Hadronic Charmed Decays of Charmed Baryons HaiYang Cheng

Hadronic. Charmed Decays of Charmed Baryons Hai-Yang Cheng (鄭海揚) Academia Sinica, Taipei l Hadronic decays l Lifetimes HIPEA, March 19, 2018 Beijing, China

Hadronic weak decays of singly charmed baryons 2

Hadronic weak decays Progress is relatively slow, both theoretically & experimentally Complications from theory: u Baryons are made of three quarks u Factorization approximation generally doesn’t work W-exchange is not subject to helicity & color suppression u Current algebra is not supposed to work well as the outgoing meson is far from being “soft”. Also this soft-meson technique is not applicable to vector meson production u Perturbative approaches (p. QCD, QCDF, SCET) do not make much sense as 1/mc expansion is not under control 3

Hadronic weak decays n Diagrammatic scheme (Chau, HYC, Tseng; Kohara) A least-model-dependent approach n Two distinct internal W emission diagrams, three different W exchange diagrams n Need information of decay asymmetry to extract s-wave and p-wave amplitudes separately SU(3) approach Savage, Springer (’ 90); Sharma, Verma (’ 97); Lu, Wang, Yu (’ 16); Geng, Hsiao, Liu, Tsai (’ 17) 4

n Dynamical model calculation 1. pole model: Consider low-lying pole contributions: s-wave is governed by ½- resonances p-wave is dominated by ½+ ground-state baryons 2. Relativistic QM: Korner, Kramer, Ivanov, … overlap integrals 5

Nearly all BFs of c are measured relative to p. K- + n Based on ARGUS & CLEO data, PDG made a modeldependent determination of the absolute branching fraction BF( c+ p. K- +) = (5. 0 1. 3)% n Belle (’ 14) reported a value of (6. 84 0. 24+0. 21 -0. 27)% from the reconstruction of D*p recoiling against the c production in e+e- annihilation. This measurement is model independent. n A direct measurement by BESIII (’ 15): (5. 84 0. 27 0. 23)% New world average: BF( c+ p. K- +) = (6. 35 0. 33)% 6

Absolute BFs measured by BESIII (’ 15) for the first time (2014) PDG(’ 16) 1. 58 0. 08 6. 35 0. 33 1. 99 0. 13 1. 66 0. 12 4. 9 0. 4 1. 30 0. 07 7. 1 0. 4 3. 7 0. 4 1. 29 0. 07 1. 24 0. 10 4. 57 0. 29 1. 74 0. 21 PDG values for BFs before 2016 version become obsolete 7

BFs of Cabibbo-allowed decays RQM Pole C. A. 0. 59 0. 09 n Non-factorizable contributions play an essential role as c+ 0 +, + 0, 0 K+ proceed only through W-exchange or internal W-emission n All the model calculations were done before millennium n Except current algebra, predictions are generally below experiment 8

Decay asymmetry for Cabibbo-allowed decays RQM Pole C. A. n Pole model & RQM predict positive in c+ + 0, 0 +. However, CLEO (’ 95) measured = -0. 45 0. 31 0. 06 for + 0. n Current algebra leads to negative , -0. 49 by HYC et al. , -0. 76 by Zenczykowski (hep-ph/9309265), -0. 47 by Datta (hep-ph/9504428), 0. 31 by Sharma et al. n S-wave of c+ 0 K+ is very small = 0 9

n Presumably the pole model is more general than current algebra: (i) It reduces to C. A. in soft pseudoscalar limit (ii) It is applicable to vector meson production n To compute nonfactorizable S-wave in the pole model requires information of odd-party baryon resonances, but not so in C. A. n Consider c+ + 0 as an example, Apole = -2. 20, while ACA = 7. 66. The on-shell correction (A- ACA) in A = ACA + (A - ACA) is probably overestimated in current pole model calculations which need to be improved. 10

