Lattice studies of multiply charmed baryons

Transcription

1 Lattice studies of multiply charmed baryons Gunnar Bali (Regensburg) QWG13, IHEP Beijing,

2 Outline Motivation Simulation parameters Multiply charmed baryons Summary Gunnar Bali (Uni Regensburg) multiply charmed baryons 2 / 23

3 What I will (not) cover I concentrate on recent results of SFB-TR55 (Regensburg-Wuppertal): P Pérez-Rubio, and preliminary n f = HEX and SLiNC 2-HEX Charmonium: Craig McNeile, Thursday 10:20 Hadron Spectrum Collaboration: M Padmanath et al, preliminary, n f = 2+1 anisotropic clover-wilson Charmonia: Christopher Thomas, earlier today. Recent results not covered in detail: L Liu et al clover-wilson and DW on n f = 2+1 asqtad C Alexandrou et al [ETMC] n f = 2 Twisted Mass, 2 a s R Briceño et al clover on n f = HISQ, 3 a s S Basak et al [ILGTI] overlap on n f = HISQ Y Namekawa et al [PACS-CS] n f = 2+1 NP clover-wilson Gunnar Bali (Uni Regensburg) multiply charmed baryons 3 / 23

4 Singly charmed baryons Bar. M(MeV) (qqq) I(J P ) St. Bar. M(MeV) (qqq) I(J P ) St Λ + c 2625 (udc) 0(3/2 + +) ) /2 ( +) 1/2 Ξ (usc) 1/2(1/2 + ) ( ) 1/2 Ξ (dsc) 1/2(1/2 + ) ( (??) /2(3/2 + ) 2790 (usc), 0(?? ) Ξ c /2(3/2 ) Σ c 2520 (udc), 1(3/2) /2(?? ) 2455 (uuc), 1(1/2 + ) 2980 (dsc) 1(?? ) 2800 (ddc) 1(?? ) (1/2 + ) Ω c (ssc) Ξ + c 2468 (usc) 1/2(1/2 + ) (3/2 + ) Ξ 0 c 2470 (dsc) 1/2(1/2 + ) Ξ + cc 3519 (dcc)?(?? ) m Σ + c m Σ + c = (64.6 ± 2.3) MeV m Ξ + c m Ξ + c m Ω c m Ω + c = (70.9 ± 3.4) MeV = (70.8 ± 1.5) MeV Charmed baryon mass (GeV) pd pd? 5/2 + 3/2 1/2 1/2 + Λ c ππ ππ Δ (a) Charmed baryons π Σ cπ π? π 3/2 + π 3/2 1/2 3/2 + 1/2 + 1/2 + 1/2 + 1/2 + Λ c Σ c Ξ c Ω c [PDG]?? Λ c K π Λ c K π π π γ π Δ 3/2 + γ Gunnar Bali (Uni Regensburg) multiply charmed baryons 4 / 23

5 Doubly charmed baryons HQET picture for r Λ Q Q r Λ Gunnar Bali (Uni Regensburg) multiply charmed baryons 5 / 23

6 Doubly charmed baryons Q 1 Λ r Q r Λ: NRQCD/Charmonium-alike? Gunnar Bali (Uni Regensburg) multiply charmed baryons 5 / 23

7 Previous lattice calculations [R A Briceño, D Bolten, H-W Lin 11] J P = 1/2 + J P = 3/2 + Gunnar Bali (Uni Regensburg) multiply charmed baryons 6 / 23

8 Landscape of current lattice simulations Figures taken from C Hoelbling Gunnar Bali (Uni Regensburg) multiply charmed baryons 7 / 23

9 QCDSF: m u + m d + m s m 2 π + 2m 2 K const. = physical QCDSF + UKQCD: W Bietenholz et al. 10 Gunnar Bali (Uni Regensburg) multiply charmed baryons 8 / 23

10 BMW-c: chiral extrapolation and the continuum limit 2 O 2000 M [GeV] physical M p N a~0.125 fm a~0.085 fm a~0.065 fm M p 2 [GeV 2 ] M[MeV] p K r K* N S X S* D L O X* experiment width input QCD S Dürr et al. 09/10 Gunnar Bali (Uni Regensburg) multiply charmed baryons 9 / 23

11 Analyzed configurations, N f = 2+1 BMW-c: 2-HEX action β Volume a (fm) M π (MeV) no. β Volume a (fm) M π (MeV) no Gunnar Bali (Uni Regensburg) multiply charmed baryons 10 / 23

12 Analyzed configurations, N f = 2+1 QCDSF: SLiNC action * m u + m s + m d kept constant (2M 2 π + M 2 K const,) β Volume a (fm) M π (MeV) M K (MeV) (3) (3) (3) (3) (3) (3) (3) (3) HadSpect (Padmanath et al): anisotropic clover-wilson a s 0.12 fm, a t fm, Volumes: , , M π 390 MeV. Gunnar Bali (Uni Regensburg) multiply charmed baryons 11 / 23

13 SU(4) representations Flavour symmetry is not respected but simplest way to see which baryons should exist. SU(4): = = Gunnar Bali (Uni Regensburg) multiply charmed baryons 12 / 23

