Measurements of the branching fractions of Λ_c^+ \to p η and Λ_c^+ \to p π^0 decays at Belle
Belle Collaboration, S. X. Li, C. P. Shen, I. Adachi, J. K. Ahn, H. Aihara, D. M. Asner, T. Aushev, R. Ayad, V. Babu, S. Bahinipati, P. Behera, J. Bennett, F. Bernlochner, M. Bessner, V. Bhardwaj, B. Bhuyan, T. Bilka, J. Biswal, A. Bobrov, A. Bozek, M. Bracko, T. E. Browder, M. Campajola, L. Cao, D. ?ervenkov, M.-C. Chang, A. Chen, B. G. Cheon, K. Chilikin, H. E. Cho, K. Cho, Y. Choi, S. Choudhury, D. Cinabro, S. Cunliffe, S. Das, N. Dash, G. De Nardo, R. Dhamija, F. Di Capua, Z. Doležal, T. V. Dong, S. Eidelman, D. Epifanov, T. Ferber, D. Ferlewicz, B. G. Fulsom, R. Garg, V. Gaur, A. Garmash, A. Giri, P. Goldenzweig, B. Golob, O. Grzymkowska, K. Gudkova, C. Hadjivasiliou, O. Hartbrich, K. Hayasaka, H. Hayashii, M. T. Hedges, W.-S. Hou, C.-L. Hsu, T. Iijima, K. Inami, G. Inguglia, A. Ishikawa, R. Itoh, M. Iwasaki, Y. Iwasaki, W. W. Jacobs, E.-J. Jang, S. Jia, Y. Jin, C. W. Joo, K. K. Joo, A. B. Kaliyar, K. H. Kang, G. Karyan, Y. Kato, T. Kawasaki, H. Kichimi, B. H. Kim, C. H. Kim, D. Y. Kim, K.-H. Kim, S. H. Kim, Y.-K. Kim, K. Kinoshita, P. Kodyš, T. Konno, A. Korobov, S. Korpar, E. Kovalenko, P. Križan, R. Kroeger, P. Krokovny, T. Kuhr, M. Kumar, K. Kumara, et al. (107 additional authors not shown)
aa r X i v : . [ h e p - e x ] F e b Measurements of the branching fractions of Λ + c → pπ and Λ + c → pη decays at Belle S. X. Li, C. P. Shen, I. Adachi,
19, 15
J. K. Ahn, H. Aihara, D. M. Asner, T. Aushev, R. Ayad, V. Babu, S. Bahinipati, P. Behera, J. Bennett, F. Bernlochner, M. Bessner, V. Bhardwaj, B. Bhuyan, T. Bilka, J. Biswal, A. Bobrov,
4, 67
A. Bozek, T. E. Browder, M. Campajola,
33, 58
L. Cao, D. ˇCervenkov, M.-C. Chang, A. Chen, B. G. Cheon, K. Chilikin, H. E. Cho, K. Cho, Y. Choi, S. Choudhury, D. Cinabro, S. Cunliffe, S. Das, N. Dash, G. De Nardo,
33, 58
R. Dhamija, F. Di Capua,
33, 58
Z. Doleˇzal, T. V. Dong, S. Eidelman,
4, 67, 44
D. Epifanov,
4, 67
T. Ferber, D. Ferlewicz, B. G. Fulsom, R. Garg, V. Gaur, A. Garmash,
4, 67
A. Giri, P. Goldenzweig, B. Golob,
46, 35
O. Grzymkowska, K. Gudkova,
4, 67
C. Hadjivasiliou, O. Hartbrich, K. Hayasaka, H. Hayashii, M. T. Hedges, W.-S. Hou, C.-L. Hsu, T. Iijima,
57, 56
K. Inami, G. Inguglia, A. Ishikawa,
19, 15
R. Itoh,
19, 15
M. Iwasaki, Y. Iwasaki, W. W. Jacobs, E.-J. Jang, S. Jia, Y. Jin, C. W. Joo, K. K. Joo, A. B. Kaliyar, K. H. Kang, G. Karyan, Y. Kato, T. Kawasaki, H. Kichimi, B. H. Kim, C. H. Kim, D. Y. Kim, K.-H. Kim, S. H. Kim, Y.-K. Kim, K. Kinoshita, P. Kodyˇs, T. Konno, A. Korobov,
4, 67
S. Korpar,
50, 35
E. Kovalenko,
P. Kriˇzan,
46, 35
R. Kroeger, P. Krokovny,
T. Kuhr, M. Kumar, K. Kumara, A. Kuzmin,
4, 67
Y.-J. Kwon, K. Lalwani, J. S. Lange, I. S. Lee, S. C. Lee, C. H. Li, L. K. Li, Y. B. Li, L. Li Gioi, J. Libby, K. Lieret, D. Liventsev,
92, 19
M. Masuda,
86, 73
T. Matsuda, D. Matvienko,
4, 67, 44
M. Merola,
33, 58
F. Metzner, R. Mizuk,
44, 21
S. Mohanty,
83, 90
T. Mori, M. Nakao,
19, 15
Z. Natkaniec, A. Natochii, L. Nayak, M. Niiyama, N. K. Nisar, S. Nishida,
19, 15
H. Ono,
64, 65
Y. Onuki, P. Pakhlov,
44, 55
G. Pakhlova,
21, 44
T. Pang, S. Pardi, H. Park, S.-H. Park, S. Patra, S. Paul,
84, 51
T. K. Pedlar, R. Pestotnik, L. E. Piilonen, T. Podobnik,
46, 35
V. Popov, E. Prencipe, M. T. Prim, M. R¨ohrken, A. Rostomyan, N. Rout, G. Russo, D. Sahoo, Y. Sakai,
19, 15
S. Sandilya, A. Sangal, L. Santelj,
46, 35
T. Sanuki, V. Savinov, G. Schnell,
1, 23
J. Schueler, C. Schwanda, Y. Seino, K. Senyo, M. E. Sevior, M. Shapkin, C. Sharma, V. Shebalin, J.-G. Shiu, B. Shwartz,
4, 67
E. Solovieva, S. Staniˇc, M. Stariˇc, Z. S. Stottler, M. Sumihama, T. Sumiyoshi, W. Sutcliffe, M. Takizawa,
77, 20, 74
K. Tanida, Y. Tao, F. Tenchini, K. Trabelsi, M. Uchida, S. Uehara,
19, 15
T. Uglov,
44, 21
K. Uno, S. Uno,
19, 15
