Double-charmed Baryons

Transcription

1 Double-charmed Baryons The only experimental information about DCB gives SELEX collaboration: There are several questions to SELEX results: 1) Lifetime 2) Cross sections Theoretical information about DCB: 1) Mass spectrum 2) Life time and leading decay modes 3) Cross section + * cc ( ccd ) + Ξ = M = 3443 MeV, cc ( ccd ) Ξ = M = 3520 MeV, ( ccu) ++ Ξ = M = 3541MeV, cc Ξ Ξ Ξ + + * ++

2 Double-charmed Baryons Mass spectrum theoretical predictions: Potential Models (two step calculation) QCD Sum Rules QCD Effective field theory Lattice QCD PM predictions for ground state cc-diquark 3 c are [V. Kiselev, A.Onishchenko, A.L.] M M + ( cc ) + ( cc ) Ξ = 3478 MeV, 1S1S 1/2 Ξ = 3610 MeV, 1S1S 3/2 * + + M ~ 40 MeV Metastable state (2P1S) ½ - (3702) have L=1, S=0 for diquark. Transitions to the ground state (L=0, S=1) requires simultaneous change of orbital momentum and spin.

3 Double-charmed Baryons Sum Rules ( Ξ cc ) = 3.47GeV, (without HF splitting) M + [V. Kiselev, A.Onishchenko, A.L.] Lattice QCD ( Ξ cc ) = GeV ± 20 MeV M + [R.Lewis et al] Spin-dependent potential * Hyperfine splitting M cc PM: = 130 MeV ± 30 MeV QCDEFT = 120 MeV ± 40 MeV Lat.QCD = 76.6 MeV + + ( ) M ( cc ) = Ξ Ξ [V. Kiselev, A.Onishchenko, A.L.] [N.Brambilla et al] [R.Lewis et al]

4 Excited states spectrum

5 (*) cc Lifetimes of DCB 1 (*) (*) 4 Γ (*) = Ξcc T Ξ T = Im ( ) ( ) Ξ cc eff eff 0 cc 2M d x T H x H F Where 2 2 c-quark transitions Ξ G * H eff = Vuq V ( ) ( ).. 1 cq C µ O C µ O h c { } is standard hamiltonian of weak In decays of heavy quarks released energy is significant, so it is possible to expand H eff in the series of local operators suppressed by inverse powers of heavy quark mass spectator Pauli interference EW scattering

6 Lifetimes of DCB For example, for semileptonic decay mode where Γ = V c cs GFmc, 3 192π ( ) ( id) 2 αβ ( ) ( ) σ ( ) K = Ξ v c c Ξ v, G = Ξ v c G c Ξ v, E = G + K (*) (*) (*) (*) c cc v 2 v cc c cc v αβ v cc c c c 2mc In numerical estimates we have used following parameter values: m c =1.6 GeV m s =0.45 GeV m q =0.3 GeQ M(Ξ ++ cc )=M(Ξ+ cc )=3.56 GeV M HF =0.1 GeV ψ diq (0) = 0.17 GeV 3/2

7 Lifetimes of DCB τ Ξ = 0.43ps, τ = 0.12 ps ++ + cc Ξcc ++ + ( cc ν ) ( cc ν ) Br Ξ l + X = 16%, Br Ξ l + X = 4%,

8 Exclusive decays in NRQCD sum rules Quark loop for 3-point correlator in the baryon decay For 1/2 1/2 transition there are 6 form-factors: { } ( ) ( ) ( ) ( ) V I V F V ( A I A F A µ γ µ µ µ γ γ µ 1 µ 2 µ 3 ) Ξ p J Ξ p = u p G + v G + v G + G + v G + v G u p F F I I F I These 6 f.f. are independent. However, in NRQCD in LO for small recoil it is possible to obtain following relations: ( ), ξ ( ) G + G + G = ξ w G = w V V V IW A IW Only 2 f.f. are not suppressed by heavy quark mass: V A IW 1 1 ( ) G = G = ξ w

9 In the case of zero recoil ξ IW (1) is determined from Borell transfromation For transition For calculation of exclusive widths one can adopt pole model

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11 Production of Ξ cc -baryons In all papers it was assumed, that [ cc ] ( cc) 3 σ Ξ σ This is quite reasonable assumption in the framework of NRQCD, where, for example, octet states transforms to heavy quarkonium. Analogously, we have to assume, that dissociation of (cc) 3 into DD is small. Similar to cc-quarkonium production cross sections factorizes into hard (pertubative) and soft (non-pertubative) parts. In both cases second part is described by wave function of bound state at origin. That s why it is reasonable to compare J/ψcc and Ξcc final states. In this case only one uncertainty remains the of squared wave functions at origin.

12 4c-sector LO calculations for σ(4c) at s = 10.6GeV gives at m c =1.25 GeV α s =0.24 It should be compared with This gives At Z-pole ( e e cccc ) 372fb σ + σ tot ( cc ) ( e e cc ) 1.03nb σ + ( 4c) ( 2c) σ R = ~ σ R Z ~ Main uncertainties come from errors in m c and α s 2 4

13 X cc final state ( ) ( ) X = cc = η, J / ψ, χ 1 P, ψ ', c c 1) Fragmetation mechanism e X c e + c ( J + ) R ( 0) Dc X ( z) 3 s ( z) 27π m α φ = 2E z = X s M 2 /s corrections are neglected (M 2 /s <<1)

14 X cc final state 2) Complete calculations (with M 2 /s corrections) σ( η c ) = 40 (49) fb, σ( J/ ψ) = 104 (148) fb, σ( χ c0 ) = (48.8) fb σ( χ c1 ) = (13.5) fb σ( χ c2 ) = (6.3) fb [A.Berezhnoi, A.L.] [K.Y. Liu, Z.G. He, K.T. Chao] Complete calculations deviate from fragmetation calculations at s = 10.6GeV M 2 /s terms are important

15 X cc final state 3) Quark-Hadron duality 2m D 2m c ( ( ) sing ) + dσ e + e cc + c + c dmcc dm cc = 280fb m = 1.25GeV α s = 0.24 c = 0.5GeV ( ) S=1 dσ e + e cc + c + c = sing 204 fb ( ) S=0 dσ e + e cc + c + c = 76 fb sing It should be compared with total sum of complete calculations. tot ( QQ) σ = 216 fb Q-H duality does not contradict Color Singlet model within uncertainties in m c α s and

16 X cc final state a) fragmentation approach S=1 D c cc (z) similar to D c J/ψ (z) Difference in wave functions Ψ J/ ψ (0) 2 and Ψ cc (0) 2 Again, similar to J/ψ case, at s = 10.6GeV complete calculations for vector (cc) 3 -diquark are needed

17 X cc final state b) Quark-Hadron duality One inclusive cross section for vector 3 c in S=1 σ ( Ξ cc + c + c ) ~ fb Uncertainties are caused by errors in α s and This value is close to results of complete calculations with Ψ cc (0) taken from PM.

18 ( e e ) cc X ~ 100fb Conclusion σ + Ξ + s = 10.6GeV ( at LHC σ e + e Ξ + X ) 1) at ( ) cc ~ 122 nb 2) For lumonocity L=10 34 cm -2 s -1 it gives ~10 4 Ξ cc -baryons per year 3) Taking into account Br ~10-1 in exclusive modes we expect 10 3 Ξ cc events per year DIXI