Tcc and double charm production

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Presentation transcript:

Tcc and double charm production arXiv:1209.6207 [hep-ph] Shigehiro Yasui (KEK, IPNS) Hyodo Tetsuo (Tokyo Tech.) Yan-Rui Liu (Tokyo Tech./Shandong U.) Makoto Oka (Tokyo Tech.) Kazutaka Sudoh (Nishogakusha U.) International Workshop on using Heavy Flavors to Probe New Hadron Spectroscopies/Dynamics @Haeundae Grand Hotel, Busan, 18-21 Nov. 2012

Contents 1. What’s doubly charmed exotic meson Tcc? – Mass spectroscopy 2. Tcc production in e+e- collisions 3. Summary & perspectives

1. Doubly charmed mesons (Tcc) Tetraquark Tcc1 Flavor Exotic Lee, SY, Liu and Ko (2008) Lee and SY (2009) ✓ no annihilation Tcc1 Important for study of quark-quark correlation color confinement c d u I(JP)=0(1+) strong ud attraction Gluon exchange force induces color-spin interaction ud pair 1/mC0 dominant attraction (3c, I=0, 1S0) cu pair 1/mC1 suppressed cc pair 1/mC2 more suppressed

1. Doubly charmed mesons (Tcc) Tetraquark Tcc1 Flavor Exotic Lee, SY, Liu and Ko (2008) Lee and SY (2009) ✓ no annihilation Tcc1 c d u Tcc is double charm |C|=2. cf. X(3872) is |C|=0. I(JP)=0(1+) strong ud attraction Gluon exchange force induces color-spin interaction ud pair 1/mC0 dominant attraction (3c, I=0, 1S0) cu pair 1/mC1 suppressed cc pair 1/mC2 more suppressed

1. Doubly charmed mesons (Tcc) Doubly charmed compact tetraquark I(JP)=0(1+) ・ J. P. Ader, J. M. Richard and P. Taxil, Phys. Rev. D 25, 2370 (1982). ・ S. Zouzou, B. Silvestre-Brac, C. Gignoux, J. M. Richard, Z. Phys. C30, 457 (1986). ・ H. J. Lipkin, Phys. Lett. B 172, 242 (1986). ・ L. Heller and J. A. Tjon, Phys. Rev. D 35, 969 (1987). ・ J. Carlson, L. Heller, J. A. Tjon, Phys. Rev. D37, 744 (1988). ・ B. Silvestre-Brac and C. Semay, Z. Phys. C 57, 273 (1993). ・ B. Silvestre-Brac and C. Semay, Z. Phys. C 59, 457 (1993). ・ C. Semay, B. Silvestre-Brac, Z. Phys. C61, 271-275 (1994). ・ S. Pepin, F. Stancu, M. Genovese and J. M. Richard, Phys. Lett. B 393, 119 (1997). ・ J. Schaffner-Bielich and A. P. Vischer, Phys. Rev. D 57 4142 (1998). ・ D. M. Brink and F. Stancu, Phys. Rev. D 57, 6778 (1998). ・ D. Janc and M. Rosina, Few Body Syst. 35, 175 (2004). ・ N. Barnea, J. Vijande, A. Valcarce, Phys. Rev. D73, 054004 (2006). ・ J. Vijande, E. Weissman, N. Barnea and A. Valcarce, Phys. Rev. D 76, 094022 (2007). ・ J. Vijande, E. Weissman, A. Valcarce, N. Barnea, Phys. Rev. D76, 094027 (2007). ・ J. Vijande, A. Valcarce and J. M. Richard, Phys. Rev. D 76, 114013 (2007). ・ D. Ebert, R. N. Faustov, V. O. Galkin and W. Lucha, Phys. Rev. D 76, 114015 (2007). ・ F. S. Navarra, M. Nielsen and S. H. Lee, Phys. Lett. B 649, 166 (2007). ・ M. Zhang, H. X. Zhang and Z. Y. Zhang, Commun. Theor. Phys. 50, 437 (2008). ・ S. H. Lee, S. Yasui, W. Liu, C. M. Ko, Eur. Phys. J. C54, 259-265 (2008). ← Diquark model ・ S. H. Lee, S. Yasui, Eur. Phys. J. C64, 283-295 (2009). ← Diquark model ・ Y. Yang, C. Deng, J. Ping and T. Goldman, Phys. Rev. D 80, 114023 (2009). ・ J. Vijande, A. Valcarce, N. Barnea, Phys. Rev. D79, 074010 (2009). ・ T. F. Carames, A. Valcarce and J. Vijande, Phys. Lett. B 699, 291 (2011). ・ J. Vijande, A. Valcarce and T. F. Carames, Few Body Syst. 50, 195 (2011). D(*)D(*) molecules with I(JP)=0(0-), 0(1+), 0(1-), 0(2+), 0(2-), 1(0-) ・ A. V. Manohar and M. B. Wise, Nucl. Phys. B 399 (1993) 17. ・ N. A. Tornqvist, Z. Phys. C 61, 525 (1994). ・ G. -J. Ding, J. -F. Liu and M. -L. Yan, Phys. Rev. D 79, 054005 (2009). ・ R. Molina, T. Branz and E. Oset, Phys. Rev. D 82, 014010 (2010). ・ S. Ohkoda, Y. Yamaguchi, S.Y., K. Sudoh, A. Hosaka, Phys. Rev. D86, 034019 (2012). ← Heavy Quark Symmetry + OPEP Lattice QCD (bottom) with I(JP)=0(0+) (?) ・ P. Bicudo, M. Wagner, arXiv:1209.6274 [hep-ph]. ・ Z. S. Brown, K. Orginos, arXiv:1210.1953 [hep-lat]. c d u Tetraquark Tcc1 Flavor Exotic Lee, SY, Liu and Ko (2008) Lee and SY (2009) ✓ no annihilation c d u Tcc1 I(JP)=0(1+) cc pair 1/mC2 ud pair 1/mC0 cu pair 1/mC1 Gluon exchange force induces color-spin interaction more suppressed dominant attraction (3c, I=0, 1S0) suppressed strong ud attraction D*- D0 ≈ 75 MeV (Binding energy) D* threshold (3880 MeV) D Stable bound state (weak decay only; D*Kπ) u c d +

