EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2014-268 LHCb-PAPER-2014-058

Measurement of the $C\\!P$-violating phase $\beta$ in ${{B}^{0}}\rightarrow
J/\psi\pi^{+}\pi^{-}$ decays and limits on penguin effects

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

Time-dependent $C\\!P$ violation is measured in the $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\pi^{+}\pi^{-}$ channel for each $\pi^{+}\pi^{-}$ resonant final state
using data collected with an integrated luminosity of 3.0 fb-1 in $pp$
collisions using the LHCb detector. The final state with the largest rate,
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rho^{0}(770)$, is used to
measure the $C\\!P$-violating angle $2\beta^{\rm eff}$ to be $(41.7\pm
9.6_{-6.3}^{+2.8})^{\circ}$. This result can be used to limit the size of
penguin amplitude contributions to $C\\!P$ violation measurements in, for
example, $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}_{\\!\\!s}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ decays. Assuming approximate SU(3) flavour symmetry and
neglecting higher order diagrams, the shift in the $C\\!P$-violating phase
$\phi_{s}$ is limited to be within the interval [$-1.05^{\circ}$,
+$1.18^{\circ}$] at 95% confidence level. Changes to the limit due to SU(3)
symmetry breaking effects are also discussed.

Submitted to Phys. Lett. B

© CERN on behalf of the LHCb collaboration, license CC-BY-4.0.

##  1 Introduction

Measurements of $C\\!P$ violation in neutral $B$ meson decays are used either
to search for physics beyond the Standard Model (SM) [1, *Weinberg:1967tq] or
set limits on combinations of Cabibbo-Kobayashi-Maskawa couplings $(V_{ij})$
[3]. Interpretations of the measurement of the $C\\!P$-violating phase
$2\beta$ via the interference of mixing and decays in the $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ channel, and the phase $\phi_{s}$
in $\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\
[-.7ex]
$\kern-1.79993ptB$}{}^{0}_{\\!\\!s}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ and ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\pi^{+}\pi^{-}$ decays,111$C\\!P$ violation measurements in $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ determine the sum of $2\beta\equiv
2\arg(-V_{cd}V_{cb}^{*})/(V_{td}V_{tb}^{*})$ and contributions from higher
order diagrams. Similar measurements in the $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}_{\\!\\!s}$ system determine $\phi_{s}$ which is the
sum of $-2\beta_{s}\equiv-2\arg(-V_{ts}V_{tb}^{*})/(V_{cs}V_{cb}^{*})$ and
higher order corrections. are made assuming that the decays are dominated by
tree-level processes. However penguin processes are also possible, and they
may have large enough amplitudes to influence the results. Here we use $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\pi^{+}\pi^{-}$ decays to set limits on possible changes due to penguin
contributions. This mode has both tree and penguin diagrams, as shown in Fig.
1. Theoretical models, to be discussed later, predict that the ratio of
penguin to tree amplitudes is greatly enhanced in this decay relative to
$\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\
[-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ [4, 5, *Faller:2008gt]. Thus, the
effects of penguin topologies can be investigated by using the
$J/\psi\pi^{+}\pi^{-}$ decay and comparing different measurements of the
$C\\!P$-violating phase $2\beta$ in ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$, and individual channels such as
$\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\
[-.7ex] $\kern-1.79993ptB$}{}^{0}\rightarrow J/\psi\rho^{0}(770)$.222In the
following $\rho^{0}$ or $\rho$ refers to the $\rho^{0}(770)$ meson.

Figure 1: (a) Tree level and (b) penguin diagram for ${{\kern
1.61993pt\overline{\kern-1.61993ptB}{}}{}^{0}}$ decays into
$J/\psi\pi^{+}\pi^{-}$.

Next, we discuss the time-dependent decay rate, taking into account that the
$\pi^{+}\pi^{-}$ system is composed of the resonances previously reported in
Ref. [7]. This analysis largely follows the measurement procedure used in the
study of $C\\!P$ violation in $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}_{\\!\\!s}$ decays into $J/\psi\pi^{+}\pi^{-}$ [8].
The total decay amplitude for $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}$ at a decay time of zero is taken to be the sum over
individual $\pi^{+}\pi^{-}$ resonant transversity amplitudes [9], and possibly
one non-resonant amplitude, with each component labelled as ${A}_{i}$
($\overline{A}_{i}$). The quantities $q$ and $p$ relate the mass eigenstates
to the flavour eigenstates [10]. By introducing the parameter
$\lambda_{i}\equiv\frac{q}{p}\frac{\overline{A}_{i}}{A_{i}}$, relating $C\\!P$
violation in the interference between mixing and decay associated with the
state $i$, the amplitudes ${\cal A}$ and $\overline{{\cal A}}$ can be
expressed as the sums of the individual $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}$ amplitudes, ${\cal A}=\sum A_{i}$ and
$\overline{{\cal
A}}=\sum\frac{q}{p}\overline{A}_{i}=\sum\lambda_{i}A_{i}=\sum\eta_{i}|\lambda_{i}|e^{-i2\beta_{i}^{\rm
eff}}A_{i}$. For each transversity state $i$ the $C\\!P$-violating phase
$2\beta_{i}^{\rm eff}\equiv-\arg(\eta_{i}\lambda_{i})$ with $\eta_{i}$ being
the $C\\!P$ eigenvalue of the state.333Note that while ${q}/{p}$ and
${\overline{A}_{i}}/{A_{i}}$ are phase convention dependent, $\lambda_{i}$ is
not. The decay rates are444We assume ${\Delta\Gamma_{{d}}}=0$ and $|p/q|=1$.
The averages of current measurements are $\Delta\Gamma_{d}/\Gamma_{d}=0.001\pm
0.010$ and $|p/q|=1.0005\pm 0.0011$ [11].

$\Gamma(t)={\cal N}e^{-{\Gamma_{{d}}}t}\left\\{\frac{|{\cal
A}|^{2}+|\overline{{\cal A}}|^{2}}{2}+\frac{|{\cal A}|^{2}-|\overline{{\cal
A}}|^{2}}{2}\cos({\Delta m_{{d}}}t)-\mathcal{I}m({\cal A}^{*}\overline{{\cal
A}})\sin({\Delta m_{{d}}}t)\right\\},~{}~{}~{}~{}$ $\overline{\Gamma}(t)={\cal
N}e^{-{\Gamma_{{d}}}t}\left\\{\frac{|{\cal A}|^{2}+|\overline{{\cal
A}}|^{2}}{2}-\frac{|{\cal A}|^{2}-|\overline{{\cal A}}|^{2}}{2}\cos({\Delta
m_{{d}}}t)+\mathcal{I}m({\cal A}^{*}\overline{{\cal A}})\sin({\Delta
m_{{d}}}t)\right\\}.$ (1)

##  2 Penguin and tree amplitudes

The decay ${{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ can be written as the sum of one
tree level amplitude, similar to that shown in Fig. 1(a), but where the
virtual $W^{-}$ transforms to a $\overline{c}s$ pair, and three penguin
amplitudes similar to those shown in Fig. 1(b). Here we neglect higher order
diagrams. The $t$-quark mediated penguin amplitude can be expressed in terms
of the other two using CKM unitarity. The resulting decay amplitude is [4]

$A({{B}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}})=\left(1-\frac{\widetilde{\lambda}^{2}}{2}\right){\mathscr{A}}\left[1+\frac{\widetilde{\lambda}^{2}}{1-\widetilde{\lambda}^{2}}ae^{i\theta}e^{i\gamma}\right],$
(2)

where $\widetilde{\lambda}=|V_{us}|=0.2252$ [12],
$\gamma\equiv\arg\left(-{V_{ud}V_{ub}^{*}}/{V_{cd}V_{cb}^{*}}\right)$,
${\mathscr{A}}$ denotes the sum of tree and penguin strong amplitudes, and $a$
and $\theta$ are the magnitude and phase of the strong parts of the effective
penguin amplitude relative to the tree amplitude.

For the case of $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\pi^{+}\pi^{-}$ decays, the $\pi^{+}\pi^{-}$ pairs are in spin states
ranging from zero to two. Since they are in a final state with a spin-1
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ resonance, the amplitudes in
the different transversity states $f$ need to be distinguished for all spins
above zero. For example, the amplitude for each
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rho^{0}(770)$ transversity
state is

$-\sqrt{2}A({{B}^{0}}\rightarrow({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rho)_{f})=\widetilde{\lambda}{\mathscr{A^{\prime}}}\left[1-a_{f}^{\prime}e^{i\theta_{f}^{\prime}}e^{i\gamma}\right],$
(3)

where the primed quantities are defined in analogy with the unprimed ones in
Eq. (2). For ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ decays
only the sign in front of $i\gamma$ changes. We are only concerned here with
the relative size of the tree and penguin amplitudes. For
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle
S}}$ the penguin is suppressed relative to the tree by an additional factor of
$\epsilon\equiv\widetilde{\lambda}^{2}/({1-\widetilde{\lambda}^{2}})=0.0534$.
Thus, comparing even a relatively poor measurement of $2\beta^{\rm eff}$
measured in ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rho^{0}$ with
$2\beta$ measured in ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ allows us to set stringent limits
on the penguin contribution. Using approximate SU(3) flavour symmetry the size
of the penguin contribution in $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rho^{0}$ can be related to that in $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}_{\\!\\!s}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ decays as pointed out in Refs. [5, *Faller:2008gt, 13].

