Published for SISSA by

Springer

Received: November 20, 2023
Accepted: February 4, 2024
Published: February 16, 2024

The LHCb collaboration
E-mail: seophine.stanislaus@cern.ch
Abstract: A measurement of CP -violating observables in B ± → D∗ K ± and B ± → D∗ π ±decays is made where the photon or neutral pion from the D∗ → Dγ or D∗ → Dπ 0 decay
is not reconstructed. The D meson is reconstructed in the self-conjugate decay modes,
D → KS0 π + π − or D → KS0 K + K − . The distribution of signal yields in the D decay phasespace is analysed in a model-independent way. The measurement uses a data sample collectedin proton-proton collisions at centre-of-mass energies of 7, 8, and 13 TeV, corresponding toa total integrated luminosity of approximately 9 fb−1 . The B ± → D∗ K ± and B ± → D∗ π ±CP -violating observables are interpreted in terms of hadronic parameters and the CKM angle◦
γ, resulting in a measurement of γ = (92+21−17 ) . The total uncertainty includes the statisticaland systematic uncertainties, and the uncertainty due to external strong-phase inputs.
Keywords: B Physics, CKM Angle Gamma, CP Violation, Hadron-Hadron Scattering
ArXiv ePrint: 2311.10434

Open Access, Copyright CERN,
for the benefit of the LHCb Collaboration.
Article funded by SCOAP3 .

https://doi.org/10.1007/JHEP02(2024)118

JHEP02(2024)118

A model-independent measurement of the CKM angle
γ in partially reconstructed B ± → D ∗h± decays with
D → KS0 h+h− (h = π, K)

Contents
1

2 Analysis overview

2

3 LHCb detector and simulation

44 Candidate selection

5

5 Reconstructed mass fit

6

6 Determination of the CP -violating observables

9

7 Systematic uncertainties

128 Interpretation

15

9 Conclusion

17

A Correlation matrices

18

The LHCb collaboration

23

1

Introduction

In the Standard Model, CP violation in the quark sector is described using the CabibboKobayashi-Maskawa (CKM) matrix [1, 2]. One representation of this matrix is the Unitarity
Triangle [3]. The CKM angle γ ≡ arg(−Vud Vub ∗ /Vcd Vcb ∗ ) can be measured using tree-level
decays. Assuming tree-level processes do not include physics beyond the Standard Model [4, 5],
a comparison of direct γ measurements and indirect determinations can test the Standard
Model [6]. This is because indirect determinations come from global CKM fits using other
CKM observables, which are sensitive to physics beyond the Standard Model. In addition,measurements of γ have negligible theoretical uncertainty [7] because all hadronic parameters
are determined directly from data, removing the need to model non-perturbative hadronic
effects that can result in large theoretical uncertainties. The current value of the indirect◦
determination is γ = (65.5+1.1−2.7 ) [8] whilst the latest γ combination using LHCb data yields+3.5 ◦
γ = (63.8−3.7 ) [9].
The interference of b → c and b → u amplitudes can be used to measure γ. This
paper presents a study of B ± → [Dγ/π 0 ]D∗ h± decays, h = {π, K}. The D∗ meson is asuperposition of the D∗0 (2007)0 and D∗0 (2007)0 states and decays to a neutral D meson andan accompanying photon or neutral pion. The D meson is a superposition of the D0 and D0
states and subsequently decays to KS0 h+ h− . Therefore, the effects of the interference manifest
themselves as differences in the D-decay Dalitz-plot distributions for decays originating from

–1–

JHEP02(2024)118

1 Introduction

2

Analysis overview

In B − → [Dγ/π 0 ]D∗ h− decays, the D meson is a superposition of the D0 and D0 states.
Therefore, the favoured contribution (via D0 ) and the suppressed contribution (via D0 ) caninterfere if the decay products of the D meson are common to both D0 and D0 . As an
example, the overall amplitude for B − → [Dπ 0 ]D∗ K − can be written as,
∗

∗

∗

∗

D K
D K
− γ)]AD ),A(B − → [Dπ 0 ]D∗ K − ) = AB (AD + rB
exp[i(δB(2.1)

and for B − → [Dγ]D∗ K − as
D K
D K
A(B − → [Dγ]D∗ K − ) = AB (AD − rB
exp[i(δB− γ)]AD ),(2.2)

where AB is the amplitude of the favoured B − decay, and AD(D) is the amplitude of theD ∗ K and δ D ∗ K , are the ratio of the magnitudes
D0 (D0 ) decay. The hadronic parameters, rB
Bof the suppressed and favoured B ± decays and the strong-phase difference between them,–2–

JHEP02(2024)118

a B + or B − meson. The D → KS0 h+ h− modes are considered golden channels given their richinterference structures. These can be exploited to measure γ [10–13] by binning the Dalitz
plots. To interpret the Dalitz-plot distributions in terms of γ, strong-phase information for
the D decays is required. In this study, a model-independent approach is adopted, whichuses strong-phase measurements from BESIII [14, 15] and CLEO [16]. The strong-phaseparameters were determined using quantum correlated D0 D0 pairs produced at the ψ(3770)
resonance. The use of these directly measured parameters results in systematic uncertainties
on γ that are reliably determined. This avoids use of any amplitude model where theassociated uncertainty is difficult to estimate.
The decay chain of B ± → D∗ K ± with D∗ → Dπ 0 or D∗ → Dγ, followed by the
D → KS0 h+ h− decay, has been studied in the Belle [17] and BaBar [18] experiments. For eachexperiment, it was analysed alongside other B ± decays using a model-dependent method.
Recently, this decay has also been studied at LHCb [19], leading to a measurement of
γ = (69 ± 14)◦ . The key difference between the measurement presented in ref. [19] and that
presented here is the treatment of the photon and neutral pion from the decay of the D∗ meson.
Here, no reconstruction requirements are placed on these neutral particles, leading to a highselection efficiency, but with the additional complication of a higher background level. The
B ± → D∗ K ± CP -violating observables are better constrained here, but the large backgroundcontributions lead to, comparatively, worse constraints on the B ± → D∗ π ± CP -violating
observables. In ref. [19], the photon and neutral pion from the D∗ decay are reconstructed andthe selection requirements placed on them reduce the signal efficiency by approximately 75%
due to the complex reconstruction of low momentum neutral particles at LHCb [20]. Since
no requirement is placed on the neutral particle in the present analysis, the D∗ → Dγ andD∗ → Dπ 0 components are distinguished using their different distributions in the invariant
mass combination of the D meson and its companion hadron, m(Dh). This exploits the
spin-parity structure of the D∗ decays. The measurement in this analysis is performed using
a data sample collected in proton-proton (pp) collisions at centre-of-mass energies of 7, 8,
and 13 TeV, corresponding to a total integrated luminosity of approximately 9 fb−1 .

R+ |AD (s− , s+ )| AD (s+ , s− ) cos(δD (s− , s+ ) − δD (s+ , s− ))i ds− dsq
,
R
2
2R
ds
ds
|A
(s
,
s
)|
ds
ds
A
(s
,
s
)
−
+
+
−
−
+
−
+
D
i
i
D

R

+ |AD (s− , s+ )| AD (s+ , s− ) sin(δD (s− , s+ ) − δD (s+ , s− ))i ds− ds
qR
,
2
2R
ds
ds
|A
(s
,
s
)|
ds
ds
A
(s
,
s
)
−
+
−
+
−
+
+
−
D
i
i
D

ci ≡
si ≡

(2.3)

where i ds− ds+ denotes integration over the phase space of the ith Dalitz bin. These
measurements are efficiency-corrected at BESIII and CLEO and assumed to be directly
applicable in an LHCb analysis as the efficiency correction is small.
In this analysis, effects from CP violation in D decays and from D mixing are assumed
to be negligible, considering the current experimental sensitivity [23]. In addition, KS0
mixing, regeneration in KS0 interactions with matter, and KS0 CP violation are similarly
ignored [24]. As a result, the CP transformation of the D decay amplitudes results in
AD (s− , s+ ) = AD (s+ , s− ). The expected yield of the B ± decays per Dalitz bin is calculated
by squaring the overall amplitudes and integrating over phase space and decay time. When
doing so, the observed fractional yield of D0 decays in bin i is defined as,R2i ds− ds+ η(s− , s+ ) |AD (s− , s+ )|Fi ≡ R,ds− ds+ η(s− , s+ ) |AD (s− , s+ )|2

R

(2.4)

where η(s− , s+ ) is the experimental efficiency. Furthermore, a set of CP -violating observables–3–

JHEP02(2024)118

respectively. The sign change between eqs. (2.1) and (2.2) arises from a phase shift of π
between the strong-phase differences due to the quantum numbers of the pion and photon [21].
In order to use a single strong-phase parameter for all B ± → [Dγ/π 0 ]D∗ K ± decays, the phaseshift is propagated through as a sign change. Similar amplitudes to eqs. (2.1) and (2.2) can be
written for B + decays where AD is replaced by AD and vice versa, and −γ is replaced by +γ.
This sign change on γ allows a measurement to be extracted using B + and B − decays. Similar
amplitudes can also be written for the B ± →D∗ π ± decays with replacements for rB and δB .
The Dalitz-plot formalism is used to describe the D → KS0 h+ h− phase space with twodegrees of freedom: s+ , the squared invariant mass of the KS0 h+ system, and s− , the squared
invariant mass of the KS0 h− system. Each point on the Dalitz plot represents a different
kinematic final state of the D decay described by the corresponding hadronic parameters.
The analysis is performed in 2 × N bins of the Dalitz plot (referred to as Dalitz bins), labelled
i = −N to +N excluding zero. The Dalitz bins are symmetrical about the line s+ = s− ,with positive bins where s− > s+ and negative bins where s− < s+ . The Dalitz binningschemes for D → KS0 π + π − and D → KS0 K + K − decays are known as the ‘optimal’ (N = 8)
and ‘2-bins’ (N = 2) binning schemes, respectively. These were constructed such that the
average of the strong phases across a bin maximises sensitivity to γ and are detailed inref. [16]. These are the same binning schemes used in ref. [22] which studied B ± → Dh±decays with the D meson decaying to the same final state.
The analysis presented in this paper uses a model-independent approach, taking strongphase measurements for the D decays from BESIII [14, 15] and CLEO [16] in the form of ci
and si parameters. These are the amplitude-averaged cosine and sine of the strong-phasedifference between the D0 and D0 decays,∗∗

