EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2021-036 LHCb-PAPER-2021-001 June 14, 2021

Search for $C\\!P$ violation in $D_{(s)}^{+}\\!\rightarrow h^{+}{{\pi}^{0}}$
and $D_{(s)}^{+}\\!\rightarrow h^{+}\eta$ decays

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

Searches for $C\\!P$ violation in the two-body decays
$D_{(s)}^{+}\\!\rightarrow h^{+}{{\pi}^{0}}$ and $D_{(s)}^{+}\\!\rightarrow
h^{+}\eta$ (where $h^{+}$ denotes a ${\pi}^{+}$ or ${K}^{+}$ meson) are
performed using $p$ $p$ collision data collected by the LHCb experiment
corresponding to either 9$\text{\,fb}^{-1}$ or 6$\text{\,fb}^{-1}$ of
integrated luminosity. The ${\pi}^{0}$ and $\eta$ mesons are reconstructed
using the ${e^{+}}{e^{-}}\gamma$ final state, which can proceed as three-body
decays ${{\pi}^{0}}\\!\rightarrow{e^{+}}{e^{-}}\gamma$ and
$\eta\\!\rightarrow{e^{+}}{e^{-}}\gamma$, or via the two-body decays
${{\pi}^{0}}\\!\rightarrow\gamma\gamma$ and $\eta\\!\rightarrow\gamma\gamma$
followed by a photon conversion. The measurements are made relative to the
control modes $D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+}$ to cancel
the production and detection asymmetries. The $C\\!P$ asymmetries are measured
to be

$\displaystyle\mathcal{A}_{{C\\!P}}({{D}^{+}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{0}})$
$\displaystyle=(-$ $\displaystyle 1.3$ $\displaystyle\pm 0.9$
$\displaystyle\pm 0.6$ $\displaystyle)\%,$
$\displaystyle\mathcal{A}_{{C\\!P}}({{D}^{+}}\\!\rightarrow{{K}^{+}}{{\pi}^{0}})$
$\displaystyle=(-$ $\displaystyle 3.2$ $\displaystyle\pm 4.7$
$\displaystyle\pm 2.1$ $\displaystyle)\%,$
$\displaystyle\mathcal{A}_{{C\\!P}}({{D}^{+}}\\!\rightarrow{{\pi}^{+}}\eta)$
$\displaystyle=(-$ $\displaystyle 0.2$ $\displaystyle\pm 0.8$
$\displaystyle\pm 0.4$ $\displaystyle)\%,$
$\displaystyle\mathcal{A}_{{C\\!P}}({{D}^{+}}\\!\rightarrow{{K}^{+}}\eta)$
$\displaystyle=(-$ $\displaystyle 6$ $\displaystyle\pm 10$ $\displaystyle\pm
4$ $\displaystyle)\%,$
$\displaystyle\mathcal{A}_{{C\\!P}}({{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{\pi}^{0}})$
$\displaystyle=(-$ $\displaystyle 0.8$ $\displaystyle\pm 3.9$
$\displaystyle\pm 1.2$ $\displaystyle)\%,$
$\displaystyle\mathcal{A}_{{C\\!P}}({{D}^{+}_{s}}\\!\rightarrow{{\pi}^{+}}\eta)$
$\displaystyle=($ $\displaystyle 0.8$ $\displaystyle\pm 0.7$ $\displaystyle\pm
0.5$ $\displaystyle)\%,$
$\displaystyle\mathcal{A}_{{C\\!P}}({{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}\eta)$
$\displaystyle=($ $\displaystyle 0.9$ $\displaystyle\pm 3.7$ $\displaystyle\pm
1.1$ $\displaystyle)\%,$

where the first uncertainties are statistical and the second systematic. These
results are consistent with no $C\\!P$ violation and mostly constitute the
most precise measurements of $\mathcal{A}_{{C\\!P}}$ in these decay modes to
date.

Published in JHEP 06 (2021) 019

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

##  1 Introduction

The observation of Charge-Parity ($C\\!P$) violation in two-body decays of
neutral $D$ mesons [1] motivates searches for similar effects in charged $D$
meson decays. The two-body $D_{(s)}^{+}\\!\rightarrow h^{+}{{\pi}^{0}}$ and
$D_{(s)}^{+}\\!\rightarrow h^{+}\eta$ decays, where $h^{+}$ denotes a
${\pi}^{+}$ or ${K}^{+}$ meson,111Inclusion of charge conjugated processes is
implied throughout, except when discussing asymmetry definitions. are mediated
by Cabibbo favoured (CF), singly Cabibbo suppressed (SCS) or doubly Cabibbo
suppressed (DCS) processes. The contributing decay topologies are shown in
Fig. 1. The SCS modes ${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{\pi}^{0}}$,
${{D}^{+}}\\!\rightarrow{{\pi}^{+}}\eta$ and
${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}\eta$ receive contributions from two
different weak phases, proportional to the products of the CKM matrix elements
${V_{{c}{d}}^{\phantom{\ast}}}{V_{{u}{d}}^{\ast}}$ and
${V_{{c}{s}}^{\phantom{\ast}}}{V_{{u}{s}}^{\ast}}$, allowing $C\\!P$ violation
at tree-level. In the Standard Model (SM), the $C\\!P$ asymmetries are
expected to be of the order $10^{-4}$–$10^{-3}$ [2, 3, 4, 5, 6, 7]. The CF
mode ${{D}^{+}_{s}}\\!\rightarrow{{\pi}^{+}}\eta$ and the DCS modes
${{D}^{+}}\\!\rightarrow{{K}^{+}}{{\pi}^{0}}$ and
${{D}^{+}}\\!\rightarrow{{K}^{+}}\eta$ receive contributions from only one
weak phase at tree-level. The
${{D}^{+}_{s}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{0}}$ mode proceeds via an
annihilation topology decay and is therefore highly suppressed.

Figure 1: Processes that contribute to the studied decays at tree-level
include (top left) colour-favoured, (top right) colour-suppressed and (bottom
left) annihilation topology decays. Contributions can also be received at
loop-level from processes such as (bottom right) penguin topology decays.

The SCS ${{D}^{+}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{0}}$ mode is of particular
interest as the $C\\!P$ asymmetry in the SM is expected to be zero as a result
of isospin constraints [3, 4, 5, 6]. The $C\\!P$ asymmetries of the signal
decays are defined to be

$\mathcal{A}_{{C\\!P}}(D_{(s)}^{+}\\!\rightarrow
h^{+}h^{0})\equiv\frac{\Gamma(D_{(s)}^{+}\\!\rightarrow
h^{+}h^{0})-\Gamma(D_{(s)}^{-}\\!\rightarrow
h^{-}h^{0})}{\Gamma(D_{(s)}^{+}\\!\rightarrow
h^{+}h^{0})+\Gamma(D_{(s)}^{-}\\!\rightarrow h^{-}h^{0})},$ (1)

where $\Gamma$ is the partial decay rate and $h^{0}$ denotes either a
${\pi}^{0}$ or an $\eta$ meson. A non-zero value of
$\mathcal{A}_{{C\\!P}}({{D}^{+}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{0}})$,
coupled with a verification that the isospin sum rule

$R=\frac{\mathcal{A}_{{C\\!P}}({{D}^{0}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{-}})}{1+\frac{\tau_{{{D}^{0}}}}{{\mathcal{B}}_{+-}}\left(\frac{{\mathcal{B}}_{00}}{\tau_{{{D}^{0}}}}+\frac{2}{3}\frac{{\mathcal{B}}_{+0}}{\tau_{{{D}^{+}}}}\right)}+\frac{\mathcal{A}_{{C\\!P}}({{D}^{0}}\\!\rightarrow{{\pi}^{0}}{{\pi}^{0}})}{1+\frac{\tau_{{{D}^{0}}}}{{\mathcal{B}}_{00}}\left(\frac{{\mathcal{B}}_{+-}}{\tau_{{{D}^{0}}}}+\frac{2}{3}\frac{{\mathcal{B}}_{+0}}{\tau_{{{D}^{+}}}}\right)}-\frac{\mathcal{A}_{{C\\!P}}({{D}^{+}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{0}})}{1+\frac{3}{2}\frac{\tau_{{{D}^{+}}}}{{\mathcal{B}}_{+0}}\left(\frac{{\mathcal{B}}_{00}}{\tau_{{{D}^{0}}}}+\frac{{\mathcal{B}}_{+-}}{\tau_{{{D}^{0}}}}\right)}$
(2)

is consistent with zero, would be an indication of physics beyond the SM [8,
9, 7, 10]. Here, $\tau_{{{D}^{+}}}$ and $\tau_{{{D}^{0}}}$ represent the
${D}^{+}$ and ${D}^{0}$ lifetimes and ${\mathcal{B}}_{+-}$,
${\mathcal{B}}_{00}$ and ${\mathcal{B}}_{+0}$ represent the branching
fractions of ${{D}^{0}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{-}}$,
${{D}^{0}}\\!\rightarrow{{\pi}^{0}}{{\pi}^{0}}$ and
${{D}^{+}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{0}}$ decays, respectively. A recent
measurement from the Belle collaboration determined the $C\\!P$ asymmetry to
be $\mathcal{A}_{{C\\!P}}({{D}^{+}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{0}})=$
$(2.31\pm 1.24\pm 0.23)\%$ [10], where the first uncertainty is statistical
and the second is systematic, corresponding to a value of $R=(-2.2\pm
2.7)\times 10^{-3}$.

