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Hidden local symmetry and infinite tower of vector mesons for baryons

Hidden local symmetry and infinite tower of vector mesons for baryons. Yang, Ghil-Seok ( 梁 吉錫 ) . Department of Physics & CHEP ( C enter for H igh E nergy P hysics) Kyungpook Nat'l University.

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Hidden local symmetry and infinite tower of vector mesons for baryons

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  1. Hidden local symmetry and infinite tower of vector mesons for baryons Yang, Ghil-Seok (梁 吉錫) Department of Physics & CHEP (Center for High Energy Physics) Kyungpook Nat'l University Recent progress in hadron physics -From hadrons to quark and gluon- 2013 (Feb. 18-22, Yonsei Univ.)

  2. incollaboration withYongseok Oh (Kyungpook Nat’l Univ.) Yong-Liang Ma (Nagoya Univ., Japan) Masayasu Harada (Nagoya Univ., Japan) Hyun Kyu Lee (Hanyang Univ.) Byung-Yoon Park (Chungnam Nat’l Univ.) Mannque Rho (CEA Saclay, France & Hanyang Univ.)

  3. Outline • Motivation & Soliton Picture / Vector mesons • HLS Lagrangian up to O(p4) • Soliton mass & ΔM= mΔ– mN • Results : Three models • HLS(π, ρ, ω) model • HLS(π, ρ) model • HLS(π) model • Summary References: Y.-L. Ma, Y. Oh, G.-S. Yang, M. Harada, H.K. Lee, B.-Y. Park, M. Rho, “Hidden local symmetry and infinite tower of vector mesons for baryons”, Phys.Rev.D86, 074025 (2012) [arXiv:1206.5460] Y.-L. Ma, G.-S. Yang, Y. Oh, M. Harada, “Skyrmions with vector mesons in the hidden local symmetry approach”, Phys.Rev.D 87, 034023 (2013) [arXiv:1209.3554]

  4. Motivation & SolitonPicture • Dense baryonic matter • Studies for nucleon structure, compact stars, and so on • Possible approach • With a chiral Lagrangian, unify both elementary baryons and multi-baryons system *Skyrme model : (Skyrmion) (multi-Skyrmions) Brown, Rho, “The Multifaceted Skyrmions” (Book) H.-J.Lee, B.-Y.Park, D.-P.Min, M.Rho, and V.Vento, Nucl.Phys.A723,427(2003) - single baryon is generated as a Skyrmion - multi-Skyrmions can be put on the crystal lattice to simulate many-body system and dense matter

  5. Skyrme model 1960s: T.H.R. Skyrme Baryons are topological solitons within a nonlinear theory of pions. T.H.R. Skyrme: Proc. Roy. Soc. (London) 260, 127 (1961), Nucl. Phys. 31, 556 (1962)

  6. Skyrme(1961) • Baryons are solitons in the non-linear sigma model • ‘t Hooft (1974) • In large-Nc limit, QCD becomes equivalent to EFT of mesons • Witten (1979) • Baryons may emerge as solitons in large-Nctheory of mesons Hedgehog solution

  7. To give correct quantum numbers • SUf(2) collective coordinate quantization & Mass formulae • Mass formulae : infinite tower of I =J ΔM= mΔ– mN Adjust fπand e to reproduce the nucleon and Delta masses fπ = 64.5 MeV, e = 5.45 Empirically, fπ= 93 MeV, e = 5.85(?)

  8. Best-fitted results from Skyrme model G.S. Adkins, C.R. Nappi, and E. Witten, Nucl. Phys. B228, 552 (1983) A.D. Jackson and M. Rho, Phys. Rev. Lett. 51, 751 (1983)

  9. Skyrme model for Nuclear Physics single baryon nuclear matter • Improvement of the model • more degrees of freedom • (mesons) • 1/Nc corrections • … • Topics • Properties of single baryon • Equation of state • Phase transition • Application to nucleus Hidden Local Symmetry(HLS) As energy scale goes up, infinite number of local symmetries appear HLS: corresponding gauge fields → infinite vector & axial-vector mesons

  10. Why vector mesons ? • Witten: QCD ~ weakly interacting mesons in large Nc • The lightest meson is π. • The next low-lying mesons are vector mesons (ρ, ω). • Stability of the soliton • Without the Skyrme term, the soliton collapses [Derrick’s theorem] • However, vector mesons can stabilize the solitonwithout the Skyrme term • Skyrmions with HLS and hQCD • - ρ meson stabilized model : Igarashi et al.(1985) • - ρand ω mesons stabilized model : Meissner, Kaiser, Weise(1987) • - ρ, ω and a1 mesons stabilized model : Kaiser, Meissner(1990), Zhang, Mukhopadhyay(1994) • - hQCD : Y. Kim / D.K.Hong, M.Rho, H.-U.Yee, and P.Yi (2007) • - O(p4) : Tanabashi (1993), Harada, Yamawaki (hQCD, 2003), Nawa, Suganuma, Hosaka, Kojo (2007,2009) Skyrme term

