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arXiv2012

Scattering of unstable particles in a finite volume: the case of pi rho scattering and the a1(1260) resonance

We present a way to evaluate the scattering of unstable particles quantized in a finite volume with the aim of extracting physical observables for infinite volume from lattice data. We illustrate the method with the $πρ$ scattering which generates dynamically the axial-vector $a_1(1260)$ resonance. Energy levels in a finite box are evaluated both considering the $ρ$ as a stable and unstable resonance and we find significant differences between both cases. We discuss how to solve the problem to get the physical scattering amplitudes in the infinite volume, and hence phase shifts, from possible lattice results on energy levels quantized inside a finite box.

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arXiv2012

Density of states and Fisher's zeros in compact U(1) pure gauge theory

We present high-accuracy calculations of the density of states using multicanonical methods for lattice gauge theory with a compact gauge group U(1) on 4^4, 6^4 and 8^4 lattices. We show that the results are consistent with weak and strong coupling expansions. We present methods based on Chebyshev interpolations and Cauchy theorem to find the (Fisher's) zeros of the partition function in the complex beta=1/g^2 plane. The results are consistent with reweighting methods whenever the latter are accurate. We discuss the volume dependence of the imaginary part of the Fisher's zeros, the width and depth of the plaquette distribution at the value of beta where the two peaks have equal height. We discuss strategies to discriminate between first and second order transitions and explore them with data at larger volume but lower statistics. Higher statistics and even larger lattices are necessary to draw strong conclusions regarding the order of the transition.

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arXiv2012

Lattice Gauge Theory - Gravity duality and Coulomb's constant in five dimensions

The purpose of this paper is to perform a quantitative check of gauge theory - gravity duality in a nonconformal, nonsupersymmetric context. In order to do so we define k5, an object extracted from the Wilson Loop, that plays the role of Coulomb's constant for SU(N) gauge theories in five dimensions and we argue that one of its virtues is that it could be minimally sensitive to N. This allows us to compute k5 on one hand from the gravitational backreation of a large number N of D4-branes, and on the other from a lattice mean-field expansion for N=2. We find a 2% numerical agreement between the two approaches.

hep-th↗

arXiv2012

Next-to-leading-order corrections to $B \to π$ form factors in $k_T$ factorization

We calculate next-to-leading-order (NLO) corrections to the $B\toπ$ transition form factors at leading twist in the $k_T$ factorization theorem. Light partons off-shell by $k_T^2$ are considered in the quark diagrams, in the effective diagrams for the $B$ meson wave function defined with the effective heavy-quark field, and in the effective diagrams for the pion wave function. It is explicitly demonstrated that the infrared logarithms $\ln k_T^2$ cancel between the above sets of diagrams, as deriving the $k_T$-dependent NLO hard kernel from their difference. The infrared finiteness of the hard kernel confirms the application of the $k_T$ factorization theorem to $B$ meson semileptonic decays. The NLO pion wave function is identical to those constructed from the pion transition and electromagnetic form factors, consistent with its universality. Choosing the renormalization and factorization scales lower than the $B$ meson mass, the NLO corrections are under control: they amount only up to 30% of the form factors at large recoil of the pion, when varying models for the meson wave functions.

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arXiv2012

SU(4) lattice gauge theory with decuplet fermions: Schrödinger functional analysis

We complete a program of study of SU(N) gauge theories coupled to two flavors of fermions in the two-index symmetric representation by performing numerical simulations in SU(4). The beta function, defined and calculated via the Schrödinger functional, runs more slowly than the two-loop perturbative result. The mass anomalous dimension levels off in strong coupling at a value of about 0.45, rendering this theory unsuitable for walking technicolor. A large-N comparison of this data with results from SU(2) and SU(3) reveals striking regularities.

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arXiv2012

Kaon mixing matrix elements from beyond-the-Standard-Model operators in staggered chiral perturbation theory

Models of new physics induce K-Kbar mixing operators having Dirac structures other than the "left-left" form of the Standard Model. We calculate the functional form of the corresponding B-parameters at next-to-leading order in both SU(3) and SU(2) staggered chiral perturbation theory (SChPT). Numerical results for these matrix elements are being generated using improved staggered fermions; our results can be used to extrapolate these matrix elements to the physical light and strange quark masses. The SU(3) SChPT results turn out to be much simpler than that for the Standard Model B_K operator, due to the absence of chiral suppression in the new operators. The SU(2) SChPT result is of similar simplicity to that for B_K. In fact, in the latter case, the chiral logarithms for two of the new B-parameters are identical to those for B_K, while those for the other two new B-parameters are of opposite sign. In addition to providing results for the 2+1 flavor theory in SU(3) SChPT and the 1+1+1 flavor theory in SU(2) SChPT, we present the corresponding continuum partially quenched results, as these are not available in the literature.

