Charm baryon spectroscopy from heavy quark symmetry

Transcription

1 Charm baryon spectroscopy from heavy quark symmetry Phys. Rev. D91, (2015) Tokyo Institute of Technology Shigehiro YASUI Hadrons and Hadron Interaction in QCD (HHIQCD 16 Feb. 20 Mar. 2015

2 Contents 1. Heavy quark symmetry 3. Conclusion

3 u 2 MeV d 5 MeV 1. Heavy quark symmetry t c J-PARC GSI-FAIR 1300 MeV s 100 MeV 173,000 MeV b LHCb 4200 MeV

4 1. Heavy quark symmetry 1/m Q expansion (positive energy state Q v with velocity v) Manohar, Wise, Luke, Grinstein,... LO Heavy quark spin in m Q is conserved. Heavy quark symmetry (HQS)

5 1. Heavy quark symmetry Heavy quark symmetry (HQS) ρ K* Spin MeV D* 890 MeV B* 2010 MeV 1870 MeV D 5325 MeV 630 MeV 390 MeV 140 MeV 45 MeV 5280 MeV B 140 MeV π 500 MeV K Spin 0 0, 1 HQS doublet

6 1. Heavy quark symmetry Heavy quark symmetry (HQS) Δ 1230 MeV 5830 MeV 290 MeV 195 MeV 65 MeV 20 MeV 2455 MeV 5810 MeV 1190 MeV 940 MeV N Σ* 1385 MeV Σ 1115 MeV Λ Spin 3/2 Spin 1/2 Spin 1/2 3/2, 1/2 HQS doublet Σ c * 2520 MeV Σ c 2286 MeV Λ c Σ b * Σ b 5619 MeV Λ b 1/2 HQS singlet

7 1. Heavy quark symmetry Heavy quark symmetry (HQS) Heavy baryon (Qqq) Ψ (j) J Heavy quark with spin 1/2 j J=j±1/2 Brown Muck : Light quarks and gluons with definite total spin (j), quark # = 2 and color 3 bar diquark (?) Mass spectrum HQS doublet/singlet (j 0) (j=0)

8 1. Heavy quark symmetry Heavy baryon Diquark phase diagram? Diquarks in light baryon (qqq) and scalar meson (qqqq)? Exciting energy Color superconductivity and Diquarks as Bose-Einstein condensate Brown Muck baryon number density

9 1. Heavy quark symmetry HQS doublet/singlet Quark model W.Roberts, M.Pervin, Int. J. Mod. Phys. A23, 19 (2008); Y.Yamaguchi, S.Ohkoda, T.Hyodo, A.Hosaka, S.Y., arxiv: [hep-ph] Cf. Skyrme model; Y. Oh, B-Y. Park, D-P. Min Phys. Rev. D50, 3350 (1994)

10

11 Transition decay width Heavy baryon (Qqq) Ψ (j) J j J=j±1/2

12 Transition decay width Heavy baryon (Qqq) π Ψ (j) J j L J=j±1/2 j Ψ (j ) J Heavy quark limit (M ) J =j ±1/2 Isgur and Wise, Phys. Rev. Lett. 66, 1130 (1991) Question: what is O(1/M)?

13 Heavy-baryon effective Lagrangian 1. Heavy quark symmetry is conserved at O(1). Heavy quark with spin 1/2 Brown Muck = 2. Inv. under velocity rearrangement at O(1)+O(1/M). v-frame H v (x) v w = v + q/m ( q/m << 1 ) v w-frame H w (x) Velocity rearrangement : Lorentz boost between v-frame and w-frame up to O(1/M) w = v + q/m Question: what is O(1/M)? Luke, Manohar, PLB286, 348 (1992), Kitazawa, Kurimoto, PLB323, 65 (1994)

14 Heavy-baryon effective Lagrangian 1. Heavy quark symmetry is conserved at O(1). Heavy quark with spin 1/2 Brown Muck = 2. Inv. under velocity rearrangement at O(1)+O(1/M). v w = v + q/m ( q/m << 1 ) 3. Heavy quark symmetry breaking terms at O(1/M).

