\pm 1.8\pm 0.3$

Table 4. Table 4: Results of the fit to the semileptonic data sample. The first contribution to the uncertainty is statistical, the second systematic.

Parameter	Value	Stat. correlations			Syst. correlations
	[${10}^{-3}$]	$y_{CP}$	$\Delta x$	$\Delta y$	$y_{CP}$	$\Delta x$	$\Delta y$
$x_{CP}$	$2.3\pm 2.8\pm 1.0$	$-0.08$	$0.03$	$0.03$	$0.14$	$0.00$	$-0.03$
$y_{CP}$	$8.5\pm 6.3\pm 0.7$		$0.01$	$0.02$		$-0.06$	$-0.03$
$\Delta x$	$-0.9\pm 1.7\pm 0.3$			$-0.07$			$0.13$
$\Delta y$	$2.2\pm 4.0\pm 0.2$

Equations

$$R_{bj}^{\pm }\approx \frac{r_b+\frac{1}{4}{r}_b⟨t^2{⟩}_j\mathrm{Re}\left(z_{CP}^2-\Delta z^2\right)+\frac{1}{4}⟨t^2{⟩}_j{\left|z_{CP}\pm \Delta z\right|}^2+\sqrt{r_b}⟨t{⟩}_j\mathrm{Re}\left[X_b^{\ast }(z_{CP}\pm \Delta z)\right]}{1+\frac{1}{4}⟨t^2{⟩}_j\mathrm{Re}\left(z_{CP}^2-\Delta z^2\right)+r_b\frac{1}{4}⟨t^2{⟩}_j{\left|z_{CP}\pm \Delta z\right|}^2+\sqrt{r_b}⟨t{⟩}_j\mathrm{Re}\left[X_b(z_{CP}\pm \Delta z)\right]}.$$

$${\chi }^2\equiv$$

$$+\sum _{b,b^{\prime }}\left(X_b^{\mathrm{CLEO}}-X_b\right)(V_{\mathrm{CLEO}}^{-1}{)}_{b{b}^{\prime }}\left(X_{b^{\prime }}^{\mathrm{CLEO}}-X_{b^{\prime }}\right).$$

Full text

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

​​​

CERN-EP-2019-032

LHCb-PAPER-2019-001

March 7, 2019

Measurement of the mass difference between neutral charm-meson eigenstates

LHCb collaboration†††Authors are listed at the end of this paper.

We report a measurement of the mass difference between neutral charm-meson eigenstates using a novel approach that enhances sensitivity to this parameter. We use $2.3\times 10^{6}$ ${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}}$ decays reconstructed in proton-proton collisions collected by the LHCb experiment in 2011 and 2012. Allowing for $C\!P$ violation in mixing and in the interference between mixing and decay, we measure the $C\!P$-averaged normalized mass difference $x_{{C\!P}}=\left[2.7\pm 1.6\text{\,(stat)}\pm 0.4\text{\,(syst)}\right]\times 10^{-3}$ and the $C\!P$-violating parameter $\Delta x=\left[-0.53\pm 0.70\text{\,(stat)}\pm 0.22\text{\,(syst)}\right]\times 10^{-3}$. The results are consistent with $C\!P$ symmetry. These determinations are the most precise from a single experiment and, combined with current world-average results, yield the first evidence that the masses of the neutral charm-meson eigenstates differ.

Published in Phys. Rev. Lett. 122 (2019) 231802

© 2024 CERN for the benefit of the LHCb collaboration. CC-BY-4.0 licence.

Flavor oscillations are transitions between neutral flavored mesons and their corresponding antimesons that follow an oscillating pattern as a function of decay time. In the standard model, these transitions are mediated by weak-interaction amplitudes involving exchanges of virtual $W^{\pm}$ bosons and heavy quarks. Unknown particles of arbitrarily high mass can contribute as virtual particles in the amplitude, possibly enhancing the average oscillation rate or the difference between the rates of mesons and antimesons. This makes flavor oscillations sensitive to non-standard-model dynamics at large energy scales [1].

Oscillations occur because the mass eigenstates of neutral flavored mesons are linear combinations of the flavor eigenstates. In particular, for charm mesons one writes $|D_{1,2}\rangle\equiv p|{{D}^{0}}\rangle\pm q|{{\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\rangle$, where $p$ and $q$ are complex parameters. In the limit of charge-parity ($C\!P$) symmetry, and by defining $D_{1(2)}$ as the $C\!P$-even (odd) state, the oscillation rate depends only on the dimensionless mixing parameters $x\equiv(m_{1}-m_{2})c^{2}/\Gamma$ and $y\equiv(\Gamma_{1}-\Gamma_{2})/(2\Gamma)$, where $m_{1(2)}$ and $\Gamma_{1(2)}$ are the mass and decay width of the $D_{1(2)}$ state, respectively, and $\Gamma$ equals $(\Gamma_{1}+\Gamma_{2})/2$ [2]. If $C\!P$ symmetry is violated, the oscillation rates for mesons produced as ${D}^{0}$ and ${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ differ. The difference is generated in the mixing amplitude if $|q/p|\neq 1$ or in the interference between mixing and decay if $\phi_{f}\equiv\arg(q\bar{A}_{f}/pA_{f})\neq 0$. The amplitude $A_{f}$ ($\bar{A}_{f}$) refers to the decay ${{D}^{0}}\rightarrow f$ (${{\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\rightarrow f$), where $f$ is a common final state. If $C\!P$ is conserved in the decay amplitude ($|A_{f}|^{2}=|\bar{A}_{f}|^{2}$), the $C\!P$-violating phase is independent of the final state, $\phi_{f}\approx\phi=\arg(q/p)$ [3, 4].