D K , δ D K , and γ,
can be defined using the physical parameters, rB
B
∗

∗

∗

∗

∗

∗

K
D K
D K
D K
D K
D K
xD
≡ rB
cos(δB± γ) and y±≡ rBsin(δB
± γ).
±

(2.5)

A parameterisation [25] for the B ± → D∗ π ± decays, because γ is common among all decays,
involves the introduction of a new quantity,
∗

D π
rB
D∗ π
D∗ K
ξ≡ D
− δB
)].
∗ K exp[i(δB
rB

(2.6)

∗

∗

∗

∗

∗

∗

π
K
D K
D π
D K
K
xD
= ℜ(ξ)xD− ℑ(ξ)y±and y±= ℜ(ξ)y±+ ℑ(ξ)xD
.
±
±
±

(2.7)

The resulting yield equations for B ± → [Dπ 0 /γ]D∗ h± decays with the appropriate CP violating observables, where the superscripts have been omitted for brevity, are
0

0

p

0

0

p

Dπ
2
Ni+, Dπ = h+,[F−i + (x2+ + y+
)F+i + 2 F−i F+i (ci x+ − si y+ )],B
Dπ2
Ni−, Dπ = h−,[F+i + (x2− + y−
)F−i + 2 F+i F−i (ci x− + si y− )],BDγ
2Ni+, Dγ = h+,[F−i + (x2+ + y+
)F+i − 2 F−i F+i (ci x+ − si y+ )],
B

p

(2.8)

Dγ
2
Ni−, Dγ = h−,[F+i + (x2− + y−
)F−i − 2 F+i F−i (ci x− + si y− )],
B

p

0

Dγ
Dπ
where h±,and h±,
are normalisation constants. The separate normalisation for eachB
B∗
B charge and D decay absorbs production and most detection asymmetries. To fix thisnormalisation, the yield per Dalitz bin is determined using,Y±±
Ni± = P i ± Ntotal
,
j Yj

(2.9)

where Yi± is the fractional yield in a Dalitz bin, i.e. eq. (2.8) without the normalisation
constants, and is therefore determined via the Fi parameters and CP -violating observables.
The total yield for a signal component over the entire D decay phase space is determined±in a fit to the reconstructed mass and denoted by Ntotal. In deriving eq. (2.8), the effect ofdetector efficiency is taken into account in the measured Fi values.
From the above description, the analysis strategy can be summarised as follows. A
sample is selected as described in section 4. Then the m(Dh) distribution of every signal
and background component is determined using a global fit, as described in section 5. The
resulting mass shapes and yields are used in a subsequent fit to determine the CP -violating
observables, as described in section 6. The associated systematic uncertainties are evaluatedin section 7. The CP -violating observables are then interpreted in terms of the physicalparameters, including γ, as described in section 8.

3

LHCb detector and simulation

The LHCb detector [26, 27] is a single-arm forward spectrometer covering the pseudorapidity
range 2 < η < 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–4–

JHEP02(2024)118

Using the real and imaginary parts of the ξ parameter, the CP -violating observables for
B ± → D∗ π ± can be recovered,

4

Candidate selection

The candidate selection used in this paper is built on that used to select B ± → [KS0 h+ h− ]D h′±
decays in ref. [22]. This reconstructs the same final state as in the present analysis, wherereconstruction of the photon or neutral pion from the D∗ decay is not required.
A B decay candidate is built by first reconstructing a KS0 meson using two tracks identified
as oppositely charged pions. If the pion tracks are reconstructed in the vertex detector, they
form a long KS0 candidate, otherwise they form a downstream KS0 candidate. This distinction
is important since long KS0 candidates have better mass, vertex, and momentum resolution.
For this reason, long and downstream KS0 candidates are treated separately. The KS0 meson
is combined with two further tracks identified as either oppositely charged pions or kaons toform a D meson candidate. Particle identification (PID) requirements are applied to thesecharged kaons and pions. The D meson candidate is then combined with a companion kaon orpion, again distinguished using PID requirements, to form a B meson candidate. To improve–5–

JHEP02(2024)118

the pp interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw
drift tubes placed downstream of the magnet. The tracking system provides a measurementof the momentum, p, of charged particles with a relative uncertainty that varies from 0.5% at
low momentum to 1.0% at 200 GeV/c for tracks that are reconstructed in the vertex detector.
For these, 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/pT ) µm, where pT is the componentof the momentum transverse to the beam, in GeV/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 calorimeter 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. The latter is further split into two stages. First,
at least one particle is required to have high pT and high χ2IP , where χ2IP is defined as
the difference in the primary vertex fit χ2 with and without the inclusion of that particle.
Then a multivariate algorithm [28] is used to identify secondary vertices consistent withbeing a two-, three-, or four-track b-hadron decay. The PVs are fitted with and without
the tracks of the decay products of the B candidate, and the PV that gives the smallest
χ2IP is associated with the B candidate.
Simulation is primarily used to model mass distributions of the signal and backgroundcomponents and determine efficiencies. In the simulation, pp collisions are generated using
Pythia [29, 30] with a specific LHCb configuration [31]. Decays of unstable particles aredescribed by EvtGen [32], in which final-state radiation is generated using Photos [33].
The interaction of the generated particles with the detector and its response are implemented
using the Geant4 toolkit [34, 35] as described in ref. [36]. The underlying pp interaction
is reused multiple times, with an independently generated signal decay for each [37]. In
addition, fast simulation [38, 39] is used to model backgrounds with broad mass distributions.

5

Reconstructed mass fit

The global fit is a binned extended maximum-likelihood fit to the reconstructed mass, m(Dh),over the range 4900–5600 MeV/c2 . There are four signal components, B ± → [Dγ]D∗ K ± ,B ± → [Dγ]D∗ π ± , B ± → [Dπ 0 ]D∗ K ± , and B ± → [Dπ 0 ]D∗ π ± where a photon or a neutralpion are missed, and a number of background components from both charged and neutral
B hadrons.
The signals from the two D∗ decay modes are distinguished using their different m(Dh)spectra which depend on the spin-parity and mass of the missing neutral particle. For B ± →[Dγ]D∗ h± decays, the m(Dh) distribution is described by a parabola exhibiting a maximum,
where the range is defined by kinematic limits, a and b. Mass-dependent reconstruction andselection efficiencies require the introduction of a linear dependence defined by the asymmetry
parameter, ζ. Detector resolution effects are accounted for by convolving the parabola and⃗ defined by a set of variables θ.
⃗ Thisasymmetry term with a resolution function, pRes (m|θ),results in a broad structure described by the following probability density function (PDF),
Z b⃗ 1 − ζ µ + bζ − a .
B → [Dγ]D∗ h : p(m) = −dµ(µ − a)(µ − b)pRes (m|θ)
b−a
b−a
a
±

±



–6–



(5.1)

JHEP02(2024)118

the mass resolution of the reconstructed B candidate, a kinematic fit [40] is applied, where
the reconstructed masses of the KS0 and D mesons are constrained to their known values.
The optimal PID requirement for the companion track is determined using pseudoexperiments to evaluate the sensitivity to γ. A tighter identification requirement for the
DK sample than that in ref. [22] is found to be favourable, resulting in around 70% oftrue companion kaons reconstructed in the B ± → DK ± data sample, with the remainder
misidentified and reconstructed in the B ± → Dπ ± sample. The requirement results in only
5% of the true companion pions being misidentified and reconstructed in the B ± → DK ±data sample. Further PID requirements are placed on the D decay products to reduce
background from semileptonic D decays.
The background contributions from B ± → D∗ h± decays with D → π + π − π + π − or
D → K + K − π + π − are reduced by requiring the decay vertex of long KS0 candidates tobe significantly displaced from the D decay vertex. Also, the background from B decaysthat reach the final state without an intermediate D meson is reduced by requiring well
separated D and B decay vertices.
The large combinatorial background is suppressed using a boosted decision tree (BDT) [41,42] classifier. The details of this can be found in ref. [43], with separate BDT classifiers for longand downstream KS0 candidates and for data collected from 2011–2012 and 2015–2018. The
optimal thresholds that maximise the sensitivity to γ are determined using pseudoexperiments.
Compared to ref. [22], which used the same BDT classifier, a tighter threshold is found to benecessary, due to the higher rate of combinatorial background in the region of the B → D∗ hdecays compared to B → Dh decays in the m(Dh) spectra.
Reconstructed candidates are assigned to one of 8 categories according to the B decay, D
decay, and KS0 candidate type: (Dπ, DK) × (KS0 ππ, KS0 KK) × (downstream, long). A global
fit is performed simultaneously in these categories.

