A Lattice Test of 1/N_c Baryon Mass Relations

1/N_c baryon mass relations are compared with lattice simulations of baryon masses using different values of the light-quark masses, and hence different values of SU(3) flavor-symmetry breaking. The lattice data clearly display both the 1/N_c and SU(3) flavor-symmetry breaking hierarchies. The validity of 1/N_c baryon mass relations derived without assuming approximate SU(3) flavor-symmetry also can be tested by lattice data at very large values of the strange quark mass. The 1/N_c expansion constrains the form of discretization effects; these are suppressed by powers of 1/N_c by taking suitable combinations of masses. This 1/N_c scaling is explicitly demonstrated in the present work.Comment: 13 pages, 20 figures; v2 version to be published in PR

Electromagnetic and spin polarisabilities in lattice QCD

We discuss the extraction of the electromagnetic and spin polarisabilities of nucleons from lattice QCD. We show that the external field method can be used to measure all the electromagnetic and spin polarisabilities including those of charged particles. We then turn to the extrapolations required to connect such calculations to experiment in the context of finite volume chiral perturbation theory. We derive results relevant for lattice simulations of QCD, partially-quenched QCD and quenched QCD. Our results for the polarisabilities show a strong dependence on the lattice volume and quark masses, typically differing from the infinite volume limit by ~10% for current lattice volumes and quark masses.Comment: Minor change

Present Constraints on the H-dibaryon at the Physical Point from Lattice QCD

The current constraints from lattice QCD on the existence of the H-dibaryon are discussed. With only two significant lattice QCD calculations of the H-dibaryon binding energy at approximately the same lattice spacing, the forms of the chiral and continuum extrapolations to the physical point are not determined. In this brief report, we consider the constraints on the H-dibaryon imposed by two simple chiral extrapolations. In both instances, the extrapolation to the physical pion mass allows for a bound H-dibaryon or a near-threshold scattering state. Further lattice QCD calculations are required to clarify this situation.Comment: 8 pages, 2 figures, 1 table; revised for the journa

Universality of Mixed Action Extrapolation Formulae

Mixed action theories with chirally symmetric valence fermions exhibit very desirable features both at the level of the lattice calculations as well as in the construction and implementation of the low energy mixed action effective field theory. In this work we show that when such a mixed action effective field theory is projected onto the valence sector, both the Lagrangian and the extrapolation formulae become universal in form through next to leading order, for all variants of discretization methods used for the sea fermions. Our conclusion relies on the chiral nature of the valence quarks. The result implies that for all sea quark methods which are in the same universality class as QCD, the numerical values of the physical coefficients in the various mixed action chiral Lagrangians will be the same up to lattice spacing dependent corrections. This allows us to construct a prescription to determine the mixed action extrapolation formulae for a large class of hadronic correlation functions computed in partially quenched chiral perturbation theory at the one-loop level. For specific examples, we apply this prescription to the nucleon twist--2 matrix elements and the nucleon--nucleon system. In addition, we determine the mixed action extrapolation formula for the neutron EDM as this provides a nice example of a theta-dependent observable; these observables are exceptions to our prescription.Comment: 36 pages, appendix on twisted mass sea fermions added, expanded discussion of NLO operators, version published in JHEP; typographical errors corrected in Eqs. (68) and (69

Finite volume corrections to pi-pi scattering

Lattice QCD studies of hadron-hadron interactions are performed by computing the energy levels of the system in a finite box. The shifts in energy levels proportional to inverse powers of the volume are related to scattering parameters in a model independent way. In addition, there are non-universal exponentially suppressed corrections that distort this relation. These terms are proportional to exp(-m_pi L) and become relevant as the chiral limit is approached. In this paper we report on a one-loop chiral perturbation theory calculation of the leading exponential corrections in the case of I=2 pi-pi scattering near threshold.Comment: 17 pages, 2 figures, 1 table. Version published in PR

Baryon mass splittings and strong CP violation in SU(3) chiral perturbation theory

We study SU(3) flavor-breaking corrections to the relation between the octet baryon masses and the nucleonmeson CP-violating interactions induced by the QCD (theta) over bar term. We work within the framework of SU(3) chiral perturbation theory andwork through next-to-next-to-leading order in the SU(3) chiral expansion, which isO(m(q)(2)). At lowest order, the CP-odd couplings induced by the QCD (theta) over bar term are determined bymass splittings of the baryon octet, the classic result of Crewther et al. [Phys. Lett. B 88, 123 (1979)]. We show that for each isospin-invariant CP-violating nucleon-meson interaction there exists one relation that is respected by loop corrections up to the order we work, while other leading-order relations are violated. With these relations we extract a precise value of the pion-nucleon coupling (g) over bar (0) by using recent lattice QCD evaluations of the proton-neutron mass splitting. In addition, we derive semiprecise values for CP-violating coupling constants between heaviermesons and nucleons with similar to 30% uncertainty and discuss their phenomenological impact on electric dipole moments of nucleons and nuclei

