First branching fraction measurement of the suppressed decay Ξ

First branching fraction measurement of the suppressed decay Ξ

→ π

Λ

R. Aaijet al.^* (LHCb Collaboration)

(Received 23 July 2020; accepted 11 September 2020; published 12 October 2020) TheΞ⁰c baryon is unstable and usually decays into charmless final states by the c → su ¯d transition.

It can, however, also disintegrate into aπ⁻meson and aΛ^þc baryon via s quark decay or via cs → dc weak scattering. The interplay between the latter two processes governs the size of the branching fraction BðΞ⁰c→ π⁻Λ^þcÞ, first measured here to be ð0.55  0.02  0.18Þ%, where the first uncertainty is statistical and second systematic. This result is compatible with the larger of the theoretical predictions that connect models of hyperon decays using partially conserved axial currents and SU(3) symmetry with those involving the heavy-quark expansion and heavy-quark symmetry. In addition, the branching fraction of the normalization channel,BðΞ^þc → pK⁻π^þÞ ¼ ð1.135  0.002  0.387Þ% is measured.

DOI:10.1103/PhysRevD.102.071101

Baryons containing both an s quark and a heavy c or b quark, denoted as Q, usually decay via the disintegration of the heavy quark. There is, however, the possibility of s quark decay causing the transformation. Theoretical pre- dictions concerning the decay widths of ΞQ→ πΛQ tran- sitions are based on the size of the s quark decay amplitude s → uð ¯udÞ (SUUD) and the weak scattering (WS) ampli- tude Qs → dQ [1]. Feynman diagrams corresponding to these amplitudes are shown in Fig. 1forΞ⁰c decay.

Studies of theseΞQbaryon decays provide a connection to theories concerning hyperon decays with those for the heavy b and c quarks. The former use partially conserved axial currents (PCAC) and SU(3) symmetry [2], whereas the latter apply more modern approaches using four-quark operators, including the heavy quark expansion, and heavy- quark symmetry (HQS). As theΞ⁻_b baryon consists of b, s, and d quarks, the WS amplitude is not present in Ξ⁻_b → π⁻Λ⁰_bdecays, so the measurement of that decay rate can be used to determine the SUUD amplitude. This information can be used to predict theΞ⁰_c decay rate that, in principle, involves both amplitudes. Whenever a specific final state is mentioned additional use of the charge-conjugated state is implied.

The well-known Ξ⁰c baryon consists of the c, s, and d quarks, and has a lifetime of 154.5  1.7  1.6  1.0 fs [3]. The branching fraction BðΞ⁰_c → π⁻Λ^þ_cÞ has not been previously measured. Several authors have made predic- tions using the measured SUUD amplitude and the

measured lifetimes of the SU(3) triplet baryons Ξ⁰c, Λ^þc, andΞ^þ_c, as input for determining the WS amplitude. This method was pioneered by Voloshin [1] where he used SU(3) symmetry, PCAC and the heavy-quark limit to determine an upper limit on ΓðΞ⁻_b → π⁻Λ⁰_bÞ. In a sub- sequent paper, he uses the input from the LHCb measure- ment of BðΞ⁻_b→π⁻Λ⁰_bÞ¼ð0.600.18Þ%[4] and updated values for the charmed baryon lifetimes to find the SUUD rate and then calculates the WS amplitude. He predicts BðΞ⁰_c → π⁻Λ^þ_cÞ⪆ ð0.25  0.15Þ × 10⁻³[5], assuming neg- ative interference between the two strangeness-changing amplitudes.

Gronau and Rosner, using the same approach as Voloshin, predict two possible branching fractions for Ξ⁰c→ π⁻Λ^þc decay, depending on the sign of the interfer- ence between the two decay amplitudes[6]. Based on the measuredBðΞ⁻_b → π⁻Λ⁰_b) [4], and using charmed-baryon lifetimes available at that time, they predict BðΞ⁰_c → π⁻Λ^þ_cÞ ¼ ð0.19  0.07Þ% for constructive interference and BðΞ⁰c → π⁻Λ^þcÞ ⪅ 0.01% for destructive interference between the SUUD and WS contributions. We have redone their calculation using updated lifetime measurements [3,7], finding BðΞ⁰c→ π⁻Λ^þcÞ ¼ ð0.14  0.07Þ% for con- structive interference and BðΞ⁰_c → π⁻Λ^þ_cÞ ⪅ ð0.018  0.015Þ% for destructive interference. Faller and Mannel, on the other hand, predictBðΞ⁰c→ π⁻Λ^þcÞ < 0.3%, an upper limit obtained by assuming constructive interference [8].

