EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2017-195 LHCb-PAPER-2017-021 December 13, 2017

Measurement of $C\\!P$ observables in $B^{\pm}\rightarrow D^{(*)}K^{\pm}$ and
$B^{\pm}\rightarrow D^{(*)}\pi^{\pm}$ decays

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

Measurements of $C\\!P$ observables in $B^{\pm}\rightarrow D^{(*)}K^{\pm}$ and
$B^{\pm}\rightarrow D^{(*)}\pi^{\pm}$ decays are presented, where $D^{(*)}$
indicates a neutral ${D}$ or ${{D}^{*}}$ meson that is an admixture of
$D^{(*)0}$ and $\bar{D}^{(*)0}$ states. Decays of the ${{D}^{*}}$ meson to the
${D}{{\pi}^{0}}$ and ${D}\gamma$ final states are partially reconstructed
without inclusion of the neutral pion or photon, resulting in distinctive
shapes in the $B$ candidate invariant mass distribution. Decays of the ${D}$
meson are fully reconstructed in the ${{K}^{\pm}}{{\pi}^{\mp}}$,
${{K}^{+}}{{K}^{-}}$ and ${{\pi}^{+}}{{\pi}^{-}}$ final states. The analysis
uses a sample of charged $B$ mesons produced in $pp$ collisions collected by
the LHCb experiment, corresponding to an integrated luminosity of 2.0, 1.0 and
2.0$\mbox{\,fb}^{-1}$ taken at centre-of-mass energies of $\sqrt{s}$ = 7, 8
and 13$\mathrm{\,Te\kern-1.00006ptV}$, respectively. The study of
${{B}^{\pm}}\rightarrow{{D}^{*}}{{K}^{\pm}}$ and
${{B}^{\pm}}\rightarrow{{D}^{*}}{{\pi}^{\pm}}$ decays using a partial
reconstruction method is the first of its kind, while the measurement of
${{B}^{\pm}}\rightarrow{D}{{K}^{\pm}}$ and
${{B}^{\pm}}\rightarrow{D}{{\pi}^{\pm}}$ decays is an update of previous LHCb
measurements. The ${{B}^{\pm}}\rightarrow{D}{{K}^{\pm}}$ results are the most
precise to date.

Published in Phys. Lett. B777 (2018) 16$-$30

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

##  1 Introduction

Overconstraining the Unitarity Triangle (UT) derived from the Cabibbo-
Kobayashi-Maskawa (CKM) quark-mixing matrix is central to testing the Standard
Model (SM) description of $C\\!P$ violation [1, *Kobayashi:1973fv]. The least
well known angle of the UT is
$\gamma\equiv\text{arg}(-V_{ud}V_{ub}^{*}/V_{cd}V_{cb}^{*})$, which has been
determined with a precision of about $7^{\circ}$ from a combination of
measurements [3, 4] (${cf.}$ $3^{\circ}$ and $<1^{\circ}$ on the angles
$\alpha$ and $\beta$ [5, 6]). Among the UT angles, $\gamma$ is unique in that
it does not depend on any top-quark coupling, and can thus be measured in
decays that are dominated by tree-level contributions. In such decays, the
interpretation of physical observables (rates and $C\\!P$ asymmetries) in
terms of the underlying UT parameters is subject to small theoretical
uncertainties [7]. Any disagreement between these measurements of $\gamma$ and
the value inferred from global CKM fits performed without any $\gamma$
information would invalidate the SM description of $C\\!P$ violation.

The most powerful method for determining $\gamma$ in decays dominated by tree-
level contributions is through the measurement of relative partial widths in
${{{B}^{-}}}\rightarrow D{{K}^{-}}$ decays, where $D$ represents an admixture
of the ${D}^{0}$ and ${\kern 1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$
states.111The inclusion of charge-conjugate processes is implied except in any
discussion of asymmetries. The amplitude for the
${{{B}^{-}}}\rightarrow{{D}^{0}}{{K}^{-}}$ decay, which at the quark level
proceeds via a $b\rightarrow c\bar{u}s$ transition, is proportional to
$V_{cb}$. The corresponding amplitude for the ${{{B}^{-}}}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}{{K}^{-}}$ decay, which proceeds
via a $b\rightarrow u\bar{c}s$ transition, is proportional to $V_{ub}$. By
studying hadronic $D$ decays accessible to both ${D}^{0}$ and ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ mesons, phase information can
be extracted from the interference between these two amplitudes. The degree of
the resulting $C\\!P$ violation is governed by the size of $r_{B}^{DK}$, the
ratio of the magnitudes of the ${{{B}^{-}}}\rightarrow{{\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}}{{K}^{-}}$ and
${{{B}^{-}}}\rightarrow{{D}^{0}}{{K}^{-}}$ amplitudes. The relatively large
value of $r_{B}^{DK}\approx 0.10$ [4] in ${{{B}^{-}}}\rightarrow D{{K}^{-}}$
decays allows the determination of the relative phase of the two interfering
amplitudes. This relative phase has both $C\\!P$-violating ($\gamma$) and
$C\\!P$-conserving ($\delta_{B}^{DK}$) contributions; a measurement of the
decay rates for both ${{B}^{+}}$ and ${{B}^{-}}$ gives sensitivity to
$\gamma$. Similar interference effects also occur in ${{{B}^{-}}}\rightarrow
D{{\pi}^{-}}$ decays, albeit with lower sensitivity to the phases. The reduced
sensitivity is the result of additional Cabibbo suppression factors, which
decrease the ratio of amplitudes relative to ${{{B}^{-}}}\rightarrow
D{{K}^{-}}$ decays by around a factor of 20.

The ${{{B}^{-}}}\rightarrow{{D}^{*}}{{K}^{-}}$ decay, in which the vector
${{D}^{*}}$ meson222 ${{D}^{*}}$ represents an admixture of the
$D^{*}(2007)^{0}$ and $\bar{D}^{*}(2007)^{0}$ states. decays to either the
${D}{{\pi}^{0}}$ or ${D}\gamma$ final state, also exhibits $C\\!P$-violating
effects when hadronic $D$ decays accessible to both ${D}^{0}$ and ${\kern
1.99997pt\overline{\kern-1.99997ptD}{}}{}^{0}$ mesons are studied. In this
decay, the exact strong phase difference of $\pi$ between
${{D}^{*}}\rightarrow{D}{{\pi}^{0}}$ and ${{D}^{*}}\rightarrow{D}\gamma$
decays can be exploited to measure $C\\!P$ observables for states with
opposite $C\\!P$ eigenvalues [8]. The degree of $C\\!P$ violation observed in
${{{B}^{-}}}\rightarrow{{D}^{*}}{{K}^{-}}$ decays is set by the magnitude of
the ratio $r_{B}^{{{D}^{*}}\\!K}\approx 0.12$ [4], and measurement of the
phase for both ${{B}^{+}}$ and ${{B}^{-}}$ allows $\gamma$ and
$\delta_{B}^{{{D}^{*}}\\!K}$ to be disentangled.

The study of ${{{B}^{-}}}\rightarrow D^{(*)}{{K}^{-}}$ decays for measurements
of $\gamma$ was first suggested for $C\\!P$ eigenstates of the $D$ decay, for
example the $C\\!P$-even ${D}\rightarrow{{K}^{+}}{{K}^{-}}$ and
${D}\rightarrow{{\pi}^{+}}{{\pi}^{-}}$ decays, labelled here as GLW modes [9,
10]. In this work, the GLW decays ${D}\rightarrow{{K}^{+}}{{K}^{-}}$ and
${D}\rightarrow{{\pi}^{+}}{{\pi}^{-}}$ are considered along with the Cabibbo-
favoured ${D}\rightarrow{{K}^{-}}{{\pi}^{+}}$ decay, where the latter decay is
used for normalisation purposes and to define shape parameters in the fit to
data (see Sec. 4).

The ${{{B}^{-}}}\rightarrow[h_{1}^{+}h_{2}^{-}]_{D}h^{-}$ decays, in which
$h_{1}^{+}$, $h_{2}^{-}$ and $h^{-}$ can each represent either a charged kaon
or pion and the $D$-meson decay products are denoted inside square brackets,
have been studied at the $B$ factories [11, 12] and at LHCb [13]. This Letter
reports updated and improved results using a sample of charged $B$ mesons from
$pp$ collisions collected by the LHCb experiment, corresponding to an
integrated luminosity of 2.0, 1.0 and 2.0$\mbox{\,fb}^{-1}$ taken at centre-
of-mass energies of $\sqrt{s}$ = 7, 8 and 13$\mathrm{\,Te\kern-1.00006ptV}$,
respectively. The data taken at $\sqrt{s}$ = 13$\mathrm{\,Te\kern-1.00006ptV}$
benefits from a higher ${B}^{\pm}$ meson production cross-section and a more
efficient trigger, so this update of the
${{{B}^{-}}}\rightarrow[h_{1}^{+}h_{2}^{-}]_{D}h^{-}$ modes gains
approximately a factor of two in signal yield relative to Ref. [13]. The
${{{B}^{-}}}\rightarrow([h_{1}^{+}h_{2}^{-}]_{D}{{\pi}^{0}})_{{{D}^{*}}}h^{-}$
and ${{{B}^{-}}}\rightarrow([h_{1}^{+}h_{2}^{-}]_{D}\gamma)_{{{D}^{*}}}h^{-}$
decays, where the ${D}^{*}$-meson decay products are denoted in parentheses,
have also been studied by the $B$ factories [14, 15], while this work presents
the first analysis of these decays at LHCb.

The small ${{D}^{*}}-{D}$ mass difference and the conservation of angular
momentum in ${{D}^{*}}\rightarrow{D}{{\pi}^{0}}$ and
${{D}^{*}}\rightarrow{D}\gamma$ decays results in distinctive signatures for
the ${{{B}^{-}}}\rightarrow{{D}^{*}}{{K}^{-}}$ signal in the ${D}{{K}^{-}}$
invariant mass, allowing yields to be obtained with a partial reconstruction
technique. Since the reconstruction efficiency for low momentum neutral pions
and photons is relatively low in LHCb [16], the partial reconstruction method
provides significantly larger yields compared to full reconstruction, but the
statistical sensitivity per signal decay is reduced due to the need to
distinguish several signal and background components in the same region of
$D{{K}^{-}}$ invariant mass.

A total of 19 measurements of $C\\!P$ observables are reported, eight of which
correspond to the fully reconstructed
${{{B}^{-}}}\rightarrow[h_{1}^{+}h_{2}^{-}]_{D}h^{-}$ decays while the
remaining 11 relate to the partially reconstructed
${{{B}^{-}}}\rightarrow([h_{1}^{+}h_{2}^{-}]_{D}{{\pi}^{0}}/\gamma)_{{{D}^{*}}}h^{-}$
decays. In the latter case, the neutral pion or photon produced in the decay
of the ${D}^{*}$ vector meson is not reconstructed in the final state. A
summary of all measured $C\\!P$ observables is provided in Table 1. In
addition, the branching fractions
$\mathcal{B}({{{B}^{-}}}\rightarrow{{D}^{*0}}{{\pi}^{-}})$ and
$\mathcal{B}({{D}^{*0}}\rightarrow{{D}^{0}}{{\pi}^{0}})$, along with the ratio
of branching fractions
$\frac{\mathcal{B}({{{B}^{-}}}\rightarrow{{D}^{*0}}{{K}^{-}})}{\mathcal{B}({{{B}^{-}}}\rightarrow{{D}^{0}}{{K}^{-}})}$,
are reported.