We now turn to the expressions for $C\\!P$ violation in the presence of both
tree and penguin amplitudes. The complex-valued $C\\!P$ parameter
$\lambda_{f}$ is given by

$\lambda_{f}\equiv\frac{q}{p}\frac{A({{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rho)_{f})}{A({{B}^{0}}\rightarrow({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rho)_{f})}=\eta_{f}\frac{1-a_{f}^{\prime}e^{i\theta_{f}^{\prime}}e^{-i\gamma}}{1-a_{f}^{\prime}e^{i\theta_{f}^{\prime}}e^{i\gamma}}e^{-2i\beta},$
(4)

where $\beta$ is the phase induced by mixing. Thus the measured phase
$\beta^{\rm eff}_{f}$ is related to $\beta$ by

$\eta_{f}\lambda_{f}\equiv|\lambda_{f}|e^{-i2\beta^{\rm
eff}_{\\!f}}=\frac{1-a_{f}^{\prime}e^{i\theta_{f}^{\prime}}e^{-i\gamma}}{1-a_{f}^{\prime}e^{i\theta_{f}^{\prime}}e^{i\gamma}}e^{-i2\beta},$
(5)

separating real and imaginary parts gives

$|\lambda_{f}|=\left|\frac{1-a_{f}^{\prime}e^{i\theta_{f}^{\prime}}e^{-i\gamma}}{1-a_{f}^{\prime}e^{i\theta_{f}^{\prime}}e^{i\gamma}}\right|,{\rm~{}and~{}}\Delta
2\beta_{f}\equiv 2\beta_{f}^{\rm
eff}-2\beta=-\arg\left(\frac{1-a_{f}^{\prime}e^{i\theta_{f}^{\prime}}e^{-i\gamma}}{1-a_{f}^{\prime}e^{i\theta_{f}^{\prime}}e^{i\gamma}}\right).$
(6)

For the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$ mode we replace $a^{\prime}_{f}$
and $\theta^{\prime}_{f}$ in Eq. (6) by $-\epsilon a_{f}$ and $\theta_{f}$,
respectively. In addition, we take $a^{\prime}=a$ and
$\theta^{\prime}=\theta$. The relationship between the penguin influence on
the mixing induced $C\\!P$ violation phase in favoured decays and the
measurements in $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow({{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rho^{0})_{f}$ is then given by

$\delta_{P}=-\arg\left(\frac{(\lambda^{\prime}_{f}e^{2i\gamma}-1)+\epsilon(\lambda^{\prime}_{f}-1)}{(\lambda^{\prime}_{f}e^{2i\gamma}-1)+\epsilon(\lambda^{\prime}_{f}-1)e^{2i\gamma}}\right)~{}{\rm
where~{}}\lambda_{f}^{\prime}\equiv|\lambda_{f}|e^{-i\Delta 2\beta_{f}}.$ (7)

We will show that the penguin shift has a weak dependence on $|\lambda_{f}|$,
resulting in $\delta_{P}\approx-\epsilon\Delta 2\beta_{f}$. Since the
uncertainty on the current measurement of 2$\beta$ is
$(^{+1.6}_{-1.5})^{\circ}$, a measurement of $\Delta 2\beta_{f}$, even with an
uncertainty ten times larger, could limit penguin contributions to be well
below the current statistical uncertainty, which is the main aim of this
analysis.

##  3 Detector software and event selection

The LHCb detector [14] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, designed for the study of particles
containing $b$ or $c$ quarks. The detector includes a high-precision tracking
system consisting of a silicon-strip vertex detector surrounding the $pp$
interaction region [15], a large-area silicon-strip detector located upstream
of a dipole magnet with a bending power of about $4{\rm\,Tm}$, and three
stations of silicon-strip detectors and straw drift tubes [16] placed
downstream of the magnet. The tracking system provides a measurement of
momentum555We use natural units where $\hbar$=c=1., $p$, with a relative
uncertainty that varies from 0.4% at low momentum to 0.6% at 100 GeV. The
minimum distance of a track to a primary vertex (PV), the impact parameter
(IP), is measured with a resolution of $(15+29/\mbox{$p_{\rm T}$}){\,\upmu\rm
m}$, where $p_{\rm T}$ is the component of $p$ transverse to the beam, in GeV.
Different types of charged hadrons are distinguished using information from
two ring-imaging Cherenkov detectors [17]. Photon, electron and hadron
candidates are identified by a calorimeter system consisting of scintillating-
pad and preshower detectors, an electromagnetic calorimeter and a hadronic
calorimeter. Muons are identified by a system composed of alternating layers
of iron and multiwire proportional chambers [18].

The trigger [19] consists of a hardware stage, based on information from the
calorimeter and muon systems, followed by a software stage that applies a full
event reconstruction [19]. Events selected for this analysis are triggered by
a $J/\psi\rightarrow\mu^{+}\mu^{-}$ decay, where the $J/\psi$ meson is
required at the software level to be consistent with coming from the decay of
a $\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\
[-.7ex] $\kern-1.79993ptB$}{}^{0}$ meson by use of either of IP requirements
or detachment of the $J/\psi$ meson decay vertex from the primary vertex. In
the simulation, $pp$ collisions are generated using Pythia [20,
*Sjostrand:2007gs] with a specific LHCb configuration [22]. Decays of hadronic
particles are described by EvtGen [23], in which final state radiation is
generated using Photos [24]. The interaction of the generated particles with
the detector and its response are implemented using the Geant4 toolkit [25,
*Agostinelli:2002hh] as described in Ref. [27].

A $\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\
[-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\pi^{+}\pi^{-}$ candidate is reconstructed by combining a
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rightarrow\mu^{+}\mu^{-}$
candidate with two pions of opposite charge. The like-sign combinations
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\pi^{\pm}\pi^{\pm}$ are also
reconstructed for background studies. The event selection is described in
detail in the time-integrated amplitude analysis [7]. The only difference here
is that we reject ${{K}^{0}_{\rm\scriptscriptstyle
S}}\rightarrow\pi^{+}\pi^{-}$ candidates by excluding the events in the region
within $\pm$20 MeV of the ${{K}^{0}_{\rm\scriptscriptstyle S}}$ mass peak.

Only candidates with dimuon invariant mass between
$-$48$\mathrm{\,Me\kern-1.00006ptV}$ and +43$\mathrm{\,Me\kern-1.00006ptV}$
relative to the observed ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ mass
peak are selected, corresponding a window of about $\pm 3\sigma$. The two
muons subsequently are kinematically constrained to the known
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ mass. Other requirements are
imposed to isolate ${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}$
candidates with high signal yield and minimum background. This is accomplished
by combining the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow\mu^{+}\mu^{-}$ candidate with a pair of pion candidates of
opposite charge, and then testing if all four tracks form a common decay
vertex. Pion candidates are each required to have $p_{\rm T}$ greater than
250$\mathrm{\,Me\kern-1.00006ptV}$, and the scalar sum of the two transverse
momenta, $\mbox{$p_{\rm T}$}(\pi^{+})+\mbox{$p_{\rm T}$}(\pi^{-})$, must be
larger than 900$\mathrm{\,Me\kern-1.00006ptV}$. To test for inconsistency with
production at the PV, the IP $\chi^{2}$ is computed as the difference between
the $\chi^{2}$ of the PV reconstructed with and without the considered track.
Each pion must have an IP $\chi^{2}$ greater than 9. Pion and kaon candidates
are positively identified using the RICH system. The four-track ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$ candidate must have a flight
distance of more than 1.5 mm, where the average decay length resolution is
0.17 mm. The angle between the combined momentum vector of the decay products
and the vector formed from the positions of the PV and the decay vertex
(pointing angle) is required to be less than $2.5^{\circ}$. Events satisfying
this preselection are then further filtered using a multivariate analyzer
based on a Boosted Decision Tree (BDT) technique [28]. The BDT uses eight
variables that are chosen to provide separation between signal and background.
These are the minimum of DLL($\mu-\pi$) of the $\mu^{+}$ and $\mu^{-}$,
$\mbox{$p_{\rm T}$}(\pi^{+})+\mbox{$p_{\rm T}$}(\pi^{-})$, the minimum of IP
$\chi^{2}$ of the $\pi^{+}$ and $\pi^{-}$, and the ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}$ properties of vertex
$\chi^{2}$, pointing angle, flight distance, $p_{\rm T}$ and IP $\chi^{2}$,
where DLL($\mu-\pi$) is a logarithm of the likelihood ratio between ${\mu}$
and ${\pi}$ hypotheses for the muon candidates.

The BDT is trained on a simulated sample of two million ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\pi^{+}\pi^{-}$ signal events generated uniformly in phase space with
unpolarized $J/\psi\rightarrow\mu^{+}\mu^{-}$ decays, and a background data
sample from the sideband $5566<m(J/\psi\pi^{+}\pi^{-})<5616$
$\mathrm{\,Me\kern-1.00006ptV}$. Then separate samples are used to train and
test the BDT.

Figure 2: Invariant mass of $J/\psi\pi^{+}\pi^{-}$ combinations with
${{K}^{0}_{\rm\scriptscriptstyle S}}$ veto. The data have been fitted with
double-Crystal ball signal and several background functions. The (purple)
solid line shows the ${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}$
signal, the (brown) dotted line shows the combinatorial background, the
(green) short-dashed shows the $B^{-}$ background, the (red) dot-dashed is
${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow
J/\psi\pi^{+}\pi^{-}$, the (light blue) long-dashed is the sum of ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow
J/\psi\eta^{\prime}$, ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow J/\psi\phi$ when
$\phi\rightarrow\pi^{+}\pi^{-}\pi^{0}$ backgrounds and the ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{-}p$ reflection, the (black) dot-long dashed is the ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow J/\psi K^{-}\pi^{+}$
reflection and the (blue) solid line is the total.

The invariant mass of the selected ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\pi^{+}\pi^{-}$ combinations, where the dimuon pair is constrained to
have the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ mass, is shown in
Fig. 2. There is a large peak at the ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}$ mass and a smaller one at
the ${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}$ mass on top of
the background. A double Crystal Ball function with common means models the
radiative tails and is used to fit each of the signals [29]. Other components
in the fit model take into account background contributions from
$B^{-}\rightarrow J/\psi K^{-}$ and $B^{-}\rightarrow J/\psi\pi^{-}$ decays
combined with a random $\pi^{+}$, ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow
J/\psi\eta(^{\prime})$ with $\eta(^{\prime})\rightarrow\pi^{+}\pi^{-}\gamma$,
${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow
J/\psi\phi$ with $\phi\rightarrow\pi^{+}\pi^{-}\pi^{0}$, ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow J/\psi K^{-}\pi^{+}$
and ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{-}}{p}$ reflections, and combinatorial backgrounds. The
exponential combinatorial background shape is taken from like-sign
combinations, that are the sum of $\pi^{+}\pi^{+}$ and $\pi^{-}\pi^{-}$
candidates. The shapes of the other components are taken from the simulation
with their normalizations allowed to vary. Only the candidates within $\pm 20$
MeV of the ${{B}^{0}}$ mass peak are retained for CP violation measurements;
the fit gives $17\,650\pm 200$ signal and $9\,840\pm 160$ background
candidates.