Finally, Cheng et al. predict BðΞ⁰_c → π⁻Λ^þ_cÞ ∼ 0.0087%, assuming negative interference[9]. We have not updated these last predictions; the effect would be to lower Faller and Mannel’s positive interference prediction and raise the Cheng et al. negative one, giving somewhat better agree- ment with Gronau and Rosner’s predictions.

In this paper we measure BðΞ⁰_c→ π⁻Λ^þ_cÞ using data collected by the LHCb detector, corresponding to3.8 fb⁻¹

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of integrated luminosity in 13 TeV center-of-mass energy pp collisions taken in 2017 and 2018. Natural units are used in this paper with c ¼ ℏ ¼ 1. The LHCb detector is a single-arm forward spectrometer covering the pseudora- pidity range2 < η < 5, described in detail in Refs.[10,11].

The trigger [12] consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, which reconstructs charged particles.

Simulation is required to model the effects of the detector acceptance and selection requirements. We generate pp collisions using PYTHIA [13] with a specific LHCb con- figuration[14]. Decays of unstable particles are described by EVTGEN [15], where final-state radiation is generated usingPHOTOS[16]. The interaction of the particles with the detector, and its response, are implemented using the

GEANT4 toolkit[17]as described in Ref.[18].

In our analysis we use the prompt Ξ⁰_c sample, i.e., baryons, and their excitations, produced directly in the pp collisions. Measurement ofBðΞ⁰c→ π⁻Λ^þcÞ is hampered by the lack of accurately measuredΞ⁰c branching fractions[7]

to be used for normalization. A measurement of BðΞ⁰_c→ π^þΞ⁻Þ with a 29% uncertainty exists [19], but the effi- ciency for reconstructing Ξ⁻ baryons is low in LHCb, in particular without a dedicated trigger line, so using this mode would lead to an unacceptably large error. We overcome this difficulty by using two indirect methods, described below, that require additional measurements of promptΛ^þc andΞ^þc yields, both reconstructed in the pK⁻π^þ decay mode. The same decay mode is also used to reconstructΛ^þ_c from theΞ⁰_c → π⁻Λ^þ_c decays.

We use a two-step process to maximize the statistical significance of our signal channel, as well as the two normalization channels. First, we apply a set of loose selection criteria to obtain samples with large signal efficiencies and suppressed background. Subsequently, we use three different boosted decision trees (BDT) [20,21], one for each baryon decay, implemented in the TMVA toolkit [22], to further separate signal from background.

The loose selection criteria for the pK⁻π^þ final states include requirements on the tracks to have sufficient transverse momenta (pT), be separated from the primary pp collision vertex (PV), form a three-track vertex, and be identified as the hypothesized particle species. For the Ξ⁰_c → π⁻Λ^þ_c decay we require, in addition, that the pK⁻π^þ

has a mass within 20 MeV of the Λ^þ_c mass peak; that there is an additional π⁻ meson, which when combined with the Λ^þ_c candidate, has an invariant mass from

−85 MeV below the known Ξ⁰_c mass [7] to 115 MeV above; and that the pT of the Ξ⁰c candidate is greater than 5 GeV.

The BDTs are trained with background samples from data and simulated signal samples. Background training samples for theΛ^þc andΞ^þc candidates are taken from the sideband regions on both sides of the mass peaks. For the Λ^þ_c baryon background the intervals are 40–65 MeV away from the knownΛ^þ_c mass[7]. For theΞ^þ_c baryon training the lower and higher sidebands are taken 40–58 MeV and 40–72 MeV from the known Ξ^þ_c mass[7], respectively. The Ξ⁰c background is constructed from like-signπ^þΛ^þc candi- dates within 5 MeV of the known Ξ⁰c baryon mass [7].

For the Λ^þc and Ξ^þc candidates, we compute the pK⁻π^þ invariant mass after constraining the three decay particles to form a common vertex and the summed momentum vector to point to the PV; this fitter is referred to as the“decay tree fitter” (DTF)[23]. In the case of theΞ⁰_c baryon we add the additionalπ^∓ meson before performing the fit. Only1=10 of the available Λ^þ_c → pK⁻π^þ data sample is used to measure the Λ^þc yield due to the large samples available relative to the other channels.