In this article measurements of $C\\!P$ asymmetries of seven
$D_{(s)}^{+}\\!\rightarrow h^{+}{{\pi}^{0}}$ and $D_{(s)}^{+}\\!\rightarrow
h^{+}\eta$ modes are performed, using samples corresponding to either
9$\text{\,fb}^{-1}$ or 6$\text{\,fb}^{-1}$ of integrated luminosity,
respectively, collected by the LHCb experiment in proton-proton ($p$ $p$)
collisions at the LHC. The 6$\text{\,fb}^{-1}$ data set comprises data
collected during 2015–2018 (Run 2) at a centre-of-mass energy of
$13\text{\,Te\kern-1.00006ptV}$, whilst the 9$\text{\,fb}^{-1}$ data set
additionally includes data collected during 2011–2012 (Run 1) at centre-of-
mass energies of $7\text{\,Te\kern-1.00006ptV}$ and
$8\text{\,Te\kern-1.00006ptV}$. The neutral ${\pi}^{0}$ and $\eta$ mesons are
reconstructed via decays to the ${e^{+}}{e^{-}}\gamma$ final state. The
reconstruction of electron and positron tracks, in addition to the charged
hadron track from the $D^{+}_{(s)}$ meson decay, enables the determination of
the displaced $D^{+}_{(s)}$ meson decay vertex and suppresses background from
particles originating from the primary $p$ $p$ interaction. The signal
receives contributions from the suppressed three-body Dalitz decays
${{\pi}^{0}}\\!\rightarrow{e^{+}}{e^{-}}\gamma$ and
$\eta\\!\rightarrow{e^{+}}{e^{-}}\gamma$ with branching fractions $(1.174\pm
0.035)\%$ and $(6.9\pm 0.4)\times 10^{-3}$, respectively [11], as well as the
more common ${{\pi}^{0}}\\!\rightarrow\gamma\gamma$ and
$\eta\\!\rightarrow\gamma\gamma$ decays with branching fractions $(98.823\pm
0.034)\%$ and $(39.41\pm 0.20)\%$ [11], where one of the photons subsequently
interacts with the detector material and is converted to an ${e^{+}}{e^{-}}$
pair. Converted photons have been previously exploited at LHCb [12, 13, 14,
15, 16], but this is the first measurement to use converted photons to
reconstruct ${\pi}^{0}$ and $\eta$ mesons.

Experimentally, the raw asymmetry of each signal mode is measured, which is
defined to be

$A_{\text{Raw}}(D_{(s)}^{+}\\!\rightarrow
h^{+}h^{0})\equiv\frac{N(D_{(s)}^{+}\\!\rightarrow
h^{+}h^{0})-N(D_{(s)}^{-}\\!\rightarrow
h^{-}h^{0})}{N(D_{(s)}^{+}\\!\rightarrow
h^{+}h^{0})+N(D_{(s)}^{-}\\!\rightarrow h^{-}h^{0})},$ (3)

where $N$ is the signal yield. This can be approximated by

$A_{\text{Raw}}(D_{(s)}^{+}\\!\rightarrow
h^{+}h^{0})\approx\mathcal{A}_{{C\\!P}}(D_{(s)}^{+}\\!\rightarrow
h^{+}h^{0})+A_{\text{Prod}}(D_{(s)}^{+})+A_{\text{Det}}(h^{+}),$ (4)

where $A_{\text{Prod}}(D_{(s)}^{+})$ and $A_{\text{Det}}(h^{+})$ represent the
production and detection asymmetries of the corresponding hadrons. In order to
cancel the production and detection asymmetries, the raw asymmetry of
$D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+}$ control decays is
subtracted, approximated by

$A_{\text{Raw}}(D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+})\approx\mathcal{A}_{{C\\!P}}(D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+})+A_{\text{Prod}}(D_{(s)}^{+})+A_{\text{Det}}(h^{+})+A_{\text{Mix}}(K^{0}),$
(5)

where the extra term $A_{\text{Mix}}(K^{0})$ arises due to the $C\\!P$
asymmetry induced by mixing and decay of the neutral ${K}^{0}_{\mathrm{S}}$
meson [17]. As the nuisance asymmetries are known to be kinematically
dependent, the $D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+}$ samples
are weighted to match the kinematic distributions of the signal candidates to
optimally reduce the impact of the production and detection asymmetries. The
$C\\!P$ asymmetry for the signal modes can then be determined as

$\displaystyle\begin{split}\mathcal{A}_{{C\\!P}}(D_{(s)}^{+}\\!\rightarrow
h^{+}h^{0})={}&A_{\text{Raw}}(D_{(s)}^{+}\\!\rightarrow
h^{+}h^{0})-A_{\text{Raw}}^{\text{w}}(D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+})\\\
&+\mathcal{A}_{{C\\!P}}(D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+})+A_{\text{Mix}}(K^{0}),\end{split}$
(6)

where $A_{\text{Raw}}^{\text{w}}$ represents the raw asymmetry determined from
weighted samples, the values of
$\mathcal{A}_{{C\\!P}}(D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+})$
are accounted for using external inputs with sub-percent precision [18], and
$A_{\text{Mix}}(K^{0})$ is calculated using a description of the detector
material and the distribution of ${K}^{0}_{\mathrm{S}}$ decay times and
momentum in the selected data, as detailed in Refs. [18, 19].

This article is structured as follows: the LHCb experiment is described in
Section 2; the requirements used to reconstruct the signal samples are given
in Section 3; a description of the fits to the invariant mass distributions
can be found in Section 4; the treatment of the
$D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+}$ control modes is given
in Section 5; the sources of systematic uncertainty are detailed in Section 6;
and finally the results and conclusions are summarised in Section 7.

##  2 Detector

The LHCb detector [20, 21] is a single-arm forward spectrometer covering the
pseudorapidity range between 2 and 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 (VELO), 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 the
momentum, $p$, of charged particles with a relative uncertainty that varies
from 0.5% at low momentum to 1.0% at 200$\text{\,Ge\kern-1.00006ptV\\!/}c$.
The minimum distance of a track to a primary $pp$ collision vertex (PV), the
impact parameter (IP), is measured with a resolution of
$(15+29/p_{\mathrm{T}})\,\upmu\text{m}$, where $p_{\mathrm{T}}$ is the
component of the momentum transverse to the beam, in
$\text{\,Ge\kern-1.00006ptV\\!/}c$. Different types of charged hadrons are
distinguished using information from two ring-imaging Cherenkov detectors.
Photons, electrons and hadrons are identified by a calorimeter system
consisting of scintillating-pad and preshower detectors, an electromagnetic
and a hadronic calorimeter. Muons are identified by a system composed of
alternating layers of iron and multiwire proportional chambers. The online
event selection is performed by a trigger, which consists of a hardware stage,
based on information from the calorimeter and muon systems, followed by a
software stage, which applies a full event reconstruction.

Simulation is required to determine the invariant-mass distributions of the
signal decays, develop the selection and constrain the yields of background
from other particles misidentified as the signal-decay products. In the
simulation, $pp$ collisions are generated using Pythia [22] with a specific
LHCb configuration [23]. Decays of unstable particles are described by EvtGen
[24], in which final-state radiation is generated using Photos [25]. The
interaction of the generated particles with the detector, and its response,
are implemented using the Geant4 toolkit [26, *Agostinelli:2002hh] as
described in Ref. [28]. The underlying $pp$ interaction is reused multiple
times, with an independently generated signal decay for each [29].

##  3 Event selection

To reconstruct the ${D}_{(s)}^{+}$ meson candidate a well-identified kaon or
pion track is combined with a neutral meson to form a secondary decay vertex
displaced from any PV. The neutral ${\pi}^{0}$ and $\eta$ candidates are
formed from two oppositely charged electron tracks that are combined with a
photon candidate to create a neutral-meson decay vertex. A bremsstrahlung-
recovery algorithm associates additional deposits from soft photons to those
produced by the electrons in the electromagnetic calorimeter. To improve the
resolution, the electron tracks must include a track segment within the VELO.

At the hardware trigger level, candidates are selected by either directly
identifying high transverse-momentum deposits from the signal in the
electromagnetic or hadronic calorimeters, or by independently identifying
another energetic particle produced in the $p$ $p$ collision. Inclusive
multivariate (MVA) software triggers ensure the presence of well-reconstructed
tracks that are inconsistent with originating from any PV. A second high-level
software trigger performs a full event reconstruction to form the
$D^{+}_{(s)}$ candidates. In Run 1, no dedicated exclusive triggers for the
signal modes were implemented, but small samples of $D_{(s)}^{+}\\!\rightarrow
h^{+}{{\pi}^{0}}$ candidates are reconstructable as a result of the overlap
with existing exclusive two- and three-body $D$-meson-decay triggers. No
attempt is made to reconstruct $D_{(s)}^{+}\\!\rightarrow h^{+}\eta$
candidates using the Run 1 data set. In Run 2, dedicated exclusive software
triggers were added to form both $D_{(s)}^{+}\\!\rightarrow h^{+}{{\pi}^{0}}$
and $D_{(s)}^{+}\\!\rightarrow h^{+}\eta$ signal candidates. These require the
presence of a photon and three well-reconstructed tracks, inconsistent with
originating from any PV. The invariant masses of the ${\pi}^{0}$ ($\eta$)
meson candidates are required to be in the range
$70<m({e^{+}}{e^{-}}\gamma)<210\text{\,Me\kern-1.00006ptV\\!/}c^{2}$
($450<m({e^{+}}{e^{-}}\gamma)<650\text{\,Me\kern-1.00006ptV\\!/}c^{2}$) with
$p_{\mathrm{T}}>200\text{\,Me\kern-1.00006ptV\\!/}c$
($500\text{\,Me\kern-1.00006ptV\\!/}c$). The $D^{+}_{(s)}$ candidate is
required to have a transverse momentum
$p_{\mathrm{T}}>3000\text{\,Me\kern-1.00006ptV\\!/}c$ and a good quality
vertex with an associated p-value of greater than 0.0018, created by first
combining the ${e^{+}}{e^{-}}$ candidates to form the photon conversion or
$h^{0}$ Dalitz decay vertex, which is then further combined with a photon and
charged hadron to create the $D^{+}_{(s)}$ decay vertex.

