Branching fraction and charge asymmetry measurements in B to J/psi pi pi decays

TL;DR

This paper reports measurements of branching fractions and charge asymmetry in B meson decays to J/psi and two pions, using a large data sample from the BaBar experiment, including intermediate resonances and setting upper limits for non-resonant decays.

Contribution

First precise measurements of branching fractions and charge asymmetry in B to J/psi pi pi decays, including resonance contributions and upper limits for non-resonant modes.

Findings

Measured B(B0 -> J/psi rho0) = (2.7 +/- 0.3 +/- 0.17) x 10^-5

Measured B(B+ -> J/psi rho+) = (5.0 +/- 0.7 +/- 0.31) x 10^-5

Charge asymmetry in B+ decays to J/psi rho is -0.11 +/- 0.12 +/- 0.08

Abstract

We study the decays B0 to J/psi pi+pi- and B+ to J/psi pi+pi0, including intermediate resonances, using a sample of 382 million BBbar pairs recorded by the BaBar detector at the PEP-II e+e- B factory. We measure the branching fractions B(B0 ->J/psi rho0) = (2.7 +/- 0.3 +/- 0.17) x 10-5 and B(B+ ->J/psi rho+) = (5.0 +/- 0.7 +/-0.31) x 10-5. We also set the following upper limits at the 90% confidence level: B(B0 -> J/psi pi+ \pi- non-resonant) < 1.2 x 10-5, B(B0 -> J/psi f_2(1270)) < 4.6 x 10-6, and B(B+ -> J/psi pi+ pi0 non-resonant) < 4.4 x 10-6. We measure the charge asymmetry in charged B decays to J/psi rho to be -0.11 +/- 0.12 +/- 0.08.

Figures

Tables

Table 1. Table 1: Signal yields, detection efficiencies, and branching fractions for the signal decay channels. The fit bias, product of secondary branching fractions ( ℬ ​ ( J / ψ → l + ​ l − ) ℬ → 𝐽 𝜓 superscript 𝑙 superscript 𝑙 \mathcal{B}({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rightarrow l^{+}l^{-}) and ℬ ​ ( π 0 → γ ​ γ ) ℬ → superscript 𝜋 0 𝛾 𝛾 \mathcal{B}(\pi^{0}\rightarrow\gamma\gamma) ), and significances of the signals (using statistical uncertainties only) are also listed. The corrected yields are obtained by subtracting the fit bias from the fitted yields. For the yields, efficiencies, and branching fractions, the first errors are statistical and the second are systematic. For decay channels where no significant signal is observed, we quote an upper limit at the 90 % percent 90 90\% confidence level.

Mode	Fit bias (events)	Corrected yield (events)	$ϵ$(%)	$\prod {ℬ}_i$(%)	Signif. ($\sigma$)	$ℬ(\times {10}^{-5})$
$J/\psi {\rho }^0$	$0$	$251.1\pm 27.5\pm 11.2$	$20.6\pm 0.1\pm 0.8$	$\mathrm{\hspace{0.33em}\hspace{0.33em}11.87}\pm 0.12$	$13.0$	$2.7\pm 0.3\pm 0.2$
$J/\psi {\pi }^{+}{\pi }^{-}$	$0$	$64.5\pm 35.5\pm 7.7$	$20.3\pm 0.1\pm 0.8$	$\mathrm{\hspace{0.33em}\hspace{0.33em}11.87}\pm 0.12$	$2.0$	(90% C.L.)
$J/\psi f_2$	$0$	$24.4\pm 13.8\pm 1.8$	$20.3\pm 0.1\pm 0.8$	$\mathrm{\hspace{0.33em}\hspace{0.33em}11.87}\pm 0.12$	$2.0$	(90% C.L.)
$J/\psi {\rho }^{+}$	$-6.8\pm 1.1$	$218.5\pm 28.8\pm 9.5$	$9.7\pm 0.1\pm 0.4$	$\mathrm{\hspace{0.33em}\hspace{0.33em}11.73}\pm 0.12$	$11.6$	$5.0\pm 0.7\pm 0.3$
$J/\psi {\pi }^{+}{\pi }^0$	$+8.2\pm 0.9$	$-12.7\pm 27.1\pm 4.7$	$11.9\pm 0.1\pm 0.5$	$\mathrm{\hspace{0.33em}\hspace{0.33em}11.73}\pm 0.12$	$0$	(90% C.L.)

