Measurement of b hadron fractions in 13 TeV pp collisions
Onderwater, C. J. G.; LHCb Collaboration
Published in: Physical Review D DOI: 10.1103/PhysRevD.100.031102IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below.
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Onderwater, C. J. G., & LHCb Collaboration (2019). Measurement of b hadron fractions in 13 TeV pp collisions. Physical Review D, 100(3), [031102]. https://doi.org/10.1103/PhysRevD.100.031102
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Measurement of b hadron fractions in 13 TeV pp collisions
R. Aaijet al.* (LHCb Collaboration)
(Received 18 February 2019; published 27 August 2019)
The production fractions of ¯B0s and Λ0b hadrons, normalized to the sum of B−and ¯B0 fractions, are measured in 13 TeV pp collisions using data collected by the LHCb experiment, corresponding to an integrated luminosity of1.67 fb−1. These ratios, averaged over the b hadron transverse momenta from 4 to 25 GeV and pseudorapidity from 2 to 5, are0.122 0.006 for ¯B0s, and0.259 0.018 for Λ0b, where the uncertainties arise from both statistical and systematic sources. TheΛ0bratio depends strongly on transverse momentum, while the ¯B0s ratio shows a mild dependence. Neither ratio shows variations with pseudorapidity. The measurements are made using semileptonic decays to minimize theoretical un-certainties. In addition, the ratio of Dþ to D0 mesons produced in the sum of ¯B0and B− semileptonic decays is determined as0.359 0.006 0.009, where the uncertainties are statistical and systematic.
DOI:10.1103/PhysRevD.100.031102
Knowledge of the fragmentation fractions of ¯B0s(fs) and
Λ0
b (fΛ0b) hadrons is essential for determining absolute
branching fractions (B) of decays of these hadrons at the LHC, allowing measurements, e.g., ofBð ¯B0s → μþμ−Þ [1] and the future evaluation of jVcbj from Λ0b→ Λþcμ−¯νμ decays[2].1Once these fractions are determined, measure-ments of absolute branching fractions of B−and ¯B0mesons performed at eþe− colliders operating at the ϒð4SÞ resonance can be used to determine the ¯B0s and Λ0b
branching fractions [3].
In this paper we measure the ratios fs=ðfuþ fdÞ and
fΛ0
b=ðfuþ fdÞ, where the denominator is the sum
of B− and ¯B0 contributions, in the LHCb acceptance of pseudorapidity 2 < η < 5 and transverse momentum 4 < pT< 25 GeV,2in 13 TeV pp collisions. These ratios
can depend on pTandη; therefore, we perform the analysis
using two-dimensional binning.
Much of the analysis method adopted in this study is an evolution of our previous b hadron fraction measurements for 7 TeV pp collisions [4]. We use the inclusive semi-leptonic decays Hb→ HcXμ−¯νμ, where Hb indicates a b
hadron, Hc a charm hadron, and X possible additional
particles. Each of the different Hc plus muon final states
can originate from the decay of different b hadrons.
Semileptonic decays of ¯B0 mesons usually result in a mixture of D0 and Dþ mesons, while B− mesons decay predominantly into D0mesons with a smaller admixture of Dþmesons. Both include a tiny component of Dþs ¯K meson
pairs. Similarly, ¯B0s mesons decay predominantly into Dþs
mesons, but can also decay into D0Kþ and DþK0meson pairs; this is expected if the ¯B0s meson decays into an
excited Dþs state that is heavy enough to decay into a DK
pair. We measure this contribution using D0KþXμ−¯νμ
events. Finally,Λ0b baryons decay semileptonically mostly intoΛþc final states, but can also decay into D0p and Dþn pairs. We ignore the contributions of b → u decays that comprise approximately 1% of semileptonic b hadron decays and contribute almost equally to all b hadron species. The detailed equations relating these yields to the final results are given in Ref. [4] and in the Supplemental Material [5].
