Harleen Dahiya Panjab University, Chandigarh IMPLICATIONS OF  ´ COUPLING IN THE CHIRAL CONSTITUENT QUARK MODEL

Outline Introduction ``Proton Spin Problem’’ Methodology Chiral Constituent Quark Model with Configuration Mixing Quark Spin and Flavor Distribution Functions Role of the ninth Goldstone boson Summary and Conclusions

Introduction Structure of matter cm Fundamental constituents Quarks Leptons Interactions SU(3) C ×SU(2) L ×U(1) Y Standard Model (SM) Quantum chromodynamics q-q and q-q interactions Mesons and Baryons are made up of quarks and antiquarks Hadronic physics explained through QCD and properties through the constituent quarks Example: Spin of proton (uud) =1/2

Inside the Nucleon High Energy Short distance Coupling constant small Asymptotic freedom Perturbative treatment applicable Low Energy Large distance Coupling constant large Infrared slavery QCD cannot be solved exactly Lattice techniques Non Relativistic Quark Model Spin-spin forces generated configuration mixing Remarkable fit to hadron spectroscopy data Subtle features-neutron charge radius, N-  mass difference, photohelicity amplitudes, baryon magnetic moments etc.

“Proton Spin Crisis” 1988 European Muon Collaboration Valence quarks carry 30% of proton spin Data  u=0.85,  d= -0.41,  s= -0.07,  =0.36 NRQM  u=1.33,  d= -0.33,  s=0,  =1 SMC, E142-3 and HERMES “Proton Spin Problem” Bjorken Sum Rule G A /G V =  3 =  u-  d Ellis-Jaffe Sum Rule  8 =  u+  d-2  s  8 =  Strange quark fraction f s  0.10 GSR NMC Asymmetric nucleon sea E866 and HERMES

Chiral Constituent Quark Model Early 80’s Weinberg Manohar and Georgi Cheng and Li ``quark sea’’  qqqqGBq o   )(

Chiral structure of QCD intimate connection with the  and  ´ dynamics In the context of  CQM, S.D. Bass has reiterated in detail the deep relationship of the nonperturbative aspects of QCD, gluon anomaly, and the comparatively large masses of the  and  ´ mesons. Gluon degrees of freedom mix with the flavor singlet Goldstone state to increase the masses of  and  ´. As shown earlier by Ohta et al. and recently advocated by Cheng and Li that  ´ could play an important role in the formulation of the  CQM. Recently been observed on phenomenological grounds that the new measurement of both the u/d asymmetry as well as u-d asymmetry by the NuSea collaboration may not require substantial contribution of  ´. Interesting to understand the extent to which the contribution of  ´ is required in the  CQM thereby giving vital clues to the dynamics of nonperturbative regime of QCD.

Configuration Mixing Non-trivial mixing

Spin polarizations in NRQM Spin polarizations in  CQM config

Flavor distribution functions

Baryon Magnetic Moments Generalization of the Cheng-Li mechanism Coleman Glashow sum rule  (B) total =  (B) val +  (B) sea +  (B) orbit  (B) val =   q B val  q  q =e q /2M q  (B) sea =   q B sea  q  (B) orbit =   q val B [  (q + )]

 CQM config involves 5 parameters a, , , ,   from neutron charge radius consideration a>  2 a>  2 a>  2 a broader analysis to find the ranges Case I higher values Case II Case III Case IV lower values

Partitioning of the nucleon spin Angular momentum sum rule

Summary and Conclusions  CQM config developed Spin polarization functions, quark distribution functions, magnetic moments studied by generalizing Cheng-Li mechanism a>  2 a>  2 a>  2 a lower values of  and correspondingly higher values of a are preferred over the higher values of  and lower values of a. Best fit a=0.13,  =  =0.45,  =|0.10| Excellent fit for baryon magnetic moments Partitioning of the nucleon spin among its constituents At leading order, appropriate degrees of freedom are : constituent quarks and weakly interacting GBs Small but nonzero value of  within the dynamics of chiral constituent quark model suggests an important role for  ´ in the nonperturbative regime of QCD

List of Research Publications Chiral quark model with configuration mixing Harleen Dahiya and Manmohan Gupta Phys. Rev. D 64, (2001) Octet magnetic moments and the Coleman-Glashow sum rule violation in the chiral quark model Harleen Dahiya and Manmohan Gupta Phys. Rev. D 66(Rapid Communication), (2002) SU(4) chiral quark model with configuration mixing Harleen Dahiya and Manmohan Gupta Phys. Rev. D 67, (2003) Octet and decuplet baryon magnetic moments in the chiral quark model Harleen Dahiya and Manmohan Gupta Phys. Rev. D 67, (2003) What is inside the nucleon? Manmohan Gupta and Harleen Dahiya “Physics of Particles, Nuclei and Materials-Recent Trends”, Narosa Publishers (2002) Chiral quark model and the nucleon spin Harleen Dahiya and Manmohan Gupta Int. Jol. of Mod. Phys. A, Vol. 19, No. 29, (2004) Chiral constituent quark model with configuraton mixing Manmohan Gupta and Harleen Dahiya, Paper presented in the International Quarks and Nuclear Physics Conference held in Indiana University, Bloomington, USA in May 2004 Singlet GB contributions in the chiral constituent quark model Harleen Dahiya, Manmohan Gupta and J.M.S. Rana, Paper presented in the 17th National Nuclear Physics Summer School held at the Clark Kerr Campus, U.C. Berkeley, Berkeley, California, USA in June Chiral constituent quark model and the coupling strength of eta’ Harleen Dahiya, Manmohan Gupta and J.M.S. Rana, Int. Jol. of Mod. Phys. A, Vol. 21, No. 21, (2006)