Current global averages of charm-mixing parameters have large uncertainties and are consistent with $C\!P$ symmetry, yielding $x=(3.6\,^{+\,2.1}_{-\,1.6})\times 10^{-3}$, $y=(6.7\,^{+\,0.6}_{-\,1.3})\times 10^{-3}$, $|q/p|=0.94\,^{+\,0.17}_{-\,0.07}$, and $\phi=-0.13\,^{+\,0.26}_{-\,0.17}$ [5]. Improving the knowledge of $x$, which has not been shown to differ significantly from zero, is especially critical because the sensitivity to the small phase $\phi$ relies predominantly on observables proportional to $x\sin\phi$.

Direct experimental access to charm-mixing parameters is offered by self-conjugate multibody decays, such as ${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}}$. Inclusion of charge-conjugate processes is implied unless stated otherwise. A joint fit of the Dalitz-plot and decay-time distributions of these decays allows the identification of a ${D}^{0}$ component that increases as a function of decay time in a sample of candidates produced as ${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ mesons, and vice versa. This approach is challenging because it requires analyzing the decay-time evolution of signal decays across the Dalitz plot with a detailed amplitude model while accounting for efficiencies, resolutions, and background [6, 7, 8]. Model-independent approaches that obviate the need for an amplitude analysis exist [9, 10, 11], but they rely on an accurate description of the efficiencies.

This Letter reports on a measurement of charm oscillations in ${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}}$ decays based on a novel model-independent approach, called the bin-flip method, which is optimized for the measurement of the parameter $x$ [12]. The method relies on ratios between charm decays reconstructed in similar kinematic and decay-time conditions, thus avoiding the need for an accurate modeling of the efficiency variation across phase space and decay time. We express the ${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}}$ dynamics with two invariant masses following the Dalitz formalism [13, 14], where $m_{\pm}^{2}$ is the squared invariant mass $m^{2}({{K}^{0}_{\mathrm{S}}}\pi^{\pm})$ for ${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}}$ decays and $m^{2}({{K}^{0}_{\mathrm{S}}}\pi^{\mp})$ for ${{\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}}$ decays. We partition the Dalitz plot into disjoint regions (“bins”) that preserve nearly constant strong-phase differences $\Delta\delta(m_{-}^{2},m_{+}^{2})$ between the ${D}^{0}$ and ${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ amplitudes within each bin (see Supplemental material). Two sets of eight bins are formed, and they are organized symmetrically about the principal bisector $m_{+}^{2}=m_{-}^{2}$. Bins are labeled with the indices $\pm b$, where $b=1,...,8$. Positive indices refer to the (lower) $m_{+}^{2}>m_{-}^{2}$ region, where unmixed Cabibbo-favored ${{D}^{0}}\!\rightarrow{{K}^{*}}(892)^{-}\pi^{+}$ decays dominate; negative indices refer to the symmetric (upper) $m_{+}^{2}<m_{-}^{2}$ region, which receives a larger contribution from decays following oscillation. The data are further split into bins of decay time, which are indexed with $j$. For each, we measure the ratio $R_{bj}^{+}$ ($R_{bj}^{-}$) between initially produced ${D}^{0}$ (${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$) mesons in Dalitz bin $-b$ and Dalitz bin $b$. For small mixing parameters and $C\!P$-conserving decay amplitudes, which are good approximations here, the ratios are [12]

[TABLE]

Here $\langle t\rangle_{j}$ ($\langle t^{2}\rangle_{j}$) is the average (squared) decay time of unmixed decays in bin $j$, in units of the ${D}^{0}$ lifetime $\tau=\hbar/\Gamma$ [2]. The parameter $r_{b}$ is the ratio of signal yields in symmetric Dalitz-plot bins $\mp b$ at $t=0$, and $X_{b}$ quantifies the average strong-phase difference in these bins [12]. The $z_{{C\!P}}$ and $\Delta z$ parameters, defined by $z_{{C\!P}}\pm\Delta z\equiv-\left(q/p\right)^{\pm 1}(y+ix)$, are obtained, along with $r_{b}$, from a joint fit of the observed $R_{bj}^{\pm}$ ratios in which external information on $c_{b}\equiv{{\rm\,Re}\!\left(X_{b}\right)}$ and $s_{b}\equiv-{{\rm\,Im}\!\left(X_{b}\right)}$ [15] is used as a constraint. The results are expressed in terms of the $C\!P$-averaged mixing parameters $x_{{C\!P}}\equiv-{{\rm\,Im}\!\left(z_{{C\!P}}\right)}$ and $y_{{C\!P}}\equiv-{{\rm\,Re}\!\left(z_{{C\!P}}\right)}$, and of the $C\!P$-violating differences $\Delta x\equiv-{{\rm\,Im}\!\left(\Delta z\right)}$ and $\Delta y\equiv-{{\rm\,Re}\!\left(\Delta z\right)}$. Conservation of $C\!P$ symmetry in mixing, or in the interference between mixing and decay, implies $x_{{C\!P}}=x$, $y_{{C\!P}}=y$, and $\Delta x=\Delta y=0$.

