Charmed Baryons HaiYang Cheng Academia Sinica Taipei l

Charmed Baryons Hai-Yang Cheng Academia Sinica, Taipei l Spectroscopy l Strong & EM decays Charm 2007, Cornell, August 5 -8, 2007

Spectroscopy In SU(3) representation, diquark = 3 3 = 3+6 3: c+, c 0, all decay weakly 6: c 0, ’+c, ’ 0 c, c++, +, 0 only c 0 decays weakly *0 c , *+c, *0 c, c*++, +, 0 S=1 Many new resonances observed: n Ground state: c*(2770) with mass = 2768. 3 3. 0 Me. V (Ba. Bar) n Orbitally excited p-wave states: L=1 e. g. c(2593), c(2625), … etc. (CLEO) n Positive parity excitations: L=2, 1, 0 e. g. JP[ c(2880)]=5/2+ (Belle) 2

Orbitally excited charmed baryon states L½+L¸=Ll (not L½+L¸=L !) Two possible p-wave states (L +L =1): 1. L½=1, L¸=0; antisymmetric under q 1 q 2 2. L½=0, L¸=1; symmetric under q 1 q 2 Jl=Sl+Ll, ¤ c. J (J P ) J=Sc+Jl In HQ limit, Jl & Sc are separately conserved ` symmetric antisymmetric (denoted by a 3 tilde)

First positive parity excitations (L +L =2): 1. L½=2, L¸=0; L½=0, L¸=2 symmetric under q 1 q 2; 2. L½=L¸=1 Ll=2 antisymmetric under q 1 q 2; Ll=2, 1, 0 4

½ 3/2 - Only the parity of c & c(2880) has been measured 3/23/23/2 - ½½ 3/23/2 - 5

Antitriplet charmed baryons: ½+ ( c, c+, c 0) ½- ( c(2595)+, c(2790)0) 3/2 - ( c(2625)+, c(2815)0) n c(2595), c(2625) → c 1(1/2 -, 3/2 -) c 1(1/2 -)![ c ]S, c 1(3/2 -)![¤c¼¼]P, [ c ]D ⇒ ¤c(2625) is narrower than ¤c(2595) n c(2790), c(2815) → c 1(1/2 -, 3/2 -) n c(2800): c 2(3/2 -), c 1(3/2 -), c 0(1/2 -) c 0→[ c ]S, c 1→[ c ]P, c 2→[ c ]D Since c(2880) observed in c spectrum has a width 65 Me. V, and ( c 0→ c ) 405 Me. V from HHCh. PT ⇒ c(2880) is most likely to be a c 2(3/2 -) 6

c(2880): first positive parity excited charmed baryon Angular analysis of c(2880)→ c by Belle ⇒ J=5/2 is preferred Candidates for spin-5/2 states: ⇒HQS parity assignment for c(2880) JP=5/2 - is n disfavored n However, c 2(5/2+) can decay into c* in a P-wave n robust prediction c(2880) could be an admixture of 7 Chua, HYC (’ 07)

Remarks: u Based on the diquark idea, JP[ c(2880)]=5/2+ has been predicted by Wilczek and Selem before Belle experiment u Peking group (Zhu et al. , hep-ph/0704. 0075) has studied the strong decays of charmed baryons using 3 P 0 model ⇒ Since c(2880) decays into D 0 p, it cannot be a radial excitation ⇒ c(2880) is a pure state c 2(5/2+) leads to too large ratio of c* / c for L =0, L =2, and too large width ( 78 Me. V) for L =2, L =0 An issue about mass: According to QM, m[ c 2(5/2+)] 2910 Me. V, The mass of is even higher 8

Other even-parity excitated states ? l c(2765): even-parity orbital excitation ½+, supported by or c(2765) QM (Capstick, Isgur ‘ 86) & Skyrme model (Oh & Park ‘ 96) radial excitation 2½ + (Ebert, Faustov, Galkin ‘ 07) l c(2940): 3/2+, 5/2 -, can be tested by measuring the ratio c* / c m(D*0)+m(p)=2945 Me. V ⇒ a D*0 p molecular ½- state for c(2940) with binding energy 5 Me. V ? (X. G. He et al. ) first radial excitation of c with JP=3/2+ (Ebert et al. ) M( c)-M( c) 180 200 Me. V for JP= ½+, ½-, 3/2⇒ c(2980) & c(3077) considered as counterparts of c(2765) & c(2880) l c(2980): ½+, or 2½+ l c(3077): 5/2+, l c(3055): ? c(2980) is broader than c(3077); both are above D threshold c(3123): ? 9

