手征夸克模型的一些应用 钟显辉 湖南师范大学物理与信息科学学院

Meson-Baryon scattering in the quark model e.g. πNηN, KNΣ π,… Photo-production process in the quark model e.g. γNηN, γNNπ,… Strong decay of the heavy hadrons in the quark model e.g. Λc,Σc , Ξc , Ξ ; D, Ds, B, Bs

The chiral quark model : Glozman and Riska: Phys. Rept. 268,263(1996); Nucl. Phys. A663,103c(2000) Z Y Zhang, A. Faessler, U. Straub, L. Ya. Glozman, Nucl. Phys.A578,573(1994) Z Y Zhang Y W. Yu,P. N. Shen, et al., Nucl. Phys.A625,59(1997) L.R.Dai, Z.Y.Zhang,Y.W.Yu,P.Wang, Nucl.Phys.A727,321(2003) ……

Part I: Meson-Baryon scattering in the quark model Meson-Baryon scatterings at low energies inform us much information of meson-baryon interactions, coupling constants, the properties of baryon resonances,… M.Doring, E. Oset, B. S. Zou, arXiv:0805.1799; J J Xie, B. S.Zou, Phys.Lett.B649:405,2007; B.C Liu, B.S. Zou, Phys.Rev.Lett.96:042002,2006. Fei Huang et al., Chin.Phys. C33 (2009) 1291-1295 Puze Gao, Jun Shi, B.S. Zou, Phys.Rev. C86 (2012) 025201 …

1) quark-meson interactions A. The model 1) quark-meson interactions The effective Lagrangian of quark-meson interactions: The quark-meson pseudovector coupling at tree level:

quark-meson interactions The non-relativistic form: Vector pj is the internal momentum for the j-th quark in the baryon rest frame, q is the meson momentum, Ij is the isospin operator,… See series papers of Zhenping Li and Qiang Zhao

2) Scattering amplitudes Two kinds of amplitudes for s- and u-channels, one is the mesons couple with the same quark, the other is the mesons couple with different quarks.

Amplitudes for the s-channel

Amplitudes for the u-channel

Breit-Wigner

Partial wave amplitudes

1) Resonance contribution B. πpηn 1) Resonance contribution a) the n=0 shell In the case of n=0, only the nucleon pole term contributes to the transition amplitude (P-wave). XH Zhong Q Zhao, J He , B Saghai, PRC76,065205(07)

b) In the n=1 shell In n=1 shell, both S-wave and D-wave resonances contribute to the amplitude. The S-wave resonances: S11(1535), S11(1650) The D-wave resonances: D13(1520), D13(1700), D15(1675)

c) In the n=2 shell In n=2 shell, both P-wave and F-wave resonances contribute to the amplitude. The P-wave resonances: P11(1440), P11(1710), P13(1720), P13(1900),… The F-wave resonances: F15(1680), F15(2000)

2) results

results Near threshold, the S11(1535) dominates the reactions, while the interferences from the S11(1650) turn out to be destructive around W<1.6 GeV. The D13(1520) is crucial to give correct shapes of the differential cross sections. The nucleon pole term contributions are significant.

1) Resonance contribution n=0 shell: Λ pole C. Kp Σπ 1) Resonance contribution n=0 shell: Λ pole n=1 shell: Λ(1670)S01 , Λ(1405) S01 Λ(1520)D03, Λ(1690) D03 XH Zhong and Q Zhao, PRC79,045202(09); PRC88,015208(13)

2) Results:differential cross section

2) Results: polarizations

2) Results: cross section

conclusion dominant resonance: Λ(1405) S01 ,Λ(1520)D03 obvious evidences: Λ(1670) S01 ,Λ(1690)D03 configuration mixings:Λ(1405) S01 , Λ(1670) S01

D. Kp Λπ 1) Resonance contribution P wave: Σ(1193),Σ(1385) S wave: [70,210]S11? , [70,28]S11? , [70,48]S11 ? D wave: [70,210]D13 ?, [70,28]D13 ?, [70,48]D13?, [70,48]D15

2) Results:differential cross section

2) Results: polarizations

2) Results: cross section

conclusion dominant contributors: u and t backgrounds and Σ(1385) P13 obvious evidences: Σ(1750) [70,48]S11 , Σ(1775) [70,48]D15

Part II: strong decays of hadrons The strong decays of hadrons is sensitive to their structures, thus, study their decay properties is useful to classify the hadrons, especially to the new found hadrons at Belle, Babar,...

I. Charmed baryon strong decays New charmed baryons: Λc(2880,2940,2765), Σc(2800) , Ξc(2980,3055,3080,3123)… How to classify these states? XH Zhong and Q Zhao, PRD77,074008(08) LH Liu, LY Xiao, XH Zhong,PRD77,034024(12)

1) spectroscopy in the quark model The SU(3)f symmetry is broken by the heavy quark. How to classify the heavy baryons, we can see series papers of Isgur et al.

