arXiv subjects
Publications and source records attributed to Martin J. Savage.
Lattice QCD is progressing toward being able to impact our understanding of nuclei and nuclear processes. I discuss areas of nuclear physics that are becoming possible to explore with lattice QCD, the techniques that are currently available and the status of numerical explorations.
The break-up of the deuteron during deeply-virtual Compton scattering, gamma* d --> gamma(*) n p, is explored. In the effective field theory describing nucleon dynamics at momenta below the pion mass, the EMC effect results from four-nucleon interactions with the twist-2 operators, appropriate for describing forward, and near-forward, matrix elements in the two-nucleon system. We point out that the break-up of the deuteron to low-energy final states during deeply-virtual Compton scattering is a process with which to explore strong-interaction physics closely related to that responsible for the EMC effect. The single-nucleon contribution to the break-up depends on the moments of the spin-dependent structure functions and contributions from local four-nucleon operators. Experimental deviations from the single-nucleon prediction would provide a probe of strong interactions complimentary to the EMC effect.
We study the properties of the nucleon in highly asymmetric volumes where the spatial dimensions are small but the time dimension is large in comparison to the inverse pion mass. To facilitate power-counting at the level of Feynman diagrams, we introduce $ε^\prime$-power-counting which is a special case of Leutwyler's $δ$-power-counting. Pion zero-modes enter the $ε^\prime$-counting perturbatively, in contrast to both the $ε$- and $δ$-power-countings, since $m_q < q\bar{q}> V$ remains large. However, these modes are enhanced over those with non-zero momenta and enter at lower orders in the $ε^\prime$-expansion than they would in large volume chiral perturbation theory. We discuss an application of $ε^\prime$-counting by determining the nucleon mass, magnetic moment and axial matrix element at the first nontrivial order in the $ε^\prime$-expansion.
We compute finite-volume corrections to nucleon matrix elements of the axial-vector current. We show that knowledge of this finite-volume dependence --as well as that of the nucleon mass-- obtained using lattice QCD will allow a clean determination of the chiral-limit values of the nucleon and Delta-resonance axial-vector couplings.
We demonstrate how to make rigorous predictions for electroweak matrix elements in nuclear systems directly from QCD. More precisely, we show how to determine the short-distance contributions to low-momentum transfer electroweak matrix elements in the two-nucleon sector from lattice QCD. In potential model descriptions of multi-nucleon systems, this is equivalent to uniquely determining the meson-exchange currents, while in the context of nuclear effective field theory, this translates into determining the coefficients of local, gauge-invariant, multi-nucleon-electroweak current operators. The energies of the lowest-lying states of two nucleons on a finite volume lattice with periodic boundary conditions in the presence of a background magnetic field are sufficient to determine the local four-nucleon operators that contribute to the deuteron magnetic moment and to the threshold cross-section of n + p -> d + gamma. Similarly, the energy-levels of two nucleons immersed in a background isovector axial weak field can be used to determine the coefficient of the leading local four-nucleon operator contributing to the neutral- and charged-current break-up of the deuteron. This is required for the extraction of solar neutrino fluxes at SNO and future neutrino experiments.
We examine soft-pion emission in deeply virtual Compton scattering. Contrary to previous claims, we find that the amplitude for soft-pion emission is not directly related to the generalized parton distributions in the nucleon.
Properties of the proton and neutron are studied in partially-quenched chiral perturbation theory at finite lattice spacing. Masses, magnetic moments, the matrix elements of isovector twist-2 operators and axial-vector currents are examined at the one-loop level in a double expansion in the light-quark masses and the lattice spacing. This work will be useful in extrapolating the results of simulations using Wilson valence and sea quarks, as well as simulations using Wilson sea quarks and Ginsparg-Wilson valence quarks, to the continuum.
At the high densities present in the interior of neutron stars, the neutrons are condensed into the 3P2 superfluid phase. While this condensation has little impact on the equation of state, it can have an important role in determining the low-temperature energy-momentum transport properties. The spontaneous breaking of baryon number by the condensate gives rise to the familiar Goldstone boson, but in addition, the spontaneous breaking of rotational invariance by the condensate gives rise to three Goldstone bosons, in general, one for each broken generator of rotations. These Goldstone bosons, which couple to the Z0, provide a new mechanism for neutrino emission. Using a low-energy effective field theory to describe the dynamics of these Goldstone bosons we estimate the neutrino emissivity of dense neutron matter and show that their annihilation is the dominant energy-loss mechanism over a range of temperatures.