The variables used in the Λ^þc and Ξ^þc BDTs are the particle identification probabilities; theχ²IP of the pK⁻π^þ with respect to the primary vertex, whereχ²_IPis defined as the difference in the vertex fitχ² with and without the p, K⁻, and π^þ tracks; the angle between the particle’s momentum vector and the vector from the original PV before the DTF refitting to the particle’s decay vertex; the decay distance from the PV, and the DTF χ². The Ξ⁰_c candidates are selected by a separate BDT using the same criteria used for theΛ^þ_c by adding similar extra variables associated with the additional pion.

The BDT selections are optimized by maximizing the ratio of signal efficiency to the square root of the number of candidates in the regions where we expect signal peaks. We show the resulting mass spectra in Fig.2; the data are fitted using the signal and background shapes described in the figure caption. The fit yields are 6320  230 Ξ⁰c, 2667200  3300 Λ^þc, and 1613000  3500 Ξ^þc signal decays. To take into account the efficiency variation we perform the fits in four bins, two in pT and two inη, and apply efficiencies calculated in each bin.

W ^-

s c

u d

{

Ξ ^c

} ^} Λ ^{π c}

-

W

c

{

Ξ c

0

d

d c u u

} π ^-

} ^{Λ c}

(a) (b)

FIG. 1. Decay diagrams forΞ⁰c→ π⁻Λ^þc transitions. (a) The SUUD amplitude, and (b) the WS amplitude.

Trigger efficiencies are estimated from data, using the technique described in Ref.[25]. Selection efficiencies are determined using simulated events, which are weighted to reproduce the resonance structures in the pK⁻π^þfinal states visible in theΛ^þc andΞ^þc signal samples.

The overall detection efficiencies are ð0.11  0.02Þ%,

½ð0.35  0.01Þ=10%, and ð1.18  0.03Þ% for Ξ⁰_c, Λ^þ_c, and Ξ^þc decays, respectively, where the factor of 10 is the prescale.

The first normalization method uses the LHCb meas- urement of the relative production fractions of theΞ⁻_b and Λ⁰_b beauty baryons, fΞ⁻_b=f_Λ⁰

b ¼ ð8.2  0.7  2.6Þ% [26].

Using HQS we equate the unmeasured production ratio of Ξ⁰c to Λ^þc baryons, f_Ξ⁰_c=f_Λ^þ_c, toC · fΞ⁻_b=f_Λ⁰

b, whereC is a correction factor for feed-downs of excitedΞbbaryons that do not have equal rates toΞ⁻_b andΞ⁰_bfinal states. This feed- down is not symmetric primarily because the Ξ⁰_bð5935Þ⁰ state always decays toπ⁰(orγ) Ξ⁰_b[27], since its mass is too low to decay intoπ^þΞ⁻_b. On the other hand, both theΞ⁰⁻_b andΞ^−_b states are seen to decay into bothπ⁻Ξ⁰_bandπ⁰Ξ⁻_b final states[28]. Any not yet observed higher mass states would be isospin symmetric in their decays. Accounting for all the known excited states, and the associated phase-space

corrections, results in C ¼ 1.18  0.04, where the uncer- tainty arises from the errors on the relative branching fraction measurements.

The second method uses the recent Belle measurement BðΞ^þc → pK⁻π^þÞ ¼ ð0.45  0.21  0.07Þ%[29]. Here we take the production ofΞ⁰c baryons equal to that of Ξ^þc by isospin symmetry, e.g., f_Ξ⁰_c=f_Ξ^þ_c ¼ 1.00  0.01 [30]. As the final state particles in theΞ^þ_c decay are the same as in theΛ^þc decay, many systematic uncertainties cancel.