In the case of B ± → [Dπ 0 ]D∗ h± decays, the m(Dh) distribution is described by a parabolathat exhibits a minimum. Reconstruction and detector effects lead to a double-peaked structure with corresponding a, b, and ζ parameters taking into account the difference between
B ± → [Dγ]D∗ h± and B ± → [Dπ 0 ]D∗ h± decays. It is described by the following PDF,
Z ba+b
B → [Dπ ]D∗ h : p(m) =dµ µ −
2
a
±

0

±



2

⃗ 1 − ζ µ + bζ − a .
pRes (m|θ)
b−a
b−a




(5.2)

The resolution function for these signals is that used for the fully reconstructed backgrounddecays, B ± → Dh± . This is the sum of a Gaussian and a modified Gaussian function,

2σ 2 +α

R

G

(∆m)2

if ∆m < 0(5.3)

if ∆m > 0,

where pG (m|µ, σ) is a Gaussian function and αL , αR , and β are used to model radiative tails.
The parameter ∆m is m − mB where mB is the B-meson mass, a freely varying parameterin the fit. For the signal modes and the B ± → Dh± background, the shape parameters
are initially determined according to the full LHCb simulation. To obtain a good-quality
description of the simulated signal samples, the B ± → [Dπ 0 ]D∗ h± signal is parameterised
by summing two instances of the function described in eq. (5.2). In the fit to data someparameters are allowed to vary to account for resolution differences between simulation anddata. These include the width parameters for the B ± → [Dπ 0 ]D∗ h± signal and the fullyreconstructed backgrounds, and the asymmetry parameters for the B ± → [Dγ]D∗ h± signal.
The asymmetry parameters for the B ± → [Dπ 0 ]D∗ h± component are also allowed to vary.
The remaining parameters are fixed from simulation.
The background contribution from B 0 → [Dπ ∓ ]D∗∓ h± decays where the pion is missed
has a similar decay topology to B ± → [Dπ 0 ]D∗ h± decays. As a result, the background ismodelled using the same parameterisation. In the fit to data the asymmetry and widthparameters are shared with the B ± → [Dπ 0 ]D∗ h± component, and other parameters are
fixed from simulation.
There are a number of background contributions from various B decays, where one ormore particles are not reconstructed and the companion hadron h is correctly identified.
The PDFs for these background components are determined from simulation. The functions
with which the simulation samples are modelled are eq. (5.1) or eq. (5.2) with additional
Gaussian components as appropriate, convolved with a resolution function. The resolutionfunction is either a single or double Gaussian function as needed for a good description ofsimulated events. Simulated samples come from one of three sources: full simulation, which
is typically used to generate the dominant two-body decays; a fast simulation [38], which istypically used to generate multi-body decays or less common two-body decays; and a second
fast simulation package called Laura++ [39], which generates three-body decays from anamplitude model and then smears the generated momenta. The background components
modelled by fast simulation have m(Dh) distributions which are typically very broad (on theorder of 100 MeV/c2 ) compared to the B ± → Dh± . This means that resolution differences
between simulation and data are negligible and are not considered.
The dominant background contribution in m(Dπ) is from B ± → Dπ ± π 0 decays, specifically due to B ± → Dρ± decays for which the PDF is determined from simulation. In m(DK)–7–

JHEP02(2024)118
2 (1+β(∆m)2 )f exp −(∆m)+ (1 − f )pG (m|µ, σ),22L (∆m)
 2σ +αp(m) =
2 (1+β(∆m)2 )−(∆m)
f exp+ (1 − f )p (m|µ, σ),N (Bs0 → D0 K − π + )K 0 hh =S

N (Bs0 → D0 K − π + )πK
× N (B − → D0 π − )K 0 hh ,S
N (B − → D0 π − )Kπ(5.4)

where charge-conjugate processes are implied. The KS0 hh subscript denotes yields in thisanalysis, πK denotes yields from decays reconstructed as D(→ π ± K ∓ )K ± in ref. [48], andKπ denotes yields from decays reconstructed as D(→ K ± π ∓ )π ± in ref. [48]. The same
parameterisation is also used for the following backgrounds: Bs0 → D∗ K ∓ π ± , B 0 → Dπ + π − ,0−
B ± → Dh± π 0 , B → D∗ ππ, B ± → D∗ K ± π 0 , B ± → Da±
1 , and Λb → Dpπ .

–8–

JHEP02(2024)118

the largest background is from B ± → DK ± π 0 decays. This is modelled using fast simulation [38] for the B ± → D[K ± π 0 ]K ∗ (892)± and B ± → K ± [Dπ 0 ]D∗ (2400) resonances. These
resonances are combined into a single sample using fit fractions from ref. [44] with branchingratios from ref. [45]. The m(Dh) distributions for B → D∗ hπ decays are determined fromsimulation for the B ± → D∗ ρ± and B ± → D∗ K ∗± resonances, where the former is used tomodel contributions from both B ± → D∗ π ± π 0 and B 0 → D∗ π + π − decays.
Background contributions from Bs0 → DKπ and B 0 → Dhπ decays are generated using
Laura++ with amplitude models as determined in refs. [44, 46, 47]. A number of m(Dh)components are parameterised using fast simulation [38], namely, for Bs0 → D∗ Kπ and±
0 ±nonresonant B ± → Dπ ± π 0 decays, as well as B ± → Da±
1 decays with a1 → ρ π . In thelatter contribution, only the component where two pions with same-sign charges are missed
is considered, since this leads to a background component that requires careful distinctionin the subsequent CP fit. The component where two oppositely charged pions are missed
is similar in shape to the B ± → D∗ π ± π 0 and combinatorial background components and istherefore absorbed by them. There is also a small background contribution from Λ0b → Dpπ −decays, where the pion is missed and the proton is misidentified as a kaon. The m(Dh)distribution for this component is taken from ref. [48].
For each component, there is an associated cross-feed component where the companion
hadron is misidentified. Simulated samples are modified to assign the wrong particle hypothesis
and weighted to take into account the momentum-dependent misidentification efficiency. The
resulting shape is then fitted with a number of Gaussian and/or Crystal Ball functions [49] asrequired to achieve a high-quality fit. The combinatorial background is parameterised using
an exponential function where the slope is allowed to vary freely in the fit to data.
For each component, a yield is specified in the fit. The yields for the fully reconstructed±
B → Dπ ± decays vary freely in each category. The signal yields and those corresponding to
the B ± → DK ± background decays are parameterised in terms of the B ± → Dπ ± yields withratios of branching fractions and efficiencies. For the B 0 → [Dπ ∓ ]D∗∓ h± background, theratios are Gaussian-constrained to the values and uncertainties for the efficiencies, determinedfrom simulation, and for branching fractions from ref. [45]. For the majority of the remaining
background components, their branching fractions and efficiencies are not known reliably
and carry large uncertainties. A more accurate parameterisation uses fitted yields fromref. [48] where CP violation in the global yields is assumed to be negligible. For example,
this is a good assumption for the Cabibbo-favoured B ± → Dπ ± and Bs0 → D0 K − π + decays
where the corresponding value of rB is small. Therefore, the yield for the Bs0 → D0 K − π +background can be parameterised as

B ± → D∗(→ D[π 0])K ±B ± → D∗(→ D[γ])K ±0±Part. Reco. Crossfeed
Bs0 → D(∗) K ∓[π ±]B 0/± → DK ±[π]400Combinatorial
Other Backgrounds
B ± → DK ±B ± → Dπ ±

200
5000

5200

Data
Total

9 fb

B ± → D∗(→ D[π 0])K ±−1

B ± → D∗(→ D[γ])K ±400

B 0 → D∗(→ D[π ∓])K ±B 0/± → D∗[π]K ±300

Part. Reco. Crossfeed
Bs0 → D(∗) K ∓[π ±]
B

200

±

→ DK [π]Combinatorial
Other Backgrounds
B ± → DK ±B ± → Dπ ±

100
0

0/±

5000

5200

LHCb

Data
Total

9 fb

B ± → D∗(→ D[π 0])π ±−1

B ± → D∗(→ D[γ])π ±15000

B 0 → D∗(→ D[π ∓])π ±B 0/± → D∗[π]π ±Part. Reco. Crossfeed

10000

B 0/± → Dπ ±[π]Combinatorial
Other Backgrounds
B ± → Dπ ±B ± → DK ±

5000
0

5400
5600
m(DK ±) [MeV/c2]

LHCb

20000

8000

5000

5200

LHCb

Data
Total

9 fb

B ± → D∗(→ D[π 0])π ±−1

B ± → D∗(→ D[γ])π ±B 0 → D∗(→ D[π ∓])π ±6000

B 0/± → D∗[π]π ±Part. Reco. Crossfeed
B 0/± → Dπ ±[π]4000Combinatorial
Other Backgrounds
B ± → Dπ ±B ± → DK ±

2000

5400
5600
m(DK ±) [MeV/c2]

5400
5600
m(Dπ ±) [MeV/c2]

0

5000

5200

5400
5600
m(Dπ ±) [MeV/c2]

Figure 1. Mass distributions for (left) DK samples and (right) Dπ samples, with D → KS0 π + π − decays reconstructed with a (top) downstream KS0 candidate and a (bottom) long KS0 candidate. The projections of the fit results are overlaid. In the legend, particles in square brackets are not reconstructed.

The yield of the B 0 → D(∗) K ± π ∓ background is parameterised using that of theBs0 → D(∗) K ± π ∓ background using ratios of branching fractions, fragmentation fractions,and efficiencies due to the mass range. For the B ± → Dπ ± π 0 background, the total yieldis parameterised similarly to eq. (5.4), however the ratio of the B ± → Dρ± resonance tothe nonresonant component is unknown. Thus, the fraction between these two components
varies freely in the fit to data and the resonant decay is found to be dominant. All cross-feedcomponents are parameterised in terms of the yield of the correctly identified component
and corrected for the misidentification rate. The yield of the combinatorial background isallowed to vary freely in each category.
The results of the global fit are shown in figures 1 and 2 with signal and backgroundyields over the fit region, 4900–5600 MeV/c2 , quoted in table 1. For most components, the uncertainty on their yield is smaller than their Poisson uncertainty. These are components where
the ratio of yields has been fixed from external measurements or simulation. The yields of the
fully reconstructed B ± → Dh± components can be compared to those in ref. [22] where these
decays were treated as signal, and are found to be consistent considering selection differences.