Lattice QCD simulations of the potential between two baryons, each containing a heavy quark and two light quarks, such as the Lambda_Q-Lambda_Q potential, will provide insight into the nucleon-nucleon interaction. As one-pion exchange does not contribute to the Lambda_Q-Lambda_Q potential, the long-distance behavior is dominated by physics that contributes to the intermediate-range attraction between two nucleons. We compute the leading long-distance contributions to the Lambda_Q-Lambda_Q potential in QCD and in partially-quenched QCD in the low-energy effective field theory.
We explore the quark-mass dependence of two-nucleon systems. Allowed regions for the scattering lengths in the 1S0 and 3S1 channels as functions of the light-quark masses are determined from the current uncertainty in strong-interaction parameters that appear at next-to-leading order in the effective field theory. Where experimental constraints are absent, as is the case for the quark-mass dependent four-nucleon operators, we use naive dimensional analysis. We find it likely that there is no bound state in the 1S0 channel in the chiral limit. However, given the present uncertainties in strong-interaction parameters it is unclear whether the deuteron is bound or unbound in the chiral limit.
I review the current status of the application of effective field theory to nuclear physics, and its present implications for nuclear astrophysics.
We conjecture that in the chiral limit of QCD the spectrum of hadrons is comprised of decoupled, reducible chiral multiplets. A simple rule is developed which identifies the chiral representations filled out by the ground-state hadrons. Our arguments are based on the algebraic structure of superconvergence relations derived by Weinberg from the high-energy behavior of pion-hadron scattering amplitudes.
Nucleon-nucleon scattering is studied to next-to-leading order in a partially-quenched extension of an effective field theory used to describe multi-nucleon systems in QCD. The partially-quenched nucleon-nucleon amplitudes will play an important role in relating lattice simulations of the two-nucleon sector to nature.
I discuss the inclusion of baryons into partially-quenched chiral perturbation theory and describe one-loop calculations that have been performed.
In current lattice simulations of nucleon properties, the up and down quark masses are significantly larger than their physical values, while the strange quark can be included in simulations with its physical mass. When the up and down quark masses are much smaller than the strange-quark mass the chiral extrapolation of strange-quark matrix elements in the nucleon from the lattice up and down quark masses to their physical values can be performed with two-flavor chiral perturbation theory, thereby avoiding the slow convergence problem of the three-flavor chiral expansion. We explore the chiral expansion of several matrix elements of strange operators in the nucleon in two-flavor chiral perturbation theory and two-flavor partial-quenched chiral perturbation theory.
The dependence of the nuclear force on standard model parameters plays an important role in bounding time and space variations of fundamental couplings over cosmological time scales. We discuss the quark-mass dependence of deuteron and di-neutron binding in a systematic chiral expansion. The leading quark-mass dependence of the nuclear force arises from one-pion exchange and from local quark-mass dependent four-nucleon operators with coefficients that are presently unknown. By varying these coefficients while leaving nuclear observables at the physical values of the quark masses invariant, we find scenarios where two-nucleon physics depends both weakly and strongly on the quark masses. While the determination of these coefficients is an exciting future opportunity for lattice QCD, we conclude that, at present, bounds on time and space variations of fundamental parameters from the two-nucleon sector are much weaker than previously claimed. This brings into question the reliability of coupling-constant bounds derived from more complex nuclei and nuclear processes.
We compute the leading non-analytic quark mass dependence of the matrix elements of isovector twist-2 operators between octet baryon states in quenched QCD using quenched chiral perturbation theory. There are contributions of the form m_q log m_q, in analogy with QCD, but there are also contributions of the form log m_q from hairpin interactions. The nucleon does not receive such hairpin contributions.
We show that processes involving pions that remain very near their mass-shell can be reliably computed in the pionless effective field theory, with the pion integrated in as a heavy field. As an application, we compute the pion-deuteron scattering amplitude near threshold to next-to-leading order in the momentum expansion. This amplitude is formally dominated by an infrared logarithm of the form log(gamma/mpi), where gamma is the deuteron binding momentum, and mpi is the mass of the pion. The coefficient of this logarithm is determined by the S-wave pion-nucleon scattering lengths.