Semileptonic Kaon Decay in Staggered Chiral Perturbation Theory

The determination of $\vert V_{us}\vert$ from kaon semileptonic decays requires the value of the form factor $f_+(q^2=0)$, which can be calculated precisely on the lattice. We provide the one-loop partially quenched staggered chiral perturbation theory expressions that may be employed to analyze staggered simulations of $f_+(q^2)$ with three light flavors. We consider both the case of a mixed action, where the valence and sea sectors have different staggered actions, and the standard case where these actions are the same. The momentum transfer $q^2$ of the form factor is allowed to have an arbitrary value. We give results for the generic situation where the $u$, $d$, and $s$ quark masses are all different, $N_f=1+1+1$, and for the isospin limit, $N_f=2+1$. The expression we obtain for $f_+(q^2)$ is independent of the mass of the (valence) spectator quark. In the limit of vanishing lattice spacing, our results reduce to the one-loop continuum partially quenched expression for $f_+(q^2)$, which has not previously been reported in the literature for the $N_f=1+1+1$ case. Our expressions have already been used in staggered lattice analyses of $f_+(0)$, and should prove useful in future calculations as well.Comment: 33 pages, 5 figures; v2: some referencing change

Tests of non-standard electroweak couplings of right-handed quarks

The standard model can be interpreted as the leading order of a Low-Energy Effective Theory (LEET) invariant under a higher non linearly realized symmetry $S_{nat}\supset SU(2)_W \times U(1)_Y$ equipped with a systematic power counting. Within the minimal version of this ``not quite decoupling'' LEET, the dominant non-standard effect appears at next-to-leading order (NLO) and is a modification of the couplings of fermions to W and Z. In particular, the coupling of right-handed quarks to Z is modified and a direct coupling of right-handed quarks to W emerges. Charged right-handed lepton currents are forbidden by an additional discrete symmetry in the lepton sector originally designed to suppress Dirac neutrino masses. A complete NLO analysis of experimental constraints on these modified couplings is presented. Concerning couplings of light quarks, the interface of the electroweak tests with QCD aspects is discussed in detail.Comment: 56 pages, 14 figures, v2: references added, minor modifications in the text, accepted for publication in JHE

The pion charge radius from charged pion electroproduction

We analyze a low-energy theorem of threshold pion electroproduction which allows one to determine the charge radius of the pion. We show that at the same order where the radius appears, pion loops induce a correction to the momentum dependence of the longitudinal dipole amplitude $L_{0+}^{(-)}$. This model-independent correction amounts to an increase of the pion charge radius squared from the electroproduction data by about 0.26~fm$^2$. It sheds light on the apparent discrepancy between the recent determination of the pion radius from electroproduction data and the one based on pion-electron scattering.Comment: 3 pp, REVTeX, uses eps

Pion-Nucleon Phase Shifts in Heavy Baryon Chiral Perturbation Theory

We calculate the phase shifts in the pion-nucleon scattering using the heavy baryon formalism. We consider phase shifts for the pion energy range of 140 to $200$ MeV. We employ two different methods for calculating the phase shifts - the first using the full third order calculation of the pion-nucleon scattering amplitude and the second by including the resonances $\Delta$ and $N^*$ as explicit degrees of freedom in the Lagrangian. We compare the results of the two methods with phase shifts extracted from fits to the pion-nucleon scattering data. We find good to fair agreement between the calculations and the phase shifts from scattering data.Comment: 14 pages, Latex, 6figures. Revised version to appear in Phys.Rev.

Staggered Chiral Perturbation Theory and the Fourth-Root Trick

Staggered chiral perturbation theory (schpt) takes into account the "fourth-root trick" for reducing unwanted (taste) degrees of freedom with staggered quarks by multiplying the contribution of each sea quark loop by a factor of 1/4. In the special case of four staggered fields (four flavors, nF=4), I show here that certain assumptions about analyticity and phase structure imply the validity of this procedure for representing the rooting trick in the chiral sector. I start from the observation that, when the four flavors are degenerate, the fourth root simply reduces nF=4 to nF=1. One can then treat nondegenerate quark masses by expanding around the degenerate limit. With additional assumptions on decoupling, the result can be extended to the more interesting cases of nF=3, 2, or 1. A apparent paradox associated with the one-flavor case is resolved. Coupled with some expected features of unrooted staggered quarks in the continuum limit, in particular the restoration of taste symmetry, schpt then implies that the fourth-root trick induces no problems (for example, a violation of unitarity that persists in the continuum limit) in the lowest energy sector of staggered lattice QCD. It also says that the theory with staggered valence quarks and rooted staggered sea quarks behaves like a simple, partially-quenched theory, not like a "mixed" theory in which sea and valence quarks have different lattice actions. In most cases, the assumptions made in this paper are not only sufficient but also necessary for the validity of schpt, so that a variety of possible new routes for testing this validity are opened.Comment: 39 pages, 3 figures. v3: minor changes: improved explanations and less tentative discussion in several places; corresponds to published versio

The Internal Proper Motions Of Stars In The Open Cluster M35

Relative proper motions, based on 108 orbits of Hubble Space Telescope Fine Guidance Sensor data extending from 1992 to 2006, are reported for 74 stars in the open cluster M35 (NGC 2168). A subset of 22 of these objects are then used to compute the cluster's internal proper motion dispersions in both right ascension and declination. We find that these dispersions are equal to within their measurement errors. The average one-dimensional dispersion is 0.018 +/- 0.002 arcsec century(-1). When combined with the M35 radial velocity dispersion of 0.65 +/- 0.10 km s(-1) found by Geller et al., this produces a cluster distance of 762 +/- 145 pc. Using isochrone fits to the cluster main sequence, this distance suggests that M35 has an age of about 133 Myr. Although this age is consistent with that typically found for M35, the formal error in the dynamical distance of +/- 19% can accommodate ages between 65 Myr and 201 Myr.McDonald Observator

Threshold Photo/Electro Pion Production - Working Group Summary

We summarize the pertinent experimental and theoretical developments in the field of pion photo- and electroproduction in the threshold region. We discuss which experiments and which calculations should be done/performed in the future.Comment: plain TeX (macro included), 6pp, summary talk presented at the workshop on "Chiral Dynamics: Theory and Experiments", MIT, July 25-29, 199