Equations

$${\mathcal{A}}_{CP}=\frac{N(B^{-}\to J/\psi {\rho }^{-})-N(B^{+}\to J/\psi {\rho }^{+})}{N(B^{-}\to J/\psi {\rho }^{-})+N(B^{+}\to J/\psi {\rho }^{+})}.$$

$$\mathcal{B}=\frac{N_{sig}}{N_{B\overline{B}}\times {ϵ}_{sig}\times \mathcal{B}(J/\psi \to l^{+}{l}^{-})},$$

$$\mathcal{L}=\frac{1}{N!}{e}^{-N^{\prime }}(N^{\prime }{)}^N\prod _{i=1}^N{\mathcal{P}}_i,$$

$$F_{\rho }(m_{\pi \pi })=\frac{m_{\pi \pi }\Gamma (m_{\pi \pi })P^{2L_{eff}+1}}{((m_{\rho }^2-m_{\pi \pi }^2{)}^2+m_{\rho }^2\Gamma (m_{\pi \pi }{)}^2)},$$

$${\mathcal{P}}_i$$

$$\displaystyle CB(m)=\left\{\begin{array}[]{ll}\exp\left(-\frac{(m-\mu)^{2}}{2\sigma^{2}}\right)&m>\mu-\alpha\sigma\\ \frac{(n/\alpha)^{n}\exp(-\alpha^{2}/2)}{((\mu-m)/\sigma+n/\alpha-\alpha)^{n}}&m<\mu-\alpha\sigma\end{array}\right.$$

$$A(m)=y\sqrt{1-y^2}\exp (\xi (1-y^2))y$$

$$A(m)=0y$$

$$W(m)=CV(m-M_{\mathrm{on}}{)}^{(C-1)}\exp [-V(m-M_{\max }{)}^C],$$

Full text

We also set the following upper limits at the 90% confidence level: $\mathcal{B}(B^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{-}$non-resonant) $<1.2\times 10^{-5}$, $\mathcal{B}(B^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}f_{2})<4.6\times 10^{-6}$, and $\mathcal{B}(B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{0}$ non-resonant)$<4.4\times 10^{-6}$. We measure the charge asymmetry in charged $B$ decays to ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rho$ to be $-0.11\pm 0.12\pm 0.08$.

††preprint: BABAR-PUB-07/017††preprint: SLAC-PUB-12441††preprint: MAN/HEP/2007/5

The decay $B^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rho^{0}$ chargeConj can in principle be used to measure the $CP$ violation parameter $\sin\!2\beta$. However, the measurement is not as straightforward as for ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{0}_{\scriptscriptstyle S}$ sin2bBabar ; sin2bBelle , because it involves the decay of a pseudoscalar meson to two vector mesons, resulting in both $CP$-odd and $CP$-even final states. Furthermore, the decay can proceed through either a color-suppressed tree diagram, or a penguin diagram, both shown in Fig. 1, and interference between them could result in direct $CP$ violation dunietz . Direct $CP$ violation may also occur in $B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rho^{+}$ decays, where it would manifest itself as a non-zero charge asymmetry:

[TABLE]

The large intrinsic width of the $\rho$ meson necessitates an analysis of a significant portion of the invariant mass spectrum of the dipion system.

The branching fraction for $B^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{-}$ has previously been measured at BABAR to be $(4.6\pm 0.7\pm 0.6)\times 10^{-5}$ babarJpsipipi , including a ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rho^{0}$ component with a branching fraction of $(1.6\pm 0.6\pm 0.4)\times 10^{-5}$. This measurement used a data sample containing approximately 56 million $B\kern 1.79993pt\overline{\kern-1.79993ptB}{}$ pairs, which is a subset of the sample used in this analysis. The charged $B$ decay to ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rho^{+}$ has not previously been observed, the CLEO collaboration set an upper limit $\mathcal{B}(B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rho^{+})<7.7\times 10^{-4}$ at the 90% confidence level CLEO .

