Pseudoscalar correlators and the problem of the chiral limit in the compact lattice QED with Wilson fermions

The phase diagram for the compact lattice QED with Wilson fermions is shown. We discuss different methods for the calculation of the 'pion' mass $m_{\pi}$ near the chiral transition point $\kappa_c(\beta )$.Comment: 3 pages, TALK GIVEN AT THE LATTICE '94 INTERNATIONAL SYMPOSIUM LATTICE FIELD THEORY, BIELEFELD, GERMANY, SEPTEMBER 27 -- OCTOBER 1, 1994 Three figures are included as ps-files. Look for %%%%% FIG1.PS %%%% , et

Chiral power counting of one- and two-body currents in direct detection of dark matter

We present a common chiral power-counting scheme for vector, axial-vector, scalar, and pseudoscalar WIMP-nucleon interactions, and derive all one- and two-body currents up to third order in the chiral expansion. Matching our amplitudes to non-relativistic effective field theory, we find that chiral symmetry predicts a hierarchy amongst the non-relativistic operators. Moreover, we identify interaction channels where two-body currents that so far have not been accounted for become relevant.Comment: 8 pages, 1 table; journal versio

Improved predictions for μ→e\mu\to e conversion in nuclei and Higgs-induced lepton flavor violation

Compared to $\mu \to e \gamma$ and $\mu \to e e e$, the process $\mu \to e$ conversion in nuclei receives enhanced contributions from Higgs-induced lepton flavor violation. Upcoming $\mu \to e$ conversion experiments with drastically increased sensitivity will be able to put extremely stringent bounds on Higgs-mediated $\mu \to e$ transitions. We point out that the theoretical uncertainties associated with these Higgs effects, encoded in the couplings of quark scalar operators to the nucleon, can be accurately assessed using our recently developed approach based on $SU(2)$ Chiral Perturbation Theory that cleanly separates two- and three-flavor observables. We emphasize that with input from lattice QCD for the coupling to strangeness $f_s^N$, hadronic uncertainties are appreciably reduced compared to the traditional approach where $f_s^N$ is determined from the pion--nucleon $\sigma$-term by means of an $SU(3)$ relation. We illustrate this point by considering Higgs-mediated lepton flavor violation in the Standard Model supplemented with higher-dimensional operators, the two-Higgs-doublet model with generic Yukawa couplings, and the Minimal Supersymmetric Standard Model. Furthermore, we compare bounds from present and future $\mu \to e$ conversion and $\mu \to e \gamma$ experiments.Comment: 9 pages, 5 figures, journal versio

Remarks on the pion-nucleon sigma-term

The pion-nucleon $\sigma$-term can be stringently constrained by the combination of analyticity, unitarity, and crossing symmetry with phenomenological information on the pion-nucleon scattering lengths. Recently, lattice calculations at the physical point have been reported that find lower values by about $3\sigma$ with respect to the phenomenological determination. We point out that a lattice measurement of the pion-nucleon scattering lengths could help resolve the situation by testing the values extracted from spectroscopy measurements in pionic atoms.Comment: 5 pages, 2 figures; version published in PL

Extracting the chiral anomaly from gamma pi --> pi pi

We derive dispersive representations for the anomalous process gamma pi --> pi pi with the pi pi P-wave phase shift as input. We investigate how in this framework the chiral anomaly can be extracted from a cross-section measurement using all data up to 1 GeV, and discuss the importance of a precise representation of the gamma pi --> pi pi amplitude for the hadronic light-by-light contribution to the anomalous magnetic moment of the muon.Comment: 10 pages, 3 figures; version published in Phys. Rev.

Isospin violation in low-energy pion-nucleon scattering revisited

We calculate isospin breaking in pion-nucleon scattering in the threshold region in the framework of covariant baryon chiral perturbation theory. All effects due to quark mass differences as well as real and virtual photons are consistently included. As an application, we discuss the energy dependence of the triangle relation that connects elastic scattering on the proton pi+- p --> pi+- p with the charge exchange reaction pi- p --> pi0 n.Comment: 82 pages, 22 figures, version published in Nucl. Phys.

Two-pion contribution to hadronic vacuum polarization

We present a detailed analysis of $e^+e^-\to\pi^+\pi^-$ data up to $\sqrt{s}=1\,\text{GeV}$ in the framework of dispersion relations. Starting from a family of $\pi\pi$ $P$-wave phase shifts, as derived from a previous Roy-equation analysis of $\pi\pi$ scattering, we write down an extended Omn\`es representation of the pion vector form factor in terms of a few free parameters and study to which extent the modern high-statistics data sets can be described by the resulting fit function that follows from general principles of QCD. We find that statistically acceptable fits do become possible as soon as potential uncertainties in the energy calibration are taken into account, providing a strong cross check on the internal consistency of the data sets, but preferring a mass of the $\omega$ meson significantly lower than the current PDG average. In addition to a complete treatment of statistical and systematic errors propagated from the data, we perform a comprehensive analysis of the systematic errors in the dispersive representation and derive the consequences for the two-pion contribution to hadronic vacuum polarization. In a global fit to both time- and space-like data sets we find $a_\mu^{\pi\pi}|_{\leq 1\,\text{GeV}}=495.0(1.5)(2.1)\times 10^{-10}$ and $a_\mu^{\pi\pi}|_{\leq 0.63\,\text{GeV}}=132.8(0.4)(1.0)\times 10^{-10}$. While the constraints are thus most stringent for low energies, we obtain uncertainty estimates throughout the whole energy range that should prove valuable in corroborating the corresponding contribution to the anomalous magnetic moment of the muon. As side products, we obtain improved constraints on the $\pi\pi$ $P$-wave, valuable input for future global analyses of low-energy $\pi\pi$ scattering, as well as a determination of the pion charge radius, $\langle r_\pi^2 \rangle = 0.429(1)(4)\,\text{fm}^2$.Comment: 40 pages, 16 figures, 13 tables; version published in JHE

Accurate evaluation of hadronic uncertainties in spin-independent WIMP-nucleon scattering: Disentangling two- and three-flavor effects

We show how to avoid unnecessary and uncontrolled assumptions usually made in the literature about soft SU(3) flavor symmetry breaking in determining the two-flavor nucleon matrix elements relevant for direct detection of WIMPs. Based on SU(2) Chiral Perturbation Theory, we provide expressions for the proton and neutron scalar couplings $f_u^{p,n}$ and $f_d^{p,n}$ with the pion-nucleon sigma-term as the only free parameter, which should be used in the analysis of direct detection experiments. This approach for the first time allows for an accurate assessment of hadronic uncertainties in spin-independent WIMP-nucleon scattering and for a reliable calculation of isospin-violating effects. We find that the traditional determinations of $f_u^p-f_u^n$ and $f_d^p-f_d^n$ are off by a factor of 2.Comment: 6 pages, 2 figures; improved numerical analysis, journal versio