##  4 The signal likelihood

We fit the entire $\pi^{+}\pi^{-}$ mass spectrum, by including the resonance
contributions found in the amplitude analysis [7], in order to measure the
$C\\!P$-violating parameters of all the states, the most important being
$\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\
[-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rho^{0}$ as it has the largest fit fraction of approximately 65%. The
same likelihood construction as was used to determine the $C\\!P$-violating
quantities $\phi_{s}$ and $|\lambda|$ in $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}_{\\!\\!s}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\pi^{+}\pi^{-}$ decays [8] is employed. Here the value of
$\Delta\Gamma_{d}\approx 0$ simplifies some terms, and the smaller value of
$\Delta m_{d}$ makes the decay time resolution function less important. In
addition, a different same-sign flavour tagging algorithm is used.

The determination of the $C\\!P$ violation parameters relies upon the
formalism developed in Ref. [30]. For ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}$ decays to $\mu^{+}\mu^{-}$ final states the amplitudes are themselves
functions of four variables: the $\pi^{+}\pi^{-}$ invariant mass
$m_{hh}=m(\pi^{+}\pi^{-})$, and three angles $\Omega$, defined in the helicity
basis. These consist of: $\theta_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}}$, the angle between the $\mu^{+}$ direction in the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ rest frame with respect to
the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ direction in the $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}$ rest frame; $\theta_{hh}$, the angle between the
$h^{+}$ direction in the $h^{+}h^{-}$ rest frame with respect to the
$h^{+}h^{-}$ direction in the $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}$ rest frame; and $\chi$, the angle between the
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ and $h^{+}h^{-}$ decay planes
in the $\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})}
\\\ [-.7ex] $\kern-1.79993ptB$}{}^{0}$ rest frame [30, 31].

We perform a simultaneous unbinned maximum likelihood fit to the decay time
$t$, $m_{hh}$, and the three helicity angles $\Omega$, along with information
on the initial flavour of the decaying hadron, $i.e.$ whether it was produced
as a ${B}^{0}$ or a ${\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$
meson. The probability density function (PDF) used in the fit consists of
signal and background components that include detector resolution and
acceptance effects. The predicted decay time error for each event is used for
the decay time resolution model, and similarly the measured per-event
misidentification probability is used for determining the initial flavour of
the neutral $B$ meson. The $\pi^{+}\pi^{-}$ invariant mass distribution is
shown in Fig. 3 along with the fitted components of the different resonances
using the “Best model” [7] for the $\pi^{+}\pi^{-}$ resonance content.

Figure 3: Fit projection of $m(\pi^{+}\pi^{-})$ showing the different resonant
contributions in the “Best model” [7]. The ${K}^{0}_{\rm\scriptscriptstyle S}$
veto causes the absence of events near 500 MeV. The shape variation near 780
MeV is due to interference between the $\rho(770)$ and $\omega(782)$ states.
The total fit is the sum of the individual components plus their
interferences.

Knowledge of the $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}$ flavour at production, called “tagging”, is
necessary to measure $C\\!P$ violation. We use both opposite-side (OS) [32]
and same-side pion (SS$\pi$) tagging information; here we use the same
procedure as for same-side kaon tagging used in the $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}_{\\!\\!s}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\pi^{+}\pi^{-}$ and ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ analyses [31], but identify the tag from a pion rather than a
kaon. The wrong-tag probability $\eta$ is estimated based on the output of a
neural network trained on simulated data. It is calibrated with data using
flavour-specific decay modes in order to predict the true wrong-tag
probability of the event
$\accentset{\scalebox{0.4}{(}\raisebox{-1.7pt}{--}\scalebox{0.4}{)}}{\omega}(\eta)$
for an initial flavour $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}$ meson, which has a linear dependence on $\eta$. The
calibration is performed separately for the OS and the SS$\pi$ taggers. If
events are tagged by both OS and SS$\pi$ algorithms, a combined tag decision
and wrong-tag probability are given by the algorithm defined in Ref. [32].
This combined algorithm is implemented in the overall fit. The effective
tagging power obtained is characterized by $\varepsilon_{\rm
tag}D^{2}=(3.26\pm 0.17)\%$, where $D\equiv(1-2\omega_{\rm avg})$ is the
dilution, $\omega_{\rm avg}$ is the average wrong-tag probability for $\omega$
and $\bar{\omega}$, and $\varepsilon_{\rm tag}=(42.1\pm 0.6)\%$ is the signal
tagging efficiency.

The signal decay time distribution including flavour tagging is

$\displaystyle R(\hat{t},m_{hh},\Omega,\mathfrak{q}|\eta)=$
$\displaystyle\frac{1}{1+|\mathfrak{q}|}\bigg{[}\left[1+\mathfrak{q}\left(1-2\omega(\eta)\right)\right]\Gamma(\hat{t},m_{hh},\Omega)\bigg{.}$
$\displaystyle\bigg{.}+\left[1-\mathfrak{q}\left(1-2\bar{\omega}(\eta)\right)\right]\frac{1+A_{\rm
P}}{1-A_{\rm P}}\bar{\Gamma}(\hat{t},m_{hh},\Omega)\bigg{]},$ (8)

where $\hat{t}$ is the true decay time,
$\accentset{\scalebox{0.4}{(}\raisebox{-1.7pt}{--}\scalebox{0.4}{)}}{\Gamma}$
is defined in Eq. (1), and $A_{\rm P}=-0.0035\pm 0.0081$ [33, *Aaij:2014nxa]
is the ${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}-{{B}^{0}}$
production asymmetry in the LHCb acceptance. The flavour tag parameter
$\mathfrak{q}$ takes values of $-1$ or +1 if the signal meson is tagged as
${{\kern 1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}$, ${{B}^{0}}$
respectively, or 0 if untagged.

The signal function is convolved with the decay time resolution and multiplied
by the acceptance:

$F^{\rm
sig}(t,m_{hh},\Omega,\mathfrak{q}|\eta,\delta_{t})=\left[R(\hat{t},m_{hh},\Omega,\mathfrak{q}|\eta)\otimes
T(t-\hat{t};\delta_{t})\right]\cdot{\cal
E}_{t}(t)\cdot\varepsilon(m_{hh},\Omega),$ (9)

where $\varepsilon(m_{hh},\Omega)$ is the efficiency as a function of the
$h^{+}h^{-}$ mass and angles, obtained from the simulation as described in
Ref. [7], $T(t-\hat{t};\delta_{t})$ is the decay time resolution function
which depends upon the estimated decay time error for each event $\delta_{t}$,
and ${\cal E}_{t}(t)$ is the decay time acceptance function. The decay time
resolution function $T(t-\hat{t};\delta_{t})$ is described by a sum of three
Gaussian functions with a common mean. Studies using simulated data show that
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\pi^{+}\pi^{-}$ combinations
produced directly in the $pp$ interaction (prompt) have nearly identical
resolution to signal events. Specifically, the time resolution is determined
using prompt $J/\psi$ decays into a dimuon pair, using a dedicated trigger for
calibration purposes, plus two oppositely charged tracks from the primary
vertex with the similar selection criteria as for $J/\psi\pi^{+}\pi^{-}$ and
an invariant mass within $\pm$20 MeV of the ${{B}^{0}}$ mass. The effective
resolution is found to be about 40 fs by using the weighted average widths of
the three Gaussians. This is negligibly small compared to the ${\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}$-${B}^{0}$ oscillation time.

The decay time distribution is influenced by acceptance effects that are
introduced by track reconstruction, trigger and event selection. The decay
time acceptance is obtained using control samples of $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow J/\psi\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptK$}{}^{*0}(\rightarrow K^{\mp}\pi^{\pm})$ decays, corrected by
the acceptance ratio between ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{\mp}\pi^{\pm}$ and ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{\pi}^{+}}{{\pi}^{-}}$ derived from simulation.

The acceptance function for the control sample is defined as

$A(t;a,n,t_{0},\beta_{1},\beta_{2})=\frac{\left[a(t-t_{0})\right]^{n}}{1+\left[a(t-t_{0})\right]^{n}}\times(1+\beta_{1}t+\beta_{2}t^{2}),$
(10)

where $a$, $n$, $t_{0}$, $\beta_{1}$, $\beta_{2}$ are parameters determined by
the fit. The decay time distribution of $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow J/\psi K^{\mp}\pi^{\pm}$ candidates is
described by the function

$\displaystyle P^{0}(t)=$ $\displaystyle\left(f_{\rm
0}A(t;a,n,t_{0},\beta_{1},\beta_{2})\frac{e^{-\hat{t}/\tau_{{{B}^{0}}}}}{\tau_{{{B}^{0}}}{\cal
N}_{{{B}^{0}}}}+(1-f_{\rm 0})A(t;a_{\rm bkg}^{0},n_{\rm
bkg}^{0},0,0,0)\frac{e^{-\hat{t}/\tau^{0}_{\rm bkg}}}{\tau^{0}_{\rm bkg}{\cal
N}^{0}_{\rm bkg}}\right)$ $\displaystyle\otimes T(t-\hat{t};\delta_{t}),$ (11)

where $f_{0}$ is the signal fraction, and ${\cal N}_{{{B}^{0}}}$ and ${\cal
N}^{0}_{\rm bkg}$ are normalizations necessary to construct PDFs of signal and
background, respectively. The background acceptance function in Eq. (11) uses
the same form as the signal and its parameters $a_{\rm bkg}^{0}$, $n_{\rm
bkg}^{0}$ and $\tau^{0}_{\rm bkg}$ are obtained from mass sideband regions of
5180$-$5205$\mathrm{\,Me\kern-1.00006ptV}$ and
5400$-$5425$\mathrm{\,Me\kern-1.00006ptV}$. The lifetime is constrained to
$\tau_{{{B}^{0}}}=1.519\pm 0.007$ ps [12].