The theoretical basis for this measurement is the near equality of semileptonic widths, ΓSL, for all b hadron
species[6]whose differences are predicted to precisions of about 1%. The values we use for the individual Hb
semileptonic branching fractions (BSL) are listed in Table I. The Hc decay modes used and their branching
fractions are given in Table II.
The ratio of Dþ to D0meson production in the sum of semileptonic ¯B0and B−decays, fþ=f0, is used to check the
analysis method. This result can be related to models of the hadronic final states in B−and ¯B0semileptonic decays[11]. The data sample corresponds to 1.67 fb−1 of integrated luminosity obtained with the LHCb detector in 13 TeV pp collisions during 2016. The LHCb detector [12,13] is a single-arm forward spectrometer covering the pseudora-pidity range2 < η < 5, designed for the study of particles containing b or c quarks.
*Full author list given at end of the article.
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
1Mention of a particular decay mode implies the use of the charge-conjugate one as well.
2
We use natural units where c ¼ ℏ ¼ 1.
The online event selection is performed by a trigger[14] 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. At the hardware trigger stage, events are required to have a muon with large pT or a hadron, photon or electron with
high transverse energy in the calorimeters. For hadrons, the transverse energy threshold is 3.5 GeV. The software trigger requires a two-, three- or four-track secondary vertex with a significant displacement from any primary pp interaction vertex (PV). At least one charged particle must have pT> 1.6 GeV and be inconsistent with
origi-nating from a PV. A multivariate algorithm[15]is used for the identification of secondary vertices consistent with the decay of a b hadron.
Simulation is required to model the effects of the detector acceptance and the imposed selection requirements. Here pp collisions are generated using PYTHIA [16] with a
specific LHCb configuration [17]. Decays of unstable particles are described by EVTGEN [18], in which final-state radiation is generated using PHOTOS [19]. The interaction of the generated particles with the detector and its response are implemented using the GEANT4 toolkit
[20]as described in Ref. [21].
Selection criteria are applied to muons and Hc decay
particles. The transverse momentum of each hadron must
be greater than 0.3 GeV, and that of the muon larger than 1.3 GeV. Each track cannot point to any PV, implemented by requiringχ2IP> 9 with respect to any PV, where χ2IP is
defined as the difference in the vertex-fitχ2of a given PV reconstructed with and without the track under consider-ation being included. All final-state particles are required to be positively identified using information from the Ring Imaging CHerenkov detectors particle identification (PID). Particles from Hc decay candidates must have a good fit to
a common vertex with χ2/ndof < 9, where ndof is the number of degrees of freedom. They must also be well separated from the nearest PV, with the flight distance divided by its uncertainty greater than 5.
Candidate b hadrons are formed by combining Hc and
muon candidates originating from a common vertex with χ2/ndof < 9 and an H
cμ− invariant mass, mHcμ−, in the
range 3.0–5.0 GeV for D0 and Dþ, 3.1–5.1 GeV for Dþs and 3.3–5.3 GeV for Λþc candidates. In addition, we define mcorr≡ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m2Hcμþ p 2 ⊥ q
þ p⊥, where p⊥is the magnitude of
the combination’s momentum component transverse to the b hadron flight direction; we require that mcorr > 4.2 or
4.5 GeV for ¯B0s or Λ0b candidates, respectively. For the
Dþs → KþK−πþ decay mode, vetoes are employed to
remove backgrounds from real Dþ or Λþc decays where the particle assignments are incorrect.
Background from prompt Hcproduction at the PV needs
to be considered. We use the natural logarithm of the Hc
impact parameter, IP, with respect to the PV in units of mm. Requiring lnðIP=mmÞ > −3 is found to reduce the prompt component to be below 0.1%, while preserving 97% of all signals. This restriction allows us to perform fits only to the Hc candidate mass spectra to find the b hadron decay
yields.
