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Rajan Gupta

Publications and source records attributed to Rajan Gupta.

At least 145 records · Page 8Linked to original sources
arXiv1998

Matrix Elements of 4-fermion Operators with Quenched Wilson Fermions

We presents results for the matrix elements of a variety of four-fermion operators calculated using quenched Wilson fermions. Our simulations are done on 170 lattices of size $32^3 x 64$ at $β= 6.0$. We find $B_K=0.74 +- 0.04 +- 0.05$, $B_D= 0.78 +- 0.01$, $B_7^{3/2}= 0.58 +- 0.02 {+0.07 \atop -0.03}$, $B_8^{3/2}= 0.81 +- 0.03 {+.03 \atop -0.02}$, with all results being in the NDR scheme at $μ=2 GeV$. We also calculate the B-parameter for the operator $\CQ_s$, which is needed in the study of the difference of B-meson lifetimes. Our best estimate is $B_s(NDR,μ=1/a)=0.80 +- 0.01$. This is given at the lattice scale since the required 2-loop anomalous dimension matrix is not known. In all these estimates, the first error is statistical, while the second is due to the use of truncated perturbation theory to match continuum and lattice operators. Errors due to quenching and lattice discretization are not included. We also present new results for the perturbative matching coefficients, extending the calculation to all Lorentz scalar four-fermion operators, and using NDR as the continuum scheme.

hep-lat↗
arXiv1998

Introduction to Lattice QCD

These notes aim to provide a pedagogical introduction to Lattice QCD. The topics covered include the scope of LQCD calculations, lattice discretization of gauge and fermion (naive, Wilson, and staggered) actions, doubling problem, improved gauge and Dirac actions, confinement and strong coupling expansions, phase transitions in the lattice theory, lattice operators, a general discussion of statistical and systematic errors in simulations of LQCD, the analyses of the hadron spectrum, glueball masses, the strong coupling constant, and the quark masses.

hep-lat↗
arXiv1997

Advances in the Determination of Quark Masses

Significant progress has been made in the determination of the light quark masses, using both lattice QCD and sum rule methods, in the last year. We discuss the different methods and review the status of current results. Finally, we review the calculations of bottom and charm quark masses.

hep-lat↗
arXiv1997

B-parameters of 4-fermion operators from lattice QCD

This talk summarizes the status of the calculations of $B_K$, $B_7$, $B_8$, and $B_s$, done in collaboration with T. Bhattacharya, G. Kilcup, and S. Sharpe. Results for staggered, Wilson, and Clover fermions are presented.

hep-lat↗
arXiv1997

Light Quark Masses from Lattice QCD

We present estimates of the masses of light quarks using lattice data. Our main results are based on a global analysis of all the published data for Wilson, Sheikholeslami-Wohlert (clover), and staggered fermions, both in the quenched approximation and with $n_f=2$ dynamical flavors. We find that the values of masses with the various formulations agree after extrapolation to the continuum limit for the $n_f=0$ theory. Our best estimates, in the MSbar scheme at $μ=2 GeV$, are $\mbar=3.4 +- 0.4 +- 0.3 MeV$ and $m_s = 100 +- 21 +- 10 MeV$ in the quenched approximation. The $n_f=2$ results, $\mbar = 2.7 +- 0.3 +- 0.3 MeV$ and $m_s = 68 +- 12 +- 7 MeV$, are preliminary. (A linear extrapolation in $n_f$ would further reduce these estimates for the physical case of three dynamical flavors.) These estimates are smaller than phenomenological estimates based on sum rules, but maintain the ratios predicted by chiral perturbation theory. The new results have a significant impact on the extraction of $ε'/ε$ from the Standard Model. Using the same lattice data we estimate the quark condensate using the Gell-Mann-Oakes-Renner relation. Again the three formulations give consistent results after extrapolation to $a=0$, and the value turns out to be correspondingly larger, roughly preserving $m_s \vev{\bar ψψ}$.

hep-lat↗
arXiv1997

Staggered fermion matrix elements using smeared operators

We investigate the use of two kinds of staggered fermion operators, smeared and unsmeared. The smeared operators extend over a $4^4$ hypercube, and tend to have smaller perturbative corrections than the corresponding unsmeared operators. We use these operators to calculate kaon weak matrix elements on quenched ensembles at $β=6.0$, 6.2 and 6.4. Extrapolating to the continuum limit, we find $B_K(NDR, 2 GeV)= 0.62\pm 0.02(stat)\pm 0.02(syst)$. The systematic error is dominated by the uncertainty in the matching between lattice and continuum operators due to the truncation of perturbation theory at one-loop. We do not include any estimate of the errors due to quenching or to the use of degenerate $s$ and $d$ quarks. For the $ΔI = {3/2}$ electromagnetic penguin operators we find $B_7^{(3/2)} = 0.62\pm 0.03\pm 0.06$ and $B_8^{(3/2)} = 0.77\pm 0.04\pm 0.04$. We also use the ratio of unsmeared to smeared operators to make a partially non-perturbative estimate of the renormalization of the quark mass for staggered fermions. We find that tadpole improved perturbation theory works well if the coupling is chosen to be $α_\MSbar(q^*=1/a)$.

