Lifetimes of singly doubly Charmedand Baryons charmed baryons

Lifetimes of singly doubly Charmedand Baryons charmed baryons Hai-Yang Cheng Academia Sinica Workshop on singly and doubly charmed baryons LPNHE, Paris, June 27, 2018

10 -12 s 10 -13 s D 0 d 4. 101 0. 015 B 0 d 1. 520 0. 004 D+ 10. 40 0. 07 B 0 s 1. 510 0. 005 D+ s 5. 00 0. 07 B+ 1. 638 0. 004 10 -13 s 10 -12 s c + 4. 42 0. 26 b 0 1. 470 0. 009 c + 2. 00 0. 06 b 0 1. 479 0. 030 c 0 1. 12+0. 13 -0. 10 1. 571 0. 030 c 0 b - 0. 69 0. 12 b - 1. 64+0. 18 -0. 17 due mainly to FOCUS Lifetimes of c 0 & cc++ measured by LHCb recently 2

Lifetimes of heavy baryons Heavy quark expansion: n A 0 term from the decay of heavy quark Q Lifetimes of all heavy hadrons HQ are the same in m. Q limit n No linear 1/m. Q corrections, known as Luke’s theorem n A 2 term arises from the interaction of heavy quark spin with gluon n Spectator effects described by dim-6 four-quark operators in A 3 term are responsible for lifetime differences. Though 1/m. Q 3 suppressed, they are numerically important due to a p. s. enhancement factor of 16 2 relative to heavy quark decay 3

Optical theorem Under OPE Spectator effects described by dim-6 four-quark operators: W-exchange destructive P. I. (Pauli interference) constructive P. I. (only for charmed baryons) 4

Examples of dim-6 four-quark operators for spectator effects How to evaluate hadronic matrix elements? n Meson matrix elements: bag parameters guided by vacuum insertion approx. (VIA) VIA Bi = 1, i= 0 estimated using QCD sum rules, LQCD, . . . , and updated recently by Kirk, Lenz, Rauch using HQET sum rules (’ 17) 5 See T. Rauh’s talk

n Baryon matrix elements: quark model : antitriplet baryon Tb or sextet baryon b r is a wave function ratio B defined by B=1 in valence-quark approx, valid at hadronic scale 6

Lifetimes of bottom mesons n Inclusive semileptonic rate of B Xce+ e is very sensitive to mb. n Two short-distance b-quark masses: kinetic & 1 S schemes. n A global fit to B Xce+ e yields mbkin(1 Ge. V) = 4. 546 0. 021 Ge. V Gambino, Healey, Turczyk (’ 16) Using the bag parameters obtained by Kirk, Lenz, Rauh as input -12 Dec Ann Int(-) Semi (10 s) Expt (10 s) 1 1 1. 717 1. 638 0. 004 B+ 1 Bd 0 1 1. 589 1. 520 0. 004 Bs 0 1 1. 583 1. 510 0. 005 in excellent with experiment! 7

Lifetimes of singly bottom baryons Dec Ann Int (-) Semi (10 -12 s) Expt (10 -12 s) b 0 1 1 1. 520 1. 470 0. 009 b 0 1 1 1. 529 1. 479 0. 030 b - 1 2 1 1. 630 1. 571 0. 030 b - 1 10/3 1 1. 725 1. 64+0. 18 -0. 17 Lifetime hierarchy ( b > ( b ~ ( b -) -) 0) 0) HYC (’ 18) Heavy quark expansion (HQE) in 1/mb works very well for B mesons and bottom baryons! 8

Lifetimes of charmed mesons D+, D 0 semileptonic widths fitted by mc=1. 56 Ge. V D+ D 0 c 1( )=1. 346, c 2( )=-0. 636 free c-quark decay destructive P. I. semileptonic Bag parameters in VIA (B 1=1, 1=0) or others large destructive P. I. negative D+ lifetime! under VIA RD = 3. 98, even if (D+) <0 R’D = -0. 18 (D+) <0 (RD)expt = 2. 536 0. 019, (R’D)expt = 0. 394 0. 003 9