Observable | Definition
---|---
$R_{K/\pi}^{K\pi}$ | $\frac{\Gamma({{{B}^{-}}}\rightarrow[{{K}^{-}}{{\pi}^{+}}]_{D}{{K}^{-}})+\Gamma({{{B}^{+}}}\rightarrow[{{K}^{+}}{{\pi}^{-}}]_{{D}}{{K}^{+}})}{\Gamma({{{B}^{-}}}\rightarrow[{{K}^{-}}{{\pi}^{+}}]_{D}{{\pi}^{-}})+\Gamma({{{B}^{+}}}\rightarrow[{{K}^{+}}{{\pi}^{-}}]_{{D}}{{\pi}^{+}})}$
$R^{KK}$ | $\frac{\Gamma({{{B}^{-}}}\rightarrow[{{K}^{-}}{{K}^{+}}]_{D}{{K}^{-}})+\Gamma({{{B}^{+}}}\rightarrow[{{K}^{+}}{{K}^{-}}]_{{D}}{{K}^{+}})}{\Gamma({{{B}^{-}}}\rightarrow[{{K}^{-}}{{K}^{+}}]_{D}{{\pi}^{-}})+\Gamma({{{B}^{+}}}\rightarrow[{{K}^{+}}{{K}^{-}}]_{{D}}{{\pi}^{+}})}\times\frac{1}{R_{K/\pi}^{K\pi}}$
$R^{\pi\pi}$ | $\frac{\Gamma({{{B}^{-}}}\rightarrow[{{\pi}^{-}}{{\pi}^{+}}]_{D}{{K}^{-}})+\Gamma({{{B}^{+}}}\rightarrow[{{\pi}^{+}}{{\pi}^{-}}]_{{D}}{{K}^{+}})}{\Gamma({{{B}^{-}}}\rightarrow[{{\pi}^{-}}{{\pi}^{+}}]_{D}{{\pi}^{-}})+\Gamma({{{B}^{+}}}\rightarrow[{{\pi}^{+}}{{\pi}^{-}}]_{{D}}{{\pi}^{+}})}\times\frac{1}{R_{K/\pi}^{K\pi}}$
$A_{K}^{K\pi}$ | $\frac{\Gamma({{{B}^{-}}}\rightarrow[{{K}^{-}}{{\pi}^{+}}]_{D}K^{-})-\Gamma({{{B}^{+}}}\rightarrow[{{K}^{+}}{{\pi}^{-}}]_{{D}}K^{+})}{\Gamma({{{B}^{-}}}\rightarrow[{{K}^{-}}{{\pi}^{+}}]_{D}K^{-})+\Gamma({{{B}^{+}}}\rightarrow[{{K}^{+}}{{\pi}^{-}}]_{{D}}K^{+})}$
$A_{K}^{KK}$ | $\frac{\Gamma({{{B}^{-}}}\rightarrow[{{K}^{-}}{{K}^{+}}]_{D}K^{-})-\Gamma({{{B}^{+}}}\rightarrow[{{K}^{+}}{{K}^{-}}]_{{D}}K^{+})}{\Gamma({{{B}^{-}}}\rightarrow[{{K}^{-}}{{K}^{+}}]_{D}K^{-})+\Gamma({{{B}^{+}}}\rightarrow[{{K}^{+}}{{K}^{-}}]_{{D}}K^{+})}$
$A_{K}^{\pi\pi}$ | $\frac{\Gamma({{{B}^{-}}}\rightarrow[{{\pi}^{-}}{{\pi}^{+}}]_{D}K^{-})-\Gamma({{{B}^{+}}}\rightarrow[{{\pi}^{+}}{{\pi}^{-}}]_{{D}}K^{+})}{\Gamma({{{B}^{-}}}\rightarrow[{{\pi}^{-}}{{\pi}^{+}}]_{D}K^{-})+\Gamma({{{B}^{+}}}\rightarrow[{{\pi}^{+}}{{\pi}^{-}}]_{{D}}K^{+})}$
$A_{\pi}^{KK}$ | $\frac{\Gamma({{{B}^{-}}}\rightarrow[{{K}^{-}}{{K}^{+}}]_{D}\pi^{-})-\Gamma({{{B}^{+}}}\rightarrow[{{K}^{+}}{{K}^{-}}]_{{D}}\pi^{+})}{\Gamma({{{B}^{-}}}\rightarrow[{{K}^{-}}{{K}^{+}}]_{D}\pi^{-})+\Gamma({{{B}^{+}}}\rightarrow[{{K}^{+}}{{K}^{-}}]_{{D}}\pi^{+})}$
$A_{\pi}^{\pi\pi}$ | $\frac{\Gamma({{{B}^{-}}}\rightarrow[{{\pi}^{-}}{{\pi}^{+}}]_{D}\pi^{-})-\Gamma({{{B}^{+}}}\rightarrow[{{\pi}^{+}}{{\pi}^{-}}]_{{D}}\pi^{+})}{\Gamma({{{B}^{-}}}\rightarrow[{{\pi}^{-}}{{\pi}^{+}}]_{D}\pi^{-})+\Gamma({{{B}^{+}}}\rightarrow[{{\pi}^{+}}{{\pi}^{-}}]_{{D}}\pi^{+})}$
$R_{K/\pi}^{K\pi,{{\pi}^{0}}/\gamma}$ | $\frac{\Gamma({{{B}^{-}}}\rightarrow([{{K}^{-}}{{\pi}^{+}}]_{D}{{\pi}^{0}}/\gamma)_{{{D}^{*}}}{{K}^{-}})+\Gamma({{{B}^{+}}}\rightarrow([{{K}^{+}}{{\pi}^{-}}]_{D}{{\pi}^{0}}/\gamma)_{{{D}^{*}}}{{K}^{+}})}{\Gamma({{{B}^{-}}}\rightarrow([{{K}^{-}}{{\pi}^{+}}]_{D}{{\pi}^{0}}/\gamma)_{{{D}^{*}}}{{\pi}^{-}})+\Gamma({{{B}^{+}}}\rightarrow([{{K}^{+}}{{\pi}^{-}}]_{D}{{\pi}^{0}}/\gamma)_{{{D}^{*}}}{{\pi}^{+}})}$
$R^{{C\\!P},{{\pi}^{0}}}$ | $\frac{\Gamma({{{B}^{-}}}\rightarrow([{C\\!P}]_{D}{{\pi}^{0}})_{{{D}^{*}}}{{K}^{-}})+\Gamma({{{B}^{+}}}\rightarrow([{C\\!P}]_{D}{{\pi}^{0}})_{{{D}^{*}}}{{K}^{+}})}{\Gamma({{{B}^{-}}}\rightarrow([{C\\!P}]_{D}{{\pi}^{0}})_{{{D}^{*}}}{{\pi}^{-}})+\Gamma({{{B}^{+}}}\rightarrow([{C\\!P}]_{D}{{\pi}^{0}})_{{{D}^{*}}}{{\pi}^{+}})}\times\frac{1}{R_{K/\pi}^{K\pi,{{\pi}^{0}}/\gamma}}$
$R^{{C\\!P},\gamma}$ | $\frac{\Gamma({{{B}^{-}}}\rightarrow([{C\\!P}]_{D}\gamma)_{{{D}^{*}}}{{K}^{-}})+\Gamma({{{B}^{+}}}\rightarrow([{C\\!P}]_{D}\gamma)_{{{D}^{*}}}{{K}^{+}})}{\Gamma({{{B}^{-}}}\rightarrow([{C\\!P}]_{D}\gamma)_{{{D}^{*}}}{{\pi}^{-}})+\Gamma({{{B}^{+}}}\rightarrow([{C\\!P}]_{D}\gamma)_{{{D}^{*}}}{{\pi}^{+}})}\times\frac{1}{R_{K/\pi}^{K\pi,{{\pi}^{0}}/\gamma}}$
$A_{K}^{K\pi,{{\pi}^{0}}}$ | $\frac{\Gamma({{{B}^{-}}}\rightarrow([{{K}^{-}}{{\pi}^{+}}]_{D}{{\pi}^{0}})_{{{D}^{*}}}K^{-})-\Gamma({{{B}^{+}}}\rightarrow([{{K}^{+}}{{\pi}^{-}}]_{{D}}{{\pi}^{0}})_{{{D}^{*}}}K^{+})}{\Gamma({{{B}^{-}}}\rightarrow([{{K}^{-}}{{\pi}^{+}}]_{D}{{\pi}^{0}})_{{{D}^{*}}}K^{-})+\Gamma({{{B}^{+}}}\rightarrow([{{K}^{+}}{{\pi}^{-}}]_{{D}}{{\pi}^{0}})_{{{D}^{*}}}K^{+})}$
$A_{\pi}^{K\pi,{{\pi}^{0}}}$ | $\frac{\Gamma({{{B}^{-}}}\rightarrow([{{K}^{-}}{{\pi}^{+}}]_{D}{{\pi}^{0}})_{{{D}^{*}}}\pi^{-})-\Gamma({{{B}^{+}}}\rightarrow([{{K}^{+}}{{\pi}^{-}}]_{{D}}{{\pi}^{0}})_{{{D}^{*}}}\pi^{+})}{\Gamma({{{B}^{-}}}\rightarrow([{{K}^{-}}{{\pi}^{+}}]_{D}{{\pi}^{0}})_{{{D}^{*}}}\pi^{-})+\Gamma({{{B}^{+}}}\rightarrow([{{K}^{+}}{{\pi}^{-}}]_{{D}}{{\pi}^{0}})_{{{D}^{*}}}\pi^{+})}$
$A_{K}^{K\pi,\gamma}$ | $\frac{\Gamma({{{B}^{-}}}\rightarrow([{{K}^{-}}{{\pi}^{+}}]_{D}\gamma)_{{{D}^{*}}}K^{-})-\Gamma({{{B}^{+}}}\rightarrow([{{K}^{+}}{{\pi}^{-}}]_{{D}}\gamma)_{{{D}^{*}}}K^{+})}{\Gamma({{{B}^{-}}}\rightarrow([{{K}^{-}}{{\pi}^{+}}]_{D}\gamma)_{{{D}^{*}}}K^{-})+\Gamma({{{B}^{+}}}\rightarrow([{{K}^{+}}{{\pi}^{-}}]_{{D}}\gamma)_{{{D}^{*}}}K^{+})}$
$A_{\pi}^{K\pi,\gamma}$ | $\frac{\Gamma({{{B}^{-}}}\rightarrow([{{K}^{-}}{{\pi}^{+}}]_{D}\gamma)_{{{D}^{*}}}\pi^{-})-\Gamma({{{B}^{+}}}\rightarrow([{{K}^{+}}{{\pi}^{-}}]_{{D}}\gamma)_{{{D}^{*}}}\pi^{+})}{\Gamma({{{B}^{-}}}\rightarrow([{{K}^{-}}{{\pi}^{+}}]_{D}\gamma)_{{{D}^{*}}}\pi^{-})+\Gamma({{{B}^{+}}}\rightarrow([{{K}^{+}}{{\pi}^{-}}]_{{D}}\gamma)_{{{D}^{*}}}\pi^{+})}$
$A_{K}^{{C\\!P},{{\pi}^{0}}}$ | $\frac{\Gamma({{{B}^{-}}}\rightarrow([{C\\!P}]_{D}{{\pi}^{0}})_{{{D}^{*}}}K^{-})-\Gamma({{{B}^{+}}}\rightarrow([{C\\!P}]_{{D}}{{\pi}^{0}})_{{{D}^{*}}}K^{+})}{\Gamma({{{B}^{-}}}\rightarrow([{C\\!P}]_{D}{{\pi}^{0}})_{{{D}^{*}}}K^{-})+\Gamma({{{B}^{+}}}\rightarrow([{C\\!P}]_{{D}}{{\pi}^{0}})_{{{D}^{*}}}K^{+})}$
$A_{\pi}^{{C\\!P},{{\pi}^{0}}}$ | $\frac{\Gamma({{{B}^{-}}}\rightarrow([{C\\!P}]_{D}{{\pi}^{0}})_{{{D}^{*}}}\pi^{-})-\Gamma({{{B}^{+}}}\rightarrow([{C\\!P}]_{{D}}{{\pi}^{0}})_{{{D}^{*}}}\pi^{+})}{\Gamma({{{B}^{-}}}\rightarrow([{C\\!P}]_{D}{{\pi}^{0}})_{{{D}^{*}}}\pi^{-})+\Gamma({{{B}^{+}}}\rightarrow([{C\\!P}]_{{D}}{{\pi}^{0}})_{{{D}^{*}}}\pi^{+})}$
$A_{K}^{{C\\!P},\gamma}$ | $\frac{\Gamma({{{B}^{-}}}\rightarrow([{C\\!P}]_{D}\gamma)_{{{D}^{*}}}K^{-})-\Gamma({{{B}^{+}}}\rightarrow([{C\\!P}]_{{D}}\gamma)_{{{D}^{*}}}K^{+})}{\Gamma({{{B}^{-}}}\rightarrow([{C\\!P}]_{D}\gamma)_{{{D}^{*}}}K^{-})+\Gamma({{{B}^{+}}}\rightarrow([{C\\!P}]_{{D}}\gamma)_{{{D}^{*}}}K^{+})}$
$A_{\pi}^{{C\\!P},\gamma}$ | $\frac{\Gamma({{{B}^{-}}}\rightarrow([{C\\!P}]_{D}\gamma)_{{{D}^{*}}}\pi^{-})-\Gamma({{{B}^{+}}}\rightarrow([{C\\!P}]_{{D}}\gamma)_{{{D}^{*}}}\pi^{+})}{\Gamma({{{B}^{-}}}\rightarrow([{C\\!P}]_{D}\gamma)_{{{D}^{*}}}\pi^{-})+\Gamma({{{B}^{+}}}\rightarrow([{C\\!P}]_{{D}}\gamma)_{{{D}^{*}}}\pi^{+})}$
Table 1: Summary table of the 19 measured $C\\!P$ observables, defined in
terms of $B$ meson decay widths. Where indicated, $C\\!P$ represents an
average of the ${D}\rightarrow{{K}^{+}}{{K}^{-}}$ and
${D}\rightarrow{{\pi}^{+}}{{\pi}^{-}}$ modes. The $R$ observables represent
partial width ratios and double ratios, where
$R_{K/\pi}^{K\pi,{{\pi}^{0}}/\gamma}$ is an average over the
${{D}^{*}}\rightarrow{D}{{\pi}^{0}}$ and ${{D}^{*}}\rightarrow{D}\gamma$
modes. The $A$ observables represent $C\\!P$ asymmetries.

All of the charge asymmetry measurements are affected by an asymmetry in the
${B}^{\pm}$ production cross-section and any charge asymmetry arising from the
LHCb detector efficiency, together denoted as $\sigma^{\prime}$. This
effective production asymmetry, defined as $A^{\rm
eff}_{{{B}^{\pm}}}=\textstyle{\frac{\sigma^{\prime}({{{B}^{-}}})-\sigma^{\prime}({{{B}^{+}}})}{\sigma^{\prime}({{{B}^{-}}})+\sigma^{\prime}({{{B}^{+}}})}}$,
is measured from the charge asymmetry of the most abundant
${{{B}^{-}}}\rightarrow[{{K}^{-}}{{\pi}^{+}}]_{D}{{\pi}^{-}}$ mode. In this
mode, the $C\\!P$ asymmetry is fixed to have the value
$A_{\pi}^{K\pi}=(+0.09\pm 0.05)\%$, which is determined using knowledge of
$\gamma$ and $r_{B}^{DK}$ from Ref. [3], where $A_{\pi}^{K\pi}$ was not used
as an input observable. This uncertainty is smaller than that of previous
measurements of the ${B}^{\pm}$ production asymmetry measured at $\sqrt{s}=7$
and 8$\mathrm{\,Te\kern-1.00006ptV}$ [17, 18], and reduces the systematic
uncertainties of the asymmetries listed in Table 1. The value of $A^{\rm
eff}_{{{B}^{\pm}}}$ is applied as a correction to all other charge
asymmetries. The remaining detection asymmetries, most notably due to
different numbers of ${K}^{+}$ and ${K}^{-}$ mesons appearing in each final
state, are corrected for using independent calibration samples. These
corrections transform the measured charge asymmetries into $C\\!P$
asymmetries.

##  2 Detector and simulation

The LHCb detector [19, 16] 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, a large-area silicon-strip detector located upstream of a
dipole magnet with a bending power of about $4{\mathrm{\,Tm}}$, and three
stations of silicon-strip detectors and straw drift tubes placed downstream of
the magnet. The tracking system provides a measurement of momentum, $p$, of
charged particles with a relative uncertainty that varies from 0.5% at low
momentum to 1.0% at 200${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. 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_{\mathrm{T}}$}){\,\upmu\mathrm{m}}$, where $p_{\mathrm{T}}$
is the component of the momentum transverse to the beam, in
${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. Different types of charged hadrons are
distinguished using information from two ring-imaging Cherenkov detectors
(RICH) [20, 21]. Photons, electrons and hadrons 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.

The trigger consists of a hardware stage, based on information from the
calorimeter and muon systems, followed by a software stage, in which all
charged particles with
$\mbox{$p_{\mathrm{T}}$}>500\,(300)\mathrm{\,Me\kern-1.00006ptV}$ are
reconstructed for 2011 (2012) data, and
$\mbox{$p_{\mathrm{T}}$}>70\mathrm{\,Me\kern-1.00006ptV}$ for 2015 and 2016
data. At the hardware trigger stage, events are required to contain a muon
with high $p_{\mathrm{T}}$ or a hadron, photon or electron with high
transverse energy in the calorimeters. For hadrons, the transverse energy
threshold varied between 3 and 4 GeV between 2011 and 2016. The software
trigger requires a two-, three- or four-track secondary vertex with
significant displacement from all primary $pp$ interaction vertices. A
multivariate algorithm [22, 23] is used for the identification of secondary
vertices consistent with the decay of a $b$ hadron.

In the simulation, $pp$ collisions are generated using Pythia8 [24] with a
specific LHCb configuration [25]. Decays of hadronic particles are described
by EvtGen [26], in which final-state radiation is generated using Photos [27].
The interaction of the generated particles with the detector, and its
response, are implemented using the Geant4 toolkit [28, *Agostinelli:2002hh]
as described in Ref. [30].

##  3 Event selection

After reconstruction of the $D$-meson candidate from two oppositely charged
particles, the same event selection is applied to all ${{{B}^{-}}}\rightarrow
D^{(*)}h^{-}$ channels. Since the neutral pion or photon from the vector
${D}^{*}$ decay is not reconstructed, partially reconstructed
${{{B}^{-}}}\rightarrow{{D}^{*}}h^{-}$ decays and fully reconstructed
${{{B}^{-}}}\rightarrow{D}h^{-}$ decays contain the same reconstructed
particles, and thus appear in the same sample. These decays are distinguished
according to the reconstructed invariant mass $m(Dh)$, as described in Sec. 4.