Offline, the $D^{+}_{(s)}$ candidate selection is refined by requiring that
the momentum of the tracks is in the range
$3<p<100\text{\,Ge\kern-1.00006ptV\\!/}c$ and their pseudorapidity is between
$1.5$ and $5.0$. The $D^{+}_{(s)}$ candidates are required to have a mass in
the range $1600<m(D^{+}_{(s)})<2200\text{\,Me\kern-1.00006ptV\\!/}c^{2}$, be
consistent with originating at a primary interaction and have a proper decay
time of $t>0.15\text{\,ps}$ ($0.25\text{\,ps}$) for $D_{(s)}^{+}\\!\rightarrow
h^{+}{{\pi}^{0}}$ ($D_{(s)}^{+}\\!\rightarrow h^{+}\eta$) candidates.
Additionally, the angle between the momentum direction and the vector joining
the PV and $D^{+}_{(s)}$ decay vertex, referred to as the direction angle,
must be smaller than 10 mrad.

Fiducial requirements are placed on the charged-hadron tracks to remove
regions of large detection asymmetries, for example regions where a track of
one charge would be bent out of the acceptance by the magnetic field whilst
the opposite charge would be detected; the same criteria are used as in the
previous measurements of the control modes [18].

Particle identification (PID) requirements are applied using MVA-based PID
variables for the charged particles and the photon to reduce the amount of
combinatorial and misidentification background [30, 31]. Loose PID
requirements are applied to the pion and electron tracks. Tighter requirements
are applied to kaon candidates to reduce the rate of
${{\pi}^{+}}\\!\rightarrow{{K}^{+}}$ misidentification from the more abundant
pion modes into the suppressed kaon modes. When reconstructing ${\pi}^{0}$
mesons, a loose requirement is placed on an MVA-based photon-quality variable
[32], whilst for $\eta$ mesons, a tighter condition is required to reduce the
level of combinatorial background. Requirements are placed on electron
bremsstrahlung PID variables that match the bremsstrahlung calorimeter deposit
to the electron track before passing through the magnetic field to ensure that
the correct photon deposits are recovered. Decays with a total of either zero
or one bremsstrahlung photon per ${e^{+}}{e^{-}}$ pair are used in this
analysis. For ${{D}^{+}}\\!\rightarrow h^{+}{{\pi}^{0}}$
(${{D}^{+}}\\!\rightarrow h^{+}\eta$) decays this corresponds to 62% and 38%
(31% and 48%) of the reconstructed candidates, respectively. Decays with two
or more bremsstrahlung photons per ${e^{+}}{e^{-}}$ pair are removed as they
result in a poor $D_{(s)}^{+}$ invariant mass resolution and high background
level.

The same offline selection requirements are used for candidates selected with
different numbers of bremsstrahlung photons, and also between candidates
decaying via photon conversions or three-body
$h^{0}\\!\rightarrow{e^{+}}{e^{-}}\gamma$ decays. The requirements give a
reasonable compromise between the efficiency of each type of decay with
efficiencies of the order ${\mathcal{O}}(10^{-6})$ in Run 1 and
${\mathcal{O}}(10^{-5})$ in Run 2.

After the full selection has been applied, approximately 3% (2%) of events are
found to have multiple $D_{(s)}^{+}\\!\rightarrow h^{+}{{\pi}^{0}}$
($D_{(s)}^{+}\\!\rightarrow h^{+}\eta$) candidates predominately due to
combinations with alternative photon candidates, of which all are retained.
The signal decays are found to be dominated by
${{\pi}^{0}}\\!\rightarrow\gamma\gamma$ and $\eta\\!\rightarrow\gamma\gamma$
decays followed by a photon conversion, rather than the three-body Dalitz
decays ${{\pi}^{0}}\\!\rightarrow{e^{+}}{e^{-}}\gamma$ and
$\eta\\!\rightarrow{e^{+}}{e^{-}}\gamma$, with approximately 86% of the
candidates resulting from photon conversions.

##  4 Signal modes and fit model

The raw asymmetries of the signal modes are measured using two-dimensional
extended simultaneous unbinned maximum-likelihood fits to the invariant mass
$m({e^{+}}{e^{-}}\gamma)$ and the invariant mass difference
$m(h^{+}h^{0})\equiv
m(h^{+}{e^{+}}{e^{-}}\gamma)-m({e^{+}}{e^{-}}\gamma)+M(h^{0})_{\text{PDG}}$,
where $M(h^{0})_{\text{PDG}}$ corresponds to the known ${\pi}^{0}$ and $\eta$
masses [11]. The quantity $m(h^{+}h^{0})$ is constructed to reduce the
correlations between the two dimensions, and is referred to as the
$D_{(s)}^{+}$ candidate mass henceforth. The $m(h^{+}h^{0})$ and
$m({e^{+}}{e^{-}}\gamma)$ mass distributions are shown for
$D_{(s)}^{+}\\!\rightarrow h^{+}{{\pi}^{0}}$ and $D_{(s)}^{+}\\!\rightarrow
h^{+}\eta$ candidates in Figs. 2 and 3. The fits are performed for
$D_{(s)}^{+}\\!\rightarrow h^{+}{{\pi}^{0}}$ candidates in the ranges
$1750<m(h^{+}h^{0})<2100\text{\,Me\kern-1.00006ptV\\!/}c^{2}$ and
$90<m({e^{+}}{e^{-}}\gamma)<180\text{\,Me\kern-1.00006ptV\\!/}c^{2}$, and for
$D_{(s)}^{+}\\!\rightarrow h^{+}\eta$ candidates in the ranges
$1775<m(h^{+}h^{0})<2100\text{\,Me\kern-1.00006ptV\\!/}c^{2}$ and
$470<m({e^{+}}{e^{-}}\gamma)<640\text{\,Me\kern-1.00006ptV\\!/}c^{2}$.

Figure 2: Distribution of the (left) $m(h^{+}{{\pi}^{0}})$ and (right)
$m({e^{+}}{e^{-}}\gamma)$ mass for (top)
$D_{(s)}^{+}\\!\rightarrow{{\pi}^{+}}{{\pi}^{0}}$ and (bottom)
$D_{(s)}^{+}\\!\rightarrow{{K}^{+}}{{\pi}^{0}}$ candidates, summed over all
categories of the simultaneous fit. Projections of the total fit result and
individual fit components are overlaid. This includes ${{D}^{+}}\\!\rightarrow
h^{+}{{\pi}^{0}}$ decays in dashed red, ${{D}^{+}_{s}}\\!\rightarrow
h^{+}{{\pi}^{0}}$ decays in solid grey, pure combinatorial decays in dashed
black and real-${\pi}^{0}$ combinatorial background in dotted green. The
misidentification background is too small to be seen in these distributions.

Figure 3: Distribution of the (left) $m(h^{+}\eta)$ and (right)
$m({e^{+}}{e^{-}}\gamma)$ mass for (top)
$D_{(s)}^{+}\\!\rightarrow{{\pi}^{+}}\eta$ and (bottom)
$D_{(s)}^{+}\\!\rightarrow{{K}^{+}}\eta$ candidates, summed over all
categories of the simultaneous fit. Projections of the total fit result and
individual fit components are overlaid. This includes ${{D}^{+}}\\!\rightarrow
h^{+}\eta$ decays in dashed red, ${{D}^{+}_{s}}\\!\rightarrow h^{+}\eta$
decays in solid grey, pure combinatorial decays in dashed black and partially
reconstructed background in dotted magenta. The misidentification background
is too small to be seen in these distributions.

The fits are performed simultaneously on candidates in categories that depend
on the running period, the presence of bremsstrahlung photons, charged-hadron
type (pion or kaon) and the candidate charge. All $D_{(s)}^{+}\\!\rightarrow
h^{+}\eta$ candidates were collected during Run 2. The
$D_{(s)}^{+}\\!\rightarrow h^{+}{{\pi}^{0}}$ candidates are split into three
running period categories, 2011, 2012 and Run 2, where the centre-of-mass
energies were 7, 8, and 13 TeV, respectively. Candidates with either zero or
one bremsstrahlung photon per ${e^{+}}{e^{-}}$ pair are split into two
categories as they have different mass resolutions. The fits are performed on
candidates with ${\pi}^{+}$ and ${K}^{+}$ mesons simultaneously to allow the
signal yields in either category to determine the misidentification-background
yields in the corresponding category.

Two-dimensional probability density functions (PDFs) are used to model
different contributions within the mass windows. These contributions can be
categorised as signal decays, misidentification background, partially
reconstructed low-mass background and combinatorial background. The sum of
positively- and negatively-charged candidate yields and raw asymmetry of all
signal and background components are free to vary in the fits. A component for
${{D}^{+}_{s}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{0}}$ signal is included in the
fit, but due to the insignificant yield no corresponding raw asymmetry is
measured. The PDFs are assumed to be the same for positively and negatively
charged candidates, but otherwise allowed to differ for the other categories
of the simultaneous fit. In the fit to $D^{+}_{(s)}\\!\rightarrow
h^{+}{{\pi}^{0}}$ candidates the same raw asymmetries are shared between
different running periods.