Kaon thresholds and two-flavor chiral expansions for hyperons

Two-flavor chiral expansions provide a useful perturbative framework to study hadron properties. Such expansions should exhibit marked improvement over the conventional three-flavor chiral expansion. Although one can theoretically formulate two-flavor theories for the various hyperon multiplets, the nearness of kaon thresholds can seriously undermine the effectiveness of the perturbative expansion in practice. We investigate the importance of virtual kaon thresholds on hyperon properties, specifically their masses and isovector axial charges. Using a three-flavor expansion that includes SU(3) breaking effects, we uncover the underlying expansion parameter governing the description of virtual kaon thresholds. For spin-half hyperons, this expansion parameter is quite small. Consequently virtual kaon contributions are well described in the two-flavor theory by terms analytic in the pion mass-squared. For spin three-half hyperons, however, one is closer to the kaon production threshold, and the expansion parameter is not as small. Breakdown of SU(2) chiral perturbation theory is shown to arise from a pole in the expansion parameter associated with the kaon threshold. Estimating higher-order corrections to the expansion parameter is necessary to ascertain whether the two-flavor theory of spin three-half hyperons remains perturbative. We find that, despite higher-order corrections, there is a useful perturbative expansion for the masses and isovector axial charges of both spin-half and spin three-half hyperons. (C) 2010 Elsevier B.V. All rights reserved

High Statistics Analysis using Anisotropic Clover Lattices: (I) Single Hadron Correlation Functions

We present the results of high-statistics calculations of correlation functions generated with single-baryon interpolating operators on an ensemble of dynamical anisotropic gauge-field configurations generated by the Hadron Spectrum Collaboration using a tadpole-improved clover fermion action and Symanzik-improved gauge action. A total of 292,500 sets of measurements are made using 1194 gauge configurations of size 20^3 x 128 with an anisotropy parameter \xi= b_s/b_t = 3.5, a spatial lattice spacing of b_s=0.1227\pm 0.0008 fm, and pion mass of m_\pi ~ 390 MeV. Ground state baryon masses are extracted with fully quantified uncertainties that are at or below the ~0.2%-level in lattice units. The lowest-lying negative-parity states are also extracted albeit with a somewhat lower level of precision. In the case of the nucleon, this negative-parity state is above the N\pi threshold and, therefore, the isospin-1/2 \pi N s-wave scattering phase-shift can be extracted using Luescher's method. The disconnected contributions to this process are included indirectly in the gauge-field configurations and do not require additional calculations. The signal-to-noise ratio in the various correlation functions is explored and is found to degrade exponentially faster than naive expectations on many time-slices. This is due to backward propagating states arising from the anti-periodic boundary conditions imposed on the quark-propagators in the time-direction. We explore how best to distribute computational resources between configuration generation and propagator measurements in order to optimize the extraction of single baryon observables

Ginsparg-Wilson Pions Scattering in a Sea of Staggered Quarks

We calculate isospin 2 pion-pion scattering in chiral perturbation theory for a partially quenched, mixed action theory with Ginsparg-Wilson valence quarks and staggered sea quarks. We point out that for some scattering channels, the power-law volume dependence of two pion states in nonunitary theories such as partially quenched or mixed action QCD is identical to that of QCD. Thus one can extract infinite volume scattering parameters from mixed action simulations. We then determine the scattering length for both 2 and 2+1 sea quarks in the isospin limit. The scattering length, when expressed in terms of the pion mass and the decay constant measured on the lattice, has no contributions from mixed valence-sea mesons, thus it does not depend upon the parameter, C_Mix, that appears in the chiral Lagrangian of the mixed theory. In addition, the contributions which nominally arise from operators appearing in the mixed action O(a^2 m_q) Lagrangian exactly cancel when the scattering length is written in this form. This is in contrast to the scattering length expressed in terms of the bare parameters of the chiral Lagrangian, which explicitly exhibits all the sicknesses and lattice spacing dependence allowed by a partially quenched mixed action theory. These results hold for both 2 and 2+1 flavors of sea quarks.Comment: 27 pages, 3 figures. Mistakes corrected in Eqs. (37), (42). Improved discussion in section 4 and related results in Eqs. (33), (37), (40) and (42). Added references. Version to be published in PR