Samples of ${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}}$ decays are reconstructed from proton-proton collisions collected by the LHCb experiment in 2011 and 2012, corresponding to integrated luminosities of 1$\text{\,fb}^{-1}$ and 2$\text{\,fb}^{-1}$, respectively. In the 2012 data, both the strong-interaction decay ${{D}^{*+}}\rightarrow{{D}^{0}}{{\pi}^{+}}$ and the semileptonic $b$-hadron decay ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}\rightarrow{{D}^{0}}{\mu^{-}}X$, where $X$ generically indicates unreconstructed particles, are used to determine whether a ${D}^{0}$ or a ${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ is produced. In the 2011 data, only the ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}\rightarrow{{D}^{0}}{\mu^{-}}X$ decays were used because the online-selection efficiency for ${{D}^{*+}}\rightarrow{{D}^{0}}{{\pi}^{+}}$ decays was low. Throughout this Letter, ${D}^{*+}$ indicates the ${{D}^{*}}(2010)^{+}$ meson and soft pion indicates the pion from its decay.

The LHCb detector is a single-arm forward spectrometer covering the pseudorapidity range $2<\eta<5$ equipped with charged-hadron identification detectors, calorimeters, and muon detectors; and it is designed for the study of particles containing $b$ or $c$ quarks [16, 17].

The online selection of ${{D}^{*+}}\rightarrow{{D}^{0}}(\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}}){{\pi}^{+}}$ decays (prompt sample) uses criteria on momenta and final-state charged-particle displacements from any proton-proton primary interaction. Offline, we apply criteria consistent with the decay topology on momenta, vertex and track displacements, particle-identification information, and invariant masses of the ${D}^{*+}$ decay products. Specifically, the mass of the ${D}^{0}$ candidate is required to meet $1.84<m({{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}})<1.89\text{\,Ge\kern-1.00006ptV\!/}c^{2}$ and the difference between the ${D}^{*+}$ and ${D}^{0}$ candidate masses is required to satisfy ${\Delta m}<151.1\text{\,Me\kern-1.00006ptV\!/}c^{2}$. The ${D}^{0}$ and soft pion candidates are required to point back to one of the proton-proton interactions (the primary vertex) to suppress signal candidates originating from decays of $b$ hadrons (secondary decays). A kinematic fit constrains the tracks according to the decay topology and the ${D}^{*+}$ candidate to originate from the primary vertex [18]. In the reconstruction of the Dalitz-plot coordinates, we additionally constrain the ${K}^{0}_{\mathrm{S}}$ and ${D}^{0}$ meson masses to the known values [2] to ensure that all candidates populate the kinematically allowed phase space.

The online selection of ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}\rightarrow{{D}^{0}}(\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}}){\mu^{-}}X$ decays (semileptonic sample) requires at least one displaced high-transverse-momentum muon and a vertex consistent with the decay of a $b$ hadron. Offline, we apply criteria consistent with the decay topology on momenta, vertex and track displacements, particle identifications, and invariant masses of the ${D}^{0}$ decay products. In addition, candidate ${{D}^{0}}{\mu^{-}}$ pairs are formed by requiring $2.5<m({{D}^{0}}{\mu^{-}})<6.0\text{\,Ge\kern-1.00006ptV\!/}c^{2}$ and the corrected mass $\sqrt{m^{2}({{D}^{0}}{\mu^{-}})+p_{\perp}^{2}({{D}^{0}}{\mu^{-}})}+p_{\perp}({{D}^{0}}{\mu^{-}})$, where the momentum component $p_{\perp}({{D}^{0}}{\mu^{-}})$ of the ${{D}^{0}}{\mu^{-}}$ system transverse to the ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}$ flight direction partially compensates for the momentum of unreconstructed decay products, to be smaller than $5.8\text{\,Ge\kern-1.00006ptV\!/}c^{2}$. The ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}$ flight direction is inferred from the measured positions of the primary and ${{D}^{0}}{\mu^{-}}$ vertices. A kinematic fit constrains the ${D}^{0}$ and ${K}^{0}_{\mathrm{S}}$ masses to their known values.

In both samples, two categories of signal candidates are used, those with ${{K}^{0}_{\mathrm{S}}}\!\rightarrow{{\pi}^{+}}{{\pi}^{-}}$ candidates reconstructed in the vertex detector (long ${K}^{0}_{\mathrm{S}}$) and those with ${K}^{0}_{\mathrm{S}}$ candidates reconstructed after the vertex detector (downstream ${K}^{0}_{\mathrm{S}}$).

About 2% (3%) of the selected ${D}^{*+}$ (${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}$) candidates belong to events in which multiple candidates are reconstructed by pairing the same ${D}^{0}$ candidate with different soft pions (muons). For these events, we randomly choose a single candidate. We consider the prompt and semileptonic samples independent because their overlap amounts to less than 0.1% of the semileptonic sample size.