The signal modes are modelled by the sum of a two-dimensional Gaussian
function and two two-dimensional Crystal Ball functions [33]. The shape
parameters and fraction of each function are determined from fits to simulated
decays passing the full selection. To account for residual correlations
between $m(h^{+}h^{0})$ and $m({e^{+}}{e^{-}}\gamma)$ resulting in part from
radiative tails, the mean $h^{0}$ ($D^{+}_{(s)}$) mass is allowed to vary
quadratically as a function of the $D^{+}_{(s)}$ ($h^{0}$) mass in the fits to
$D_{(s)}^{+}\\!\rightarrow h^{+}{{\pi}^{0}}$ ($D_{(s)}^{+}\\!\rightarrow
h^{+}\eta$) candidates. When performing fits to data, freely varying scaling
factors are applied to the widths of the PDFs, and freely varying offsets are
added to the mean positions and quadratic correlation coefficients to account
for differences between data and simulation. Different parameters are
introduced for each running period and bremsstrahlung category. When
determining PDFs from simulated decays, the candidates are weighted to account
for the PID requirements using input from calibration samples [31].

The fit model accounts for misidentified signal decays, where a ${\pi}^{+}$
track has been incorrectly assigned the ${K}^{+}$ mass hypothesis, or vice
versa, using the same two-dimensional parameterisation as the signal shapes.
The PDF parameters are determined from fits to the corresponding simulated
signal decays passing the full selection for the charged hadron with the wrong
mass hypothesis, including weights to account for the misidentification
probabilities. When performing the fits to data, the yield of the
misidentification background is constrained to the yield of signal in the
other charged-hadron category multiplied by the relevant ratio of efficiencies
determined from simulated decays and PID calibration samples. The yields of
misidentification background contributions are below approximately 3% of the
corresponding signal yields.

Combinatorial background resulting from random combinations of tracks and
photons is modelled with an exponential function in the $m(h^{+}h^{0})$
dimension and a second-order Chebychev polynomial function in the
$m({e^{+}}{e^{-}}\gamma)$ dimension. The exponential coefficient and Chebychev
polynomial coefficients freely vary in the fit. In the fit to
$D_{(s)}^{+}\\!\rightarrow h^{+}{{\pi}^{0}}$ candidates, it is found necessary
to include a combinatorial component comprising a real ${\pi}^{0}$ meson
combined with an unrelated track. The PDF is constructed from a peaking
distribution in the $m({e^{+}}{e^{-}}\gamma)$ dimension and an exponential
function in the $m(h^{+}h^{0})$ dimension. The peaking distribution is
constructed from the sum of two Crystal Ball functions, whose shape is
determined from one-dimensional fits to the simulated signal decays. However,
when fitting data a freely varying mass offset and resolution scaling factor
are included to allow the ${\pi}^{0}$ mass distribution to differ from that of
the signal decays. No significant contribution from combinatorial decays with
a real $\eta$ meson and an unrelated track is found when fitting
$D_{(s)}^{+}\\!\rightarrow h^{+}\eta$ decays, therefore no corresponding
component is included.

Decays of charm mesons to $h^{+}h^{0}X$ final states, where $X$ is at least
one unreconstructed particle, appear as partially reconstructed background
below the $D^{+}_{(s)}$ meson masses. Using external input on branching
fractions and charm-meson production cross-section ratios [11, 34] it is
determined that only the decay
${{D}^{+}_{s}}\\!\rightarrow{{\pi}^{+}}\eta{{\pi}^{0}}$ has a significant
contribution in the fit to $D^{+}_{(s)}\\!\rightarrow{{\pi}^{+}}\eta$
candidates. To account for this component, a shape comprising an exponential
function in the $m(h^{+}\eta)$ dimension with a freely varying coefficient and
a peaking $m({e^{+}}{e^{-}}\gamma)$ distribution constructed from two Crystal
Ball functions is added.

The fit to $D_{(s)}^{+}\\!\rightarrow h^{+}{{\pi}^{0}}$
($D_{(s)}^{+}\\!\rightarrow h^{+}\eta$) candidates includes 91 (54) freely
varying parameters. The models are validated using pseudo-experiments and no
significant biases in the values or statistical uncertainties of the raw
asymmetries are observed. The projections of the fits to
$D_{(s)}^{+}\\!\rightarrow h^{+}{{\pi}^{0}}$ and $D_{(s)}^{+}\\!\rightarrow
h^{+}\eta$ candidates, summed over all relevant categories, are shown in Figs.
2 and 3, respectively. The pull distributions are examined for each category
of the fit in both projections and in two dimensions, and no significant
biases are seen. The goodness-of-fit is quantified by calculating the
$\chi^{2}$ value for each projection and category separately, and combining to
determine $\chi^{2}/N_{\text{dof}}=0.90$ and $\chi^{2}/N_{\text{dof}}=1.06$
for the fits to $D_{(s)}^{+}\\!\rightarrow h^{+}{{\pi}^{0}}$ and
$D_{(s)}^{+}\\!\rightarrow h^{+}\eta$ candidates, where $N_{\text{dof}}$ is
the total number of degrees of freedom. The corresponding signal yields and
raw asymmetries are listed in Table 1.

Table 1: Signal yields in each running period and corresponding raw asymmetries for $D_{(s)}^{+}\\!\rightarrow h^{+}{{\pi}^{0}}$ and $D_{(s)}^{+}\\!\rightarrow h^{+}\eta$ candidates. The uncertainties are statistical.  Mode | Yield |  $A_{\text{Raw}}$ (%)
---|---|---
| 2011 | 2012 | Run 2 |
${{D}^{+}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{0}}$ | 740 $\pm$ | 60 | 2 240 $\pm$ | 120 | 25 750 $\pm$ | 430 | $-1.64\pm\phantom{0}0.93$
${{D}^{+}_{s}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{0}}$ | 20 $\pm$ | 30 |  $-50$ $\pm$ | 50 | 450 $\pm$ | 120 | -
${{D}^{+}}\\!\rightarrow{{K}^{+}}{{\pi}^{0}}$ | 10 $\pm$ | 13 | 90 $\pm$ | 30 | 2 440 $\pm$ | 110 | $-2.53\pm\phantom{0}4.75$
${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{\pi}^{0}}$ | 54 $\pm$ | 13 | 150 $\pm$ | 30 | 2 580 $\pm$ | 90 | $-0.25\pm\phantom{0}3.87$
${{D}^{+}}\\!\rightarrow{{\pi}^{+}}\eta$ | - | - | 32 760 $\pm$ | 380 | $-0.55\pm\phantom{0}0.76$
${{D}^{+}_{s}}\\!\rightarrow{{\pi}^{+}}\eta$ | - | - | 37 950 $\pm$ | 340 | $\phantom{+}0.75\pm\phantom{0}0.65$
${{D}^{+}}\\!\rightarrow{{K}^{+}}\eta$ | - | - | 880 $\pm$ | 70 | $-5.39\pm 10.40$
${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}\eta$ | - | - | 2 520 $\pm$ | 70 | $\phantom{+}1.28\pm\phantom{0}3.67$

The ${D}^{+}$ and ${D}^{+}_{s}$ signal distributions overlap, leading to small
correlations between the measured raw asymmetries. The correlation
coefficients are listed in Table 2 and the largest correlation is 10%.

Table 2: Correlation coefficients between the raw asymmetries determined for
$D_{(s)}^{+}\\!\rightarrow h^{+}{{\pi}^{0}}$ and $D_{(s)}^{+}\\!\rightarrow
h^{+}\eta$ decays.

| ${{D}^{+}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{0}}$ | ${{D}^{+}}\\!\rightarrow{{K}^{+}}{{\pi}^{0}}$ | ${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{\pi}^{0}}$
---|---|---|---
${{D}^{+}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{0}}$ | $\phantom{+}1.00$ |  |
${{D}^{+}}\\!\rightarrow{{K}^{+}}{{\pi}^{0}}$ | $-0.01$ | $1.00$ |
${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{\pi}^{0}}$ | $-0.09$ | $0.10$ | $\phantom{+}1.00$

| ${{D}^{+}}\\!\rightarrow{{\pi}^{+}}\eta$ | ${{D}^{+}}\\!\rightarrow{{K}^{+}}\eta$ | ${{D}^{+}_{s}}\\!\rightarrow{{\pi}^{+}}\eta$ | ${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}\eta$
---|---|---|---|---
${{D}^{+}}\\!\rightarrow{{\pi}^{+}}\eta$ | $\phantom{+}1.00$ |  |  |
${{D}^{+}}\\!\rightarrow{{K}^{+}}\eta$ | $-0.00$ | $\phantom{+}1.00$ |  |
${{D}^{+}_{s}}\\!\rightarrow{{\pi}^{+}}\eta$ | $\phantom{+}0.01$ | $\phantom{+}0.00$ | $\phantom{+}1.00$ |
${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}\eta$ | $-0.06$ | $\phantom{+}0.10$ | $-0.00$ | $\phantom{+}1.00$

##  5 Control modes

The impact of production and detection asymmetries of the signal modes is
accounted for using large samples of
$D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+}$ decays. The samples are
selected using similar requirements to the signal modes, where possible.
Candidates are built at the high-level software trigger stage by first
combining two well-reconstructed hadronic tracks that are inconsistent with
originating from any PV to create the ${K}^{0}_{\mathrm{S}}$ decay vertex.
Similar to the electrons, these tracks must also have track segments within
the VELO. The ${K}^{0}_{\mathrm{S}}$ candidate is combined with a hadronic
track with either the pion or kaon mass hypothesis to form the $D^{+}_{(s)}$
decay vertex. The same momentum, pseudorapidity and fiducial requirements are
placed on the tracks as used for the signal. The candidates are required to
have $482<m({{\pi}^{+}}{{\pi}^{-}})<512\text{\,Me\kern-1.00006ptV\\!/}c^{2}$
and
$1800<m({{K}^{0}_{\mathrm{S}}}h^{+})<2050\text{\,Me\kern-1.00006ptV\\!/}c^{2}$,
a proper decay time of $t>0.25\text{\,ps}$, and the same direction angle and
$p_{\mathrm{T}}$ requirements as the signal. Tighter PID requirements are
placed on the control mode candidates than the signal to remove larger
contamination from misidentification background.