Λc spectroscopy

Σc spectroscopy

Ξc spectroscopy

2) Strong decay amplitudes

3) Λc,Σc baryons

Λc(2880) observed in Λcππ[PRL86,4479 (01) ,CLEO], Σcπ,Σ*cπ[PRL98,262001(07)Belle],Dp[PRL98,012001(07)BaBar]

Λc(2880) as the possible states Seems to favor a JP=3/2+ state

Λc(2940) observed in Dp [PRL98, 012001(07) BaBar] ;Σcπ,Σ*cπ [PRL98, 262001 (07) Belle]

Λc(2940) as the possible states Seems to favor a JP=5/2+ state

Λc(2765) Observed inΛcππ,resonated through Σcπ&Σc(2520) π(PRL86,4479 (01) CLEO) Γ≈ 50 MeV

Λc(2765) is possible a Pρ mode Λc excite state, according to the mass in the quark model prediction If Σcπdominates the decay, it seems to favor a JP=1/2- state.

Σc(2800) Observed in the Λc πchannel. PRL94,122002(05)[Belle]

Σc(2800) Seems to favor a JP=1/2- state, JP=5/2- can not be excluded

4) Charm-strange baryon Newly observed charmed strange baryons

Results for well-established states

Ξc(2980/2970) observed in ΛcKπ[PRL97,162001 (06) ,Belle; PRD77,012002(08)]. M=2980 MeV, Γ=45 MeV M=2970 MeV, Γ=27 MeV observed in Ξc(2645)π [PLB665,9(08) Belle] M=2970 MeV, Γ=18 MeV The same state or two different state?

Two cases are possible! One state: Ξc(2980) might be the JP=1/2- state! Two states: Ξc(2980/2970) might be the JP=1/2- and 3/2- states, respectively!

Ξc(3080) observed in ΛcKπ[PRL97,162001 (06) ,Belle]. M=3077 MeV, Γ=6.2 MeV observed in ΛcKπ, Σc(2455,2520)K [PRD77,012002(08),BaBar] M=3077 MeV, Γ=5.5 MeV

Ξc(3080) might be the 2S state with JP=1/2+

Other prediction

5) conclusions Λc(2880) andΛc(2940) maybe favor JP=3/2+ and Jp=5/2+, respectively. Λc(2765) maybe favor a P-wave ρ-mode excited states with JP=1/2-, the other possibilities can not be excluded. Σc(2800) maybe favor a JP=1/2- state, JP=5/2- can not be excluded. Ξc(2980/2970) maybe favor a JP=1/2- state, two sate case can not be excluded. Ξc(3080) favors the 2S ρ-mode excited states with JP=1/2+

II. Heavy-light meson strong decays New heavy-light mesons: Ds(2860), Ds (2700), B1(5725) ,B*2(5740), Bs1(5829), B(5970) Bs2(5840), D(2550), D(2600), D(2750,2760) Undetermined mesons (old): D(2640), Ds(2632)… Can find other new heavy mesons? S L Zhu (group); Z. Y. Zhang(group); P N Shen, F K Guo, et al.

1) The heavy-light meson spectroscopy flavor symmetry is broken, no longer the charge conjugation eigenstates XH Zhong and Q Zhao, PRD78,014029(08); 81,014031(10). XH Zhong, PRD82,114014(10) LY Xiao and XH Zhong, PRD90,074029(14)

D and Ds mesons

B and Bs mesons

2) Strong decay amplitudes

3) Decay widths

Results for well established shates Mixed states:

Mixed states for P waves The broad state should have larger mass, which is in agreement with the PDG

23S1-13D1 mixing D(2600) favors the low-mass mixed state |SD>L! Its high-mass partner is a broad state.

23S1-13D1 mixing Ds(2710) favors the low-mass mixed state |SD>L! Its higher mass partner might be Ds1(2850)!

13D2 -11D2 mixing D(2750) favors the high-mass mixed state |D2>H! Its low-mass partner might be broad!

13D2 -11D2 mixing The high-mass mixed state Ds(|D2>H) with JP=2- might have been observed around 2.86 GeV.

3D3-wave state D(2760) D(2760) favors 3D3-wave state!

3D3-wave state 3D3-wave state DS3(2860) DS3(2860) favors 3D3-wave state!

DS(3040) DS(3040) favors the Low-mass mixed state |P1>L!

D (3000) is the partner of Ds(3040) observed in D*π[JHEP09,145 (13) ,LHCb]. M=2972 MeV, Γ=188 MeV

B (5970) as the 3D3 state observed in Bπ[PRD90,012013 (14) ,CDF]. M=5970 MeV , Γ=70 MeV

4) conclusion D(2600), Ds(2710): a SD mixing state D(2760), Ds3(2860), B(5970): 13D3 state D(2750): 1D2-3D2 mixing state, Ds2(2860): observed a partner of D(2750)? Ds1(2850): a SD mixing state, the partner of Ds(2710) Ds(3040): 1P1-3P1 mixing state D(3000): 1P1-3P1 mixing state, the partner of Ds(3040) We can find more heavy-light mesons in future.

Thanks!