P. Urquijo, R. Van Tonder, G. Varner, A. Vossen, C. H. Wang, E. Wang, M.-Z. Wang, P. Wang, S. Watanuki, E. Won, X. Xu, B. D. Yabsley, W. Yan, S. B. Yang, H. Ye, J. Yelton, J. H. Yin, C. Z. Yuan, Y. Yusa, Z. P. Zhang, V. Zhilich,
4, 67
V. Zhukova, and V. Zhulanov
4, 67 (The Belle Collaboration) Department of Physics, University of the Basque Country UPV/EHU, 48080 Bilbao University of Bonn, 53115 Bonn Brookhaven National Laboratory, Upton, New York 11973 Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090 Faculty of Mathematics and Physics, Charles University, 121 16 Prague Chonnam National University, Gwangju 61186 University of Cincinnati, Cincinnati, Ohio 45221 Deutsches Elektronen–Synchrotron, 22607 Hamburg Duke University, Durham, North Carolina 27708 University of Florida, Gainesville, Florida 32611 Department of Physics, Fu Jen Catholic University, Taipei 24205 Key Laboratory of Nuclear Physics and Ion-beam Application (MOE)and Institute of Modern Physics, Fudan University, Shanghai 200443 Justus-Liebig-Universit¨at Gießen, 35392 Gießen Gifu University, Gifu 501-1193 SOKENDAI (The Graduate University for Advanced Studies), Hayama 240-0193 Gyeongsang National University, Jinju 52828 Department of Physics and Institute of Natural Sciences, Hanyang University, Seoul 04763 University of Hawaii, Honolulu, Hawaii 96822 High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801 J-PARC Branch, KEK Theory Center, High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801 Higher School of Economics (HSE), Moscow 101000 Forschungszentrum J¨ulich, 52425 J¨ulich IKERBASQUE, Basque Foundation for Science, 48013 Bilbao Indian Institute of Science Education and Research Mohali, SAS Nagar, 140306 Indian Institute of Technology Bhubaneswar, Satya Nagar 751007 Indian Institute of Technology Guwahati, Assam 781039 Indian Institute of Technology Hyderabad, Telangana 502285 Indian Institute of Technology Madras, Chennai 600036 Indiana University, Bloomington, Indiana 47408 Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049 Institute of High Energy Physics, Vienna 1050 Institute for High Energy Physics, Protvino 142281 INFN - Sezione di Napoli, 80126 Napoli Advanced Science Research Center, Japan Atomic Energy Agency, Naka 319-1195 J. Stefan Institute, 1000 Ljubljana Institut f¨ur Experimentelle Teilchenphysik, Karlsruher Institut f¨ur Technologie, 76131 Karlsruhe Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa 277-8583 Kitasato University, Sagamihara 252-0373 Korea Institute of Science and Technology Information, Daejeon 34141 Korea University, Seoul 02841 Kyoto Sangyo University, Kyoto 603-8555 Kyungpook National University, Daegu 41566 Universit´e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow 119991 Liaoning Normal University, Dalian 116029 Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana Ludwig Maximilians University, 80539 Munich Luther College, Decorah, Iowa 52101 Malaviya National Institute of Technology Jaipur, Jaipur 302017 University of Maribor, 2000 Maribor Max-Planck-Institut f¨ur Physik, 80805 M¨unchen School of Physics, University of Melbourne, Victoria 3010 University of Mississippi, University, Mississippi 38677 University of Miyazaki, Miyazaki 889-2192 Moscow Physical Engineering Institute, Moscow 115409 Graduate School of Science, Nagoya University, Nagoya 464-8602 Kobayashi-Maskawa Institute, Nagoya University, Nagoya 464-8602 Universit`a di Napoli Federico II, 80126 Napoli Nara Women’s University, Nara 630-8506 National Central University, Chung-li 32054 National United University, Miao Li 36003 Department of Physics, National Taiwan University, Taipei 10617 H. Niewodniczanski Institute of Nuclear Physics, Krakow 31-342 Nippon Dental University, Niigata 951-8580 Niigata University, Niigata 950-2181 University of Nova Gorica, 5000 Nova Gorica Novosibirsk State University, Novosibirsk 630090 Osaka City University, Osaka 