Figure 1 shows the $\Delta m$ and $m({{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}})$ distributions of the prompt and semileptonic samples, respectively. The prompt sample contains $1.3\times 10^{6}$ signal decays (45% with downstream ${K}^{0}_{\mathrm{S}}$ candidates) and a small background dominated by genuine ${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}}$ decays associated to random soft pions. Secondary ${D}^{*+}$ decays contribute approximately 3% to the signal yield, as determined using ${D}^{0}$ candidates not pointing to the primary vertex. The semileptonic sample contains $1.0\times 10^{6}$ signal decays ($66\%$ with downstream ${K}^{0}_{\mathrm{S}}$ candidates) and a sizable background dominated by unrelated ${{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}}$ combinations. Genuine ${D}^{0}$ decays associated with random muons contribute less than 1% to the ${D}^{0}$ yield, as determined from the yield of false $\kern 1.79993pt\overline{\kern-1.79993ptB}{}$ candidates formed by associating ${{D}^{*+}}\rightarrow{{D}^{0}}{{\pi}^{+}}$ with same-sign $\mu^{+}$ candidates. Contributions from backgrounds due to misreconstructed ${D}^{0}$ decays, such as ${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}}\pi^{0}$ and ${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+}h^{({\mkern-1.0mu\prime})-}$, where $h^{+}h^{({\mkern-1.0mu\prime})-}$ indicates a pair of light hadrons other than $\pi^{+}\pi^{-}$, are negligible.

Simulated [19, 20] prompt decays show that the online requirements on displacement and momenta of the ${D}^{0}$ decay products introduce efficiency variations that are correlated between the squared mass of the two final-state pions, $m^{2}({{\pi}^{+}}{{\pi}^{-}})$, and the ${D}^{0}$ decay time. Because $\left(m^{2}({{\pi}^{+}}{{\pi}^{-}}),t\right)$ correlations can bias the results, we correct for them using data. The smallness of the mixing parameters [5], along with the known ${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}}$ decay amplitudes [6, 7, 8], rules out any measurable $\left(m^{2}({{\pi}^{+}}{{\pi}^{-}}),t\right)$ correlation introduced by ${D}^{0}$–${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ mixing with current sample sizes. Hence, we ascribe any observed dependence between $m^{2}({{\pi}^{+}}{{\pi}^{-}})$ and $t$ to instrumental effects. We use the background-subtracted $\left(m^{2}({{\pi}^{+}}{{\pi}^{-}}),t\right)$ distribution to determine the decay-time efficiency, normalized to the average decay-time distribution, as a function of $m^{2}({{\pi}^{+}}{{\pi}^{-}})$. This two-dimensional map is smoothed and used to assign per-candidate weights proportional to the inverse of the relative efficiency at each candidate’s $\left(m^{2}({{\pi}^{+}}{{\pi}^{-}}),t\right)$ coordinates, effectively removing the correlated nonuniformities. The corrections are determined separately for long and downstream ${K}^{0}_{\mathrm{S}}$ candidates because they feature different correlations. Figure 2 shows the smoothed $\left(m^{2}({{\pi}^{+}}{{\pi}^{-}}),t\right)$ map for the sample with downstream ${K}^{0}_{\mathrm{S}}$ candidates, where the correlations are more prominent. The 6% of candidates reconstructed with $t<0.9\tau$ are discarded because the corresponding weights cannot be determined precisely. No $\left(m^{2}({{\pi}^{+}}{{\pi}^{-}}),t\right)$ correlations are observed in ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}\rightarrow{{D}^{0}}(\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}}){\mu^{-}}X$ decays.

We divide prompt and semileptonic samples according to the ${K}^{0}_{\mathrm{S}}$ category, ${D}^{0}$ meson flavor, Dalitz-plot position, and decay time. In each subsample, we determine the signal yield and — for each decay-time bin — the average decay time and average squared decay time of the signal candidates. Finally, we fit the decay-time dependence of the ratio of the signal yields symmetric with respect to the Dalitz-plot bisector.

We determine the signal yields by fitting the $\Delta m$ distribution, weighted to correct for the $\left(m^{2}({{\pi}^{+}}{{\pi}^{-}}),t\right)$ correlations, for the ${{D}^{*+}}\rightarrow{{D}^{0}}(\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}}){{\pi}^{+}}$ candidates and the $m({{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}})$ distribution for the ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}\rightarrow{{D}^{0}}(\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}}){\mu^{-}}X$ candidates. All components are modeled empirically. The $\Delta m$ model combines a ${D}^{*+}$ signal with a smooth phase-space-like background. The $m({{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}})$ model combines a ${D}^{0}$ signal with a linear background. Signal and background shape parameters are determined independently for long and downstream ${K}^{0}_{\mathrm{S}}$ candidates, for ${D}^{0}$ and ${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ mesons, and in each decay-time and Dalitz-plot bin. The signal model assumes the same parameters for each pair of positive and negative Dalitz-plot bins.

