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

Chiral Logs in the Presence of Staggered Flavor Symmetry Breaking

Chiral logarithms in $m_\pi^2$ are calculated at one loop, taking into account the leading contributions to flavor symmetry breaking due to staggered fermions. I treat both the full QCD case (2+1 light dynamical flavors) and the quenched case; finite volume corrections are included. My starting point is the effective chiral Lagrangian introduced by Lee and Sharpe. It is necessary to understand the one-loop diagrams in the ``quark flow'' picture in order to adjust the calculation to correspond to the desired number of dynamical quarks.Comment: version to be published in Phys Rev D: clarifications of finite size corrections and chiral fits added; typo in eq.(5) corrected. 27 pages, 5 eps figure

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.

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

Staggered Chiral Perturbation Theory for Heavy-Light Mesons

We incorporate heavy-light mesons into staggered chiral perturbation theory, working to leading order in 1/m_Q, where m_Q is the heavy quark mass. At first non-trivial order in the chiral expansion, staggered taste violations affect the chiral logarithms for heavy-light quantities only through the light meson propagators in loops. There are also new analytic contributions coming from additional terms in the Lagrangian involving heavy-light and light mesons. Using this heavy-light staggered chiral perturbation theory, we perform the one-loop calculation of the B (or D) meson leptonic decay constant in the partially quenched and full QCD cases. In our treatment, we assume the validity both of the "fourth root trick" to reduce four staggered tastes to one, and of the prescription to represent this trick in the chiral theory by insertions of factors of 1/4 for each sea quark loop.Comment: 48 pages, 6 figures. v3: Some clarifying comments/caveats added; typos fixed. Corresponds to published versio