arXiv subjects

Paulo F. Bedaque

Publications and source records attributed to Paulo F. Bedaque.

At least 73 records · Page 4Linked to original sources

arXiv2007

Fitting two nucleons inside a box: exponentially suppressed corrections to the Luscher's formula

Scattering observables can be computed in lattice field theory by measuring the volume dependence of energy levels of two particle states. The dominant volume dependence, proportional to inverse powers of the volume, is determined by the phase shifts. This universal relation (\Lu's formula) between energy levels and phase shifts is distorted by corrections which, in the large volume limit, are exponentially suppressed. They may be sizable, however, for the volumes used in practice and they set a limit on how small the lattice can be in these studies. We estimate these corrections, mostly in the case of two nucleons. Qualitatively, we find that the exponentially suppressed corrections are proportional to the {\it square} of the potential (or to terms suppressed in the chiral expansion) and the effect due to pions going ``around the world'' vanishes. Quantitatively, the size of the lattice should be greater than $\approx(5 {fm})^3$ in order to keep finite volume corrections to the phase less than $1^\circ$ for realistic pion mass.

hep-lat↗

arXiv2006

Hyperon-Nucleon Scattering from Fully-Dynamical Lattice QCD

We present results of the first fully-dynamical lattice QCD determination of hyperon-nucleon scattering. One s-wave phase shift was determined for n Lambda scattering in both spin-channels at pion masses of 350, 490, and 590 MeV, and for n Sigma- scattering in both spin channels at pion masses of 490, and 590 MeV. The calculations were performed with domain-wall valence quarks on dynamical, staggered gauge configurations with a lattice spacing of b ~ 0.125 fm.

hep-lat↗

arXiv2006

Pi-K Scattering in Full QCD with Domain-Wall Valence Quarks

We calculate the pi+ K+ scattering length in fully-dynamical lattice QCD with domain-wall valence quarks on MILC lattices with rooted staggered sea-quarks at a lattice spacing of b=0.125 fm, lattice spatial size of L =2.5 fm and at pion masses of m_pi=290, 350, 490 and 600 MeV. The lattice data, analyzed at next-to-leading order in chiral perturbation theory, allows an extraction of the full pi K scattering amplitude at threshold. Extrapolating to the physical point gives m_pi a_3/2 = -0.0574 (+- 0.0016)(+0.0024 -0.0058) and m_pi a_1/2 = 0.1725 (+- 0.0017)(+0.0023 -0.0156) for the I=3/2 and I=1/2 scattering lengths, respectively, where the first error is statistical and the second error is an estimate of the systematic due to truncation of the chiral expansion.

hep-lat↗

arXiv2006

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.

hep-lat↗

arXiv2006

I=2 pi-pi Scattering from Fully-Dynamical Mixed-Action Lattice QCD

We compute the I=2 pi-pi scattering length at pion masses of m_pi ~ 294, 348 and 484 MeV in fully-dynamical lattice QCD using Luscher's finite-volume method. The calculation is performed with domain-wall valence-quark propagators on asqtad-improved MILC configurations with staggered sea quarks at a single lattice spacing, b ~ 0.125 fm. Chiral perturbation theory is used to perform the extrapolation of the scattering length from lattice quark masses down to the physical value, and we find m_pi a_2 = -0.0426 +- 0.0006 +- 0.0003 +- 0.0018, in good agreement with experiment. The I=2 pi-pi scattering phase shift is calculated to be delta = -43 +- 10 +- 5 degrees at |p| ~ 544 MeV for m_pi ~ 484 MeV.

hep-lat↗

arXiv2006

Superfluid phases of the three-species fermion gas

We discuss the zero temperature phase diagram of a dilute gas with three fermionic species. We make use of solvable limits to conjecture the behavior of the system in the "unitary" regions. The physics of the Thomas-Efimov effect plays a role in these considerations. We find a rich phase diagram with superfluid, gapless superfluid and inhomogeneous phases with different symmetry breaking patterns. We then discuss one particular possible experimental implementation in a system of ^6Li atoms and the possible phases arising in this system as an external magnetic field is varied across three overlaping Feshbach resonances. We also suggest how to experimentally distinguish the different phases.

cond-mat.other↗

arXiv2005

A nucleon in a tiny box

We use Chiral Perturbation Theory to compute the nucleon mass-shift due to finite volume and temperature effects. Our results are valid up to next-to-leading order in the "\eps-regime" (mL ~ mβ<< 1) as well as in the "p-regime" (mL ~ mβ>> 1). Based on the two leading orders, we discuss the convergence of the expansion as a function of the lattice size and quark masses. This result can be used to extrapolate lattice results obtained from lattice sizes smaller than the pion cloud, avoiding the numerical simulation of physics under theoretical control. An extraction of the low-energy coefficient c_3 of the chiral Lagrangean from lattice simulations at small volumes and a ``magic'' ratio β=1.22262 L might be possible.

hep-lat↗

arXiv2005

Twisted valence quarks and hadron interactions on the lattice

We consider QCD with valence and sea quarks obeying different boundary conditions. We point out that the energy of low lying two hadron states do not depend on the boundary condition of the sea quarks (up to exponentially small corrections). Thus, the advantages in using twisted boundary conditions on the lattice QCD extraction of nucleon-nucleon phase shifts can be gained without the need of new gauge configurations, even in fully unquenched calculations.