6

Determination of the CP -violating observables

At this stage, a binned extended maximum-likelihood fit is performed to determine theCP -violating observables. The categories are additionally split by B meson charge and–9–

JHEP02(2024)118

Candidates / (6 MeV/c2)∓

B 0/± → D∗[π]K ±

600

500

∗

B → D (→ D[π ])K

800

0Candidates / (6 MeV/c2)

9 fb−1

Candidates / (6 MeV/c2)

Candidates / (6 MeV/c2)

1000

Data
Total

LHCb

Candidates / (6 MeV/c2)

9 fb−1

B ± → D∗(→ D[π 0])K ±B ± → D∗(→ D[γ])K ±0∗∓

B → D (→ D[π ])K±

B 0/± → D∗[π]K ±Part. Reco. Crossfeed

100

Bs0 → D(∗) K ∓[π ±]B 0/± → DK ±[π]Combinatorial
Other Backgrounds
B ± → DK ±B ± → Dπ ±

50

5200

9 fb−1

B ± → D∗(→ D[π 0])K ±B ± → D∗(→ D[γ])K ±B 0 → D∗(→ D[π ∓])K ±60

B 0/± → D∗[π]K ±Part. Reco. Crossfeed
Bs0 → D(∗) K ∓[π ±]40

B 0/± → DK ±[π]Combinatorial
Other Backgrounds
B ± → DK ±B ± → Dπ ±

20
0

5000

5200

9 fb

B ± → D∗(→ D[π 0])π ±B ± → D∗(→ D[γ])π ±B 0 → D∗(→ D[π ∓])π ±2000

B 0/± → D∗[π]π ±Part. Reco. Crossfeed

1500

B 0/± → Dπ ±[π]Combinatorial
Other Backgrounds
B ± → Dπ ±B ± → DK ±

1000

0

5400
5600
m(DK ±) [MeV/c2]
Data
Total

LHCb

Data
Total

−1

1250

5000

5200

5400
5600
m(Dπ ±) [MeV/c2]
Data
Total

LHCb
9 fb−1

B ± → D∗(→ D[π 0])π ±B ± → D∗(→ D[γ])π ±1000

B 0 → D∗(→ D[π ∓])π ±B 0/± → D∗[π]π ±Part. Reco. Crossfeed

750

B 0/± → Dπ ±[π]Combinatorial
Other Backgrounds
B ± → Dπ ±B ± → DK ±

500
250
0

5400
5600
m(DK ±) [MeV/c2]

5000

5200

5400
5600
m(Dπ ±) [MeV/c2]

Figure 2. Mass distributions for (left) DK samples and (right) Dπ samples, with D → KS0 K + K −decays reconstructed with a (top) downstream KS0 candidate and a (bottom) long KS0 candidate.
The projections of the fit results are overlaid. In the legend, particles in square brackets are notreconstructed.

Dalitz bins. It is performed in the same mass range as the global fit from which all shapeparameters are fixed.
Different components have different distributions over the Dalitz plot depending on how
they decay and whether the decay is CP -violating. The signal is described using the setof equations shown in eq. (2.8) where the CP -violating observables, x± and y± , and thenormalisation factors are free in the fit. The same is true for the B ± → Dh± backgroundwhere corresponding CP -violating observables and normalisation factors are free in the fit.
For other backgrounds originating from B hadrons the integrated yield over the phase spaceis fixed from the global fit. Some of these background components are CP -violating and aredescribed using similar equations to eq. (2.8) but with the addition of a coherence factor,
κ, diluting the interference term, for example2
Ni+ ∝ [F−i + (x2+ + y+
)F+i + 2κ F−i F+i (ci x+ − si y+ )].

p

(6.1)

Since these background contributions include multiple resonances, the coherence factor is
not necessarily unity. These CP -violating background components are parameterised with
their own set of CP -violating observables, which are fixed using hadronic parameters fromref. [9] unless stated otherwise. For the B 0 → DK ± π ∓ and B 0 → D∗ K ± π ∓ backgrounddecays, rB values of 0.25 are used as this corresponds to that of the B 0 → DK ∗0 decay.
The same resonance is used to fix the strong phase for B 0 → DK ± π ∓ decays to 197◦ . For– 10 –JHEP02(2024)118

80

5000

2500

LHCb

500

Candidates / (6 MeV/c2)

Candidates / (6 MeV/c2)

150

0

Candidates / (6 MeV/c2)

Data
Total

LHCb

Reconstructed as:
D decay

Component

D → KS0 π + π −B ± → D∗ [Dπ 0 ]K ±B ± → Dπ ±6244 ± 122716 ± 5±

340 ± 1

113 170 ± 229∗±

3144 ± 61247 ± 2∗±

166 ± 160 285 ± 121

10 398 ± 214726 ± 9590 ± 1

196 804 ± 398

B

±

∗

→ D [Dπ ]πB±→ D [Dγ]K

B

±

B

±

→ DK

±

B

±

±

0

→ D [Dγ]π→ DπOther backgrounds

10 402 ± 105 206 664 ± 592

Combinatorial background1343 ± 147

15 177 ± 706

B

±

∗

0

±

B

±

790 ± 3344 ± 1∗0±43 ± 114 327 ± 65

B ± → D∗ [Dγ]K ±397 ± 1157 ± 1

→ D [Dπ ]K→ D [Dπ ]π

B

±

∗

21 ± 17636 ± 34

B

±

→ DK

±

1527 ± 6

694 ± 2B±±

88 ± 129 786 ± 135

Other backgrounds

1573 ± 15

31 278 ± 115

Combinatorial background

263 ± 46

4413 ± 261→ D [Dγ]π→ Dπ±Table 1. Signal and background yields from the global fit over the full mass range, 4900˘5600 MeV/c2 .
All yields and uncertainties are rounded to the nearest integer and uncertainties of 1 mean one or fewer.
Backgrounds that are not written explicitly in this table are included in the ‘Other Backgrounds’
component.

the background from B 0 → D∗ K ± π ∓ decays a strong phase of 70◦ is chosen from auxiliary
studies of B 0 → DK ∗0 used in ref. [50], while for those from B ± → D(∗) K ± π 0 decays the
B ± → DK ∗± decay is used to fix the rB values to 0.106 and the strong phases at 35◦ . For
the B ± → D(∗) π ± π 0 backgrounds, B ± → Dπ ± decays are used to fix the rB values at 0.0048.
The strong phases are arbitrarily chosen to be 100◦ for the B ± → Dπ ± π 0 background and200◦ for the B ± → D∗ π ± π 0 background decay since their values are unknown. The fullrange of values is used to determine the associated systematic uncertainty. The value ofκ is not well known for any of these decays. Hence, the central value is estimated using
a single decay, by calculating the fraction of the B 0 → DK ∗0 decay in the B 0 → DK ± π ∓background contribution using branching fractions and efficiencies. The result is 0.5, and
it is used as the nominal coherence factor for all the CP -violating background components,
except the B ± → Dπ ± π 0 background decay. Here, it is well established that the backgroundis dominated by the B ± → Dρ± resonant process [44] and therefore a coherence factor of
one is used. The systematic uncertainty associated with all these choices is determined byconsidering the full spectrum of reasonable variations in all hadronic parameters.
There are also CP -conserving background components, which can exhibit one of three
types of Dalitz-plot distributions. If the background decays via a D0 (D0 ) and is reconstructed
as a B − (B + ) decay, it has the Dalitz-plot distribution of a D0 meson. In this case the yield per– 11 –JHEP02(2024)118

D → KS0 K + K −B ± → DK ±

7

Systematic uncertainties

The various sources of systematic uncertainty are summarised in table 2. A systematic
uncertainty is assigned to account for the fact that the D decay phase-space efficiency is– 12 –JHEP02(2024)118

Dalitz bin for the B ± decay, Ni± , is proportional to F∓i . Background decays that fall into thiscategory are B 0 → D∗− h+ and B 0 → [Dπ − ]D∗− K + π 0 decays. Conversely, if the backgrounddecays via a D0 (D0 ) and is assigned as a B − (B + ) decay, it has the Dalitz-plot distributionof a D0 meson. Here the yield per Dalitz bin for the B ± decay, Ni± , is proportional to F±i .
The Bs0 → D(∗) K − π + and B − → Dπ − π − π + decays where pions with same-sign charges
are not reconstructed fall into this category. Lastly, there are backgrounds which decay via
either a D0 or D0 with equal probability. The yield per Dalitz bin is proportional to theaverage of the F+i and F−i values. The B 0 → D(∗) π + π − decays fall into this category. The
yields of the associated cross-feed components are determined with the same parameterisation
used in the global fit. The distribution of the combinatorial background is not known andhence the yield varies freely in every Dalitz bin.
The CP -violating backgrounds are parameterised similarly to eq. (2.8) with fixed values
of x± and y± that have large associated uncertainties. To avoid contamination of the signal
measurements, two sets of Fi values are introduced, one is used to parameterise the signal
components, and another for all backgrounds, except the combinatorial background which
has no dependence on Fi . Additionally, separate Fi values are used for long and downstream
KS0 candidates. The Fi parameters are implemented in the fit in terms of recursive fractions,
identically to ref. [22], and vary freely in the CP fit. For the signal Fi parameters, thevalues are driven by the B ± → D∗ π ± component, and for the background Fi parameters thedominant contribution comes from the B ± → Dπ ± and B ± → Dρ± components.
In summary, in the CP fit the parameters that are allowed to vary are the two setsof six cartesian CP -violating observables for the signal and B ± → Dh± decays, two setsof Fi parameters, the yields of the combinatorial background in each Dalitz bin, and thenormalisation factors given in eq. (2.8).
Instabilities and biases in the fit are studied using pseudoexperiments that are generated
and fitted using the baseline fit model. All CP -violating observables show normalised residuals∗
consistent with a normal Gaussian distribution except the ℜ(ξ D π ) parameter that exhibits abias of 15% and a 6% over-coverage in its statistical uncertainty. Both the bias and the overestimated uncertainty are found to be due to statistical fluctuations leading to small data yields in∗certain bins and are reduced if a larger data sample is generated. The measured ℜ(ξ D π ) parameter is corrected for both of these features. The CP -violating observables for the B ± → Dh±decays are cross-checked against results from ref. [22] and are found to be consistent.
The results of the CP -violating observables for the signal are shown in figure 3. The
68.3% and 95.5% confidence regions are determined using a likelihood scan and include
only statistical uncertainties. In the left-hand plot of figure 3, the angle between the two
D ∗ K . In the right-handlines converging at the origin is 2γ, and the length of each line is rB
plot of figure 3, the CP -violating observables for the B ± → D∗ π ± decay is shown, whereD ∗ π /r D ∗ K , which isthe distance from the origin to the central value point is the ratio rB
Baround 0.1 as expected [9].