1. Doubly charmed mesons (Tcc) Λc,Σc,Σc*(cqq) Tcc(ccqq) q=u,d,s cc qq flavor SU(3) qq flavor SU(3) Σc 1/2+ Σc* 3/2+ 0+ 1+ 2+ 3c(3S1) × 3c(3S1) 3c(3S1) “bad” diquark D*D* threshold color-spin interaction (fine mass-splitting) 200 MeV DD* threshold 75 MeV “good” diquark Tcc1 Λc 1/2+ 1+ × 3c(1S0) 3c(3S1) 3c(1S0)

1. Doubly charmed mesons (Tcc) Λc,Σc,Σc*(cqq) Tcc(ccqq) q=u,d,s cc qq flavor SU(3) × qq new!! 6c(1S0) 6c(1S0) flavor SU(3) 0+ Σc 1/2+ Σc* 3/2+ 0+ 1+ 2+ 3c(3S1) × 3c(3S1) 3c(3S1) “bad” diquark D*D* threshold × 1+ new!! 6c(1S0) 6c(3S1) color-spin interaction (fine mass-splitting) 200 MeV DD* threshold 75 MeV “good” diquark Tcc1 Λc 1/2+ 1+ × 3c(1S0) 3c(3S1) 3c(1S0)

1. Doubly charmed mesons (Tcc) Λc,Σc,Σc*(cqq) Tcc(ccqq) q=u,d,s cc 3c(1S0) 6c(3S1) 3c(3S1) 6c(1S0) 125 MeV 75 MeV 25 MeV 1+ 0+ 1+ 2+ 0+ qq flavor SU(3) × qq new!! 6c(1S0) flavor SU(3) Σc 1/2+ Σc* 3/2+ 3c(3S1) × 3c(3S1) “bad” diquark D*D* threshold × new!! 6c(1S0) color-spin interaction (fine mass-splitting) 200 MeV DD* threshold 75 MeV “good” diquark Tcc1 Λc 1/2+ × 3c(1S0) 3c(3S1)

1. Doubly charmed mesons (Tcc) Λc,Σc,Σc*(cqq) Tcc(ccqq) q=u,d,s cc 3c(1S0) 6c(3S1) 3c(3S1) 6c(1S0) 125 MeV 75 MeV 25 MeV 1+ 0+ 1+ 2+ 0+ qq flavor SU(3) × qq new!! 6c(1S0) flavor SU(3) Σc 1/2+ Σc* 3/2+ 3c(3S1) × 3c(3S1) “bad” diquark D*D* threshold × new!! 6c(1S0) color-spin interaction (fine mass-splitting) 200 MeV DD* threshold State mixing is suppressed by O(1/mc) in color-spin int. 75 MeV “good” diquark Tcc1 Λc 1/2+ × 3c(1S0) 3c(3S1)

