New lessons from the nucleon mass, lattice QCD and heavy baryon chiral perturbation theory

I will review heavy baryon chiral perturbation theory for the nucleon delta degrees of freedom and then examine the recent dynamical lattice calculations of the nucleon mass from the BMW, ETM, JLQCD, LHP, MILC, NPLQCD, PACS-CS, QCDSF/UKQCD and RBC/UKQCD Collaborations. Performing the chiral extrapolations of these results, one finds remarkable agreement with the physical nucleon mass, from each lattice data set. However, a careful examination of the lattice data and the resulting extrapolation functions reveals some unexpected results, serving to highlight the significant challenges in performing chiral extrapolations of baryon quantities. All the N_f=2+1 dynamical results can be quantitatively described by theoretically unmotivated fit function linear in the pion mass with m_pi ~ 750 -190 MeV. When extrapolated to the physical point, the results are in striking agreement with the physical nucleon mass. I will argue that knowledge of each lattice datum of the nucleon mass is required at the 1-2% level, including all systematics, in order to conclusively determine if this is a bizarre conspiracy of lattice artifacts or rather a mysterious phenomenon of QCD.Comment: Plenary talk presented at the XXVI International Symposium on Lattice Field Theory, July 14-19, 2008, Williamsburg, Virginia, USA; added references; typo corrected in Eq. (2.16

Hadronic Interactions with Lattice QCD

I discuss recent results of the NPLQCD Collaboration regarding the calculation of hadronic interactions with lattice QCD. A particular emphasis will be spent on pi-pi scattering and other meson interactions.Comment: Talk given at the 8th Conference "Quark Confinement and the Hadron Spectrum", Mainz, Germany, 1-6 September 200

Towards a direct lattice calculation of m_d - m_u

We describe an independent method for determining the strong-isospin breaking mass parameter, 2delta = m_d - m_u, which utilizes the baryon spectrum. We use a prudent partially quenched choice of splitting the valence quark masses symmetrically about the light sea quark mass. This choice has the consequence of mitigating the most severe partial quenching artifacts. We also discuss the most significant hurdle to this method which is determining the electromagnetic self-energy of the neutron-proton mass splitting, a challenge which lacks a satisfactory answer. Despite these issues, the phenomenologically interesting dependence of m_n - m_p on delta can be determined.Comment: 7 pages, talk given at the XXVIII International Symposium on Lattice Filed Theory, June 14-19,2010, Villasimius, Sardinia Ital

The Scalar Strange Content of the Nucleon from Lattice QCD

The scalar strange-quark matrix element of the nucleon is computed with lattice QCD. A mixed-action scheme is used with domain-wall valence fermions computed on the staggered MILC sea-quark configurations. The matrix element is determined by making use of the Feynman-Hellmann theorem which relates this strange matrix element to the change in the nucleon mass with respect to the strange-quark mass. The final result of this calculation is m_s < N | s-bar s| N > = 49 +-10 +- 15 MeV and, correspondingly f_s = m_s / m_N = 0.051 +- 0.011 +- 0.016. Given the lack of a quantitative comparison of this phenomenologically important quantity determined from various lattice QCD calculations, we take the opportunity to present such an average. The resulting conservative determination is f_s = 0.043 +- 0.011.Comment: 20 pages, 19 figures: v2. improved discussion of scale setting, Matrix-Prony method and lattice average. Updated references. Version accepted for publication in PRD: v3, improved figure

Restless pions from orbifold boundary conditions: an explicit construction for noise reduction in lattice QCD

The exponentially decreasing signal to noise ratio in multibaryon correlators is the main obstacle to a first principles, QCD-based calculation of the nuclear force. Recently, we have proposed an orbifold boundary condition ("restless pions") that can dramatically improve this matter. Here we develop the idea further by proposing an explicit algorithm that can be used with purely periodic, "off the shelf" gauge configurations. We also discuss finite volume corrections with the new boundary conditions and the use of the "Luscher formula'' for the phase shifts.Comment: 8 pages, 3 figure

Strong Isospin Breaking in the Nucleon and Delta Masses on the Lattice

Strong isospin breaking in the spectrum of the nucleons and deltas can be studied in lattice QCD with the help of chiral perturbation theory. At leading order in the chiral expansion, the mass splittings between the proton and neutron and between the deltas are linear in the quark mass difference. The next-to-leading order contributions to these splittings vanish even away from the strong-isospin limit. Therefore, any non-linear quark mass dependence of these mass splittings is a signal of the next-to-next-to-leading order mass contributions, thus providing access to LECs at this order. We determine the mass splittings of the nucleons and deltas in two-flavor, heavy baryon chiral perturbation theory to next-to-next-to-leading order. We also derive expressions for the nucleon and delta masses in partially quenched chiral perturbation theory to the same order. The resulting mass expressions will be useful both for the extrapolation of lattice data on baryon masses, and for the study of strong isospin breaking.Comment: 24 pages, revised version with slight modifications to text and formula

