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unquenched quark model for mesons

unquenched quark model for mesons. Jialun Ping Nanjing Normal university. Contents. Motivations Unquenched quark model for light mesons UQM for charmonium Summary. Motivations. Since 2003, a lot of new hadron states reported by Belle, BARBAR, BESIII, D0, CDF, LHCb , ……

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unquenched quark model for mesons

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  1. unquenched quark model for mesons Jialun Ping Nanjing Normal university MENU2019, Pittsburgh, 2019.6

  2. Contents • Motivations • Unquenched quark model for light mesons • UQM for charmonium • Summary MENU2019, Pittsburgh, 2019.6

  3. Motivations Since 2003, a lot of new hadron states reported by Belle, BARBAR, BESIII, D0, CDF, LHCb, …… They are difficult to be accommodated by quark models “exotic states” --------------- “XYZ” particles MENU2019, Pittsburgh, 2019.6

  4. Motivations The spectrum of bottomonium and bottomoniumlike mesons The spectrum of charmonium and charmoniumlike mesons S. L. Olsen, A new hadron spectroscopy,Front. Phys. 10 (2015) 101401 MENU2019, Pittsburgh, 2019.6

  5. XYZ particles (Rev. Mod. Phys. 90, 015004 (2018)) …… MENU2019, Pittsburgh, 2019.6

  6. Light systems exotic hadronic states: exotic quantum numbers • candidates (1400) PLB 657 (2007) 27-31 • (1600) PRL 104 (2010) 241803 • ,…… ； States cannot be described well: • for meson: • for baryon: missing states, N(1440), MENU2019, Pittsburgh, 2019.6

  7. Other exotic states (Rev. Mod. Phys. 90, 015004 (2018)) MENU2019, Pittsburgh, 2019.6

  8. XYZ particles MENU2019, Pittsburgh, 2019.6 : Ordinary Charmonium T. Barnes et al., Phys. Rev. D69, 054008 (2004) …… : *molecule. N.A. Tornqvist, Z. Phys. C61, 525(1994); arXiv:hep-ph/0308277 E.S. Swanson, Phys. Lett. B588, 189 )2004) …… : hadronic state mixing with * Yu. S. Kalashnikova, Phys. Rev. D72, 034010 (2005) P.G. Ortega, et al. Phys. Rev. D81, 054023 (2010) M. Cardoso, et al. Eur. J. Phys. C75, 26 (2015) ……

  9. Our work Unify the description of ordinary and exotic hadrons Unquenched quark model principle: valence quark model：a good approximation Calculating method: Gaussian expansion Method (GEM) Key problem: The transition operators: 3P0 operator MENU2019, Pittsburgh, 2019.6

  10. Quark model • 1964, Gell-Mann / Zweig: quark model / Ace model • 1964, discovery of Ω (1961, predicted) • open the gate for setting up of QCD • So far, the most successful phenomenological method • describing the experimental data • Ω, predicted, then discovered • d* (dibaryon), predicted, “discovered”

  11. The chiral quark model (ChQM) • The chiral quark model: The most used QM • describes properties of hadrons，hadron-hadron interactions well • In ChQM: • Confinement: confining potential (phenomenology) • Asmptotic freedom: one-gluon-exchange • Chiral symmetry spontaneous breaking: Goldstone exchange

  12. The central part of potential Color confinement + One gluon exchange + One boson exchange + Vσ J Vijande, F Fern´andez and A Valcarce, J. Phys. G 31 (2005) 481–506

  13. Gaussian Expansion Method 3 3 3 r1 r2 R1 R3 R2 2 2 2 r3 1 1 1 Basis functions of each Jacobi coordinate (c=1-3) ， Determined by diagonalizing H MENU2019, Pittsburgh, 2019.6

  14. Gaussian Expansion Method • Gaussian size parameters in geometric progression: Dense distribution in the short-range region ⇒ Short-range correlations Coherent superposition in the asymptotic region ⇒ Exponentially-damped tails • Infinitesimally-shifted Gaussian basis functions(ISG): E. HIYAMA,Progress in Particle and Nuclear Physics 51(2003) 223 -307 Radial part Gaussian function: MENU2019, Pittsburgh, 2019.6

