RRecent charm results from Belle
Longke Li β On behalf of the Belle Collaboration
University of Cincinnati,Cincinnati, Ohio 45221, U.S.
E-mail: [email protected]
Recent charm results from Belle experiment are presented in this proceedings, including (1)measurement of mixing parameter π¦ πΆπ = ( . Β± . Β± . + . β . ) % in πΆπ -odd decay for theο¬rst time, (2) the ο¬rst Dalitz-plot analysis of π· β πΎ β π + π , (3) measurement of branchingfractions of Ξ + π β π Ξ π + and π Ξ£ π + and intermediate processes Ξ + π β [ Ξ ( ) β π Ξ ] π + and Ξ + π β π Ξ£ ( ) + relative to Ξ + π β ππΎ β π + : 0 . Β± . Β± . . Β± . Β± . ( . Β± . Β± . ) Γ β , and 0 . Β± . Β± . Ξ π ( ) + which is consistent with the HQSSprediction for π½ π ( π π ) = / + ( ) . β Speaker Β© Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/ a r X i v : . [ h e p - e x ] F e b ecent charm results from Belle Longke Li
1. Introduction to Belle at KEKB
KEKB [1] is an asymmetric-energy π + π β collider operating at and near Ξ₯ ( π ) mass peak. Asthe only detector installed in KEKB, Belle detector has a good performance on momentum andvertex resolution, πΎ / π separation etc. A detailed description of the Belle detector can be foundelsewhere [2]. It has been ten years since the ο¬nal full data set ( βΌ β ) was accumulated, however,fruitful results on physics are lasting to be produced. Here we select some recent charm resultsfrom Belle to present in this proceedings.
2. Charm-mixing parameter π¦ πΆπ in π· β πΎ π π The mixing parameter π¦ πΆ π is measured in π· decays to the πΆπ -odd ο¬nal state πΎ π π for theο¬rst time [3]. Considering mixing parameters | π₯ | and | π¦ | (cid:28)
1, the decay-time dependence of π· to a πΆπ eigenstate is approximately exponential, π Ξ / ππ‘ β π β Ξ ( + π π π¦ ππ ) π‘ where π π = + β
1) for πΆπ -even (-odd) decays. Along with the decay rate in ο¬avored eigenstate decays π Ξ / ππ‘ β π β Ξ π‘ , the π¦ πΆ π is determined by the decay proper-time value with the formula π¦ πΆ π = β π ( π· β πΎ β π + ) π ( π· β πΎ π π ) , where π· β πΎ β π + is the chosen normalization mode with ο¬avor eigenstate ο¬nal state.Based on the full Belle data sample of 976 fb β , we obtain 91 thousands of π· β πΎ π π and 1.4millions of reference mode π· β πΎ β π + in π β Ξ π signal region, where π is the invariant massof reconstructed π· and Ξ π is the mass diο¬erence of reconstructed π· β+ and π· . Using unbinnedmaximum-likelihood ο¬ts for lifetime on these two samples with high purities, the proper decay-timeof π· is determined as π πΎ π π = ( . Β± . ) fs and π πΎ π = ( . Β± . ) fs, as shown in Fig. 1.Thus, we calculate π¦ πΆ π = ( . Β± . Β± . + . β . ) %, where the ο¬rst uncertainty is statistical, thesecond is systematic due to event selection and background, and the last is due to possible presenceof CP-even decays in the data sample. This π¦ πΆ π result is consistent with the world average value. Inthe future, comparing more precise measurements of π¦ πΆ π with that of π¦ may test the SM preciselyor reveal new physics eο¬ects in the charm system.
3. Dalitz-plot analysis of π· β πΎ β π + π decays The understanding of hadronic charmed-meson decay is theoretically challenging due to thesigniο¬cant non-perturbative contributions, and input from experimental measurements thus playsan important role. A Dalitz-plot analysis of π· β πΎ β π + π is performed for the ο¬rst time atBelle based on 953 fb β of data [4]. Using a π - π two-dimensional ο¬t where π is the invariant-mass of reconstructed π· meson, π = π ( πΎ + π β π ) , and π is the released energy of π· β+ decay, π = π ( πΎ β π + ππ π ) β π β π π π , a signal yield of 105 197 Β±
990 is obtained in the signal regionof 1 .