14 Interpolating fields: SU(4) reps SU(4) 20-plet containing SU(3) octets * N-alike: Ω + cc,ξ + cc,ξ ++ cc. O P γ(x) = ǫ abc [ q a 1(x) T (Cγ 5)q b 2(x) ] q c 2γ(x). SU(4) 20-plet containing SU(3) decuplet * ++ -alike: Ω ++ ccc. O ++ γ * Σ -alike: Ξ + cc,ξ ++ cc,ω + cc. O Σ γ Correlators = ǫ abc { 2 ( q at 1 (Cγ µ)q b 2 = ǫ abc ( q at 1 (Cγ µ)q b 1) q c 1γ ) q c 2γ + ( ) } q2 at (Cγ µ)q2 b q c 1γ C(t, p = 0) = T γγ O γ (x)o γ (0), where T γ is a parity and spin projection matrix. Gunnar Bali (Uni Regensburg) multiply charmed baryons 13 / 23 x

15 Interpolating fields: HQET cc diquark: 3 3 = 3+6 diquark spin s d, parity π d. J P = 1+ J P = (S) (I) s π d d (qq)q O Name Name (0) ( 1 2 ) (1)+ (cc)u O µ = ǫ abc (c at Cγ µc b )u c Ξ cc Ξ cc ( 1) (0) (1) + (cc)s O µ = ǫ abc (c at Cγ µc b )s c Ω cc Ω cc All O x s require projections T γγ. Correlators, C µν(t) from O ( ) µ need projections into the desired J = 1/2, /3/2. Projectors Pµν 3/2, Pµν 1/2 used. Gunnar Bali (Uni Regensburg) multiply charmed baryons 14 / 23

16 Singly charmed baryons: SLiNC preliminary 3.2 EXP pos P EXP neg P GT pos P GT neg P HQET pos P HQET neg P 3 m fit (GeV) * * Σ c Σ c Ω c Ω c Ξ c Ξ * c Ξ c Λ c QUARKS: (uuc) (ssc) (usc) (udc) SPIN: 1/2 3/2 1/2 3/2 1/2 3/2 1/2 1/2 m s /m u 2.9 light quarks too heavy. Gunnar Bali (Uni Regensburg) multiply charmed baryons 15 / 23

17 cc baryons: other groups, SLiNC + 2-HEX preliminary 4.1 ETMC Liu Na Durr Briceno Mathur PACS-CS Mathur neg P SLiNC SU(4) SLiNC HQET SLiNC neg P SU(4) SLiNC neg P HQET 2-HEX m fit (GeV) * Ξ cc Ξ cc Ω cc Ω * cc QUARKS: (ucc) (scc) SPIN: 1/2 3/2 1/2 3/2 Gunnar Bali (Uni Regensburg) multiply charmed baryons 16 / 23

18 2-HEX continuum limit extrapolation: preliminary! Spin 3/2 ccs baryon Fit model: 1 + O(a 2 ) Fit model: 1 + O(aα s ) Averaged and shifted data Mass GeV a 2 /fm 2 Gunnar Bali (Uni Regensburg) multiply charmed baryons 17 / 23

19 Mass dependence of ccs-ccu splittings: SLiNC preliminary 3.7 S=1/2 Ω cc HQET Ξ cc HQET Ω cc SU(4) Ξ cc SU(4) m (GeV) M 2 π /X2 π 3.75 S=3/2 Ω * cc HQET Ξ* cc HQET Ω* cc SU(4) Ξ* cc SU(4) m (GeV) M 2 π /X2 π Gunnar Bali (Uni Regensburg) multiply charmed baryons 18 / 23

20 ccs-ccu splittings II: SLiNC preliminary m (GeV) S=1/2 Ω cc - Ξ cc SU(4) Ω cc - Ξ cc HQET Ξ - Σ Ξ - Σ EXP M 2 π /X2 π S=3/2 0.2 Ω * cc - Ξ* cc SU(4) Ω - Ξ * Ω * cc - Ξ* cc HQET Ω * - Ξ * EXP m (GeV) M 2 π /X2 π Gunnar Bali (Uni Regensburg) multiply charmed baryons 19 / 23

21 ccu baryons: Padmanath et al, preliminary mass -m ηc [GeV] /2 + 3/2 + 5/2 + 7/2 + 1/2-3/2-5/2-7/2 - Gunnar Bali (Uni Regensburg) multiply charmed baryons 20 / 23

22 ccc ground state: Padmanath et al, preliminary 0.21 mass Ωccc,g - 3/2 mass J/ψ (GeV) c SW =2.0 c SW =1.35 a ~ 0.06fm a ~ 0.09fm 0.06 This work ILGTI, 2012 PACS-CS 2012 Gunnar Bali (Uni Regensburg) multiply charmed baryons 21 / 23

23 Triply charmed baryons: Padmanath et al, preliminary mass -3/2 mass ηc (GeV) /2 + 3/2 + 5/2 + 7/2 + 1/2-3/2-5/2-7/2 - Gunnar Bali (Uni Regensburg) multiply charmed baryons 22 / 23

24 Summary and outlook Hidden and open charm states are narrower and experimentally cleaner than many light quark resonances. Theoretically, the heavy quark limit provides guidance. Particularly interesting are the baryonic analogues of charmonia. Unfortunately, these states are still awaiting to be discovered. In the doubly charmed baryon sector we aim to establish if the spectrum resembles that of D, D s heavy mesons : (cc)u,(cc)s (HQET picture) or that of c(cu), c(cs) charmonia. Positive parity ccs ground states (Ω cc and Ω cc) have been interpolated to the physical point and the continuum limit taken. Lattice studies of other states are of a more qualitative nature. The tip of the pyramid even less discoverable: Ω ++ ccc. Gunnar Bali (Uni Regensburg) multiply charmed baryons 23 / 23