Divergence Of Axial-vector Current Research Articles

Up- and down-quark masses from QCD sum rules

The QCD up- and down-quark masses are determined from an optimized QCD Finite Energy Sum Rule (FESR) involving the correlator of axial-vector current divergences. In the QCD sector this correlator is known to five loop order in perturbative QCD (PQCD), together with non-perturbative corrections from the quark and gluon condensates. This FESR is designed to reduce considerably the systematic uncertainties arising from the hadronic spectral function. The determination is done in the framework of both fixed order and contour improved perturbation theory. Results from the latter, involving far less systematic uncertainties, are: {overline{m}}_uleft(2 mathrm{GeV}right)=left(2.6pm 0.4right) MeV, {overline{m}}_dleft(2 mathrm{GeV}right)=left(5.3pm 0.4right) MeV, and the sum {overline{m}}_{ud}equiv left({overline{m}}_u+{overline{m}}_dright)/2 , is {overline{m}}_{ud}left(2 mathrm{GeV}right)=left(3.9pm 0.3right) MeV.

Determination of the strange-quark mass from QCD pseudoscalar sum rules

A new determination of the strange-quark mass is discussed, based on the two-point function involving the axial-vector current divergences. This Green function is known in perturbative QCD up to order O ( α s 3), and up to dimension-six in the non-perturbative domain. The hadronic spectral function is parametrized in terms of the kaon pole, followed by its two radial excitations, and normalized at threshold according to conventional chiral-symmetry. The result of a Laplace transform QCD sum rule analysis of this two-point functions is: m s(1GeV 2) = 155±25 MeV

The strange-quark mass from QCD sum rules: An update

Three different ways of determining the strange quark mass using QCD sum rules are reviewed. First, from a QCD sum rule determination of the up and down quark masses, together with the current algebra ratio m s (m u + m d) . Second and third, from QCD sum rules involving the strangeness changing vector and axial-vector current divergences, respectively. Present results are encompassed in the value: m s (1 GeV) = 150±70 MeV. It is argued that until direct, and precision measurements of the relevant spectral functions become availabel, the above error is not likely to be reduced.

The strange-quark mass from QCD sum rules in the pseudoscalar channel

QCD Laplace transform sum rules, involving the axial-vector current divergences, are used in order to determine the strange quark mass. The two-point function is known in QCD up to four loops in perturbation theory, and up to dimension-six in the non-perturbative sector. The hadronic spectral function is reconstructed using threshold normalization from chiral symmetry, together with experimental data for the two radial excitations of the kaon. The result for the running strange quark mass, in the MS scheme at a scale of 1 GeV 2 is: m ̄ s(1 GeV 2)=155±25 MeV .

Axial vector current divergences and the pseudoscalar meson spectrum

The strong anomaly in the axial vector current divergence is simply related to the mass of the ninth pseudoscalar meson in an SU (3) × SU (3) quark model. A discussion is given of the dependence of the pseudoscalar meson masses upon quark masses as well as upon the strong coupling; the SU (3) character of the states is also treated.

ChiralSU 4×SU 4 breaking, axial vector current divergences and kaon PCAC

The chiralSU4×SU4 symmetry breaking of the Hamiltonian is investigated by assuming the symmetry-breaking part of the Hamiltonian belongs to a single\((4,\bar 4) + (\bar 4,4)\) representation ofSU4×SU4. We classify the simplest possibilities, identify each with critical orbits in the space of the\((4,\bar 4) + (\bar 4,4)\) representation and indicate their relations to quark masses. The divergences of the axial vector currents are discussed and their matrix elements are used to obtain relations among masses and coupling constants involving the recently discovered charmed pseudoscalar mesons. Finally, it is pointed out that soft-kaon theorems can be obtained for certain processes involving charmed particles by using kaon PCAC due to the relative smallness of the kaon mass. In this case the symmetry breaking is approximately on the critical orbit corresponding to the subgroupSU3×SU3×U 1 d .

Chiral-SU(3)-symmetry breaking for the pseudoscalar mesons

In the framework of the quark-vector-gluon model, with chiral symmetry broken by a quark mass term, careful use of the algebraic properties of the Hamiltonian and of the divergences of axial-vector currents leads to a consistent picture of symmetry breaking in the pseudoscalar nonet. The ${\ensuremath{\eta}}^{\ensuremath{'}}(960)$ emerges with a large gluon component.

Process π± → π0π± in coulomb field and anomalous divergence of neutral axial-vector current

The amplitude of the process γπ → ππ is expressed through the π 0-decay constant. The obtained relation is fulfilled if Adler's anomalous condition for the divergence of axial-vector current has taken place. So the relation may be used for verifying the hypothesis of Adler.

Mass-Dispersion Relations and Asymptotic Constraints on Form Factors

The mass extrapolation procedure of Fubini and Furlan and of de Alfaro and Rossetti, together with current algebra and partial conservation of axial-vector current, is used to derive asymptotic relations between the vector and axial-vector form factors of the nucleon. These relations are compared with the ones obtained recently by Gordon and Peccei. We are led to the nonrenormalization of the axial-vector coupling constant, provided that the time derivative of the divergence of axial-vector current is assumed to transform like the time component of the axial-vector current.

Axial-Vector Vertex in Spinor Electrodynamics

Working within the framework of perturbation theory, we show that the axial-vector vertex in spinor electrodynamics has anomalous properties which disagree with those found by the formal manipulation of field equations. Specifically, because of the presence of closed-loop the divergence of axial-vector current is not the usual expression calculated from the field equations, and the axial-vector current does not satisfy the usual Ward identity. One consequence is that, even after the external-line wave-function renormalizations are made, the axial-vector vertex is still divergent in fourth- (and higher-) order perturbation theory. A corollary is that the radiative corrections to ${\ensuremath{\nu}}_{l}l$ elastic scattering in the local current-current theory diverge in fourth (and higher) order. A second consequence is that, in massless electrodynamics, despite the fact that the theory is invariant under ${\ensuremath{\gamma}}_{5}$ tranformations, the axial-vector current is not conserved. In an Appendix we demonstrate the uniqueness of the triangle diagrams, and discuss a possible connection between our results and the ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}2\ensuremath{\gamma}$ and $\ensuremath{\eta}\ensuremath{\rightarrow}2\ensuremath{\gamma}$ decays. In particular, we argue that as a result of triangle diagrams, the equations expressing partial conservation of axial-vector current (PCAC) for the neutral members of the axial-vector-current octet must be modified in a well-defined manner, which completely alters the PCAC predictions for the ${\ensuremath{\pi}}^{0}$ and the $\ensuremath{\eta}$ two-photon decays.

Current commutators and the meson bootstrap

The commutation relations between the time components and divergences of axial vector currents are applied to the meson spectrum suggested by bootstrap. In an idealized system, a unique solution is obtained for the masses and coupling constants of spin-0 mesons, which is in crude agreement with experiment. Of particular interest is the structural similarity between the relations here obtained and the usual bootstrap equations.