Chiral constituent quark model and the coupling strength of eta'

Abstract

Using the latest data pertaining to \bar u-\bar d asymmetry and the spin polarization functions, detailed implications of the possible values of the coupling strength of the singlet Goldstone boson \eta' have been investigated in the \chiCQM with configuration mixing. Using \Delta u, \Delta_3, \bar u-\bar d and \bar u/\bar d, the possible ranges of the coupling parameters a, \alpha^ 2, \beta^ 2 and \zeta^ 2, representing respectively the probabilities of fluctuations to pions, K, \eta and \eta^{'}, are shown to be 0.10 \lesssim a \lesssim 0.14, 0.2\lesssim \alpha \lesssim 0.5, 0.2\lesssim \beta \lesssim 0.7 and 0.10 lesssim |\zeta| \lesssim 0.70. To constrain the coupling strength of \eta', detailed fits have been obtained for spin polarization functions, quark distribution functions and baryon octet magnetic moments corresponding to the following sets of parameters: a=0.1, \alpha=0.4, \beta=0.7, |\zeta|=0.65 (Case I); a=0.1, \alpha=0.4, \beta=0.6, |\zeta|=0.70 (Case II); a=0.14, \alpha=0.4, \beta=0.2, \zeta=0 (Case III) and a=0.13, \alpha=\beta=0.45, |\zeta|=0.10 (Case IV). Case I represents the calculations where a is fixed to be 0.1, in accordance with earlier calculations, whereas other parameters are treated free and the Case IV represents our best fit. The fits clearly establish that a small non-zero value of the coupling of \eta' is preferred over the higher values of \eta' as well as when \zeta=0, the latter implying the absence of \eta' from the dynamics of \chiCQM. Our best fit achieves an overall excellent fit to the data, in particular the fit for \Delta u, \Delta d, \Delta_8 as well as the magnetic moments \mu_{n}, \mu_{\Sigma^-}, \mu_{\Sigma^+} and \mu_{\Xi^-} is almost perfect, the \mu_{\Xi^-} being a difficult case for most of the similar calculations.