The Hc candidates’ mass distributions integrated over
pTðHbÞ and η are shown in Fig. 1. They consist of a
prominent peak resulting from signal and a small contri-bution due to combinatorial background from random combinations of particles that pass the selection. They are fit with a signal component comprised of two Gaussian functions and a combinatorial background compo-nent modeled as a linear function. The total signal yields for D0Xμ−¯νμ, DþXμ−¯νμ, DsþXμ−¯νμ and Λþcμ−X ¯νμ are
13 775 000, 4 282 700, 845 300, and 1 753 600, respectively. Background contributions to the b hadron candidates include hadrons faking muons, false combinations of charm hadrons and muons from the two b hadrons in the event, as well as real muons and charm hadrons from B → D ¯DX decays, where one of the D mesons decays into a muon. All the backgrounds are evaluated in two-dimensionalη and pT intervals. The first two backgrounds are evaluated using events where the Hcis combined with a muon of the wrong
sign (e.g., D0μþ), forbidden in a semileptonic b hadron decay. The wrong-sign backgrounds are <1% for each Hc
species. The background from B → D ¯DX decays is TABLE I. Branching fractions of semileptonic b hadron
decays from direct measurements for ¯B0 and B− mesons, (hBi ≡ h ¯B0þ B−i), and derived for ¯B0s and Λ0b hadrons based on the equality of semileptonic widths and the lifetime ratios[3,6]. Corrections toΓSLfor ¯B0sð−1.0 0.5Þ% and Λ0bð3.0 1.5Þ% are applied [6]. Correlations in the ¯B0 and B− branching fraction measurements have been taken into account. See Ref.[7]for more information.
τ (ps) BSL(%) BSL(%)
Particle measured measured used
¯B0 1.520 0.004 10.30 0.19 10.30 0.19 B− 1.638 0.004 11.08 0.20 11.08 0.20 hBi 10.70 0.19 10.70 0.19 ¯B0 s 1.526 0.015 10.24 0.21 Λ0 b 1.470 0.010 10.26 0.25
TABLE II. Charm-hadron branching fractions for the decay modes used in this analysis. Note that theΛþc branching fraction has been significantly improved since the previous analysis.
Decay B (%) Source D0→ K−πþ 3.93 0.05 PDG average[3] Dþ→ K−πþπþ 9.22 0.17 CLEO-c[8] Dþs → K−Kþπþ 5.44 0.18 PDG average[3] Λþ c → pK−πþ 6.23 0.33 From Refs.[9,10]
determined by simulating a mixture of these decays using their measured branching fractions[3]. The only decay mode significantly affected is ¯B0s→ DþsXμ−¯νμwith contributions
varying from 0.1% for D0D−sX to 1.8% for DþsD−sX due to
the large Dþs → μþν decay rate. The total B → D ¯DX
back-ground isð5.8 0.9Þ%.
The dominant component in ¯B0s semileptonic decays is
DþsXμ−¯νμ, where X contains possible additional hadrons.
However, the ¯B0smeson also can decay into D0Kþor DþK0
instead of Dþs, so we must add this component to the ¯B0srate
and subtract it from the fuþ fd fraction. Similarly, inΛ0b
semileptonic decays we find a D0pX component. The selection criteria for these final states are similar to those for the D0Xμ−¯νμ and ΛþcXμ−¯νμ final states described above
with the addition of a kaon or proton with pT> 300 MeV
that has been positively identified. A veto is also applied to reject Dþ→ πþD0decays where the pion mimics a kaon or a proton.
These samples contain background, resonant and non-resonant decays. Separation of these components is achieved by using both right-sign (Hc with μ−) and wrong-sign
(Hc withμþ) candidates. In addition, the logarithm of the
difference between the vertexχ2formed by the added hadron track and the Dμ system and the vertex χ2of the Dμ system, lnðΔχ2VÞ, provides separation between combinatorial back-ground and nonresonant semileptonic decays. True resonant and nonresonant ¯B0s→ D0Kþμ−¯νμ or Λ0b→ D0pμ−¯νμ
decays peak in the lnðΔχ2VÞ distribution at a value of unity
while the background is smooth and rises at higher values as the added track is generally not associated with the D0μ− vertex. To distinguish signal from background we define mðD0hÞC≡ mðD0hÞ − mðD0Þ þ mðD0ÞPDG and perform
two-dimensional fits to the mðD0hÞCand lnðΔχ2VÞ
distribu-tions, where h ¼ KþðpÞ for right-sign ¯B0s (Λ0b) decays.