85 GeV / π < π < .
88 GeV / π and 5 .
35 MeV / π < π < .
35 MeV / π with a high purity ( . Β± . ) %. The Dalitz plot is well described by a combination of the six resonant decaychannels Β― πΎ β ( ) π , πΎ β π ( ) + , πΎ β π ( ) + , Β― πΎ β ( ) π , πΎ β ( ) β π + and πΎ β ( ) β π + ,together with πΎ π and πΎπ S-wave components, as shown in Fig. 2. The dominant contributionsto the decay amplitude arise from Β― πΎ β ( ) , π ( ) + and the πΎ π
S-wave component. The πΎπ S-wave component, including πΎ β ( ) β , is observed with a statistical signiο¬cance of more than2 ecent charm results from Belle Longke Li (a) (b)
Figure 1:
The ο¬t of π· proper lifetime: (a) π· β πΎ π π and (b) π· β πΎ β π + . The dashed red curves are thesignal contribution, and the shaded surfaces beneath are the background estimated from π β Ξ π sidebands. π , and the decays πΎ β ( ) β β πΎ β π and πΎ β ( ) β β πΎ β π are observed for the ο¬rst time andhave statistical signiο¬cances of 16 π and 17 π , respectively.We extract the signal yield from the π· invariant mass distribution in 1 .
78 GeV / π < π < .
94 GeV / π and | π β . | < . π , and obtain for the ο¬rst time the branching ratio B ( π· β πΎ β π + π )B ( π· β πΎ β π + ) = . Β± . ( stat ) Β± . ( syst ) Β± . (B PDG ) , which corresponds to B ( π· β πΎ β π + π ) = ( . Β± . ( stat ) Β± . ( syst ) Β± . (B PDG )) %. Then utilizing the world averagebranching fractions of intermediate resonant decays, the relative branching ratio B ( πΎ β ( ) β β πΎ β π )B ( πΎ β ( ) β β πΎ β π ) is determined to be 0 . Β± . ( stat ) + . β . ( syst ) Β± . (B PDG ) . This is not consistent with thetheoretical prediction under an assumption of a pure 1 π· state [5]. We also determine the productof branching fraction B ( π· β [ πΎ β ( ) β β πΎ β π ] π + ) = ( . + . β . ) Γ β . For π ( ) + , weconο¬rm the ππ (cid:48) contribution in the three-channel FlattΓ© model with a statistical signiο¬cance of10 . π . We have also determined the branching fraction B ( π· β Β― πΎ β ( ) π ) = ( . + . β . ) %,which is consistent with, and more precise than, the current world average of ( . Β± . ) %. Itdeviates from the various theoretical predictions of (0.51-0.92)% [6] with a signiο¬cance of morethan 3 π .
4. Measurement of Branching Fractions of Ξ + π β π Ξ π + , π Ξ£ π + , Ξ ( ) π + , and π Ξ£ ( ) + The branching fractions of weakly decaying charmed baryons provide a way to study bothstrong and weak interactions. The Ξ + π β π Ξ π + decay mode is especially interesting since it hasbeen suggested that it is an ideal decay mode to study the Ξ ( ) and π ( ) because, for anycombination of two particles in the ο¬nal state, the isospin is ο¬xed. Based on a 980 fb β data sample,the branching fractions of Ξ + π β π Ξ π + , π Ξ£ π + , Ξ ( ) π + , and π Ξ£ ( ) + are measured [7]. The π ( π Ξ π + ) spectrum is shown in Fig. 3 (a). The Ξ + π β π Ξ£ π + is observed indirectly as a feed-down component and it has eο¬ciency-corrected yield π πππ = ( . Β± . ) Γ . Considering3 ecent charm results from Belle Longke Li ) /c (GeV Ο K2 m ) / c ( G e V Ξ· Ο m (a) ) /c (GeV Ο K2 m / c E ve n t s / . G e V Γ Exp. dataTotal fitCombinatorial *(892)K + (980) a + (1320) a *(1410)K K*(1680) *(1980) K S wave Ο K S wave Ξ· K (b) ) /c (GeV Ξ·Ο m / c E ve n t s / . G e V Γ (c) ) /c (GeV Ξ· K2 m / c E ve n t s / . G e V Γ (d) Figure 2:
The Dalitz plot of π· β πΎ β π + π in (a) π - π signal region 1 .