1. Doubly charmed mesons (Tcc) Λc,Σc,Σc*(cqq) Tcc(ccqq) q=u,d,s cc 3c(1S0) 6c(3S1) 3c(3S1) 6c(1S0) 125 MeV 75 MeV 25 MeV 1+ 0+ 1+ 2+ 0+ qq flavor SU(3) × qq new!! 6c(1S0) flavor SU(3) Σc 1/2+ Σc* 3/2+ 3c(3S1) × 3c(3S1) “bad” diquark D*D* threshold × new!! 6c(1S0) color-spin interaction (fine mass-splitting) 200 MeV Tcc1 [6c] DD* threshold State mixing is suppressed by O(1/mc) in color-spin int. 75 MeV “good” diquark Tcc1 [3cbar] Tcc1 Λc 1/2+ × 3c(1S0) 3c(3S1)

Question to be addressed What is the production of Tcc1 [3cbar] and Tcc1 [6c] from e+e- collisions in Belle? Tcc1 [3cbar] ??? Tcc1 [6c] ??? cc e+ e- X (unobserved for cbarcbar) Cf. double charm production (cccbarcbar) in e+e- collisions (Belle, Phys. Rev. Lett. 89, 142001 (2002))

2. Tcc production in e+e- collisions L.O. p/2 inclusive process c Tcc1 [3cbar] or Tcc1 [6c] Tcc e- c g γ* c p/2 + (p3 ←→ p4) √ s p4 e+ cbar p3 (unobserved) cbar Factorization (Ansatz) short distance long distance h3 for [cc]3cbar(3S1) in Tcc1 [3cbar] h6 for [cc]6c(1S0) in Tcc1 [6c] unknown parameter: based on NRQCD formalism Cf. Bodwin, Braaten Lepage, PRD51, 1125 (1995)

+ 2. Tcc production in e+e- collisions p p/2 c Tcc e- γ* c p/2 g L.O. p/2 inclusive process c Tcc1 [3cbar] or Tcc1 [6c] Tcc e- γ* c + p/2 g + (p3 ←→ p4) √ s p4 cbar e+ cbar p3 (unobserved) cbar Factorization (Ansatz) short distance long distance h3 for [cc]3cbar(3S1) in Tcc1 [3cbar] h6 for [cc]6c(1S0) in Tcc1 [6c] unknown parameter: based on NRQCD formalism Cf. Bodwin, Braaten Lepage, PRD51, 1125 (1995)

2. Tcc production in e+e- collisions p uk(p/2) p/2 Tcc1 [3cbar] or Tcc1 [6c] c Tcc e- Projection for Tcc1 [3cbar](3S1) c g uj(p/2) γ* c p/2 anti-symmetric √ s p4 Projection for Tcc1 [6c](1S0) cbar e+ symmetric p3 (unobserved) cbar

2. Tcc production in e+e- collisions Tcc1 [3cbar] or Tcc1 [6c] Θ p √s=10.6 GeV (Belle) mc=1.5 GeV αs=0.26 Numerical Results Tcc1 [3cbar] [1/GeV] Tcc1 [6c] Remark : independent of h3(6) value.

2. Tcc production in e+e- collisions Tcc1 [3cbar] or Tcc1 [6c] Θ p √s=10.6 GeV (Belle) mc=1.5 GeV αs=0.26 Numerical Results Tcc1 [3cbar] Different behavior for Tcc1 [3cbar] and Tcc1 [6c] ・ Peak position and height ・ Θ-dependence ・ Threshold behavior [1/GeV] Tcc1 [6c] Remark : independent of h3(6) value.

2. Tcc production in e+e- collisions Numerical Results Absolute value of the cross section σ ? → How to fix h3 for Tcc1 [3cbar] and h6 for Tcc1 [6c] ?

2. Tcc production in e+e- collisions Numerical Results Absolute value of the cross section σ ? → How to fix h3 for Tcc1 [3cbar] and h6 for Tcc1 [6c] ? Estimate by quark model (crude approximation) c u d Tcc1 [3cbar] Tcc1 [6c] H.O. potential Cf. Ξcc production based on NRQCD formalism ・ Ma, Si, Physics Letters B568, 135 (2003) ・ Jian, Wu, Liao, Zheng, Fang, arXiv:1208.3051 [hep-ph]

2. Tcc production in e+e- collisions Numerical Results Absolute value of the cross section σ ? → How to fix h3 for Tcc1 [3cbar] and h6 for Tcc1 [6c] ? Estimate by quark model (crude approximation) c u d Tcc1 [3cbar] ≈ 0.089 GeV3 Tcc1 [6c] H.O. potential Cf. Ξcc production based on NRQCD formalism ・ Ma, Si, Physics Letters B568, 135 (2003) ・ Jian, Wu, Liao, Zheng, Fang, arXiv:1208.3051 [hep-ph]

