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Charmed Baryons

Charmed Baryons. Charmed Baryons. Hai-Yang Cheng Academia Sinica, Taipei Spectroscopy Strong & EM decays. Charm 2007, Cornell, August 5-8, 2007. Spectroscopy. In SU(3) representation, diquark = 3  3 = 3 +6

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Charmed Baryons

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

  2. Spectroscopy In SU(3) representation, diquark = 33 = 3+6 3: c+,c+,c0, all decay weakly 6: c0,’+c,’0c,c++,+,0 only c0 decays weakly c*0,*+c,*0c,c*++,+,0 S=0 S=1 • Many new resonances observed: • Ground state: c*(2770)with mass = 2768.33.0 MeV (BaBar) • Orbitally excited p-wave states: L=1 • e.g. c(2593), c(2625), … etc. (CLEO) • Positive parity excitations: L=2,1,0 • e.g. JP[c(2880)]=5/2+ (Belle)

  3. P ( ) ¤ J J c ` Orbitally excited charmed baryon states L½+L¸=Ll (not L½+L¸=L !) • Two possible p-wave states (L+L=1): • L½=1, L¸=0; antisymmetric under q1q2 • L½=0, L¸=1; symmetric under q1q2 Jl=Sl+Ll, J=Sc+Jl In HQ limit, Jl & Sc are separately conserved symmetric antisymmetric (denoted by a tilde)

  4. First positive parity excitations (L+L=2): • L½=2, L¸=0; L½=0, L¸=2 symmetric under q1q2; Ll=2 • L½=L¸=1 antisymmetric under q1q2; Ll=2,1,0

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

  6. Antitriplet charmed baryons: ½+ (c, c+, c0) ½- (c(2595)+, c(2790)+, c(2790)0) 3/2- (c(2625)+, c(2815)+, c(2815)0) • c(2595), c(2625) → c1(1/2-,3/2-) c1(1/2-)![c]S, c1(3/2-)![¤c¼¼]P, [c]D ⇒ ¤c(2625) is narrower than ¤c(2595) • c(2790), c(2815) → c1(1/2-,3/2-) • c(2800): c2(3/2-), c1(3/2-), c0(1/2-) c0→[c]S, c1→[c]P, c2→[c]D Since c(2880) observed in c spectrum has a width  65 MeV, and (c0→c)  405 MeV from HHChPT ⇒ c(2880) is most likely to be a c2(3/2-)

  7. 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 disfavored However, c2(5/2+) can decay into c* in a P-wave robust prediction Chua,HYC (’07) c(2880) could be an admixture of

  8. Remarks: • Based on the diquark idea, JP[c(2880)]=5/2+ has been predicted by Wilczek and Selem before Belle experiment • Peking group (Zhu et al., hep-ph/0704.0075) has studied the strong decays of charmed baryons using 3P0 model ⇒ Since c(2880) decays into D0p, it cannot be a radial excitation ⇒ c(2880) is a pure state c2(5/2+) leads to too large ratio of c*/c for L=0, L=2, and too large width ( 78 MeV) for L=2, L=0 An issue about mass: According to QM, m[c2(5/2+)]  2910MeV, The mass of is even higher

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

  10. ½+,2½+ 3/2+,5/2- ½+,2½+ ½+,2½+ 5/2+ 5/2+

  11. 5/2+ 1/2+ 5/2+ 3/2+ 1/2+ 3/2- cccc

  12. An ideal place for testing heavy quark symmetry and chiral symmetry: heavy hadron chiral perturbation theory (HHChPT) Wise; Yan et al.; Burdman, Donoghue (’92) Strong decays of s-wave charmed baryons are governed by two couplings g1 & g2. While info on g1 is absent due to the lack of c*→c, g2 is fixed to be 0.61±0.04by the measured rate of c++→c++ (in units of MeV) (c*)  7(c), though they have same widths in HQ limit

  13. S-wave (D-wave) transitions between s-wave and p-wave baryons are described by six couplings h2,…,h7 (eight couplings h8,…,h15) Pirjol, Yan (’97) h2 h10 & h8=h10 h10 Chau, HYC

  14. Strong decays of p-wave charmed baryons • Strong decays of c(2593) are near threshold⇒ sensitive to  masses ⇒ isospin violation: c+0 2 c0+ , c00c+-as 0 is lighter than  • (c0(1/2-)→c) 405 MeV

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

  16. Other topics: • Hadronic weak decays of c+,c+,c0,c0 • Charm-flavor-conserving weak decays • Lifetime differences • Semileptonic decays • 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

  17. Conclusions • 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 • We need more strong decay measurements to pin down spin- parity assignment • HQS & S can be nicely tested in charmed baryon sector. Strong couplings g2, h2 & h10 are updated

  18. Back-up Slides

  19. Lifetimes 10-15s heavy quark expansion: Pauli interference & W-exchange are 1/mc3 corrections, enhanced by p.s. enhancement factor of 162 W-exchange c decay destructive P.I. constructive P.I.

  20. s=sinC, c=cosC • Lifetime hierarchy (c+)>(c+)>(c0)>(c0) is qualitatively understandable, but not quantitatively. • It has been claimed that lifetimes can be accommodated (except c+) provided that hybrid renormalization is employed and replacement of fD by FD is made (Shifman, Blok, Guberina, Bigi…..) • It is difficult to explain (c+)/(c+)=2.210.15 • 1/mc expansion is not well convergent and sensible

  21. Hadronic weak decays • Complications: • Baryons are made of three quarks • Factorization approximation generally doesn’t work W-exchange is not subject to helicity & color suppression • 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

  22. Hadronic weak decays • Diagrammatic scheme (Chau, HYC, Tseng ‘96) • Two distinct internal W emission diagrams, three different W exchange diagrams • Need information of decay asymmetry to extract s-wave and p-wave amplitudes separately

  23. 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,…

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

  25. 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 ??

  26. Decay modes that proceed through factorizable diagrams c+→ p⇒ |a2|=0.600.10, close to c2 1/Nc is also applicable to charmed baryon sector c0→-+ ⇒ a1 c0→*0K0 ⇒ a2

  27. Charm-flavor-conserving weak decays: Light quarks undergo weak transitions, while c quark behaves as a “spectator” e.g. cc, c’c Br(c0c+-) = 2.9 10-4 Br(c+c+0) = 6.7 10-4 Br(c0’+c-)= 4.5 10-6 should be readily accessible soon

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

  29. Weak radiative decays • Charm-flavor-changing • c+→+, c0→0 • 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

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