The wrong-sign shapes are used to model the back-grounds. The resonant structures are modeled with rela-tivistic Breit-Wigner functions convoluted with Gaussians to take into account the experimental resolution, except for the narrow Ds1ð2536Þþ which is modeled with the sum of
two Gaussians with a fixed mean. The nonresonant shape for the lnðΔχ2VÞ distribution is taken as the same as the resonant one. Figure2shows the data and result of the fits for ¯B0s andΛ0b candidates.
For the ¯B0s case, we find 22 610 210 Ds1ð2536Þþ,
14 290 260 D
s2ð2573Þþ, and38 140 460 nonresonant
decays, confirming the existence of both the Dþs1 [22,23]
and Dþs2 [23] particles in semileptonic ¯B0s decays with
substantially more data, and showing the existence of the nonresonant component. To account for the unmeasured DþK0channel we take different mixtures of Dand D final states for the different resonant and nonresonant compo-nents. The Dþs1 decays dominantly into D, while the Dþs2 decays dominantly into D mesons[3]. For the nonresonant part we assume equal Dand D yields.
In theΛ0b case, we find6120 460 Λþcð2860Þ, 2200 200 Λþ cð2880Þ, 1200 260 Λþcð2940Þ, and 29 770 690 [MeV] ) + π − m(K 1800 1850 1900 Candidates / ( 1 MeV ) 0 100000 200000 300000 400000 500000 600000 700000 LHCb (a) [MeV] ) + π + π − m(K 1800 1850 1900 Candidates / ( 1 MeV ) 0 50000 100000 150000 200000 LHCb (b) [MeV] ) + π − K + m(K 1900 1950 2000 Candidates / ( 1 MeV ) 0 10000 20000 30000 40000 50000 LHCb (c) [MeV] ) + π − m(pK 2250 2300 2350 Candidates / ( 1 MeV ) 0 20000 40000 60000 80000 100000 LHCb (d)
FIG. 1. Fit to the mass spectra of the Hccandidates of the selected Hbdecays: (a) D0, (b) Dþ, (c) Dþs mesons, and (d) theΛþc baryon. The data are shown as black points with error bars. The signal component is shown as the dashed (green) line and the combinatorial background component is shown as the dashed (red) line. The solid (blue) line shows all components added together.
nonresonant events. The decay rate into D0p is assumed to be equal to that into Dþn using isospin conservation. All decays with an extra hadron have lower detection efficien-cies than the sample without.
Efficiencies for all the samples are determined using data in two-dimensional pTandη bins. Trigger efficiencies are
determined using a sample of B−→ J=ψK−, with J=ψ → μþμ− decays where only one muon track is positively
identified, in conjunction with viewing the effects of combinations of different triggers[24]. This sample is also used to determine muon identification efficiencies. Decays of J=ψ mesons to muons reconstructed using partial information from the tracking system, e.g., eliminating the vertex locator information, are also used to determine tracking efficiencies using data and to correct the simu-lation. Finally, the PID efficiencies are evaluated using kaons and pions from Dþ→ πþD0 decays, with D0→ K−πþ, and protons from Λ → pπ− and Λþc → pK−πþ decays [25]. In the measurement of b hadron fraction ratios many of the efficiencies cancel and we are left with only residual effects to which we assign systematic uncertainties.
The b hadron η and pT, pTðHbÞ, must be known because
the b fractions can depend on production kinematics. While η can be evaluated directly using the measured primary and
secondary b vertices, the value of pTðHbÞ must be
determined to account for the missing neutrino plus extra particles. The correction factor k is given by the ratio of the average reconstructed to true pTðHbÞ as a function of
mðHcμ−Þ and is determined using simulation. It varies from
0.75 for mðHcμ−Þ¼3 GeV to unity at mðHcμ−Þ ¼ mðHbÞ.