We estimate $\langle t\rangle_{j}$ and $\langle t^{2}\rangle_{j}$ from the background-subtracted $t$ distribution in each decay-time bin $j$ separately for prompt and semileptonic samples, as well as for long and downstream ${K}^{0}_{\mathrm{S}}$ candidates. Background is subtracted using weights derived from the mass fits [21] of candidates restricted to the lower half ($m^{2}_{-}<m^{2}_{+}$) of the Dalitz plot, which is enriched in ${D}^{0}$ mesons that did not undergo oscillations. We neglect the decay-time resolutions, which are typically $0.1\tau$ and $0.25\tau$ for the ${{D}^{*+}}\rightarrow{{D}^{0}}(\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}}){{\pi}^{+}}$ and ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}\rightarrow{{D}^{0}}(\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}}){\mu^{-}}X$ samples, respectively; and account for this approximation in the systematic uncertainties.

The mixing parameters are determined by minimizing a least-squares function that compares the decay-time evolution of signal yields ($N$) observed in Dalitz bins $-b$ and $+b$, along with their uncertainties ($\sigma$), with the expected values reported in Eq. 1,

[TABLE]

We fit simultaneously the prompt (pr) and semileptonic (sl) samples, separated between long (l) and downstream (d) ${K}^{0}_{\mathrm{S}}$ candidates, as well as between ${D}^{0}$ ($+$) and ${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ ($-$) flavors, across all decay-time bins $j$ and Dalitz-plot bins $b$. We constrain the parameters $X_{b}$ to the values $X_{b}^{\rm{CLEO}}$ measured by the CLEO collaboration through a Gaussian penalty term that uses the sum $V_{\rm{CLEO}}$ of the statistical and systematic covariance matrices [15]. In the fit, the parameters $r_{b}$ are determined independently for each subsample (pr, sl, l, d) because they are affected by the sample-specific variation of the efficiency over the Dalitz plot [12]. The values of $x_{{C\!P}}$, $\Delta x$, and $\Delta y$ were kept blind until the analysis was finalized.

Figure 3 shows the yield ratios with fit projections overlaid for prompt and semileptonic data. The offsets between semileptonic and prompt data are due to sample-specific efficiency variations across the Dalitz plot; their slopes, due to charm oscillations, are consistent across samples. Table 1 lists the results. The data are consistent with $C\!P$ symmetry ($\Delta x=\Delta y=0$). The precision is dominated by the statistical contribution, which incorporates a subleading component due to the precision of the CLEO measurements.

The dominant systematic uncertainties on $x_{{C\!P}}$ are associated with the 3% contamination from secondary ${D}^{*+}$ decays in the prompt sample ($0.24\times 10^{-3}$) and from the 1% contamination of genuine ${D}^{0}$ mesons associated with random muons in the semileptonic sample ($0.34\times 10^{-3}$). Biases due to the neglected decay-time and $m_{\pm}^{2}$ resolutions, and the neglected efficiency variations across decay time and Dalitz plot, constitute the dominant systematic uncertainty on $y_{{C\!P}}$ ($0.94\times 10^{-3}$). Possible asymmetric nonuniformities with respect to the bisector in the Dalitz plot induced by reconstruction inefficiencies dominate the systematic uncertainty on $\Delta x$ ($0.22\times 10^{-3}$) and $\Delta y$ ($0.25\times 10^{-3}$). Other minor effects, such as mismodeling in the signal-yield fits or in the determination of the bin-averaged decay times, are also considered. The consistency between results on the prompt and semileptonic sample (see Supplemental material), and on various partitions of the data, supports the robustness of the analysis, including the correction of the $\left(m^{2}({{\pi}^{+}}{{\pi}^{-}}),t\right)$ correlations.

In summary, we report a measurement of the normalized mass difference between neutral charm-meson eigenstates using the recently proposed bin-flip method. Allowing for $C\!P$ violation in charm mixing, or in the interference between mixing and decay, we measure the $C\!P$-averaged normalized mass difference $x_{{C\!P}}=[2.7\pm 1.6\text{\,(stat)}\pm 0.4\text{\,(syst)}]\times 10^{-3}$, and the $C\!P$-violating parameter $\Delta x=[-0.53\pm 0.70\text{\,(stat)}\pm 0.22\text{\,(syst)}]\times 10^{-3}$. In addition, we report the $C\!P$-averaged normalized width difference $y_{{C\!P}}=[7.4\pm 3.6\text{\,(stat)}\pm 1.1\text{\,(syst)}]\times 10^{-3}$, along with the corresponding $C\!P$-violating parameter $\Delta y=[0.6\pm 1.6\text{\,(stat)}\pm 0.3\text{\,(syst)}]\times 10^{-3}$. We use the results to form a likelihood function of $x$, $y$, $|q/p|$, and $\phi$; and we derive confidence intervals (Table 2) using a likelihood-ratio ordering that assumes the observed correlations to be independent of the true parameter values [22]. The resulting determination of the mass difference is the most precise from a single experiment, as are the determinations of the $C\!P$-violation parameters. Although our result is consistent with $x=0$ within two standard deviations, combined with the current global knowledge, it yields $x=(3.9\,^{+\,1.1}_{-\,1.2})\times 10^{-3}$ [5], strongly contributing to the emerging evidence for a nonzero (positive) mass difference between the neutral charm-meson eigenstates. The global constraints on $C\!P$ violation in the ${D}^{0}$-${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ system are also greatly improved, with precisions on $|q/p|$ and $\phi$ more than doubled as compared to previous averages [5].

Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments for the excellent performance of the LHC. We thank the technical and administrative staff at the LHCb institutes. We acknowledge support from CERN and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); MOST and NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN (Italy); NWO (Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MSHE (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC (United Kingdom); NSF (USA). We acknowledge the computing resources that are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN (Italy), SURF (Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-GRID (Poland) and OSC (USA). We are indebted to the communities behind the multiple open-source software packages on which we depend. Individual groups or members have received support from AvH Foundation (Germany); EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union); ANR, Labex P2IO and OCEVU, and Région Auvergne-Rhône-Alpes (France); Key Research Program of Frontier Sciences of CAS, CAS PIFI, and the Thousand Talents Program (China); RFBR, RSF and Yandex LLC (Russia); GVA, XuntaGal and GENCAT (Spain); the Royal Society and the Leverhulme Trust (United Kingdom); Laboratory Directed Research and Development program of LANL (USA).

Supplemental material

Dalitz-plot distribution and binning scheme

Figure 4 shows the decay-time-integrated Dalitz-plot distribution of the background-subtracted ${{D}^{0}}\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}{{\pi}^{-}}$ candidates used in the analysis, together with the Dalitz-plot binning scheme. No efficiency corrections are applied. All samples are combined.

Prompt- and semileptonic-only fit results

Tables 3 and 4 report results obtained by fitting independently the prompt and semileptonic data samples, respectively.