hep-lat↗
arXiv1996

Comparison of Inversion Algorithms for Wilson Fermions on the CM5

This talk presents results of a comparitive study of iterative algorithms like minimal residue ($MR$) and conjugate gradient ($CG$, $BiCGγ_5$, and \bicgstab) used for inverting the Dirac matrix $M$. The tests were done on the Connection Machine CM-5 using $32^3 \times 64$ lattices. The fermion action used is of Wilson type, both with and without the clover term. The overall conclusion is that preconditioned over-relaxed $MR$ is the simplest, uses the least memory, and is comparable in performance to \bicgstab. We find these two algorithms to be equally robust, $i.e.$ insensitive to the starting solution and to round-off errors.

hep-lat↗
arXiv1996

Critical Exponents of the 3-D Ising Model

We present a status report on the ongoing analysis of the 3D Ising model with nearest-neighbor interactions using the Monte Carlo Renormalization Group (MCRG) and finite size scaling (FSS) methods on $64^3$, $128^3$, and $256^3$ simple cubic lattices. Our MCRG estimates are $K_{nn}^c=0.221655(1)(1)$ and $ν=0.625(1)$. The FSS results for $K^c$ are consistent with those from MCRG but the value of $ν$ is not. Our best estimate $η= 0.025(6)$ covers the spread in the MCRG and FSS values. A surprise of our calculation is the estimate $ω\approx 0.7$ for the correction-to-scaling exponent. We also present results for the renormalized coupling $g_R$ along the MCRG flow and argue that the data support the validity of hyperscaling for the 3D Ising model.

cond-mat↗
arXiv1995

Hadron Spectrum with Wilson fermions

We present results of a high statistics study of the quenched spectrum using Wilson fermions at $β=6.0$ on $32^3 \times 64$ lattices. We calculate the masses of mesons and baryons composed of both degenerate and non-degenerate quarks. Using non-degenerate quark combinations allows us to study baryon mass splittings in detail. We find significant deviations from the lowest order chiral expansion, deviations that are consistent with the expectations of quenched chiral perturbation theory. We find that there is a $\sim 20%$ systematic error in the extracted value of $m_s$, depending on the meson mass ratio used to set its value. Using the largest estimate of $m_s$ we find that the extrapolated octet mass-splittings are in agreement with the experimental values, as is $M_Δ- M_N$, while the decuplet splittings are 30% smaller than experiment. Combining our results with data from the GF11 collaboration we find considerable ambiguity in the extrapolation to the continuum limit. Our preferred values are $M_N / M_ρ= 1.38(7)$ and $M_Δ/ M_ρ= 1.73(10)$, suggesting that the quenched approximation is good to only $\sim 10-15%$. We also analyze the $O(ma)$ discretization errors in heavy quark masses.

hep-lat↗
arXiv1995

Status Report on Weak Matrix Element Calculations

This talk presents results of weak matrix elements calculated from simulations done on 170 $32^3 \times 64$ lattices at $β= 6.0$ using quenched Wilson fermions. We discuss the extraction of pseudoscalar decay constants $f_π$, $f_K$, $f_D$, and $f_{D_s}$, the form-factors for the rare decay $B \to K^* γ$, and the matrix elements of the 4-fermion operators relevant to $B_K$, $B_7$, $B_8$. We present an analysis of the various sources of systematic errors, and show that these are now much larger than the statistical errors for each of these observables. Our main results are $f_D=186(29) \MeV$, $f_{D_s}=224(16) MeV$, $T_1=T_2=0.24(1)$, $B_K(NDR, 2\GeV)=0.67(9)$, and $B_8(NDR, 2\GeV)=0.81(1)$.

hep-lat↗
arXiv1995

Lattice analysis of semi-leptonic form factors

We present preliminary results from simulations done on 170 $32^3 \times 64$ lattices at $β= 6.0$ using quenched Wilson fermions. This talk focuses on the $Q^2$ behavior of the form-factors, extrapolation in quark masses, dependence on renormalization scheme, and comparison with heavy-quark effective theory (HQET). Even though we cannot estimate errors due to quenching and discretization, our results are consistent with experimental results for $D$ decays. We present results for the Isgur-Wise function and estimate $ξ'(w=1) = 0.97(6)$.