The kinematic distributions of the signal and control candidates are
determined using the sPlot technique [35] with
$m({{K}^{0}_{\mathrm{S}}}h^{+})$ as the discriminating variable for the
latter. Binned maximum-likelihood fits are performed on the control-mode
candidates using signal models comprising a Gaussian function and Johnson
$S_{U}$ function [36] as described in Ref. [18]. The results are shown in Fig.
4. The weighting procedure is performed separately for Run 1 and Run 2 to
allow for differences in the signal selection during these periods. To ensure
the cancellation of the production and detection asymmetries, the relevant
$D^{+}_{(s)}$ and $h^{+}$ kinematics ($p$, azimuthal angle and pseudorapidity)
are weighted to match those of the signal. Due to the large correlation
between the $D^{+}_{(s)}$ and $h^{+}$ kinematics the weights for each variable
are determined using a two-dimensional binning of the $D^{+}_{(s)}$ and
$h^{+}$ distributions. In addition to the kinematics, weights are determined
for the trigger category and IP distributions for the $D^{+}_{(s)}$
candidates. At the hardware trigger stage the candidates can be split into
exclusive categories according to the origin of the positive trigger decision:
the first category contains any candidate with a calorimeter deposit
associated to the $h^{0}$ or ${K}^{0}_{\mathrm{S}}$ decay; the second category
contains any remaining candidate with a deposit not associated to any of the
signal particles; and the third category contains candidates still remaining
with a high $p_{\mathrm{T}}$ deposit associated to the charged pion or kaon.
The control-mode candidates are weighted to reproduce the populations of
signal candidates in each of these three categories.

Figure 4:  Distributions of the (left) $m({{K}^{0}_{\mathrm{S}}}{{\pi}^{+}})$
and (right) $m({{K}^{0}_{\mathrm{S}}}{{K}^{+}})$ mass of control mode
candidates in (top) Run 1 and (bottom) Run 2. The total PDF and individual fit
components are overlaid, including
${{D}^{+}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+}$ decays in dashed red,
${{D}^{+}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+}$ decays in solid grey
and background decays in dashed black.

The IP of the $D_{(s)}^{+}$ candidate is indicative of whether the meson was
produced in the primary interaction, or as a product of a $b$-hadron decay,
and therefore with a significant IP with respect to the PV, referred to as a
secondary decay. In the latter case the production asymmetry of the parent
$b$-hadron could differ from that of the ${D}^{+}$ or ${D}^{+}_{s}$ meson. The
signal and control mode selections require that the $D^{+}_{(s)}$ candidates
are consistent with originating at a PV, suppressing the fraction of
candidates from secondary decays to less than 10%. If the fraction of
$D_{(s)}^{+}$ candidates from the primary interaction and secondary decays
varies between the signal and control mode then the production asymmetries may
not exactly cancel, therefore the control sample is weighted to match the IP
distribution of the signal.

Binned maximum-likelihood fits are performed to the charge-split samples to
determine the raw asymmetries separately for Run 1 and Run 2. The signals are
described using the sum of a Gaussian function and Johnson $S_{U}$ function,
using the same model as described in Ref. [18]. The fits are performed after
the samples have been weighted to match the kinematics of the signal modes,
and the statistical uncertainty is calculated using the weights to account for
the loss of precision resulting from the weighting procedure.

##  6 Systematic uncertainties

The systematic uncertainty on the $C\\!P$ asymmetries receives contributions
from a number of sources, including the signal and background
parameterisations, the control modes and selection requirements.

Table 3: Absolute systematic uncertainties (%) on the $C\\!P$ asymmetries for ${D}^{+}_{(s)}\\!\rightarrow h^{+}{{\pi}^{0}}$ decays. Source | ${{D}^{+}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{0}}$ | ${{D}^{+}}\\!\rightarrow{{K}^{+}}{{\pi}^{0}}$ | ${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{\pi}^{0}}$
---|---|---|---
Fit model | $\phantom{<\,}0.59$ | $\phantom{<\,}1.55$ | $\phantom{<\,}1.01$
PID asymmetry | $\phantom{<\,}0.06$ | $\phantom{<\,}0.27$ | $\phantom{<\,}0.15$
Secondary decays | $<0.01$ | $\phantom{<\,}0.01$ | $\phantom{<\,}0.02$
Combined $A_{\text{Raw}}$ Run 1 and Run 2 | $\phantom{<\,}0.23$ | $\phantom{<\,}0.65$ | $\phantom{<\,}0.30$
Control modes | $\phantom{<\,}0.03$ | $\phantom{<\,}1.18$ | $\phantom{<\,}0.59$
$A_{\text{Mix}}(K^{0})$ | $<0.01$ | $<0.01$ | $<0.01$
$\mathcal{A}_{{C\\!P}}(D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+})$ | $\phantom{<\,}0.12$ | $\phantom{<\,}0.08$ | $\phantom{<\,}0.26$
Total | $\phantom{<\,}0.65$ | $\phantom{<\,}2.07$ | $\phantom{<\,}1.24$
Table 4: Absolute systematic uncertainties (%) on the $C\\!P$ asymmetries for ${D}^{+}_{(s)}\\!\rightarrow h^{+}\eta$ decays. Source | ${{D}^{+}}\\!\rightarrow{{\pi}^{+}}\eta$ | ${{D}^{+}_{s}}\\!\rightarrow{{\pi}^{+}}\eta$ | ${{D}^{+}}\\!\rightarrow{{K}^{+}}\eta$ | ${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}\eta$
---|---|---|---|---
Fit model | $\phantom{<\,}0.35$ | $\phantom{<\,}0.15$ | $\phantom{<\,}4.04$ | $\phantom{<\,}1.08$
PID asymmetry | $\phantom{<\,}0.06$ | $\phantom{<\,}0.01$ | $\phantom{<\,}0.87$ | $\phantom{<\,}0.16$
Secondary decays | $<0.01$ | $\phantom{<\,}0.02$ | $\phantom{<\,}0.01$ | $\phantom{<\,}0.04$
Control modes | $\phantom{<\,}0.05$ | $\phantom{<\,}0.39$ | $\phantom{<\,}0.14$ | $\phantom{<\,}0.12$
$A_{\text{Mix}}(K^{0})$ | $<0.01$ | $<0.01$ | $<0.01$ | $<0.01$
$\mathcal{A}_{{C\\!P}}(D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+})$ | $\phantom{<\,}0.12$ | $\phantom{<\,}0.20$ | $\phantom{<\,}0.08$ | $\phantom{<\,}0.26$
Total | $\phantom{<\,}0.38$ | $\phantom{<\,}0.46$ | $\phantom{<\,}4.13$ | $\phantom{<\,}1.13$

The assumptions used when creating the signal and background parameterisations
are varied and the corresponding systematic uncertainty is quantified using
the resulting difference in the raw asymmetries in the fits to data. This
includes using: alternative signal parameterisation comprising Johnson $S_{U}$
functions instead of Crystal Ball functions; different pure-combinatorial
$m(h^{+}h^{0})$ parameterisations of a constant plus exponential function;
alternative pure-combinatorial $m({e^{+}}{e^{-}}\gamma)$ parameterisations of
a third-order Chebychev polynomial function; alternative real-${\pi}^{0}$
combinatorial parameterisation of a double Johnson $S_{U}$; and different
misidentification-background parameterisations using Johnson $S_{U}$ functions
instead of Crystal Ball functions. The efficiencies used to constrain the
level of misidentification background are varied within the corresponding
uncertainties in 100 fits and the spread in the raw asymmetries is used to
estimate the systematic uncertainty. The impact on the raw asymmetries is
quantified when various neglected background components are included in the
model, including semileptonic $D^{+}_{(s)}\\!\rightarrow
h^{0}{e^{+}}{{\nu}_{e}}$ and $D^{+}_{(s)}\\!\rightarrow
h^{0}{\mu^{+}}{{\nu}_{\mu}}$ decays, partially reconstructed
${{D}^{0}}\\!\rightarrow{{K}^{-}}{{\pi}^{+}}{{\pi}^{0}}$ decays and a
combinatorial component with a real-$\eta$ distribution. Additionally, the
assumption that the pure-combinatorial $m(h^{+}h^{0})$ exponential slope is
independent of $m({e^{+}}{e^{-}}\gamma)$ is relaxed by allowing a linear
dependence. The signal tail parameters that are fixed to values obtained from
simulation are allowed to vary with an overall scaling factor and the impact
on the raw asymmetries is quantified. The assumption that the mean
$D^{+}_{(s)}$ mass positions are the same for $D_{(s)}^{+}$ and $D_{(s)}^{-}$
candidates is tested by allowing different values. The systematic uncertainty
from the fit model is dominated by the fixed tail parameters for
${{D}^{+}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{0}}$, the fixed misidentification
efficiency ratio for ${{D}^{+}}\\!\rightarrow{{K}^{+}}{{\pi}^{0}}$ and
${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{\pi}^{0}}$ decays, the signal
parameterisation for ${{D}^{+}}\\!\rightarrow{{\pi}^{+}}\eta$ decays and the
lack of real-$\eta$ combinatorial contribution for
${{D}^{+}_{s}}\\!\rightarrow{{\pi}^{+}}\eta$,
${{D}^{+}}\\!\rightarrow{{K}^{+}}\eta$ and
${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}\eta$ decays.

