Renormalization of the flavor-singlet axial-vector current and its anomaly in dimensional regularization

The renormalization constant ZJ of the flavor-singlet axial-vector current with a non-anticommuting γ5 in dimensional regularization is determined to order $$ {\alpha}_s^3 $$ α s 3 in QCD with massless quarks. The result is obtained by computing the matrix elements of the operators appearing in the axial-anomaly equation $$ {\left[{\partial}_{\mu }{J}_5^{\mu}\right]}_R=\frac{\alpha_s}{4\pi }{n}_f{\mathrm{T}}_F{\left[F\tilde{F}\right]}_R $$ ∂ μ J 5 μ R = α s 4 π n f T F F F ˜ R between the vacuum and a state of two (off-shell) gluons to 4-loop order. Furthermore, through this computation, the equality between the $$ \overline{\mathrm{MS}} $$ MS ¯ renormalization constant $$ {Z}_{F\tilde{F}} $$ Z F F ˜ associated with the operator $$ {\left[F\tilde{F}\right]}_R $$ F F ˜ R and that of αs is verified explicitly to hold true at 4-loop order. This equality automatically ensures a relation between the respective anomalous dimensions, $$ {\gamma}_J=\frac{\alpha_s}{4\pi }{n}_f{\mathrm{T}}_F{\gamma}_{FJ} $$ γ J = α s 4 π n f T F γ FJ , at order $$ {\alpha}_s^4 $$ α s 4 given the validity of the axial-anomaly equation which was used to determine the non-$$ \overline{\mathrm{MS}} $$ MS ¯ piece of ZJ for the particular γ5 prescription in use.

Nuclear currents in chiral effective field theory

In this article, we review the status of the calculation of nuclear currents within chiral effective field theory. After formal discussion of the unitary transformation technique and its application to nuclear currents we give all available expressions for vector, axial-vector currents. Vector and axial-vector currents are discussed up to order Q with leading-order contribution starting at order $$Q^{-3}$$ Q - 3 . Pseudoscalar and scalar currents will be discussed up to order $$Q^0$$ Q 0 with leading-order contribution starting at order $$Q^{-4}$$ Q - 4 . This is a complete set of expressions in next-to-next-to-next-to-leading-order (N$$^3$$ 3 LO) analysis for nuclear scalar, pseudoscalar, vector and axial-vector current operators. Differences between vector and axial-vector currents calculated via transfer-matrix inversion and unitary transformation techniques are discussed. The importance of a consistent regularization is an additional point which is emphasized: lack of a consistent regularization of axial-vector current operators is shown to lead to a violation of the chiral symmetry in the chiral limit at order Q. For this reason a hybrid approach at order Q, discussed in various publications, is non-applicable. To respect the chiral symmetry the same regularization procedure needs to be used in the construction of nuclear forces and current operators. Although full expressions of consistently regularized current operators are not yet available, the isoscalar part of the electromagnetic charge operator up to order Q has a very simple form and can be easily regularized in a consistent way. As an application, we review our recent high accuracy calculation of the deuteron charge form factor with a quantified error estimate.

The constraint equation of the vertex function of quantum anomaly and Dyson–Schwinger equations in massless QED2 theory

In this paper, we calculate the quantum anomaly for the longitudinal and the transverse Ward–Takahashi (WT) identities for vector and axial-vector currents in QED2 theory by means of the point-splitting method. It is found that the longitudinal WT identity for vector current and transverse WT identity for axial-vector current have no anomaly while the longitudinal WT identity for axial-vector current and the transverse WT identity for vector current have anomaly in QED2 theory. Moreover, we study the four WT identities in massless QED2 theory and get the result that the four WT identities together give the constraint equation of the vertex function of quantum anomaly. At last, we discuss the Dyson–Schwinger equations in massless QED2 theory. It is found that the vertex function of the quantum anomaly has corrections for the fermion propagator and Schwinger model.

Analysis of the Zc(4200) as axial-vector molecule-like state

In this paper, we assume the [Formula: see text] as the color octet–octet type axial-vector molecule-like state, and construct the color octet–octet type axial-vector current to study its mass and width with the QCD sum rules. The numerical values [Formula: see text] and [Formula: see text] are consistent with the experimental data [Formula: see text] and [Formula: see text], and support assigning the [Formula: see text] to be the color octet–octet type molecule-like state with [Formula: see text]. Furthermore, we discuss the possible assignments of the [Formula: see text], [Formula: see text] and [Formula: see text] as the diquark–antidiquark type tetraquark states with [Formula: see text].