hep-lat↗

arXiv2004

A dilute atomic Fermi system with a large positive scattering length

We show that a dilute atomic Fermi system at sufficiently low temperatures, can display fermionic superfluidity, even in the case of a repulsive atom-atom interaction, when the scattering length is positive. The attraction leading to the formation of Cooper pairs is provided by the exchange of Bogoliubov phonons if a fraction of the atoms form a BEC of weakly bound molecules.

cond-mat.stat-mech↗

arXiv2004

Aharonov-Bohm effect and nucleon-nucleon phase shifts on the lattice

We propose a method for the lattice QCD computation of nucleon-nucleon low-energy interactions. It consists in simulating QCD in the background of a ''electromagnetic" field whose potential is non-vanishing, but whose field strength is zero. By tuning the background field, phase-shifts at any (but small) momenta can be determined by measuring the shift of the ground state energy. Lattice sizes as small as 5 Fermi can be sufficient for the calculation of phase shifts up to momenta of order of $m_π/2$.

nucl-th↗

arXiv2003

Quantum Corrections to Dilute Bose Liquids

It was recently shown (A. Bulgac. Phys. Rev. Lett. {\bf 89}, 050402 (2002)) that an entirely new class of quantum liquids with widely tunable properties could be manufactured from bosons (boselets), fermions (fermilets) and their mixtures (ferbolets) by controlling their interaction properties by the means of a Feshbach resonance. We extend the previous mean--field analysis of these quantum liquids by computing the lowest order quantum corrections to the ground state energy and the depletion of the Bose--Einstein condensate and by estimating higher order corrections as well. We show that the quantum corrections are relatively small and controlled by the diluteness parameter $\sqrt{n|a|^3} \ll 1$, even though strictly speaking in this case there is no low density expansion.

cond-mat.stat-mech↗

arXiv2003

Phase separation in asymmetrical fermion superfluids

Motivated by recent developments on cold atom traps and high density QCD we consider fermionic systems composed of two particle species with different densities. We argue that a mixed phase composed of normal and superfluid components is the energetically favored ground state. We suggest how this phase separation can be used as a probe of fermion superfluidity in atomic traps.

cond-mat↗

arXiv2003

Goldstone Bosons in the 3P2 Superfluid Phase of Neutron Matter and Neutrino Emission

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.

nucl-th↗

arXiv2003

Atomic-Molecular Condensates with Large Positive Scattering Length

We show that in the limit of large and positive atom--atom scattering length the properties of an atomic--molecular Bose--Einstein Condensate (amBEC) are determined by an universal energy density functional (EDF). We find that the optimal conditions for the formation of a stable amBEC are in the regime where there are no shallow trimers and the atom--dimer scattering length is negative and comparable in magnitude with the atom--atom scattering length. At temperatures lower than $T_c$ the chemical potentials for the atoms and molecules can be specified independently. Besides three--body recombinations processes into dimers of large size, inelastic processes involving the formation of deeply bound small size molecular states are possible. These inelastic processes do not lead to an efficient heating of the amBEC and can be used for its mostly non--destructive monitoring.

cond-mat.stat-mech↗

arXiv2002

Low Energy Expansion in the Three Body System to All Orders and the Triton Channel

We extend and systematise the power counting for the three-body system, in the context of the ``pion-less'' Effective Field Theory approach, to all orders in the low-energy expansion. We show that a sub-leading part of the three-body force appears at the third order and delineate how the expansion proceeds at higher orders. After discussing the renormalisation issues in a simple bosonic model, we compute the phase shifts for neutron-deuteron scattering in the doublet S wave (triton) channel and compare our results with phase shift analysis and potential model calculations.

nucl-th↗

arXiv2002

Dilute resonating gases and the third virial coefficient

We study dilute gases with short range interactions and large two-body scattering lengths. At temperatures between the condensation temperature and the scale set by therange of the potential there is a high degree of universality. The first two terms in the expansion of thermodynamic functions in powers of the fugacity $z$, which measures the diluteness of the system, are determined by the scattering length only. The term proportional to $z^3$ depends only on one new parameter describing the three-body physics. We compute the third term of the expansion and show that, for many values of this new parameter, the $z^3$ term may be the dominant one.

cond-mat↗

arXiv2001

Charged kaon condensation in high density quark matter

We show that at asymptotically high densities the ``color-flavor-locked + neutral kaon condensate'' phase of QCD develops a {\it charged} kaon condensate through the Coleman-Weinberg mechanism. At densities achievable in neutron stars a charged kaon condensate forms only for some (natural) values of the low energy constants describing the low-lying excitations of the ground state.

nucl-th↗

arXiv2000

From Hadrons to Nuclei: Crossing the Border

The study of nuclei predates by many years the theory of quantum chromodynamics. More recently, effective field theories have been used in nuclear physics to ``cross the border'' from QCD to a nuclear theory. We are now entering the second decade of efforts to develop a perturbative theory of nuclear interactions using effective field theory. This work describes the current status of these efforts.

nucl-th↗