We use the product of the acceptance $A(a,n,t_{0},\beta_{1},\beta_{2})$
determined from $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow J/\psi\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptK$}{}^{*0}$ and the correction ratio found from simulation as
the time acceptance function for $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\pi^{+}\pi^{-}$ events,

${\cal
E}_{t}(t;a,n,t_{0},\beta_{1},\beta_{2},p_{1},p_{2})=\frac{\left[a(t-t_{0})\right]^{n}}{1+\left[a(t-t_{0})\right]^{n}}\times(1+\beta_{1}t+\beta_{2}t^{2})\times(1-p_{2}e^{-p_{1}t}),$
(12)

with parameter values and correlations given in Table 1.

Table 1: Parameter values and correlations for the acceptance function $\varepsilon_{t}(t)$ in Eq. (12). P | $n$ | $a$ | $\beta_{1}$ | $\beta_{2}$ | $t_{0}$ | $p_{1}$ | $p_{2}$ |  Values
---|---|---|---|---|---|---|---|---
$n$ |  1.000 |  0.444 |  0.574 |  $-$0.536 |  $-$0.862 |  0.000 |  0.000 | $2.082\pm 0.036$
$a$ |  |  1.000 |  0.739 |  $-$0.735 |  $-$0.050 |  0.000 |  0.000 |  $1.981\pm 0.024$ ps-1
$\beta_{1}$ |  |  |  1.000 |  $-$0.899 |  $-$0.374 |  0.000 |  0.000 |  $0.077\pm 0.009$ ps-1
$\beta_{2}$ |  |  |  |  1.000 |  0.343 |  0.000 |  0.000 |  $\\!-0.008\pm 0.001$ ps-2
$t_{0}$ |  |  |  |  |  1.000 |  0.000 |  0.000 |  $0.104\pm 0.003$ ps
$p_{1}$ |  |  |  |  |  |  1.000 |  $-$0.885 |  $6.237\pm 1.669$ ps-1
$p_{2}$ |  |  |  |  |  |  |  1.000 | $\\!-0.739\pm 0.424$

##  5 Measurements of 2$\beta^{\rm eff}$

The $C\\!P$-violating parameters are determined from a fit that uses the
amplitude model with six final state $\pi^{+}\pi^{-}$ resonances. In our
previous amplitude analysis [7] we used two parameterizations of the
$f_{0}(500)$ resonance, “default” and “alternate”. The default used a Breit-
Wigner resonance shape, with relatively poorly measured parameters, while the
alternate used a function suggested by Bugg [35], with more theoretically
motivated shape parameters. In this analysis we choose to switch to the shape
suggested by Bugg, while the Breit-Wigner shape of the previous default
parameterization is used to assess systematic uncertainties. A Gaussian
constraint using $\Delta m_{d}=0.510\pm 0.003$ ps-1 [12] is applied in the
fit. All other parameters, such as the time resolution, and those describing
the tagging are fixed. In addition to the $C\\!P$-violating parameters, the
other free parameters are the amplitudes and phases of the resonances. To
minimize correlations in the fitted results, we choose as free parameters the
$C\\!P$ asymmetry $\alpha^{i}_{CP}=\frac{1-|\lambda_{i}|}{1+|\lambda_{i}|}$,
$2\beta_{i}^{\rm eff}$ of the largest polarization component, and $\Delta
2\beta^{\rm eff}_{i}$ of the other components with respect to the largest one.

As ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rho$ is the final state
with the largest contribution, we treat it specially and perform two fits. In
both cases all resonances other than the $\rho$ share a common $C\\!P$
violation parameter $\lambda^{\prime}$. For Fit 1 the three $\rho$
transversity states share the same $C\\!P$ violation parameter $\lambda$,
while for Fit 2 each $\rho$ transversity state has its own $C\\!P$ violation
parameter $\lambda_{i}$. The results are shown in Table 2. The statistical
uncertainties are within $\pm 15\%$ of the precision estimated using toy Monte
Carlo simulation. To determine $\Delta 2\beta_{f}$ we use the measured value
in $b\rightarrow c\overline{c}s$ transitions of $(42.8^{+1.6}_{-1.5})^{\circ}$
found in $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}$ decays [11]. Our measurement of $2\beta^{\rm eff}$
is consistent with this value for both Fit 1 and Fit 2. The correlation
between $\alpha_{{C\\!P}}^{\rho}$ and $2\beta_{\rho}^{\rm eff}$ is $-0.01$ in
Fit 1. Table 3 shows the correlation matrix for the $C\\!P$-violating
parameters in Fit 2.

Table 2: Fit results for $2\beta_{i}^{\rm eff}$ and $\alpha_{{C\\!P}}^{i}$. Condition |  $2\beta_{i}^{\rm eff}$ (∘) | $\alpha_{{C\\!P}}^{i}(\times 10^{-3})$
---|---|---
Fit 1 | $\rho$ | $~{}~{}41.7\pm 9.6_{-6.3}^{+2.8}$ | $\rho$ | $-32\pm 28_{-~{}7}^{+~{}9}$
other$-\rho$ | $~{}~{}~{}~{}3.6\pm 3.6_{-0.8}^{+0.9}$ | other | $~{}\\!-1\pm 25_{-14}^{+~{}7}$
| $\rho_{0}$ | $~{}~{}44.1\pm 10.2_{-6.9}^{+3.0}$ | $\rho_{0}$ | $\,-47\pm 34_{-10}^{+11}$
Fit 2 | $\rho_{\|}-\rho_{0}$ | $-0.8\pm 6.5_{-1.3}^{+1.9}$ | $\rho_{\|}$ | $~{}-61\pm 60_{-~{}6}^{+~{}8}~{}~{}$
$\rho_{\perp}-\rho_{0}$ | $-3.6\pm 7.2_{-1.4}^{+2.0}$ | $\rho_{\perp}$ | $~{}~{}~{}~{}17\pm 109_{-15}^{+22}$
| other$-\rho_{0}$ | $~{}~{}2.7\pm 3.9_{-0.9}^{+1.0}$ | other | $~{}~{}~{}~{}6\pm 27_{-14}^{+~{}9}$
Table 3: The correlation matrix for the $C\\!P$-violating parameters determined using Fit 2, where $\Delta 2\beta^{\rm eff}_{i}=2\beta^{\rm eff}_{i}-2\beta^{\rm eff}_{\rho_{0}}$.  | $\alpha_{{C\\!P}}^{\rm other}$ | $\alpha_{{C\\!P}}^{\rho_{0}}$ | $\alpha_{{C\\!P}}^{\rho_{\perp}}$ | $\alpha_{{C\\!P}}^{\rho_{\|}}$ | $\Delta 2\beta^{\rm eff}_{\rm other}$ | $\Delta 2\beta^{\rm eff}_{\rho_{\perp}}$ | $\Delta 2\beta^{\rm eff}_{\rho_{\|}}$ | $2\beta^{\rm eff}_{\rho_{0}}$
---|---|---|---|---|---|---|---|---
$\alpha_{{C\\!P}}^{\rm other}$ | $~{}~{}1.00$ | $-0.62$ | $-0.28$ | $-0.13$ | $~{}~{}0.05$ | $-0.42$ | $-0.19$ | $~{}~{}0.05$
$\alpha_{{C\\!P}}^{\rho_{0}}$ |  | $~{}~{}1.00$ | $~{}~{}0.03$ | $~{}~{}0.16$ | $~{}~{}0.29$ | $~{}~{}0.22$ | $~{}~{}0.16$ | $-0.11$
$\alpha_{{C\\!P}}^{\rho_{\perp}}$ |  |  | $~{}~{}1.00$ | $-0.21$ | $-0.19$ | $~{}~{}0.59$ | $-0.07$ | $~{}~{}0.10$
$\alpha_{{C\\!P}}^{\rho_{\|}}$ |  |  |  | $~{}~{}1.00$ | $~{}~{}0.01$ | $-0.04$ | $-0.25$ | $-0.09$
$\Delta 2\beta^{\rm eff}_{\rm other}$ |  |  |  |  | $~{}~{}1.00$ | $~{}~{}0.00$ | $~{}~{}0.26$ | $-0.16$
$\Delta 2\beta^{\rm eff}_{\rho_{\perp}}$ |  |  |  |  |  | $~{}~{}1.00$ | $~{}~{}0.39$ | $-0.08$
$\Delta 2\beta^{\rm eff}_{\rho_{\|}}$ |  |  |  |  |  |  | $~{}~{}1.00$ | $-0.10$
$2\beta^{\rm eff}_{\rho_{0}}$ |  |  |  |  |  |  |  | $~{}~{}1.00$

Table 4 lists the fit fractions and three transversity fractions of
contributing resonances from Fit 1, consistent with the results shown in the
amplitude analysis [7]. For a $P$\- or $D$-wave resonance, we report its total
fit fraction by summing all three transversity components.

Table 4: Fit and transversity fractions of contributing resonances from Fit 1. Uncertainties are statistical only. These results are presented only as a cross-check. |  | Transversity fractions (%)
---|---|---
Component | Fit fraction (%) | $0$ | $\|$ | $\perp$
$\rho(770)$ | $65.6\pm 1.9$ | $56.7\pm 1.8$ | $23.5\pm 1.5$ | $19.8\pm 1.7$
$f_{0}(500)$ | $20.1\pm 0.7$ | 1 | 0 | 0
$f_{2}(1270)$ | $7.8\pm 0.6$ | $64\pm 4$ | $9\pm 5$ | $27\pm 5$
$\omega(782)$ | $0.64_{-0.13}^{+0.19}$ | $44\pm 14$ | $53\pm 14$ | $3_{-3}^{+10}$
$\rho(1450)$ | $9.0\pm 1.8$ | $47\pm 11$ | $39\pm 12$ | $14\pm 8$
$\rho(1700)$ | $3.1\pm 0.7$ | $29\pm 12$ | $42\pm 15$ | $29\pm 15$

This time-dependent analysis determines the phase difference between the
$C\\!P$-odd component of $\rho(770)_{\perp}$ and the $C\\!P$-even component of
$\rho(770)_{0}$ to be $(167\pm 11)^{\circ}$ in Fit 1. This quantity is not
accessible in the time-integrated amplitude analysis. Figure 4 shows the decay
time distribution superimposed with the fit projection.