  15. The Unquenched quark model (UQM) Meson Bayron q q q q q q q q Goal: We try to give an unified explanation about the ordinary and the exotica states. q q q q q q …… …… …… MENU2019, Pittsburgh, 2019.6 In the conventional quenched quark model: In the unquenched quark model:

  16. QM for meson: q MENU2019, Pittsburgh, 2019.6

  17. GEM and SHO E.Hiyama, Y. Kino and M. Kamimura, Progress in Particle and Nuclear Physics 51 (2003) 223 -307. The radial function of meson(1S, 2S, 3S state). The radial function of meson(1P, 2P, 3P state). MENU2019, Pittsburgh, 2019.6

  18. Four-bodysystem: wavefunctions for two sub-clusters: Antisymmetric operator: The total function of four-quark: the eigenstates of the system is obtained by solving the Schrdinger equation: wavefunction (meson-meson configuration ): MENU2019, Pittsburgh, 2019.6

  19. q q q …… In unquenched quark model, ++ The matrix elements of Hamiltonian: |++|> <||> + <||> MENU2019, Pittsburgh, 2019.6

  20. = 0 MENU2019, Pittsburgh, 2019.6 Next, by solving eigenstate problem, we get eigen-energy and unknown coefficients

  21. The transition operator (QPC or 3P0 model) Fourier transformation || MENU2019, Pittsburgh, 2019.6

  22. The negative mass shifts are alarmingly large when considering the hadron-loop effects. MENU2019, Pittsburgh, 2019.6 Larger mass shifts are obtained with lighter quarks. For system, ~100MeV; Forsystem, ~800MeV; For system,~1500MeV; For system,~2500MeV.

  23. Improvement one MENU2019, Pittsburgh, 2019.6

  24. The first improvement: Where, Fourier transform Where, MENU2019, Pittsburgh, 2019.6

  25. Bare mass: =139.00MeV MENU2019, Pittsburgh, 2019.6

  26. Improvement Two MENU2019, Pittsburgh, 2019.6

  27. Hello, little V, don’t be far away from me! B OK! A V C MENU2019, Pittsburgh, 2019.6

  28. Improvement 2 MENU2019, Pittsburgh, 2019.6

  29. Improvement Three:Combined Effect MENU2019, Pittsburgh, 2019.6

  30. MENU2019, Pittsburgh, 2019.6

  31. :Bare mass MENU2019, Pittsburgh, 2019.6

  32. :Bare mass MENU2019, Pittsburgh, 2019.6

  33. :Bare mass MENU2019, Pittsburgh, 2019.6

  34. ƞ:Bare mass MENU2019, Pittsburgh, 2019.6

  35. Mass shifts should neither be too large nor too small MENU2019, Pittsburgh, 2019.6

  36. MENU2019, Pittsburgh, 2019.6

  37. Isospin symmetry In the isospin symmetric limit, they require 1、 should have same contribution to and 2、 should have same contribution toand 3、to = (1/3) to 4、ƞto = to MENU2019, Pittsburgh, 2019.6

  38. A: parameters un-changed, B: change a little MENU2019, Pittsburgh, 2019.6

  39. Fractions of two-quark and four-quark components PRD89, 094016 (2018) MENU2019, Pittsburgh, 2019.6

  40. UQM for charmonium MENU2019, Pittsburgh, 2019.6 Understand X(3872) in UQM --------our goal Three charmonia investigated. Check the validity of accumulating approach

  41. UQM for charmonium MENU2019, Pittsburgh, 2019.6 : ~94% : ~70%

  42. Summary 1、When developing the unquenched quark model, the quark-pair creation operator is crucial. 2、The operator T in the model needed to be modified to ensure the validity of the naive quark model. 3、The improvements introduced here work well for the ground state non-strange mesons and charmonium. 4、To give a uniform description about the ordinary mesons and the exotica are possible in UQM. Thank you for your attention ! MENU2019, Pittsburgh, 2019.6

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