  11. Early Attempts to include VM

  12. Early Attempts : Results

  13. Status of the Skyrme model with HLS • - Hidden Local Symmetry (HLS) free parameter: a dependence • normally taken as (hadronic medium) 1≤ a ≤2 (free space) • Ex) Msol within a ρ-meson stabilized model • (Igarashi et al, Nucl.Phys.B259,1985) : • Msol= (667~1575)MeV for 1≤ a ≤4, • Msol= 1045MeV for a =2 • → ambiguity of the value ofaresults in • a large uncertainty of the soliton mass mρ2= ag2 fπ2

  14. - Difficulties for systematic studies from higher order terms 1) In HLS, higher order terms such as O(p4) are at O(Nc) like the O(p2) terms 2) More complicated form of the Lagrangian due to the higher order terms 3) Uncontrollably large number of low energy constants Ex) 6 anomalous terms of the ω mesons at O(p2), 14 anomalous terms for the axial vector mesons at O(p2) In this work, 1. Introduce holographic QCD (hQCD) : Integrating out of the tower of vector mesons except ρ, ω → O (p4) with ρ and ω mesons 2. All LECs are fixed by only two phenomenological inputs in hQCD 3. Skyrmion properties and roles of vector mesons

  15. HLS Lagrangianup to O(p4) homogenous Wess-Zumino term (ω) where where 17 parameters !

  16. Solitonmass in HLS up to O(p4)

  17. 17 parameters ! but they can be fixed by using two values (fπ, mρ) • hQCD models • SS (Sakai-Sugimoto) model • BPS (Bogomol’nyi-Prasad-Sommerfeld) model • Merit of this work: • Precise set of parameter-free calculation • that have not been done previously in the field. • (first complete and parameter-free soliton cal. • with vector mesons up to O(p4) ) Low energy constants of the HLS Lagrangianat O(p4) with a=2

  18. Comparison with SkyrmeL Original SkyrmeL effective Skyrme parameter e=5.45 After integrating out VM in HLS e=7.31 : SS model e=10.02 : BPS model Since I ~ 1/e3, large e → small I → large ΔM= mΔ- mN

  19. Results : Three Models • HLS(π, ρ, ω) model • : full O(p4) Lagrangian with hWZ terms • HLS(π, ρ) model • : without hWZ terms, the ω meson decouples • HLS(π) model • : integrates out VMs • same as the LSkyrme but e is fixed by the HLS

  20. Comparison of the three models Msol≈1184 MeV, (emp.: 867 MeV) ΔM= mΔ- mN≈ 448 MeV, (emp.: 292 MeV) in HLS(π, ρ, ω) model : improved Msolthan “minimal model” of HLS up to O(p2) ρ meson : shrink the soliton wave function (Msol↘ ) ω meson : expand the soliton wave function (Msol↗) * ω interacts with other mesons through hWZ terms

  21. Skyrmion mass and size calculated in the HLS with the SS and BPS models The role of the ρ and ω in ΔM is opposite to the case of Msol Without ω meson, ΔMof O(1/Nc) >Msolof O(Nc)

  22. a independence of the Skyrme properties

  23. Summary • Thefirst step in series of studies made to arrive at a description of dense baryonic matterrelevant for the physics of nuclear structure or compact star in unified scheme in which both single baryon and multi-baryon are treated on the same footing. (The first complete and parameter-free soliton calculation with VMs up to O(p4) ) • The role of ρ meson • reduction of the soliton mass: from 922 MeV to 834 MeV • increase of the Δ-N mass difference: from 1014 MeV to 1707 MeV • shrink the soliton profile: from 0.417 fm to0.371 fm • The role of ω meson • increase of the soliton mass: from 834 MeV to 1184 MeV • decrease of the Δ-N mass difference: from 1707 MeV to 448 MeV • expand the soliton profile: from 0.371 fm to 0.608 fm • Without ωmeson • ΔMof O(1/Nc) >Msolof O(Nc) • The independence of a • Direct consequence from hQCD

  24. Theoretical Nuclear and Hadron Physics Department of Physics Kyungpook National University Prof. Yongseok Oh & visiting Prof. Kochelev Hiroaki Kohyama: Dimensional regularization in NJL model (Inagaki, Kimura @ Hiroshima) Ghil-Seok Yang : Nuclear structure by shell model & Hypernuclei by EFT (Otsuka@CNS, Suzuki@Hihon & Ando@Daegu) MyunghwanMun: Nuclear fission/fusion for SHEs (YM Kim@RISP, Antonenko@BLTP) Hana Gil : Hypernuclei (Hiyama@RIKEN) Two freshmen for master course

  25. Theoretical Nuclear and Hadron Physics Department of Physics Kyungpook National University Prof. Yongseok Oh & visiting Prof. Kochelev Hiroaki Kohyama: Dimensional regularization in NJL model (Inagaki, Kimura @ Hiroshima) Ghil-Seok Yang : Nuclear structure by shell model & Hypernuclei by EFT (Otsuka@CNS, Suzuki@Hihon & Ando@Daegu) MyunghwanMun: Nuclear fission/fusion for SHEs (YM Kim@RISP, Antonenko@BLTP) Hana Gil : Hypernuclei (Hiyama@RIKEN) Two freshmen for master course

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