The data sample used here contains 382 million $B\kern 1.79993pt\overline{\kern-1.79993ptB}{}$ pairs collected with the BABAR detector at the PEP-II asymmetric-energy $e^{+}e^{-}$ storage ring, taken at a center-of-mass (CM) energy equivalent to the mass of the $\mathchar 28935\relax{(4S)}$ resonance. An additional data sample, corresponding to an integrated luminosity of $36.8\mbox{\,fb}^{-1}$, taken at a CM energy 40$\mathrm{\,Me\kern-1.00006ptV}$ below the $\mathchar 28935\relax{(4S)}$ resonance, is used to study backgrounds from continuum $q\overline{q}$ production, where $q$ = $u,d,s,c$.

A detailed description of the BABAR detector can be found elsewhere NIM . Charged-particle trajectories are measured by a five-layer silicon vertex tracker (SVT) and a 40-layer drift chamber (DCH) operating in a 1.5 T solenoidal magnetic field. A detector of internally reflected Cherenkov light (DIRC) is used for charged hadron identification. Surrounding this is a CsI(Tl) electromagnetic calorimeter (EMC), and finally the instrumented flux return (IFR) of the solenoid, which consists of layers of iron interspersed with resistive plate chambers or limited streamer tubes.

The ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ meson is reconstructed in decays to $l^{+}l^{-}$, where $l^{\pm}$ refers to a charged lepton, $e^{\pm}$ or $\mu^{\pm}$. Electrons are selected on the basis of the ratio of EMC shower energy to track momentum, and the energy profile of the EMC shower. For ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rightarrow e^{+}e^{-}$, an attempt is made to recover energy losses from bremsstrahlung, by looking for showers in the EMC close to those from the electron candidates. This procedure increases the selection efficiency for ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rightarrow e^{+}e^{-}$ candidates by approximately $30\%$ exclCharmon . The muon selection algorithm uses a neural network, for which the most important input is the number of interaction lengths traversed in the IFR. The lepton pairs are fitted to a common vertex and the invariant mass of the combination is required to be in the range 2.98 (3.06) to 3.14${\mathrm{\,Ge\kern-1.00006ptV\!/}c^{2}}$ for the $e^{+}e^{-}$ ($\mu^{+}\mu^{-}$) channels. In order to reduce the background from $B^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{*0}(K^{*0}\rightarrow K^{+}\pi^{-})$ decays, charged pion candidates are required to satisfy stringent particle identification criteria, based on combined ionization energy loss ($\mathrm{d}E/\mathrm{d}x$) in the DCH and SVT with the Cherenkov angle measured in the DIRC.

All tracks are required to originate close to the interaction point, and to lie in polar angle ranges where particle identification efficiency is well measured. The allowed ranges correspond to the geometric acceptances of the DIRC for pions, the EMC for electrons, and the IFR for muons.

Neutral pion candidates are formed by combining pairs of isolated showers in the EMC. These are required to spread over a minimum of three crystals, and to have an energy greater than $200\mathrm{\,Me\kern-1.00006ptV}$.

To form a $B$ candidate, the reconstructed ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ is combined with either a pair of oppositely charged pions, or a charged pion and a $\pi^{0}$, and a kinematic and geometric fit is used to ensure that all final state particles are consistent with coming from the same decay point. In this fit, we constrain the invariant mass of the $l^{+}l^{-}$ and the $\gamma\gamma$ to have the nominal mass of the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and $\pi^{0}$, respectively  PDG06 . The energy difference, $\mathrm{\Delta E}$, between the candidate energy and the single beam energy, $E_{beam}^{CM}$, (both in the CM frame) is expected to be close to zero for signal events, and is therefore required to be in the interval $-40$ to $40\mathrm{\,Me\kern-1.00006ptV}$ ($-60$ to $80\mathrm{\,Me\kern-1.00006ptV}$) for $B^{0}$ ($B^{+}$) candidates, corresponding to approximately $\pm 3\sigma$ of the $\mathrm{\Delta E}$ resolution. Note that the range is asymmetric for $B^{+}$ candidates because the $\pi^{0}$ in the final state gives rise to a tail on the low side of the distribution, due to the EMC response to photons. For events where more than one $B$ candidate passes the selection criteria, the candidate with the smallest value of |$$\mathrm{\Delta E}$$| is chosen.