The distribution of fs=ðfuþ fdÞ as a function of pTðHbÞ
is shown in Fig.3. We perform a linearχ2fit incorporating a full covariance matrix which takes into account the bin-by-bin correlations introduced from the kaon kinematics, and PID and tracking systematic uncertainties. The factor A in Eq.(1) incorporates the global systematic uncertainties described later, which are independent of pTðHbÞ. The
resulting function is fs
fuþ fd
ðpTÞ ¼ A½p1þ p2×ðpT− hpTiÞ; ð1Þ
where pT here refers to pTðHbÞ, A ¼ 1 0.043, p1¼
0.119 0.001, p2¼ ð−0.91 0.25Þ × 10−3GeV−1, and
hpTi ¼ 10.1 GeV. The correlation coefficient between
the fit parameters is 0.20. After integrating over pTðHbÞ,
no η dependence is observed (see the Supplemental Material[5]). [MeV] C ) ± K 0 D ( m 2500 3000 3500 4000 Candidates / ( 5 MeV ) 0 2000 4000 6000 8000 10000 12000 LHCb (a) ) V 2 χ Δ ( ln -4 -2 0 2 4 Candidates / ( 0.25 ) 0 5000 10000 15000 20000 25000 30000 35000 LHCb (b) [MeV] C ) ) − ( p 0 D ( m 3000 3500 4000 Candidates / ( 5 MeV ) 0 200 400 600 800 1000 1200 1400 1600 1800 LHCb (c) ) V 2 χ Δ ( ln -4 -2 0 2 4 Candidates / ( 0.25 ) 0 1000 2000 3000 4000 5000 6000 7000 LHCb (d)
FIG. 2. Projections of the two-dimensional fits to the (a) mðD0KÞCand (c) mðD0p ð−Þ
ÞCmass distributions and (b),(d) lnðΔχ2VÞ for (top) D0KXμ−¯νμcandidates and for (bottom) D0ð−ÞpX ¯νμcandidates. The curves show projections of the 2D fit. The dashed (red) curves show the Dþs1and Dþs2 resonant components in (a) and (b), andΛþcð2860Þ, Λþcð2880Þ and Λþcð2940Þ resonant components in (c) and (d). The long-dashed-dotted (green) curves show the nonresonant component, the dotted (black) curves are the background components, whose shapes are determined from wrong-sign combinations, and the solid (blue) curves shows all components added together.
We determine an average value for fs=ðfuþ fdÞ by
dividing the yields of ¯B0ssemileptonic decays by the sum of
¯B0 and B− semileptonic yields, which are all
efficiency-corrected, between the limits of pTðHbÞ of 4 and 25 GeV
andη of 2 and 5, resulting in fs
fuþ fd
¼ 0.122 0.006;
where the uncertainty contains both statistical and systematic components, with the latter being dominant, and discussed subsequently. The total relative uncertainty is 4.8%.
Figure 3 also shows the Λ0b fraction as a function of pTðHbÞ demonstrating a large pT dependence. The
dis-tribution inη is flat. We perform a similar fit as in the ¯B0s fraction case, using
fΛ0 b
fuþ fd
ðpTÞ ¼ A½p1þ exp ðp2þ p3× pTÞ; ð2Þ
where pT here refers to pTðHbÞ, A ¼ 1 0.061, p1¼
ð7.93 1.41Þ × 10−2, p
2¼ −1.022 0.047, and p3¼
−0.107 0.002 GeV−1. The correlation coefficients
among the fit parameters are 0.40 (ρ12), −0.95 (ρ13), and−0.63 (ρ23).
The average value for fΛ0
b=ðfuþ fdÞ is determined using
the same method as in the ¯B0s case. The result is
fΛ0 b
fuþ fd
¼ 0.259 0.018;
where the dominant uncertainty is systematic, and the statistical uncertainty is included. The overall uncertainty is 6.9%.