85 GeV / π < π < .
88 GeV / π and5 .
35 MeV / π < π < .
35 MeV / π , and projections on (b) π πΎ π , (c) π π π and (d) π πΎ π . In projections theο¬tted contributions of individual components are shown, along with contribution of combinatorial background(grey-ο¬lled) from sideband region. Ξ + π β π Ξ π + and Ξ + π β ππΎ β π + have suο¬ciently large statistic, the yields in individual bins of Dalitzplots are determined: π πππ ( π Ξ π + ) = ( . Β± . ) Γ and π πππ ( ππΎ β π + ) = ( . Β± . ) Γ .Finally, the branching ratios of Ξ + π β π Ξ π + and Ξ + π β π Ξ£ π + relative to Ξ + π β ππΎ β π + are0 . Β± . Β± .
014 and 0 . Β± . Β± . Ξ + π β π Ξ π + shown in Fig. 3 (b), bands corresponding to Ξ + π β Ξ ( ) π + / π Ξ£ ( ) + resonant sub-channels are seen clearly, along with Ξ + π β Ξ π ( ) + . Forevery 2 MeV/ π bin of π ( π Ξ ) and π ( Ξ π + ) distributions, the Ξ + π yield is obtained by ο¬tting π ( π Ξ π + ) . Then, a relativistic Breit-Wigner with momentum-dependent width is used to describethe S-wave Ξ ( ) and the P-wave Ξ£ ( ) , as shown in Fig. 3 (c, d). Then, we determine therelative branching ratio B ( Ξ + π β[ Ξ ( )β π Ξ ] π + )B ( Ξ + π β ππΎ β π + ) = ( . Β± . Β± . ) % and B ( Ξ + π β π Ξ£ ( ) + )B ( Ξ + π β ππΎ β π + ) = . Β± . Β± . B ( Ξ + π β ππΎ β π + ) , we have B ( Ξ + π β[ Ξ ( ) β π Ξ ] π + ) = ( . Β± . Β± . Β± . ) Γ β and B ( Ξ + π β π Ξ£ ( ) + ) = ( . Β± . Β± . Β± . ) %, where the ο¬rst two uncertainties are statistical and systematic uncertainties,and the third uncertainty is from B ( Ξ + π β ππΎ β π + ) .4 ecent charm results from Belle Longke Li (a) (b)(c) (d)
Figure 3:
Top ο¬gures are (a) the invariant mass of π Ξ π + and (b) its Dalitz plot in signal region. Bottomο¬gures are ο¬ts to the Ξ + π yield in the (c) π ( π Ξ ) and (d) π ( Ξ π + ) spectra, where the curves indicate thetotal ο¬t result (solid red), the signal modeled with a relativistic Breit-Wigner function (dashed blue), and thebackground (long-dashed green).
5. First determination of the Spin and Parity of Ξ π ( ) + The unclear theoretical situation motivates an experimental determination of spin and parity ofa charmed-strange baryon Ξ π ( ) , which provides important information to test predictions andhelp decipher its nature. Using a 980 fb β data sample, the spin and parity of a charmed-strangebaryon Ξ π ( ) + is measured [8] by (1) studies of the helicity angle distributions, π β of Ξ π ( ) and π π of Ξ π ( ) in Ξ π ( ) + β Ξ π ( ) π + β Ξ + π π β π + , and (2) a measurement of the Ξ π ( ) + decay branching ratio π = B ( Ξ π ( ) + β Ξ π ( ) π + )/B ( Ξ π ( )+ β Ξ (cid:48) π π + ) .The angular distribution are obtained by dividing the data into 10 equal bins for cos π β andcos π π , each within intervals of 0.2. The yield of Ξ π ( ) + β Ξ π ( ) π + for each bin is obtainedby ο¬tting the invariant-mass distribution of π ( Ξ + π π β π + ) for the Ξ π ( ) signal region (within5 MeV/ π of Ξ π ( ) nominal mass) and sidebands (interval from 15 to 25 MeV/ π away from Ξ π ( ) nominal mass). The background-subtracted and eο¬ciency-corrected yield distributionin Fig. 4 is ο¬tted with expected decay-angle distributions π π½ for diο¬erent spin hypotheses. Thebest ο¬t is for π½ = /
