arXiv subjects
Publications and source records attributed to Rajan Gupta.
This talk provides a brief summary of the status of lattice QCD calculations of the light quark masses and the kaon bag parameter B_K. Precise estimates of these four fundamental parameters of the standard model, i.e., m_u, m_d, m_s and the CP violating parameter eta, help constrain grand unified models and could provide a window to new physics.
We present preliminary results for $ε'/ε$ calculated using HYP staggered fermions in the quenched approximation. We compare different choices of quenched penguin operators.
This talk reviews the progress made in the determination of the light quark masses using lattice QCD and QCD sum rules. Based on preliminary calculations with three flavors of dynamical quarks, the lattice estimate is $m_s = 75(15)$ MeV, a tantalizingly low value. On the other hand the leading estimates from scale and pseudo-scalar sum rules are $99(16)$ and $100(12)$ MeV respectively. The $τ$-decay sum rule estimates depend very sensitively on the value of $|V_{us}|$. The central values from different analyses lie in the range 115-120 MeV if unitarity of CKM matrix is imposed, and in the range 100-105 MeV if the Particle Data Group values for $|V_{us}|$ are used. I also give my reasons for why the lattice result is not yet in conflict with rigorous lower bounds from sum rule analyses.
We summarize the extent to which one can use Ward identities to non-perturbatively improve flavor singlet and non-singlet bilinears with three flavors of non-degenerate dynamical Wilson-like fermions.
A brief review of lattice calculations of the bag parameter B_K relevant for understanding indirect CP violation in the neutral kaon sector is given. A status report on current state-of-the-art calculations is presented as well as a discussion of the value of B_K exported to phenomenologists. This is a condensed and updated version of the review presented at the CKM Unitarity Triangle Workshop held at CERN during Feburary 13-16, 2002 (http://ckm-workshop.web.cern.ch/ckm-workshop/).
We show that given one O(a) improvement constant, b_m, all the remaining quantities needed to define the renormalized and O(a) improved dimension-3 quark bilinears can be obtained by studying the matrix elements of these operators between external quark states in a fixed gauge.
This talk summarizes results for all the scale independent renormalization constants for bilinear currents ($Z_A$, $Z_V$, and $Z_S/Z_P$), the improvement constants ($c_A$, $c_V$, and $c_T$), the quark mass dependence of $Z_O$, and the coefficients of the equation of motion operators for $O(a)$ improved lattice QCD. Using data at $β=6.0$, 6.2 and 6.4 we study the scaling behavior of these quantities and quantify residual discretization errors.
We present a status report on our calculation of the renormalization constants for the quark bilinears in quenched (O(a)) improved Wilson theory at (beta=6.4) using quark states in Landau gauge.
We present non-perturbative results for the constants needed for on-shell $O(a)$ improvement of bilinear operators composed of Wilson fermions. We work at $β=6.0$ and 6.2 in the quenched approximation. The calculation is done by imposing axial and vector Ward identities on correlators similar to those used in standard hadron mass calculations. A crucial feature of the calculation is the use of non-degenerate quarks. We also obtain results for the constants needed for off-shell $O(a)$ improvement of bilinears, and for the scale and scheme independent renormalization constants, (Z_A), (Z_V) and (Z_S/Z_P). Several of the constants are determined using a variety of different Ward identities, and we compare their relative efficacies. In this way, we find a method for calculating $c_V$ that gives smaller errors than that used previously. Wherever possible, we compare our results with those of the ALPHA collaboration (who use the Schrödinger functional) and with 1-loop tadpole-improved perturbation theory.
A summary of the extraction of light quark masses from both QCD sumrules and lattice QCD simulations is presented. The focus is on providing a careful statement of the potential weaknesses in each calculation, and on integrating the work of different collaborations to provide a coherent picture.
We present results at beta=6.0 and 6.2 for the O(a) improvement and renormalization constants for bilinear operators using axial and vector Ward identities. We discuss the extraction of the mass dependence of the renormalization constants and the coefficients of the equation of motion operators.
We present a status report on the construction of the classical perfect action using the $ b=\sqrt{3} $ renormalization group transformation (RGT). We investigate finite volume corrections and map the locality of the fixed-point action by tuning the RGT parameter, $κ$. We compare results with the previous calculation for b=2 RGT.
We present highlights of the spectrum of mesons and baryons calculated using NRQCD for heavy quarks and tadpole improved clover action for the light quarks.
An overview of lattice results for the strange quark mass, $B_K$, $B_6$, $B_7$, and $B_8$ is presented. I give my assessment of the reliability of various estimates and prospects for future improvements.
In this introductory article a brief description of Quantum Field Theories (QFT) is presented with emphasis on the distinction between strongly and weakly coupled theories. A case is made for using numerical simulations to solve QCD, the regnant theory describing the interactions between quarks and gluons. I present an overview of what these calculations involve, why they are hard, and why they are tailor made for parallel computers. Finally, I try to communicate the excitement amongst the practitioners by giving examples of the quantities we will be able to calculate to within a few percent accuracy in the next five years.
We extend the application of axial Ward identities to calculate $b_A, b_P$ and $b_T$, coefficients that give the mass dependence of the renormalization constants of the corresponding bilinear operators in the quenched theory. The extension relies on using operators with non-degenerate quark masses. It allows a complete determination of the O(a) improvement coefficients for bilinears in the quenched approximation using Ward Identities alone. Only the scale dependent normalization constants $Z_P^0$ (or $Z_S^0$) and $Z_T$ are undetermined. We present results of a pilot numerical study using hadronic correlators.
We re-examine the use of sum rules in the extraction of light quark masses and discuss a number of potential problems with existing analyses. The most important issue is that of the overall normalization of the hadronic spectral functions should not be fixed by assuming complete resonance dominance of the continuum threshold region as it can overestimate the resonance contributions to spectral integrals by factors as large as $\sim 5$. The second important uncertainty comes from the assumed location, $s_0$, of the onset of duality with perturbative QCD, as the extracted quark masses depend very sensitively on this parameter. The assumption of duality and the requirement of positivity of $ρ_5(s)$ imposes very severe constraints on the shape of the relevant spectral function in the dual region, and leads to rigorous lower bounds for $m_u+m_d$ as a function of $s_0$. In the extractions of $m_s$ we find that the conventional choice of the value of $s_0$ is not physical. For a more reasonable choice of $s_0$ we are not able to find a solution that is stable with respect to variations of the Borel transform parameter. This problem can be overcome only if the hadronic spectral function is determined up to significantly larger values of $s$ than is currently possible. Finally, we also estimate the error associated with the convergence of perturbative QCD expressions used in the sum rule analyses. Our conclusion is that, taking all of these issues into account, the resulting sum rule estimates for both $m_u+m_d$ and $m_s$ could easily have uncertainties as large as a factor of 2.
We present evidence for improvement with tadpole improved clover fermions based on an analysis of the chiral behavior of $B_K$ and the quark condensate. Also presented are a comparison of the mass splittings in the baryon octet and decuplet, a calculation of $c_A$ using standard 2-point correlation functions, and the problem of zero modes of the Dirac operator.