558-8585 Pacific Northwest National Laboratory, Richland, Washington 99352 Panjab University, Chandigarh 160014 Peking University, Beijing 100871 University of Pittsburgh, Pittsburgh, Pennsylvania 15260 Research Center for Nuclear Physics, Osaka University, Osaka 567-0047 Meson Science Laboratory, Cluster for Pioneering Research, RIKEN, Saitama 351-0198 Department of Modern Physics and State Key Laboratory of Particle Detection and Electronics,University of Science and Technology of China, Hefei 230026 Seoul National University, Seoul 08826 Showa Pharmaceutical University, Tokyo 194-8543 Soochow University, Suzhou 215006 Soongsil University, Seoul 06978 Sungkyunkwan University, Suwon 16419 School of Physics, University of Sydney, New South Wales 2006 Department of Physics, Faculty of Science, University of Tabuk, Tabuk 71451 Tata Institute of Fundamental Research, Mumbai 400005 Department of Physics, Technische Universit¨at M¨unchen, 85748 Garching Department of Physics, Tohoku University, Sendai 980-8578 Earthquake Research Institute, University of Tokyo, Tokyo 113-0032 Department of Physics, University of Tokyo, Tokyo 113-0033 Tokyo Institute of Technology, Tokyo 152-8550 Tokyo Metropolitan University, Tokyo 192-0397 Utkal University, Bhubaneswar 751004 Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 Wayne State University, Detroit, Michigan 48202 Yamagata University, Yamagata 990-8560 Yonsei University, Seoul 03722
We report measurements of the branching fractions of singly Cabibbo-suppressed decays Λ + c → pη and Λ + c → pπ using the full Belle data sample corresponding to an integrated luminosity of 980.6fb − . The data were collected by the Belle detector at the KEKB e + e − asymmetric-energy collider.A clear Λ + c signal is seen in the invariant mass distribution of pη . The signal yield of the Λ + c → pη process is 7734 ± B (Λ + c → pη ) / B (Λ + c → pK − π + ) = (2 . ± . . ) ± . . )) × − , from which we infer the branching fraction B (Λ + c → pη ) = (1 . ± . . ) ± . . )) × − . In addition, no significant signal forΛ + c → pπ is found so an upper limit on the branching fraction of B (Λ + c → pπ ) < . × − at90% credibility level is set, more than three times better than the best current upper limit. I. INTRODUCTION
Weak decays of charmed baryons are useful for testingmany contradictory theoretical models and methods [1– 4]. In contrast with the decays of charmed mesons, thedecays of some charmed baryons are helicity suppressed,making the W -boson exchange allowed [5]. The under-standing of charmed baryons has progressed relativelyslowly compared to that of charmed mesons. The mainreason is that the cross section for the generation ofcharmed baryons is smaller than that of the mesons, sothat some reactions with small decay branching fractionsare difficult to observe experimentally [6–8]. Addition-ally, in the electron-positron collision environment, theabsence of a cleanly observable Λ + c ¯Λ − c resonance resultsin large uncertainties in the direct measurements of Λ + c decays. Although there have been many improved mea-surements of the properties of charmed baryons, precisionmeasurements of the decay branching fractions still re-main poor for many Cabibbo favored (CF) decay modesand even worse for some decay modes dominated byCabibbo suppression and W -boson exchange [9].In theory, the singly Cabibbo-suppressed (SCS) decaysΛ + c → pπ and Λ + c → pη proceed predominantly throughinternal W emission and W exchange. Typical decaydiagrams of two SCS decays are shown in Fig. 1. Theinternal W emission involving an s quark in Fig. 1(f)is allowed in Λ + c → pη but absent in Λ + c → pπ . Thetheoretical calculations predict the branching fraction ofΛ + c → pη at least an order of magnitude greater than thatof Λ + c → pπ and give different assumption-dependentresults for the branching fractions of