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Register a new user$1/N_c$ Rotational Corrections to $g_A$ and Isovector Magnetic Moment of the Nucleon
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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 %.
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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.
Baryon magnetic moments are computed in baryon chiral perturbation theory in the large-$N_c$ limit at one-loop order, where $N_c$ is the number of color charges. Orders $mathcal{O}(m_q^{1/2})$ and $mathcal{O}(m_q ln m_q)$ corrections are both evaluated including all the operator structures that participate at the physical value $N_c=3$. The complete expressions for octet and decuplet baryon magnetic moments in addition to decuplet-octet baryon transition moments are thus compared to their available counterparts obtained in heavy baryon chiral perturbation theory for degenerate intermediate baryons in the loops. Theoretical expressions fully agree at the physical values $N_c=3$ and $N_f=3$ flavors of light quarks. Some numerical evaluations are produced via a least-squares fit to explore the free parameters in the analysis. Results point out the necessity of incorporating the effects of non-degenerate intermediate baryons in the loops for a consistent determination of these free parameters.
The Goldberger-Treiman relation $M=2pi/sqrt{3}f^{rm cl}_pi$ where $M$ is the constituent quark mass in the chiral limit (cl) and $f^{rm cl}_pi$ the pion decay constant in the chiral limit predicts constituent quark masses of $m_u=328.8pm 1.1$ MeV and $m_d=332.3pm 1.1$ MeV for the up and down quark, respectively, when $f^{rm cl}_pi=89.8pm 0.3$ MeV is adopted. Treating the constituent quarks as bare Dirac particles the following zero order values $mu^{(0)}}_p=2.850pm 0.009$ and $mu^{(0)}}_n= -1.889pm 0.006$ are obtained for the proton and neutron magnetic moments, leading to deviations from the experimental data of 2.0% and 1.3%, respectively. These unavoidable deviations are discussed in terms of contributions to the magnetic moments proposed in previous work.
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 $lambda=-1.2756(13)$
We present high-statistics results for the isovector and flavor diagonal charges of the proton using 11 ensembles of 2+1+1 flavor HISQ fermions. In the isospin symmetric limit, results for the neutron are given by the $u leftrightarrow d$ interchange. A chiral-continuum fit with leading order corrections was made to extract the connected and disconnected contributions in the continuum limit and at $M_pi=135$ MeV. All results are given in the $overline{MS}$ scheme at 2 GeV. The isovector charges, $g_A^{u-d} = 1.218(25)(30)$, $g_S^{u-d} = 1.022(80)(60) $ and $g_T^{u-d} = 0.989(32)(10)$, are used to obtain low-energy constraints on novel scalar and tensor interactions, $epsilon_{S}$ and $epsilon_{T}$, at the TeV scale. The flavor diagonal axial charges are: $g_A^u equiv Delta u equiv langle 1 rangle_{Delta u^+} = 0.777(25)(30)$, $g_A^d equiv Delta d equiv langle 1 rangle_{Delta d^+} = -0.438(18)(30)$, and $g_A^s equiv Delta s equiv langle 1 rangle_{Delta s^+} = -0.053(8)$. Their sum gives the total quark contribution to the proton spin, $sum_{q=u,d,s} (frac{1}{2} Delta q) = 0.143(31)(36)$. This result is in good agreement with the recent COMPASS analysis $0.13 < frac{1}{2} Delta Sigma < 0.18$. Implications of results for the flavor diagonal tensor charges, $g_T^u = 0.784(28)(10)$, $g_T^d = -0.204(11)(10)$ and $g_T^s = -0.0027(16)$ for constraining the quark electric dipole moments and their contributions to the neutron electric dipole moment are discussed. These flavor diagonal charges also give the strength of the interaction of dark matter with nucleons via axial and tensor mediators.
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