Hyperfine Structure of Ground-State Nucleon in Chiral Quark Model Duojie Northwest Normal University The 7th International Symposium on Chiral Symmetry in Hadrons and Nuclei (Behang Univ. Beijing,Sept.,27-30,Oct ) 1 Suported partially by NNSF of China (No ) NNSF of China (No ) Collaborated with RuiBin Wan, WenBo Dang, YuBin Dong; Thanks for discussions with A. Jarah, J. He, X. Liu

Outline 2 Motivation Quark masses in QCD and models Mass role and pion role in models Chromo-magnetic interaction in ChQM Hyperfine splitting of nucleon spectrums Summary

QCD is very different at long and short distances ( ＜ Λ QCD ): q Condensing or melting, depending the scale(momentum) at which you see it! Motivation In explaining neclear force and hadron structures, QCD is still challenging due to its complex nonpertubative nature ： （ 1 ） gluon/quark condensate vacuum （ 2 ） absence of confining dimension (by itself) （ 3 ） Complicated phases Condensate QCD vacuum Jan. 8, Condensate Homogeneous at long distance Inhomogeneo us at short distance

Motivation QCD(continuum): Nontrivial vacuum, Lack of unified degrees of freedom at long and short distances( ＜ Λ QCD ) ; Few parameters : m i (current masses) ; g  (quark-gluon coupling) : running; μ (energy scale ) 4 Hard to model the hadrons Besides Lattice QCD, ChPT, with appro. global symmetry (ChSymmetry) of QCD, and spontaneously broken, gives the pion-octet pseudoscalar(pseudo-Nambu- Goldstone), a Chiral Lagrangian (pion octet +other SU(3) V hadron multiplets ) Compute hadron observables at low E fix the light quark masses by extraploting Lattice QCD

Motivation First-principle QCD(Lattice): The parameters : m i (current masses) ; g  (quark-gluon coupling) : running a (the lattice spacing ) 5 What does a quark mass mean when free quarks don’t exist? adjust the bare quark masses in doing a lattice calculation to match physical hadron properties. For the continuum limit, the bare quark masses flow along the renormalization group, ---- extract a renormalized quark mass (asymptotic freedom + a renormalization scheme). In real world, isospin broken by the non-degeneracy of u and d, and by electromagnetism, both comparable order to the hadron spectrumts: u d - The light quark masses, important parameter for hadron physics and nuclear physics, -is of interest to determine them, and to see their effects

Quark masses in QCD and models Lattice prediciton: m ud =3.5MeV,ms=95MeV [Budapest–Marseille–Wuppertal Collaboration / PLB 701 (2011) 265–268] The precision below 2% level; ms/mud = 27.53(20)(08), which is scheme independent( better than 1%).

Quark masses in QCD and models Quark models use the concept of constituent mass, not well-defined in QCD, model- dependent. It used in Chiral quark model(ChQM). [A.Manohar, H. Georgi, NPB234(1984)189] may come from chiral rotation [ P. Simic, PRL. 55, ] Quark mass varys, depending on models For nonrelativistic QM(NRp), m u =m d = ,m s =0.5GeV For RQM, quite smaller, e.g.PChQM, m u =m d =7MeV,m s =175MeV bag model : m u =m d ～ 0,ms=300MeV

Quark masses in bag models In the bag model, With degrees of freedom (quark, gluon): Masses: m ud =0; m s =0.3GeV

Mass role and pion role in models Quark current Diag-gluon The pion(NG particles) enters as requiring local Ch.Symmetry In the effective field theory of Quark-meson ----Chiral rotation

Why QM works? Mahohar-Georgi model in ChQT: 2 scales occurs(2 phases) (250MeV) Λ QCD ＜ Q ＜ Λ χ (1GeV), Confining Mixing Free Strong coupling (  s ) weak due to the presence of constituent mass 10 Constitiuent quark Constituent Mass(soft mass), corresponding to CS breaking. Gluons M invarinat under chiral SU(3) L ×SU(3) R Non-renormalizable terms suppressed by

Quark mass role in Baryons The simplest fit for baryon masses: 11 Fine fit, so why RQM? (1) More constraints on models(including ChSymmetry) (2) Less parameters for spin-interaction The NRp estimate for baryon masses:[ PRD12(1975)147 ] m u =363 m s =583 m u =300 m P = % Smaller

Quark mass in bag pictures The MIT bag-RQM, degrees (quark and/or gluons), Confinement put in by Bag boundary condition/effective mass 12 m0m0 Mass scale 300MeV2-5MeV The consititent mass( ～ 1/R) mainly from BC while the current mass contributes a few MeV: A mechanism for mass splitting

The MIT bag prediction with chromo- electric and magnetic interation: 13 Reasonable except for pion m ud =0 Allowed mass splitting for nucleons: 1)Kinetic energy splitting i=u,d,s 2) Chromo-magnetic splitting ( i,j=u,d,s ) Mass splitting in bag pictures Data:Δm ud =2.5MeV, Δm su =100MeV When mq changes so do the kinetic and chromo-magnetic energies slightly.

Mass role in ChQM The consti. mass varying Δm i and the EM effects breaks the flavor SU(3) mainly; The mass varying dominates for p-n spliting, in ground states 14 a=0.3/0.2;L=0.75/0.2; M=0.3;S0=0;kappa=-1; d=1.0;alpha0=0.8; Vc

Chromo-magnetic interaction in ChQM The plot of effective mass for n 15 The chromo-magnetic interaction is similar to that of bag models The mass-term [m i +S(r)U 5 ] contributes to (1)Confinement through the S-potential (2)Quark wavefuntion and pion configurations (3) Magnetic moment via quark magnetic moment; (4) Hadron mass and its splitting

Chromo-magnetic interaction in ChQM The radial Eq. of Motion of a quark: With Y determined by Y equations 16 The Y profile determined by a dynamics, eg., the Coupled Skyme lagrangian here, it can be set by comparing with ChPT

Quark configuration in ChQM Length scale L=3.75GeV -1

Chromo-magnetic interaction in ChQM D. Jia, L.Yu,R. Wan, arXiv: v1

Hyperfine splitting in nucleon masses ⊿ m (MeV) u/d mass / / / / / /312.0

Hyperfine splitting in nucleon masses The CSB explained by NJL model, with quark pair condensation The lator is fixed by the gap equation 20 m d (MeV) ΔM=M n -M p (MeV) m u = =md

Summary The hyperfine structure of ground-state nucleon is studied in chiral quark model with nonlinear pion interaction in which quarks move in the potential of Coulomb-like plus linear form. The mass splitting of ground-state nucleon is given by taking into account the colour magnetic interaction between quarks and found to be in agreement with data. The connection of the model with the bag models is discussed 21 Thanks !!!