Figure 4: Decay time distribution of $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\pi^{+}\pi^{-}$ candidates. The signal component is shown with a (red)
dashed line, the background with a (black) dotted line, and the (blue) solid
line represents the total. The lower plot shows the normalized residual
distribution.

The statistical significance of the $C\\!P$ measurements are ascertained by
fitting the data requiring that $C\\!P$-violating components are zero. We find
that for the entire final state, this requirement changes $-2$ times the
logarithm of the likelihood ($-2\ln{\cal{L}}$) by 28.6, corresponding to 4.4
standard deviations for four degrees of freedom (ndf), and for the $\rho(770)$
component only, the change is 24.0, corresponding to 4.5 standard deviations
for two ndf. Here we only consider the statistical uncertainties.

Table 5: Results allowing for different $C\\!P$-violating effects for resonances other than the $\rho$ in an extension of Fit 1. $2\beta_{i}^{\rm eff}$ (∘) |  $\alpha_{{C\\!P}}^{i}$ ($\times 10^{-3}$)
---|---
$\rho$ | $41.8\pm 9.6$ | $\rho$ | $~{}~{}~{}~{}2\pm 39$
$f_{0}(500)-\rho$ | $~{}~{}2.7\pm 3.8$ | $f_{0}(500)$ | $-58\pm 46$
$f_{2}(1270)-\rho$ | $~{}~{}1.8\pm 7.5$ | $f_{2}(1270)$ | $~{}~{}~{}~{}\,9\pm 63$
other spin-1 $-\rho$ | $~{}~{}~{}3.7\pm 11.1$ | other spin-1 | $~{}\,\,\,\,15\pm 58$

We also perform a fit by extending Fit 1 to allow different $C\\!P$-violating
effects in final states with either the $f_{0}(500)$, the $f_{2}(1270)$, or
spin-1 resonances. The results are shown in Table 5. We find that these fits
all give consistent values of the $C\\!P$-violating parameters.

The systematic uncertainties evaluated for both fit configurations are
summarized for the $C\\!P$-violating phases in Table 6 and for the magnitudes
of the asymmetries in Table 7. They are small compared to the statistical
ones. The two largest contributions result from the resonance fit model and
the resonance parameters. Fit model uncertainties are determined by adding an
additional resonance to the default six-resonance model, either the
$f_{0}(980)$, the $f_{0}(1500)$, the $f_{0}(1700)$, or non-resonant
$\pi^{+}\pi^{-}$, replacing the $f_{0}(500)$ model by a Breit-Wigner function,
and using the alternative Gounaris-Sakurai model shapes [36] for the various
$\rho$ mesons. The largest variation among those changes is assigned as the
systematic uncertainty for modelling. Including a non-resonant component gives
the largest negative change on $2\beta^{\rm eff}$ for the $\rho$ and
$\rho_{0}$ categories.

Table 6: Systematic uncertainties on $C\\!P$-violating phases $2\beta_{i}^{\rm eff}$ (∘). Statistical uncertainties are also shown. Fit | Fit 1 | Fit 2
---|---|---
Sources | $\rho$ | other$-\rho$ | $\rho_{0}$ | $\rho_{\|}-\rho_{0}$ | $\rho_{\perp}-\rho_{0}$ | other$-\rho_{0}$
Resonance model | ${}_{-5.94}^{+1.85}$ | ${}_{-0.33}^{+0.51}$ | ${}_{-6.56}^{+1.99}$ | ${}_{-0.05}^{+1.35}$ | ${}_{-0.59}^{+1.50}$ | ${}_{-0.52}^{+0.68}$
Resonance parameters | $\pm 1.21$ | $\pm 0.43$ | $\pm 1.35$ | $\pm 0.68$ | $\pm 0.57$ | $\pm 0.60$
Mass $\&$ angular acceptance | $\pm 0.27$ | $\pm 0.05$ | $\pm 0.28$ | $\pm 0.21$ | $\pm 0.16$ | $\pm 0.05$
Angular acc. correlation | $\pm 0.22$ | $\pm 0.03$ | $\pm 0.22$ | $\pm 0.21$ | $\pm 0.08$ | $\pm 0.03$
Decay time acceptance | $\pm 0.05$ | $\pm 0.02$ | $\pm 0.06$ | $\pm 0.04$ | $\pm 0.04$ | $\pm 0.03$
Bkg. mass $\&$ angular PDF | $\pm 0.43$ | $\pm 0.09$ | $\pm 0.47$ | $\pm 0.22$ | $\pm 0.26$ | $\pm 0.11$
Bkg. decay time PDF | $\pm 0.14$ | $\pm 0.05$ | $\pm 0.12$ | $\pm 0.06$ | $\pm 0.08$ | $\pm 0.07$
Bkg. model | $\pm 0.49$ | $\pm 0.23$ | $\pm 0.15$ | $\pm 0.97$ | $\pm 0.38$ | $\pm 0.13$
Flavour Tagging | $\pm 1.46$ | $\pm 0.03$ | $\pm 1.66$ | $\pm 0.44$ | $\pm 0.86$ | $\pm 0.01$
Production asymmetry | $\pm 0.17$ | $\pm 0.50$ | $\pm 0.28$ | $\pm 0.09$ | $\pm 0.49$ | $\pm 0.42$
Total systematic uncertainty | ${}_{-6.3}^{+2.8}$ | ${}_{-0.8}^{+0.9}$ | ${}_{-6.9}^{+3.0}$ | ${}_{-1.3}^{+1.9}$ | ${}_{-1.4}^{+2.0}$ | ${}_{-0.9}^{+1.0}$
Statistical uncertainty | $\pm 9.6$ | $\pm 3.6$ | $\pm 10.2$ | $\pm 6.5$ | $\pm 7.2$ | $\pm 3.9$
Table 7: Systematic uncertainties for the magnitude of the asymmetries $\alpha_{{C\\!P}}^{i}$ ($\times 10^{-3}$). Statistical uncertainties are also shown. Fit | Fit 1 | Fit 2
---|---|---
Sources | $\rho$ | other$-\rho$ | $\rho_{0}$ | $\rho_{\|}$ | $\rho_{\perp}$ | other$-\rho_{0}$
Resonance model | ${}_{-0.0}^{+6.0}$ | ${}_{-11.4}^{+0.0}$ | ${}_{-0.0}^{+3.7}$ | ${}_{-2.7}^{+5.0}$ | ${}_{-0.0}^{+16.4}$ | ${}_{-11.0}^{+0.4}$
Resonance parameters | $\pm 5.2$ | $\pm 6.1$ | $\pm 7.8$ | $\pm 3.1$ | $\pm 9.2$ | $\pm 7.3$
Mass $\&$ angular acceptance | $\pm 0.6$ | $\pm 0.5$ | $\pm 0.8$ | $\pm 0.8$ | $\pm 1.6$ | $\pm 0.7$
Angular acc. correlation | $\pm 0.2$ | $\pm 0.9$ | $\pm 0.2$ | $\pm 0.9$ | $\pm 0.6$ | $\pm 0.9$
Decay time acceptance | $\pm 0.1$ | $\pm 0.1$ | $\pm 0.2$ | $\pm 0.3$ | $\pm 1.1$ | $\pm 0.1$
Bkg. mass $\&$ angular PDF | $\pm 0.9$ | $\pm 1.5$ | $\pm 0.8$ | $\pm 2.5$ | $\pm 4.6$ | $\pm 1.2$
Bkg. decay time PDF | $\pm 0.5$ | $\pm 0.4$ | $\pm 0.6$ | $\pm 0.5$ | $\pm 1.7$ | $\pm 0.4$
Bkg. model | $\pm 2.6$ | $\pm 2.9$ | $\pm 5.2$ | $\pm 3.5$ | $\pm 0.9$ | $\pm 4.6$
Flavour Tagging | $\pm 2.8$ | $\pm 2.5$ | $\pm 0.5$ | $\pm 1.0$ | $\pm 10.7$ | $\pm 1.6$
Production asymmetry | $\pm 3.0$ | $\pm 0.5$ | $\pm 2.5$ | $\pm 1.1$ | $\pm 0.4$ | $\pm 0.3$
Total systematic uncertainty | ${}_{-7}^{+9}$ | ${}_{-14}^{+~{}7}$ | ${}_{-10}^{+11}$ | ${}_{-6}^{+8}$ | ${}_{-15}^{+22}$ | ${}_{-14}^{+~{}9}$
Statistical uncertainty | $\pm 28$ | $\pm 25$ | $\pm 34$ | $\pm 60$ | $\pm 109$ | $\pm 27$

To evaluate the uncertainties due to the fixed parameters of resonances, we
repeat the amplitude fit by varying the mass and width of all the resonances
used in the six-resonance model within their errors one at a time, and add the
changes in quadrature. To evaluate the systematic uncertainties due to the
other fixed parameters including those in the decay time acceptance, the
background decay time PDF, the $m(\pi^{+}\pi^{-})$ distribution, the angular
acceptance, and background mass PDF, the data fit is repeated by varying the
fixed parameters from their nominal values according to the error matrix, one
hundred times for each source. The matrix elements are determined using
simulation, $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})}
\\\ [-.7ex] $\kern-1.79993ptK$}{}^{*0}$ data, and like-sign
${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\pi^{\pm}\pi^{\pm}$ data. The
r.m.s. of the fitted physics parameter of interest is taken as its uncertainty
for each source.

The acceptance model for each of the three angles as a function of $m_{hh}$ is
determined independently. To evaluate the reliability of this method we
parameterize the mass and angle efficiencies as a combination of Legendre
polynomials and spherical harmonics that takes into account all correlations.
The amplitude fit is repeated using the new acceptance parameterizations;
changes are found to be small and taken as the systematic uncertainty.