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arXiv2012

A study of the lightest glueball states in SU(2) Euclidean Yang-Mills theory in the maximal Abelian gauge

A qualitative study of the lightest glueball states in Euclidean SU(2) Yang-Mills theory quantized in the maximal Abelian gauge is presented. The analysis is done by generalizing to the maximal Abelian gauge the so-called replica model, already successfully introduced in the Landau gauge. As it will be shown, the gluon and ghost propagators obtained from the replica model are of the same type of those already introduced in Phys. Rev. D77, 105023 (2008) [arXiv:0801.0566], whose behavior turns out to be in agreement with that available from the lattice data on the maximal Abelian gauge. The model turns out to be renormalizable to all orders, while enabling us to introduce gauge invariant composite operators for the study of the lightest glueballs $J^{PC}=0^{++}$, $2^{++}$ and $0^{-+}$. The spectral representation for the correlation functions of these operators are evaluated to the first order, and the corresponding spectral densities are shown to be positive. Under the assumption of Abelian dominance, it turns out that the hierarchy for the masses of the lightest glueballs in the maximal Abelian gauge is in agreement with that already obtained in the Landau gauge, a feature which provides evidence for the gauge independence of the spectrum of the theory.

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arXiv2012

The Gribov horizon and the one-loop color-Coulomb potential

We recalculate the color-Coulomb potential to one-loop order, under the assumption that the effect of the Gribov horizon is to make i) the transverse gluon propagator less singular; and ii) the color-Coulomb potential more singular, than their perturbative behavior in the low-momentum limit. As a first guess, the effect of the Gribov horizon is mimicked by introducing a transverse momentum-dependent gluon mass term, leading to a propagator of the Gribov form, with the prescription that the mass parameter should be adjusted to the unique value where the infrared behavior of the Coulomb potential is enhanced. We find that this procedure leads to a Coulomb potential rising asymptotically as a linear term modified by a logarithm.

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arXiv2012

The No-Pole Condition in Landau gauge: Properties of the Gribov Ghost Form-Factor and a Constraint on the 2d Gluon Propagator

We study the Landau-gauge Gribov ghost form-factor sigma(p^2) for SU(N) Yang-Mills theories in the d-dimensional case. We find a qualitatively different behavior for d=3,4 w.r.t. d=2. In particular, considering any (sufficiently regular) gluon propagator D(p^2) and the one-loop-corrected ghost propagator G(p^2), we prove in the 2d case that sigma(p^2) blows up in the infrared limit p -> 0 as -D(0)\ln(p^2). Thus, for d=2, the no-pole condition σ(p^2) < 1 (for p^2 > 0) can be satisfied only if D(0) = 0. On the contrary, in d=3 and 4, sigma(p^2) is finite also if D(0) > 0. The same results are obtained by evaluating G(p^2) explicitly at one loop, using fitting forms for D(p^2) that describe well the numerical data of D(p^2) in d=2,3,4 in the SU(2) case. These evaluations also show that, if one considers the coupling constant g^2 as a free parameter, G(p^2) admits a one-parameter family of behaviors (labelled by g^2), in agreement with Boucaud et al. In this case the condition sigma(0) <= 1 implies g^2 <= g^2_c, where g^2_c is a 'critical' value. Moreover, a free-like G(p^2) in the infrared limit is obtained for any value of g^2 < g^2_c, while for g^2 = g^2_c one finds an infrared-enhanced G(p^2). Finally, we analyze the Dyson-Schwinger equation (DSE) for sigma(p^2) and show that, for infrared-finite ghost-gluon vertices, one can bound sigma(p^2). Using these bounds we find again that only in the d=2 case does one need to impose D(0) = 0 in order to satisfy the no-pole condition. The d=2 result is also supported by an analysis of the DSE using a spectral representation for G(p^2). Thus, if the no-pole condition is imposed, solving the d=2 DSE cannot lead to a massive behavior for D(p^2). These results apply to any Gribov copy inside the so-called first Gribov horizon, i.e. the 2d result D(0) = 0 is not affected by Gribov noise. These findings are also in agreement with lattice data.