The branching fraction for each signal channel is obtained from:

[TABLE]

where $N_{sig}$ and $\epsilon_{sig}$ are the observed yield and selection efficiency, respectively, for a specific signal channel, and $N_{B\kern 1.25995pt\overline{\kern-1.25995ptB}{}}$ is the number of $B$ meson pairs. We assume that the $\mathchar 28935\relax{(4S)}$ decays equally often into neutral and charged $B$ meson pairs. The ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rightarrow l^{+}l^{-}$ branching fraction is taken to be $(11.87\pm 0.12)\%$ PDG06 .

We extract the signal yields for the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rho^{0}$, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{-}$  non-resonant, and ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}f_{2}$ channels by performing a fit on the sample of reconstructed $B^{0}$ candidates. We also perform a similar fit to the sample of charged $B$ candidates in order to obtain the signal yields for the decay channels $B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rho^{+}$ and $B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{0}$ non-resonant. The fits are two-dimensional, extended, unbinned maximum likelihood fits to the distributions of $m_{\rm ES}$ and $m_{\pi\pi}$, Seven event categories are considered: (i) ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rho$ signal, (ii) ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi\pi$ non-resonant signal, (iii) ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}f_{2}$ signal, (iv) ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ $K^{0}_{\scriptscriptstyle S}$ events, (v) background events that do not contain a ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ (non-${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ background), (vi) background events containing a ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ (inclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ background), and (vii) selected background channels that have been studied in more detail (exclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ backgrounds). In the fit to neutral $B$ candidates, the decay channels that comprise category (vii) are ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{*0}$, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{*+}$, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K_{1}(1270)$, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rho^{+}$ jpsirhoch , and ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}$. For the fit to charged $B$ candidates, the exclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ background channels are ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{*0}$, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{*+}$, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K_{1}(1270)$, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{+}$, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{0}_{\scriptscriptstyle S}$, and ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{0}_{\scriptscriptstyle L}$. In both cases, these decay channels are not included in category (vi). Of course, categories (iii) and (iv) are only present in the fit to neutral $B$ candidates.

A probability density function (PDF) is constructed for each category, and the sum of these PDFs is used to fit the data. The likelihood function for the total sample is the product of the PDF values for each candidate, multiplied by a Poisson factor:

[TABLE]

where $N$ and $N^{\prime}$ are the numbers of observed and expected events, respectively, and $\mathcal{P}_{i}$ is the value of the total PDF for event $i$. For all event categories except for the exclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ background, $P_{i}$ is a product of one-dimensional PDFs in $m_{\rm ES}$  and $m_{\pi\pi}$.

Fig. 2 shows the $m_{\rm ES}$ and $m_{\pi\pi}$ distributions for the data, and the projections of the PDFs for each category. The functional forms of these PDFs are as follows. For the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rho^{0}$, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{-}$, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}f_{2}$, and ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{0}_{\scriptscriptstyle S}$  components, the $m_{\rm ES}$ distributions are parametrized by Gaussian functions, all with the same values for the mean and width, which are allowed to float in the fit. In the fit to charged $B$ candidates, a Crystal Ball function CB is used instead for the $m_{\rm ES}$ distributions of the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rho^{+}$ and ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{0}$ signal components, as the presence of a $\pi^{0}$ in the final state gives rise to a tail on the low mass side of the peak.

The ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ $\rho$ signal component is modeled by a relativistic $P$-wave Breit-Wigner function BW in $m_{\pi\pi}$:

[TABLE]

where $\Gamma(m_{\pi\pi})=\Gamma_{0}\left(\frac{q}{q_{0}}\right)^{3}\left(\frac{m_{\rho}}{m_{\pi\pi}}\right)\left(\frac{1+R^{2}q_{0}^{2}}{1+R^{2}q^{2}}\right)$. The parameter $q(m_{\pi\pi})$ is the pion momentum in the dipion rest frame, with $q_{0}=q(m_{\rho})$; $P$ is the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ momentum in the $B$ rest frame; $L_{eff}$ is the orbital angular momentum between the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and the $\rho$ which can be 0, 1 or 2; $R$ is the radius of the Blatt-Weisskopf barrier factor Blatt ; radius , which is taken to be $(0.5\pm 0.5){\rm\,fm}$, and $m_{\rho}$ is the $\rho$ meson mass.

The $m_{\pi\pi}$ distribution for the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi\pi$ non-resonant signal is $F_{\pi\pi}=q(m_{\pi\pi})P^{3}$, the product of a three-body phase space factor $q(m_{\pi\pi})P$ and a factor $P^{2}$ motivated by angular momentum conservation.

For the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}f_{2}$ component, the $m_{\pi\pi}$  distribution is described by a relativistic $D$-wave Breit-Wigner, similar to Eq. 4, but with an extra factor $(q/q_{0})^{2}$ in the expression for $\Gamma(m_{\pi\pi})$.

The decays to ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{0}_{\scriptscriptstyle S}$ are not considered signal for this analysis. Most of them are removed by the requirement that all tracks are consistent with coming from the same vertex. The $m_{\pi\pi}$ distribution of the remaining ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{0}_{\scriptscriptstyle S}$ events are modeled by a narrow Gaussian function.

Non-${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ background events are modeled by an ARGUS function argus in $m_{\rm ES}$. The $m_{\pi\pi}$ PDF is the sum of two Weibull functions wiebull , and a Breit-Wigner to describe the $\rho$ component of the continuum background. The parameters of this PDF are fixed to values obtained from fits to the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mass sidebands of the data.

The $m_{\rm ES}$ distribution of the inclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ background is an ARGUS function plus a Gaussian at the $B$ mass. The width of this Gaussian is somewhat wider than that used for signal components as it represents $B$ candidates that are not correctly reconstructed. The $m_{\pi\pi}$ PDF is a 4th-order polynomial. The PDF parameters for this component are fixed to values obtained by fits to a large sample of $B\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}(\rightarrow l^{+}l^{-})X$ Monte Carlo (MC) simulated events, with signal events and exclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ background channels removed.

Each of the exclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ background channels is modeled by a two-dimensional PDF derived from the distribution of MC events for that decay channel. The normalizations of these PDFs are determined by taking into account the selection efficiency on MC simulation, and the world average branching fractions PDG06 .

For the branching fraction fit to neutral $B$ candidates there are twelve free parameters: the yields of the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rho$, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi\pi$, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}f_{2}$, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{0}_{\scriptscriptstyle S}$, and inclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ background components, the mean and width of the Gaussian used for the signal distribution in $m_{\rm ES}$, the parameters $m_{\rho}$, $\Gamma_{0}$, and $L_{eff}$ in the $\rho$ lineshape, and the mean and width of the $m_{\pi\pi}$ distribution for the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{0}_{\scriptscriptstyle S}$ component. All other parameters are fixed, including those describing lineshape of the $f_{2}(1270)$, the normalizations and shapes of the exclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ background PDFs, and the shapes of the inclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ and non-${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ background PDFs. We also fix the ratio of non-${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ to ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ (inclusive plus exclusive) background yields to a value obtained from fitting to data in the region \mbox{m_{\rm ES}}<5.26 (i.e. lower in mass than the signal region), and extrapolated to the fit region using distributions from MC simulation.

The configuration for the charged $B$ branching fraction fit is very similar. Here, there are eight free parameters, since there are no ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{0}_{\scriptscriptstyle S}$ or ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}f_{2}$ components.

We find from MC simulation studies that correlations between $m_{\rm ES}$ and $m_{\pi\pi}$ give rise to small biases in the numbers of ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rho^{+}$ and ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{0}$ non-resonant signal candidates found in the charged $B$ fit. The sizes of these biases are evaluated by examining the distribution of residuals ($N_{obs}-N_{input}$) for a large number of MC experiments, and are listed in Table 1. The yields obtained from the branching fraction fit are therefore corrected to take account of this by subtracting these quantities from the fitted yields.