The reconstructed $D$-meson candidate mass is required to be within $\pm
25{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the known ${D}^{0}$ mass [31],
which corresponds to approximately three times the mass resolution. The kaon
or pion originating from the ${{B}^{-}}$ decay, subsequently referred to as
the companion particle, is required to have $p_{\mathrm{T}}$ in the range
0.5–10${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and $p$ in the range
5–100${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$. These requirements ensure that
the track is within the kinematic coverage of the RICH detectors, which are
used to provide particle identification (PID) information. Details of the PID
calibration procedure are given in Sec. 4. A kinematic fit is performed to
each decay chain, with vertex constraints applied to both the ${{B}^{-}}$ and
$D$ decay products, and the $D$ candidate constrained to its known mass [32].
Events are required to have been triggered by either the decay products of the
signal candidate, or by particles produced elsewhere in the $pp$ collision.
Each ${{B}^{-}}$ candidate is associated to the primary vertex (PV) to which
it has the smallest $\chi^{2}_{\text{IP}}$, which is quantified as the
difference in the vertex fit $\chi^{2}$ of a given PV reconstructed with and
without the considered particle. The ${{B}^{-}}$ meson candidates with
invariant masses in the interval
4900–5900${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ are retained. This range
is wider than that considered in Ref. [13], in order to include the partially
reconstructed
${{{B}^{-}}}\rightarrow([h_{1}^{+}h_{2}^{-}]_{D}{{\pi}^{0}})_{{{D}^{*}}}h^{-}$
and ${{{B}^{-}}}\rightarrow([h_{1}^{+}h_{2}^{-}]_{D}\gamma)_{{{D}^{*}}}h^{-}$
decays, which fall at $m(Dh)$ values below the known ${{B}^{-}}$ meson mass.

A pair of boosted decision tree (BDT) classifiers, implementing the gradient
boost algorithm [33], is employed to achieve further background suppression.
The BDTs are trained using simulated
${{{B}^{-}}}\rightarrow[{{K}^{-}}{{\pi}^{+}}]_{D}{{K}^{-}}$ decays and a
background sample of ${{K}^{-}}{{\pi}^{+}}{{K}^{-}}$ combinations in data with
invariant mass in the range
5900–7200${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$; the training was also
repeated using partially reconstructed
${{{B}^{-}}}\rightarrow([{{K}^{-}}{{\pi}^{+}}]_{D}{{\pi}^{0}})_{{{D}^{*}}}{{K}^{-}}$
and
${{{B}^{-}}}\rightarrow([{{K}^{-}}{{\pi}^{+}}]_{D}{{\pi}^{0}})_{{{D}^{*}}}{{K}^{-}}$
decays, and the difference in performance found to be negligible. No evidence
of overtraining was found in the training of either BDT. For the first BDT,
background candidates with a reconstructed $D$-meson mass more than
$30$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ from the known ${D}^{0}$ mass
are used in the training. In the second BDT, background candidates with a
reconstructed $D$-meson mass within $\pm
25$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the known ${D}^{0}$ mass are
used. A loose requirement on the classifier response of the first BDT is
applied prior to training the second one. This focuses the second BDT training
on a background sample enriched with fully reconstructed $D$ mesons. Both BDT
classifier responses are found to be uncorrelated with the $B$-candidate
invariant mass.

The input to both BDTs is a set of features that characterise the signal
decay. These features can be divided into two categories: (1) properties of
any particle and (2) properties of composite particles only (the $D$ and
${{B}^{-}}$ candidates). Specifically:

  1. 1.

$p$, $p_{\mathrm{T}}$ and $\chi^{2}_{\text{IP}}$;

  2. 2.

decay time, flight distance, decay vertex quality, radial distance between the
decay vertex and the PV, and the angle between the particle’s momentum vector
and the line connecting the production and decay vertices.

In addition, a feature that estimates the imbalance of $p_{\mathrm{T}}$ around
the ${{B}^{-}}$ candidate momentum vector is also used in both BDTs. It is
defined as

$I_{\mbox{$p_{\mathrm{T}}$}}=\frac{\mbox{$p_{\mathrm{T}}$}({{{B}^{-}}})-\Sigma\mbox{$p_{\mathrm{T}}$}}{\mbox{$p_{\mathrm{T}}$}({{{B}^{-}}})+\Sigma\mbox{$p_{\mathrm{T}}$}}\,,$
(1)

where the sum is taken over tracks inconsistent with originating from the PV
which lie within a cone around the ${{B}^{-}}$ candidate, excluding tracks
used to make the signal candidate. The cone is defined by a circle with a
radius of 1.5 units in the plane of pseudorapidity and azimuthal angle
(expressed in radians). Including the $I_{\mbox{$p_{\mathrm{T}}$}}$ feature in
the BDT training gives preference to ${{B}^{-}}$ candidates that are either
isolated from the rest of the event, or consistent with a recoil against
another $b$ hadron.

Since no PID information is used in the BDT classifier, the efficiency for
${{{B}^{-}}}\rightarrow D^{(*)}{{K}^{-}}$ and ${{{B}^{-}}}\rightarrow
D^{(*)}{{\pi}^{-}}$ decays is similar, with insignificant variations arising
from small differences in the decay kinematics. The criteria applied to the
two BDT responses are optimised by minimising the expected statistical
uncertainty on $R^{{C\\!P},{{\pi}^{0}}}$ and $R^{{C\\!P},\gamma}$, as measured
with the method described below. The purity of the sample is further improved
by requiring that all kaons and pions in the $D$ decay are positively
identified by the RICH. This PID selection used to separate the $D\pi$ and
$DK$ samples has an efficiency of about 85% per final-state particle.

Peaking background contributions from charmless decays that result in the same
final state as the signal are suppressed by requiring that the flight distance
of the $D$ candidate from the ${{B}^{-}}$ decay vertex is larger than two
times its uncertainty. After the above selections, multiple candidates exist
in 0.1% of the events in the sample. When more than one candidate is selected,
only the candidate with the best ${{B}^{-}}$ vertex quality is retained. The
overall effect of the multiple-candidate selection is negligible.

##  4 Fit to data

The values of the $C\\!P$ observables are determined using a binned extended
maximum likelihood fit to the data. Distinguishing between ${{B}^{+}}$ and
${{B}^{-}}$ candidates, companion particle hypotheses, and the three $D$ decay
product final states, yields 12 independent samples which are fitted
simultaneously. The total probability density function (PDF) is built from six
signal functions, one for each of the ${{{B}^{-}}}\rightarrow{D}{{\pi}^{-}}$,
${{{B}^{-}}}\rightarrow{D}{{K}^{-}}$,
${{{B}^{-}}}\rightarrow({D}{{\pi}^{0}})_{{{D}^{*}}}{{\pi}^{-}}$,
${{{B}^{-}}}\rightarrow({D}{{\pi}^{0}})_{{{D}^{*}}}{{K}^{-}}$,
${{{B}^{-}}}\rightarrow({D}\gamma)_{{{D}^{*}}}{{\pi}^{-}}$, and
${{{B}^{-}}}\rightarrow({D}\gamma)_{{{D}^{*}}}{{K}^{-}}$ decays. In addition,
there are functions which describe the combinatorial background components,
background contributions from $B$ decays to charmless final states and
background contributions from partially reconstructed decays. All functions
are identical for ${{B}^{+}}$ and ${{B}^{-}}$ decays.

### ${{{B}^{-}}}\rightarrow{D}{{\pi}^{-}}$

The ${{{B}^{-}}}\rightarrow D{{\pi}^{-}}$ signal component is modelled using
an asymmetric double-Gaussian-like function

$f(m)=f_{\text{core}}\text{
exp}\left(\frac{-(m-\mu)^{2}}{2\sigma_{c}^{2}+(m-\mu)^{2}\alpha_{L,R}}\right)+(1-f_{\text{core}})\text{
exp}\left(\frac{-(m-\mu)^{2}}{2\sigma_{w}^{2}}\right)$ (2)

which has a peak position $\mu$ and core width $\sigma_{c}$, where
$\alpha_{L}(m<\mu)$ and $\alpha_{R}(m>\mu)$ parameterise the tails. The $\mu$
and $\alpha$ parameters are shared across all samples but the core width
parameter varies independently for each $D$ final state. The additional
Gaussian function, with a small fractional contribution, is necessary to model
satisfactorily the tails of the peak.

The ${{{B}^{-}}}\rightarrow D{{\pi}^{-}}$ decays misidentified as
${{{B}^{-}}}\rightarrow D{{K}^{-}}$ are displaced to higher mass in the
$D{{K}^{-}}$ subsamples. These misidentified candidates are modelled by the
sum of two Gaussian functions with a common mean, modified to include tail
components as in Eq. 2. The mean, widths and $\alpha_{R}$ are left to vary
freely, while $\alpha_{L}$ is fixed to the value found in simulation.

### ${{{B}^{-}}}\rightarrow{D}{{K}^{-}}$

In the $D^{(*)0}{{K}^{-}}$ samples, Eq. 2 is used for the
${{{B}^{-}}}\rightarrow D{{K}^{-}}$ signal function. The peak position $\mu$
and the two tail parameters $\alpha_{L}$ and $\alpha_{R}$ are shared with the
${{{B}^{-}}}\rightarrow D{{\pi}^{-}}$ signal function, as are the wide
component parameters $f_{\text{core}}$ and $\sigma_{w}$. The core width
parameter in each $D$ mode is related to the corresponding
${{{B}^{-}}}\rightarrow D{{\pi}^{-}}$ width by a freely varying ratio common
to all $D$ final states.

Misidentified ${{{B}^{-}}}\rightarrow D{{K}^{-}}$ candidates appearing in the
$D^{(*)0}{{\pi}^{-}}$ subsamples are described by a fixed shape obtained from
simulation, which is later varied to determine a systematic uncertainty
associated with this choice.

### ${{{B}^{-}}}\rightarrow({D}{{\pi}^{0}})_{{{D}^{*}}}{{\pi}^{-}}$

In partially reconstructed decays involving a vector meson, the ${D}h^{-}$
invariant mass distribution depends upon the spin and mass of the missing
particle. In the case of
${{{B}^{-}}}\rightarrow({D}{{\pi}^{0}})_{{{D}^{*}}}{{\pi}^{-}}$ decays, the
missing neutral pion has spin-parity $0^{-}$. The distribution is
parameterised by an upward-open parabola, whose range is defined by the
kinematic endpoints of the decay. It is convolved with a Gaussian resolution
function, resulting in

$f(m)=\int_{a}^{b}\\!\left(\mu-\frac{a+b}{2}\right)^{2}\left(\frac{1-\xi}{b-a}\mu+\frac{b\xi-a}{b-a}\right)e^{-\frac{(\mu-m)^{2}}{2\sigma^{2}}}\text{d}\mu\\\
\,.$ (3)

The resulting distribution has a characteristic double-peaked shape, visible
in Figs. 1$-$3 as the light grey filled regions appearing to the left of the
fully reconstructed $B^{-}\rightarrow D^{0}h^{-}$ peaks. The lower and upper
endpoints of the parabola are $a$ and $b$, respectively, while the relative
height of the lower and upper peaks is determined by the $\xi$ term. When
$\xi=1$, both peaks are of equal height, and deviation of $\xi$ from unity
accounts for mass-dependent reconstruction and selection efficiency effects.
The values of $a$, $b$ and $\xi$ are taken from fits to simulated events,
while the convolution Gaussian width $\sigma$ is allowed to vary freely in the
mass fit in each $D$ mode subsample.

Partially reconstructed
${{{B}^{-}}}\rightarrow({D}{{\pi}^{0}})_{{{D}^{*}}}{{\pi}^{-}}$ decays, where
the companion pion is misidentified as a kaon, are parameterised with a
semiempirical function, formed from the sum of Gaussian and error functions.
The parameters of this function are fixed to the values found in fits to
simulated events, and are varied to determine the associated systematic
uncertainty.

### ${{{B}^{-}}}\rightarrow({D}{{\pi}^{0}})_{{{D}^{*}}}{{K}^{-}}$

Equation 3 is also used to describe partially reconstructed
${{{B}^{-}}}\rightarrow({D}{{\pi}^{0}})_{{{D}^{*}}}{{K}^{-}}$ decays, where
the width $\sigma$ in each of the $D{{K}^{-}}$ samples is related to the
$D{{\pi}^{-}}$ width by a freely varying ratio $r_{\sigma}$, which is shared
across all functions describing partially reconstructed decays. All other
shape parameters are shared with the
${{{B}^{-}}}\rightarrow({D}{{\pi}^{0}})_{{{D}^{*}}}{{\pi}^{-}}$ function.

Partially reconstructed
${{{B}^{-}}}\rightarrow({D}{{\pi}^{0}})_{{{D}^{*}}}{{K}^{-}}$ decays, where
the companion kaon is misidentified as a pion, are parameterised with a
semiempirical function, formed from the sum of Gaussian and error functions.
The parameters of this function are fixed to the values found in fits to
simulated events, and are varied to determine the associated systematic
uncertainty.

### ${{{B}^{-}}}\rightarrow({D}\gamma)_{{{D}^{*}}}{{\pi}^{-}}$

Partially reconstructed
${{{B}^{-}}}\rightarrow({D}\gamma)_{{{D}^{*}}}{{\pi}^{-}}$ decays involve a
missing particle of zero mass and spin-parity $1^{-}$. The ${D}{{\pi}^{-}}$
invariant mass distribution is described by a parabola exhibiting a maximum,
convolved with a Gaussian resolution function. The functional form of this
component is

$f(m)=\int_{a}^{b}\\!-(\mu-a)(\mu-b)\left(\frac{1-\xi}{b-a}\mu+\frac{b\xi-a}{b-a}\right)e^{-\frac{(\mu-m)^{2}}{2\sigma^{2}}}\text{d}\mu\,.$
(4)

This distribution exhibits a broad single peak, as opposed to the double-
peaked ${{{B}^{-}}}\rightarrow({D}{{\pi}^{0}})_{{{D}^{*}}}{{\pi}^{-}}$
distribution described by Eq. 3. In Figs. 1$-$3, this component is visible as
the wide hatched regions bounded by solid black curves, which appear below the
fully reconstructed $B^{-}\rightarrow D^{0}h^{-}$ peaks.

The values of $a$, $b$, $\xi$ and $\sigma$ are fixed using fits to simulated
events. The clear difference between the invariant mass distributions of
${{{B}^{-}}}\rightarrow({D}\gamma)_{{{D}^{*}}}{{\pi}^{-}}$ and
${{{B}^{-}}}\rightarrow({D}{{\pi}^{0}})_{{{D}^{*}}}{{\pi}^{-}}$ decays enables
their statistical separation, and hence the determination of $C\\!P$
observables for each mode independently.

Partially reconstructed
${{{B}^{-}}}\rightarrow({D}\gamma)_{{{D}^{*}}}{{\pi}^{-}}$ decays where the
companion pion is misidentified as a kaon are treated in an equivalent manner
to misidentified
${{{B}^{-}}}\rightarrow({D}{{\pi}^{0}})_{{{D}^{*}}}{{\pi}^{-}}$ decays, as
described above.

### ${{{B}^{-}}}\rightarrow({D}\gamma)_{{{D}^{*}}}{{K}^{-}}$

Equation 4 is also used to describe partially reconstructed
${{{B}^{-}}}\rightarrow({D}\gamma)_{{{D}^{*}}}{{K}^{-}}$ decays, where the
width $\sigma$ in each of the $D{{K}^{-}}$ samples is related to the
$D{{\pi}^{-}}$ width by the ratio $r_{\sigma}$. All other shape parameters are
shared with the ${{{B}^{-}}}\rightarrow({D}\gamma)_{{{D}^{*}}}{{\pi}^{-}}$
function. Partially reconstructed
${{{B}^{-}}}\rightarrow({D}{{\pi}^{0}})_{{{D}^{*}}}{{K}^{-}}$ decays where the
companion kaon is misidentified as a pion are treated in an equivalent manner
to misidentified ${{{B}^{-}}}\rightarrow({D}{{\pi}^{0}})_{{{D}^{*}}}{{K}^{-}}$
decays.

