Lattice Study of Trapped Fermions at Unitarity
Institute for Nuclear Theory, University of Washington, Seattle, WA 98195-1550E-mail: jwlee823@u.washington.eduWe present a lattice study of up to N = 20 unitary fermions conﬁned to a harmonic trap. Ourpreliminary results show better than 1% agreement with high precision solutions to the many-bodySchrodinger equation for up to N = 6. We are able to make predictions for larger N which wereinaccessible by the Hamiltonian approach due to computational limitations. Harmonic traps areused experimentally to study cold atoms tuned to a Feshbach resonance. We show that they alsoprovide certain beneﬁts to numerical studies of many-body correlators on the lattice. In particular,we anticipate that the methods described here could be used for studying nuclear physics.The XXVIII International Symposium on Lattice Field TheoryJune 14-19,2010Villasimius, Sardinia Italy

title: Listening to Noise
abstract: We show how sign problems in simulations of many-body systems can manifest themselves in the form of heavy-tailed correlator distributions, similar to what is seen in electron propagation through disordered media. We propose an alternative statistical approach for extracting ground state energies in such systems, illustrating the method with a toy model and with lattice data for unitary fermions and for baryons in QCD.

title: Large Nc volume reduction and chiral random matrix theory
abstract: Motivated by recent progress on the understanding of the Eguchi-Kawai (EK) volume equivalence and growing interest in conformal window, we simultaneously use the large-Nc volume reduction and Chiral Random Matrix Theory (chRMT) to study the chiral symmetry breaking of four dimensional SU(Nc) gauge theory with adjoint fermions in the large Nc limit. Although some cares are required because the chRMT limit and 't Hooft limit are not compatible in general, we show that the breakdown of the chiral symmetry can be detected in large-Nc gauge theories. As a first step, we mainly focus on the quenched approximation to establish the methodology. We first confirm that heavy adjoint fermions, introduced as the center symmetry preserver, work as expected and thanks to them the volume reduction holds. Using massless overlap fermion as a probe, we then calculate the low-lying Dirac spectrum for fermion in the adjoint representation to compare to that of chRMT, and find that chiral symmetry is indeed broken in the quenched theory.

title: Lattice Monte Carlo calculations for unitary fermions in a harmonic trap
abstract: We present a lattice Monte Carlo approach developed for studying large numbers of strongly interacting nonrelativistic fermions and apply it to a dilute gas of unitary fermions confined to a harmonic trap. In place of importance sampling, our approach makes use of high statistics, an improved action, and recently proposed statistical techniques. We show how improvement of the lattice action can remove discretization and finite volume errors systematically. For N=3 unitary fermions in a box, our errors in the energy scale as the inverse lattice volume, and we reproduce a previous high-precision benchmark calculation to within our 0.3% uncertainty; as additional benchmarks we reproduce precision calculations of N=3,...,6 unitary fermions in a harmonic trap to within our {approx}1% uncertainty. We then use this action to determine the ground-state energies of up to 70 unpolarized fermions trapped in a harmonic potential on a lattice as large as 64{sup 3}x72. In contrast to variational calculations, we find evidence for persistent deviations from the thermodynamic limit for the range of N considered.

title: A new approach for studying large numbers of fermions in the unitary regime
abstract: A novel lattice approach is presented for studying systems comprising a large number of interacting nonrelativistic fermions. The construction is ideally suited for numerical study of fermions near unitarity--a strongly coupled regime corresponding to the two-particle s-wave scattering phase shift delta_0 = pi/2. Such systems may be achieved experimentally with trapped atoms, and provide a starting point for an effective field theory description of nuclear physics. We discuss the construction of our lattice theory, which allows us to study systems of up to (but by no means limited to) 38 fermions with high accuracy and modest computational resources, and offer an overview of several applications of the technique. A more detailed discussion of applications and simulation results will be described in companion proceedings by A. N. N. and J-W. L.

title: Extended study for unitary fermions on a lattice using the cumulant expansion technique
abstract: A recently developed lattice method for large numbers of strongly interacting nonrelativistic fermions exhibits a heavy tail in the distributions of correlators for large Euclidean time {\tau} and large number of fermions N, which only allows the measurement of ground state energies for a limited number of fermions using standard techniques. In such cases, it is suggested that measuring the log of the correlator is more efficient, and a cumulant expansion of this quantity can be exactly related to the correlation function. The cumulant expansion technique allows us to determine the ground state energies of up to 66 unpolarized unitary fermions on lattices as large as 72$\times$14^3, and up to 70 unpolarized unitary fermions trapped in a harmonic potential on lattices as large as 72$\times$64^3. We have also improved our lattice action with a Galilean invariant form for the four-fermion interaction, which results in predictive volume scaling of the lowest energy of three fermions in a periodic box and in good agreement of our results for N \leq 6 trapped unitary fermions with those from other benchmark calculations.