The selection of the signal and control modes uses different requirements for
the PID variables. Tighter conditions are needed for the control modes to
reduce misidentification background such as ${{\mathchar
28931\relax}^{+}_{c}}\\!\rightarrow{p}{{K}^{0}_{\mathrm{S}}}$ decays. The size
of a possible charge asymmetry induced by these different requirements is
quantified by first computing the asymmetry of the PID efficiencies,
$\epsilon_{\text{PID}}$, when determined separately for positively and
negatively charged hadrons,
$A_{\text{PID}}=[\epsilon_{\text{PID}}(h^{+})-\epsilon_{\text{PID}}(h^{-})]/[\epsilon_{\text{PID}}(h^{+})+\epsilon_{\text{PID}}(h^{-})]$.
Then, the difference in PID asymmetry when calculated using signal and control
mode PID requirements, $\Delta
A_{\text{PID}}=A_{\text{PID}}^{\text{signal}}-A_{\text{PID}}^{\text{control}}$,
is used to quantify the corresponding systematic uncertainty. Additionally,
the difference in the raw asymmetries when not performing the IP weighting is
used to quantify the systematic uncertainty arising from the secondary decays.

The asymmetries for ${D}^{+}_{(s)}\\!\rightarrow h^{+}{{\pi}^{0}}$ decays are
determined from simultaneous fits to data sets taken during Run 1 and Run 2,
with a single $C\\!P$ asymmetry shared between the categories for each mode.
In contrast, the control-mode fits are performed separately for Run 1 and Run
2 and then a weighted average is performed to combine the measurements, where
the weighting is determined from the yields of signal mode decays. The
systematic uncertainty arising from this method is quantified by performing
the signal fits separately for Run 1 and Run 2, taking the appropriate
difference with the control-mode asymmetries and then combining the Run 1 and
Run 2 results to get an alternative estimate.

The control-mode weighting is performed in nearly equally populated bins. The
binning scheme is varied to determine the associated systematic uncertainty.
After performing the weighting procedure, the remaining discrepancies in the
kinematic distributions are quantified by summing the difference in the
normalised distributions of signal and control modes, multiplied by the local
asymmetry minus the average asymmetry. The fit model used to measure the
control-mode raw asymmetries is varied from the sum of a Johnson $S_{U}$
function and a Gaussian function to the sum of a Crystal Ball function and a
Gaussian function. The contribution to the control mode raw asymmetry from the
neutral-kaon mixing and decay asymmetry is calculated and the corresponding
uncertainty of this calculation is dominated by the knowledge of the detector
material. The uncertainties of the external values of the control mode
$\mathcal{A}_{{C\\!P}}$ are included as systematic uncertainties.

The systematic uncertainties are listed for the ${D}^{+}_{(s)}\\!\rightarrow
h^{+}{{\pi}^{0}}$ modes in Table 3 and for the ${D}^{+}_{(s)}\\!\rightarrow
h^{+}\eta$ modes in Table 4. These are dominated by the fit-model uncertainty
in most cases, except for the mode
${{D}^{+}_{s}}\\!\rightarrow{{\pi}^{+}}\eta$ which is dominated by the
uncertainty arising from the control mode
${{D}^{+}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}}$, the smallest
of the control samples.

As a crosscheck, the fits are performed in various subsamples: split by year
of data taking; magnet polarity; trigger category; bremsstrahlung category;
$D^{+}_{(s)}$ kinematics and $h^{+}$ kinematics. No significant biases are
found with respect to the nominal results.

##  7 Results and conclusions

The $C\\!P$ asymmetries are calculated using Eq. 6, where for each mode the
corresponding control channel $A_{\text{Raw}}^{\text{w}}$, independently
measured
$\mathcal{A}_{{C\\!P}}(D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+})$
and calculated $A_{\text{Mix}}(K^{0})$ are taken. The final results are listed
in Tables 5 and 6. The results are shown with the corresponding statistical
uncertainty from the fits and the total systematic uncertainty as listed in
Tables 3 and 4. The systematic uncertainties attributed to
$A_{\text{Raw}}^{\text{w}}(D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+})$,
$\mathcal{A}_{{C\\!P}}(D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+})$
and $A_{\text{Mix}}(K^{0})$ are listed separately.

Table 5: Final $\mathcal{A}_{C\\!P}$ (%) results for the $D_{(s)}^{+}\\!\rightarrow h^{+}{{\pi}^{0}}$ modes. The uncertainties of $\mathcal{A}_{{C\\!P}}(D_{(s)}^{+}\\!\rightarrow h^{+}{{\pi}^{0}})$ are statistical and systematic respectively. The uncertainties of $A_{\text{Raw}}(D_{(s)}^{+}\\!\rightarrow h^{+}{{\pi}^{0}})$ are purely statistical. The uncertainties of $A_{\text{Mix}}(K^{0})$ are systematic. Externally measured values of $\mathcal{A}_{{C\\!P}}(D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+})$ are taken from Refs. [37, 18, 38, 39, 40, 41]. For comparison the unweighted control asymmetries are $\mathcal{A}_{\text{Raw}}({{D}^{+}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}})=-0.45\pm 0.02$, $\mathcal{A}_{\text{Raw}}({{D}^{+}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{+}})=0.47\pm 0.05$ and $\mathcal{A}_{\text{Raw}}({{D}^{+}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{+}})=0.51\pm 0.04$. | ${{D}^{+}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{0}}$ | ${{D}^{+}}\\!\rightarrow{{K}^{+}}{{\pi}^{0}}$ | ${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{\pi}^{0}}$
---|---|---|---
$A_{\text{Raw}}(D_{(s)}^{+}\\!\rightarrow h^{+}{{\pi}^{0}})$ | $-1.64\phantom{0}\pm 0.93\phantom{0}$ | $-2.53\phantom{0}\pm 4.75\phantom{0}$ | $-0.25\phantom{0}\pm 3.87\phantom{0}$
$A_{\text{Raw}}^{\text{w}}(D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+})$ | $-0.45\phantom{0}\pm 0.02\phantom{0}$ | $\phantom{+}0.58\phantom{0}\pm 0.08\phantom{0}$ | $\phantom{+}0.60\phantom{0}\pm 0.07\phantom{0}$
$\mathcal{A}_{{C\\!P}}(D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+})$ | $-0.02\phantom{0}\pm 0.12\phantom{0}$ | $-0.01\phantom{0}\pm 0.08\phantom{0}$ | $\phantom{+}0.09\phantom{0}\pm 0.26\phantom{0}$
$A_{\text{Mix}}(K^{0})$ | $-0.070\pm 0.004$ | $-0.072\pm 0.004$ | $-0.072\pm 0.004$
$\mathcal{A}_{{C\\!P}}(D_{(s)}^{+}\\!\rightarrow h^{+}{{\pi}^{0}})$ | $-1.3\pm 0.9\pm 0.6$ | $-3.2\pm 4.7\pm 2.1$ | $-0.8\pm 3.9\pm 1.2$
Table 6: Final $\mathcal{A}_{C\\!P}$ (%) results for the
$D_{(s)}^{+}\\!\rightarrow h^{+}\eta$ modes. The uncertainties of
$\mathcal{A}_{{C\\!P}}(D_{(s)}^{+}\\!\rightarrow h^{+}\eta)$ are statistical
and systematic respectively. The uncertainties of
$A_{\text{Raw}}(D_{(s)}^{+}\\!\rightarrow h^{+}\eta)$ are purely statistical.
The uncertainties of $A_{\text{Mix}}(K^{0})$ are systematic. Externally
measured values of
$\mathcal{A}_{{C\\!P}}(D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+})$
are taken from Refs. [37, 18, 38, 39, 40, 41]. For comparison the unweighted
control asymmetries are
$\mathcal{A}_{\text{Raw}}({{D}^{+}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}})=-0.45\pm
0.02$,
$\mathcal{A}_{\text{Raw}}({{D}^{+}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{\pi}^{+}})=-0.13\pm
0.17$,
$\mathcal{A}_{\text{Raw}}({{D}^{+}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{+}})=0.47\pm
0.05$ and
$\mathcal{A}_{\text{Raw}}({{D}^{+}_{s}}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}{{K}^{+}})=0.51\pm
0.04$.

| ${{D}^{+}}\\!\rightarrow{{\pi}^{+}}\eta$ | ${{D}^{+}_{s}}\\!\rightarrow{{\pi}^{+}}\eta$
---|---|---
$A_{\text{Raw}}(D_{(s)}^{+}\\!\rightarrow h^{+}\eta)$ | $-0.55\phantom{0}\pm 0.76\phantom{0}$ | $\phantom{+}0.75\phantom{0}\pm 0.65\phantom{0}$
$A_{\text{Raw}}^{\text{w}}(D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+})$ | $-0.46\phantom{0}\pm 0.04\phantom{0}$ | $-0.02\phantom{0}\pm 0.37\phantom{0}$
$\mathcal{A}_{{C\\!P}}(D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+})$ | $-0.02\phantom{0}\pm 0.12\phantom{0}$ | $\phantom{+}0.13\phantom{0}\pm 0.20\phantom{0}$
$A_{\text{Mix}}(K^{0})$ | $-0.070\pm 0.004$ | $-0.070\pm 0.004$
$\mathcal{A}_{{C\\!P}}(D_{(s)}^{+}\\!\rightarrow h^{+}\eta)$ | $-0.2\pm 0.8\pm 0.4$ | $0.8\pm 0.7\pm 0.5$

| ${{D}^{+}}\\!\rightarrow{{K}^{+}}\eta$ | ${{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}\eta$
---|---|---
$A_{\text{Raw}}(D_{(s)}^{+}\\!\rightarrow h^{+}\eta)$ | $-5.39\phantom{0}\pm 10.40\phantom{0}$ | $\phantom{+}1.28\phantom{0}\pm 3.67\phantom{0}$
$A_{\text{Raw}}^{\text{w}}(D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+})$ | $\phantom{+}0.33\phantom{0}\pm\phantom{0}0.10\phantom{0}$ | $\phantom{+}0.36\phantom{0}\pm 0.10\phantom{0}$
$\mathcal{A}_{{C\\!P}}(D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+})$ | $-0.01\phantom{0}\pm\phantom{0}0.08\phantom{0}$ | $\phantom{+}0.09\phantom{0}\pm 0.26\phantom{0}$
$A_{\text{Mix}}(K^{0})$ | $-0.073\pm\phantom{0}0.004$ | $-0.073\pm 0.004$
$\mathcal{A}_{{C\\!P}}(D_{(s)}^{+}\\!\rightarrow h^{+}\eta)$ | $-6\pm 10\pm 4$ | $0.9\pm 3.7\pm 1.1$