The signal yields and statistical errors obtained from the branching fraction fits are listed in Table 1. We also list the statistical significances of the observed signals, $\sqrt{-2\ln(\mathcal{L}_{Null}/\mathcal{L}_{Max})}$, where $\mathcal{L}_{Max}$ is the likelihood from the fit, and $\mathcal{L}_{Null}$ is the value of the likelihood function when the fit is performed with the signal yield constrained to zero events.

We obtain signal efficiencies using samples of MC signal events, produced in monthly blocks so as to match variations in detector and background conditions. Particle identification efficiency is corrected using data control samples of electrons, muons, and pions. The sizes of these corrections vary with momentum and polar angle, and average corrections are about $1.5\%$ for electrons, $5.9\%$ for muons, and $1.8\%$ for pions. With these corrections applied, about $85\%$ ($50\%$) of electron (muon) pairs, and about $85\%$ of pions, satisfy their respective particle identification requirements. A small, energy-dependent correction (typically about $-2\%$ relative) is also applied to decay modes containing a $\pi^{0}$ to account for known differences in photon detection efficiency between data and MC simulation. The corrected signal efficiencies are listed in Table 1.

Systematic errors on the branching fraction measurements arise from uncertainties on the signal efficiency, on the fitted yield, on the number of $B^{0}{\kern-1.60004pt\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}}$ or $B^{+}B^{-}$ events in the sample, and on the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rightarrow l^{+}l^{-}$ branching fraction. The number of $B\kern 1.79993pt\overline{\kern-1.79993ptB}{}$ pairs is known to $1.1\%$ accuracy, and an additional $1.6\%$ uncertainty is assigned corresponding to the assumption that the $\mathchar 28935\relax{(4S)}$ decays 50% of the time into $B^{0}{\kern-1.60004pt\kern 1.79993pt\overline{\kern-1.79993ptB}{}^{0}}$ and 50% of the time into $B^{+}B^{-}$ PDG06 . The fractional uncertainty on $\mathcal{B}({J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rightarrow l^{+}l^{-})$ is $1.0\%$ PDG06 .

The systematic uncertainties on the efficiency are largely due to imperfect simulation of the detector performance. These effects are studied using various data control samples. The largest sources of uncertainty are pion identification efficiency, a $2.0\%$ ($3.4\%$) relative error for charged (neutral) $B$ decay channels, and $\pi^{0}$ efficiency ($3\%$ for charged $B$ decays). Tracking efficiency ($1.5\%$) and lepton identification efficiency ($1.0\%$) also contribute to the uncertainty on the efficiency. The polarization of the $\rho$ in $B\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rho$ decays is unknown. We use an MC sample in which the $\rho$ mesons are unpolarized to obtain the central value of the signal efficiency. We also evaluate the efficiency using MC data samples with different $\rho$ polarizations, and observe a relative variation of 2%, which is assigned as a systematic uncertainty on the branching fraction measurement.

We evaluate the impact of the fit procedure by observing the changes in the yields when varying the PDF parameters that were fixed in the fit within their uncertainties. The resulting differences are added quadratically for sets of parameters that are relatively uncorrelated, and added linearly for highly correlated sets of parameters. We also repeat the fit using alternative functional forms for some PDFs, namely the shape of the inclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ background in $m_{\pi\pi}$, and the $\rho$ lineshape, and include the resulting differences in the yield in the systematic uncertainty. In addition, for the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rho^{+}$ and ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{0}$ channels, systematic uncertainties equal to half of the bias corrections listed in Table 1 are assigned. The total systematic uncertainties on the yield vary from 1.8 events for the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}f_{2}$ channel, to 11.2 events for the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rho^{0}$ channel.