=(ξ D π )

0.15

LHCb
9 fb−1

B+

0.10

0.00

0.0
−0.1

B−
−0.1

−0.2
0.0

0.1

∗

0.2

xD K

−0.3
−0.3

−0.2

−0.1

0.0

0.1

0.2
0.3
∗
<(ξ D π )Figure 3. Contours at 68.3% and 95.5% confidence levels indicated by the darker and lighter regions,
∗
∗
K
D∗ K
K
D∗ K
respectively, for (left, red) (xD, y−) which is labelled B − and (left, purple) (xD, y+) which−+∗∗is labelled B + , and (right) (ℜ(ξ D π ), ℑ(ξ D π )), including only statistical uncertainty. The black points
indicate the central values.

assumed to be uniform. The strong-phase inputs are based on measurements at CLEO andBESIII and have been corrected for efficiency effects at these charm factories. As a result,
there is a small difference between the strong-phase inputs used in this paper and those thatwould be determined if the strong-phase inputs were modulated by η(s). The systematic
uncertainty is evaluated using amplitude models in ref. [51] to calculate strong phases withand without efficiency corrections which are determined using simulation. Pseudoexperiments
are then generated using strong phases with efficiency corrections and fitted using strong
phases without efficiency corrections. The mean bias in each CP -violating observable istaken as the associated systematic uncertainty.
There is a considerable systematic uncertainty due to the mass shape parameterisation.
This refers to any fixed mass shape parameter in the fits to simulation or in the global
fit. A bootstrapping method [52] is used to ensure statistical uncertainties from the global
fit and correlations between shape parameters are accounted for in the error propagation.
First, the simulation samples are re-sampled with replacement and the fits to simulation
are repeated many times. For each fit result, data are re-sampled with replacement and theglobal and CP fits are repeated. The standard deviation of each CP -violating observable
is an estimate of the associated systematic uncertainty.
There are a number of fixed quantities in the global and CP fits. The systematic
uncertainties for these are estimated by varying each fixed quantity within its uncertainty
and repeating the fits. The standard deviation of the fitted CP -violating observables is theassociated systematic uncertainty. The fixed quantities that are varied include the asymmetry
parameters for the B ± → [Dγ]D∗ h± signal, ξDγ , the branching fractions, the efficiencies,
and the yield ratios from ref. [48]. The latter also includes an uncertainty associated withthe assumption in the parameterisation of eq. (5.4) that the efficiencies in this analysis and– 13 –JHEP02(2024)118

−0.20
−0.2

9 fb−1

2γ

−0.05

−0.15

LHCb
0.2
0.1

0.05

−0.10

0.3

∗

∗

yD K

0.20

ref. [48] are the same. Differences of up to 3% are estimated with the simulation, and areincluded in the variations.
A bias correction is applied to the CP -violating observables from the CP fit, which isdetermined using pseudoexperiments. The size of the biases can vary depending on the input
parameters. To determine the systematic uncertainty associated with this the range of biases
on the CP -violating observables are assessed by testing alternative inputs.

There are a number of CP -violating background contributions which are fixed in the
CP fit. Their inputs carry uncertainties, therefore a systematic uncertainty is assigned. It isevaluated by generating pseudoexperiments with alternative inputs and fitting to the baselinemodel. In two sets of studies, the hadronic parameters are varied to the upper and lower
limits of their 68% confidence levels given in ref. [9]. Then, the larger mean bias in each
CP -violating observable from these two studies is taken as its systematic uncertainty. The
coherence factors are varied conservatively as there is no prior knowledge for most backgroundcomponents. For the B 0 → DK ± π ∓ background decay the coherence factor is shifted to
0.958, the value measured for the B 0 → DK ∗0 (892) decay in an amplitude measurement of
the B 0 → DK + π − decay [44]. For all other backgrounds a value of one is used, except for
the B ± → Dπ ± π 0 decay for which there is no variation.
The leading sources of experimental systematic uncertainties (mass shape parametrisation,
fixed branching ratios, fixed yield ratios, and inputs for CPV backgrounds) are driven by
the parameterisation of two background components, B ± → DK ± π 0 and B ± → Dπ ± π 0
decays. Further direct study of these decays will provide the information necessary to reduce
systematic uncertainties in a future version of the measurement described here.
The systematic uncertainty due to the external strong-phase inputs is evaluated by varying
the ci and si values within their measured uncertainties taking into account correlations
between them and repeating the fits many times. The standard deviation of the resulting
CP -violating observables is assigned as the systematic uncertainty.
As determined in ref. [22] the systematic uncertainties associated with ignoring CP
violation and regeneration in KS0 interactions with matter and charm mixing are expected
to be minimal and are not evaluated. The total systematic uncertainty is found to be atleast a factor of two smaller than the statistical uncertainty.

– 14 –JHEP02(2024)118

There is also a systematic uncertainty due to the resolution of the momentum measurements leading to event migration between neighbouring Dalitz bins. The effect is accounted
for at first order in the Fi parameters, but second order effects remain due to differing
intensity distributions between the Dalitz plots for B ± → D∗ K ± and B ± → D∗ π ± decays.
The size of the systematic uncertainty is determined in the same way as in ref. [22] andfound to be negligible.

K
xD
−

∗

D K
y−

∗

K
xD
+

∗

D K
y+

∗

ℜ(ξ D π )∗ℑ(ξ D π )∗Efficiency correction of (ci , si )

0.23

0.29

0.21

0.20

0.47

0.31

Mass shape parameterisation

0.35

0.58

0.38

0.33

1.17

0.90

Fixed ξDγ parameter

0.14

0.19

0.15

0.08

0.22

0.32

Fixed branching ratios

0.58

0.44

0.33

0.50

1.09

0.54

Fixed efficiencies

0.23

0.48

0.18

0.27

0.70

0.38

Fixed yield ratios

0.66

0.85

0.46

0.43

1.45

0.77

Bias Correction

0.29

0.35

0.12

0.16

0.62

0.51

Dalitz-bin migration

0.00

0.02

0.04

0.10

0.03

0.11

Inputs for CPV backgrounds

0.35

0.33

0.38

0.21

2.22

1.93

Total of above uncertainties

1.11

1.36

0.85

0.87

3.28

2.46

Strong-phase inputs

0.57

1.54

0.18

0.41

2.33

2.13

Total systematic uncertainty

1.25

2.05

0.87

0.95

4.02

3.26

Statistical uncertainty

2.93

5.69

2.58

2.87

9.37

9.67

Table 2. Summary of the systematic uncertainties. Values are expressed in units of 10−2 .

8Interpretation

The CP -violating observables are measured to be∗KxD= (−6.3 ± 2.9 ± 1.1 ± 0.6) × 10−2 ,
−
∗

D K
y−
= (−4.8 ± 5.7 ± 1.4 ± 1.5) × 10−2 ,∗KxD= ( 6.0 ± 2.6 ± 0.9 ± 0.2) × 10−2 ,
+
∗

D K
y+
= ( 5.4 ± 2.9 ± 0.9 ± 0.4) × 10−2 ,∗ℜ(ξ D π ) = ( 11.5 ± 9.4 ± 3.3 ± 2.3) × 10−2 ,∗ℑ(ξ D π ) = (−0.9 ± 9.7 ± 2.5 ± 2.1) × 10−2 ,where the first uncertainty is statistical, the second is systematic, and the third is due toexternal strong-phase inputs from BESIII [14, 15] and CLEO [16]. The correlation matrices
for each of these uncertainties are given in tables 3–5 in appendix A. The CP -violating
D ∗ K , δ D ∗ K , r D ∗ π , δ D ∗ π , andobservables are interpreted in terms of the physical parameters, rBBBB
γ using a maximum-likelihood fit with a frequentist approach [53]. The 68.3% and 95.5%
confidence regions are shown in figures 4 and 5. The parameterisation in eq. (2.5) allows
a two-fold symmetry with solutions where γ → γ + 180◦ and δB → δB + 180◦ . Choosing
0 < γ < 180◦ , the numerical solutions are◦
γ = (92+21−17 ) ,∗

D K
rB
= 0.080+0.022−0.023 ,
∗

D K
◦
δB
= (310+15−20 ) ,∗

D π
rB
= 0.009+0.005−0.007 ,
∗

D π
◦
δB
= (304+37−38 ) .

– 15 –JHEP02(2024)118

Source

1−CL

1

LHCb
9 fb-1

0.8
0.6
0.4

68.3%

0.2
50

100

150

γ [°]
Figure 4. Confidence intervals at 68.3% and 95.5% for the CKM angle γ.

The solution for γ is consistent with the latest γ combination using LHCb data,◦γ = (63.8+3.5−3.7 ) [9].
In order to compare results from this analysis and ref. [19], it is necessary to ascertain thelevel of statistical correlation between them. All selected events in ref. [19] also appear in thisanalysis. The analysis in ref. [19] has 45% (18%) of the B ± → [Dγ]D∗ K ± (B ± → [Dπ 0 ]D∗ K ± )signal yield compared to this analysis. However, a number of differences between the twoanalyses mean common candidates do not carry the same weight. First, different D∗ decays
drive the sensitivity of each analysis. Furthermore, in ref. [19], the two signal channels arewell separated, whereas here, both decays occupy the same m(Dh) region and dilute eachothers’ sensitivities. Finally, the background environments differ between the two analyses.
These differences are incorporated into studies with pseudoexperiments which are used toestimate the statistical correlation. It is determined to be a maximum of 3%, and cantherefore be treated as negligible. It is noted that the experimental systematic uncertainties
are uncorrelated and those of the external inputs are determined.
The CP -violating observables determined in this analysis and ref. [19] are compared∗K
D ∗ K observables this analysis has overall
and found to be consistent. For the xDand y±±∗
D K where it is 30% larger. The uncertainties
uncertainties that are 30% smaller, except for y−∗on the ξ D π parameter are almost twice as large as those in ref. [19] due to the dominantpresence of the B ± → Dρ± background which is suppressed when the D∗ decay is reconstructed. In ref. [19], the uncertainty on γ is smaller at 14◦ where the sensitivity to γ isD ∗ K . The central values can also be comparedenhanced by the corresponding larger value of rB
to the B ± → D∗ K ± , D → hh results in ref. [48], and are also found to be consistent. The
measurement presented in this paper adds further information on CP violation in B ± → D∗ h±decays and, in combination with other measurements of the same B decay mode [19, 48],
it will set strong constraints on the CKM angle γ and associated hadronic parameters byremoving the ambiguities resulting from multiple solutions in the results of ref. [48].

