arXiv subjects
Publications and source records attributed to Andreas S. Kronfeld.
It is widely believed that the pole mass of a quark is infrared-finite and gauge-independent to all orders in perturbation theory. This seems not to have been proved in the literature. A proof is provided here.
We address the perturbative renormalization of massive lattice fermions. We derive expressions-valid to all orders in perturbation theory and for all values of the bare fermion mass-for the rest mass, the kinetic mass, and the wave-function renormalization factor. We obtain the fermion's self energy at the one-loop level with a mass-dependent, $O(a)$ improved action. Numerical results for two interesting special cases, the Wilson and Sheikholeslami-Wohlert actions, are given. The mass dependence of these results smoothly connects the massless and infinite-mass limits, as expected. Combined with Monte Carlo calculations our results can be employed to determine the quark masses in common renormalization schemes.
We have calculated the decay constants of B and $D$ mesons with lattice QCD. We use an $O(a)$ improved action that takes light quark actions as a starting point, tuned so that it can be directly applied at the physical masses of the $b$ and $c$ quarks. Our results are $f_B = 164 \err{+14}{-11} \pm 8$ MeV, $f_{B_s} = 185 \err{+13}{-8} \pm 9$ MeV, $f_D = 194 \err{+14}{-10} \pm 10$ MeV, and $f_{D_s} = 213 \err{+14}{-11} \pm 11$ MeV in the quenched approximation. The first error in each case is statistical, and the second is from perturbation theory. We show that discretization errors are under control in our approach, and smaller than our statistical errors. The effects of the quenched approximation may raise our quenched result by up to 10%.
The charm quark's mass is determined from Monte Carlo calculations of the $\bar{c}c$ spectrum. The main sources of uncertainty are perturbation theory (for conversion to $\MSbar$), the continuum-limit extrapolation, Monte Carlo statistics, and the effects of quenching. The (preliminary) result for the $\MSbar$ mass is $\bar{m}_{ch}(m_{ch})=1.33\pm 0.08$ GeV.
We investigate the masses of the light quarks with lattice QCD. We show that most of the large dependence on the lattice spacing, a, observed in previous determinations using Wilson fermions is removed with the use of an O(a) corrected action. In the quenched approximation, we obtain for the strange quark MS bar mass m_s(2 GeV) = 95 (16) MeV, and for the average of the up and down quark masses m_l(2 GeV) = 3.6 (6) MeV. Short distance arguments and existing staggered fermion calculations make it likely that the answers including the effects of quark loops lie 20 % to 40 % below this: m_s(2 GeV) in the range 54-92 MeV, and m_l(2 GeV) in the range 2.1-3.5 MeV. We argue that almost all lattice determinations of the light quark masses are consistent with these values. These low values are outside the range usually given by conventional phenomenology.
Relativistic corrections communicate the binding energy of a bound state to its kinetic mass. This mechanism is reviewed and used to explain anomalous results of Collins, Edwards, Heller, and Sloan (hep-lat/9512026), which compared rest and kinetic masses of heavy-light mesons and quarkonia.
This paper presents a formulation of lattice fermions applicable to all quark masses, large and small. We incorporate interactions from previous light-fermion and heavy-fermion methods, and thus ensure a smooth connection to these limiting cases. The couplings in improved actions are evaluated for arbitrary fermion mass~$m_q$, without expansions around small- or large-mass limits. We treat both the action and external currents. By interpreting on-shell improvement criteria through the lattice theory's Hamiltonian, one finds that cutoff artifacts factorize into the form $b_n(m_qa)[\vek{p}a]^{s_n}$, where $\vek{p}$ is a momentum characteristic of the system under study, $s_n$ is related to the dimension of the $n$th interaction, and $b_n(m_qa)$ is a bounded function, numerically always~$\order(1)$ or less. In heavy-quark systems $\vek{p}$ is typically rather smaller than the fermion mass~$m_q$. Therefore, artifacts of order $(m_qa)^s$ do not arise, even when $m_qa\gsim1$. An important by-product of our analysis is an interpretation of the Wilson and Sheikholeslami-Wohlert actions applied to nonrelativistic fermions.
Chiral fermions can (presumably) be constructed by introducing two regulators, one for the gauge fields (e.g. a lattice), and another for the fermion functional integrals in a fixed (regulated) gauge field. This talk discusses cutoff effects arising from the regulator of the fermions.
Lattice fermions have well-known difficulties with chiral symmetry. To evade them it is possible to couple continuum fermions to lattice gauge fields, by introducing an interpolation of the latter. Following this line of thinking, this paper presents two Euclidean formulations of the effective action that appears after functional integration over fermion fields, one for vector-like and the other for chiral couplings. With suitable finite-mode regulators both effective actions can be evaluated in a finite computation. The prescriptions provided here contain some details not found in previous work marrying continuum fermions to the lattice via an interpolation. For example, the counter-terms needed to maintain chiral gauge invariance are explicitly given. By construction coupling-constant renormalization, anomaly structure, and (in the chiral gauge theory) fermion nonconserving amplitudes all satisfy one's expectations from perturbative and semi-classical analyses.
Most of the poorly known parameters of the Standard Model cannot be determined without reliable calculations in nonperturbative QCD. Lattice gauge theory provides a first-principles definition of the required functional integrals, and hence offers ways of performing these calculations. This paper reviews the progress in computing hadron spectra and electroweak matrix elements needed to determine $α_S$, the quark masses, and the Cabibbo-Kobayashi-Maskawa matrix.
We discuss lattice artifacts for matrix elements of hadrons containing one or more heavy quark. In particular, we analyze interrelations between lattice artifacts and the $1/m_Q$ expansion. The implications for calculations of heavy-light decay constants and of semi-leptonic form factors are discussed.
The role lattice QCD can play in $B$ physics is surveyed. We include results for the decay constant, and discuss upcoming calculations of semileptonic form factors and neutral-meson mixing. Together with experimental measurements, these calculations can determine the unitarity triangle. Plenary talk presented at the Workshop on $B$ Physics at Hadron Accelerators, Snowmass, Colo., 21 June--2 July, 1993.
We formulate lattice fermions in a way that encompasses Wilson fermions as well as the static and non-relativistic approximations. In particular, we treat $m_qa$ systematically ($m_q$ is the fermion mass) showing how to understand the Wilson action as an effective action for systems with $\vek{p}\ll m_q$. The results show how to extract matrix elements and the spectrum from simulations with $m_qa\approx1$, which is relevant for the charm quark.