these SCS de-cays [1, 3, 10–12]. In contrast with the strong decays ofheavy-flavor mesons, the W -boson exchange mechanismplays an important role in the decay of charmed baryons.Thus, measuring the branching fractions of these twoSCS decays will help elucidate the decay mechanism ofcharmed baryons.The first evidence for the decay Λ + c → pη with a sta-tistical significance of 4.2 σ and a branching fraction of B (Λ + c → pη ) = (1 . ± . × − was reported bythe BESIII Collaboration [13]. They found no significantΛ + c → pπ signal and set an upper limit on its branchingfraction B (Λ + c → pπ ) < . × − at 90% credibilitylevel (C.L.) [13].To improve the measurement precision, we measure theratio of the branching fractions of the two SCS processeswith respect to the CF Λ + c → pK − π + decay mode: B (SCS) B (CF) = N obs (SCS) ǫ MC (SCS) × B ( π /η → γγ ) × ǫ MC (CF) N obs (CF) , (1) where B , ǫ MC , and N obs are the branching fraction, sig-nal efficiency, and the fitted yield of signal events fromdata, respectively. The value of the branching fractionof the CF decay is (6 . ± . × − [9]. The valuesof B ( π → γγ ) and B ( η → γγ ) are 0 . ± . . ± . II. THE DATA SAMPLE AND THE BELLEDETECTOR
The measurements of the two SCS branching frac-tions are based on a data sample taken at or near the cdu + W ddudu }} p η / π (a) dcu + W ddudu }} p η / π (b) cdu ± W ddduu }} p η / π (c) dcu ± W uuudu }} p η / π (d) ucd ± W uuudu }} p η / π (e) cdu + W ssudu }} p η (f) FIG. 1: Feynman diagrams for the weak Cabibbo-suppresseddecays Λ + c → pπ and Λ + c → pη : (a, b) Internal W emission,(c, d, e) W exchange, and (f) Internal W emission for Λ + c → pη . Υ(1 S ), Υ(2 S ), Υ(3 S ), Υ(4 S ), and Υ(5 S ) resonances col-lected with the Belle detector at the KEKB asymmetric-energy e + e − collider [14]. The integrated luminosity ofthe data samples is 980.6 fb − , including 711 fb − onthe Υ(4 S ) resonance, 89.4 fb − off the Υ(4 S ) resonance,121.4 fb − on the Υ(5 S ) resonance, and 58.8 fb − atthe Υ(1 S, S, S ) resonances. The Belle detector is alarge-solid-angle magnetic spectrometer that consists ofa silicon vertex detector (SVD), a 50-layer central driftchamber (CDC), an array of aerogel threshold Cherenkovcounters (ACC), a barrel-like arrangement of time-of-flight scintillation counters (TOF), and an electromag-netic calorimeter comprised of CsI(Tl) crystals (ECL)located inside a superconducting solenoid coil that pro-vides a 1.5 T magnetic field. An iron flux-return locatedoutside of the coil is instrumented to detect K L mesonsand to identify muons (KLM). The detector is describedin detail elsewhere [15].Signal MC samples of e + e − → c ¯ c ; c ¯ c → Λ + c X with X denoting anything; Λ + c → pK − π + /pπ /pη are usedto optimize the selection criteria and estimate the recon-struction and selection efficiency, and are generated un-der the Υ(4 S ) resonance condition with pythia [16] and EvtGen [17] and propagated with geant3 [18] to sim-ulate the detector performance. The charged-conjugatemodes are included unless otherwise stated.Inclusive MC samples of Υ(4 S ) → B + B − /B ¯ B ,Υ(5 S ) → B ( ∗ ) s ¯ B ( ∗ ) s , e + e − → q ¯ q ( q = u, d, s, c ) at √ s = 10.58 and 10.867 GeV, and Υ(1 S, S, S ) decayscorresponding to two times the integrated luminosity ofeach data set are used to characterize the (potentiallypeaking) backgrounds [19]. III. EVENT SELECTION CRITERIA