### Combinatorial background

An exponential function is used to describe the combinatorial background. The
exponential function is widely used to describe combinatorial backgrounds to
${{{B}^{-}}}$ decays in LHCb, and has been validated for numerous different
decay modes. Independent and freely varying exponential parameters and yields
are used to model this component in each subsample, with the constraint that
the ${{B}^{+}}$ and ${{B}^{-}}$ yields are required to be equal. The
systematic uncertainty associated with this constraint is negligible.

### Charmless background

Charmless ${{{B}^{-}}}\rightarrow h_{1}^{+}h_{2}^{-}h^{-}$ decays, where
$h_{1}^{+}$, $h_{2}^{-}$ and $h^{-}$ each represent a charged kaon or pion,
peak at the ${{B}^{-}}$ mass and cannot be distinguished effectively from the
fully reconstructed ${{{B}^{-}}}\rightarrow{D}h^{-}$ signals in the invariant
mass fit. A Gaussian function is used to model this component, with a $25\pm
2{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ width parameter that is taken from
simulation; this is about 50% wider than the ${{{B}^{-}}}\rightarrow{D}h^{-}$
signal function, due to the application of a $D$ mass constraint in the
calculation of the $B$-candidate invariant mass. This constraint improves the
invariant mass resolution for signal decays, but worsens it for charmless
background contributions.

Partially reconstructed charmless decays of the type $B\rightarrow
h_{1}^{+}h_{2}^{-}h^{-}X$, where $X$ is a charged pion, neutral pion or photon
that has not been reconstructed, contribute at low invariant mass. Their
contributions are fixed to the fully reconstructed charmless components scaled
by relative branching fractions [31] and efficiencies determined from
simulated samples. A parabola with negative curvature convolved with a
Gaussian resolution function is used to model this component, with shape
parameter values taken from simulation [34].

The charmless contribution is interpolated from fits to the ${{B}^{-}}$ mass
spectrum in both the lower and upper $D$-mass sidebands, without the kinematic
fit of the decay chain. The charmless yields are determined independently for
${{B}^{+}}$ and ${{B}^{-}}$ candidates and are then fixed in the analysis.
Their uncertainties contribute to the systematic uncertainties of the final
results. The largest charmless contribution is in the
${{{B}^{-}}}\rightarrow[{{\pi}^{+}}{{\pi}^{-}}]_{D}{{K}^{-}}$ mode, which has
a yield corresponding to 7% of the measured signal yield.

### Partially reconstructed background

Several additional partially reconstructed $b$-hadron decays contribute at low
invariant mass values. The dominant contributions are from
${{{B}^{-}}}\rightarrow{D}h^{-}{{\pi}^{0}}$ and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow({D}{{\pi}^{+}})_{{{D}^{*+}}}{{\pi}^{-}}$
decays, where a neutral pion or positively charged pion is missed in the
reconstruction.333 When considering partially reconstructed background
contributions, the assumption is made that the production fractions $f_{u}$
and $f_{d}$ are equal. The invariant mass distribution of these sources
depends upon the spin and mass of the missing particle, as with the
${{{B}^{-}}}\rightarrow{{D}^{*}}h^{-}$ signals. In both cases, the missing
particle has spin-parity $0^{-}$, such that the $Dh^{-}$ distribution is
parameterised using Eq. 3, with shape parameter values taken from simulation.
The Dalitz structure of ${{{B}^{-}}}\rightarrow{D}h^{-}{{\pi}^{0}}$ decays is
modelled using Laura++ [35].

Decays in which a particle is missed and a companion pion is misidentified as
a kaon are parameterised with a semiempirical function, formed from the sum of
Gaussian and error functions. The parameters of each partially reconstructed
function are fixed to the values found in fits to simulated events, and are
varied to determine the associated systematic uncertainty. The yields of the
${{{B}^{-}}}\rightarrow{D}{{\pi}^{-}}{{\pi}^{0}}$ and
${{{B}^{-}}}\rightarrow{D}{{K}^{-}}{{\pi}^{0}}$ contributions vary
independently in each subsample, with a $C\\!P$ asymmetry that is fixed to
zero in the case of the favoured mode but allowed to vary freely in the GLW
samples. The yields of the ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow({D}{{\pi}^{+}})_{{{D}^{*+}}}{{\pi}^{-}}$
and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow({D}{{\pi}^{+}})_{{{D}^{*+}}}{{K}^{-}}$
contributions, where the ${{\pi}^{+}}$ is not reconstructed, are fixed
relative to the corresponding ${{{B}^{-}}}\rightarrow{D}{{\pi}^{-}}$ yields
using branching fractions [31, 36, 37] and efficiencies derived from
simulation. Their $C\\!P$ asymmetries are fixed to zero in all subsamples as
no $C\\!P$ violation is expected.

Further contributions from partially reconstructed
${{{B}^{-}}}\rightarrow({D}{{\pi}^{0}}/\gamma)_{{{D}^{*}}}h^{-}{{\pi}^{0}}$
and ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}}\rightarrow({D}{{\pi}^{+}})_{{{D}^{*+}}}h^{-}{{\pi}^{0}}$
decays occur at the lowest values of invariant mass, where two particles are
not reconstructed. These decays are described by the sum of several parabolas
convolved with resolution functions according to Eqs. 3 and 4, with shape
parameters fixed to the values found in fits to simulated samples. The yields
and $C\\!P$ asymmetries of these contributions vary freely in each subsample.

Colour-suppressed ${{B}^{0}}\rightarrow{D}h^{-}{{\pi}^{+}}$ and
${{B}^{0}}\rightarrow{{D}^{*}}h^{-}{{\pi}^{+}}$ decays also contribute to the
background. The rates of these small contributions are fixed relative to their
corresponding colour-favoured mode yields using the known relative branching
fractions [31, 38, 39, 40, 41]. In the
${{{B}^{-}}}\rightarrow[{{K}^{+}}{{K}^{-}}]_{D}h^{-}$ samples, ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow[p^{+}{{K}^{-}}{{\pi}^{+}}]_{{{\mathchar
28931\relax}^{+}_{c}}}h^{-}$ decays contribute to the background when the pion
is missed and the proton is misidentified as the second kaon. The wide
function describing this component is fixed from simulation, but the yield in
the ${{{B}^{-}}}\rightarrow[{{K}^{+}}{{K}^{-}}]_{D}{{\pi}^{-}}$ subsample
varies freely. The ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow[p^{+}{{K}^{-}}{{\pi}^{+}}]_{{{\mathchar
28931\relax}^{+}_{c}}}{{K}^{-}}$ yield is constrained using a measurement of
$\mathcal{B}({{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}{{K}^{-}})/\mathcal{B}({{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar 28931\relax}^{+}_{c}}{{\pi}^{-}})$
[42]. In both the ${{{B}^{-}}}\rightarrow[{{K}^{+}}{{K}^{-}}]_{D}K^{-}$ and
${{{B}^{-}}}\rightarrow[{{\pi}^{+}}{{\pi}^{-}}]_{D}K^{-}$ samples,
${{B}^{0}_{s}}\rightarrow{D}{{K}^{-}}{{\pi}^{+}}$ decays in which the
companion pion is missed contribute to the background. The function describing
this component is fixed from fits to simulated samples generated according the
the Dalitz model in Ref. [43, 35], and the yield is constrained relative to
the corresponding ${{{B}^{-}}}\rightarrow{D}{{\pi}^{-}}$ mode yield scaled by
branching fractions [31, 36, 44], efficiencies determined from simulation, and
the relative production rates of ${{B}^{0}_{s}}$ and ${{B}^{0}}$ mesons at
$\sqrt{s}=7$$\mathrm{\,Te\kern-1.00006ptV}$ [45]. The increase in relative
production rate at 13$\mathrm{\,Te\kern-1.00006ptV}$ is small [46], and so the
7$\mathrm{\,Te\kern-1.00006ptV}$ value is used to describe all data in the
analysis.

### PID efficiencies

In the $D^{(*)}{{K}^{-}}$ subsamples, the ${{{B}^{-}}}\rightarrow
D^{(*)}{{\pi}^{-}}$ cross-feed is determined by the fit to data. The
${{{B}^{-}}}\rightarrow D^{(*)}{{K}^{-}}$ cross-feed into the
$D^{(*)}{{\pi}^{-}}$ subsamples is not well separated from background, so the
expected yield is determined by a PID calibration procedure using
approximately 20 million
${{D}^{*+}}\rightarrow[{{K}^{-}}{{\pi}^{+}}]_{D}{{\pi}^{+}}$ decays. The
reconstruction of this decay is performed using kinematic variables only, and
thus provides a pure sample of ${K}^{\mp}$ and ${\pi}^{\pm}$ particles
unbiased in the PID variables. The PID efficiency is parameterised as a
function of particle momentum and pseudorapidity, as well as the charged-
particle multiplicity in the event. The effective PID efficiency of the signal
is determined by weighting the calibration sample such that the distributions
of these variables match those of selected
${{{B}^{-}}}\rightarrow{{D}^{0}}{{\pi}^{-}}$ signal decays. It is found that
71.2% of ${{{B}^{-}}}\rightarrow{D}{{K}^{-}}$ decays pass the companion kaon
PID requirement, with negligible statistical uncertainty due to the size of
the calibration sample; the remaining 28.8% cross-feed into the
${{{B}^{-}}}\rightarrow D^{(*)}{{\pi}^{-}}$ sample. With the same PID
requirement, approximately 99.5% of the ${{{B}^{-}}}\rightarrow{D}{{\pi}^{-}}$
decays are correctly identified. These efficiencies are also taken to
represent ${{{B}^{-}}}\rightarrow({D}{{\pi}^{0}})_{{{D}^{*}}}h^{-}$ and
${{{B}^{-}}}\rightarrow({D}\gamma)_{{{D}^{*}}}h^{-}$ signal decays in the fit,
since the companion kinematics are similar across all decay modes considered.
The related systematic uncertainty is determined by the size of the signal
samples used, and thus increases for the lower yield modes. The systematic
uncertainty ranges from 0.1% in
${{{B}^{-}}}\rightarrow[{{K}^{-}}{{\pi}^{+}}]_{D}{{K}^{-}}$ to 0.4% in
${{{B}^{-}}}\rightarrow[{{\pi}^{+}}{{\pi}^{-}}]_{D}{{K}^{-}}$.

### Production and detection asymmetries

In order to measure $C\\!P$ asymmetries, the detection asymmetries for
${K}^{\pm}$ and ${\pi}^{\pm}$ mesons must be taken into account. A detection
asymmetry of $(-0.87\pm 0.17)$% is assigned for each kaon in the final state,
primarily due to the fact that the nuclear interaction length of ${K}^{-}$
mesons is shorter than that of ${K}^{+}$ mesons. It is computed by comparing
the charge asymmetries in
${{D}^{-}}\rightarrow{{K}^{+}}{{\pi}^{-}}{{\pi}^{-}}$ and
${{D}^{-}}\rightarrow{{K}^{0}_{\mathrm{\scriptscriptstyle S}}}{{\pi}^{-}}$
calibration samples, weighted to match the kinematics of the signal kaons. The
equivalent asymmetry for pions is smaller $(-0.17\pm 0.10)$% [17]. The $C\\!P$
asymmetry in the favoured
${{{B}^{-}}}\rightarrow[{{K}^{-}}{{\pi}^{+}}]_{D}{{\pi}^{-}}$ decay is fixed
to $(+0.09\pm 0.05)\%$, calculated from current knowledge of $\gamma$ and
$r_{B}$ in this decay [3], with no assumption made about the strong phase,
$\delta_{B}^{D\pi}$. This enables the effective production asymmetry, $A^{\rm
eff}_{{{B}^{\pm}}}$, to be measured and simultaneously subtracted from the
charge asymmetry measurements in other modes.

### Yields and selection efficiencies

The total yield for each mode is a sum of the number of correctly identified
and cross-feed candidates; their values are given in Table 2. The
corresponding invariant mass spectra, separated by charge, are shown in Figs.
1$-$3.

To obtain the observable $R_{K/\pi}^{K\pi}$
($R_{K/\pi}^{K\pi,{{\pi}^{0}}/\gamma}$), which is defined in Table 1, the
ratio of yields must be corrected by the relative efficiency with which
${{{B}^{-}}}\rightarrow{D}{{K}^{-}}$ and
${{{B}^{-}}}\rightarrow{D}{{\pi}^{-}}$
(${{{B}^{-}}}\rightarrow{{D}^{*}}{{K}^{-}}$ and
${{{B}^{-}}}\rightarrow{{D}^{*}}{{\pi}^{-}}$) decays are reconstructed and
selected. Both ratios are found to be consistent with unity within their
assigned uncertainties, which take into account the size of the simulated
samples and the imperfect modelling of the relative pion and kaon absorption
in the detector material.

To determine the branching fraction
$\mathcal{B}({{D}^{*0}}\rightarrow{{D}^{0}}{{\pi}^{0}})$, the yields of the
${{{B}^{-}}}\rightarrow({D}{{\pi}^{0}})_{{{D}^{*}}}{{\pi}^{-}}$ and
${{{B}^{-}}}\rightarrow({D}\gamma)_{{{D}^{*}}}{{\pi}^{-}}$ modes are corrected
for the relative efficiencies of the neutral pion and photon modes as
determined from simulation. As both of these modes are partially reconstructed
with identical selection requirements, the relative efficiency is found to be
unity within its assigned uncertainty, and is varied to determine the
associated systematic uncertainty. In the measurement of
$\mathcal{B}({{D}^{*}}\rightarrow{D}{{\pi}^{0}})$, the assumption is made that
$\mathcal{B}({{D}^{*}}\rightarrow{D}{{\pi}^{0}})+\mathcal{B}({{D}^{*}}\rightarrow{D}\gamma)=1$
[31].

The branching fraction
$\mathcal{B}({{{B}^{-}}}\rightarrow{{D}^{*0}}{{\pi}^{-}})$ is determined from
the total ${{{B}^{-}}}\rightarrow{{D}^{*}}{{\pi}^{-}}$ yield, the total
${{{B}^{-}}}\rightarrow{D}{{\pi}^{-}}$ yield, the relative efficiencies
determined from simulation, and the ${{{B}^{-}}}\rightarrow{D}{{\pi}^{-}}$
branching fraction [31, 36]. Both the efficiencies and external input
branching fraction are varied to determine the associated systematic
uncertainty.

