Asit K. De

Phase diagram of a lattice SU(2) ⊗ SU(2) scalar-fermion model with naive and Wilson fermions

Abstract We present the phase structure of the chiral SU(2) L ⊗ SU(2) R scalar-fermion model on the lattice with on-site Yukawa coupling y and Wilson-Yukawa coupling w for positive y and w . The hopping parameter κ of the four-component scalar field of fixed length is both positive and negative. From the different behaviour of several observables ferromagnetic, paramagnetic and antiferromagnetic phases can be distinguished. They split into different regions or phases with small and large y + 4 w . A similar structure is also found in the quenched approximation. In addition, in the unquenched case a ferrimagnetic phase is found at negative κ around y + 4 w ≈ √2. We discuss fermion masses in various regions and point out the possibilities of decoupling the unwanted fermion doublers in the continuum limit in analogy to the Wilson mechanism.

Unquenched investigation of fermion masses in a chiral fermion theory on the lattice

Abstract Using dynamical fermions we study the decoupling of the fermion doublers of chiral lattice fermions in the broken symmetry phase of a scalar-fermion model. The model uses a chiral invariant Wilson term, called a Wilson-Yukawa term with coupling strength w , in addition to the usual Yukawa coupling y . We find qualitative agreement with our results obtained before in the quenched approximation. First in the w = 0 case we establish a strong Yukawa coupling region. Then for relatively large but fixed w we confirm that the fermion doublers can be easily decoupled by giving them masses of the order of the cutoff as the symmetry restoring transition is approached.

Search for an upper bound of the renormalized Yukawa coupling in a lattice fermion-Higgs model ☆

Abstract We study the scaling laws for the fermion mass and the scalar field expectation value in the weak coupling region of the broken phase of a lattice regularized chiral-invariant SU(2)L ⊗ SU(2)R fermion-Higgs model with bare Yukawa coupling y and Wilson-Yukawa coupling w. In particular we concentrate on the region in the vicinity of the line A, which is the line of maximal values of y + 4w on the critical surface containing the gaussian fixed point. We have not found any indication for the existence of a nontrivial fixed point on that line or anywhere else in the weak coupling region. The renormalized Yukawa coupling yR as a function of the fermionic correlation length appears to be bounded from above. The upper bound obtained from the numerical data at w = 0 is compatible with the perturbative unitarity bound. Furthermore, in the weak coupling region, including the line A, it is not possible to choose w such that the unwanted fermion doublers would be removed from the physical particle pectrum.

Probing the SU(2) gauge-Higgs system with fermions

Quenched fermion calculations are carried out on the βg = 2.3 line of the lattice SU(2) gauge-Higgs system. Chiral symmetry is always broken on the confinement side of the Higgs transition. For l = 12 fermions the symmetry is restored the moment one enters the Higgs region. However, for l = 1 fermions it is possible to have both chirally broken and chirally symmetric Higgs regions. These conclusions follow from evaluations of a3〈ΨΨ〉l and from spectrum calculations in the pseudoscalar meson and the fermion-scalar bound-state channels.

Fermion masses at strong Wilson-Yukawa coupling in the symmetric phase☆

Abstract The fermion mass spectrum is studied in the strong-coupling symmetric (PMS) phase of a scalar-fermion model derived from a lattice proposal of the standard model with Wilson-Yukuwa coupling. We find that the fermions are massive and argue for the following interpretation of our numerical results in this PMS phase. The lowest lying fermion spectrum in this phase consists only of a Dirac fermion which is a singlet with respect to the SU(2) L group (the “neutral” fermion). We give evidence that the SU(2) L doublet fermion (the “charged” fermion), in terms of which the model is originally formulated and which is present in the weak-coupling symmetric phase, is absent in the PMS phase. The neutral fermion is only weakly coupled to the scalar particles and appears to become non-interacting in the scaling region. If this interpretation is correct, the Wilson-Yukawa approach does not lead to a satisfactory lattice formulation of the standard model.