In the nominal fit the background is divided into three sources: background to
the $\rho^{0}$ component from $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}_{\\!\\!s}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\eta^{\prime},\eta^{\prime}\rightarrow\rho^{0}\gamma$, reflection from
$\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\
[-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})}
\\\ [-.7ex] $\kern-1.79993ptK$}{}^{*0}$ when the kaon is misidentified as a
pion, and the remaining background. The latter includes the reflections from
$\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\
[-.7ex] $\kern-1.79993pt\mathchar
28931\relax$}{}^{0}_{\\!\\!b}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}K^{\mp}\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993pt{p}$}{}$ decays, where both the kaon and proton are
misidentified, and combinatorial background. The dependence on $m_{hh}$ of the
decay time distribution for this remaining background is modelled by using
different decay time PDFs in different $m_{hh}$ regions. We also change the
background modelling by dividing the remaining background into separate
combinatorial and ${{\mathchar 28931\relax}^{0}_{b}}$ reflection components.
The fit is repeated with the new background model, and changes are taken as
the systematic uncertainty.

The systematic uncertainty due to the tagging parameter calibration is given
by the difference in quadrature of the statistical uncertainties for each
physics parameter between the nominal fit and an alternative fit where the
tagging parameters are Gaussian constrained by their total uncertainties. The
systematic uncertainty due to the asymmetry of ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}-{{B}^{0}}$ meson production is
estimated by varying the central value $A_{\rm P}=-0.0035\pm 0.0081$ [33] by
its uncertainty.

##  6 Discussion of results and conclusions

We compare the $\rho$-only Fit 1 result of
$2\beta^{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rho}=2\beta^{\rm
eff}=(41.7\pm 9.6_{-6.3}^{+2.8})^{\circ}$ with the Cabibbo-favoured $B$ to
charmonium result, denoted ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$. The measured difference is

$\Delta 2\beta_{f}=2\beta^{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rho}-2\beta^{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}}=(-0.9\pm
9.7^{+2.8}_{-6.3})^{\circ}.$ (13)

Since the result is consistent with zero we determine limits on the magnitude
of the $C\\!P$-violating phase shift due to a possible penguin component in
$b\rightarrow c\overline{c}s$ decays, $\delta_{P}$. The limit is evaluated
using pseudo-experiments by generating datasets with different values of
$\alpha_{{C\\!P}}$, $2\beta^{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rho}-2\beta^{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}}$, and
$\gamma=(70.0_{-9.0}^{+7.7})^{\circ}$ [11] according to the measured
uncertainties, including the correlation of $-0.01$ between $\alpha_{{C\\!P}}$
and $2\beta^{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rho}$. Then
$\delta_{P}$ for each dataset is calculated using Eq. (7). We find a Gaussian
distribution with a 95% confidence level (CL) interval of
$[-1.05^{\circ},1.18^{\circ}]$. This result is consistent with that obtained
by projecting a contour of $\alpha_{{C\\!P}}$ and
$2\beta^{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rho}-2\beta^{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}}$ with regions proportional to the
total uncertainties of the two physics variables as shown in Fig. 5.

Figure 5: The magnitude of the penguin induced shift $\delta_{P}$ on the
$C\\!P$-violating phase in favoured decays, assuming SU(3) flavour symmetry,
shown in grey or colour scale in degrees, as a function of the measured
difference $\Delta 2\beta_{f}$ ($x$-axis) and
$\alpha_{{C\\!P}}=\frac{1-|\lambda_{f}|}{1+|\lambda_{f}|}$ ($y$-axis). Here we
use fixed values for $\gamma=70^{\circ}$ and $\epsilon=0.0534$. The projected
68% (solid) and 95% (dashed) confidence levels on $\delta_{P}$ are shown by
the egg-shaped contours.

The two reactions $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rho^{0}$ and $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}_{s}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ are related by SU(3) symmetry if we also assume that the
difference between the $\phi$ being mostly a singlet state, and the $\rho^{0}$
an octet state causes negligible breaking. Taking the magnitudes of the
penguin amplitudes $a=a^{\prime}$ and the strong phases
$\theta=\theta^{\prime}$ to be equal in $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rho^{0}$ and $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}_{\\!\\!s}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ decays, and neglecting higher order diagrams [4], we find
$\delta_{P}=(0.05\pm 0.56)^{\circ}=0.9\pm 9.8$ mrad. At 95% CL, the penguin
contribution in $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}_{\\!\\!s}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\phi$ decay is within the interval from $-1.05^{\circ}$ to
+$1.18^{\circ}$. Relaxing these assumptions changes the limits on the possible
penguin induced shift. Figure 6 shows how $\delta_{P}$ varies as a function of
$\theta-\theta^{\prime}$, indicating that the 95% CL limit on penguin
pollution can increase to at most $\pm 1.2^{\circ}$. The variation in
$\delta_{P}$ is proportional to $a/a^{\prime}$. Thus, when changing
$a/a^{\prime}$ over the interval 0.5 to 1.5, the limit on the penguin shift at
95% CL varies between $\pm 0.9^{\circ}$ to $\pm 1.8^{\circ}$, even allowing
for maximal breaking between $\theta^{\prime}$ and $\theta$.

Figure 6: The limit on the penguin induced phase change $\delta_{P}$ as a
function of the difference in the penguin amplitude strong phases in
$b\rightarrow c\bar{c}s$ and $b\rightarrow c\bar{c}d$ transitions
$\theta-\theta^{\prime}$, for $a=a^{\prime}$.

It may be expected that the effect of penguin contributions in other decays,
such as $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}{{K}^{0}_{\rm\scriptscriptstyle S}}$, should be limited to similar
values, even if there is no strict flavour symmetry relating the mode to
$\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\
[-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rho^{0}$. Our limit is consistent with theoretical predictions [37,
*Li:2006vq, *Jung:2012vd, *Ciuchini:2011kd, *Ciuchini:2005mg].

We also set limits on the strong decay amplitude. Figure 7 shows the 68% and
95% confidence levels contours for the penguin amplitude parameters of
$a^{\prime}$ and $\theta^{\prime}$ with a $-2\ln{\cal{L}}$ change of 2.3 and 6
units, for ndf equals two, including systematic uncertainties. They are
obtained by converting the corresponding contours for
$\alpha_{{C\\!P}}^{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rho}$ and
$\Delta 2\beta_{f}$ using their relationship given in Eq. (5). The uncertainty
on the angle $\gamma=(70.0_{-9.0}^{+7.7})^{\circ}$ only introduces about a
0.2% increase in the mean contour radius of $a^{\prime}$ versus
$\theta^{\prime}$. The one-dimensional 68% confidence level intervals are
found by changing $-2\ln{\cal{L}}$ by one unit, giving $a^{\prime}<0.12$ and
$\theta^{\prime}\in(190^{\circ},355^{\circ})$, or
$a^{\prime}=0.035_{-0.035}^{+0.082}$ and
$\theta^{\prime}=(285_{-95}^{+69})^{\circ}$.

Figure 7: Contours corresponding to 68% (dashed) and 95% (solid) confidence
levels for ndf of two, respectively, for the penguin amplitude parameters
$a^{\prime}$ and $\theta^{\prime}$.

The decay $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\pi^{0}$ proceeds through a similar diagram to that shown in Fig. 1,
and thus the $C\\!P$-violating parameters $S$ and $C$ should be similar to
those we find in $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rho^{0}$. These parameters are related to the parameter $\lambda_{f}$
via the relationships

$S_{f}\equiv\frac{2{\cal
I}m(\lambda_{f})}{1+|\lambda_{f}|^{2}}=-2\eta_{f}\frac{|\lambda_{f}|\sin{2\beta^{\rm
eff}_{f}}}{1+|\lambda_{f}|^{2}},\quad{\rm and}\quad
C_{f}\equiv\frac{1-|\lambda_{f}|^{2}}{1+|\lambda_{f}|^{2}},$ (14)

where we set the $C\\!P$ eigenvalue $\eta_{f}=1$ to compare with the
$C\\!P$-even mode $\kern
1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex]
$\kern-1.79993ptB$}{}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\pi^{0}$.

Using $S_{f}$ and $C_{f}$ as fit parameters, we obtain from Fit 1
$S_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rho}=-0.66_{-0.12-0.03}^{+0.13+0.09}$ and
$C_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rho}=-0.063\pm
0.056^{+0.019}_{-0.014}$, with a correlation of $-0.01$. Table 8 shows the
comparison of $S_{f}$ and $C_{f}$ from this measurement with that obtained
from the Belle [42] and BaBar [43] collaborations. Our measurements are in
good agreement with the Belle results.

Table 8: Comparison of $S_{f}$ and $C_{f}$ between different measurements. $f$ | Experiment | $S_{f}$ | $C_{f}$ | Correlation
---|---|---|---|---
$\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex] $\kern-1.79993ptB$}{}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rho^{0}$ | LHCb | $-0.66_{-0.12-0.03}^{+0.13+0.09}$ | $-0.063\pm 0.056^{+0.019}_{-0.014}$ |  $-0.01$ (stat)
$\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex] $\kern-1.79993ptB$}{}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\pi^{0}$ | Belle [42] | $-0.65\pm 0.21\pm 0.05$ | $-0.08\pm 0.16\pm 0.05$ |  $-0.10$ (stat)
$\kern 1.79993pt\shortstack{{(\rule[2.15277pt]{12.50002pt}{0.51212pt})} \\\ [-.7ex] $\kern-1.79993ptB$}{}^{0}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\pi^{0}$ | BaBar [43] | $-1.23\pm 0.21\pm 0.04$ | $-0.20\pm 0.19\pm 0.03$ |  0.20 (stat)

In conclusion, the measured value of the penguin contribution is
$\delta_{P}=(0.05\pm 0.56)^{\circ}=0.9\pm 9.8$ mrad. Taking the maximum
breaking in phase and a range of breaking $0.5<a/a^{\prime}<1.5$ the
uncertainty on $\delta_{P}$ becomes $\pm 18$ mrad. The measured value of
$\phi_{s}$ currently has an uncertainty of about 35 mrad, and the value of
$2\beta$ of 1.5∘ or 26 mrad [11]. Thus our limit is smaller than the current
uncertainties, but will need to become more precise as the $C\\!P$-phase
measurements improve.