As a systematic check of the analysis method, and a useful measurement to test the knowledge of known semileptonic branching fractions and extrapolations used to saturate the unknown portion of the inclusive hadron spectrum, we measure the ratio of the D0Xμ−¯νμ to
DþXμ−¯νμ corrected yields fþ=f0. We subtract the small
contributions from ¯B0s and Λ0b decays, and a very small
contribution from B → Dþs ¯Kμ−X decays has been taken
into account[26], as in all the fractions measured above. Assuming fuequals fd, Ref.[11]estimates the fraction
of Dþμ with respect to D0μ modes in the sum of B−and ¯B0 decays as 0.387 0.012 0.026. The first uncertainty comes from the uncertainties on known measurements. The second uncertainty comes from the different extrap-olations from excited D mesons used to saturate the remaining portion of the inclusive rate.
The fþ=f0 ratio must be independent of η and pT. To
derive an overall value for fþ=f0, the pTðHbÞ distribution
is fit to a constant. Only the PID and tracking systematic uncertainties on the second pion in the Dþ decay need be considered. Performing a χ2 fit using the full covariance matrix we find fþ=f0¼ 0.359 0.006 0.009, where the
first uncertainty is from bin-by-bin statistical and system-atic uncertainties, including correlations, and the second is systematic. Theχ2=ndof is 0.63, in agreement with a flat spectrum. The measurement is consistent with the predic-tion and places some constraints on the D content of semileptonic B decays[11].
The dominant global systematic uncertainties are listed in Table III. Simulation uncertainties are due to the
) [GeV] b H ( T p 5 10 15 20 25 fractionsb Λ and s B 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 LHCb = 13 TeV s u f + d f s f u f + d f b Λ f
FIG. 3. The ratios fs=ðfuþ fdÞ and fΛ0
b=ðfuþ fdÞ in bins of
pTðHbÞ. The ¯B0s data are indicated by solid circles, while theΛ0b by triangles. The smaller (black) error bars show the combined bin-by-bin statistical and systematic uncertainties, and the larger (blue) ones show the global systematics added in quadrature. The fits to the data are shown as the solid (green) bands, whose widths represents the1σ uncertainty limits on the fit shapes, and the dashed (black) lines give the total uncertainty on the fit results including the global scale uncertainty. In the highest two pTbins the points have been displaced from the center of the bin.
TABLE III. Global systematic uncertainties. The D0 and Dþ branching fraction uncertainties are scaled by the fraction of each decay, f0 and fþ for fs=ðfuþ fdÞ and fΛ0
b=ðfuþ fdÞ uncertainties. Value (%) Source fs=ðfuþ fdÞ fΛ0 b=ðfuþ fdÞ fþ=f0 Simulation 1.7 2.4 Backgrounds 0.9 0.3 Cross feeds 1.2 0.4 0.2 BðD0→ K−πþÞ 1.0 1.0 1.3 BðDþ→ Kþπ−π−Þ 0.6 0.6 1.8 BðDþ s → KþK−πþÞ 3.3 BðΛþ c → pKþπ−Þ 5.3
Measured lifetime ratio 1.2 0.7
ΓSL correction 0.5 1.5
modeling of excited charm states for the fs=ðfuþ fdÞ
determination and the weighting required for the fΛ0
b=ðfuþ fdÞ ratio, due to differences between the
simu-lated and measured pT spectra. Background uncertainties
arise from D ¯DX final states with uncertain branching fractions. Cross-feed uncertainties come from errors on efficiency estimates and the assumed D to D mixtures. Other smaller uncertainties depend on pTðHbÞ and include
tracking 0.2%–1.8%, particle identification 0.4%–3.0%, trigger 0.3%–3.9% and k-factor 0.2%–1.8%.
