Staggered Chiral Perturbation Theory

We discuss how to formulate a staggered chiral perturbation theory. This amounts to a generalization of the Lee-Sharpe Lagrangian to include more than one flavor (i.e. multiple staggered fields), which turns out to be nontrivial. One loop corrections to pion and kaon masses and decay constants are computed as examples in three cases: the quenched, partially quenched, and full (unquenched) case. The results for the one loop mass and decay constant corrections have already been presented in Ref. [1].Comment: talk presented by C. Aubin at Lattice2002(spectrum); 3 pages, 1 figur

Lattice Calculations of Decay Constants

Lattice attempts to compute the leptonic decay constants of heavy-light pseudoscalar mesons are described. I give a short historical overview of such attempts and then discuss some current calculations. I focus on three of the most important sources of systematic error: the extrapolation to the continuum, the chiral extrapolation in light quark mass, and the effects of quenching. I briefly discuss the ``bag parameters'' $B_B$ and $B_{B_s}$, and then conclude with my expectations of the precision in decay constants and bag parameters that will be possible in the next few years.Comment: 12 pages, 3 included postscript figures, uses sprocl.sty and epsfig. Review talk presented at the "Seventh International Symposium on Heavy Flavor Physics," Santa Barbara, July 7-11, 199

Staggered Chiral Perturbation Theory for Neutral B Mixing

I describe a calculation of B meson mixing at one-loop in staggered chiral perturbation theory, for the complete set of Standard Model and beyond-the-Standard Model operators. The particular lattice representation of the continuum operators used by the Fermilab Lattice/MILC collaborations (and earlier by the HPQCD collaboration) turns out to be important, and results in the presence of "wrong-spin" operators, whose contributions however vanish in the continuum limit. The relation between staggered and naive fermions also plays a key role.Comment: 7 pages, 5 pdf figures. Presented at Lattice 2012, June 24-29, 2012, Cairns, Australia. To be published as PoS(Lattice2012), 20

Heavy-Light Semileptonic Decays in Staggered Chiral Perturbation Theory

We calculate the form factors for the semileptonic decays of heavy-light pseudoscalar mesons in partially quenched staggered chiral perturbation theory (\schpt), working to leading order in $1/m_Q$, where $m_Q$ is the heavy quark mass. We take the light meson in the final state to be a pseudoscalar corresponding to the exact chiral symmetry of staggered quarks. The treatment assumes the validity of the standard prescription for representing the staggered ``fourth root trick'' within \schpt by insertions of factors of 1/4 for each sea quark loop. Our calculation is based on an existing partially quenched continuum chiral perturbation theory calculation with degenerate sea quarks by Becirevic, Prelovsek and Zupan, which we generalize to the staggered (and non-degenerate) case. As a by-product, we obtain the continuum partially quenched results with non-degenerate sea quarks. We analyze the effects of non-leading chiral terms, and find a relation among the coefficients governing the analytic valence mass dependence at this order. Our results are useful in analyzing lattice computations of form factors $B\to\pi$ and $D\to K$ when the light quarks are simulated with the staggered action.Comment: 53 pages, 8 figures, v2: Minor correction to the section on finite volume effects, and typos fixed. Version to be published in Phys. Rev.

Renormalization-group analysis of the validity of staggered-fermion QCD with the fourth-root recipe

I develop a renormalization-group blocking framework for lattice QCD with staggered fermions. Under plausible, and testable, assumptions, I then argue that the fourth-root recipe used in numerical simulations is valid in the continuum limit. The taste-symmetry violating terms, which give rise to non-local effects in the fourth-root theory when the lattice spacing is non-zero, vanish in the continuum limit. A key role is played by reweighted theories that are local and renormalizable on the one hand, and that approximate the fourth-root theory better and better as the continuum limit is approached on the other hand.Comment: Minor corrections. Revtex, 58 page

SU(3) Flavor Breaking in Hadronic Matrix Elements for B−BˉB - \bar B Oscillations

We present an analysis, using quenched configurations at $6/g^2=$5.7, 5.85, 6.0, and 6.3 of the matrix element \MP\equiv\langle \bar P_{hl}|\bar h \gamma_\mu (1-\gamma_5)l \bar h \gamma_\mu(1-\gamma_5)l|P_{hl}\rangle for heavy-light pseudoscalar mesons. The results are extrapolated to the physical $B$ meson states, \Bd and \Bs. We directly compute the ratio \MS/\MB, and obtain the preliminary result \MS/\MB=1.54(13)(32). A precise value of this SU(3) breaking ratio is important for determining $V_{td}$ once the mixing parameter $x_s$ for \Bs-\bar\Bs is measured experimentally. We also determine values for the corresponding B parameters, $B_{bs}(2 \rm{GeV})=B_{bd}(2 \rm{GeV})=1.02(13)$, which we cannot distinguish in the present analysis.Comment: Poster presented at LATTICE96(heavy quarks). LaTeX, uses espcrc2.sty and epsf, 4 pages, 4 postscript figures include