15 (A part of) brief history of Qqq baryon effective theory Brown Muck spin and parity LO: O(1) Heavy Mass Expansion NLO: O(1/M) j P =0 +, 1 + T-M. Yan, H-Y Cheng, C-Y. Cheung, G-L Lin, Y-C. Lin,, H-L. Yu PRD46, 1148 (1992) (P-wave decay) H-Y Cheng, C-Y. Cheung, G-L Lin, Y-C. Lin, T-M. Yan, H-L. Yu PRD49, 2490 (1994) (P-wave decay) j P =0 ±, 1 ± (j P,j P ) and (j P,j+1 P ) H-Y Cheng, C-K Chua PRD75, (2007) (S-, P-, D-wave decay) Arbitrary j P (j,j) P and (j,j+1) P SY. PRD91, (2015) (P-wave decay)

16 Falk, Nucl. Phys. B378, 79 (1992) Effective baryon field with brown muck spin j - Constraint conditions Brown muck with spin j Heavy quark spin 1/2 Total spin j±1/2 Cf. Rarita-Schwinger field for spin 3/2 - Projection to j-1/2 and j+1/2 states

17 Interaction Lagrangian at LO+NLO SY. PRD91, (2015) (j,j+1) transitions -- different brown-muck spin j, j+1 in initial and final states -- LO (HQS conserving) Cf. For j=0,1; Cheng, et al., PRD49, 2490 (1994) Ψ (j+1) NLO (HQS breaking) J Ψ(j) J +π p-wave j+1 Pauli-Lubanski vector (spin operator) j J=j+3/2, j+1/2 J =j±1/2

18 Constraint among decay widths SY. PRD91, (2015) (j,j+1) transitions -- different brown-muck spin j, j+1 in initial and final states -- For any j 1... A constraint on different decay channels at O(1/M). This is a weaker constraint to Isgur-Wise s constraint.

19 SY. PRD91, (2015) Analogy Gell-Mann, Okubo relation Flavor SU(3) symmetry breaking (Gell-Mann, Oaks, Renner relation)

20 Interaction Lagrangian at LO+NLO (j,j) transitions -- same brown-muck spin j in initial and final states -- j 1 SY. PRD91, (2015) NLO (velocity-rearrangement) NLO (HQS breaking) j = 0 Σ c (3062)(QM) Λ c π Ξ c (2924)(QM) Ξ c π 1/2 ± 1/2 ± transition (HQS singlet) is very small; O(1/M 2 ).

21 1. Heavy quark symmetry O(1/M 2 ) O(1/M2 ) HQS doublet/singlet Quark model W.Roberts, M.Pervin, Int. J. Mod. Phys. A23, 19 (2008); Y.Yamaguchi, S.Ohkoda, T.Hyodo, A.Hosaka, S.Y., arxiv: [hep-ph] Cf. Skyrme model; Y. Oh, B-Y. Park, D-P. Min Phys. Rev. D50, 3350 (1994)

22 Interaction Lagrangian at LO+NLO (j,j) transitions -- same brown-muck spin j in initial and final states -- j 1 SY. PRD91, (2015) NLO (velocity-rearrangement) NLO (HQS breaking)

23 Interaction Lagrangian at LO+NLO (j,j) transitions -- same brown-muck spin j in initial and final states -- SY. PRD91, (2015) For any j 1... This holds not only at O(1/M) but also at O(1).

24 Some numerical studies... SY. PRD91, (2015) How small is NLO to LO?

25 (0,1) transitions Some numerical studies... Σ Q (*) Λ Q π j=1 j=0 SY. PRD91, (2015) Charm Belle, arxiv: : p-wave π transition assumed

26 (0,1) transitions Some numerical studies... Σ Q (*) Λ Q π j=1 j=0 SY. PRD91, (2015) ~ 6 % (?)

27 (0,1) transitions Some numerical studies... Σ Q (*) Λ Q π j=1 j=0 SY. PRD91, (2015) Bottom PDG MeV (theory) 9.6 MeV (theory) : p-wave transition supposed

28 3. Conclusion 1. Strong decays of one-pion emission from excited heavy baryons are discussed. 2. Heavy quark symmetry (HQS) at LO+NLO in 1/m Q expansion was considered. 3. Relations for decay widths in several channels were obtained model-independently. 4. They will be useful for identifications of the HQS doublet/singlet in experimental analysis. 5. Other higher order contributions? (isospin breaking, chiral expansion, etc.)

29

30 Charmed(Baryon(Spectroscopy Using Missing(Mass(Techniques Inclusive p( -,D* % ) Y c * + Noumi 2014 (Target) Y c *+ p( -,D* % p)d 0 p D 0 (Y c ) ( p( -,D* % )Y c )1 Conducted(by(the(E50 experiment(at(japarc 12

31 Missing Mass Spectrum (Sim.) ~1000"Y c* /nb/100"days Sensitivity:" ~0.1"nb for"y c* w/" =100"MeV 1/2+ L ="0 HQS"doublet 1/2' 3/2' 5/2+ 3/2+ L ="1 L"="2 c (2625)' Noumi 2014 HQS"doublet? ~1"nb c c (2595)' c (2880)' c c * 1":"2 c (2800) c (2940)' 3":"2

32 (j,j+1) transitions Constraint among decay widths SY. PRD91, (2015) Example: j=1 For any j 1... A constraint on different decay channels at O(1/M). This is a weaker constraint to Isgur-Wise s constraint.