Apoorva Patel

Non-singlet axial vector couplings of the baryon octet in lattice QCD*

We calculate in the quenched approximation the F and D parameters characterising the axial vector matrix elements of the baryon octet. The use of an improved fermion action and smeared interpolating fields enables us to go down in quark mass to the SU ( 3 ) symmetric point. Both the F/D ratio and g A are in good agreement with the experimental values within a statistical error of a≈10%.

Mass-splittings in the baryon octet and the nucleon σ-term in lattice QCD☆

Abstract We calculate in the valence approximation the F and D parameters governing the mass-splittings in the baryon octet. The use of an improved fermion action enables us to go down in quark mass to the SU (3) symmetric point. The F parameter is consistent with its experimental value. On the other hand, the D parameter turns out to be large and shows a strong dependence on the quark mass. This is evidence that the Σ − gL mass-splitting is not a first-order SU (3) flavour symmetry breaking effect. We also estimate the contribution of the valence quarks to the nucleon σ-term.

Theβ-function for pure gauge SU(3)

Abstract We present detailed results for the non-perturbative s-function of the SU(3) lattice gauge theory using theb = √3 renormalization group transformation (RGT). The results are compared to those obtained from theb = 2RGT, and from measurements of the deconfinement temperature, the string tension and the scalar glueball mass. Above6/g 2 ≈ 6.75our results are consistent with asymptotic scaling, while for6.0 2 g 2 , in the region where the s-function shows a dip, the glueball mass shows significant deviations from scaling.

On the finite-temperature transition of QCD

Abstract Using an exact algorithm to incorporate dynamical quarks, we present evidence from numerical simulations that the finite-temperature transition in QCD is first order for realistic quark masses. For two light flavors of quarks we see a two state signal, with flip-flops between these states. For four flavors we show that the first-order transition extends to quark masses heavier than T c .

An improved lattice fermion action from block-diagonalisation

Abstract We derive an improved lattice fermion action using approximate block-diagonalisation. Following real space renormalisation group ideas, an effective action for the infra-red modes is obtained by integrating out the heavy modes. We expand this effective action perturbatively in the contribution of the heavy modes. With a systematic improvement of this expansion, we hope to extract continuum properties of QCD from coarse lattices.

Sea quarks and the hadron spectrum

Abstract We present lattice Monte Carlo results demonstrating the effects of dynamical quarks on the hadron spectrum. We show that the sea quarks do not influence the nucleon and the rho in an identical manner, and the ratio M N M p decreases as the sea quark mass is decreased. We also find a large value for the sea quark contribution to the matrix element 〈N| u u+ d d|N〉 .

Current algebra parameters on the lattice with a renormalisation group improved Wilson action

Abstract Using our renormalisation group improved Wilson fermion action in the quenched approximation and working on an 83 × 16 lattice with a lattice spacing of a ≈ 0.15 fm, we determine: (a) the baryon decuplet and vector meson octet mass splittings, (b) the lattice renormalisations of the non-singlet axial and vector currents and (c) fπ and fϱ down to rather small values of the quark mass. As a result, we gain an insight into the chiral behaviour and proximity to continuum of our improved action at this lattice spacing.

The proton mass, the π-N sigma term and the scale anomaly

Abstract It is argued that the scale anomaly of QCD makes the nucleon mass more strongly dependent on the sea quark masses than the naive inference.

Improved Fermion Actions and Hadronic Matrix Elements in Lattice QCD

The Renormalisation Group is a powerful framework for extracting infra-red properties of lattice theories. Its basic principle is to integrate out the high frequency modes within a block on a fine lattice, leaving behind an effective theory of the low lying modes on a coarse block lattice. The long distance behaviour of the theory is preserved, but at the expense of creating a lattice action with more complicated couplings. Such an action is expected to be less dependent on lattice artifacts and is generically referred to as an improved action. Though this methodology has been extensively applied to scalar and gauge fields using both linear and non-linear block transformations, progress with fermions has not been as rapid. Fermions, it turns out, are easier to deal with than scalar or gauge fields, the essential ingredient being that anti-commuting Grassmann variables allow only linear block transformations.

Weak interaction matrix elements in strong coupling lattice QCD

Abstract Amplitude of many non-leptonic processes require a non-perturbative calculation of matrix elements between pseudo-Goldstone boson states, after the standard perturbation theory in the Electro-Weak sector. Several such matrix elements are estimated using the techniques of strong coupling lattice QCD.