In conclusion, we measure the ratios of ¯B0s and Λ0b
production to the sum of B− and ¯B0 to be pTðHbÞ
dependent [see Eqs. (1) and (2)]. The averages in the ranges 4 < pTðHbÞ < 25 GeV and 2 < η < 5 are
fs=ðfuþ fdÞ ¼ 0.122 0.006 and fΛ0
b=ðfuþ fdÞ ¼
0.259 0.018, respectively. Using 7 TeV data, LHCb determined fs=ðfuþfdÞ¼0.12950.0075 with a pTðHbÞ
slope larger than, but consistent with, these 13 TeV results [27]; no dependence onη was observed. For the Λ0bbaryon, the fraction ratio is consistent with the 7 TeV measurements after taking into account the different pTðHbÞ ranges used
[4,28,29]. We observe no rapidity dependence over a
similar pTðHbÞ range as in Ref. [29].
These results are crucial for determining absolute branching fractions of ¯B0s and Λ0b hadron decays in LHC
experiments. We also determine the ratio of D0 to Dþ mesons produced in the sum of ¯B0 and B− semileptonic decays as fþ=f0¼ 0.359 0.006 0.009.
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); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC (United Kingdom); 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 OSC (USA). We are indebted to the communities behind the multiple open-source software packages on which we depend. Individual groups or members have received support from the AvH Foundation (Germany); EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union); ANR, Labex P2IO and OCEVU, and R´egion Auvergne-Rhône-Alpes (France); Key Research Program of Frontier Sciences of CAS, CAS PIFI, and the Thousand Talents Program (China); RFBR, RSF and Yandex LLC (Russia); GVA, XuntaGal and GENCAT (Spain); the Royal Society and the Leverhulme Trust (United Kingdom); and Laboratory Directed Research and Development program of LANL (USA).
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Y. Zheng,4X. Zhu,3 V. Zhukov,11,37 J. B. Zonneveld,54and S. Zucchelli17,e (LHCb Collaboration)
1
Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil 2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3
Center for High Energy Physics, Tsinghua University, Beijing, China 4University of Chinese Academy of Sciences, Beijing, China
5
Institute of High Energy Physics (ihep), Beijing, China
6University Grenoble Alpes, University Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy, France 7
Universit´e Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France 8Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
9
LAL, University Paris-Sud, CNRS/IN2P3, Universit´e Paris-Saclay, Orsay, France 10LPNHE, Sorbonne Universit´e, Paris Diderot Sorbonne Paris Cit´e, CNRS/IN2P3, Paris, France
11
I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany 12Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
13
Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
15School of Physics, University College Dublin, Dublin, Ireland 16
INFN Sezione di Bari, Bari, Italy 17INFN Sezione di Bologna, Bologna, Italy
18
INFN Sezione di Ferrara, Ferrara, Italy 19INFN Sezione di Firenze, Firenze, Italy 20
INFN Laboratori Nazionali di Frascati, Frascati, Italy 21INFN Sezione di Genova, Genova, Italy 22
INFN Sezione di Milano-Bicocca, Milano, Italy 23INFN Sezione di Milano, Milano, Italy 24
INFN Sezione di Cagliari, Monserrato, Italy 25INFN Sezione di Padova, Padova, Italy
26
INFN Sezione di Pisa, Pisa, Italy 27INFN Sezione di Roma Tor Vergata, Roma, Italy 28
INFN Sezione di Roma La Sapienza, Roma, Italy
29Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands 30
Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, Netherlands 31Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Kraków, Poland
32
AGH—University of Science and Technology, Faculty of Physics and Applied Computer Science, Kraków, Poland
33
National Center for Nuclear Research (NCBJ), Warsaw, Poland
34Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania 35
Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia 36Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia 37
Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia 38Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS), Moscow, Russia
39
Yandex School of Data Analysis, Moscow, Russia 40Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
41
Institute for High Energy Physics (IHEP), Protvino, Russia 42ICCUB, Universitat de Barcelona, Barcelona, Spain 43
Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de Santiago de Compostela, Santiago de Compostela, Spain
44
European Organization for Nuclear Research (CERN), Geneva, Switzerland
45Institute of Physics, Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne, Switzerland 46
Physik-Institut, Universität Zürich, Zürich, Switzerland
47NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine 48
Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine 49University of Birmingham, Birmingham, United Kingdom
50
H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom 51Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
52
Department of Physics, University of Warwick, Coventry, United Kingdom 53STFC Rutherford Appleton Laboratory, Didcot, United Kingdom 54
School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom 55School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom
56
Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom 57Imperial College London, London, United Kingdom
58
School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom 59Department of Physics, University of Oxford, Oxford, United Kingdom
60
Massachusetts Institute of Technology, Cambridge, Massachusetts, USA 61University of Cincinnati, Cincinnati, Ohio, USA
62
University of Maryland, College Park, Maryland, USA 63Syracuse University, Syracuse, New York, USA 64
Laboratory of Mathematical and Subatomic Physics, Constantine, Algeria [associated to Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil] 65
Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil [associated to Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil]
66
South China Normal University, Guangzhou, China
(associated to Center for High Energy Physics, Tsinghua University, Beijing, China) 67
School of Physics and Technology, Wuhan University, Wuhan, China (associated to Center for High Energy Physics, Tsinghua University, Beijing, China)
68Institute of Particle Physics, Central China Normal University, Wuhan, Hubei, China (associated to Center for High Energy Physics, Tsinghua University, Beijing, China)
69Departamento de Fisica, Universidad Nacional de Colombia, Bogota, Colombia
(associated to LPNHE, Sorbonne Universit´e, Paris Diderot Sorbonne Paris Cit´e, CNRS/IN2P3, Paris, France)
70
Institut für Physik, Universität Rostock, Rostock, Germany
(associated to Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany) 71
Van Swinderen Institute, University of Groningen, Groningen, Netherlands (associated to Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands)
72
National Research Centre Kurchatov Institute, Moscow, Russia
[associated to Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia] 73
National University of Science and Technology“MISIS,” Moscow, Russia [associated to Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia]
74
National Research University Higher School of Economics, Moscow, Russia (associated to Yandex School of Data Analysis, Moscow, Russia) 75
National Research Tomsk Polytechnic University, Tomsk, Russia
[associated to Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia] 76
Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia—CSIC, Valencia, Spain (associated to ICCUB, Universitat de Barcelona, Barcelona, Spain)
77
University of Michigan, Ann Arbor, Michigan, USA (associated to Syracuse University,
Syracuse, New York, USA)
78Los Alamos National Laboratory (LANL), Los Alamos, New Mexico, USA (associated to Syracuse University, Syracuse, New York, USA) †Deceased.
a
Universidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil. bLaboratoire Leprince-Ringuet, Palaiseau, France.
c
P.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia. dUniversit`a di Bari, Bari, Italy.
e
Universit`a di Bologna, Bologna, Italy. fUniversit`a di Cagliari, Cagliari, Italy. g
Universit`a di Ferrara, Ferrara, Italy. hUniversit`a di Genova, Genova, Italy.
i
Universit`a di Milano Bicocca, Milano, Italy. jUniversit`a di Roma Tor Vergata, Roma, Italy. k
Universit`a di Roma La Sapienza, Roma, Italy.
lAGH—University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, Kraków, Poland.
mLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain. n
Hanoi University of Science, Hanoi, Vietnam. oUniversit`a di Padova, Padova, Italy.
p
Universit`a di Pisa, Pisa, Italy.
qUniversit`a degli Studi di Milano, Milano, Italy. r
Universit`a di Urbino, Urbino, Italy. sUniversit`a della Basilicata, Potenza, Italy. t
Scuola Normale Superiore, Pisa, Italy.
uUniversit`a di Modena e Reggio Emilia, Modena, Italy. v
H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom. wMSU—Iligan Institute of Technology (MSU-IIT), Iligan, Philippines.
x
Novosibirsk State University, Novosibirsk, Russia. ySezione INFN di Trieste, Trieste, Italy.
z
School of Physics and Information Technology, Shaanxi Normal University (SNNU), Xi’an, China. aaPhysics and Micro Electronic College, Hunan University, Changsha City, China.
ab