Decay modes that proceed only through factorizable diagrams External W-emission : c 0→ - + Internal W-emission : c 0→ *0 K 0 , c+ p Recall that large-Nc approach works well in describing hadronic D decays. Is this also applicable to charmed baryon sector ? Br( c+ p ) = (1. 04 0. 21) 10 -3 |a 2| = 0. 45 0. 03 Since a 2 = c 2 + c 1/Nceff & c 2(mc) -0. 636 Nceff 7 1/Nc expansion is also valid in charmed baryon decays (but not true in bottom sector!) 11

Singly Cabibbo-suppressed decays of c+: K+, p 0, p , n +, 0 K+, +K 0. HYC, Xian-Wei Kang, Fanrong Xu [1801. 08625] n Evidence of c+ p found by BESIII, a stringent limit set on c+ p 0 n Predictions were mostly based on SU(3) argument Sharma, Verma (’ 97); Lu, Wang, Yu (’ 16); Geng, Hsiao, Liu, Tsai (’ 17) We carry out a dynamical calculation based on current algebra. 12

In soft pion limit, nonfactorizable pole contributions are reduced to the commutator term for S-wave and CA pole terms for P-wave A = Afac + Acom , B = Bfac + BCA 13

Singly Cabibbo-suppressed modes: c+ p 0, p A( c+ p )fac Vcs. Vus f s + Vcd. Vud f q /� 2 A( c+ p 0) fac Vcd. Vud f�q /� 2 BF( c+ p )fac = 4. 0 10 -4, f q = 102 Me. V f s = -112 Me. V BF( c+ p 0)fac = 0. 9 10 -4 Nonfactorizable terms contribute constructively to p and destructively to p 0 BF( c+ p ) = 1. 28 10 -3, BF( c+ p 0) = 0. 8 10 -4 14

SU(3) QM Fac. SU(3) C. A. (10 -3 ) SU(3)-symmetry approach: assumption of sextet 6 dominance over 15 (i. e. c O >> c+O+) The predicted c+ p 0 exceeds current experimental limit Sextet dominance is respected by baryon matrix elements, but not by factorizable amplitudes 15

Charm-flavor-conserving weak decays n Light quarks undergo weak transitions, while c quark behaves as a “spectator” e. g. c c. Can be studied using HHCh. PT. n HQS & S weak transitions between 3 & 3, 6 & 6, 6* & 6* n MIT bag and diquark models only 3 to 3 transition is allowed Br( c 0 c+ -) = 0. 87 10 -4 Br( c+ c+ 0) = 0. 93 10 -4 not yet readily accessible? Cheng, Cheung, Lin, Yan, Yu (’ 92, ’ 15) Recall that BF( b- b 0 -) = (1. 9 0. 7) 10 -3 ~ (5. 7 2. 1) 10 -3 LHCb (’ 14) 16

Hadronic weak decays of doubly charmed baryons 17

Doubly charmed baryon discovered by LHCb Yu, Jiang, Li, Lu, Wang, Zhao [1703. 09086] M = 3621. 40 0. 72 0. 27 0. 14 Me. V 18

Nonleptonic decays of doubly charmed baryons n SU(3) approach W. Wang, Z. P. Xing, J. Xu [1707. 06570] Y. J. Shi, W. Wang, Y. Xing, J. Xu [1712. 03830] Geng, Hsiao, Liu, Tsai [1801. 03276, 1709. 00808] n Dynamical approach 1. factorizable W. Wang, F. S. Yu, Z. X. Zhao [1707. 02834] Gutsche, Ivanov, Korner, Lyubovitskii [1708. 00703] X. H. Hu, Y. L. Shen, W. Wang, Z. X. Zhao [1711. 10289] 2. nonfactorizable Sharma, Dhir [1709. 08217] have considered nonfactorizable effects, but only for p-wave amplitudes Need to know lifetimes in order to estimate BFs. 19

n Using the form factors for cc++- c+ transition calculated by Wang, Yu, Zhao via LFQM and applying the relation f( cc++- c++)= 2 f( cc++- c+), we obtain to be compared with Yu, Jiang, Li, Lu, Wang, Zhao Gutsche, Ivanov et al.