Mode | Yield
---|---
${{B}^{\pm}}\rightarrow[K\pi]_{D}{{\pi}^{\pm}}$ | 862 785 $\pm$ 0945
${{B}^{\pm}}\rightarrow[KK]_{D}{{\pi}^{\pm}}$ | 105 923 $\pm$ 0368
${{B}^{\pm}}\rightarrow[\pi\pi]_{D}{{\pi}^{\pm}}$ |  033 381 $\pm$ 0173
${{B}^{\pm}}\rightarrow[K\pi]_{D}{{K}^{\pm}}$ |  066 987 $\pm$ 0326
${{B}^{\pm}}\rightarrow[KK]_{D}{{K}^{\pm}}$ |  008125 $\pm$ 0129
${{B}^{\pm}}\rightarrow[\pi\pi]_{D}{{K}^{\pm}}$ |  002571 $\pm$ 0070
${{B}^{\pm}}\rightarrow([K\pi]_{D}{{\pi}^{0}})_{{{D}^{*}}}{{\pi}^{\pm}}$ | 519 211 $\pm$ 3747
${{B}^{\pm}}\rightarrow([KK]_{D}{{\pi}^{0}})_{{{D}^{*}}}{{\pi}^{\pm}}$ |  063 742 $\pm$ 0460
${{B}^{\pm}}\rightarrow([\pi\pi]_{D}{{\pi}^{0}})_{{{D}^{*}}}{{\pi}^{\pm}}$ |  020 088 $\pm$ 0145
${{B}^{\pm}}\rightarrow([K\pi]_{D}{{\pi}^{0}})_{{{D}^{*}}}{{K}^{\pm}}$ |  040 988 $\pm$ 0569
${{B}^{\pm}}\rightarrow([KK]_{D}{{\pi}^{0}})_{{{D}^{*}}}{{K}^{\pm}}$ |  005725 $\pm$ 0165
${{B}^{\pm}}\rightarrow([\pi\pi]_{D}{{\pi}^{0}})_{{{D}^{*}}}{{K}^{\pm}}$ |  001804 $\pm$ 0052
${{B}^{\pm}}\rightarrow([K\pi]_{D}\gamma)_{{{D}^{*}}}{{\pi}^{\pm}}$ | 291 372 $\pm$ 2103
${{B}^{\pm}}\rightarrow([KK]_{D}\gamma)_{{{D}^{*}}}{{\pi}^{\pm}}$ |  035 771 $\pm$ 0258
${{B}^{\pm}}\rightarrow([\pi\pi]_{D}\gamma)_{{{D}^{*}}}{{\pi}^{\pm}}$ |  011 273 $\pm$ 0081
${{B}^{\pm}}\rightarrow([K\pi]_{D}\gamma)_{{{D}^{*}}}{{K}^{\pm}}$ |  022 752 $\pm$ 0316
${{B}^{\pm}}\rightarrow([KK]_{D}\gamma)_{{{D}^{*}}}{{K}^{\pm}}$ |  002520 $\pm$ 0245
${{B}^{\pm}}\rightarrow([\pi\pi]_{D}\gamma)_{{{D}^{*}}}{{K}^{\pm}}$ |  000794 $\pm$ 0077
Table 2: Signal yields as measured in the fit to the data.

Figure 1: Invariant mass distributions of selected
${{B}^{\pm}}\rightarrow[{{K}^{\pm}}{{\pi}^{\mp}}]_{D}h^{\pm}$ candidates,
separated by charge, with ${{{B}^{-}}}{\rm(}{{{B}^{+}}}{\rm)}$ candidates on
the left (right). The top panels contain the ${{B}^{\pm}}\rightarrow
D^{(*)0}K^{\pm}$ candidate samples, as defined by a PID requirement on the
companion particle. The remaining candidates are placed in the bottom panels,
reconstructed with a pion hypothesis for the companion. The result of the fit
is shown by the thin solid black line, and each component is listed in the
legend. The component referred to as ‘Part. reco. mis-ID’ is the total
contribution from all partially reconstructed and misidentified decays.
Figure 2: Invariant mass distributions of selected
${{B}^{\pm}}\rightarrow[{{K}^{+}}{{K}^{-}}]_{D}h^{\pm}$ candidates, separated
by charge. See Fig. 1 for details of each component.  Figure 3: Invariant mass
distributions of selected
${{B}^{\pm}}\rightarrow[{{\pi}^{+}}{{\pi}^{-}}]_{D}h^{\pm}$ candidates,
separated by charge. See Fig. 1 for details of each component.

##  5 Systematic uncertainties

The 21 observables of interest are free parameters of the fit, and each of
them is subject to a set of systematic uncertainties that result from the use
of fixed terms in the fit. The systematic uncertainties associated with using
these fixed parameters are assessed by repeating the fit many times, varying
the value of each external parameter within its uncertainty according to a
Gaussian distribution. The resulting spread (RMS) in the value of each
observable is taken as the systematic uncertainty on that observable due to
the external source. The systematic uncertainties, grouped into six
categories, are listed in Tables 3 and 4 for the $C\\!P$ observables measured
in a partially reconstructed and fully reconstructed manner, respectively. The
systematic uncertainties for the branching fraction measurements are listed in
Table 5. Correlations between the categories are negligible, but correlations
within categories are accounted for. The total systematic uncertainties are
summed in quadrature.

The first systematic category, referred to as PID in Tables 3$-$5, accounts
for the uncertainty due to the use of fixed PID efficiency values in the fit.
The second category Bkg rate corresponds to the use of fixed background yields
in the fit. For example, the rate of $B^{0}\rightarrow D^{*-}{{\pi}^{+}}$
decays is fixed in the fit using known branching fractions as external inputs.
This category also accounts for charmless background contributions, each of
which have fixed rates in the fit. The Bkg func and Sig func categories refer
to the use of fixed shape parameters in background and signal functions,
respectively; each of these parameters is determined using simulated samples.
The category Sim accounts for the use of fixed selection efficiencies derived
from simulation, for instance the relative efficiency of selecting
${{{B}^{-}}}\rightarrow({D}{{\pi}^{0}})_{{{D}^{*}}}{{\pi}^{-}}$ and
${{{B}^{-}}}\rightarrow{D}{{\pi}^{-}}$ decays. The final category, Asym,
refers to the use of fixed asymmetries in the fit. This category accounts for
the use of fixed $C\\!P$ asymmetries and detection asymmetries in the fit, as
described earlier.

Table 3: Systematic uncertainties for the $C\\!P$ observables measured in a
partially reconstructed manner, quoted as a percentage of the statistical
uncertainty on the observable.

[%] $A_{K}^{K\pi,\gamma}$ $A_{\pi}^{K\pi,\gamma}$ $A_{K}^{K\pi,{{\pi}^{0}}}$
$A_{\pi}^{K\pi,{{\pi}^{0}}}$ $A_{K}^{CP,\gamma}$ $A_{\pi}^{CP,\gamma}$
$A_{K}^{CP,{{\pi}^{0}}}$ $A_{\pi}^{CP,{{\pi}^{0}}}$ $R^{CP,\gamma}$
$R^{CP,{{\pi}^{0}}}$ $R_{K/\pi}^{K\pi,{{\pi}^{0}}/\gamma}$ PID 4.0 11.4 4.4
3.8 9.1 5.0 4.7 4.4 22.0 16.9 74.8 Bkg rate 3.5 1.6 3.2 3.6 40.8 3.5 16.5 5.7
114.0 41.9 180.3 Bkg func 8.9 1.0 3.7 0.7 24.4 1.6 27.1 1.3 42.6 25.0 417.3
Sig func 4.8 3.9 2.9 3.9 10.9 3.6 3.7 4.3 24.6 13.8 148.4 Sim 3.1 1.1 2.1 1.9
6.5 0.9 4.3 2.9 23.5 15.3 153.8 Asym 29.9 6.8 34.1 19.4 1.0 9.4 2.2 26.1 1.4
0.6 1.9 Total 32.1 14.0 35.0 20.6 50.0 11.9 32.7 27.6 128.3 55.6 507.9

Table 4: Systematic uncertainties for the $C\\!P$ observables measured in a fully reconstructed manner, quoted as a percentage of the statistical uncertainty on the observable. The Sim uncertainty on $R_{K/\pi}^{K\pi}$ is due to the limited size of the simulated samples used to determine the relative efficiency for reconstructing and selecting ${{{B}^{-}}}\rightarrow{D}{{\pi}^{-}}$ and ${{{B}^{-}}}\rightarrow{D}{{K}^{-}}$ decays.  [%] | $A_{K}^{K\pi}$ | $A_{\pi}^{KK}$ | $A_{K}^{KK}$ | $A_{\pi}^{\pi\pi}$ | $A_{K}^{\pi\pi}$ | $R^{KK}$ | $R^{\pi\pi}$ | $R_{K/\pi}^{K\pi}$
---|---|---|---|---|---|---|---|---
PID | 6.0 | 4.3 | 2.0 | 2.7 | 10.3 | 13.8 | 18.8 | 0.0
Bkg rate | 7.5 | 1.8 | 10.2 | 4.1 | 18.9 | 68.7 | 46.0 | 0.0
Bkg func | 7.6 | 0.4 | 4.2 | 0.4 | 7.2 | 9.5 | 16.7 | 0.0
Sig func | 11.1 | 0.9 | 0.8 | 0.9 | 14.3 | 7.9 | 20.9 | 0.0
Sim | 7.1 | 0.5 | 0.2 | 0.4 | 5.6 | 3.5 | 7.6 | 174.2
Asym | 37.4 | 52.7 | 3.7 | 31.2 | 2.3 | 0.1 | 0.1 | 0.0
Total | 41.5 | 52.9 | 11.9 | 31.6 | 27.5 | 71.2 | 56.9 | 174.2
Table 5: Systematic uncertainties for the branching fraction measurements, quoted as a percentage of the statistical uncertainty on the observable.  [%] | $\mathcal{B}({{D}^{*0}}\rightarrow{{D}^{0}}{{\pi}^{0}})$ | $\mathcal{B}({{{B}^{-}}}\rightarrow{{D}^{*0}}{{\pi}^{-}})$
---|---|---
PID | 85.3 | 117.7
Bkg rate | 364.4 | 672.1
Bkg func | 52.2 | 29.0
Sig func | 417.2 | 379.7
Sim | 295.4 | 509.3
Asym | 0.2 | 0.3
Total | 635.7 | 932.7

##  6 Results

The results are

$\displaystyle A_{K}^{K\pi,\gamma}$ $\displaystyle=\hskip 14.22636pt+0.001$
$\displaystyle\hskip 14.22636pt\pm 0.021\phantom{1}\text{$\mathrm{\,(stat)}$}$
$\displaystyle\hskip 14.22636pt\pm 0.007\phantom{1}\text{$\mathrm{\,(syst)}$}$
$\displaystyle A_{\pi}^{K\pi,\gamma}$ $\displaystyle=\hskip 14.22636pt+0.000$
$\displaystyle\hskip 14.22636pt\pm 0.006\phantom{1}\text{$\mathrm{\,(stat)}$}$
$\displaystyle\hskip 14.22636pt\pm 0.001\phantom{1}\text{$\mathrm{\,(syst)}$}$
$\displaystyle A_{K}^{K\pi,{{\pi}^{0}}}$ $\displaystyle=\hskip
14.22636pt+0.006$ $\displaystyle\hskip 14.22636pt\pm
0.012\phantom{1}\text{$\mathrm{\,(stat)}$}$ $\displaystyle\hskip 14.22636pt\pm
0.004\phantom{1}\text{$\mathrm{\,(syst)}$}$ $\displaystyle
A_{\pi}^{K\pi,{{\pi}^{0}}}$ $\displaystyle=\hskip 14.22636pt+0.002$
$\displaystyle\hskip 14.22636pt\pm 0.003\phantom{1}\text{$\mathrm{\,(stat)}$}$
$\displaystyle\hskip 14.22636pt\pm 0.001\phantom{1}\text{$\mathrm{\,(syst)}$}$
$\displaystyle A_{K}^{{C\\!P},\gamma}$ $\displaystyle=\hskip 14.22636pt+0.276$
$\displaystyle\hskip 14.22636pt\pm 0.094\phantom{1}\text{$\mathrm{\,(stat)}$}$
$\displaystyle\hskip 14.22636pt\pm 0.047\phantom{1}\text{$\mathrm{\,(syst)}$}$
$\displaystyle A_{\pi}^{{C\\!P},\gamma}$ $\displaystyle=\hskip
14.22636pt-0.003$ $\displaystyle\hskip 14.22636pt\pm
0.017\phantom{1}\text{$\mathrm{\,(stat)}$}$ $\displaystyle\hskip 14.22636pt\pm
0.002\phantom{1}\text{$\mathrm{\,(syst)}$}$ $\displaystyle
A_{K}^{{C\\!P},{{\pi}^{0}}}$ $\displaystyle=\hskip 14.22636pt-0.151$
$\displaystyle\hskip 14.22636pt\pm 0.033\phantom{1}\text{$\mathrm{\,(stat)}$}$
$\displaystyle\hskip 14.22636pt\pm 0.011\phantom{1}\text{$\mathrm{\,(syst)}$}$
$\displaystyle A_{\pi}^{{C\\!P},{{\pi}^{0}}}$ $\displaystyle=\hskip
14.22636pt+0.025$ $\displaystyle\hskip 14.22636pt\pm
0.010\phantom{1}\text{$\mathrm{\,(stat)}$}$ $\displaystyle\hskip 14.22636pt\pm
0.003\phantom{1}\text{$\mathrm{\,(syst)}$}$ $\displaystyle R^{{C\\!P},\gamma}$
$\displaystyle=\hskip 14.22636pt\phantom{+}0.902$ $\displaystyle\hskip
14.22636pt\pm 0.087\phantom{1}\text{$\mathrm{\,(stat)}$}$ $\displaystyle\hskip
14.22636pt\pm 0.112\phantom{1}\text{$\mathrm{\,(syst)}$}$ $\displaystyle
R^{{C\\!P},{{\pi}^{0}}}$ $\displaystyle=\hskip 14.22636pt\phantom{+}1.138$
$\displaystyle\hskip 14.22636pt\pm 0.029\phantom{1}\text{$\mathrm{\,(stat)}$}$
$\displaystyle\hskip 14.22636pt\pm 0.016\phantom{1}\text{$\mathrm{\,(syst)}$}$
$\displaystyle R_{K/\pi}^{K\pi,{{\pi}^{0}}/\gamma}$ $\displaystyle=\hskip
18.49411pt(7.930$ $\displaystyle\hskip 14.22636pt\pm
0.110\phantom{1}\text{$\mathrm{\,(stat)}$}$ $\displaystyle\hskip 14.22636pt\pm
0.560\phantom{1}\text{$\mathrm{\,(syst)}$})\times 10^{-2}$
$\displaystyle\mathcal{B}({{D}^{*0}}\rightarrow{{D}^{0}}{{\pi}^{0}})$
$\displaystyle=\hskip 14.22636pt\phantom{+}0.636$ $\displaystyle\hskip
14.22636pt\pm 0.002\phantom{1}\text{$\mathrm{\,(stat)}$}$ $\displaystyle\hskip
14.22636pt\pm 0.015\phantom{1}\text{$\mathrm{\,(syst)}$}$
$\displaystyle\mathcal{B}({{{B}^{-}}}\rightarrow{{D}^{*0}}{{\pi}^{-}})$
$\displaystyle=\hskip 18.49411pt(4.664$ $\displaystyle\hskip 14.22636pt\pm
0.029\phantom{1}\text{$\mathrm{\,(stat)}$}$ $\displaystyle\hskip 14.22636pt\pm
0.268\phantom{1}\text{$\mathrm{\,(syst)}$})\times 10^{-3}$ $\displaystyle
A_{K}^{K\pi}$ $\displaystyle=\hskip 14.22636pt-0.019$ $\displaystyle\hskip
14.22636pt\pm 0.005\phantom{1}\text{$\mathrm{\,(stat)}$}$ $\displaystyle\hskip
14.22636pt\pm 0.002\phantom{1}\text{$\mathrm{\,(syst)}$}$ $\displaystyle
A_{\pi}^{KK}$ $\displaystyle=\hskip 14.22636pt-0.008$ $\displaystyle\hskip
14.22636pt\pm 0.003\phantom{1}\text{$\mathrm{\,(stat)}$}$ $\displaystyle\hskip
14.22636pt\pm 0.002\phantom{1}\text{$\mathrm{\,(syst)}$}$ $\displaystyle
A_{K}^{KK}$ $\displaystyle=\hskip 14.22636pt+0.126$ $\displaystyle\hskip
14.22636pt\pm 0.014\phantom{1}\text{$\mathrm{\,(stat)}$}$ $\displaystyle\hskip
14.22636pt\pm 0.002\phantom{1}\text{$\mathrm{\,(syst)}$}$ $\displaystyle
A_{\pi}^{\pi\pi}$ $\displaystyle=\hskip 14.22636pt-0.008$ $\displaystyle\hskip
14.22636pt\pm 0.006\phantom{1}\text{$\mathrm{\,(stat)}$}$ $\displaystyle\hskip
14.22636pt\pm 0.002\phantom{1}\text{$\mathrm{\,(syst)}$}$ $\displaystyle
A_{K}^{\pi\pi}$ $\displaystyle=\hskip 14.22636pt+0.115$ $\displaystyle\hskip
14.22636pt\pm 0.025\phantom{1}\text{$\mathrm{\,(stat)}$}$ $\displaystyle\hskip
14.22636pt\pm 0.007\phantom{1}\text{$\mathrm{\,(syst)}$}$ $\displaystyle
R^{KK}$ $\displaystyle=\hskip 14.22636pt\phantom{+}0.988$ $\displaystyle\hskip
14.22636pt\pm 0.015\phantom{1}\text{$\mathrm{\,(stat)}$}$ $\displaystyle\hskip
14.22636pt\pm 0.011\phantom{1}\text{$\mathrm{\,(syst)}$}$ $\displaystyle
R^{\pi\pi}$ $\displaystyle=\hskip 14.22636pt\phantom{+}0.992$
$\displaystyle\hskip 14.22636pt\pm 0.027\phantom{1}\text{$\mathrm{\,(stat)}$}$
$\displaystyle\hskip 14.22636pt\pm 0.015\phantom{1}\text{$\mathrm{\,(syst)}$}$
$\displaystyle R_{K/\pi}^{K\pi}$ $\displaystyle=\hskip 18.49411pt(7.768$
$\displaystyle\hskip 14.22636pt\pm 0.038\phantom{1}\text{$\mathrm{\,(stat)}$}$
$\displaystyle\hskip 14.22636pt\pm
0.066\phantom{1}\text{$\mathrm{\,(syst)}$})\times 10^{-2}\,.$