– 16 –JHEP02(2024)118

95.5%
0
0

LHCb
9 fb-1

0.15

δ D*K
[°]
B

rD*K
B

0.2

350

LHCb
9 fb-1

300

0.1
250
0.05
200
0

50

100

150

50

100

150

π
rD*
B

LHCb
9 fb-1

0.04

350

γ [°]

LHCb
9 fb-1

300
0.03
0.02

250

0.01
200
0

50

100

150

50

γ [°]

100

150

γ [°]

Figure 5. Confidence regions at 68.3% and 95.5% indicated by the lighter and darker shades
D∗ K
D∗ K
D∗ π
respectively, for (top, left) γ vs. rB, (top, right) γ vs. δB, (bottom left) γ vs. rB, and (bottom,D∗ πright) γ vs. δB.

9Conclusion

In this work B ± → D∗ K ± and B ± → D∗ π ± decays with partially reconstructed D∗ → Dγ
and D∗ → Dπ 0 decays, followed by D → KS0 π + π − and D → KS0 K + K − decays are studied
at the LHCb experiment. The full LHCb Run 1 and Run 2 dataset is used to determine the
CKM angle γ. The measurement is performed in Dalitz bins of the D decay phase spacein a model-independent manner, using CLEO and BESIII inputs for D decay strong-phase◦
information. A measurement of the CKM angle γ = (92+21−17 ) is achieved where the dominant
contribution to the uncertainty is statistical.

Acknowledgments
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); MCID/IFA (Romania); MICINN (Spain); SNSF and SER (Switzerland);
NASU (Ukraine); STFC (United Kingdom); DOE NP and NSF (U.S.A.). We acknowledge
the computing resources that are provided by CERN, IN2P3 (France), KIT and DESY

– 17 –JHEP02(2024)118

0.05

π
δ D*
[°]
B

γ [°]

∗

D K
x−
D∗ K
y−
∗
K
xD
+
∗
D K
y+
D∗ π

ℜ(ξ
ℑ(ξ

D∗ π

K
xD
−

∗

D K
y−

∗

K
xD
+

∗

D K
y+

∗

ℜ(ξ D π )ℑ(ξ D π )

1.000

0.420

0.158

0.105

0.445

0.422

1.000

0.115

0.232

0.765

0.631

1.000

−0.095

0.012

0.409

1.000

0.263

0.112

1.000

0.597

)

∗

)

∗

1.000

Table 3. Statistical correlation matrix for the CP -violating observables.

D∗ K
y−
∗
K
xD
+
∗
D K
y+
D∗ π

ℜ(ξ
ℑ(ξ

D∗ π

∗

D K
y−

∗

D K
x+

∗

D K
y+

∗

ℜ(ξ D π )∗ℑ(ξ D π )

1.000

0.630

−0.241−0.016

0.602

0.083

1.000

0.008

0.154

0.735

0.230

1.000

0.515

0.232

0.618

1.000

0.237

0.112

1.000

−0.201

)
)

∗

1.000

Table 4. Correlation matrix associated with LHCb-related systematic uncertainties.

(Germany), INFN (Italy), SURF (Netherlands), PIC (Spain), GridPP (United Kingdom),
CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), and Polish WLCG (Poland). 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); 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); Minciencias (Colombia); EPLANET, Marie Skłodowska-Curie Actions,
ERC and NextGenerationEU (European Union); A*MIDEX, ANR, IPhU and Labex P2IO,
and Région Auvergne-Rhône-Alpes (France); AvH Foundation (Germany); ICSC (Italy);
GVA, XuntaGal, GENCAT, Inditex, InTalent and Prog. Atracción Talento, CM (Spain);
SRC (Sweden); the Leverhulme Trust, the Royal Society and UKRI (United Kingdom).

A

Correlation matrices

Table 3 provides the correlation matrix for the statistical uncertainties of the CP -violating
observables. Tables 4 and 5 provide the correlations between the experimental systematic
uncertainties and those arising from external strong-phase information, respectively.

– 18 –JHEP02(2024)118

∗

K
xD
−

K
xD
−

∗

K
xD
−
D∗ K
y−
∗
K
xD
+
∗
D K
y+
D∗ π

ℜ(ξ
ℑ(ξ

D∗ π

K
xD
−

∗

D K
y−

∗

D K
x+

∗

D K
y+

ℜ(ξ D π )ℑ(ξ D π )

1.000

0.886

−0.117−0.063

0.916

0.904

1.000

−0.124−0.115

0.935

0.889

1.000

−0.280−0.130

0.063

1.000

0.085

−0.077

1.000

0.941

)
)

∗

∗

∗

1.000

Table 5. Correlation matrix associated with the strong-phase inputs.

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A. Gooding 17 , I.V. Gorelov 41 , C. Gotti 28 , J.P. Grabowski 73 , L.A. Granado Cardoso 46 ,E. Graugés 43 , E. Graverini 47 , L. Grazette 54 , G. Graziani , A. T. Grecu 40 ,L.M. Greeven 35 , N.A. Grieser 63 , L. Grillo 57 , S. Gromov 41 , C. Gu 14 , M. Guarise 23 ,M. Guittiere 13 , V. Guliaeva 41 , P. A. Günther 19 , A.-K. Guseinov 41 , E. Gushchin 41 ,Y. Guz 6,41,46 , T. Gys 46 , T. Hadavizadeh 1 , C. Hadjivasiliou 64 , G. Haefeli 47 , C. Haen 46 ,J. Haimberger 46 , M. Hajheidari46 , T. Halewood-leagas 58 , M.M. Halvorsen 46 ,P.M. Hamilton 64 , J. Hammerich 58 , Q. Han 8 , X. Han 19 , S. Hansmann-Menzemer 19 ,L. Hao 7 , N. Harnew 61 , T. Harrison 58 , M. Hartmann 13 , C. Hasse 46 , J. He 7,c ,K. Heijhoff 35 , F. Hemmer 46 , C. Henderson 63 , R.D.L. Henderson 1,54 , A.M. Hennequin 46 ,K. Hennessy 58 , L. Henry 47 , J. Herd 59 , J. Heuel 16 , A. Hicheur 3 , D. Hill 47 ,S.E. Hollitt 17 , J. Horswill 60 , R. Hou 8 , Y. Hou 10 , N. Howarth58 , J. Hu19 , J. Hu 69 ,W. Hu 6 , X. Hu 4 , W. Huang 7 , W. Hulsbergen 35 , R.J. Hunter 54 , M. Hushchyn 41 ,D. Hutchcroft 58 , M. Idzik 37 , D. Ilin 41 , P. Ilten 63 , A. Inglessi 41 , A. Iniukhin 41 ,A. Ishteev 41 , K. Ivshin 41 , R. Jacobsson 46 , H. Jage 16 , S.J. Jaimes Elles 45,72 ,– 25 –JHEP02(2024)118

S. Jakobsen 46 , E. Jans 35 , B.K. Jashal 45 , A. Jawahery 64 , V. Jevtic 17 , E. Jiang 64 ,X. Jiang 5,7 , Y. Jiang 7 , Y. J. Jiang 6 , M. John 61 , D. Johnson 51 , C.R. Jones 53 ,T.P. Jones 54 , S. Joshi 39 , B. Jost 46 , N. Jurik 46 , I. Juszczak 38 , D. Kaminaris 47 ,S. Kandybei 49 , Y. Kang 4 , M. Karacson 46 , D. Karpenkov 41 , M. Karpov 41 , A. M.
Kauniskangas 47 , J.W. Kautz 63 , F. Keizer 46 , D.M. Keller 66 , M. Kenzie 53 , T. Ketel 35 ,B. Khanji 66 , A. Kharisova 41 , S. Kholodenko 32 , G. Khreich 13 , T. Kirn 16 ,V.S. Kirsebom 47 , O. Kitouni 62 , S. Klaver 36 , N. Kleijne 32,q , K. Klimaszewski 39 ,M.R. Kmiec 39 , S. Koliiev 50 , L. Kolk 17 , A. Konoplyannikov 41 , P. Kopciewicz 37,46 ,P. Koppenburg 35 , M. Korolev 41 , I. Kostiuk 35 , O. Kot50 , S. Kotriakhova , A. Kozachuk 41 ,P. Kravchenko 41 , L. Kravchuk 41 , M. Kreps 54 , S. Kretzschmar 16 , P. Krokovny 41 ,W. Krupa 66 , W. Krzemien 39 , J. Kubat19 , S. Kubis 77 , W. Kucewicz 38 , M. Kucharczyk 38 ,V. Kudryavtsev 41 , E. Kulikova 41 , A. Kupsc 78 , B. K. Kutsenko 12 , D. Lacarrere 46 ,A. Lai 29 , A. Lampis 29 , D. Lancierini 48 , C. Landesa Gomez 44 , J.J. Lane 1 , R. Lane 52 ,C. Langenbruch 19 , J. Langer 17 , O. Lantwin 41 , T. Latham 54 , F. Lazzari 32,r ,C. Lazzeroni 51 , R. Le Gac 12 , S.H. Lee 79 , R. Lefèvre 11 , A. Leflat 41 , S. Legotin 41 ,M. Lehuraux 54 , O. Leroy 12 , T. Lesiak 38 , B. Leverington 19 , A. Li 4 , H. Li 69 , K. Li 8 ,L. Li 60 , P. Li 46 , P.-R. Li 70 , S. Li 8 , T. Li 5 , T. Li 69 , Y. Li8 , Y. Li 5 , Z. Li 66 ,Z. Lian 4 , X. Liang 66 , C. Lin 7 , T. Lin 55 , R. Lindner 46 , V. Lisovskyi 47 , R. Litvinov 29,i ,G. Liu 69 , H. Liu 7 , K. Liu 70 , Q. Liu 7 , S. Liu 5,7 , Y. Liu 56 , Y. Liu70 , Y. L. Liu 59 ,A. Lobo Salvia 43 , A. Loi 29 , J. Lomba Castro 44 , T. Long 53 , J.H. Lopes 3 ,A. Lopez Huertas 43 , S. López Soliño 44 , G.H. Lovell 53 , C. Lucarelli 24,k , D. Lucchesi 30,o ,S. Luchuk 41 , M. Lucio Martinez 76 , V. Lukashenko 35,50 , Y. Luo 4 , A. Lupato 30 ,E. Luppi 23,j , K. Lynch 20 , X.-R. Lyu 7 , G. M. Ma 4 , R. Ma 7 , S. Maccolini 17 ,F. Machefert 13 , F. Maciuc 40 , I. Mackay 61 , L.R. Madhan Mohan 53 , M. M. Madurai 51 ,A. Maevskiy 41 , D. Magdalinski 35 , D. Maisuzenko 41 , M.W. Majewski37 , J.J. Malczewski 38 ,S. Malde 61 , B. Malecki 38,46 , L. Malentacca46 , A. Malinin 41 , T. Maltsev 41 , G. Manca 29,i ,G. Mancinelli 12 , C. Mancuso 27,13,m , R. Manera Escalero43 , D. Manuzzi 22 ,D. Marangotto 27,m , J.F. Marchand 10 , R. Marchevski 47 , U. Marconi 22 , S. Mariani 46 ,C. Marin Benito 43,46 , J. Marks 19 , A.M. Marshall 52 , P.J. Marshall58 , G. Martelli 31,p ,G. Martellotti 33 , L. Martinazzoli 46 , M. Martinelli 28,n , D. Martinez Santos 44 ,F. Martinez Vidal 45 , A. Massafferri 2 , M. Materok 16 , R. Matev 46 , A. Mathad 48 ,V. Matiunin 41 , C. Matteuzzi 66 , K.R. Mattioli 14 , A. Mauri 59 , E. Maurice 14 ,J. Mauricio 43 , P. Mayencourt 47 , M. Mazurek 46 , M. McCann 59 , L. Mcconnell 20 ,T.H. McGrath 60 , N.T. McHugh 57 , A. McNab 60 , R. McNulty 20 , B. Meadows 63 ,G. Meier 17 , D. Melnychuk 39 , M. Merk 35,76 , A. Merli 27,m , L. Meyer Garcia 3 , D. Miao 5,7 ,H. Miao 7 , M. Mikhasenko 73,e , D.A. Milanes 72 , A. Minotti 28,n , E. Minucci 66 ,T. Miralles 11 , S.E. Mitchell 56 , B. Mitreska 17 , D.S. Mitzel 17 , A. Modak 55 , A. Mödden 17 ,R.A. Mohammed 61 , R.D. Moise 16 , S. Mokhnenko 41 , T. Mombächer 46 , M. Monk 54,1 ,I.A. Monroy 72 , S. Monteil 11 , A. Morcillo Gomez 44 , G. Morello 25 , M.J. Morello 32,q ,M.P. Morgenthaler 19 , J. Moron 37 , A.B. Morris 46 , A.G. Morris 12 , R. Mountain 66 ,H. Mu 4 , Z. M. Mu 6 , E. Muhammad 54 , F. Muheim 56 , M. Mulder 75 , K. Müller 48 ,F. Mũnoz-Rojas 9 , R. Murta 59 , P. Naik 58 , T. Nakada 47 , R. Nandakumar 55 , T. Nanut 46 ,I. Nasteva 3 , M. Needham 56 , N. Neri 27,m , S. Neubert 73 , N. Neufeld 46 , P. Neustroev41 ,– 26 –JHEP02(2024)118