For charged-particle tracks, the distance of closest ap-proach with respect to the interaction point (IP) alongthe z axis (parallel to the positron beam) and in thetransverse rφ plane is required to be less than 2.0 cm and0.1 cm, respectively. In addition, each track is required tohave at least one SVD hit. Particle identification (PID)is used to discriminate the type of charged hadron tracks: R ( h | h ′ ) = L ( h ) / ( L ( h ) + L ( h ′ )) is defined as the ratio ofthe likelihoods for the h and h ′ hypotheses, where L ( h )( h = π , K , or p ) is the combined likelihood derived fromthe ACC, TOF, and CDC dE/dx measurements [20]. R ( p | π ) > . R ( p | K ) > . R ( K | p ) > . R ( K | π ) > . R ( π | p ) > . R ( π | K ) > . R ( e ), a likelihood ratio for e and h identification formed from ACC, CDC, and ECLinformation [21], is required to be less than 0.9 for allcharged tracks to remove electrons. For the typical mo-mentum range of our SCS decays, the identification ef-ficiencies of p , K , and π are 81.7%, 79.6%, and 96.9%,respectively.A Λ + c candidate for the CF decay is reconstructedfrom three tracks identified as p , K , and π , subject toa common-vertex fit. The χ of the vertex fit is requiredto be less than 40 to reject background from incorrectcombinations. The scaled momentum of the Λ + c , de-fined as x p = p ∗ / p E / − M [22], is required to begreater than 0.53 for all Λ + c candidates to suppress thecombinatorial background, especially from B -meson de-cays. Here, E cm is the center-of-mass (CM) energy, while p ∗ and M are the momentum and invariant mass, respec-tively, of the Λ + c candidates in the CM frame. All of theseoptimized selection criteria are taken from Ref. [23].An ECL cluster not matching any track is identified asa photon candidate. Each photon candidate is requiredto have a ratio of energy deposited in the central 3 × × E /E > . π → γγ . For the η → γ γ decay, the γ ( γ ) energymust exceed 220 (260) MeV, 480 (340) MeV, and 260(360) MeV in the barrel, forward, and backward end-caps, respectively. Two photon candidates are combinedto form a π /η candidate and a mass-constrained fit isperformed for this candidate. The χ value of the mass-constrained fit must be less than 7.5 and 4 for π and η candidates, respectively, to suppress the background inwhich the two-photon invariant mass is far from π and η nominal masses [9]. The momentum in the CM framemust be greater than 0.69 GeV/ c and 0.82 GeV/ c for π and η candidates, respectively. All these requirementsare optimized. An SCS Λ + c candidate is reconstructedby combining a proton candidate with a π /η candidate.Again, x p for the Λ + c → pπ /pη candidates is required toexceed 0.53.The SCS signal region in data is optimized with a con-trol sample of CF decays as well as the Λ + c mass side-bands to the hidden SCS signal region by optimizing theratio S/ √ S + B , where S and B are the expected numberof signal events for SCS decays in data and the numberof background events normalized to the signal region, re-spectively. S is obtained via S = ǫ MC (Λ + c → pπ /pη ) × N obs (Λ + c → pK − π + ) ǫ MC (Λ + c → pK − π + ) × B (Λ + c → pπ /pη ) × B ( π /η → γγ ) B (Λ + c → pK − π + ) , (2)where N obs and ǫ MC are the fitted Λ + c signal yield of dataand the detection efficiency of the signal MC sample, re-spectively; B (Λ + c → pπ /pη ) are the branching fractionsof 2 . × − and 1 . × − for Λ + c → pπ and Λ + c → pη ,respectively [13]; and B (Λ + c → pK − π + ) is the branchingfraction of the CF decay [9]. IV. EFFICIENCY ESTIMATION AND FITRESULTS
With the final selection criteria applied, the invariantmass distributions of pK − π + , pη , and pπ from data areshown in Figs. 2, 3, and 4, respectively. From the studyof the topology of inclusive MC samples [19], no peakingbackgrounds contribute to these mass distributions in theΛ + c signal region.For the CF mode, we fit the invariant mass distributionof pK − π + displayed in Fig. 2 from 2.15 to 2.42 GeV/ c using the binned maximum likelihood fit with a bin widthof 3 MeV/ c . A double-Gaussian function with the com-mon mean value is used to model the signal events and asecond-order polynomial is used to model the backgroundevents. The parameters of the signal and backgroundshapes are free in the fit. The reduced χ value of thefit is χ / ndf = 87 /
82 = 1 .