Ann Int () c + 1 s 2 1 c 2 small P. I. 3. 06 4. 42 0. 26 c + 1 c 2 1 s 2 no P. I. 2. 91 2. 00 0. 06 c 0 1 1 0 c 2 small P. I. 1. 62 1. 12+0. 13 -0. 10 c 0 1 6 s 2 10/3 c 2 large P. I. 1. 06 0. 69 0. 12 s=sin C, c=cos C Int (+) Semi (10 -13 s) Dec Expt (10 -13 s) additional constructive P. I. contribution to semi Voloshin (’ 96) n Current lifetime hierarchy ( c+) > ( c 0) is understandable qualitatively, but not quantitatively. n It is difficult to explain ( c+)/ ( c+) = 2. 21 0. 15 n 1/mc expansion not well convergent and sensible 10

A 4: dim-7 operators Consider subleading 1/mc corrections to spectator effects: 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 Gabbiani, Onishchenko, Petrov (’ 03, ’ 04) Dim-7 4 -quark operator is either 4 -quark operator times mq or 4 -quark operator with an additional derivative 11

Charmed meson lifetimes Subleading 1/mc correction contributes constructively to (D+) Fixing i =1, i =0 (VIA values), and fitting RD, R’D to the data, one of the solutions is found to be at =mc Kirk, Lenz, Rauch: at = 3 Ge. V See T. Rauh’s talk 12

n to 1/mc 3 n with 1/mc corrections to spectator effects l ( c+) enhanced, ( c+) suppressed ( c+)/ ( c+) is increased from 1. 05 to 1. 88 l Shortest-lived c becomes longest-lived one after 1/mc corrections 13

+int = 6 int + 7 int, semi = 6 semi + 7 semi Destructive contributions from 7 int & 7 semi are too large to justify the validity of HQE Introduce a parameter to describe the degree of suppression for 7 int & 7 semi guideline for : positive +int & semi with results close to that of c =0. 27 ( c+) > ( c 0) > ( c+) > ( c 0) 14

Talk presented at HIEPA 2018 Workshop (March 19 -21, 2018, Beijing) ( c 0) = 2. 31 10 -13 s for =0. 25 15

LHCb (June 8, 2018) ( c 0) = (2. 68 0. 21 0. 10 0. 02) 10 -13 s Four-times larger than the world average of (0. 69 0. 12) 10 -13 s from fixed target experiments! events 64 86 25 16

Lifetimes of doubly charmed baryons with Robert Shrock & Yan-Liang Shi 17

Lifetimes of doubly charmed baryons in units of (10 -13 s) Kiselev et al (’ 98) Kiselev et al (’ 99) cc++ 4. 3 1. 0 4. 6 0. 5 15. 5 6. 7 1. 85 cc+ 1. 1 0. 1 1. 6 0. 5 2. 2 2. 5 0. 53 2. 7 0. 6 2. 5 2. 1 cc+ Guberina et al (’ 99) Chang et al (’ 08) Karliner, Rosner (’ 14) Large theoretical uncertainties ( cc++) > ( cc+) ~ ( cc+) 18

Lifetimes of doubly charmed baryons Dec Ann Int(-) Int(+) Semi (10 -13 s) 1 1. 9~15. 5 cc++ 1 cc+ 1 1 s 2 1 + s 2 P. I. 0. 5~ 2. 5 cc+ 1 s 2 1 1 + c 2 P. I. 2. 1~ 2. 8 1 cc++ cc+ ( cc++) > ( cc+) ~ ( cc+) 19

n to 1/mc 3 ( cc++) > ( cc+) n After including 1/mc corrections to spectator effects n ( cc++) becomes shorter, while ( cc+) becomes longer n The use of HQE for int+ & semi for cc is not valid 20

Needs to suppress 7 int & 7 semi to make the use of HQE sensible! =0. 5 ( cc++) > ( cc+) with ( cc++) ~ 2. 85 10 -13 s LHCb: ( cc++) = (2. 56+0. 24 -0. 22 0. 14) 10 -13 s Caveat: Predictions of absolute lifetimes are still preliminary. Will be finalized during the summer. 21

Conclusions n HQE in 1/mb works well for the lifetimes of B mesons and bottom baryons. n HQE in 1/mc fails to provide a satisfactory description of the lifetimes of D mesons & charmed baryons to O(1/mc 3). Need to consider subleading 1/mc corrections to spectator effects. n Dim-7 operators are in the right direction to enhance ( c+) & suppress ( c+), but they will render the lifetime of c 0 longer than c 0 n For doubly charmed baryons, we found ( cc++) > ( cc+) with ( cc++) 0. 285 ps 22