The results obtained using fully reconstructed
${{{B}^{-}}}\rightarrow{D}h^{-}$ decays supersede those in Ref. [13], while
the ${{{B}^{-}}}\rightarrow{{D}^{*}}h^{-}$ results are reported for the first
time. The statistical and systematic correlation matrices are given in the
appendix. There is a high degree of anticorrelation between partially
reconstructed signal and background components in the fit, which all compete
for yield in the same invariant mass region. The anticorrelation between the
$B^{-}\rightarrow({D}\pi^{0})_{{{D}^{*}}}h^{-}$ and
$B^{-}\rightarrow({D}\gamma)_{{{D}^{*}}}h^{-}$ $C\\!P$ observables is visible
in Table 6 of the appendix. The presence of such anticorrelations is a natural
consequence of the method of partial reconstruction, and limits the precision
with which the $C\\!P$ observables can be measured using this approach.

The value of $A_{K}^{KK}$ has increased with respect to the previous result
[13], due to a larger value being measured in the
$\sqrt{s}=13$$\mathrm{\,Te\kern-1.00006ptV}$ data. The values measured in the
independent $\sqrt{s}=$ 7, 8 and 13$\mathrm{\,Te\kern-1.00006ptV}$ data sets
are consistent within 2.6 standard deviations. All other updated measurements
are consistent within one standard deviation with those in Ref. [13].

Observables involving ${D}\rightarrow{{K}^{+}}{{K}^{-}}$ and
${D}\rightarrow{{\pi}^{+}}{{\pi}^{-}}$ decays can differ due to $C\\!P$
violation in the $D$ decays or acceptance effects. The latest LHCb results
[47] show that charm $C\\!P$-violation effects are negligible for the
determination of $\gamma$, and that there is also no significant difference in
the acceptance for the two modes. Therefore, while separate results are
presented for the ${{{B}^{-}}}\rightarrow{D}h^{-}$ modes to allow comparison
with previous measurements, the combined result is most relevant for the
determination of $\gamma$. The $R^{KK}$ and $R^{\pi\pi}$ observables have
statistical and systematic correlations of +0.07 and +0.18, respectively.
Taking these correlations into account, a combined weighted average
$R^{{C\\!P}}$ is obtained

$\displaystyle R^{{C\\!P}}=0.989\pm 0.013\mathrm{\,(stat)}\pm
0.010\mathrm{\,(syst)}\,.$

The same procedure is carried out for the $A_{K}^{KK}$ and $A_{K}^{\pi\pi}$
observables, which have statistical and systematic correlations of +0.01 and
+0.05, respectively. The combined average is

$\displaystyle A_{K}^{{C\\!P}}=+0.124\pm 0.012\mathrm{\,(stat)}\pm
0.002\mathrm{\,(syst)}\,.$

The observables $R^{{C\\!P},{{\pi}^{0}}}$ and $A^{{C\\!P},{{\pi}^{0}}}$
($R^{{C\\!P},\gamma}$ and $A^{{C\\!P},\gamma}$), measured using partially
reconstructed ${{{B}^{-}}}\rightarrow{{D}^{*}}h^{-}$ decays, can be directly
compared with the world average values for $R_{{C\\!P}+}\equiv
R^{{C\\!P},{{\pi}^{0}}}$ and $A_{{C\\!P}+}\equiv A^{{C\\!P},{{\pi}^{0}}}$
($R_{{C\\!P}-}\equiv R^{{C\\!P},\gamma}$ and $A_{{C\\!P}-}\equiv
A^{{C\\!P},\gamma}$) reported by the Heavy Flavor Averaging Group [4];
agreement is found at the level of 1.5 and 0.4 (1.1 and 1.4) standard
deviations, respectively. The values of $R^{{C\\!P},{{\pi}^{0}}}$ and
$A^{{C\\!P},{{\pi}^{0}}}$ considerably improve upon the world average
precision of $R_{{C\\!P}+}$ and $A_{{C\\!P}+}$, while the measurements of
$R^{{C\\!P},\gamma}$ and $A^{{C\\!P},\gamma}$ have a precision comparable to
the previous world average.

The value of $R_{K/\pi}^{K\pi,{{\pi}^{0}}/\gamma}$ is in agreement with, and
substantially more precise than, the current world average [31, 36, 48]. The
branching fraction measurements of
$\mathcal{B}({{D}^{*0}}\rightarrow{{D}^{0}}{{\pi}^{0}})$ and
$\mathcal{B}({{{B}^{-}}}\rightarrow{{D}^{*0}}{{\pi}^{-}})$ are found to agree
with the current world average values within 0.6 and 1.3 standard deviations,
respectively [31, 49, 36]. A value for the ratio of branching fractions
$\frac{\mathcal{B}({{{B}^{-}}}\rightarrow{{D}^{*0}}{{K}^{-}})}{\mathcal{B}({{{B}^{-}}}\rightarrow{{D}^{0}}{{K}^{-}})}$
is also obtained using the measured results

$\frac{\mathcal{B}({{{B}^{-}}}\rightarrow{{D}^{*0}}{{K}^{-}})}{\mathcal{B}({{{B}^{-}}}\rightarrow{{D}^{0}}{{K}^{-}})}=\frac{R_{K/\pi}^{K\pi,{{\pi}^{0}}/\gamma}}{R_{K/\pi}^{K\pi}}\times\frac{\mathcal{B}({{{B}^{-}}}\rightarrow{{D}^{*0}}{{\pi}^{-}})}{\mathcal{B}({{{B}^{-}}}\rightarrow{{D}^{0}}{{\pi}^{-}})}=0.992\pm
0.077\,,$ (5)

where the uncertainty quoted is dominated by systematic uncertainties, and the
statistical and systematic correlations between the input observables are
fully taken into account. This value is in agreement with, and improves upon,
the current world average. The ratios $R_{K/\pi}^{K\pi}$ and
$R_{K/\pi}^{K\pi,{{\pi}^{0}}/\gamma}$ can be interpreted as
${{{B}^{-}}}\rightarrow D^{(*)0}{{K}^{-}}/{{{B}^{-}}}\rightarrow
D^{(*)0}{{\pi}^{-}}$ branching fraction ratios, in the limit that the
suppressed contributions are neglected, which is the same assumption that is
made when reporting the results for
$\mathcal{B}({{{B}^{-}}}\rightarrow{{D}^{*0}}{{\pi}^{-}})$ and
$\frac{\mathcal{B}({{{B}^{-}}}\rightarrow{{D}^{*0}}{{K}^{-}})}{\mathcal{B}({{{B}^{-}}}\rightarrow{{D}^{0}}{{K}^{-}})}$.
The branching fraction measurements demonstrate that the method of partial
reconstruction is able to measure the
${{{B}^{-}}}\rightarrow({D}{{\pi}^{0}})_{{{D}^{*}}}h^{-}$ and
${{{B}^{-}}}\rightarrow({D}\gamma)_{{{D}^{*}}}h^{-}$ signals, despite the
correlations present in the mass fit.

##  7 Conclusion

World-best measurements of $C\\!P$ observables in
${{{B}^{-}}}\rightarrow{D}h^{-}$ decays are obtained with the $D$ meson
reconstructed in the ${{K}^{-}}{{\pi}^{+}}$, ${{K}^{+}}{{K}^{-}}$ and
${{\pi}^{+}}{{\pi}^{-}}$ final states; these supersede earlier work on the GLW
modes presented in Ref. [13]. Studies of partially reconstructed
${{{B}^{-}}}\rightarrow{{D}^{*}}h^{-}$ decays are also reported for the first
time, where the measurements of $C\\!P$ observables in
${{{B}^{-}}}\rightarrow({D}\gamma)_{{{D}^{*}}}{{K}^{-}}$ decays are comparable
in precision to the current world averages; the equivalent observables
measured in ${{{B}^{-}}}\rightarrow({D}{{\pi}^{0}})_{{{D}^{*}}}{{K}^{-}}$
decays substantially improve upon the world averages. Evidence of $C\\!P$
violation in ${{{B}^{-}}}\rightarrow({D}{{\pi}^{0}})_{{{D}^{*}}}{{K}^{-}}$
decays is found with a statistical significance of 4.3 standard deviations,
while the significance of a nonzero value of $A_{K}^{{C\\!P},\gamma}$ is 2.4
standard deviations. The ${{K}^{-}}{{\pi}^{+}}$ final state, which offers
higher sensitivity to $\gamma$ due to larger interference effects [50], has
not been considered in this work, due to the presence of a large background
contribution from the poorly understood ${{\kern
1.79993pt\overline{\kern-1.79993ptB}{}}{}^{0}_{s}}\rightarrow
D^{*0}{{K}^{+}}{{\pi}^{-}}$ decay.

Using the observables $A_{K}^{K\pi,\gamma}$, $A_{K}^{K\pi,{{\pi}^{0}}}$,
$A_{K}^{{C\\!P},\gamma}$, $A_{K}^{{C\\!P},{{\pi}^{0}}}$, $R^{{C\\!P},\gamma}$
and $R^{{C\\!P},{{\pi}^{0}}}$ as input, a derivation of the fundamental
parameters $r_{B}^{D^{*}\\!K}$, $\delta_{B}^{D^{*}\\!K}$ and $\gamma$ has been
performed using the approach detailed in Ref. [3]. The profile likelihood
contours at $1\sigma$, $2\sigma$ and $3\sigma$ are shown in Fig. 4. The
preferred values of $r_{B}^{D^{*}\\!K}$ are lower than the current world
average values, owing to the fact that the values of $R^{{C\\!P},\gamma}$ and
$R^{{C\\!P},{{\pi}^{0}}}$ measured in this work are below and above unity,
respectively, in contrast to the world averages which are both larger than
unity [4]. The preferred values of $\gamma$ and $\delta_{B}^{D^{*}\\!K}$ are
consistent within 1 standard deviation with the LHCb combination [3] and the
world average.

Figure 4: $1\sigma$, $2\sigma$ and $3\sigma$ profile likelihood contours for
$r_{B}^{D^{*}\\!K}$, $\delta_{B}^{D^{*}\\!K}$ and $\gamma$, corresponding to
68.3%, 95.5% and 99.7% confidence level (CL), respectively. The contours are
measured using ${{{B}^{-}}}\rightarrow({D}{{\pi}^{0}})_{{{D}^{*}}}{{K}^{-}}$
and ${{{B}^{-}}}\rightarrow({D}\gamma)_{{{D}^{*}}}{{K}^{-}}$ decays. The
colour scale represents $1-\text{CL}$.

## Acknowledgements

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

## Appendix: Correlation matrices

The statistical uncertainty correlation matrices are given in Tables 6 and 7
for the $C\\!P$ observables measured using partially reconstructed and fully
reconstructed decays, respectively. The correlations between the systematic
uncertainties are provided in Tables 8 and 9.