## 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); NSFC
(China); CNRS/IN2P3 (France); BMBF, DFG, HGF and MPG (Germany); SFI (Ireland);
INFN (Italy); FOM and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA
(Romania); MinES and FANO (Russia); MinECo (Spain); SNSF and SER
(Switzerland); NASU (Ukraine); STFC (United Kingdom); NSF (USA). The Tier1
computing centres are supported by IN2P3 (France), KIT and BMBF (Germany),
INFN (Italy), NWO and SURF (The Netherlands), PIC (Spain), GridPP (United
Kingdom). We are indebted to the communities behind the multiple open source
software packages on which we depend. We are also thankful for the computing
resources and the access to software R&D tools provided by Yandex LLC
(Russia). Individual groups or members have received support from EPLANET,
Marie Skłodowska-Curie Actions and ERC (European Union), Conseil général de
Haute-Savoie, Labex ENIGMASS and OCEVU, Région Auvergne (France), RFBR
(Russia), XuntaGal and GENCAT (Spain), Royal Society and Royal Commission for
the Exhibition of 1851 (United Kingdom).

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LHCb collaboration

R. Aaij41, B. Adeva37, M. Adinolfi46, A. Affolder52, Z. Ajaltouni5, S. Akar6,
J. Albrecht9, F. Alessio38, M. Alexander51, S. Ali41, G. Alkhazov30, P.
Alvarez Cartelle37, A.A. Alves Jr25,38, S. Amato2, S. Amerio22, Y. Amhis7, L.
An3, L. Anderlini17,g, J. Anderson40, R. Andreassen57, M. Andreotti16,f, J.E.
Andrews58, R.B. Appleby54, O. Aquines Gutierrez10, F. Archilli38, A.
Artamonov35, M. Artuso59, E. Aslanides6, G. Auriemma25,n, M. Baalouch5, S.
Bachmann11, J.J. Back48, A. Badalov36, C. Baesso60, W. Baldini16, R.J.
Barlow54, C. Barschel38, S. Barsuk7, W. Barter47, V. Batozskaya28, V.
Battista39, A. Bay39, L. Beaucourt4, J. Beddow51, F. Bedeschi23, I. Bediaga1,
S. Belogurov31, K. Belous35, I. Belyaev31, E. Ben-Haim8, G. Bencivenni18, S.
Benson38, J. Benton46, A. Berezhnoy32, R. Bernet40, AB Bertolin22, M.-O.
Bettler47, M. van Beuzekom41, A. Bien11, S. Bifani45, T. Bird54, A.
Bizzeti17,i, P.M. Bjørnstad54, T. Blake48, F. Blanc39, J. Blouw10, S. Blusk59,
V. Bocci25, A. Bondar34, N. Bondar30,38, W. Bonivento15, S. Borghi54, A.
Borgia59, M. Borsato7, T.J.V. Bowcock52, E. Bowen40, C. Bozzi16, D. Brett54,
M. Britsch10, T. Britton59, J. Brodzicka54, N.H. Brook46, A. Bursche40, J.
Buytaert38, S. Cadeddu15, R. Calabrese16,f, M. Calvi20,k, M. Calvo Gomez36,p,
P. Campana18, D. Campora Perez38, A. Carbone14,d, G. Carboni24,l, R.
Cardinale19,38,j, A. Cardini15, L. Carson50, K. Carvalho Akiba2,38, RCM
Casanova Mohr36, G. Casse52, L. Cassina20,k, L. Castillo Garcia38, M.
Cattaneo38, Ch. Cauet9, R. Cenci23,t, M. Charles8, Ph. Charpentier38, M.
Chefdeville4, S. Chen54, S.-F. Cheung55, N. Chiapolini40, M. Chrzaszcz40,26,
X. Cid Vidal38, G. Ciezarek41, P.E.L. Clarke50, M. Clemencic38, H.V. Cliff47,
J. Closier38, V. Coco38, J. Cogan6, E. Cogneras5, V. Cogoni15, L. Cojocariu29,
G. Collazuol22, P. Collins38, A. Comerma-Montells11, A. Contu15,38, A. Cook46,
M. Coombes46, S. Coquereau8, G. Corti38, M. Corvo16,f, I. Counts56, B.
Couturier38, G.A. Cowan50, D.C. Craik48, A.C. Crocombe48, M. Cruz Torres60, S.
Cunliffe53, R. Currie53, C. D’Ambrosio38, J. Dalseno46, P. David8, P.N.Y.
David41, A. Davis57, K. De Bruyn41, S. De Capua54, M. De Cian11, J.M. De
Miranda1, L. De Paula2, W. De Silva57, P. De Simone18, C.-T. Dean51, D.
Decamp4, M. Deckenhoff9, L. Del Buono8, N. Déléage4, D. Derkach55, O.
Deschamps5, F. Dettori38, A. Di Canto38, A Di Domenico25, H. Dijkstra38, S.
Donleavy52, F. Dordei11, M. Dorigo39, A. Dosil Suárez37, D. Dossett48, A.
Dovbnya43, K. Dreimanis52, G. Dujany54, F. Dupertuis39, P. Durante38, R.
Dzhelyadin35, A. Dziurda26, A. Dzyuba30, S. Easo49,38, U. Egede53, V.
Egorychev31, S. Eidelman34, S. Eisenhardt50, U. Eitschberger9, R. Ekelhof9, L.
Eklund51, I. El Rifai5, Ch. Elsasser40, S. Ely59, S. Esen11, H.-M. Evans47, T.
Evans55, A. Falabella14, C. Färber11, C. Farinelli41, N. Farley45, S. Farry52,
R. Fay52, D. Ferguson50, V. Fernandez Albor37, F. Ferreira Rodrigues1, M.
Ferro-Luzzi38, S. Filippov33, M. Fiore16,f, M. Fiorini16,f, M. Firlej27, C.
Fitzpatrick39, T. Fiutowski27, P. Fol53, M. Fontana10, F. Fontanelli19,j, R.
Forty38, O. Francisco2, M. Frank38, C. Frei38, M. Frosini17,g, J. Fu21,38, E.
Furfaro24,l, A. Gallas Torreira37, D. Galli14,d, S. Gallorini22,38, S.
Gambetta19,j, M. Gandelman2, P. Gandini59, Y. Gao3, J. García Pardiñas37, J.
Garofoli59, J. Garra Tico47, L. Garrido36, D. Gascon36, C. Gaspar38, U.
Gastaldi16, R. Gauld55, L. Gavardi9, G. Gazzoni5, A. Geraci21,v, E.
Gersabeck11, M. Gersabeck54, T. Gershon48, Ph. Ghez4, A. Gianelle22, S.
Gianì39, V. Gibson47, L. Giubega29, V.V. Gligorov38, C. Göbel60, D.
Golubkov31, A. Golutvin53,31,38, A. Gomes1,a, C. Gotti20,k, M. Grabalosa
Gándara5, R. Graciani Diaz36, L.A. Granado Cardoso38, E. Graugés36, E.
Graverini40, G. Graziani17, A. Grecu29, E. Greening55, S. Gregson47, P.
Griffith45, L. Grillo11, O. Grünberg63, B. Gui59, E. Gushchin33, Yu. Guz35,38,
T. Gys38, C. Hadjivasiliou59, G. Haefeli39, C. Haen38, S.C. Haines47, S.
Hall53, B. Hamilton58, T. Hampson46, X. Han11, S. Hansmann-Menzemer11, N.
Harnew55, S.T. Harnew46, J. Harrison54, J. He38, T. Head39, V. Heijne41, K.
Hennessy52, P. Henrard5, L. Henry8, J.A. Hernando Morata37, E. van
Herwijnen38, M. Heß63, A. Hicheur2, D. Hill55, M. Hoballah5, C. Hombach54, W.
Hulsbergen41, N. Hussain55, D. Hutchcroft52, D. Hynds51, M. Idzik27, P.
Ilten56, R. Jacobsson38, A. Jaeger11, J. Jalocha55, E. Jans41, P. Jaton39, A.
Jawahery58, F. Jing3, M. John55, D. Johnson38, C.R. Jones47, C. Joram38, B.
Jost38, N. Jurik59, S. Kandybei43, W. Kanso6, M. Karacson38, T.M. Karbach38,
S. Karodia51, M. Kelsey59, I.R. Kenyon45, T. Ketel42, B. Khanji20,38,k, C.
Khurewathanakul39, S. Klaver54, K. Klimaszewski28, O. Kochebina7, M. Kolpin11,
I. Komarov39, R.F. Koopman42, P. Koppenburg41,38, M. Korolev32, L. Kravchuk33,
K. Kreplin11, M. Kreps48, G. Krocker11, P. Krokovny34, F. Kruse9, W.
Kucewicz26,o, M. Kucharczyk20,26,k, V. Kudryavtsev34, K. Kurek28, T.
Kvaratskheliya31, V.N. La Thi39, D. Lacarrere38, G. Lafferty54, A. Lai15, D.
Lambert50, R.W. Lambert42, G. Lanfranchi18, C. Langenbruch48, B. Langhans38,
T. Latham48, C. Lazzeroni45, R. Le Gac6, J. van Leerdam41, J.-P. Lees4, R.
Lefèvre5, A. Leflat32, J. Lefrançois7, O. Leroy6, T. Lesiak26, B.
Leverington11, Y. Li7, T. Likhomanenko64, M. Liles52, R. Lindner38, C. Linn38,
F. Lionetto40, B. Liu15, S. Lohn38, I. Longstaff51, J.H. Lopes2, P. Lowdon40,
D. Lucchesi22,r, H. Luo50, A. Lupato22, E. Luppi16,f, O. Lupton55, F.
Machefert7, I.V. Machikhiliyan31, F. Maciuc29, O. Maev30, S. Malde55, A.
Malinin64, G. Manca15,e, G. Mancinelli6, A. Mapelli38, J. Maratas5, J.F.
Marchand4, U. Marconi14, C. Marin Benito36, P. Marino23,t, R. Märki39, J.
Marks11, G. Martellotti25, M. Martinelli39, D. Martinez Santos42, F. Martinez
Vidal65, D. Martins Tostes2, A. Massafferri1, R. Matev38, Z. Mathe38, C.
Matteuzzi20, A. Mazurov45, M. McCann53, J. McCarthy45, A. McNab54, R.
McNulty12, B. McSkelly52, B. Meadows57, F. Meier9, M. Meissner11, M. Merk41,
D.A. Milanes62, M.-N. Minard4, N. Moggi14, J. Molina Rodriguez60, S. Monteil5,
M. Morandin22, P. Morawski27, A. Mordà6, M.J. Morello23,t, J. Moron27, A.-B.
Morris50, R. Mountain59, F. Muheim50, K. Müller40, M. Mussini14, B. Muster39,
P. Naik46, T. Nakada39, R. Nandakumar49, I. Nasteva2, M. Needham50, N. Neri21,
S. Neubert38, N. Neufeld38, M. Neuner11, A.D. Nguyen39, T.D. Nguyen39, C.
Nguyen-Mau39,q, M. Nicol7, V. Niess5, R. Niet9, N. Nikitin32, T. Nikodem11, A.
Novoselov35, D.P. O’Hanlon48, A. Oblakowska-Mucha27, V. Obraztsov35, S.
Ogilvy51, O. Okhrimenko44, R. Oldeman15,e, C.J.G. Onderwater66, M. Orlandea29,
J.M. Otalora Goicochea2, A. Otto38, P. Owen53, A. Oyanguren65, B.K. Pal59, A.
Palano13,c, F. Palombo21,u, M. Palutan18, J. Panman38, A. Papanestis49,38, M.
Pappagallo51, L.L. Pappalardo16,f, C. Parkes54, C.J. Parkinson9,45, G.
Passaleva17, G.D. Patel52, M. Patel53, C. Patrignani19,j, A. Pearce54, A.
Pellegrino41, G. Penso25,m, M. Pepe Altarelli38, S. Perazzini14,d, P. Perret5,
L. Pescatore45, E. Pesen67, K. Petridis53, A. Petrolini19,j, E. Picatoste
Olloqui36, B. Pietrzyk4, T. Pilař48, D. Pinci25, A. Pistone19, S. Playfer50,
M. Plo Casasus37, F. Polci8, A. Poluektov48,34, I. Polyakov31, E. Polycarpo2,
A. Popov35, D. Popov10, B. Popovici29, C. Potterat2, E. Price46, J.D. Price52,
J. Prisciandaro39, A. Pritchard52, C. Prouve46, V. Pugatch44, A. Puig
Navarro39, G. Punzi23,s, W. Qian4, B. Rachwal26, J.H. Rademacker46, B.
Rakotomiaramanana39, M. Rama23, M.S. Rangel2, I. Raniuk43, N. Rauschmayr38, G.
Raven42, F. Redi53, S. Reichert54, M.M. Reid48, A.C. dos Reis1, S.
Ricciardi49, S. Richards46, M. Rihl38, K. Rinnert52, V. Rives Molina36, P.
Robbe7, A.B. Rodrigues1, E. Rodrigues54, P. Rodriguez Perez54, S. Roiser38, V.
Romanovsky35, A. Romero Vidal37, M. Rotondo22, J. Rouvinet39, T. Ruf38, H.
Ruiz36, P. Ruiz Valls65, J.J. Saborido Silva37, N. Sagidova30, P. Sail51, B.
Saitta15,e, V. Salustino Guimaraes2, C. Sanchez Mayordomo65, B. Sanmartin
Sedes37, R. Santacesaria25, C. Santamarina Rios37, E. Santovetti24,l, A.
Sarti18,m, C. Satriano25,n, A. Satta24, D.M. Saunders46, D. Savrina31,32, M.
Schiller38, H. Schindler38, M. Schlupp9, M. Schmelling10, B. Schmidt38, O.
Schneider39, A. Schopper38, M.-H. Schune7, R. Schwemmer38, B. Sciascia18, A.
Sciubba25,m, A. Semennikov31, I. Sepp53, N. Serra40, J. Serrano6, L.
Sestini22, P. Seyfert11, M. Shapkin35, I. Shapoval16,43,f, Y. Shcheglov30, T.
Shears52, L. Shekhtman34, V. Shevchenko64, A. Shires9, R. Silva Coutinho48, G.
Simi22, M. Sirendi47, N. Skidmore46, I. Skillicorn51, T. Skwarnicki59, N.A.
Smith52, E. Smith55,49, E. Smith53, J. Smith47, M. Smith54, H. Snoek41, M.D.
Sokoloff57, F.J.P. Soler51, F. Soomro39, D. Souza46, B. Souza De Paula2, B.
Spaan9, P. Spradlin51, S. Sridharan38, F. Stagni38, M. Stahl11, S. Stahl11, O.
Steinkamp40, O. Stenyakin35, F Sterpka59, S. Stevenson55, S. Stoica29, S.
Stone59, B. Storaci40, S. Stracka23,t, M. Straticiuc29, U. Straumann40, R.
Stroili22, L. Sun57, W. Sutcliffe53, K. Swientek27, S. Swientek9, V.
Syropoulos42, M. Szczekowski28, P. Szczypka39,38, T. Szumlak27, S. T’Jampens4,
M. Teklishyn7, G. Tellarini16,f, F. Teubert38, C. Thomas55, E. Thomas38, J.
van Tilburg41, V. Tisserand4, M. Tobin39, J. Todd57, S. Tolk42, L.
Tomassetti16,f, D. Tonelli38, S. Topp-Joergensen55, N. Torr55, E. Tournefier4,
S. Tourneur39, M.T. Tran39, M. Tresch40, A. Trisovic38, A. Tsaregorodtsev6, P.
Tsopelas41, N. Tuning41, M. Ubeda Garcia38, A. Ukleja28, A. Ustyuzhanin64, U.
Uwer11, C. Vacca15, V. Vagnoni14, G. Valenti14, A. Vallier7, R. Vazquez
Gomez18, P. Vazquez Regueiro37, C. Vázquez Sierra37, S. Vecchi16, J.J.
Velthuis46, M. Veltri17,h, G. Veneziano39, M. Vesterinen11, JVVB Viana
Barbosa38, B. Viaud7, D. Vieira2, M. Vieites Diaz37, X. Vilasis-Cardona36,p,
A. Vollhardt40, D. Volyanskyy10, D. Voong46, A. Vorobyev30, V. Vorobyev34, C.
Voß63, J.A. de Vries41, R. Waldi63, C. Wallace48, R. Wallace12, J. Walsh23, S.
Wandernoth11, J. Wang59, D.R. Ward47, N.K. Watson45, D. Websdale53, M.
Whitehead48, D. Wiedner11, G. Wilkinson55,38, M. Wilkinson59, M.P. Williams45,
M. Williams56, H.W. Wilschut66, F.F. Wilson49, J. Wimberley58, J. Wishahi9, W.
Wislicki28, M. Witek26, G. Wormser7, S.A. Wotton47, S. Wright47, K. Wyllie38,
Y. Xie61, Z. Xing59, Z. Xu39, Z. Yang3, X. Yuan3, O. Yushchenko35, M.
Zangoli14, M. Zavertyaev10,b, L. Zhang3, W.C. Zhang12, Y. Zhang3, A.
Zhelezov11, A. Zhokhov31, L. Zhong3.