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arXiv2012

An updated determination of α_s from tau decays

Employing our previous framework to treat non-perturbative effects self-consistently, including duality violations, we update the determination of the strong coupling, α_s, using a modified version of the 1998 OPAL data, updated to reflect current values of exclusive mode hadronic τdecay branching fractions. Our best n_f=3 values from the updated OPAL data are α_s(m^2_τ)=0.325+-0.018 and α_s(m^2_τ)=0.347+-0.025 in fixed-order and contour-improved perturbation theory, respectively. To account for non-perturbative effects, non-linear, multi-parameter fits are necessary. We have, therefore, investigated the posterior probability distribution of the model parameters underlying our fits in more detail. We find that OPAL data alone provide only weak constraints on some of the parameters needed to model duality violations, especially in the case of fits involving axial vector channel data, making additional prior assumptions on the expected size of these parameters necessary at present. We provide evidence that this situation could be greatly improved if hadronic spectral functions based on the high-statistics BaBar and Belle data were to be made available.

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arXiv2012

The Realization of the Sharpe-Singleton Scenario

The microscopic spectral density of the Wilson Dirac operator for two flavor lattice QCD is analyzed. The computation includes the leading order a^2 corrections of the chiral Lagrangian in the microscopic limit. The result is used to demonstrate how the Sharpe-Singleton first order scenario is realized in terms of the eigenvalues of the Wilson Dirac operator. We show that the Sharpe-Singleton scenario only takes place in the theory with dynamical fermions whereas the Aoki phase can be realized in the quenched as well as the unquenched theory. Moreover, we give constraints imposed by gamma_5-Hermiticity on the additional low energy constants of Wilson chiral perturbation theory.

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arXiv2011

MCRG Minimal Walking Technicolor

We present a Monte Carlo renormalisation group study of the SU(2) gauge theory with two Dirac fermions in the adjoint representation. Using the two-lattice matching technique we measure the running of the coupling and the anomalous mass dimension. We find slow running of the coupling, compatible with an infrared fixed point. Assuming this running is negligible we find a vanishing anomalous dimension, gamma=-0.03(13), however taking this source of systematic error into account gives a much larger range of allowed values, -0.6 < gamma < 0.6. We also attempt to measure the anomalous mass dimension using the stability matrix method. We discuss the systematic errors affecting the current analysis and possible improvements.

hep-ph↗

arXiv2012

Chiral extrapolations for nucleon magnetic moments

Lattice QCD simulations have made significant progress in the calculation of nucleon electromagnetic form factors in the chiral regime in recent years. With simulation results achieving pion masses of order ~180 MeV, there is an apparent challenge as to how the physical regime is approached. By using contemporary methods in chiral effective field theory, both the quark-mass and finite-volume dependence of the isovector nucleon magnetic moment are carefully examined. The extrapolation to the physical point yields a result that is compatible with experiment, albeit with a combined statistical and systematic uncertainty of 10%. The extrapolation shows a strong finite-volume dependence; lattice sizes of L > 5 fm must be used to simulate results within 2% of the infinite-volume result for the magnetic moment at the physical pion mass.

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arXiv2011

Taste non-Goldstone, flavor-charged pseudo-Goldstone boson masses in staggered chiral perturbation theory

We calculate the masses of taste non-Goldstone pions and kaons in staggered chiral perturbation theory through next-to-leading order in the standard power counting. The results can be used to quantitatively understand taste violations in existing lattice data generated with staggered fermions and to extract the $u$, $d$, and $s$ quark masses and Gasser-Leutwyler parameters from the experimentally observed spectrum. The expressions for the non-Goldstone masses contain low-energy couplings unique to the non-Goldstone sector. With two exceptions these enter as coefficients of analytic terms; all the new couplings can be fixed by performing spectrum calculations. We report one-loop results for the quenched case and the fully dynamical and partially quenched 1+1+1 and 2+1 flavor cases in the chiral SU(3) and SU(2) theories.