LHCb Collaboration

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V. Matiunin35, C. Matteuzzi22, K.R. Mattioli77, A. Mauri46, E. Maurice9,b, B. Maurin45, M. McCann57,44, A. McNab58, R. McNulty15, J.V. Mead56, B. Meadows61, C. Meaux8, N. Meinert70, D. Melnychuk33, M. Merk29, A. Merli23,q, E. Michielin25, D.A. Milanes69, E. Millard52, M.-N. Minard6, L. Minzoni18,g, D.S. Mitzel14, A. Mödden12, A. Mogini10, R.D. Moise57, T. Mombächer12, I.A. Monroy69, S. Monteil7, M. Morandin25, G. Morello20, M.J. Morello26,t, J. Moron32, A.B. Morris8, R. Mountain63, F. Muheim54, M. Mukherjee68, M. Mulder29, D. Müller44, J. Müller12, K. Müller46, V. Müller12, C.H. Murphy59, D. Murray58, P. Naik50, T. Nakada45, R. Nandakumar53, A. Nandi59, T. Nanut45, I. Nasteva2, M. Needham54, N. Neri23,q, S. Neubert14, N. Neufeld44, R. Newcombe57, T.D. Nguyen45, C. Nguyen-Mau45,n, S. Nieswand11, R. Niet12, N. Nikitin36, N.S. Nolte44, A. Oblakowska-Mucha32, V. Obraztsov40, S. Ogilvy55, D.P. O’Hanlon17, R. Oldeman24,f, C.J.G. Onderwater71, J. D. Osborn77, A. Ossowska31, J.M. Otalora Goicochea2, T. Ovsiannikova35, P. Owen46, A. Oyanguren76, P.R. Pais45, T. Pajero26,t, A. Palano16, M. Palutan20, G. Panshin75, A. Papanestis53, M. Pappagallo54, L.L. Pappalardo18,g, W. Parker62, C. Parkes58,44, G. Passaleva19,44, A. Pastore16, M. Patel57, C. Patrignani17,e, A. Pearce44, A. Pellegrino29, G. Penso28, M. Pepe Altarelli44, S. Perazzini44, D. Pereima35, P. Perret7, L. Pescatore45, K. Petridis50, A. Petrolini21,h, A. Petrov72, S. Petrucci54, M. Petruzzo23,q, B. Pietrzyk6, G. Pietrzyk45, M. Pikies31, M. Pili59, D. Pinci28, J. Pinzino44, F. Pisani44, A. Piucci14, V. Placinta34, S. Playfer54, J. Plews49, M. Plo Casasus43, F. Polci10, M. Poli Lener20, M. Poliakova63, A. Poluektov8, N. Polukhina73,c, I. Polyakov63, E. Polycarpo2, G.J. Pomery50, S. Ponce44, A. Popov40, D. Popov49,13, S. Poslavskii40, E. Price50, C. Prouve43, V. Pugatch48, A. Puig Navarro46, H. Pullen59, G. Punzi26,p, W. Qian4, J. Qin4, R. Quagliani10, B. Quintana7, N.V. Raab15, B. Rachwal32, J.H. Rademacker50, M. Rama26, M. Ramos Pernas43, M.S. Rangel2, F. Ratnikov38,74, G. Raven30, M. Ravonel Salzgeber44, M. Reboud6, F. Redi45, S. Reichert12, F. Reiss10, C. Remon Alepuz76, Z. Ren3, V. Renaudin59, S. Ricciardi53, S. Richards50, K. Rinnert56, P. Robbe9, A. Robert10, A.B. Rodrigues45, E. Rodrigues61, J.A. Rodriguez Lopez69, M. Roehrken44, S. Roiser44, A. Rollings59, V. Romanovskiy40, A. Romero Vidal43, J.D. Roth77, M. Rotondo20, M.S. Rudolph63, T. Ruf44, J. Ruiz Vidal76, J.J. Saborido Silva43, N. Sagidova41, B. Saitta24,f, V. Salustino Guimaraes65, C. Sanchez Gras29, C. Sanchez Mayordomo76, B. Sanmartin Sedes43, R. Santacesaria28, C. Santamarina Rios43, M. Santimaria20,44, E. Santovetti27,j, G. Sarpis58, A. Sarti20,k, C. Satriano28,s, A. Satta27, M. Saur4, D. Savrina35,36, S. Schael11, M. Schellenberg12, M. Schiller55, H. Schindler44, M. Schmelling13, T. Schmelzer12, B. Schmidt44, O. Schneider45, A. Schopper44, H.F. Schreiner61, M. Schubiger45, S. Schulte45, M.H. Schune9, R. Schwemmer44, B. Sciascia20, A. Sciubba28,k, A. Semennikov35, E.S. Sepulveda10, A. Sergi49,44, N. Serra46, J. Serrano8, L. Sestini25, A. Seuthe12, P. Seyfert44, M. Shapkin40, T. Shears56, L. Shekhtman39,x, V. Shevchenko72, E. Shmanin73, B.G. Siddi18, R. Silva Coutinho46, L. Silva de Oliveira2, G. Simi25,o, S. Simone16,d, I. Skiba18, N. Skidmore14, T. Skwarnicki63, M.W. Slater49, J.G. Smeaton51, E. Smith11, I.T. Smith54, M. Smith57, M. Soares17, l. Soares Lavra1, M.D. Sokoloff61, F.J.P. Soler55, B. Souza De Paula2, B. Spaan12, E. Spadaro Norella23,q, P. Spradlin55, F. Stagni44, M. Stahl14, S. Stahl44, P. Stefko45, S. Stefkova57, O. Steinkamp46, S. Stemmle14, O. Stenyakin40, M. Stepanova41, H. Stevens12, A. Stocchi9, S. Stone63, S. Stracka26, M.E. Stramaglia45, M. Straticiuc34, U. Straumann46, S. Strokov75, J. Sun3, L. Sun67, Y. Sun62, K. Swientek32, A. Szabelski33, T. Szumlak32, M. Szymanski4, Z. Tang3, T. Tekampe12, G. Tellarini18, F. Teubert44, E. Thomas44, M.J. Tilley57, V. Tisserand7, S. T’Jampens6, M. Tobin5, S. Tolk44, L. Tomassetti18,g, D. Tonelli26, D.Y. Tou10, R. Tourinho Jadallah Aoude1, E. Tournefier6, M. Traill55, M.T. Tran45, A. Trisovic51, A. Tsaregorodtsev8, G. Tuci26,44,p, A. Tully51, N. Tuning29, A. Ukleja33, A. Usachov9, A. Ustyuzhanin38,74, U. Uwer14, A. Vagner75, V. Vagnoni17, A. Valassi44, S. Valat44, G. Valenti17, M. van Beuzekom29, E. van Herwijnen44, C.B. Van Hulse15, J. van Tilburg29, M. van Veghel29, R. Vazquez Gomez44, P. Vazquez Regueiro43, C. Vázquez Sierra29, S. Vecchi18, J.J. Velthuis50, M. Veltri19,r, A. Venkateswaran63, M. Vernet7, M. Veronesi29, M. Vesterinen52, J.V. Viana Barbosa44, D. Vieira4, M. Vieites Diaz43, H. Viemann70, X. Vilasis-Cardona42,m, A. Vitkovskiy29, M. Vitti51, V. Volkov36, A. Vollhardt46, D. Vom Bruch10, B. Voneki44, A. Vorobyev41, V. Vorobyev39,x, N. Voropaev41, R. Waldi70, J. Walsh26, J. Wang5, M. Wang3, Y. Wang68, Z. Wang46, D.R. Ward51, H.M. Wark56, N.K. Watson49, D. Websdale57, A. Weiden46, C. Weisser60, M. Whitehead11, G. Wilkinson59, M. Wilkinson63, I. Williams51, M. Williams60, M.R.J. Williams58, T. Williams49, F.F. Wilson53, M. Winn9, W. Wislicki33, M. Witek31, G. Wormser9, S.A. Wotton51, K. Wyllie44, D. Xiao68, Y. Xie68, H. Xing66, A. Xu3, M. Xu68, Q. Xu4, Z. Xu6, Z. Xu3, Z. Yang3, Z. Yang62, Y. Yao63, L.E. Yeomans56, H. Yin68, J. Yu68,aa, X. Yuan63, O. Yushchenko40, K.A. Zarebski49, M. Zavertyaev13,c, M. Zeng3, D. Zhang68, L. Zhang3, W.C. Zhang3,z, Y. Zhang44, A. Zhelezov14, Y. Zheng4, X. Zhu3, V. Zhukov11,36, J.B. Zonneveld54, S. Zucchelli17,e.