06 and the fitted signal yieldis 1476200 ± c . Inaddition, the sideband regions are defined to be (2.262,2.274) GeV/ c and (2.298, 2.310) GeV/ c .The Dalitz [24] distribution of M ( K − π + ) versus M ( pK − ) in the signal region from data is shown inFig. 5. We divide this into 120 ×
120 pixels, with size ] ) [GeV/c + π - M(pK E v en t s / M e V / c × FIG. 2: Fit to the invariant mass distribution of pK − π + fromdata. Black dots with error bars represent the data; the pinkdashed line, the blue dash-dotted line, the green dashed line,and the red solid line represent the background contribution,the core Gaussian, tail Gaussian, and the total fit, respec-tively. ] ) [GeV/c η M(p E v en t s / M e V / c DataFitSigBkg
FIG. 3: Fit to the invariant mass distribution of pη from data.Black dots with error bars represent the data; the magentadash-dotted line, the blue dashed line, and the red solid linerepresent the background component, the signal, and the totalfit, respectively. ] ) [GeV/c π M(p E v en t s / M e V / c DataFitSigBkg
FIG. 4: Fit to the invariant mass distribution of pπ . Blackdots with error bars represent the data; the magenta dash-dotted line, the blue dashed line, and the red solid line repre-sent the background component, the signal, and the total fit,respectively. /c for M ( pK − ) and 0.016 GeV /c for M ( K − π + ). The number of background events has beensubtracted using the normalized sidebands. An MC sam- ) /c (GeV + π - K2 M ) / c ( G e V - p K M FIG. 5: Dalitz plot of the selected Λ + c → pK − π + candidates. ple mixing four subchannels of CF decay weighted withthe corresponding branching fractions taken from Ref. [9]is used to assess the selection efficiency of the CF mode.The total number of reconstructed MC signal events isnormalized to that of signal candidates in data. We cal-culate the overall efficiency using the efficiency of eachpixel. The formula is ǫ = Σ i s i / Σ j ( s j /ǫ j ), where Σ i s i isthe number of reconstructed MC signal events, s j and ǫ j are the number of signal events from data and the effi-ciency from the MC sample for each pixel, respectively.The efficiency of one pixel is obtained by dividing thenumber of events remaining in the signal MC sample bythe number of generated events. The weighted efficiencyfor each bin is exhibited in Fig. 6 and the corrected effi-ciency for data is (14 . ± . ) /c (GeV + π - K2 M ) / c ( G e V - p K M E ff i c i en cy FIG. 6: Dalitz plot of efficiency distribution for Λ + c → pK − π + decay. An obvious Λ + c signal peaking in the signal region ofthe M( pη ) spectrum is observed. We use the binned max-imum likelihood method to fit the invariant mass distri-bution of pη from 2.15 to 2.42 GeV/ c with 3 MeV/ c binwidth. A combined Gaussian and Crystal Ball (CB) [25]function with a common mean value models the signal,and a second-order polynomial models the background.The parameters of the signal and background line shapesare free in the fit. Figure 3 exhibits the distribution ofinvariant mass of pη and corresponding fit result. Thereduced χ of the fit is χ / ndf = 102 /
83 = 1 .
23 and thesignal yield is 7734 ± + c → pπ . We fit the M ( pπ ) with the binnedmaximum likelihood method; the fit result is shown inFig. 4. The signal is modeled by a combined Gaussianand CB function with the a common mean convolvedwith a Gaussian function; the background is describedby a second-order polynomial. The parameters of thesignal are fixed to MC-derived values and the convolvingGaussian with width 2.1 MeV accounts for the differencein widths between data and MC for the Λ + c → pη signal.The signal yield and the parameters of the backgroundpolynomial are free in the fit. The fitting range is from2.15 to 2.42 GeV/ c with a bin width of 3 MeV/ c . Thesignal yield is 11 ± + c → pπ . The likelihood function is integratedfrom zero to the value that gives 90% of the total area.Before integrating, we include the systematic uncertainty( σ sys ) described below by convolving the likelihood dis-tribution with a Gaussian whose width is equal to σ sys .An upper limit on the branching fraction of 9 . × − at 90% C.L. is set. The likelihood distribution as a func-tion of the branching fraction, with the systematic un-certainty included, is displayed in Fig. 7. ) π p → +c Λ B( -3 × L i k e li hood FIG. 7: The likelihood distribution as a function of thebranching fraction for Λ + c → pπ with the systematic un-certainty included. The blue arrow refers to the 90% C.L.upper limit on the branching fraction. To estimate the efficiencies of the two SCS decays, wetake the ratio of the number of fitted signal events in theinvariant mass distribution of pπ /pη to that of generatedevents from signal MC samples as the efficiency. We find(8 . ± . . ± . + c → pη andΛ + c → pπ , respectively. The uncertainties are statisticalonly. V. SYSTEMATIC UNCERTAINTIES