In order to assess the charge asymmetry $\mathcal{A}^{\rho}$, we perform a second fit to the charged $B$ candidate sample. In this fit, all the shape parameters for the signal and background components are fixed to values obtained from the branching fraction fit. This reduces the number of free parameters and improves the reliability of the fit. We include terms for the asymmetries in signal and background components as follows:

[TABLE]

where $N^{\rho}$, $N^{NR}$, and $N_{j}^{bkg}$ are the yields for the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rho^{+}$ signal, the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{0}$ non-resonant signal, and the different background components $j$, respectively, $Q_{i}$ is the charge of the $B$ candidate in event $i$, and $\mathcal{A}^{\rho}$, $\mathcal{A}^{NR}$, and $\mathcal{A}_{j}^{bkg}$ are the corresponding charge asymmetries. The asymmetry parameters for the exclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ background channels are fixed to world average values PDG06 . The asymmetries for the non-${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ background and inclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ background components are assumed to be the same ($\mathcal{A}_{inc}^{bkg}=\mathcal{A}_{non}^{bkg}\equiv\mathcal{A}^{bkg}$). This fit therefore has six free parameters: the yields of the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rho^{+}$ signal, ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{0}$ non-resonant signal, and inclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ background components, and the asymmetries $\mathcal{A}^{\rho}$, $\mathcal{A}^{NR}$, and $\mathcal{A}^{bkg}$.

From the charge asymmetry fit, we obtain $A^{\rho}=-0.11\pm 0.12\mathrm{(stat.)}$. The signal and background yields obtained from this fit are entirely consistent with those from the branching fraction fit.

A potential contribution to the systematic uncertainty on the charge asymmetry $\mathcal{A}^{\rho}$ could come from different pion identification efficiencies for $\pi^{+}$ and $\pi^{-}$, leading to different signal selection efficiencies for positively and negatively charged $B$ candidates. Using data control samples, this effect is found to be negligible.

The other sources of systematic error on the asymmetry are potential differences in the backgrounds for positive and negative $B$ candidates. The parameters describing the charge asymmetries of the exclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ background channels are varied within their uncertainties PDG06 , assuming a $10\%$ uncertainty for the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K_{1}(1270)$ channel for which no measurement is available. The normalizations of the exclusive background channels, and the shape parameters of the inclusive ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ background and non-${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ background components are varied in turn, and the fit is repeated. The resulting changes to the fitted value of $\mathcal{A}^{\rho}$ are added in quadrature, and the total systematic uncertainty is found to be $\pm 0.08$.

In summary, we measure the following branching fractions, where the first error in each case is statistical and the second is systematic: $\mathcal{B}(B^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rho^{0})=(2.7\pm 0.3\pm 0.2)\times 10^{-5}$, and $\mathcal{B}(B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rho^{+})=(5.0\pm 0.7\pm 0.3)\times 10^{-5}$. The signals for $B^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}f_{2}$, $B^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{-}$ non-resonant, and $B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{0}$ non-resonant are not statistically significant, thus we set the following upper limits at the $90\%$ confidence level: $\mathcal{B}(B^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}f_{2})<4.6\times 10^{-6}$, $\mathcal{B}(B^{0}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{-})<1.2\times 10^{-5}$, and $\mathcal{B}(B^{+}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\pi^{+}\pi^{0})<4.4\times 10^{-6}$. These values are calculated by summing the statistical and systematic uncertainties in quadrature, multiplying the result by 1.28, and adding it to the central value of the branching fraction. We measure the charge asymmetry defined in Eq. 1 for the decays $B^{\pm}\rightarrow{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rho^{\pm}$, $\mathcal{A}^{\rho}=-0.11\pm 0.12\pm 0.08$.

We are grateful for the excellent luminosity and machine conditions provided by our PEP-II colleagues, and for the substantial dedicated effort from the computing organizations that support BABAR. The collaborating institutions wish to thank SLAC for its support and kind hospitality. This work is supported by DOE and NSF (USA), NSERC (Canada), IHEP (China), CEA and CNRS-IN2P3 (France), BMBF and DFG (Germany), INFN (Italy), FOM (The Netherlands), NFR (Norway), MIST (Russia), MEC (Spain), and PPARC (United Kingdom). Individuals have received support from the Marie Curie EIF (European Union) and the A. P. Sloan Foundation.