*1**Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil

2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil

3Center for High Energy Physics, Tsinghua University, Beijing, China

4University of Chinese Academy of Sciences, Beijing, China

5Institute Of High Energy Physics (ihep), Beijing, China

6Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy, France

7Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France

8Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France

9LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France

10LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3, Paris, France

11I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany

12Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany

13Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany

14Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany

15School of Physics, University College Dublin, Dublin, Ireland

16INFN Sezione di Bari, Bari, Italy

17INFN Sezione di Bologna, Bologna, Italy

18INFN Sezione di Ferrara, Ferrara, Italy

19INFN Sezione di Firenze, Firenze, Italy

20INFN Laboratori Nazionali di Frascati, Frascati, Italy

21INFN Sezione di Genova, Genova, Italy

22INFN Sezione di Milano-Bicocca, Milano, Italy

23INFN Sezione di Milano, Milano, Italy

24INFN Sezione di Cagliari, Monserrato, Italy

25INFN Sezione di Padova, Padova, Italy

26INFN Sezione di Pisa, Pisa, Italy

27INFN Sezione di Roma Tor Vergata, Roma, Italy

28INFN Sezione di Roma La Sapienza, Roma, Italy

29Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands

30Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, Netherlands

31Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Kraków, Poland

32AGH - University of Science and Technology, Faculty of Physics and Applied Computer Science, Kraków, Poland

33National Center for Nuclear Research (NCBJ), Warsaw, Poland

34Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania

35Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia

36Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia

37Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS), Moscow, Russia

38Yandex School of Data Analysis, Moscow, Russia

39Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia

40Institute for High Energy Physics (IHEP), Protvino, Russia

41Konstantinov Nuclear Physics Institute of National Research Centre ”Kurchatov Institute”, PNPI, St.Petersburg, Russia

42ICCUB, Universitat de Barcelona, Barcelona, Spain

43Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de Santiago de Compostela, Santiago de Compostela, Spain

44European Organization for Nuclear Research (CERN), Geneva, Switzerland

45Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

46Physik-Institut, Universität Zürich, Zürich, Switzerland

47NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine

48Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine

49University of Birmingham, Birmingham, United Kingdom

50H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom

51Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom

52Department of Physics, University of Warwick, Coventry, United Kingdom

53STFC Rutherford Appleton Laboratory, Didcot, United Kingdom

54School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom

55School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom

56Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom

57Imperial College London, London, United Kingdom

58School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom

59Department of Physics, University of Oxford, Oxford, United Kingdom

60Massachusetts Institute of Technology, Cambridge, MA, United States

61University of Cincinnati, Cincinnati, OH, United States

62University of Maryland, College Park, MD, United States

63Syracuse University, Syracuse, NY, United States

64Laboratory of Mathematical and Subatomic Physics , Constantine, Algeria, associated to 2

65Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to 2

66South China Normal University, Guangzhou, China, associated to 3

67School of Physics and Technology, Wuhan University, Wuhan, China, associated to 3

68Institute of Particle Physics, Central China Normal University, Wuhan, Hubei, China, associated to 3

69Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia, associated to 10

70Institut für Physik, Universität Rostock, Rostock, Germany, associated to 14

71Van Swinderen Institute, University of Groningen, Groningen, Netherlands, associated to 29

72National Research Centre Kurchatov Institute, Moscow, Russia, associated to 35

73National University of Science and Technology “MISIS”, Moscow, Russia, associated to 35

74National Research University Higher School of Economics, Moscow, Russia, associated to 38

75National Research Tomsk Polytechnic University, Tomsk, Russia, associated to 35

76Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia - CSIC, Valencia, Spain, associated to 42

77University of Michigan, Ann Arbor, United States, associated to 63

78Los Alamos National Laboratory (LANL), Los Alamos, United States, associated to 63

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil

bLaboratoire Leprince-Ringuet, Palaiseau, France

cP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia

dUniversità di Bari, Bari, Italy

eUniversità di Bologna, Bologna, Italy

fUniversità di Cagliari, Cagliari, Italy

gUniversità di Ferrara, Ferrara, Italy

hUniversità di Genova, Genova, Italy

iUniversità di Milano Bicocca, Milano, Italy

jUniversità di Roma Tor Vergata, Roma, Italy

kUniversità di Roma La Sapienza, Roma, Italy

lAGH - University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, Kraków, Poland

mLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain

nHanoi University of Science, Hanoi, Vietnam

oUniversità di Padova, Padova, Italy

pUniversità di Pisa, Pisa, Italy

qUniversità degli Studi di Milano, Milano, Italy

rUniversità di Urbino, Urbino, Italy

sUniversità della Basilicata, Potenza, Italy

tScuola Normale Superiore, Pisa, Italy

uUniversità di Modena e Reggio Emilia, Modena, Italy

vH.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom

wMSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines

xNovosibirsk State University, Novosibirsk, Russia

ySezione INFN di Trieste, Trieste, Italy

zSchool of Physics and Information Technology, Shaanxi Normal University (SNNU), Xi’an, China

aaPhysics and Micro Electronic College, Hunan University, Changsha City, China

abLanzhou University, Lanzhou, China

†Deceased *