R. Newcombe59 , J. Nicolini 17,13 , D. Nicotra 76 , E.M. Niel 47 , N. Nikitin 41 , P. Nogga73 ,N.S. Nolte 62 , C. Normand 10,i,29 , J. Novoa Fernandez 44 , G. Nowak 63 , C. Nunez 79 , H. N.
Nur 57 , A. Oblakowska-Mucha 37 , V. Obraztsov 41 , T. Oeser 16 , S. Okamura 23,j,46 ,R. Oldeman 29,i , F. Oliva 56 , M. Olocco 17 , C.J.G. Onderwater 76 , R.H. O’Neil 56 ,J.M. Otalora Goicochea 3 , T. Ovsiannikova 41 , P. Owen 48 , A. Oyanguren 45 , O. Ozcelik 56 ,K.O. Padeken 73 , B. Pagare 54 , P.R. Pais 19 , T. Pajero 61 , A. Palano 21 , M. Palutan 25 ,G. Panshin 41 , L. Paolucci 54 , A. Papanestis 55 , M. Pappagallo 21,g , L.L. Pappalardo 23,j ,C. Pappenheimer 63 , C. Parkes 60 , B. Passalacqua 23,j , G. Passaleva 24 , D. Passaro 32,q ,A. Pastore 21 , M. Patel 59 , J. Patoc 61 , C. Patrignani 22,h , C.J. Pawley 76 , A. Pellegrino 35 ,M. Pepe Altarelli 25 , S. Perazzini 22 , D. Pereima 41 , A. Pereiro Castro 44 , P. Perret 11 ,A. Perro 46 , K. Petridis 52 , A. Petrolini 26,l , S. Petrucci 56 , H. Pham 66 , L. Pica 32,q ,M. Piccini 31 , B. Pietrzyk 10 , G. Pietrzyk 13 , D. Pinci 33 , F. Pisani 46 , M. Pizzichemi 28,n ,V. Placinta 40 , M. Plo Casasus 44 , F. Polci 15,46 , M. Poli Lener 25 , A. Poluektov 12 ,N. Polukhina 41 , I. Polyakov 46 , E. Polycarpo 3 , S. Ponce 46 , D. Popov 7 , S. Poslavskii 41 ,K. Prasanth 38 , C. Prouve 44 , V. Pugatch 50 , V. Puill 13 , G. Punzi 32,r , H.R. Qi 4 ,W. Qian 7 , N. Qin 4 , S. Qu 4 , R. Quagliani 47 , R.I. Rabadan Trejo 54 , B. Rachwal 37 ,J.H. Rademacker 52 , M. Rama 32 , M. Ramírez García 79 , M. Ramos Pernas 54 , M.S. Rangel 3 ,F. Ratnikov 41 , G. Raven 36 , M. Rebollo De Miguel 45 , F. Redi 46 , J. Reich 52 , F. Reiss 60 ,Z. Ren 7 , P.K. Resmi 61 , R. Ribatti 32,q , G. R. Ricart 14,80 , D. Riccardi 32,q , S. Ricciardi 55 ,K. Richardson 62 , M. Richardson-Slipper 56 , K. Rinnert 58 , P. Robbe 13 , G. Robertson 57 ,E. Rodrigues 58,46 , E. Rodriguez Fernandez 44 , J.A. Rodriguez Lopez 72 ,E. Rodriguez Rodriguez 44 , A. Rogovskiy 55 , D.L. Rolf 46 , A. Rollings 61 , P. Roloff 46 ,V. Romanovskiy 41 , M. Romero Lamas 44 , A. Romero Vidal 44 , G. Romolini 23 ,F. Ronchetti 47 , M. Rotondo 25 , S. R. Roy 19 , M.S. Rudolph 66 , T. Ruf 46 , M. Ruiz Diaz 19 ,R.A. Ruiz Fernandez 44 , J. Ruiz Vidal 78,y , A. Ryzhikov 41 , J. Ryzka 37 , J.J. Saborido Silva 44 ,R. Sadek 14 , N. Sagidova 41 , N. Sahoo 51 , B. Saitta 29,i , M. Salomoni 28,n ,C. Sanchez Gras 35 , I. Sanderswood 45 , R. Santacesaria 33 , C. Santamarina Rios 44 ,M. Santimaria 25 , L. Santoro 2 , E. Santovetti 34 , A. Saputi 23,46 , D. Saranin 41 , G. Sarpis 56 ,M. Sarpis 73 , A. Sarti 33 , C. Satriano 33,s , A. Satta 34 , M. Saur 6 , D. Savrina 41 ,H. Sazak 11 , L.G. Scantlebury Smead 61 , A. Scarabotto 15 , S. Schael 16 , S. Scherl 58 , A. M.
Schertz 74 , M. Schiller 57 , H. Schindler 46 , M. Schmelling 18 , B. Schmidt 46 , S. Schmitt 16 ,H. Schmitz73 , O. Schneider 47 , A. Schopper 46 , N. Schulte 17 , S. Schulte 47 , M.H. Schune 13 ,R. Schwemmer 46 , G. Schwering 16 , B. Sciascia 25 , A. Sciuccati 46 , S. Sellam 44 ,A. Semennikov 41 , M. Senghi Soares 36 , A. Sergi 26,l , N. Serra 48,46 , L. Sestini 30 ,A. Seuthe 17 , Y. Shang 6 , D.M. Shangase 79 , M. Shapkin 41 , I. Shchemerov 41 ,L. Shchutska 47 , T. Shears 58 , L. Shekhtman 41 , Z. Shen 6 , S. Sheng 5,7 , V. Shevchenko 41 ,B. Shi 7 , E.B. Shields 28,n , Y. Shimizu 13 , E. Shmanin 41 , R. Shorkin 41 , J.D. Shupperd 66 ,R. Silva Coutinho 66 , G. Simi 30 , S. Simone 21,g , N. Skidmore 60 , R. Skuza 19 ,T. Skwarnicki 66 , M.W. Slater 51 , J.C. Smallwood 61 , E. Smith 62 , K. Smith 65 , M. Smith 59 ,A. Snoch 35 , L. Soares Lavra 56 , M.D. Sokoloff 63 , F.J.P. Soler 57 , A. Solomin 41,52 ,A. Solovev 41 , I. Solovyev 41 , R. Song 1 , Y. Song 47 , Y. Song 4 , Y. S. Song 6 ,F.L. Souza De Almeida 66 , B. Souza De Paula 3 , E. Spadaro Norella 27,m , E. Spedicato 22 ,J.G. Speer 17 , E. Spiridenkov41 , P. Spradlin 57 , V. Sriskaran 46 , F. Stagni 46 , M. Stahl 46 ,

1

School of Physics and Astronomy, Monash University, Melbourne, Australia
Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
3
Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
4
Center for High Energy Physics, Tsinghua University, Beijing, China
5
Institute Of High Energy Physics (IHEP), Beijing, China
6
School of Physics State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing,
China
7
University of Chinese Academy of Sciences, Beijing, China
8
Institute of Particle Physics, Central China Normal University, Wuhan, Hubei, China
9
Consejo Nacional de Rectores (CONARE), San Jose, Costa Rica
10
Université Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy, France
11
Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
12
Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
13
Université Paris-Saclay, CNRS/IN2P3, IJCLab, Orsay, France
14
Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut Polytechnique de Paris,
Palaiseau, France
15
LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3, Paris, France2– 27 –JHEP02(2024)118