title: Hard probes in heavy ion collisions at the LHC: heavy flavour physics
abstract: We present the results from the heavy quarks and quarkonia working group. This report gives benchmark heavy quark and quarkonium cross sections for $pp$ and $pA$ collisions at the LHC against which the $AA$ rates can be compared in the study of the quark-gluon plasma. We also provide an assessment of the theoretical uncertainties in these benchmarks. We then discuss some of the cold matter effects on quarkonia production, including nuclear absorption, scattering by produced hadrons, and energy loss in the medium. Hot matter effects that could reduce the observed quarkonium rates such as color screening and thermal activation are then discussed. Possible quarkonium enhancement through coalescence of uncorrelated heavy quarks and antiquarks is also described. Finally, we discuss the capabilities of the LHC detectors to measure heavy quarks and quarkonia as well as the Monte Carlo generators used in the data analysis.

title: Photometric Properties of the Near-Contact Binary GW Geminorum
abstract: New multiband CCD photometry is presented for the eclipsing binary GW Gem; the RI light curves are the first ever compiled. Four new minimum timings have been determined. Our analysis of eclipse timings observed during the past 79 years indicates a continuous period increase at a fractional rate of +(1.2 ± 0.1) × 10-10, in excellent agreement with the value +1.1 × 10-10 calculated from the Wilson-Devinney binary code. The new light curves display an inverse O'Connell effect increasing toward longer wavelengths. Hot- and cool-spot models are developed to describe these variations but we prefer a cool spot on the secondary star. Our light-curve synthesis reveals that GW Gem is in a semidetached, but near-contact, configuration. It appears to consist of a near-main-sequence primary star with a spectral type of about A7 and an evolved early K-type secondary star that completely fills its inner Roche lobe. Mass transfer from the secondary to the primary component is responsible for the observed secular period change.

title: CP violating B decays with R -parity violation
abstract: We study CP violating B decays in the minimal supersymmetric standard model with R-parity violation. We estimate how much R-parity violation modifies the SM predictions for CP asymmetries in B decays within the present bounds. The effects of R-parity- and lepton-number-violating couplings on the ratio of the decay amplitude due to R-parity violation to that of the SM can differ by one or two orders of magnitudes depending on the models of the left-handed quark mixing. It is possible to disentangle the R-parity violating effects from those of the SM and R-parity- conserving supersymmetric models within the present bounds comparing different CP violating decay amplitudes. We also study the effects of R-parity- and baryon-number-violating couplings and find that the effects could be large.

title: Bootes II: Not a Dwarf Galaxy but Possibly Shed by One
abstract: We present moderately deep V I C photometry of Boötes II, obtained using the SOAR Telescope. While identified initially as an old, metal-poor, dwarf galaxy, Boötes II appears to be a moderately metal-rich globular cluster with [Fe/H] ≈ −0.7. The slope of the red giant branch suggests that [α/Fe] ≈ 0.0, and the turn-off indicates an age of 7 to 9 Gyrs, considerably younger than most globular clusters, but similar to Palomar 12. Like that object, Boötes II lies in the direction of the Sagittarius dwarf galaxy tidal stream, and, with a distance of almost 50 kpc, is probably associated with the more distant portion of the stream, as defined by Belokurov et al. (2006a).

title: Multi-site campaign for transit timing variations of WASP-12 b: possible detection of a long-period signal of planetary origin
abstract: The transiting planet WASP-12 b was identified as a potential target for transit-timing studies because a departure from a linear ephemeris has been reported in the literature. Such deviations could be caused by an additional planet in the system. We attempt to confirm the claimed variations in transit timing and interpret their origin.  We organised a multi-site campaign to observe transits by WASP-12 b in three observing seasons, using 0.5–2.6-metre telescopes.  We obtained 61 transit light curves, many of them with sub-millimagnitude precision. The simultaneous analysis of the best-quality datasets allowed us to obtain refined system parameters, which agree with values reported in previous studies. The residuals versus a linear ephemeris reveal a possible periodic signal that may be approximated by a sinusoid with an amplitude of 0.00068 ± 0.00013 d and period of 500 ± 20 orbital periods of WASP-12 b. The joint analysis of timing data and published radial velocity measurements results in a two-planet model that explains observations better than do single-planet scenarios. We hypothesise that WASP-12 b might not be the only planet in the system, and there might be the additional 0.1 MJup body on a 3.6-d eccentric orbit. A dynamical analysis indicates that the proposed two-planet system is stable on long timescales.