2, while others are excluded with small signiο¬cance, which shows inconclusiveresult. For helicity angle π π , with an assumption that the lowest partial wave dominates, the expectedangular correlation π ( π π ) is used to describe the distribution. Finally the π½ π = / + hypothesis is5 ecent charm results from Belle Longke Libetter than 3 / β or 5 / + ones at the level of 5 . π or 4 . π . Figure 4:
The yields on the cosine of helicity angle of Ξ π ( ) (left, π½ = / π½ = / π½ = / Ξ π ( ) (right, π½ π = / + for solidblack; π½ = / β for dashed red; π½ = / + for dotted blue) in Ξ π ( ) + β Ξ π ( ) π + decay. The parity of Ξ π ( ) + is established [8] from the ratio between B ( Ξ π ( ) + β Ξ π ( ) π + ) and B ( Ξ π ( ) + β Ξ (cid:48) π π + ) by π = π β π β π ( Ξ + π )/ π + / π (cid:48) (cid:205) π π (cid:48) π π ( Ξ π ) π / π π , where Ξ π uses two modes, Ξ β π + and Ξ© β πΎ + . The yields π β , (cid:48) are obtained by ο¬tting the invariant-mass distributions in Fig. 5. Finallywe have π = . Β± . ( π π‘ππ‘ ) + . β . ( π π¦π π‘ ) Β± . ( πΌ π ) , where the last uncertainty is due to possibleisospin-symmetry-breaking eο¬ects (15%). Heavy-quark spin symmetry (HQSS) predicts π = . / + state with the spin of the light-quark degrees of freedom π π = π π =
0. We note that HQSS predictions could be largerthan the quoted value by a factor of βΌ / π π ) [10], so our result isconsistent with the HQSS prediction for π½ π ( π π ) = / + ( ) . Figure 5: Ξ + π π β π + invariant-mass distribution for Ξ π ( ) + β Ξ π ( ) π + β Ξ + π π β π + , and Ξ (cid:48) π π + invariant-mass distribution for Ξ π ( ) + β Ξ (cid:48) π π + β Ξ π πΎπ + . The ο¬t result (solid blue curve) is presentedalong with the background (dashed blue curve)
6. Summary
Belle experiment has achieved the fruitful productions of ο¬avor physics to date. Some selectedrecent charm results are presented, including charm mixing parameter π¦ πΆ π in πΆπ -odd decay6 ecent charm results from Belle Longke Li π· β πΎ π π , hadronic decays π· β πΎ β π + π and Ξ + π β π Ξ π + / π Ξ£ π + , ο¬rst determination of thespin and parity of Ξ π ( ) + . More charming charm results from Belle will come out in nearfuture. As a summary, I would like to say, "Belle is not only keeping alive but still keepingenergetic, together with its upgraded experiment Belle II who is under a rapid growth." References [1] S. Kurokawa and E. Kikutani, Nucl. Instrum. Methods Phys. Res. Sect. A , 1 (2003), andother papers included in this Volume.[2] A. Abashian et al. (Belle Collaboration), Nucl. Instrum. Methods Phys. Res. Sect. A , 117(2002).[3] M. Nayak et al. (Belle Collaboration), Phys. Rev. D , 071102(R) (2020).[4] Y. Q. Chen et al. (Belle Collaboration), Phys. Rev. D , 012002 (2020).[5] T. Barnes, N. Black, and P. R. Page, Phys. Rev. D , 054014 (2003); C. Q. Pang, J. Z. Wang,X. Liu, et al. Eur. Phys. J. C (2017) 77: 861.[6] H. Y. Cheng and C. W. Chiang, Phys. Rev. D , 074021 (2010); H. N. Li, C. D. LΓΌ, and F. S.Yu, Phys. Rev. D , 036012 (2012); Q. Qin, H. N. Li, C. D. LΓΌ, and F. S. Yu, Phys. Rev. D , 054006 (2014).[7] J. Y. Lee et al. (Belle Collaboration), arXiv:2008.11575.[8] T. J. Moon et al. (Belle Collaboration), arXiv:2007.14700[9] Hai-Yang Cheng and Chun-Khiang Chua, Phys. Rev. D , 014006 (2007).[10] Adam F. Falk and Thomas Mehen, Phys. Rev. D53