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Register a new user$1/N_c$ Rotational Corrections to $g_A$ in the NJL Model and Charge Conjugation
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We show that the $1/N_c$ rotational corrections to $g_A$, derived using the semiclassical quantization scheme in the NJL model, possess correct properties under charge conjugation.
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The $1/N_c$ rotational corrections to the axial vector constant and the isovector magnetic moment of the nucleon are studied in the Nambu -- Jona-Lasinio model. We follow a semiclassical quantization procedure in terms of path integrals in which we can include perturbatively corrections in powers of angular velocity $Omega sim frac 1{N_c}$. We find non-zero $1/N_c$ order corrections from both the valence and the Dirac sea quarks. These corrections are large enough to resolve the long-standing problem of a strong underestimation of both $g_A$ and $mu^{IV}$ in the leading order. The axial constant $g_A$ is well reproduced, whereas the isovector magnetic moment $mu^{IV}$ is still underestimated by 25 %.
We present the first and complete dispersion relation analysis of the inner radiative corrections to the axial coupling constant $g_A$ in the neutron $beta$-decay. Using experimental inputs from the elastic form factors and the spin-dependent structure function $g_1$, we determine the contribution from the $gamma W$-box diagram to a precision better than $10^{-4}$. Our calculation indicates that the inner radiative corrections to the Fermi and the Gamow-Teller matrix element in the neutron $beta$-decay are almost identical, i.e. the ratio $lambda=g_A/g_V$ is almost unrenormalized. With this result, we predict the bare axial coupling constant to be {$mathring{g}_A=-1.2754(13)_mathrm{exp}(2)_mathrm{RC}$} based on the PDG average $lambda=-1.2756(13)$
In this paper, we study the possibility of an inhomogeneous quark condensate in the 1+1 dimensional Nambu-Jona-Lasinio model in the large-$N_c$ limit at finite temperature $T$ and quark chemical potential $mu$ using dimensional regularization. The phase diagram in the $mu$--$T$ plane is mapped out. At zero temperature, an inhomogeneous phase with a chiral-density wave exists for all values of $mu>mu_c$. Performing a Ginzburg-Landau analysis, we show that in the chiral limit, the critical point and the Lifschitz point coincide. We also consider the competition between a chiral-density wave and a constant pion condensate at finite isospin chemical potential $mu_I$. The phase diagram in the $mu_I$--$mu$ plane is mapped out and shows a rich phase structure.
The commonly used $gamma_{mu}} Pomeron-quark coupling changes its sign under charge conjugation, in contradiction to the property of Pomeron. I show that the Pomeron-quark coupling is tensorial and is invariant under the charge conjugation.
We define gauge theories whose gauge group includes charge conjugation as well as standard $mathrm{SU}(N)$ transformations. When combined, these transformations form a novel type of group with a semidirect product structure. For $N$ even, we show that there are exactly two possible such groups which we dub $widetilde{mathrm{SU}}(N)_{mathrm{I,II}}$. We construct the transformation rules for the fundamental and adjoint representations, allowing us to explicitly build four-dimensional $mathcal{N}=2$ supersymmetric gauge theories based on $widetilde{mathrm{SU}}(N)_{mathrm{I,II}}$ and understand from first principles their global symmetry. We compute the Haar measure on the groups, which allows us to quantitatively study the operator content in protected sectors by means of the superconformal index. In particular, we find that both types of $widetilde{mathrm{SU}}(N)_{mathrm{I,II}}$ groups lead to non-freely generated Coulomb branches.
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