S. Stahl 46 , S. Stanislaus 61 , E.N. Stein 46 , O. Steinkamp 48 , O. Stenyakin41 , H. Stevens 17 ,D. Strekalina 41 , Y. Su 7 , F. Suljik 61 , J. Sun 29 , L. Sun 71 , Y. Sun 64 , P.N. Swallow 51 ,K. Swientek 37 , F. Swystun 54 , A. Szabelski 39 , T. Szumlak 37 , M. Szymanski 46 , Y. Tan 4 ,S. Taneja 60 , M.D. Tat 61 , A. Terentev 48 , F. Terzuoli 32,u , F. Teubert 46 , E. Thomas 46 ,D.J.D. Thompson 51 , H. Tilquin 59 , V. Tisserand 11 , S. T’Jampens 10 , M. Tobin 5 ,L. Tomassetti 23,j , G. Tonani 27,m , X. Tong 6 , D. Torres Machado 2 , L. Toscano 17 ,D.Y. Tou 4 , C. Trippl 42 , G. Tuci 19 , N. Tuning 35 , L.H. Uecker 19 , A. Ukleja 37 ,D.J. Unverzagt 19 , E. Ursov 41 , A. Usachov 36 , A. Ustyuzhanin 41 , U. Uwer 19 ,V. Vagnoni 22 , A. Valassi 46 , G. Valenti 22 , N. Valls Canudas 42 , H. Van Hecke 65 ,E. van Herwijnen 59 , C.B. Van Hulse 44,w , R. Van Laak 47 , M. van Veghel 35 ,R. Vazquez Gomez 43 , P. Vazquez Regueiro 44 , C. Vázquez Sierra 44 , S. Vecchi 23 ,J.J. Velthuis 52 , M. Veltri 24,v , A. Venkateswaran 47 , M. Vesterinen 54 , D. Vieira 63 ,M. Vieites Diaz 46 , X. Vilasis-Cardona 42 , E. Vilella Figueras 58 , A. Villa 22 , P. Vincent 15 ,F.C. Volle 13 , D. vom Bruch 12 , V. Vorobyev41 , N. Voropaev 41 , K. Vos 76 , G. Vouters10 ,C. Vrahas 56 , J. Walsh 32 , E.J. Walton 1 , G. Wan 6 , C. Wang 19 , G. Wang 8 , J. Wang 6 ,J. Wang 5 , J. Wang 4 , J. Wang 71 , M. Wang 27 , N. W. Wang 7 , R. Wang 52 , X. Wang 69 ,X. W. Wang 59 , Y. Wang 8 , Z. Wang 13 , Z. Wang 4 , Z. Wang 7 , J.A. Ward 54,1 ,N.K. Watson 51 , D. Websdale 59 , Y. Wei 6 , B.D.C. Westhenry 52 , D.J. White 60 ,M. Whitehead 57 , A.R. Wiederhold 54 , D. Wiedner 17 , G. Wilkinson 61 , M.K. Wilkinson 63 ,M. Williams 62 , M.R.J. Williams 56 , R. Williams 53 , F.F. Wilson 55 , W. Wislicki 39 ,M. Witek 38 , L. Witola 19 , C.P. Wong 65 , G. Wormser 13 , S.A. Wotton 53 , H. Wu 66 ,J. Wu 8 , Y. Wu 6 , K. Wyllie 46 , S. Xian69 , Z. Xiang 5 , Y. Xie 8 , A. Xu 32 , J. Xu 7 ,L. Xu 4 , L. Xu 4 , M. Xu 54 , Z. Xu 11 , Z. Xu 7 , Z. Xu 5 , D. Yang 4 , S. Yang 7 , X. Yang 6 ,Y. Yang 26,l , Z. Yang 6 , Z. Yang 64 , V. Yeroshenko 13 , H. Yeung 60 , H. Yin 8 , C. Y. Yu 6 ,J. Yu 68 , X. Yuan 5 , E. Zaffaroni 47 , M. Zavertyaev 18 , M. Zdybal 38 , M. Zeng 4 ,C. Zhang 6 , D. Zhang 8 , J. Zhang 7 , L. Zhang 4 , S. Zhang 68 , S. Zhang 6 , Y. Zhang 6 ,Y. Zhang61 , Y. Z. Zhang 4 , Y. Zhao 19 , A. Zharkova 41 , A. Zhelezov 19 , X. Z. Zheng 4 ,Y. Zheng 7 , T. Zhou 6 , X. Zhou 8 , Y. Zhou 7 , V. Zhovkovska 54 , L. Z. Zhu 7 , X. Zhu 4 ,X. Zhu 8 , Z. Zhu 7 , V. Zhukov 16,41 , J. Zhuo 45 , Q. Zou 5,7 , D. Zuliani 30 , G. Zunica 60

16

I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
18
Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
19
Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
20
School of Physics, University College Dublin, Dublin, Ireland
21
INFN Sezione di Bari, Bari, Italy
22
INFN Sezione di Bologna, Bologna, Italy
23
INFN Sezione di Ferrara, Ferrara, Italy
24
INFN Sezione di Firenze, Firenze, Italy
25
INFN Laboratori Nazionali di Frascati, Frascati, Italy
26
INFN Sezione di Genova, Genova, Italy
27
INFN Sezione di Milano, Milano, Italy
28
INFN Sezione di Milano-Bicocca, Milano, Italy
29
INFN Sezione di Cagliari, Monserrato, Italy
30
Università degli Studi di Padova, Università e INFN, Padova, Padova, Italy
31
INFN Sezione di Perugia, Perugia, Italy
32
INFN Sezione di Pisa, Pisa, Italy
33
INFN Sezione di Roma La Sapienza, Roma, Italy
34
INFN Sezione di Roma Tor Vergata, Roma, Italy
35
Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
36
Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, Netherlands
37
AGH — University of Science and Technology, Faculty of Physics and Applied Computer Science, Kraków,
Poland38
Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Kraków, Poland
39
National Center for Nuclear Research (NCBJ), Warsaw, Poland
40
Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania
41
Affiliated with an institute covered by a cooperation agreement with CERN42
DS4DS, La Salle, Universitat Ramon Llull, Barcelona, Spain
43
ICCUB, Universitat de Barcelona, Barcelona, Spain
44
Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de Santiago de Compostela, Santiago
de Compostela, Spain
45
Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia — CSIC, Valencia, Spain
46
European Organization for Nuclear Research (CERN), Geneva, Switzerland
47
Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
48
Physik-Institut, Universität Zürich, Zürich, Switzerland
49
NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
50
Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine
51
University of Birmingham, Birmingham, United Kingdom
52
H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom
53
Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
54
Department of Physics, University of Warwick, Coventry, United Kingdom
55
STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
56
School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom
57
School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom
58
Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
59
Imperial College London, London, United Kingdom
60
Department of Physics and Astronomy, University of Manchester, Manchester, United Kingdom
61
Department of Physics, University of Oxford, Oxford, United Kingdom
62
Massachusetts Institute of Technology, Cambridge, MA, United States
63
University of Cincinnati, Cincinnati, OH, United States
64
University of Maryland, College Park, MD, United States
65
Los Alamos National Laboratory (LANL), Los Alamos, NM, United States
66
Syracuse University, Syracuse, NY, United States
17

JHEP02(2024)118– 28 –

67

Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to 3
School of Physics and Electronics, Hunan University, Changsha City, China, associated to 8
69
Guangdong Provincial Key Laboratory of Nuclear Science, Guangdong-Hong Kong Joint Laboratory of
Quantum Matter, Institute of Quantum Matter, South China Normal University, Guangzhou, China,
associated to 4
70
Lanzhou University, Lanzhou, China, associated to 5
71
School of Physics and Technology, Wuhan University, Wuhan, China, associated to 4
72
Departamento de Fisica, Universidad Nacional de Colombia, Bogota, Colombia, associated to 15
73
Universität Bonn — Helmholtz-Institut für Strahlen und Kernphysik, Bonn, Germany, associated to 19
74
Eotvos Lorand University, Budapest, Hungary, associated to 46
75
Van Swinderen Institute, University of Groningen, Groningen, Netherlands, associated to 35
76
Universiteit Maastricht, Maastricht, Netherlands, associated to 35
77
Tadeusz Kosciuszko Cracow University of Technology, Cracow, Poland, associated to 38
78
Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden, associated to 57
79
University of Michigan, Ann Arbor, MI, United States, associated to 66
80
Departement de Physique Nucleaire (SPhN), Gif-Sur-Yvette, France
68

Universidade de Brasília, Brasília, Brazil
Centro Federal de Educacão Tecnológica Celso Suckow da Fonseca, Rio De Janeiro, BrazilcHangzhou Institute for Advanced Study, UCAS, Hangzhou, Chinad
LIP6, Sorbonne Universite, Paris, FranceeExcellence Cluster ORIGINS, Munich, Germanyf
Universidad Nacional Autónoma de Honduras, Tegucigalpa, HondurasgUniversità di Bari, Bari, Italyh
Università di Bologna, Bologna, Italyi
Università di Cagliari, Cagliari, Italyj
Università di Ferrara, Ferrara, Italyk
Università di Firenze, Firenze, Italyl
Università di Genova, Genova, Italym
Università degli Studi di Milano, Milano, Italyn
Università di Milano Bicocca, Milano, Italyo
Università di Padova, Padova, Italyp
Università di Perugia, Perugia, Italyq
Scuola Normale Superiore, Pisa, Italyr
Università di Pisa, Pisa, Italys
Università della Basilicata, Potenza, Italyt
Università di Roma Tor Vergata, Roma, Italyu
Università di Siena, Siena, Italyv
Università di Urbino, Urbino, Italyw
Universidad de Alcalá, Alcalá de Henares, Spainx
Universidade da Coruña, Coruña, Spainy
Department of Physics/Division of Particle Physics, Lund, Sweden†
Deceasedb– 29 –JHEP02(2024)118a