Table 6: Statistical correlation matrix for the $C\\!P$ observables measured using partially reconstructed decays.  | $A_{K}^{K\pi,\gamma}$ | $A_{\pi}^{K\pi,\gamma}$ | $A_{K}^{K\pi,{{\pi}^{0}}}$ | $A_{\pi}^{K\pi,{{\pi}^{0}}}$ | $A_{K}^{{C\\!P},\gamma}$ | $A_{\pi}^{{C\\!P},\gamma}$ | $A_{K}^{{C\\!P},{{\pi}^{0}}}$ | $A_{\pi}^{{C\\!P},{{\pi}^{0}}}$ | $R^{{C\\!P},\gamma}$ | $R^{{C\\!P},{{\pi}^{0}}}$ | $R_{K/\pi}^{K\pi,{{\pi}^{0}}/\gamma}$
---|---|---|---|---|---|---|---|---|---|---|---
$A_{K}^{K\pi,\gamma}$ |  $-$1.00 |  $-$0.00 |  $-$0.61 |  $-$0.01 |  $-$0.00 |  $-$0.00 |  $-$0.00 |  $-$0.01 |  $-$0.00 |  $-$0.00 |  $-$0.00
$A_{\pi}^{K\pi,\gamma}$ |  $-$0.00 |  $-$1.00 |  $-$0.04 |  $-$0.21 |  $-$0.00 |  $-$0.01 |  $-$0.01 |  $-$0.02 |  $-$0.00 |  $-$0.00 |  $-$0.01
$A_{K}^{K\pi,{{\pi}^{0}}}$ |  $-$0.61 |  $-$0.04 |  $-$1.00 |  $-$0.08 |  $-$0.00 |  $-$0.01 |  $-$0.01 |  $-$0.02 |  $-$0.00 |  $-$0.00 |  $-$0.00
$A_{\pi}^{K\pi,{{\pi}^{0}}}$ |  $-$0.01 |  $-$0.21 |  $-$0.08 |  $-$1.00 |  $-$0.01 |  $-$0.02 |  $-$0.02 |  $-$0.06 |  $-$0.00 |  $-$0.00 |  $-$0.01
$A_{K}^{{C\\!P},\gamma}$ |  $-$0.00 |  $-$0.00 |  $-$0.00 |  $-$0.01 |  $-$1.00 |  $-$0.03 |  $-$0.21 |  $-$0.02 |  $-$0.27 |  $-$0.08 |  $-$0.01
$A_{\pi}^{{C\\!P},\gamma}$ |  $-$0.00 |  $-$0.01 |  $-$0.01 |  $-$0.02 |  $-$0.03 |  $-$1.00 |  $-$0.02 |  $-$0.03 |  $-$0.01 |  $-$0.00 |  $-$0.00
$A_{K}^{{C\\!P},{{\pi}^{0}}}$ |  $-$0.00 |  $-$0.01 |  $-$0.01 |  $-$0.02 |  $-$0.21 |  $-$0.02 |  $-$1.00 |  $-$0.04 |  $-$0.07 |  $-$0.12 |  $-$0.02
$A_{\pi}^{{C\\!P},{{\pi}^{0}}}$ |  $-$0.01 |  $-$0.02 |  $-$0.02 |  $-$0.06 |  $-$0.02 |  $-$0.03 |  $-$0.04 |  $-$1.00 |  $-$0.01 |  $-$0.00 |  $-$0.01
$R^{{C\\!P},\gamma}$ |  $-$0.00 |  $-$0.00 |  $-$0.00 |  $-$0.00 |  $-$0.27 |  $-$0.01 |  $-$0.07 |  $-$0.01 |  $-$1.00 |  $-$0.26 |  $-$0.14
$R^{{C\\!P},{{\pi}^{0}}}$ |  $-$0.00 |  $-$0.00 |  $-$0.00 |  $-$0.00 |  $-$0.08 |  $-$0.00 |  $-$0.12 |  $-$0.00 |  $-$0.26 |  $-$1.00 |  $-$0.15
$R_{K/\pi}^{K\pi,{{\pi}^{0}}/\gamma}$ |  $-$0.00 |  $-$0.01 |  $-$0.00 |  $-$0.01 |  $-$0.01 |  $-$0.00 |  $-$0.02 |  $-$0.01 |  $-$0.14 |  $-$0.15 |  $-$1.00
Table 7: Statistical correlation matrix for the $C\\!P$ observables measured using fully reconstructed decays.  | $A_{K}^{K\pi}$ | $A_{\pi}^{KK}$ | $A_{K}^{KK}$ | $A_{\pi}^{\pi\pi}$ | $A_{K}^{\pi\pi}$ | $R^{KK}$ | $R^{\pi\pi}$ | $R_{K/\pi}^{K\pi}$
---|---|---|---|---|---|---|---|---
$A_{K}^{K\pi}$ |  $-$1.00 |  $-$0.09 |  $-$0.02 |  $-$0.05 |  $-$0.01 |  $-$0.00 |  $-$0.00 |  $-$0.00
$A_{\pi}^{KK}$ |  $-$0.09 |  $-$1.00 |  $-$0.00 |  $-$0.06 |  $-$0.02 |  $-$0.00 |  $-$0.00 |  $-$0.00
$A_{K}^{KK}$ |  $-$0.02 |  $-$0.00 |  $-$1.00 |  $-$0.02 |  $-$0.01 |  $-$0.02 |  $-$0.00 |  $-$0.00
$A_{\pi}^{\pi\pi}$ |  $-$0.05 |  $-$0.06 |  $-$0.02 |  $-$1.00 |  $-$0.03 |  $-$0.00 |  $-$0.00 |  $-$0.00
$A_{K}^{\pi\pi}$ |  $-$0.01 |  $-$0.02 |  $-$0.01 |  $-$0.03 |  $-$1.00 |  $-$0.00 |  $-$0.03 |  $-$0.00
$R^{KK}$ |  $-$0.00 |  $-$0.00 |  $-$0.02 |  $-$0.00 |  $-$0.00 |  $-$1.00 |  $-$0.07 |  $-$0.31
$R^{\pi\pi}$ |  $-$0.00 |  $-$0.00 |  $-$0.00 |  $-$0.00 |  $-$0.03 |  $-$0.07 |  $-$1.00 |  $-$0.17
$R_{K/\pi}^{K\pi}$ |  $-$0.00 |  $-$0.00 |  $-$0.00 |  $-$0.00 |  $-$0.00 |  $-$0.31 |  $-$0.17 |  $-$1.00
Table 8: Systematic uncertainty correlation matrix for the $C\\!P$ observables measured using partially reconstructed decays.  | $A_{K}^{K\pi,\gamma}$ | $A_{\pi}^{K\pi,\gamma}$ | $A_{K}^{K\pi,{{\pi}^{0}}}$ | $A_{\pi}^{K\pi,{{\pi}^{0}}}$ | $A_{K}^{{C\\!P},\gamma}$ | $A_{\pi}^{{C\\!P},\gamma}$ | $A_{K}^{{C\\!P},{{\pi}^{0}}}$ | $A_{\pi}^{{C\\!P},{{\pi}^{0}}}$ | $R^{{C\\!P},\gamma}$ | $R^{{C\\!P},{{\pi}^{0}}}$ | $R_{K/\pi}^{K\pi,{{\pi}^{0}}/\gamma}$
---|---|---|---|---|---|---|---|---|---|---|---
$A_{K}^{K\pi,\gamma}$ |  $-$1.00 |  $-$0.02 |  $-$0.76 |  $-$0.01 |  $-$0.01 |  $-$0.22 |  $-$0.16 |  $-$0.24 |  $-$0.04 |  $-$0.12 |  $-$0.11
$A_{\pi}^{K\pi,\gamma}$ |  $-$0.02 |  $-$1.00 |  $-$0.03 |  $-$0.61 |  $-$0.02 |  $-$0.06 |  $-$0.03 |  $-$0.21 |  $-$0.01 |  $-$0.02 |  $-$0.05
$A_{K}^{K\pi,{{\pi}^{0}}}$ |  $-$0.76 |  $-$0.03 |  $-$1.00 |  $-$0.14 |  $-$0.01 |  $-$0.46 |  $-$0.08 |  $-$0.55 |  $-$0.01 |  $-$0.03 |  $-$0.08
$A_{\pi}^{K\pi,{{\pi}^{0}}}$ |  $-$0.01 |  $-$0.61 |  $-$0.14 |  $-$1.00 |  $-$0.02 |  $-$0.25 |  $-$0.00 |  $-$0.31 |  $-$0.00 |  $-$0.00 |  $-$0.05
$A_{K}^{{C\\!P},\gamma}$ |  $-$0.01 |  $-$0.02 |  $-$0.01 |  $-$0.02 |  $-$1.00 |  $-$0.04 |  $-$0.24 |  $-$0.02 |  $-$0.90 |  $-$0.47 |  $-$0.02
$A_{\pi}^{{C\\!P},\gamma}$ |  $-$0.22 |  $-$0.06 |  $-$0.46 |  $-$0.25 |  $-$0.04 |  $-$1.00 |  $-$0.12 |  $-$0.82 |  $-$0.02 |  $-$0.03 |  $-$0.10
$A_{K}^{{C\\!P},{{\pi}^{0}}}$ |  $-$0.16 |  $-$0.03 |  $-$0.08 |  $-$0.00 |  $-$0.24 |  $-$0.12 |  $-$1.00 |  $-$0.07 |  $-$0.14 |  $-$0.15 |  $-$0.73
$A_{\pi}^{{C\\!P},{{\pi}^{0}}}$ |  $-$0.24 |  $-$0.21 |  $-$0.55 |  $-$0.31 |  $-$0.02 |  $-$0.82 |  $-$0.07 |  $-$1.00 |  $-$0.00 |  $-$0.04 |  $-$0.01
$R^{{C\\!P},\gamma}$ |  $-$0.04 |  $-$0.01 |  $-$0.01 |  $-$0.00 |  $-$0.90 |  $-$0.02 |  $-$0.14 |  $-$0.00 |  $-$1.00 |  $-$0.62 |  $-$0.06
$R^{{C\\!P},{{\pi}^{0}}}$ |  $-$0.12 |  $-$0.02 |  $-$0.03 |  $-$0.00 |  $-$0.47 |  $-$0.03 |  $-$0.15 |  $-$0.04 |  $-$0.62 |  $-$1.00 |  $-$0.00
$R_{K/\pi}^{K\pi,{{\pi}^{0}}/\gamma}$ |  $-$0.11 |  $-$0.05 |  $-$0.08 |  $-$0.05 |  $-$0.02 |  $-$0.10 |  $-$0.73 |  $-$0.01 |  $-$0.06 |  $-$0.00 |  $-$1.00
Table 9: Systematic uncertainty correlation matrix for the $C\\!P$ observables measured using fully reconstructed decays.  | $A_{K}^{K\pi}$ | $A_{\pi}^{KK}$ | $A_{K}^{KK}$ | $A_{\pi}^{\pi\pi}$ | $A_{K}^{\pi\pi}$ | $R^{KK}$ | $R^{\pi\pi}$ | $R_{K/\pi}^{K\pi}$
---|---|---|---|---|---|---|---|---
$A_{K}^{K\pi}$ |  $-$1.00 |  $-$0.75 |  $-$0.07 |  $-$0.75 |  $-$0.01 |  $-$0.03 |  $-$0.02 |  $-$0.15
$A_{\pi}^{KK}$ |  $-$0.75 |  $-$1.00 |  $-$0.08 |  $-$0.99 |  $-$0.05 |  $-$0.01 |  $-$0.01 |  $-$0.24
$A_{K}^{KK}$ |  $-$0.07 |  $-$0.08 |  $-$1.00 |  $-$0.11 |  $-$0.05 |  $-$0.48 |  $-$0.12 |  $-$0.20
$A_{\pi}^{\pi\pi}$ |  $-$0.75 |  $-$0.99 |  $-$0.11 |  $-$1.00 |  $-$0.02 |  $-$0.00 |  $-$0.01 |  $-$0.24
$A_{K}^{\pi\pi}$ |  $-$0.01 |  $-$0.05 |  $-$0.05 |  $-$0.02 |  $-$1.00 |  $-$0.01 |  $-$0.21 |  $-$0.07
$R^{KK}$ |  $-$0.03 |  $-$0.01 |  $-$0.48 |  $-$0.00 |  $-$0.01 |  $-$1.00 |  $-$0.18 |  $-$0.01
$R^{\pi\pi}$ |  $-$0.02 |  $-$0.01 |  $-$0.12 |  $-$0.01 |  $-$0.21 |  $-$0.18 |  $-$1.00 |  $-$0.04
$R_{K/\pi}^{K\pi}$ |  $-$0.15 |  $-$0.24 |  $-$0.20 |  $-$0.24 |  $-$0.07 |  $-$0.01 |  $-$0.04 |  $-$1.00

