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At least 343 records · Page 19Linked to original sources

arXiv2011

The I=2 pipi S-wave Scattering Phase Shift from Lattice QCD

The pi+pi+ s-wave scattering phase-shift is determined below the inelastic threshold using Lattice QCD. Calculations were performed at a pion mass of m_pi~390 MeV with an anisotropic n_f=2+1 clover fermion discretization in four lattice volumes, with spatial extent L~2.0, 2.5, 3.0 and 3.9 fm, and with a lattice spacing of b_s~0.123 fm in the spatial direction and b_t b_s/3.5 in the time direction. The phase-shift is determined from the energy-eigenvalues of pi+pi+ systems with both zero and non-zero total momentum in the lattice volume using Luscher's method. Our calculations are precise enough to allow for a determination of the threshold scattering parameters, the scattering length a, the effective range r, and the shape-parameter P, in this channel and to examine the prediction of two-flavor chiral perturbation theory: m_pi^2 a r = 3+O(m_pi^2/Lambda_chi^2). Chiral perturbation theory is used, with the Lattice QCD results as input, to predict the scattering phase-shift (and threshold parameters) at the physical pion mass. Our results are consistent with determinations from the Roy equations and with the existing experimental phase shift data.

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arXiv2012

Hyperon sigma terms for 2+1 quark flavours

QCD lattice simulations determine hadron masses as functions of the quark masses. From the gradients of these masses and using the Feynman-Hellmann theorem the hadron sigma terms can then be determined. We use here a novel approach of keeping the singlet quark mass constant in our simulations which upon using an SU(3) flavour symmetry breaking expansion gives highly constrained (i.e. few parameter) fits for hadron masses in a multiplet. This is a highly advantageous procedure for determining the hadron mass gradient as it avoids the use of delicate chiral perturbation theory. We illustrate the procedure here by estimating the light and strange sigma terms for the baryon octet.

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arXiv2012

Hot Quark Matter with an Axial Chemical Potential

We analyze the phase diagram of hot quark matter in presence of an axial chemical potential, $μ_5$. The latter is introduced to mimic the chirality transitions induced, in hot Quantum Chromodynamics, by the strong sphaleron configurations. In particular, we study the curvature of the critical line at small $μ_5$, the effects of a finite quark mass and of a vector interaction. Moreover, we build the mixed phase at the first order phase transition line, and draw the phase diagram in the chiral density and temperature plane. We finally compute the full topological susceptibility in presence of a background of topological charge.

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arXiv2012

Hybrid Baryons in QCD

We present the first comprehensive study of hybrid baryons using lattice QCD methods. Using a large basis of composite QCD interpolating fields we extract an extensive spectrum of baryon states and isolate those of hybrid character using their relatively large overlap onto operators which sample gluonic excitations. We consider the spectrum of Nucleon and Delta states at several quark masses finding a set of positive parity hybrid baryons with quantum numbers N_1/2+, N_1/2+, N_3/2+, N_3/2+, N_5/2+ and Delta_1/2+, Delta_3/2+ at an energy scale above the first band of `conventional' excited positive parity baryons. This pattern of states is compatible with a color octet gluonic excitation having J^P=1+ as previously reported in the hybrid meson sector and with a comparable energy scale for the excitation, suggesting a common bound-state construction for hybrid mesons and baryons.

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arXiv2012

Hadronic Parity Violation at Next-to-Leading Order

The flavor-conserving non-leptonic weak interaction can be studied experimentally through the observation of parity violation in nuclear and few-body systems. At hadronic scales, matrix elements of parity-violating four-quark operators ultimately give rise to the parity violating couplings between hadrons, and such matrix elements can be calculated non-perturbatively using lattice QCD. In this work, we investigate the running of isovector parity-violating operators from the weak scale down to hadronic scales using the renormalization group. We work at next-to-leading order in the QCD coupling, and include both neutral-current and charged-current interactions. At this order, results are renormalization scheme dependent, and we utilize 't Hooft-Veltman dimensional regularization. The evolution of Wilson coefficients at leading and next-to-leading order is compared. Next-to-leading order effects are shown to be non-negligible at hadronic scales.

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arXiv2011

Determining low-energy constants in partially quenched Wilson chiral perturbation theory

In the low energy effective theory describing the partially quenched extension of two light Wilson fermions, three low energy constants (LECs) appear in terms proportional to a^2 (a being the lattice spacing). We propose methods to separately calculate these LECs, typically called W'_6, W'_7 and W'_8. While only one linear combination of these constants enters into physical quantities, different combinations enter into the description of the spectral density and eigenvalue distributions of the lattice Dirac operator and its Hermitian counterpart. Thus it is useful to be able to determine the LECs separately. Our methods require studying certain correlation functions for either two or three pion scattering, which are accessible only in the partially quenched extension of the theory.

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arXiv2011

Thermodynamics of lattice QCD with 3 flavours of colour-sextet quarks

We have been studying QCD with 2 flavours of colour-sextet quarks to distinguish whether it is QCD-like or conformal. For comparison we are now studying QCD with 3 flavours of colour-sextet quarks, which is believed to be conformal in the chiral limit. Here we present the results of simulations of lattice QCD with 3 colour-sextet quarks at finite temperatures on lattices of temporal extent $N_t=4$ and 6, with masses small enough to yield access to the chiral limit. As for the 2-flavour case, we find well-separated deconfinement and chiral-symmetry restoration transitions, both of which move to appreciably weaker couplings as $N_t$ is increased from 4 to 6. If this theory is conformal, we would expect there to be a bulk chiral transition at a fixed coupling. For this reason we conclude that for $N_t=4$ and 6, the chiral and hence the deconfinement transitions are in the strong-coupling domain where the theory is essentially quenched. The similarity between the behaviours of the 2 and 3 flavour theories suggested that the $N_t=4$ and 6 transitions for the 2-flavour theory also lie in the strong-coupling domain. The phase structure of both theories is very similar.

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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.

hep-th↗

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.

hep-ph↗

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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