PowerPoint
Hidden local symmetry and infinite tower of vector mesons for
baryonsYang, Ghil-Seok( ) Recent progress in hadron physics -From
hadrons to quark and gluon- 2013 (Feb. 18-22, Yonsei Univ.)
Department of Physics&CHEP (Center for High Energy Physics)
Kyungpook Nat'l University in collaboration with Yongseok Oh
(Kyungpook Natl Univ.) Yong-Liang Ma (Nagoya Univ., Japan) Masayasu
Harada (Nagoya Univ., Japan) Hyun Kyu Lee (Hanyang Univ.)
Byung-Yoon Park (Chungnam Natl Univ.) Mannque Rho (CEA Saclay,
France & Hanyang Univ.)
Motivation & Soliton Picture / Vector mesons
HLS Lagrangian up to O(p4) Soliton mass & M = m mN
Results : Three modelsHLS(, , ) modelHLS(, ) modelHLS()
model
Summary
OutlineReferences: 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.D 86, 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]3Motivation & Soliton PictureDense
baryonic matter Studies for nucleon structure, compact stars, and
so onPossible 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
matterSkyrme model1960s: 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)
Skyrme (1961) Baryons are solitons in the non-linear sigma model
t Hooft (1974) In large-Nc limit, QCD becomes equivalent to EFT of
mesonsWitten (1979) Baryons may emerge as solitons in large-Nc
theory of mesons
Hedgehog solutionSUf(2) collective coordinate quantization &
Mass formulae
M = m mN To give correct quantum numbersMass formulae : infinite
tower of I =JAdjust f and e to reproduce the nucleon and Delta
masses
f = 64.5 MeV, e = 5.45Empirically, f = 93 MeV, e = 5.85(?)
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)Best-fitted results from Skyrme model Hidden Local
Symmetry(HLS) As energy scale goes up, infinite number of local
symmetries appear HLS: corresponding gauge fields infinite vector
& axial-vector mesons
Skyrme model for Nuclear Physicssingle baryonnuclear
matterImprovement of the modelmore degrees of freedom (mesons)1/Nc
correctionsTopicsProperties of single baryonEquation of statePhase
transitionApplication to nucleus Why vector mesons ?Witten: QCD ~
weakly interacting mesons in large Nc The lightest meson is . The
next low-lying mesons are vector mesons (, ).
Stability of the soliton
Without the Skyrme term, the soliton collapses [Derricks
theorem] However, vector mesons can stabilize the soliton without
the Skyrme term
Skyrmions with HLS and hQCD - meson stabilized model : Igarashi
et al.(1985) - and mesons stabilized model : Meissner, Kaiser,
Weise(1987) - , 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 termEarly Attempts to include VM
Early Attempts : Results
m2= a g 2 f 2Status 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 -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 of a results in a large uncertainty of the soliton mass
In this work, 1. Introduce holographic QCD (hQCD) : Integrating
out of the tower of vector mesons except , O (p4) with and mesons2.
All LECs are fixed by only two phenomenological inputs in hQCD3.
Skyrmion properties and roles of vector mesons - 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 mesons at O(p2), 14 anomalous terms for the axial
vector mesons at O(p2) HLS Lagrangian up to O(p4)
where
wherehomogenous Wess-Zumino term ()17 parameters !Soliton mass
in HLS up to O(p4)
Low energy constants of the HLS Lagrangian at O(p4) with a=2hQCD
modelsSS (Sakai-Sugimoto) modelBPS (Bogomolnyi-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)
)
17 parameters ! but they can be fixed by using two values (f, m)
Comparison with Skyrme LOriginal Skyrme LAfter integrating out VM
in HLS
e=5.45
e=7.31 : SS modele=10.02 : BPS modelSince I ~ 1/e3, large e
small I large M = m - mN effective Skyrme parameterResults : Three
ModelsHLS(, , ) model : full O(p4) Lagrangian with hWZ terms HLS(,
) model : without hWZ terms, the meson decouples
HLS() model : integrates out VMs same as the LSkyrme but e is
fixed by the HLSComparison of the three models
meson : shrink the soliton wave function (Msol ) meson : expand
the soliton wave function (Msol ) * interacts with other mesons
through hWZ terms Msol 1184 MeV, (emp.: 867 MeV)M = m - mN 448 MeV,
(emp.: 292 MeV) in HLS(, , ) model : improved Msol than minimal
model of HLS up to O(p2) Skyrmion mass and size calculated in the
HLS with the SS and BPS modelsinclusion ofMsolM WEThe role of the
and in M is opposite to the case of Msol
Without meson, M of O(1/Nc) > Msol of O(Nc)
a independence of the Skyrme propertiesSummaryThe first step in
series of studies made to arrive at a description of dense baryonic
matter relevant 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 mesonreduction of the soliton mass: from 922 MeV to
834 MeVincrease of the -N mass difference: from 1014 MeV to 1707
MeVshrink the soliton profile: from 0.417 fm to 0.371 fm
The role of meson increase of the soliton mass: from 834 MeV to
1184 MeVdecrease of the -N mass difference: from 1707 MeV to 448
MeVexpand the soliton profile: from 0.371 fm to 0.608 fm
Without mesonM of O(1/Nc) > Msol of O(Nc)
The independence of aDirect consequence from hQCDTheoretical
Nuclear and Hadron PhysicsDepartment of PhysicsKyungpook National
UniversityProf. Yongseok Oh & visiting Prof. KochelevHiroaki
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) Myunghwan Mun : Nuclear fission/fusion for SHEs (YM
Kim@RISP, Antonenko@BLTP) Hana Gil : Hypernuclei (Hiyama@RIKEN) Two
freshmen for master courseTheoretical Nuclear and Hadron
PhysicsDepartment of PhysicsKyungpook National UniversityProf.
Yongseok Oh & visiting Prof. KochelevHiroaki 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)
Myunghwan Mun : Nuclear fission/fusion for SHEs (YM Kim@RISP,
Antonenko@BLTP) Hana Gil : Hypernuclei (Hiyama@RIKEN) Two freshmen
for master course