Lifetimes 21

Lifetimes of singly charmed baryons (in units of 10 -15 s) c+ 442 26 c+ 200 6 c 0 112+13 -10 c 0 69 12 due mainly to FOCUS Heavy quark expansion: Pauli interference & W-exchange are 1/mc 3 corrections, enhanced by p. s. enhancement factor of 16 2 c decay destructive P. I. W-exchange constructive P. I. 22

Dec Ann Int(-) Int(+) Semileptonic c + 1 s 2 1 c 2 small P. I. c + 1 c 2 1 s 2 c 0 1 1 c 0 1 6 s 2 10/3 c 2 (10 -13 s) Expt (10 -13 s) 2. 97 4. 42 0. 26 2. 84 2. 00 0. 06 small P. I. 1. 67 1. 12+0. 13 -0. 10 large P. I. 1. 11 0. 69 0. 12 s=sin C, c=cos C HYC (’ 97) n Lifetime hierarchy ( c+) > ( c 0) is qualitatively understandable, but not quantitatively. n It is difficult to explain ( c+)/ ( c+) = 2. 21 0. 15 n 1/mc expansion is not well convergent and sensible 23

However, heavy quark expansion (HQE) in 1/mb works well for B mesons and bottom baryons HYC (’ 18) Dec Ann Int(-) Semileptonic (10 -13 s) Expt (10 -13 s) b 0 1 1 1. 520 1. 470 0. 009 b 0 1 1 1. 516 1. 479 0. 030 b - 1 2 1 1. 616 1. 571 0. 030 b - 1 10/3 1 1. 657 1. 64+0. 18 -0. 17 HYC (’ 18) Lifetime hierarchy ( b-) > ( b 0) ~ ( b 0) 24

n n n 25

Consider 1/mc corrections to spectator effects: dimension-7 operators Beneke, Buchalla, Dunietz (’ 96): width difference in Bs-Bs system Gabbiani, Onishchenko, Petrov (’ 03, ’ 04): lifetime difference of heavy hadrons Lenz, Rauh (’ 13): D meson lifetimes obtained by expanding forward scattering amplitude in light quark momentum and matching the result onto operators containing derivative insertions 26

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Lifetimes of doubly charmed baryons (10 -13 s) Dec cc++ cc 1 ++ cc+ + 1 cc + cc cc+ 1 Kiselev Guberina Chang Karliner, Ann Int(-) Int(+) Semileptonic (10 -13 s) et al (’ 99) et al (’ 08) Rosner (’ 14) 2 2 4. 6 0. 5 c s 15. 5 6. 7 cs 1. 6 0. 5 2 2 2. 2 c s 2. 5 small P. I. 0. 53 0. 5~ 2. 5 s 2. 7 0. 6 4 2. 5 c 2. 1 large P. I. 4 1. 85 1. 9~15. 5 2. 1~ 2. 8 ( cc++) > ( cc+) ~ ( cc+) With Shrock & Shi, we obtain ( cc++) = 6. 2 10 -13 s, ( cc+) = 1. 2 10 -13 s, ( cc+) = 2. 0 10 -13 s at 1/mc 3 level At 1/mc 4 level, ( cc++) = 3. 9 10 -13 s, ( cc+) = 0. 96 10 -13 s, ( cc+) = (2. 5 -2. 8) 10 -13 s ( cc++) > ( cc+) 28

Conclusions n Experimental progress in hadronic decays of charmed baryon c+ is impressive. n Progress has been made in the study of hadronic decays of doubly charmed baryons. n Need dimension-7 operators to account for charm baryon lifetimes, but c 0 may not be the shortest-lived one. 29