We determine BðΞ⁰c→ π⁻Λ^þcÞ using the two measured ratios

R1≡NðΞ⁰cÞ NðΛ^þcÞ¼ f_Ξ⁰_c

fΛ^þ_c ·BðΞ⁰c→ π⁻Λ^þcÞ

¼ ð0.095  0.003  0.012Þ%;

R₂≡NðΞ⁰_cÞ NðΞ^þcÞ¼f_Ξ⁰_c

f_Ξ^þ_c ·BðΛ^þ_c → pK⁻π^þÞ

BðΞ^þc → pK⁻π^þÞ·BðΞ⁰_c → π⁻Λ^þ_cÞ

¼ ð5.70  0.19  0.77Þ%;

where NðiÞ indicates the efficiency corrected number of signal events for baryon i, fi indicates the fraction of particle production with respect to all c- or b-quark

2440 2450 2460 2470 2480 2490 2500 2510

[MeV]

+) Λc

m(

+

+)

−π m(pK -

−) π π+

m(pK− 0

0.5 1 1.5 2 2.5 3 3.5 4

103

×

Candidates / (0.5 MeV)

Data Total fit

0

Ξc

Signal Background

LHCb (a)

2240 2260 2280 2300 2320 2340

[MeV]

+)

−π m(pK

0 10 20 30 40 50 60 70 80 90

103

×

Candidates / (0.5 MeV)

Data Total fit

+c

Λ Signal Background

LHCb (b)

2420 2440 2460 2480 2500 2520

[MeV]

+)

−π m(pK

0 10 20 30 40 50 60

103

×

Candidates / (0.5 MeV)

Data Total fit

+c

Ξ Signal Background

LHCb (c)

FIG. 2. Reconstructed invariant-mass distributions and signal fits of (a) mðpK⁻π^þπ⁻Þ showing a large Σ⁰csignal with a smallerΞ⁰c

signal, (b) mðpK⁻π^þÞ showing the Λ^þc signal, and (c) mðpK⁻π^þÞ showing the Ξ^þc signal. For (a) the signal shape is a Crystal Ball function[24]with a high-mass tail, and the background shape is linear. For (b) and (c) the signal shapes are double-sided Crystal Ball plus single Gaussian functions, while the background shapes are second-order polynomials. The data in (b) only use 1=10 of the available sample.

production, and the uncertainties are statistical and sys- tematic, respectively, a convention used in the rest of this paper. As discussed above, f_Ξ⁰_c=f_Λ^þ_c ¼ C · f_Ξ⁻

b=f_Λ⁰

b ¼ ð9.7  0.9  3.1Þ%, where we have added a 5% relative systematic uncertainty, explained later, to account for our assumption of HQS.

We also determineBðΞ^þc → pK⁻π^þÞ using R₃≡NðΞ^þ_cÞ

NðΛ^þcÞ¼f_Ξ^þ_c

f_Λ^þ_c ·BðΞ^þ_c → pK⁻π^þÞ BðΛ^þc → pK⁻π^þÞ

¼ ð1.753  0.003  0.107Þ%;

where BðΛ^þ_c → pK⁻π^þÞ ¼ ð6.23  0.33Þ% [7]. The cor- relation matrix for these three results is

0 BB B@

R₁ R₂ R₃ R₁ 1 0.71 0.15

R2 … 1 −0.18

R3 … … 1

1 CC CA

The derived branching fractions are

B₁≡ BðΞ⁰_c → π⁻Λ^þ_cÞ ¼ ð0.98  0.04  0.35Þ%;

B2≡ BðΞ⁰c → π⁻Λ^þcÞ ¼ ð0.41  0.01  0.21Þ%;

B₃≡ BðΞ^þ_c → pK⁻π^þÞ ¼ ð1.135  0.002  0.387Þ%:

Their correlation matrix is 0

BB B@

B1 B2 B3

B1 1 0.07 0.92

B₂ … 1 −0.02

B₃ … … 1

1 CC CA:

The weighted average value of B₁ and B₂, taking into account their correlated error, is

BðΞ⁰c → π⁻Λ^þcÞ ¼ ð0.55  0.02  0.18Þ%:

Systematic uncertainties dominate these results due to our reliance on external inputs. Our assumption of HQS to relate f_Ξ⁰_c=f_Λ^þ_c to fΞ⁻_b=f_Λ⁰

b is justified by considering the analogous ratios of production fractions between charm and beauty states in 13 TeV pp collisions, _f ^fDþs

D0þf_Dþ and

fB0s

f_B0þf_Bþ. The beauty ratio is measured using semimuonic decays into a charmed meson, determined in the kinematic range 4 < pT< 25 GeV, and is equal to 0.122  0.006 [31]. Using the total charm cross sections reported for 0 < pT< 15 GeV in Ref. [32], we find _f ^fDþs

D0þf_Dþ≈ 0.121, where the statistical uncertainty is negligible. The system- atic uncertainties in the charm-meson ratio including tracking, particle identification, luminosity, etc., mostly cancel. The uncertainties in the charm meson branching

fractions cancel in the comparison with the B meson ratio, because the same values are used in both. Thus we are left with a few percent uncertainty in the comparison of the charm and beauty meson ratios. The pTdistributions of the ratios are somewhat different; they fall linearly in the beauty case [31] and are flatter in the charm case [32].