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LHCb collaboration

R. Aaij40, B. Adeva39, M. Adinolfi48, Z. Ajaltouni5, S. Akar59, J. Albrecht10,
F. Alessio40, M. Alexander53, A. Alfonso Albero38, S. Ali43, G. Alkhazov31, P.
Alvarez Cartelle55, A.A. Alves Jr59, S. Amato2, S. Amerio23, Y. Amhis7, L.
An3, L. Anderlini18, G. Andreassi41, M. Andreotti17,g, J.E. Andrews60, R.B.
Appleby56, F. Archilli43, P. d’Argent12, J. Arnau Romeu6, A. Artamonov37, M.
Artuso61, E. Aslanides6, G. Auriemma26, M. Baalouch5, I. Babuschkin56, S.
Bachmann12, J.J. Back50, A. Badalov38,m, C. Baesso62, S. Baker55, V.
Balagura7,b, W. Baldini17, A. Baranov35, R.J. Barlow56, C. Barschel40, S.
Barsuk7, W. Barter56, F. Baryshnikov32, V. Batozskaya29, V. Battista41, A.
Bay41, L. Beaucourt4, J. Beddow53, F. Bedeschi24, I. Bediaga1, A. Beiter61,
L.J. Bel43, N. Beliy63, V. Bellee41, N. Belloli21,i, K. Belous37, I.
Belyaev32, E. Ben-Haim8, G. Bencivenni19, S. Benson43, S. Beranek9, A.
Berezhnoy33, R. Bernet42, D. Berninghoff12, E. Bertholet8, A. Bertolin23, C.
Betancourt42, F. Betti15, M.-O. Bettler40, M. van Beuzekom43, Ia. Bezshyiko42,
S. Bifani47, P. Billoir8, A. Birnkraut10, A. Bitadze56, A. Bizzeti18,u, M.
Bjørn57, T. Blake50, F. Blanc41, J. Blouw11,†, S. Blusk61, V. Bocci26, T.
Boettcher58, A. Bondar36,w, N. Bondar31, W. Bonivento16, I. Bordyuzhin32, A.
Borgheresi21,i, S. Borghi56, M. Borisyak35, M. Borsato39, F. Bossu7, M.
Boubdir9, T.J.V. Bowcock54, E. Bowen42, C. Bozzi17,40, S. Braun12, T.
Britton61, J. Brodzicka27, D. Brundu16, E. Buchanan48, C. Burr56, A.
Bursche16,f, J. Buytaert40, W. Byczynski40, S. Cadeddu16, H. Cai64, R.
Calabrese17,g, R. Calladine47, M. Calvi21,i, M. Calvo Gomez38,m, A.
Camboni38,m, P. Campana19, D.H. Campora Perez40, L. Capriotti56, A.
Carbone15,e, G. Carboni25,j, R. Cardinale20,h, A. Cardini16, P. Carniti21,i,
L. Carson52, K. Carvalho Akiba2, G. Casse54, L. Cassina21, L. Castillo
Garcia41, M. Cattaneo40, G. Cavallero20,40,h, R. Cenci24,t, D. Chamont7, M.
Charles8, Ph. Charpentier40, G. Chatzikonstantinidis47, M. Chefdeville4, S.
Chen56, S.F. Cheung57, S.-G. Chitic40, V. Chobanova39, M. Chrzaszcz42,27, A.
Chubykin31, P. Ciambrone19, X. Cid Vidal39, G. Ciezarek43, P.E.L. Clarke52, M.
Clemencic40, H.V. Cliff49, J. Closier40, J. Cogan6, E. Cogneras5, V.
Cogoni16,f, L. Cojocariu30, P. Collins40, T. Colombo40, A. Comerma-Montells12,
A. Contu40, A. Cook48, G. Coombs40, S. Coquereau38, G. Corti40, M. Corvo17,g,
C.M. Costa Sobral50, B. Couturier40, G.A. Cowan52, D.C. Craik58, A.
Crocombe50, M. Cruz Torres1, R. Currie52, C. D’Ambrosio40, F. Da Cunha
Marinho2, E. Dall’Occo43, J. Dalseno48, A. Davis3, O. De Aguiar Francisco54,
S. De Capua56, M. De Cian12, J.M. De Miranda1, L. De Paula2, M. De Serio14,d,
P. De Simone19, C.T. Dean53, D. Decamp4, L. Del Buono8, H.-P. Dembinski11, M.
Demmer10, A. Dendek28, D. Derkach35, O. Deschamps5, F. Dettori54, B. Dey65, A.
Di Canto40, P. Di Nezza19, H. Dijkstra40, F. Dordei40, M. Dorigo40, A. Dosil
Suárez39, L. Douglas53, A. Dovbnya45, K. Dreimanis54, L. Dufour43, G. Dujany8,
P. Durante40, R. Dzhelyadin37, M. Dziewiecki12, A. Dziurda40, A. Dzyuba31, S.
Easo51, M. Ebert52, U. Egede55, V. Egorychev32, S. Eidelman36,w, S.
Eisenhardt52, U. Eitschberger10, R. Ekelhof10, L. Eklund53, S. Ely61, S.
Esen12, H.M. Evans49, T. Evans57, A. Falabella15, N. Farley47, S. Farry54, R.
Fay54, D. Fazzini21,i, L. Federici25, D. Ferguson52, G. Fernandez38, P.
Fernandez Declara40, A. Fernandez Prieto39, F. Ferrari15, F. Ferreira
Rodrigues2, M. Ferro-Luzzi40, S. Filippov34, R.A. Fini14, M. Fiore17,g, M.
Fiorini17,g, M. Firlej28, C. Fitzpatrick41, T. Fiutowski28, F. Fleuret7,b, K.
Fohl40, M. Fontana16,40, F. Fontanelli20,h, D.C. Forshaw61, R. Forty40, V.
Franco Lima54, M. Frank40, C. Frei40, J. Fu22,q, W. Funk40, E. Furfaro25,j, C.
Färber40, E. Gabriel52, A. Gallas Torreira39, D. Galli15,e, S. Gallorini23, S.
Gambetta52, M. Gandelman2, P. Gandini57, Y. Gao3, L.M. Garcia Martin70, J.
García Pardiñas39, J. Garra Tico49, L. Garrido38, P.J. Garsed49, D. Gascon38,
C. Gaspar40, L. Gavardi10, G. Gazzoni5, D. Gerick12, E. Gersabeck12, M.
Gersabeck56, T. Gershon50, Ph. Ghez4, S. Gianì41, V. Gibson49, O.G. Girard41,
L. Giubega30, K. Gizdov52, V.V. Gligorov8, D. Golubkov32, A. Golutvin55,40, A.
Gomes1,a, I.V. Gorelov33, C. Gotti21,i, E. Govorkova43, J.P. Grabowski12, R.
Graciani Diaz38, L.A. Granado Cardoso40, E. Graugés38, E. Graverini42, G.
Graziani18, A. Grecu30, R. Greim9, P. Griffith16, L. Grillo21,40,i, L.
Gruber40, B.R. Gruberg Cazon57, O. Grünberg67, E. Gushchin34, Yu. Guz37, T.
Gys40, C. Göbel62, T. Hadavizadeh57, C. Hadjivasiliou5, G. Haefeli41, C.
Haen40, S.C. Haines49, B. Hamilton60, X. Han12, T.H. Hancock57, S. Hansmann-
Menzemer12, N. Harnew57, S.T. Harnew48, J. Harrison56, C. Hasse40, M. Hatch40,
J. He63, M. Hecker55, K. Heinicke10, A. Heister9, K. Hennessy54, P. Henrard5,
L. Henry70, E. van Herwijnen40, M. Heß67, A. Hicheur2, D. Hill57, C.
Hombach56, P.H. Hopchev41, Z.C. Huard59, W. Hulsbergen43, T. Humair55, M.
Hushchyn35, D. Hutchcroft54, P. Ibis10, M. Idzik28, P. Ilten58, R.
Jacobsson40, J. Jalocha57, E. Jans43, A. Jawahery60, F. Jiang3, M. John57, D.
Johnson40, C.R. Jones49, C. Joram40, B. Jost40, N. Jurik57, S. Kandybei45, M.
Karacson40, J.M. Kariuki48, S. Karodia53, N. Kazeev35, M. Kecke12, M.
Kelsey61, M. Kenzie49, T. Ketel44, E. Khairullin35, B. Khanji12, C.
Khurewathanakul41, T. Kirn9, S. Klaver56, K. Klimaszewski29, T. Klimkovich11,
S. Koliiev46, M. Kolpin12, I. Komarov41, R. Kopecna12, P. Koppenburg43, A.
Kosmyntseva32, S. Kotriakhova31, M. Kozeiha5, L. Kravchuk34, M. Kreps50, P.
Krokovny36,w, F. Kruse10, W. Krzemien29, W. Kucewicz27,l, M. Kucharczyk27, V.
Kudryavtsev36,w, A.K. Kuonen41, K. Kurek29, T. Kvaratskheliya32,40, D.
Lacarrere40, G. Lafferty56, A. Lai16, G. Lanfranchi19, C. Langenbruch9, T.
Latham50, C. Lazzeroni47, R. Le Gac6, A. Leflat33,40, J. Lefrançois7, R.
Lefèvre5, F. Lemaitre40, E. Lemos Cid39, O. Leroy6, T. Lesiak27, B.
Leverington12, P.-R. Li63, T. Li3, Y. Li7, Z. Li61, T. Likhomanenko68, R.
Lindner40, F. Lionetto42, V. Lisovskyi7, X. Liu3, D. Loh50, A. Loi16, I.
Longstaff53, J.H. Lopes2, D. Lucchesi23,o, M. Lucio Martinez39, H. Luo52, A.
Lupato23, E. Luppi17,g, O. Lupton40, A. Lusiani24, X. Lyu63, F. Machefert7, F.
Maciuc30, V. Macko41, P. Mackowiak10, S. Maddrell-Mander48, O. Maev31,40, K.
Maguire56, D. Maisuzenko31, M.W. Majewski28, S. Malde57, A. Malinin68, T.
Maltsev36,w, G. Manca16,f, G. Mancinelli6, P. Manning61, D. Marangotto22,q, J.
Maratas5,v, J.F. Marchand4, U. Marconi15, C. Marin Benito38, M. Marinangeli41,
P. Marino41, J. Marks12, G. Martellotti26, M. Martin6, M. Martinelli41, D.
Martinez Santos39, F. Martinez Vidal70, D. Martins Tostes2, L.M. Massacrier7,
A. Massafferri1, R. Matev40, A. Mathad50, Z. Mathe40, C. Matteuzzi21, A.
Mauri42, E. Maurice7,b, B. Maurin41, A. Mazurov47, M. McCann55,40, A. McNab56,
R. McNulty13, J.V. Mead54, B. Meadows59, C. Meaux6, F. Meier10, N. Meinert67,
D. Melnychuk29, M. Merk43, A. Merli22,40,q, E. Michielin23, D.A. Milanes66, E.
Millard50, M.-N. Minard4, L. Minzoni17, D.S. Mitzel12, A. Mogini8, J. Molina
Rodriguez1, T. Mombächer10, I.A. Monroy66, S. Monteil5, M. Morandin23, M.J.
Morello24,t, O. Morgunova68, J. Moron28, A.B. Morris52, R. Mountain61, F.
Muheim52, M. Mulder43, D. Müller56, J. Müller10, K. Müller42, V. Müller10, P.
Naik48, T. Nakada41, R. Nandakumar51, A. Nandi57, I. Nasteva2, M. Needham52,
N. Neri22,40, S. Neubert12, N. Neufeld40, M. Neuner12, T.D. Nguyen41, C.
Nguyen-Mau41,n, S. Nieswand9, R. Niet10, N. Nikitin33, T. Nikodem12, A.
Nogay68, D.P. O’Hanlon50, A. Oblakowska-Mucha28, V. Obraztsov37, S. Ogilvy19,
R. Oldeman16,f, C.J.G. Onderwater71, A. Ossowska27, J.M. Otalora Goicochea2,
P. Owen42, A. Oyanguren70, P.R. Pais41, A. Palano14,d, M. Palutan19,40, A.
Papanestis51, M. Pappagallo14,d, L.L. Pappalardo17,g, W. Parker60, C.
Parkes56, G. Passaleva18, A. Pastore14,d, M. Patel55, C. Patrignani15,e, A.
Pearce40, A. Pellegrino43, G. Penso26, M. Pepe Altarelli40, S. Perazzini40, P.
Perret5, L. Pescatore41, K. Petridis48, A. Petrolini20,h, A. Petrov68, M.
Petruzzo22,q, E. Picatoste Olloqui38, B. Pietrzyk4, M. Pikies27, D. Pinci26,
F. Pisani40, A. Pistone20,h, A. Piucci12, V. Placinta30, S. Playfer52, M. Plo
Casasus39, F. Polci8, M. Poli Lener19, A. Poluektov50,36, I. Polyakov61, E.
Polycarpo2, G.J. Pomery48, S. Ponce40, A. Popov37, D. Popov11,40, S.
Poslavskii37, C. Potterat2, E. Price48, J. Prisciandaro39, C. Prouve48, V.
Pugatch46, A. Puig Navarro42, H. Pullen57, G. Punzi24,p, W. Qian50, R.
Quagliani7,48, B. Quintana5, B. Rachwal28, J.H. Rademacker48, M. Rama24, M.
Ramos Pernas39, M.S. Rangel2, I. Raniuk45,†, F. Ratnikov35, G. Raven44, M.
Ravonel Salzgeber40, M. Reboud4, F. Redi55, S. Reichert10, A.C. dos Reis1, C.
Remon Alepuz70, V. Renaudin7, S. Ricciardi51, S. Richards48, M. Rihl40, K.
Rinnert54, V. Rives Molina38, P. Robbe7, A. Robert8, A.B. Rodrigues1, E.
Rodrigues59, J.A. Rodriguez Lopez66, P. Rodriguez Perez56,†, A. Rogozhnikov35,
S. Roiser40, A. Rollings57, V. Romanovskiy37, A. Romero Vidal39, J.W.
Ronayne13, M. Rotondo19, M.S. Rudolph61, T. Ruf40, P. Ruiz Valls70, J. Ruiz
Vidal70, J.J. Saborido Silva39, E. Sadykhov32, N. Sagidova31, B. Saitta16,f,
V. Salustino Guimaraes1, C. Sanchez Mayordomo70, B. Sanmartin Sedes39, R.
Santacesaria26, C. Santamarina Rios39, M. Santimaria19, E. Santovetti25,j, G.
Sarpis56, A. Sarti26, C. Satriano26,s, A. Satta25, D.M. Saunders48, D.
Savrina32,33, S. Schael9, M. Schellenberg10, M. Schiller53, H. Schindler40, M.
Schlupp10, M. Schmelling11, T. Schmelzer10, B. Schmidt40, O. Schneider41, A.
Schopper40, H.F. Schreiner59, K. Schubert10, M. Schubiger41, M.-H. Schune7, R.
Schwemmer40, B. Sciascia19, A. Sciubba26,k, A. Semennikov32, E.S. Sepulveda8,
A. Sergi47, N. Serra42, J. Serrano6, L. Sestini23, P. Seyfert40, M. Shapkin37,
I. Shapoval45, Y. Shcheglov31, T. Shears54, L. Shekhtman36,w, V. Shevchenko68,
B.G. Siddi17,40, R. Silva Coutinho42, L. Silva de Oliveira2, G. Simi23,o, S.
Simone14,d, M. Sirendi49, N. Skidmore48, T. Skwarnicki61, E. Smith55, I.T.
Smith52, J. Smith49, M. Smith55, l. Soares Lavra1, M.D. Sokoloff59, F.J.P.
Soler53, B. Souza De Paula2, B. Spaan10, P. Spradlin53, S. Sridharan40, F.
Stagni40, M. Stahl12, S. Stahl40, P. Stefko41, S. Stefkova55, O. Steinkamp42,
S. Stemmle12, O. Stenyakin37, M. Stepanova31, H. Stevens10, S. Stone61, B.
Storaci42, S. Stracka24,p, M.E. Stramaglia41, M. Straticiuc30, U. Straumann42,
L. Sun64, W. Sutcliffe55, K. Swientek28, V. Syropoulos44, M. Szczekowski29, T.
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Y. Xie65, Z. Xu4, Z. Yang3, Z. Yang60, Y. Yao61, H. Yin65, J. Yu65, X. Yuan61,
O. Yushchenko37, K.A. Zarebski47, M. Zavertyaev11,c, L. Zhang3, Y. Zhang7, A.
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Zucchelli15.

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 Savoie Mont-Blanc, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
10Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
11Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
12Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
13School of Physics, University College Dublin, Dublin, Ireland
14Sezione INFN di Bari, Bari, Italy
15Sezione INFN di Bologna, Bologna, Italy
16Sezione INFN di Cagliari, Cagliari, Italy
17Universita e INFN, Ferrara, Ferrara, Italy
18Sezione INFN di Firenze, Firenze, Italy
19Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
20Sezione INFN di Genova, Genova, Italy
21Universita & INFN, Milano-Bicocca, Milano, Italy
22Sezione di Milano, Milano, Italy
23Sezione INFN di Padova, Padova, Italy
24Sezione INFN di Pisa, Pisa, Italy
25Sezione INFN di Roma Tor Vergata, Roma, Italy
26Sezione INFN di Roma La Sapienza, Roma, Italy
27Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
28AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
29National Center for Nuclear Research (NCBJ), Warsaw, Poland
30Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
31Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
32Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
33Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
34Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
35Yandex School of Data Analysis, Moscow, Russia
36Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
37Institute for High Energy Physics (IHEP), Protvino, Russia
38ICCUB, Universitat de Barcelona, Barcelona, Spain
39Universidad de Santiago de Compostela, Santiago de Compostela, Spain
40European Organization for Nuclear Research (CERN), Geneva, Switzerland
41Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
42Physik-Institut, Universität Zürich, Zürich, Switzerland
43Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
44Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
45NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
46Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
47University of Birmingham, Birmingham, United Kingdom
48H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
49Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
50Department of Physics, University of Warwick, Coventry, United Kingdom
51STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
52School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
53School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
54Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
55Imperial College London, London, United Kingdom
56School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
57Department of Physics, University of Oxford, Oxford, United Kingdom
58Massachusetts Institute of Technology, Cambridge, MA, United States
59University of Cincinnati, Cincinnati, OH, United States
60University of Maryland, College Park, MD, United States
61Syracuse University, Syracuse, NY, United States
62Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
63University of Chinese Academy of Sciences, Beijing, China, associated to 3
64School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
65Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
66Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
67Institut für Physik, Universität Rostock, Rostock, Germany, associated to 12
68National Research Centre Kurchatov Institute, Moscow, Russia, associated to
32
69National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
32
70Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain, associated to 38
71Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 43

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bLaboratoire Leprince-Ringuet, Palaiseau, France
cP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
dUniversità di Bari, Bari, Italy
eUniversità di Bologna, Bologna, Italy
fUniversità di Cagliari, Cagliari, Italy
gUniversità di Ferrara, Ferrara, Italy
hUniversità di Genova, Genova, Italy
iUniversità di Milano Bicocca, Milano, Italy
jUniversità di Roma Tor Vergata, Roma, Italy
kUniversità di Roma La Sapienza, Roma, Italy
lAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
mLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
nHanoi University of Science, Hanoi, Viet Nam
oUniversità di Padova, Padova, Italy
pUniversità di Pisa, Pisa, Italy
qUniversità degli Studi di Milano, Milano, Italy
rUniversità di Urbino, Urbino, Italy
sUniversità della Basilicata, Potenza, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità di Modena e Reggio Emilia, Modena, Italy
vIligan Institute of Technology (IIT), Iligan, Philippines
wNovosibirsk State University, Novosibirsk, Russia
†Deceased