Evidence for chiral logarithms in the baryon spectrum

Using precise lattice QCD computations of the baryon spectrum, we present the first direct evidence for the presence of contributions to the baryon masses which are non-analytic in the light quark masses; contributions which are often denoted "chiral logarithms". We isolate the poor convergence of SU(3) baryon chiral perturbation theory to the flavor-singlet mass combination. The flavor-octet baryon mass splittings, which are corrected by chiral logarithms at next to leading order in SU(3) chiral perturbation theory, yield baryon-pion axial coupling constants D, F, C and H consistent with QCD values; the first evidence of chiral logarithms in the baryon spectrum. The Gell-Mann--Okubo relation, a flavor-27 baryon mass splitting, which is dominated by chiral corrections from light quark masses, provides further evidence for the presence of non-analytic light quark mass dependence in the baryon spectrum; we simultaneously find the GMO relation to be inconsistent with the first few terms in a taylor expansion in m_s - m_l, which must be valid for small values of this SU(3) breaking parameter. Additional, more definitive tests of SU(3) chiral perturbation theory will become possible with future, more precise, lattice calculations.Comment: 7 pages, 3 figures, Talk presented at the XXIX International Symposium on Lattice Field Theory (Lattice 2011), July 10-16, 2011, Squaw Valley, Lake Tahoe, California, US

Topics in Effective Field Theory for Lattice QCD

In this work, we extend and apply effective field theory techniques to systematically understand a subset of lattice artifacts which pollute the lattice correlation functions for a few processes of physical interest. Where possible, we compare to existing lattice QCD calculations. In particular, we extend the heavy baryon Lagrangian to the next order in partially quenched chiral perturbation theory and use it to compute the masses of the lightest spin-1/2 and spin-3/2 baryons to next-to-next-to leading order. We then construct the twisted mass chiral Lagrangian for baryons and apply it to compute the lattice spacing corrections to the baryon masses simulated with twisted mass lattice QCD. We extend computations of the nucleon electromagnetic structure to account for finite volume effects, as these observables are particularly sensitive to the finite extent of the lattice. We resolve subtle peculiarities for lattice QCD simulations of polarizabilities and we show that using background field techniques, one can make predictions for the 4 spin-dependent nucleon polarizabilities, quantities which are difficult to access experimentally. We then discuss the two-pion system in finite volume, determining the exponentially small volume corrections necessary for lattice determinations of the scattering parameters. We also determine the lattice spacing artifacts that arise for a mixed-action lattice simulation of the two-pion system with Ginsparg-Wilson valence quarks and staggered sea quarks. We show that the isospin 2 scattering length has a near continuum like behavior, differing from the chiral perturbation theory calculation by a computable difference.Comment: Ph.D. Thesis, 180 pages, 23 figure

Evidence for non-analytic light quark mass dependence in the baryon spectrum

Using precise lattice QCD computations of the baryon spectrum, we present the first direct evidence for the presence of contributions to the baryon masses which are non-analytic in the light quark masses; contributions which are often denoted "chiral logarithms". We isolate the poor convergence of SU(3) baryon chiral perturbation theory to the flavor-singlet mass combination. The flavor-octet baryon mass splittings, which are corrected by chiral logarithms at next to leading order in SU(3) chiral perturbation theory, yield baryon-pion axial coupling constants D, F, C and H consistent with QCD values; the first evidence of chiral logarithms in the baryon spectrum. The Gell-Mann--Okubo relation, a flavor-27 baryon mass splitting, which is dominated by chiral corrections from light quark masses, provides further evidence for the presence of non-analytic light quark mass dependence in the baryon spectrum; we simultaneously find the GMO relation to be inconsistent with the first few terms in a taylor expansion in m_s - m_l, which must be valid for small values of this SU(3) breaking parameter. Additional, more definitive tests of SU(3) chiral perturbation theory will become possible with future, more precise, lattice calculations.Comment: 20 pages, 7 figure

Strong isospin breaking with twisted mass lattice QCD

In this work we propose a method for including strong isospin breaking in twisted mass lattice calculations, while preserving flavor identification. We utilize a partially quenched construction in which the sea quarks are given by the standard twisted mass lattice action while the valence quarks have an additional strong isospin breaking mass term. This construction allows for a practical use with existing twisted-mass gauge ensembles. Additionally, we construct the relevant partially quenched twisted mass chiral perturbation theory for both mesons and baryons to O(m_q^2, m_q a, a^2). We provide explicit expressions for the pion, nucleon and delta masses, as well as the corresponding mass splittings, and discuss the resulting errors from including the strong isospin breaking in the valence sector only. Finally, we demonstrate how the application of this idea can be used, with mild approximations, to determine the values of both the up and down quark masses.Comment: 12 page