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arXiv2012

Large-N reduction in QCD with two adjoint Dirac fermions

We use lattice simulations to study the single-site version of SU(N) lattice gauge theory with two flavors of Wilson-Dirac fermions in the adjoint representation, a theory whose large volume correspondent is expected to be conformal or nearly conformal. Working with N as large as 53, we map out the phase diagram in the plane of bare `t Hooft coupling, g^2 N, and of the lattice quark mass, a*m, and look for the region where the Z_N^4 center symmetry of the theory is intact. In this region one expects the large-N equivalence of the single site and infinite volume theories to be valid. As for the N_f=1 case (see Phys. Rev. D80: 065031), we find that the center-symmetric region is large and includes both light fermion masses and masses at the cutoff scale. We study the N-dependence of the width of this region and find strong evidence that it remains of finite width as N goes to infinity. Simulating with couplings as small as g^2 N = 0.005, we find that the width shrinks slowly with decreasing g^2 N, at a rate consistent with analytic arguments. Within the center-symmetric region our results for the phase structure, when extrapolated to infinite N, apply also for the large volume theory, which is minimal walking technicolor with N=infinity. We find a first-order transition as a function of a*m for all values of b, which we argue favors that the theory is confining in the infrared. Finally, we measure the eigenvalue densities of the Wilson-Dirac operator and its hermitian version, and use large Wilson loops to study the utility of reduction for extracting physical observables.

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arXiv2012

S-wave scattering of strangeness -3 baryons

We explore the interactions of two strangeness -3 baryons in multiple spin channels with lattice QCD. This system provides an ideal laboratory for exploring the interactions of multi-baryon systems with minimal dependence on light quark masses. Model calculations of the two-$Ω^-$ system in two previous works have obtained conflicting results, which can be resolved by lattice QCD. The lattice calculations are performed using two different volumes with $L\sim2.5$ and 3.9 fm on anisotropic clover lattices at $m_π\sim 390$ MeV with a lattice spacing of $a_s \sim 0.123$ fm in the spatial direction and $a_t\sim{a}_s/3.5$ in the temporal direction. Using multiple interpolating operators from a non-displaced source, we present scattering information for two ground state $Ω^-$ baryons in both the S=0 and S=2 channels. For S=0, $k\cotδ$ is extracted at two volumes, which lead to an extrapolated scattering length of $a^{ΩΩ}_{S=0}=0.16 \pm 0.22 \ \text{fm}$, indicating a weakly repulsive interaction. Additionally, for S=2, two separate highly repulsive states are observed. We also present results on the interactions of the excited strangeness -3, spin-1/2 states with the ground spin-3/2 states for the spin-1 and spin-2 channels. Results for these interactions are consistent with attractive behavior.

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arXiv2012

The critical line of two-flavor QCD at finite isospin or baryon densities from imaginary chemical potentials

We determine the (pseudo)critical lines of QCD with two degenerate staggered fermions at nonzero temperature and quark or isospin density, in the region of imaginary chemical potentials; analytic continuation is then used to prolongate to the region of real chemical potentials. We obtain an accurate determination of the curvatures at zero chemical potential, quantifying the deviation between the case of finite quark and of finite isospin chemical potential. Deviations from a quadratic dependence of the pseudocritical lines on the chemical potential are clearly seen in both cases: we try different extrapolations and, for the case of nonzero isospin chemical potential, confront them with the results of direct Monte Carlo simulations. Finally we find that, as for the finite quark density case, an imaginary isospin chemical potential can strengthen the transition till turning it into strong first order.

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arXiv2011

Modeling the Gluon Propagator in Landau Gauge: Lattice Estimates of Pole Masses and Dimension-Two Condensates

We present an analytic description of numerical results for the Landau-gauge SU(2) gluon propagator D(p^2), obtained from lattice simulations (in the scaling region) for the largest lattice sizes to date, in d = 2, 3 and 4 space-time dimensions. Fits to the gluon data in 3d and in 4d show very good agreement with the tree-level prediction of the Refined Gribov-Zwanziger (RGZ) framework, supporting a massive behavior for D(p^2) in the infrared limit. In particular, we investigate the propagator's pole structure and provide estimates of the dynamical mass scales that can be associated with dimension-two condensates in the theory. In the 2d case, fitting the data requires a non-integer power of the momentum p in the numerator of the expression for D(p^2). In this case, an infinite-volume-limit extrapolation gives D(0) = 0. Our analysis suggests that this result is related to a particular symmetry in the complex-pole structure of the propagator and not to purely imaginary poles, as would be expected in the original Gribov-Zwanziger scenario.

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