Hyperfine Structure of GroundState Nucleon in Chiral Quark

Hyperfine Structure of Ground-State Nucleon in Chiral Quark Model Duojie JIA@Northwest Normal University Collaborated with Rui. Bin Wan, Wen. Bo Dang, Yu. Bin Dong; Thanks for discussions with A. Jarah, J. He, X. Liu Suported partially by NNSF of China (No. 10965005) NNSF of China (No. 11265014) The 7 th International Symposium on Chiral Symmetry in Hadrons and Nuclei (Behang Univ. Beijing, Sept. , 27 -30, Oct. 2013 )

Outline n n n Motivation Quark masses in QCD and models Mass role and pion role in models Chromo-magnetic interaction in Ch. QM Hyperfine splitting of nucleon spectrums Summary

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 n Condensate QCD vacuum QCD is very different at long and short distances ( ＜ ΛQCD): q Condensing or melting, depending the scale(momentum) at which you see it! Condensate Inhomogeneo us at short distance Homogeneous at long distance

Motivation QCD(continuum): Nontrivial vacuum, Lack of unified degrees of freedom at long and short distances(＜ ΛQCD) ; Few parameters : masses) ; g (quark-gluon coupling) : running; μ (energy scale ) mi(current Hard to model the hadrons Besides Lattice QCD, Ch. PT, with appro. global symmetry (Ch. Symmetry) 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 4

u Motivation d First-principle QCD(Lattice): The parameters : mi(current masses) ; g (quark-gluon coupling) : running a (the lattice spacing ) 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: -The light quark masses, important parameter for hadron physics and nuclear physics, -is of interest to determine them , and to see their effects 5

Quark masses in QCD and models Lattice prediciton: mud=3. 5 Me. V, ms=95 Me. V [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, modeldependent. It used in Chiral quark model(Ch. QM). [A. Manohar, H. Georgi, NPB 234(1984)189] may come from chiral rotation [P. Simic, PRL. 55, 40 --43 1985] Quark mass varys, depending on models n n For nonrelativistic QM(NRp), mu=md=0. 2 -0. 3, ms=0. 5 Ge. V For RQM, quite smaller, e. g. PCh. QM, mu=md=7 Me. V, ms=175 Me. V bag model : mu=md～ 0, ms=300 Me. V

Quark masses in bag models In the bag model, With degrees of freedom (quark, gluon): Masses: mud=0; ms=0. 3 Ge. V

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

Constituent Mass(soft mass), corresponding to CS breaking. Why QM works? Gluons Constitiuent quark n Mahohar-Georgi model in Ch. QT: n 2 scales occurs(2 phases) (250 Me. V)ΛQCD＜ Q ＜ Λχ (1 Ge. V), Confining Mixing Free Strong coupling (α s) weak due to the presence of constituent mass M invarinat under chiral SU(3) L×SU(3)R Non-renormalizable terms suppressed by 10

Quark mass role in Baryons The simplest fit for baryon masses: 1 -4% mu=363 ms=583 The NRp estimate for baryon masses: [PRD 12(1975)147] mu=300 m. P=336 Smaller Fine fit, so why RQM? (1) More constraints on models(including Ch. Symmetry) (2) Less parameters for spin-interaction 11

Quark mass in bag pictures n m 0 The MIT bag-RQM, degrees (quark and/or gluons), Confinement put in by Bag boundary condition/effective mass Mass scale 2 -5 Me. V 300 Me. V The consititent mass(～ 1/R) mainly from BC while the current mass contributes a few Me. V: A mechanism for mass splitting 12

Mass splitting in bag pictures n The MIT bag prediction with chromoelectric and magnetic interation: Allowed mass splitting for nucleons: 1) Kinetic energy splitting mud=0 2) 3) i=u, d, s 4) 2) Chromo-magnetic splitting (i, j=u, d, s) Data: Δmud=2. 5 Me. V, Δmsu=100 Me. V When mq changes so do the kinetic and chromo-magnetic energies slightly. Reasonable except for pion 13

Mass role in Ch. QM n n The consti. mass varying Δmi and the EM effects breaks the flavor SU(3) mainly; The mass varying dominates for p-n spliting, in ground states a=0. 3/0. 2; L=0. 75/0. 2; M=0. 3; S 0=0; kappa=-1; d=1. 0; alpha 0=0. 8; Vc 14

Chromo-magnetic interaction in Ch. QM The plot of effective mass for n The chromo-magnetic interaction is similar to that of bag models The mass-term [mi+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 0. 0740 15

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

Quark configuration in Ch. QM Length scale L=3. 75 Ge. V-1

Chromo-magnetic interaction in Ch. QM D. Jia, L. Yu, R. Wan, ar. Xiv: 1308. 0700 v 1

Hyperfine splitting in nucleon masses ⊿m (Me. V) u/d mass 0. 360 300/302. 5 0. 723 300/305. 0 1. 011 300/307. 0 1. 293 300/309. 0 1. 436 300/310. 0 1. 723 300/312. 0 19

Hyperfine splitting in nucleon masses n n The CSB explained by NJL model, with quark pair condensation The lator is fixed by the gap equation ΔM=Mn-Mp (Me. V) mu=300 md (Me. V) 309=md 20

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 n Thanks !!! 21