Taking this into account, a 5% relative uncertainty due to the HQS assumption appears reasonable. Contamination of the charm baryons from b-decay sources is estimated in simulation and subtracted. The resultant systematic uncer- tainties in the ratios are small. Table I summarizes the sources of systematic uncertainty.

In conclusion, we perform the first measurement of the branching fraction of the suppressed Ξ⁰_c→ π⁻Λ^þ_c decays, givingBðΞ⁰c→ π⁻Λ^þcÞ ¼ ð0.55  0.02  0.18Þ%. We com- pare with the theoretical predictions in Fig. 3; while our measurements are somewhat larger, we are in agreement with Gronau and Rosner’s constructive interference prediction.

Our result is also consistent with the Faller and Mannel upper limit arrived at by assuming constructive interference[8]. We

TABLE I. Systematic uncertainties in the branching fraction measurements. Ghost tracks refers to uncertainties from falsely reconstructed tracks. PID refers to particle identification effi- ciencies. Intermediate decays refers to the uncertainties caused by inexact modeling of the resonant structures in the charmed- baryon decays. The b-decay sources refer to charmed baryons originating from b-baryon decays included in our primarily prompt samples. Relative R

L refers to minor differences in the accumulated luminosities of the data samples for each of the three decays. The summed uncertainties are obtained by adding the individual components in quadrature.

Estimate (%)

BðΞ⁰c→ π⁻Λ^þcÞ BðΞ^þc → pK⁻π^þÞ

Source B1 B2 B3

fΞ⁻_b=f_Λ⁰_b 32    32

f_Ξ⁰_c=f_Λ^þ_c ¼ C · fΞ⁻_b=f_Λ⁰_b 6    6

f_Ξ⁰_c=f_Ξ^þ_c ¼ 1    1 1

BðΞ^þc → pK⁻π^þÞ    49   

BðΛ^þc → pK⁻π^þÞ    5 5

Simulation statistics 4 3 2

Trigger efficiency 7 8 2

Ghost tracks 2 2 0

PID 1 1 1

Tracking efficiencies 2 2 0

Fit yields 6 6 3

Intermediate decays 2 2 2

b-decay sources 2 0 2

Lifetimes 3 3 2

RelativeR

L    1 1

Sum of external 33 49 33

Sum of intrinsic 12 13 6

Sum of all 35 51 34

disagree, however, with Cheng’s prediction of BðΞ⁰_c→ π⁻Λ^þcÞ assuming negative interference[9]. In addition, the branching fraction of the normalization channel is found to beBðΞ^þ_c → pK⁻π^þÞ ¼ ð1.135  0.002  0.387Þ%, that is somewhat larger than, but in agreement with a previous Belle measurement[29], and has a better relative precision.

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); DOE NP and NSF (USA). We acknowledge the computing resources that are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN (Italy), SURF (Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-GRID (Poland) and OSC (USA). We are indebted to the communities behind the multiple open-source software packages on which we depend. Individual groups or members have received support from AvH Foundation (Germany); EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union); A*MIDEX, 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).

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0 c

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+) Ξc

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FIG. 3. Comparison of our two measurements of BðΞ⁰c→ π⁻Λ^þcÞ, and their average, with the lower limit of Voloshin (V) [5], the upper limit of Faller and Mannel [8]

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K. Belous,⁴³I. Belyaev,³⁸G. Bencivenni,²²E. Ben-Haim,¹²A. Berezhnoy,³⁹R. Bernet,⁴⁹D. Berninghoff,¹⁶ H. C. Bernstein,⁶⁷C. Bertella,⁴⁷E. Bertholet,¹²A. Bertolin,²⁷C. Betancourt,⁴⁹F. Betti,^19,eM. O. Bettler,⁵⁴Ia. Bezshyiko,⁴⁹

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