In summary, measurements of $C\\!P$ asymmetries in $D_{(s)}^{+}\\!\rightarrow
h^{+}{{\pi}^{0}}$ and $D_{(s)}^{+}\\!\rightarrow h^{+}\eta$ decays are
performed using $p$ $p$ collision data corresponding to 9$\text{\,fb}^{-1}$
and 6$\text{\,fb}^{-1}$ of integrated luminosity collected at the LHCb
experiment, respectively. The neutral mesons are reconstructed using the
${e^{+}}{e^{-}}\gamma$ final state, allowing the $D^{+}_{(s)}$ decay vertex to
be reconstructed. The production and detection asymmetries are cancelled using
large samples of $D_{(s)}^{+}\\!\rightarrow{{K}^{0}_{\mathrm{S}}}h^{+}$
decays, weighted to match the kinematics of the signal modes. The $C\\!P$
asymmetries are determined to be

$\displaystyle\mathcal{A}_{{C\\!P}}({{D}^{+}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{0}})$
$\displaystyle=(-$ $\displaystyle 1.3$ $\displaystyle\pm 0.9$
$\displaystyle\pm 0.6$ $\displaystyle)\%,$
$\displaystyle\mathcal{A}_{{C\\!P}}({{D}^{+}}\\!\rightarrow{{K}^{+}}{{\pi}^{0}})$
$\displaystyle=(-$ $\displaystyle 3.2$ $\displaystyle\pm 4.7$
$\displaystyle\pm 2.1$ $\displaystyle)\%,$
$\displaystyle\mathcal{A}_{{C\\!P}}({{D}^{+}}\\!\rightarrow{{\pi}^{+}}\eta)$
$\displaystyle=(-$ $\displaystyle 0.2$ $\displaystyle\pm 0.8$
$\displaystyle\pm 0.4$ $\displaystyle)\%,$
$\displaystyle\mathcal{A}_{{C\\!P}}({{D}^{+}}\\!\rightarrow{{K}^{+}}\eta)$
$\displaystyle=(-$ $\displaystyle 6$ $\displaystyle\pm 10$ $\displaystyle\pm
4$ $\displaystyle)\%,$
$\displaystyle\mathcal{A}_{{C\\!P}}({{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{\pi}^{0}})$
$\displaystyle=(-$ $\displaystyle 0.8$ $\displaystyle\pm 3.9$
$\displaystyle\pm 1.2$ $\displaystyle)\%,$
$\displaystyle\mathcal{A}_{{C\\!P}}({{D}^{+}_{s}}\\!\rightarrow{{\pi}^{+}}\eta)$
$\displaystyle=($ $\displaystyle 0.8$ $\displaystyle\pm 0.7$ $\displaystyle\pm
0.5$ $\displaystyle)\%,$
$\displaystyle\mathcal{A}_{{C\\!P}}({{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}\eta)$
$\displaystyle=($ $\displaystyle 0.9$ $\displaystyle\pm 3.7$ $\displaystyle\pm
1.1$ $\displaystyle)\%,$

where the first uncertainty is statistical and the second systematic. All of
the results are consistent with no $C\\!P$ asymmetry and the first five
constitute the most precise measurements to date. Very recently the Belle
collaboration has also reported precise measurements of
$\mathcal{A}_{{C\\!P}}({{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}{{\pi}^{0}})$,
$\mathcal{A}_{{C\\!P}}({{D}^{+}_{s}}\\!\rightarrow{{\pi}^{+}}\eta)$ and
$\mathcal{A}_{{C\\!P}}({{D}^{+}_{s}}\\!\rightarrow{{K}^{+}}\eta)$ [42]. The
result for
$\mathcal{A}_{{C\\!P}}({{D}^{+}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{0}})$ is
consistent with the SM expectation and the previous measurement by the Belle
collaboration [10]. Using the relevant lifetimes, branching fractions and
$C\\!P$ asymmetries from Ref. [11] and an updated average of
$\mathcal{A}_{{C\\!P}}({{D}^{+}}\\!\rightarrow{{\pi}^{+}}{{\pi}^{0}})=(0.43\pm
0.79)\%$ calculated using the measurements by Belle [10], CLEO [43] and the
result presented here, the isospin sum rule defined in Eq. 2 is found to be
consistent with zero, with a value of $R=(0.1\pm 2.4)\times 10^{-3}$.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments
for the excellent performance of the LHC. We thank the technical and
administrative staff at the LHCb institutes. We acknowledge support from CERN
and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); MOST
and NSFC (China); CNRS/IN2P3 (France); BMBF, DFG and MPG (Germany); INFN
(Italy); NWO (Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MSHE
(Russia); MICINN (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC
(United Kingdom); DOE NP and NSF (USA). We acknowledge the computing resources
that are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN
(Italy), SURF (Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and
Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-
GRID (Poland) and NERSC (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 ARC and ARDC (Australia); AvH Foundation
(Germany); EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union);
A*MIDEX, ANR, Labex P2IO and OCEVU, and Région Auvergne-Rhône-Alpes (France);
Key Research Program of Frontier Sciences of CAS, CAS PIFI, CAS CCEPP,
Fundamental Research Funds for the Central Universities, and Sci. & Tech.
Program of Guangzhou (China); RFBR, RSF and Yandex LLC (Russia); GVA, XuntaGal
and GENCAT (Spain); the Leverhulme Trust, the Royal Society and UKRI (United
Kingdom).