2. Tcc production in e+e- collisions Numerical Results Absolute value of the cross section σ ? → How to fix h3 for Tcc1 [3cbar] and h6 for Tcc1 [6c] ? Estimate by quark model (crude approximation) c u d Tcc1 [3cbar] σ = 129 fb almost same as Ξcc ≈ 0.089 GeV3 Tcc1 [6c] H.O. potential Cf. Ξcc production based on NRQCD formalism ・ Ma, Si, Physics Letters B568, 135 (2003) ・ Jian, Wu, Liao, Zheng, Fang, arXiv:1208.3051 [hep-ph]

2. Tcc production in e+e- collisions Numerical Results Absolute value of the cross section σ ? → How to fix h3 for Tcc1 [3cbar] and h6 for Tcc1 [6c] ? Estimate by quark model (crude approximation) u c Tcc1 [3cbar] σ = 129 fb almost same as Ξcc d c ≈ 0.089 GeV3 Tcc1 [6c] H.O. potential Cf. Ξcc production based on NRQCD formalism ・ Ma, Si, Physics Letters B568, 135 (2003) ・ Jian, Wu, Liao, Zheng, Fang, arXiv:1208.3051 [hep-ph]

2. Tcc production in e+e- collisions Numerical Results Absolute value of the cross section σ ? → How to fix h3 for Tcc1 [3cbar] and h6 for Tcc1 [6c] ? Estimate by quark model (crude approximation) u c Tcc1 [3cbar] σ = 129 fb almost same as Ξcc d c ≈ 0.089 GeV3 Tcc1 [6c] H.O. potential ≈ 0.053 GeV3 Cf. Ξcc production based on NRQCD formalism ・ Ma, Si, Physics Letters B568, 135 (2003) ・ Jian, Wu, Liao, Zheng, Fang, arXiv:1208.3051 [hep-ph]

2. Tcc production in e+e- collisions Numerical Results Absolute value of the cross section σ ? → How to fix h3 for Tcc1 [3cbar] and h6 for Tcc1 [6c] ? Estimate by quark model (crude approximation) u c Tcc1 [3cbar] σ = 129 fb almost same as Ξcc d c ≈ 0.089 GeV3 Tcc1 [6c] σ = 43 fb H.O. potential ≈ 0.053 GeV3 Cf. Ξcc production based on NRQCD formalism ・ Ma, Si, Physics Letters B568, 135 (2003) ・ Jian, Wu, Liao, Zheng, Fang, arXiv:1208.3051 [hep-ph]

2. Tcc production in e+e- collisions Numerical Results Absolute value of the cross section σ ? → How to fix h3 for Tcc1 [3cbar] and h6 for Tcc1 [6c] ? Estimate by quark model (crude approximation) u c Tcc1 [3cbar] σ = 129 fb almost same as Ξcc d Upper limit c ≈ 0.089 GeV3 Tcc1 [6c] σ = 43 fb H.O. potential ≈ 0.053 GeV3 Cf. Ξcc production based on NRQCD formalism ・ Ma, Si, Physics Letters B568, 135 (2003) ・ Jian, Wu, Liao, Zheng, Fang, arXiv:1208.3051 [hep-ph]

3. Summary and perspectives ・ Tcc1 [3cbar] and Tcc1 [6c] are flavor exotic doubly charmed tetraquarks. ・ We estimate the cross sections of Tcc1 [3cbar] and Tcc1 [6c] produced in e+e- collisions. ・ The cross sections of Tcc1 [3cbar] and Tcc1 [6c] have different momentum- and angle-dependence. → Experimental method to identify the color structure (3cbar, 6c) of a quark pair in exotic hadrons? ・ More studies should be required. - Rigorous discussion about applicability of NRQCD formalism - Higher order in velocity-expansion - Precise estimate of expectation value of long-distance operator - ...

Thank you !!

Appendix

A. Del Fabbro, D. Janc, M. Rosina, D. Treleani, PRD71, 014008 (2005)

JP=1+ JP=1+ Mixing of Tcc1 [3cbar] and Tcc1 [6c] is suppressed !! Remark Mixing of Tcc1 [3cbar] and Tcc1 [6c] is suppressed !! ubar [ubardbar]6cbar(3S1) [ubardbar]3c(1S0) dbar JP=1+ JP=1+ Tcc1 [6c] magnetic gluon Tcc1 [3cbar] c [cc]6c(1S0) [cc]3cbar(3S1) c suppressed by 1/mc Time Tcc1 [6c] will decay almost to DD* in s-wave.