hep-lat↗
arXiv1995

Testing the chiral behavior of the hadron spectrum

We analyze the chiral behavior of the hadron spectrum obtained with quenched Wilson fermions on 170 $32^3 \times 64$ lattices at $β= 6.0$. We calculate masses of hadrons composed of both degenerate and non-degenerate quarks. We reduce the statistical errors in mass splittings by directly fitting to the ratio of correlation functions. We find significant deviations from a linear dependence on the quark mass, deviations that are consistent with the higher order terms predicted by quenched chiral perturbation theory. Including these corrections yields splittings in the baryon octet that agree with those observed experimentally. Smaller higher order terms are also present in $m_ρ$ and $m_N$. By contrast, the decuplet baryons are well described by a linear mass term. We find the decuplet splittings to be 30% smaller than experiment. We extrapolate our data to $a \to 0$ by combining with the GF11 results, and the best fit suggests that the quenched approximation is only good to $10-15%$.

hep-lat↗
arXiv1995

Decay constants with Wilson fermions at $β=6.0$

We present results of a high statistics study of $f_π$, $f_K$, $f_D$, $f_{D_s}$, and $f_V^{-1}$ in the quenched approximation using Wilson fermions at $β=6.0$ on $32^3 \times 64$ lattices. We find that the various sources of systematic errors (due to setting the quark masses, renormalization constant, and lattice scale) are now larger than the statistical errors. Our best estimates, without extrapolation to the continuum limit, are $f_π=134(4) \MeV$, $f_K =159(3) \MeV$, $f_D = 229(7) \MeV$, $f_{D_s} = 260(4) \MeV$, and $f_V^{-1}(m_ρ) = 0.33(1)$, where only statistical errors have been shown. We discuss the extrapolation to the continuum limit by combining our data with those from other collaborations.

hep-lat↗
arXiv1995

Prospects of Solving Grand Challenge Problems

The recent woes of the supercomputer industry and changes in federal funding have caused some scientists to re-evaluate the means by which they hope to solve Grand Challenge problems. I evaluate the potential of Massively Parallel Processors (MPP) within this context and the state of today's MPP. I stress that for solving large-scale problems MPP are crucial and that it is essential to seek a balance between CPU performance, memory access time, inter-node communications, and I/O. To achieve this it is important to preserve certain characteristics of the hardware while selecting the hottest processor to design the machine around. I emphasize that for long term stability and growth of parallel computing priority should be given to standardizing software so that the same code can run on different platforms and on machines ranging from clusters of workstations to MPP.

hep-lat↗
arXiv1995

Chiral limit of QCD

This talk contains an analysis of quenched chiral perturbation theory and its consequences. The chiral behavior of a number of quantities such as the pion mass $m_π^2$, the Bernard-Golterman ratios $R$ and $χ$, the masses of nucleons, and the kaon B-parameter are examined to see if the singular terms induced by the additional Goldstone boson,$η'$, are visible in present data. The overall conclusion (different from what I presented at the lattice meeting) of this analysis is that, with some caveats on the extra terms induced by $η'$ loops, the standard expressions break down when extrapolating the quenched data with $m_q < m_s/2$ to physical light quarks. I then show that due to the single and double poles in the quenched $η'$, the axial charge of the proton cannot be calculated using the Adler-Bell-Jackiw anomaly condition. I conclude with a review of the status of the calculation of light quark masses from lattice QCD.

hep-lat↗
arXiv1995

Phenomenology from 100 large lattices

We present a status report on simulations being done on $32^3 \times 64$ lattices at $β= 6.0$ using quenched Wilson fermions. Phenomenologically relevant results for the spectrum, decay constants, the kaon B-parameter $B_K$, $B_7$, $B_8$, semi-leptonic and $B\to K^* γ$ form factors are given based on a statistical sample of 100 configurations.

hep-lat↗
arXiv1995

Matrix Elements of the Singlet Axial Current in the Proton

We present a method to estimate the matrix element of the singlet axial current within a polarized proton state using lattice QCD. The method relies on using the Adler-Bell-Jackiw anomaly and gives the desired result in the chiral limit. We show that this method fails in the quenched approximation. For heavy quarks one does not expect much difference between simulations including dynamical quarks and those done in the quenched approximation. For that reason we explore numerical methods on an existing set of quenched configurations. The data obtained in this exploratory study show a poor statistical signal.

hep-lat↗