1Centro 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
4LAPP, Université de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
10Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
12School of Physics, University College Dublin, Dublin, Ireland
13Sezione INFN di Bari, Bari, Italy
14Sezione INFN di Bologna, Bologna, Italy
15Sezione INFN di Cagliari, Cagliari, Italy
16Sezione INFN di Ferrara, Ferrara, Italy
17Sezione INFN di Firenze, Firenze, Italy
18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
19Sezione INFN di Genova, Genova, Italy
20Sezione INFN di Milano Bicocca, Milano, Italy
21Sezione INFN di Milano, Milano, Italy
22Sezione INFN di Padova, Padova, Italy
23Sezione INFN di Pisa, Pisa, Italy
24Sezione INFN di Roma Tor Vergata, Roma, Italy
25Sezione INFN di Roma La Sapienza, Roma, Italy
26Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
27AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
28National Center for Nuclear Research (NCBJ), Warsaw, Poland
29Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
30Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
31Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
32Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
33Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
34Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
35Institute for High Energy Physics (IHEP), Protvino, Russia
36Universitat de Barcelona, Barcelona, Spain
37Universidad de Santiago de Compostela, Santiago de Compostela, Spain
38European Organization for Nuclear Research (CERN), Geneva, Switzerland
39Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
40Physik-Institut, Universität Zürich, Zürich, Switzerland
41Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
42Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
43NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
44Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
45University of Birmingham, Birmingham, United Kingdom
46H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
47Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
48Department of Physics, University of Warwick, Coventry, United Kingdom
49STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
50School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
51School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
52Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
53Imperial College London, London, United Kingdom
54School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
55Department of Physics, University of Oxford, Oxford, United Kingdom
56Massachusetts Institute of Technology, Cambridge, MA, United States
57University of Cincinnati, Cincinnati, OH, United States
58University of Maryland, College Park, MD, United States
59Syracuse University, Syracuse, NY, United States
60Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
61Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
62Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
63Institut für Physik, Universität Rostock, Rostock, Germany, associated to 11
64National Research Centre Kurchatov Institute, Moscow, Russia, associated to
31
65Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC,
Valencia, Spain, associated to 36
66Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 41
67Celal Bayar University, Manisa, Turkey, associated to 38

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
cUniversità di Bari, Bari, Italy
dUniversità di Bologna, Bologna, Italy
eUniversità di Cagliari, Cagliari, Italy
fUniversità di Ferrara, Ferrara, Italy
gUniversità di Firenze, Firenze, Italy
hUniversità di Urbino, Urbino, Italy
iUniversità di Modena e Reggio Emilia, Modena, Italy
jUniversità di Genova, Genova, Italy
kUniversità di Milano Bicocca, Milano, Italy
lUniversità di Roma Tor Vergata, Roma, Italy
mUniversità di Roma La Sapienza, Roma, Italy
nUniversità della Basilicata, Potenza, Italy
oAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
pLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
qHanoi University of Science, Hanoi, Viet Nam
rUniversità di Padova, Padova, Italy
sUniversità di Pisa, Pisa, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità degli Studi di Milano, Milano, Italy
vPolitecnico di Milano, Milano, Italy