My main interest is in studying field theories which have strong interactions. I am working primarily with quantum chromodynamics (QCD), the theory of quarks, gluons and their bound states, hadrons. Since the coupling between quarks is large at hadronic energy scales, a nonperturbative method is required to calculate the properties of hadrons directly from QCD. Lattice field theory provides a complete formulation which allows numerical Monte Carlo calculation of many hadronic properties. Below I discuss lattice QCD contributions to the understanding of quark flavor changing processes.

My longstanding interest in lattice QCD has fostered an interest in similar problems in condensed matter and atomic physics. One very active area is with cold atomic gases; the fermionic gases being trapped and cooled presently have interesting similarities to QCD. In many cases, experimentalists can apply an external field to tune the interatomic interaction to a special point where the scattering length diverges. This system is strongly interacting and nonperturbative but simple enough that field theoretic methods can be applied. I discuss work in this direction further below.

High energy physics :: Lattice QCD :: Quark flavor

Since quarks are confined to nonperturbative bound states, lattice QCD calculations are crucial ingredients for constraining many of the Standard Model parameters. The lattice calculations connect the quark-level interactions of the Standard Model to the meson-level processes observed in experiments. My work has focused on determining the quark masses and the parameters which govern quark flavor-changing interactions. Flavor physics is particularly exciting because any physics beyond the Standard Model should contribute to some of the experimental measurements; fits to the data which only include Standard Model calculations should eventually see deviations and give indirect evidence for new physics.

In order for lattice QCD calculations to be useful, the theoretical uncertainties must be reliably estimated and systematically improved. One obstacle to such a clean calculation was the inability to include virtual up and down quark effects. An improved version of staggered lattice fermions allows Monte Carlo calculations to be performed with light enough sea quark masses that chiral perturbation theory can be applied to obtain correct physical results [1]. There are similar benefits of using staggered fermions in combination with standard heavy lattice fermions to study heavy-light mesons [2].

With this formulation, we have been working toward precise, accurate calculations of matrix elements involving B mesons (quark--antiquark states including a bottom quark). Especially interesting are lattice calculations of B0B0-bar mixing parameters, B and Bs leptonic decay constants, and semileptonic form factors for B → π l ν and B → D l ν . These are important ingredients to the entire program of constraining the CKM matrix elements of the Standard Model. Recently we published results for the B decay constant, achieving much greater control over the light quark mass extrapolation than previous work [3]. Calculations of the form factors which parametrize B → π l ν decay have also been published [4]. These will help reduce the uncertainties on |Vub|. We have also embarked on calculating the matrix elements needed to combine lattice results with experimental measurements for the B0B0-bar mass difference in order to determine |Vtd|. Results for Bs0Bs0-bar have appeared recently [5].

At the SciDAC 2005 conference, I presented a poster summarizing our results up to that point.

Many body physics :: unitary Fermi gas

Since the creation of a Bose-Einstein condensate in a gas of alkali atoms, a new genre of versatile experiments has emerged. For example, the physics of semiconductors can be modeled cleanly by atoms in an optical lattice. Vortices are more robust in dilute atomic superfluids than in liquid helium. Scattering lengths of dilute Fermi gases are tunable by application of a magnetic field, reproducing some of the physics of nuclear matter. Finally, the separation of length scales in these gases makes them amenable to description by effective field theory.

I have been focusing on dilute gases of 2-component fermions with large scattering lengths. Once the scattering length a becomes large compared to the average interparticle spacing, standard mean field analysis breaks down. Lattice field theory and Monte Carlo calculations allow one to study this system nonperturbatively. The case where 1/a = 0 is especially interesting since the system becomes universal, the only physically relevant length scale being the interparticle spacing.

My first numerical studies using this method indicated the existence of a continuum limit for the lattice theory, a necessity for the theory to be a first-principles approach to studying this system. The next step was an exploratory study searching for the critical temperature below which superfluidity occurs [6]. Presently the goal is to more precisely map the parameters of the simulations to physical quantities. As a result I will be able to determine the critical temperature from small positive scattering length where the fermions form molecules and Bose condense, to small negative scattering length where the fermions form Cooper pairs and a BCS superfluid, and the entire range of -∞ < 1/a < ∞.

Recently, Son and I have developed an effective field theory for phonon excitations in the low temperature superfluid, allowing one to calculate corrections to superfluid hydrodynamics and Thomas-Fermi theory [7]. One interesting feature of this work was the construction of a microscopic Lagrangian (for the atoms) which has a nonrelativistic general coordinate invariance. Furthermore, a conformal invariance, not just scale invariance, appears in the 2-species fermionic system at the unitary point 1/a = 0. These invariances restrict the terms which can appear in the phonon Lagrangian beyond what is dictated by Galilean and scale invariance. It would be nice to look for consequences of general coordinate invariance and conformal invariance using Monte Carlo calculations. The numerical challenge is to work at low enough temperatures that phonons are the only relevant degrees-of-freedom.

Selected papers

  1. C. T. H. Davies et al., High-precision lattice QCD confronts experiment, Phys. Rev. Lett. 92, 022001 (2004), [hep-lat/0304004].
  2. M. Wingate et al., Heavy light mesons with staggered light quarks, Phys. Rev. D 67, 054505 (2003), [hep-lat/0211014].
  3. A. Gray et al., The B meson decay constant from unquenched lattice QCD, Phys. Rev. Lett. 95, 212001 (2005), [hep-lat/0507015].
  4. E. Gulez et al., B meson semileptonic form factors from unquenched lattice QCD, Phys. Rev. D 73, 074502 (2006), [hep-lat/0601021].
  5. E. Dalgic et al., Bs0-bar – Bs0 mixing parameters from unquenched lattice QCD, [hep-lat/0610104].
  6. M. Wingate, Critical temperature for fermion pairing using lattice field theory, cond-mat/0502372.
  7. D. T. Son and M. Wingate, General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas, Annals of Physics, 321, 197 (2006), [cond-mat/0509786].

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