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Register a new userSymmetric point flavour singlet axial vector current renormalization at two loops
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Authors
J.A. Gracey
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We calculate the two loop correction to the quark 2-point function with the non-zero momentum insertion of the flavour singlet axial vector current at the fully symmetric subtraction point for massless quarks in the modified minimal subtraction (MSbar) scheme. The Larin method is used to handle $gamma^5$ within dimensional regularization at this loop order ensuring that the effect of the chiral anomaly is properly included within the construction.
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We construct the two loop Greens functions for a quark bilinear operator inserted at non-zero momentum in a quark 2-point function for the most general off-shell configuration. In particular we consider the quark mass operator, vector and tensor currents as well as the second moment of the flavour non-singlet Wilson operator.
It is commonly asserted that the electromagnetic current is conserved and therefore is not renormalized. Within QED we show (a) that this statement is false, (b) how to obtain the renormalization of the current to all orders of perturbation theory, and (c) how to correctly define an electron number operator. The current mixes with the four-divergence of the electromagnetic field-strength tensor. The true electron number operator is the integral of the time component of the electron number density, but only when the current differs from the MSbar-renormalized current by a definite finite renormalization. This happens in such a way that Gausss law holds: the charge operator is the surface integral of the electric field at infinity. The theorem extends naturally to any gauge theory.
For Wilson and clover fermions traditional formulations of the axial vector current do not respect the continuum Ward identity which relates the divergence of that current to the pseudoscalar density. Here we propose to use a point-split or one-link axial vector current whose divergence exactly satisfies a lattice Ward identity, involving the pseudoscalar density and a number of irrelevant operators. We check in one-loop lattice perturbation theory with SLiNC fermion and gauge plaquette action that this is indeed the case including order $O(a)$ effects. Including these operators the axial Ward identity remains renormalisation invariant. First preliminary results of a nonperturbative check of the Ward identity are also presented.
We investigate implications of the use of the point-split axial vector current derived from a Wilson like fermionic action. We compute the corresponding renormalization factor nonperturbatively for one beta value. The axial charge gA calculated from this nonlocal current is found to be nearer to the physical value than computed with the local axial vector current -- computed both on the same lattice with the same action.
The axial-vector form factors and axial-vector constants of the baryon decuplet are investigated within a pion mean-field approach, which is also known as the chiral quark-soliton model. Given an axial-vector current with a specified flavor, there are four different form factors of a decuplet baryon. When we consider the singlet, triplet, and octet axial-vector currents, we have twelve different form factors for each member of the baryon decuplet. We compute all these axial-vector form factors of the baryon decuplet, taking into account the rotational $1/N_c$ corrections and effects of flavor SU(3) symmetry breaking. We find that, for a given flavor, two of the form factors for a decuplet baryon are only independent within the present approach. We first examine properties of the axial-vector form factors of the $Delta^+$ isobar and $Omega^-$ hyperon. We also compare the results of the triplet axial-vector form factors of $Delta^+$ with those from lattice QCD and those of the present work for the axial-vector constants of the baryon decuplet with the lattice data. All the results for other members of the baryon decuplet are then presented. The results of the axial charges are compared with those of other works. The axial masses and axial radii are also discussed.
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