Since the branching fraction is obtained from the ratioof the corresponding quantities in Eq. 1, some system-atic uncertainties for Λ + c → pπ /pη cancel. The sourcesof systematic uncertainties include the fits of CF andSCS decays, PID, tracking efficiency, photon efficiency, χ of mass-constrained fit and momenta of π /η in theCM frame requirements, the uncertainties of branchingfractions of CF and π /η → γγ decays, and the statisticsof the signal MC samples.To estimate the uncertainties from the fits of CF andSCS decays, we modify the signal and background func-tions, bin width, and the fit range and refit. To evalu-ate the uncertainty from the signal function, the signalshape for Λ + c → pK − π + / pη is fixed to that from the fitto the MC sample, while that for Λ + c → pπ is changedfrom a Gaussian and CB combined function to a dou-ble CB function. The uncertainty from the backgroundline shape is assessed by using a first-order polynomial.Furthermore, we change the bin width to 2 MeV/ c or4 MeV/ c , and adjust the fit range of invariant massspectrum to estimate the uncertainties from binning andfit range. The difference of branching fractions betweenthe refitted and nominal conditions is taken as the un-certainty, which is 3.86% for Λ + c → pπ and 2.85% forΛ + c → pη , respectively.The systematic uncertainties from PID and trackingefficiency of the proton cancel in the branching-fractionratio. Systematic uncertainties of 1.6% and 1.2% areassigned for the K and π identification efficiencies, re-spectively. The total systematic uncertainty from PIDis 2.0%, the sum in quadrature of the individual uncer-tainties for K and π . From the study of the mid-to-high-momentum track reconstruction efficiency in D ∗ → πD decay, the uncertainty of the efficiency for each chargedtrack is 0.35%, resulting in a total uncertainty of 0.7%from tracking efficiency. We assign a 2% systematic un-certainty due to the photon efficiency per photon; thetotal systematic uncertainty from photon reconstructionis thus 4%.We consider the yields of S and B by changing the sig-nal regions in the invariant mass distributions of pπ /pη and using the determined branching fractions of Λ + c → pπ /pη to re-optimize the event selection criteria. Wetake the differences of branching fractions after applyingthe new selection criteria as the systematic uncertaintiesfrom the requirements of χ of mass-constrained fit andmomenta of π /η in the CM frame. The uncertaintiesare 1.14% and 0.63% for Λ + c → pπ and Λ + c → pη , re-spectively.The systematic uncertainties from the branching frac-tions of CF and π /η → γγ are 5.1%, 0.034%, and0.5% [9], respectively.The systematic uncertainty from the size of the signalMC sample is estimated to be 0.34% and 0.35% for Λ + c → pπ and Λ + c → pη decays, respectively.The systematic uncertainties are summarized in TableI and give in total 7.9% and 7.4% for Λ + c → pπ andΛ + c → pη , respectively, which are obtained by assumingall uncertainties are independent and therefore added inquadrature. VI. CONCLUSION
We observe the decay Λ + c → pη . A significant Λ + c signal is observed in the invariant mass distribution of TABLE I: The sources of the relative systematic uncertainties(%) on the branching fractions of Λ + c → pπ and Λ + c → pη decays. Source Λ + c → pπ Λ + c → pη Fit of signal decay 3.9 2.8PID 2.0 2.0Tracking efficiency 0.7 0.7Photon efficiency 4.0 4.0 χ and momenta requirements 1.1 0.6 B (Λ + c → pK − π + ) 5.1 5.1 B ( π /η → γγ ) 0.0 0.5Statistics of signal MC samples 0.3 0.4Total 7.9 7.4 pη from data. The measured ratio of B (Λ + c → pη ) B (Λ + c → pK − π + ) is(2 . ± . . ) ± . . )) × − . With the in-dependently measured value of B (Λ + c → pK − π + ) [9],we extract a branching fraction of B (Λ + c → pη ) =(1 . ± . . ) ± . . )) × − , which is con-sistent with both the latest published measurement of(1 . ± . × − [13], but with much improved preci-sion, and theoretical predictions within 1.3 σ [11, 12].We see no obvious signal excess in the distributionof M ( pπ ) and so set an upper limit on the ratio ofthe branching fractions B (Λ + c → pπ ) B (Λ + c → pK − π + ) at 90% C.L. of1 . × − . From this, we extract an upper limit onthe branching fraction of B (Λ + c → pπ ) < . × − at 90% C.L., more than three times more stringent thanthe best current upper limit of 2 . × − . The measured B (Λ + c → pη ) is at least an order of magnitude larger than B (Λ + c → pπ ), which validates the internal W -emissionmechanism involving an s quark in Λ + c → pη . VII. ACKNOWLEDGMENTS