5/2+ 1/2+ 5/2+ 3/2+ 1/2+ 3/2 - c c 11

An ideal place for testing heavy quark symmetry and chiral symmetry: heavy hadron chiral perturbation theory (HHCh. PT) Wise; Yan et al. ; Burdman, Donoghue (’ 92) Strong decays of s-wave charmed baryons are governed by two couplings g 1 & g 2. While info on g 1 is absent due to the lack of c*→ c , g 2 is fixed to be 0. 61± 0. 04 by the measured rate of c++→ c+ + (in units of Me. V) ( c*) 7 ( c), though they have same widths in HQ limit 12

S-wave (D-wave) transitions between s-wave and p-wave baryons are described by six couplings h 2, …, h 7 (eight couplings h 8, …, h 15) Pirjol, Yan (’ 97) h 2 h 10 & h 8=h 1 0 h 10 Chau, HYC 13

Strong decays of p-wave charmed baryons l Strong decays of c(2593) are near threshold⇒ sensitive to masses + ⇒ isospin violation: c+ 0 2 c 0 , c 0 0 c + - as 0 is lighter than l ( c 0(1/2 -)→ c ) 405 Me. V 14

Electromagnetic decays suitable framework: HHCh. PT+ QM (Yan et al. ’ 94) (in units of ke. V) It will be very difficult to measure EM decay rates 15

Other topics: l Hadronic weak decays of c+, c 0, c 0 l Charm-flavor-conserving weak decays l Lifetime differences l Semileptonic decays l Weak radiative decays discussed in back-up slides See review article on charmed baryons in Tau-Charm Physics Book at BESIII. Hope it will be posted on archive soon 16

Conclusions n Many orbitally excited charmed baryons have been observed Some form multiplets c(2880) is a first even-parity excited state. It could an admixture of n We need more strong decay measurements to pin down spinparity assignment n HQS & S can be nicely tested in charmed baryon sector. Strong couplings g 2, h 2 & h 10 are updated 17

Back-up Slides 18

Lifetimes c+ 10 -15 s 442 26 c+ 200 6 c 0 112+13 -10 c 0 69 12 D+ 1040 7 Ds+ 500 7 D 0 410. 1 1. 5 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. 19

Dec Ann Int(-) (10 -13 s) Expt 3. 68 4. 42 0. 26 2. 64 2. 00 0. 06 small P. I. 1. 93 1. 12+0. 13 -0. 10 10/3 c 2 large P. I. 1. 71 0. 69 0. 12 Int(+) Semiinclusive c+ 1 s 2 1 c 2 c+ 1 c 2 1 s 2 c 0 1 1 c 0 1 6 s 2 small P. I. s=sin C, c=cos C n Lifetime hierarchy ( c+)> ( c 0)> ( c 0) is qualitatively understandable, but not quantitatively. n It has been claimed that lifetimes can be accommodated (except c+) provided that hybrid renormalization is employed and replacement of f. D by FD is made (Shifman, Blok, Guberina, Bigi…. . ) n It is difficult to explain ( c+)/ ( c+)=2. 21 0. 15 n 1/mc expansion is not well convergent and sensible 20

Hadronic weak decays Complications: 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 no longer applicable as the outgoing meson is far from being “soft”. Also this soft-meson technique is not applicable to vector meson production 21

Hadronic weak decays n Diagrammatic scheme (Chau, HYC, Tseng ‘ 96) 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 22

n Dynamical model calculation pole model: Consider low-lying pole contributions: s-wave is governed by ½- resonances p-wave is dominated by ½+ ground-state baryons Relativistic QM: Korner, Kramer, Ivanov, … 23

BRs of Cabibbo-allowed decays W-exchange plays an essential role 24

Decay asymmetry for Cabibbo-allowed decays Longitudinal pol. of daughter baryon from unpol. parent baryon ⇒ information on the relative sign between s- and p-waves ? ? 25

Decay modes that proceed through factorizable diagrams c+→ p ⇒ |a 2|=0. 60 0. 10, close to c 2 1/Nc is also applicable to charmed baryon sector c 0→ - + ⇒ a 1 c 0→ *0 K 0 ⇒ a 2 26

Charm-flavor-conserving weak decays: Light quarks undergo weak transitions, while c quark behaves as a “spectator” e. g. c c , c ’c Br( c 0 c+ -) = 2. 9 10 -4 Br( c+ c+ 0) = 6. 7 10 -4 Br( c 0 ’+c -)= 4. 5 10 -6 should be readily accessible soon 27

Semileptonic decays Semileptonic rate depends on Bc→B form factors Six form factors are reduced to two in m. Q limit |→ NRQM | RQM LFQM QSR in units of 1010 s-1 28

Weak radiative decays l Charm-flavor-changing c+→ + , c 0→ 0 l Charm-flavor-conserving c→ c , c→ c i) e. m. penguin c u ii) emission from external quark in W-exchange emission from W boson in W-exchange 29