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LHCb collaboration

R. Aaij32, C. Abellán Beteta50, T. Ackernley60, B. Adeva46, M. Adinolfi54, H.
Afsharnia9, C.A. Aidala85, S. Aiola25, Z. Ajaltouni9, S. Akar65, J.
Albrecht15, F. Alessio48, M. Alexander59, A. Alfonso Albero45, Z. Aliouche62,
G. Alkhazov38, P. Alvarez Cartelle55, S. Amato2, Y. Amhis11, L. An48, L.
Anderlini22, A. Andreianov38, M. Andreotti21, F. Archilli17, A. Artamonov44,
M. Artuso68, K. Arzymatov42, E. Aslanides10, M. Atzeni50, B. Audurier12, S.
Bachmann17, M. Bachmayer49, J.J. Back56, P. Baladron Rodriguez46, V.
Balagura12, W. Baldini21, J. Baptista Leite1, R.J. Barlow62, S. Barsuk11, W.
Barter61, M. Bartolini24, F. Baryshnikov82, J.M. Basels14, G. Bassi29, B.
Batsukh68, A. Battig15, A. Bay49, M. Becker15, F. Bedeschi29, I. Bediaga1, A.
Beiter68, V. Belavin42, S. Belin27, V. Bellee49, K. Belous44, I. Belov40, I.
Belyaev41, G. Bencivenni23, E. Ben-Haim13, A. Berezhnoy40, R. Bernet50, D.
Berninghoff17, H.C. Bernstein68, C. Bertella48, A. Bertolin28, C.
Betancourt50, F. Betti48, Ia. Bezshyiko50, S. Bhasin54, J. Bhom35, L. Bian73,
M.S. Bieker15, S. Bifani53, P. Billoir13, M. Birch61, F.C.R. Bishop55, A.
Bitadze62, A. Bizzeti22,k, M. Bjørn63, M.P. Blago48, T. Blake56, F. Blanc49,
S. Blusk68, D. Bobulska59, J.A. Boelhauve15, O. Boente Garcia46, T.
Boettcher64, A. Boldyrev81, A. Bondar43, N. Bondar38,48, S. Borghi62, M.
Borisyak42, M. Borsato17, J.T. Borsuk35, S.A. Bouchiba49, T.J.V. Bowcock60, A.
Boyer48, C. Bozzi21, M.J. Bradley61, S. Braun66, A. Brea Rodriguez46, M.
Brodski48, J. Brodzicka35, A. Brossa Gonzalo56, D. Brundu27, A. Buonaura50, C.
Burr48, A. Bursche72, A. Butkevich39, J.S. Butter32, J. Buytaert48, W.
Byczynski48, S. Cadeddu27, H. Cai73, R. Calabrese21,f, L. Calefice15,13, L.
Calero Diaz23, S. Cali23, R. Calladine53, M. Calvi26,j, M. Calvo Gomez84, P.
Camargo Magalhaes54, A. Camboni45,84, P. Campana23, A.F. Campoverde Quezada6,
S. Capelli26,j, L. Capriotti20,d, A. Carbone20,d, G. Carboni31, R.
Cardinale24, A. Cardini27, I. Carli4, P. Carniti26,j, L. Carus14, K. Carvalho
Akiba32, A. Casais Vidal46, G. Casse60, M. Cattaneo48, G. Cavallero48, S.
Celani49, J. Cerasoli10, A.J. Chadwick60, M.G. Chapman54, M. Charles13, Ph.
Charpentier48, G. Chatzikonstantinidis53, C.A. Chavez Barajas60, M.
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M. Chrzaszcz35, A. Chubykin38, V. Chulikov38, P. Ciambrone23, M.F. Cicala56,
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C.J. Pawley79, A. Pearce48, A. Pellegrino32, M. Pepe Altarelli48, S.
Perazzini20, D. Pereima41, P. Perret9, M. Petric59,48, K. Petridis54, A.
Petrolini24,h, A. Petrov80, S. Petrucci58, M. Petruzzo25, T.T.H. Pham68, A.
Philippov42, L. Pica29,n, M. Piccini77, B. Pietrzyk8, G. Pietrzyk49, M.
Pili63, D. Pinci30, F. Pisani48, Resmi P.K10, V. Placinta37, J. Plews53, M.
Plo Casasus46, F. Polci13, M. Poli Lener23, M. Poliakova68, A. Poluektov10, N.
Polukhina82,u, I. Polyakov68, E. Polycarpo2, G.J. Pomery54, S. Ponce48, D.
Popov6,48, S. Popov42, S. Poslavskii44, K. Prasanth35, L. Promberger48, C.
Prouve46, V. Pugatch52, H. Pullen63, G. Punzi29,n, W. Qian6, J. Qin6, R.
Quagliani13, B. Quintana8, N.V. Raab18, R.I. Rabadan Trejo10, B. Rachwal34,
J.H. Rademacker54, M. Rama29, M. Ramos Pernas56, M.S. Rangel2, F.
Ratnikov42,81, G. Raven33, M. Reboud8, F. Redi49, F. Reiss62, C. Remon
Alepuz47, Z. Ren3, V. Renaudin63, R. Ribatti29, S. Ricciardi57, K. Rinnert60,
P. Robbe11, A. Robert13, G. Robertson58, A.B. Rodrigues49, E. Rodrigues60,
J.A. Rodriguez Lopez74, A. Rollings63, P. Roloff48, V. Romanovskiy44, M.
Romero Lamas46, A. Romero Vidal46, J.D. Roth85, M. Rotondo23, M.S. Rudolph68,
T. Ruf48, J. Ruiz Vidal47, A. Ryzhikov81, J. Ryzka34, J.J. Saborido Silva46,
N. Sagidova38, N. Sahoo56, B. Saitta27,e, D. Sanchez Gonzalo45, C. Sanchez
Gras32, R. Santacesaria30, C. Santamarina Rios46, M. Santimaria23, E.
Santovetti31,p, D. Saranin82, G. Sarpis59, M. Sarpis75, A. Sarti30, C.
Satriano30,o, A. Satta31, M. Saur15, D. Savrina41,40, H. Sazak9, L.G.
Scantlebury Smead63, S. Schael14, M. Schellenberg15, M. Schiller59, H.
Schindler48, M. Schmelling16, B. Schmidt48, O. Schneider49, A. Schopper48, M.
Schubiger32, S. Schulte49, M.H. Schune11, R. Schwemmer48, B. Sciascia23, S.
Sellam46, A. Semennikov41, M. Senghi Soares33, A. Sergi24,48, N. Serra50, L.
Sestini28, A. Seuthe15, P. Seyfert48, Y. Shang5, D.M. Shangase85, M.
Shapkin44, I. Shchemerov82, L. Shchutska49, T. Shears60, L. Shekhtman43,v, Z.
Shen5, V. Shevchenko80, E.B. Shields26,j, E. Shmanin82, J.D. Shupperd68, B.G.
Siddi21, R. Silva Coutinho50, G. Simi28, S. Simone19,c, N. Skidmore62, T.
Skwarnicki68, M.W. Slater53, I. Slazyk21,f, J.C. Smallwood63, J.G. Smeaton55,
A. Smetkina41, E. Smith14, M. Smith61, A. Snoch32, M. Soares20, L. Soares
Lavra9, M.D. Sokoloff65, F.J.P. Soler59, A. Solovev38, I. Solovyev38, F.L.
Souza De Almeida2, B. Souza De Paula2, B. Spaan15, E. Spadaro Norella25,i, P.
Spradlin59, F. Stagni48, M. Stahl65, S. Stahl48, P. Stefko49, O.
Steinkamp50,82, O. Stenyakin44, H. Stevens15, S. Stone68, M.E. Stramaglia49,
M. Straticiuc37, D. Strekalina82, F. Suljik63, J. Sun27, L. Sun73, Y. Sun66,
P. Svihra62, P.N. Swallow53, K. Swientek34, A. Szabelski36, T. Szumlak34, M.
Szymanski48, S. Taneja62, F. Teubert48, E. Thomas48, K.A. Thomson60, V.
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D.Y. Tou13, M.T. Tran49, E. Trifonova82, C. Trippl49, G. Tuci29,n, A. Tully49,
N. Tuning32,48, A. Ukleja36, D.J. Unverzagt17, E. Ursov82, A. Usachov32, A.
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A. Venkateswaran68, M. Veronesi32, M. Vesterinen56, D. Vieira65, M. Vieites
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Zuliani28, G. Zunica62.

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
4Institute Of High Energy Physics (IHEP), Beijing, China
5School of Physics State Key Laboratory of Nuclear Physics and Technology,
Peking University, Beijing, China
6University of Chinese Academy of Sciences, Beijing, China
7Institute of Particle Physics, Central China Normal University, Wuhan, Hubei,
China
8Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy, France
9Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
10Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
11Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France
12Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut
Polytechnique de Paris, Palaiseau, France
13LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3,
Paris, France
14I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
15Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
16Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
17Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
18School of Physics, University College Dublin, Dublin, Ireland
19INFN Sezione di Bari, Bari, Italy
20INFN Sezione di Bologna, Bologna, Italy
21INFN Sezione di Ferrara, Ferrara, Italy
22INFN Sezione di Firenze, Firenze, Italy
23INFN Laboratori Nazionali di Frascati, Frascati, Italy
24INFN Sezione di Genova, Genova, Italy
25INFN Sezione di Milano, Milano, Italy
26INFN Sezione di Milano-Bicocca, Milano, Italy
27INFN Sezione di Cagliari, Monserrato, Italy
28Universita degli Studi di Padova, Universita e INFN, Padova, Padova, Italy
29INFN Sezione di Pisa, Pisa, Italy
30INFN Sezione di Roma La Sapienza, Roma, Italy
31INFN Sezione di Roma Tor Vergata, Roma, Italy
32Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
33Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, Netherlands
34AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
35Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
36National Center for Nuclear Research (NCBJ), Warsaw, Poland
37Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
38Petersburg Nuclear Physics Institute NRC Kurchatov Institute (PNPI NRC KI),
Gatchina, Russia
39Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS),
Moscow, Russia
40Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
41Institute of Theoretical and Experimental Physics NRC Kurchatov Institute
(ITEP NRC KI), Moscow, Russia
42Yandex School of Data Analysis, Moscow, Russia
43Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
44Institute for High Energy Physics NRC Kurchatov Institute (IHEP NRC KI),
Protvino, Russia, Protvino, Russia
45ICCUB, Universitat de Barcelona, Barcelona, Spain
46Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
47Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain
48European Organization for Nuclear Research (CERN), Geneva, Switzerland
49Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
50Physik-Institut, Universität Zürich, Zürich, Switzerland
51NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
52Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
53University of Birmingham, Birmingham, United Kingdom
54H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
55Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
56Department of Physics, University of Warwick, Coventry, United Kingdom
57STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
58School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
59School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
60Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
61Imperial College London, London, United Kingdom
62Department of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
63Department of Physics, University of Oxford, Oxford, United Kingdom
64Massachusetts Institute of Technology, Cambridge, MA, United States
65University of Cincinnati, Cincinnati, OH, United States
66University of Maryland, College Park, MD, United States
67Los Alamos National Laboratory (LANL), Los Alamos, United States
68Syracuse University, Syracuse, NY, United States
69School of Physics and Astronomy, Monash University, Melbourne, Australia,
associated to 56
70Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
71Physics and Micro Electronic College, Hunan University, Changsha City,
China, associated to 7
72Guangdong Provencial Key Laboratory of Nuclear Science, Institute of Quantum
Matter, South China Normal University, Guangzhou, China, associated to 3
73School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
74Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 13
75Universität Bonn - Helmholtz-Institut für Strahlen und Kernphysik, Bonn,
Germany, associated to 17
76Institut für Physik, Universität Rostock, Rostock, Germany, associated to 17
77INFN Sezione di Perugia, Perugia, Italy, associated to 21
78Van Swinderen Institute, University of Groningen, Groningen, Netherlands,
associated to 32
79Universiteit Maastricht, Maastricht, Netherlands, associated to 32
80National Research Centre Kurchatov Institute, Moscow, Russia, associated to
41
81National Research University Higher School of Economics, Moscow, Russia,
associated to 42
82National University of Science and Technology “MISIS”, Moscow, Russia,
associated to 41
83National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
41
84DS4DS, La Salle, Universitat Ramon Llull, Barcelona, Spain, associated to 45
85University of Michigan, Ann Arbor, United States, associated to 68

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bHangzhou Institute for Advanced Study, UCAS, Hangzhou, China
cUniversità di Bari, Bari, Italy
dUniversità di Bologna, Bologna, Italy
eUniversità di Cagliari, Cagliari, Italy
fUniversità di Ferrara, Ferrara, Italy
gUniversità di Firenze, Firenze, Italy
hUniversità di Genova, Genova, Italy
iUniversità degli Studi di Milano, Milano, Italy
jUniversità di Milano Bicocca, Milano, Italy
kUniversità di Modena e Reggio Emilia, Modena, Italy
lUniversità di Padova, Padova, Italy
mScuola Normale Superiore, Pisa, Italy
nUniversità di Pisa, Pisa, Italy
oUniversità della Basilicata, Potenza, Italy
pUniversità di Roma Tor Vergata, Roma, Italy
qUniversità di Siena, Siena, Italy
rUniversità di Urbino, Urbino, Italy
sMSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines
tAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
uP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
vNovosibirsk State University, Novosibirsk, Russia
wDepartment of Physics and Astronomy, Uppsala University, Uppsala, Sweden
xHanoi University of Science, Hanoi, Vietnam