We thank the KEKB group for the excellent operationof the accelerator; the KEK cryogenics group for the ef-ficient operation of the solenoid; and the KEK computergroup, and the Pacific Northwest National Laboratory(PNNL) Environmental Molecular Sciences Laboratory(EMSL) computing group for strong computing support;and the National Institute of Informatics, and ScienceInformation NETwork 5 (SINET5) for valuable networksupport. We acknowledge support from the Ministryof Education, Culture, Sports, Science, and Technology(MEXT) of Japan, the Japan Society for the Promotionof Science (JSPS), and the Tau-Lepton Physics ResearchCenter of Nagoya University; the Australian ResearchCouncil including grants DP180102629, DP170102389,DP170102204, DP150103061, FT130100303; AustrianScience Fund (FWF); the National Natural ScienceFoundation of China under Contracts No. 11435013,No. 11475187, No. 11521505, No. 11575017,No. 11675166, No. 11705209; No. 11761141009;No. 11975076; No. 12042509; Key Research Program ofFrontier Sciences, Chinese Academy of Sciences (CAS),Grant No. QYZDJ-SSW-SLH011; the CAS Center forExcellence in Particle Physics (CCEPP); the ShanghaiPujiang Program under Grant No. 18PJ1401000; theMinistry of Education, Youth and Sports of the CzechRepublic under Contract No. LTT17020; the Carl ZeissFoundation, the Deutsche Forschungsgemeinschaft, theExcellence Cluster Universe, and the VolkswagenS-tiftung; the Department of Science and Technologyof India; the Istituto Nazionale di Fisica Nucleare ofItaly; National Research Foundation (NRF) of KoreaGrant Nos. 2016R1D1A1B01010135, 2016R1D1A1B-02012900, 2018R1A2B3003643, 2018R1A6A1A06024970,2018R1D1A1B07047294, 2019K1A3A7A09033840,2019R1I1A3A01058933; Radiation Science Research In-stitute, Foreign Large-size Research Facility Application Supporting project, the Global Science ExperimentalData Hub Center of the Korea Institute of Science andTechnology Information and KREONET/GLORIAD;the Polish Ministry of Science and Higher Education andthe National Science Center; the Ministry of Science andHigher Education of the Russian Federation, Agreement14.W03.31.0026; University of Tabuk research grantsS-1440-0321, S-0256-1438, and S-0280-1439 (SaudiArabia); the Slovenian Research Agency; Ikerbasque,Basque Foundation for Science, Spain; the Swiss Na-tional Science Foundation; the Ministry of Educationand the Ministry of Science and Technology of Taiwan;and the United States Department of Energy and theNational Science Foundation. [1] K. K. Sharma and R. C. Verma, Phys. Rev. D , 7067(1997).[2] M. A. Ivanov, J. G. Korner, V. E. Lyubovitskij, andA. G. Rusetsky, Phys. Rev. D , 5632 (1998).[3] T. Uppal, R. C. Verma, and M. P. Khanna, Phys. Rev.D , 3417 (1994).[4] P. Zenczykowski, Phys. Rev. D , 402 (1994).[5] Y. Kohara, Nuovo Cim. A , 67 (1998).[6] M. Niiyama et al. (Belle Collaboration), Phys. Rev. D , 072005 (2018).[7] B. Andersson, G. Gustafson, G. Ingelman, andT. Sj¨ostrand, Phys. Rep. , 31 (1983).[8] B. Andersson, G. Gustafson, and T. Sj¨ostrand, Phys. Scr. , 574 (1985).[9] P. A. Zyla et al. (Particle Data Group), Prog. Theor.Exp. Phys. , 083C01 (2020).[10] C. D. L¨u, W. Wang, and F. S. Yu, Phys. Rev. D ,056008 (2016).[11] H. Y. Cheng, X. W. Kang, and F. R. Xu, Phys. Rev. D , 074028 (2018).[12] J. Q. Zou, F. R. Xu, G. B. Meng, and H. Y. Cheng, Phys.Rev. D , 014011 (2020).[13] M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D , 111102 (2017).[14] S. Kurokawa and E. Kikutani, Nucl. Instrum. MethodsPhys. Res., Sect. A , 1 (2003), and other papers in- cluded in this volume; T. Abe et al. , Prog. Theor. Exp.Phys. , 03A001 (2013), and references therein.[15] A. Abashian et al . (Belle Collaboration), Nucl. Instrum.Methods Phys. Res., Sect. A , 117 (2002); also, seedetector section in J. Brodzicka et al. , Prog. Theor. Exp.Phys. , 04D001 (2012).[16] T. Sjostrand, S. Mrenna, and P. Skands, Comput. Phys.Commun. , 852 (2008).[17] D. J. Lange, Nucl. Instrum. Methods Phys. Res., Sect. A , 152 (2001).[18] R. Brun et al. , GEANT 3: user’s guide Geant 3.10, Geant3.11, CERN Report No. DD/EE/84-1, 1984.[19] X. Y. Zhou, S. X. Du, G. Li, and C. P. Shen, Comput.Phys. Commun. , 107540 (2021).[20] E. Nakano, Nucl. Instrum. Methods Phys. Res., Sect. A , 402 (2002).[21] K. Hanagaki, H. Kakuno, H. Ikeda, T. Iijima, andT. Tsukamoto, Nucl. Instrum. Methods Phys. Res., Sect.A , 490 (2002).[22] We used units in which the speed of light is c = 1.[23] S. B. Yang et al. (Belle Collaboration), Phys. Rev. Lett. , 011801 (2016).[24] R. H. Dalitz, Phil. Mag. , 1068 (1953).[25] M. Oreglia, A Study of the Reactions ψ ′ → γγψγγψ