arXiv subjects

T. Bhattacharya

Publications and source records attributed to T. Bhattacharya.

28 records · Page 2Linked to original sources

arXiv1998

Dynamics of the Conformal Mode and Simplicial Gravity

We review the derivation of the Liouville action in 2DQG via the trace anomaly and emphasize how a similar approach can be used to derive an effective action describing the long wavelength dynamics of the conformal factor in 4D. In 2D we describe how to make an explicit connection between dynamical triangulations and this continuum theory, and present results which confirm the equivalance of the two approaches. By reconstructing a lattice conformal mode from DT simulations it should be possible to test this equivalence in 4D also.

hep-lat↗

arXiv1998

B Meson Decay Constants From NRQCD

We present quenched results for B meson decay constants using NRQCD b quarks and O(a) tadpole improved clover light quarks. For the first time, one-loop matching factors between lattice and continuum currents are incorporated through O(α/M) taking operator mixing fully into account. This includes an important O(αa) discretization correction to the heavy-light axial vector current. We find f_B = 0.147(11)(^{+8}_{-12})(9)(6) MeV and f_{B_s}/f_B = 1.20(4)(^{+4}_{-0}). PACS numbers: 12.38.Gc, 12.39.Hg, 13.20.He, 14.40.Nd

hep-lat↗

arXiv1997

Heavy light mesons at a larger lattice spacing

We present results on the spectrum of B and D mesons including radial excitations and discuss the pseudoscalar decay constant. The results are obtained at beta=5.7 in the quenched approximation using NRQCD for the heavy quark. To study scaling violations we also compare to results obtained at beta=6.0.

hep-lat↗

arXiv1996

Light Quark Masses and the CP violation parameter $ε'/ε$

We present estimates of light quarks masses using lattice data. Our main results are based on a global analysis of all the published data for Wilson and Staggered fermions, both in the quenched approximation and with $n_f=2$ dynamical flavors. The Wilson and Staggered results agree after extrapolation to the continuum limit for both the $n_f=0,2$ theories. Our best estimates, in the MSbar scheme at scale $2 GeV$, are $mbar=3.2(4) MeV$ and $m_s = 90(20) MeV$ in the quenched approximation, and $mbar ~ 2.7 MeV$ and $m_s ~ 70 MeV$ for the $n_f=2$ theory. These estimates are significantly smaller than phenomenological estimates based on sum rules, but maintain the ratios predicted by chiral perturbation theory. Along with the new estimates of 4-fermion operators, lower quark masses have a significant impact on the extraction of $ε'/ε$ from the Standard Model.

hep-lat↗

arXiv1996

$B$ and $B_c$ mesons with NRQCD and Clover actions

We present preliminary results from our study of the heavy-light spectrum and decay constants. For the heavy quark, we use NRQCD at various masses around and above the $b$ quark mass. For the first time, the heavy quark action and the heavy-light current consistently include corrections at second order in the non-relativistic expansion, as well as the leading finite $a$ corrections. The light quarks are simulated using a tadpole-improved Clover action at various masses in the strange and $c$ quark region.

hep-lat↗

arXiv1996

Large q expansion of the 2D q-states Potts model

We present a recursive method to calculate a large q expansion of the 2d q-states Potts model free energies based on the Fortuin-Kasteleyn representation of the model. With this procedure, we compute directly the ordered phase partition function up to order 10 in 1/sqrt{q}. The energy cumulants at the transition can be obtained with suitable resummation and come out large for q less or around 15. As a consequence, expansions of the free energies around the transition temperature are useless for not large enough values of q. In particular the pure phase specific heats are predicted to be much larger, at q < 15, than the values extracted from current finite size scaling analysis of extrema, whereas they agree very well with recent values extracted at the transition point.

hep-lat↗

arXiv1994

Large Energy Cumulants in the 2D Potts Model and their Effects in Finite Size Analysis

We develop an ansatz for expressing the free energy of the two dimensional $q$-states Potts model for $q > 4$ near its first order phase transition point. We notice that for the moderate values of $ q \lesssim 15 $, the energy profile at the phase transition is not expressible as a sum of gaussians. We discuss how this affects the traditional finite size analysis of this phase transition. In particular, the dominant length scale governing the finite size corrections turns out to be much (${} \sim 6$ ~times) larger than the largest correlation length in the problem.

hep-lat↗

arXiv1993

Critical Behavior of the Antiferromagnetic Heisenberg Model on a Stacked Triangular Lattice

We estimate, using a large-scale Monte Carlo simulation, the critical exponents of the antiferromagnetic Heisenberg model on a stacked triangular lattice. We obtain the following estimates: $γ/ν= 2.011 \pm .014 $, $ν= .585 \pm .009 $. These results contradict a perturbative $2+ε$ Renormalization Group calculation that points to Wilson-Fisher O(4) behaviour. While these results may be coherent with $4-ε$ results from Landau-Ginzburg analysis, they show the existence of an unexpectedly rich structure of the Renormalization Group flow as a function of the dimensionality and the number of components of the order parameter.

cond-mat↗

arXiv1993

The free energy of the Potts model: from the continuous to the first-order transition region

We present a large $q$ expansion of the 2d $q$-states Potts model free energies up to order 9 in $1/\sqrt{q}$. Its analysis leads us to an ansatz which, in the first-order region, incorporates properties inferred from the known critical regime at $q=4$, and predicts, for $q>4$, the $n^{\rm th}$ energy cumulant scales as the power $(3 n /2-2)$ of the correlation length. The parameter-free energy distributions reproduce accurately, without reference to any interface effect, the numerical data obtained in a simulation for $q=10$ with lattices of linear dimensions up to L=50. The pure phase specific heats are predicted to be much larger, at $q\leq10$, than the values extracted from current finite size scaling analysis of extrema. Implications for safe numerical determinations of interface tensions are discussed.

hep-th↗

arXiv1992

Z(N) interface tension in a hot SU(N) gauge theory

The interface tension between Z(N) vacua in a hot SU(N) gauge theory (without dynamical fermions) is computed at next to leading order in weak coupling. The Z(N) interface tension is related to the instanton of an effective action, which includes both classical and quantum terms; a general technique for treating consistently the saddle points of such effective actions is developed. Loop integrals which arise in the calculation are evaluated by means of zeta function techniques. As a byproduct, up to two loop order we find that the stable vacuum is always equivalent to the trivial one, and so respects charge conjugation symmetry.

hep-ph↗