Spontaneous symmetry breaking on the lattice generated by Yukawa interaction

We study by numerical simulation a lattice Yukawa model with naive fermions at intermediate values of the Yukawa coupling constant y when the nearest-neighbour coupling κ of the scalar field Φ is very weakly ferromagnetic (κ ≈ 0) or even antiferromagnetic (κ < 0) and the non-vanishing value of 〈Φ〉 is generated by the Yukawa interaction. The renormalized Yukawa coupling yR achieves here its maximal value and this y-region is thus of particular importance for lattice investigations of strong Yukawa interaction. However, here the scalar field propagators have a very complex structure caused by fermion loop corrections and by the proximity of phases with antiferromagnetic properties. We develop methods for analyzing these propagators and for extracting the physical observables. We find that going into the negative κ region, the scalar field renormalization constant becomes small and yR does not see, to exceed the unitarity bound, making the existence of a non-trivial fixed point in the investigated Yukawa model quite unlikely.

Topological susceptibility in lattice QCD with unimproved Wilson fermions

Abstract We address a long standing problem regarding topology in lattice simulations of QCD with unimproved Wilson fermions. Earlier attempt with unimproved Wilson fermions at β = 5.6 to verify the suppression of topological susceptibility with decreasing quark mass ( m q ) was unable to unambiguously confirm the suppression. We carry out systematic calculations for two degenerate flavours at two different lattice spacings ( β = 5.6 and 5.8). The effects of quark mass, lattice volume and the lattice spacing on the spanning of different topological sectors are presented. We unambiguously demonstrate the suppression of the topological susceptibility with decreasing quark mass, expected from chiral Ward identity and chiral perturbation theory.

Topological charge density correlator in Lattice QCD with two flavours of unimproved Wilson fermions

A bstractWe study the two-point Topological Charge Density Correlator (TCDC) in lattice QCD with two degenerate flavours of unimproved Wilson fermions and Wilson gauge action at two values of lattice spacings and different volumes, for a range of quark masses. Configurations are generated with DDHMC algorithm and smoothed with HYP smearing. In order to shed light on the mechanisms leading to the observed suppression of topological susceptibility with respect to the decreasing quark mass and decreasing volume, in this work, we carry out a detailed study of the two-point TCDC. We have shown that, (1) the TCDC is negative beyond a positive core and radius of the core shrinks as lattice spacing decreases, (2) as the volume decreases, the magnitude of the contact term and the radius of the positive core decrease and the magnitude of the negative peak increases resulting in the suppression of the topological susceptibility as the volume decreases, (3) the contact term and radius of the positive core decrease with decreasing quark mass at a given lattice spacing and the negative peak increases with decreasing quark mass resulting in the suppression of the topological susceptibility with decreasing quark mass, (4) increasing levels of smearing suppresses the contact term and the negative peak keeping the susceptibility intact and (5) both the contact term and the negative peak diverge in nonintegrable fashion as lattice spacing decreases. It is gratifying to note that observations similar to 1 and 5 have been made using topological charge density operator based on chiral fermion. The observations 2 and 3 may be confirmed more precisely by using formulations based on chiral fermions.

Chiral anomaly in lattice QCD with twisted mass Wilson fermion

Abstract The flavour singlet axial Ward identity with Osterwalder–Seiler twisted mass Wilson fermion action is studied on a finite lattice, with finite fermion mass and the Wilson parameter r up to 1. Approach to the infinite volume chiral limit and emergence of the anomaly is significantly better than that obtained with O ( a ) and O ( a 2 ) improved fermion actions. We have shown explicitly that up to O ( g 2 ) , parity violating terms cancel in the Ward identity even at finite volume and finite lattice spacing.

The eigenvalue spectra in Z(2) ⊗ Z(2) and SU(2) ⊗ SU(2) fermion-Higgs models

We present an analysis of the eigenvalue spectra of the Dirac operator M and related operators M′ and M†M in an SU(2) ⊗ SU(2) and a Z(2) ⊗ Z(2) fermion-Higgs model in the quenched approximation. We especially study the spectra in the symmetric and broken symmetry phases along the crossover line which was recently discovered in these models in numerical simulations. It turns out that in the symmetric phases of both models zero modes emerge along the crossover line. In the case of the Z(2) model the zero modes follow the crossover line into the broken symmetry phase whereas in the case of the SU(2) model they appear to stop at the phase transition line between the symmetric and the broken phases.