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Thomas Schaefer

Publications and source records attributed to Thomas Schaefer.

At least 109 records · Page 6Linked to original sources
arXiv2005

Fermionic Quasiparticles in QCD at High Baryon Density

We study fermionic quasi-particles in QCD at very high baryon density. In the normal quark matter phase unscreened magnetic gluon exchanges lead to non-Fermi liquid behavior. Non-Fermi liquid effects manifest themselves in low energy Green functions that depend on logarithms and fractional powers of energy. In the superfluid phase there is an energy gap for fermionic excitations. Quark mass effects can cause the energy gap to vanish. Gapless fermions in the color flavor locked phase cause an instability towards a state with a non-zero supercurrent.

hep-ph↗
arXiv2005

Phases of QCD

In these lectures we provide an introduction to the phase structure of QCD. We begin with a brief discussion of QCD, the symmetries of QCD, and what we mean by a ``phase of QCD''. In the main part of the lectures we discuss the phase diagram of QCD as a function of the temperature and the baryon density. We focus, in particular, on the high temperature plasma phase, the low temperature and low density nuclear phase, and the high density color superconducting phases.

hep-ph↗
arXiv2005

Cold dilute neutron matter on the lattice I: Lattice virial coefficients and large scattering lengths

We study cold dilute neutron matter on the lattice using an effective field theory. We work in the unitary limit in which the scattering length is much larger than the interparticle spacing. In this paper we focus on the equation of state at temperatures above the Fermi temperature and compare lattice simulations to the virial expansion on the lattice and in the continuum. We find that in the unitary limit lattice discretization errors in the second virial coefficient are significantly enhanced. As a consequence the equation of state does not show the universal scaling behavior expected in the unitary limit. We suggest that scaling can be improved by tuning the second virial coefficient rather than the scattering length.

nucl-th↗
arXiv2005

Cold dilute neutron matter on the lattice II: Results in the unitary limit

This is the second of two papers which investigate cold dilute neutron matter on the lattice using pionless effective field theory. In the unitary limit, where the effective range is zero and scattering length is infinite, simple scaling relations relate thermodynamic functions at different temperatures. When the second virial coefficient is properly tuned, we find that the lattice results obey these scaling relations. We compute the energy per particle, pressure, spin susceptibility, dineutron correlation function, and an upper bound for the superfluid critical temperature.

nucl-th↗
arXiv2005

Many Body Methods and Effective Field Theory

In the framework of pionless nucleon-nucleon effective field theory we study different approximation schemes for the nuclear many body problem. We consider, in particular, ladder diagrams constructed from particle-particle, hole-hole, and particle-hole pairs. We focus on the problem of finding a suitable starting point for perturbative calculations near the unitary limit (k_Fa)->infinity and (k_Fr)-> 0, where k_F is the Fermi momentum, a is the scattering length and r is the effective range. We try to clarify the relationship between different classes of diagrams and the large g and large D approximations, where g is the fermion degeneracy and D is the number of space time dimensions. In the large D limit we find that the energy per particle in the strongly interacting system is 1/2 the result for free fermions.

nucl-th↗
arXiv2005

Instantons and the large N_c limit, A.D. 2004

We review our current understanding of instanton effects in the large N_c limit of QCD. We argue that the instanton liquid can have a smooth large N_c limit which is in agreement with scaling relations derived from Feynman diagrams. We also discuss certain limits of QCD, like the case of high baryon density, in which the Witten-Veneziano relation can be derived from QCD and is saturated by instantons.

hep-ph↗
arXiv2004

Neutron matter on the lattice with pionless effective field theory

We study neutron matter by combining pionless effective field theory with non-perturbative lattice methods. The neutron contact interaction is determined by zero temperature scattering data. We simulate neutron matter on the lattice at temperatures 4 and 8 MeV and densities below one-fifth normal nuclear matter density. Our results at different lattice spacings agree with one another and match bubble chain calculations at low densities. The equation of state of pure neutron matter obtained from our simulations agrees quantitatively with variational calculations based on realistic potentials.

nucl-th↗
arXiv2004

Instantons and Monte Carlo Methods in Quantum Mechanics

In these lectures we describe the use of Monte Carlo simulations in understanding the role of tunneling events, instantons, in a quantum mechanical toy model. We study, in particular, a variety of methods that have been used in the QCD context, such as Monte Carlo simulations of the partition function, cooling and heating, the random and interacting instanton liquid model, and numerical simulations of non-Gaussian corrections to the semi-classical approximation.

hep-lat↗
arXiv2004

Inequalities for Light Nuclei in the Wigner Symmetry Limit

Using effective field theory we derive inequalities for light nuclei in the Wigner symmetry limit. This is the limit where isospin and spin degrees of freedom can be interchanged. We prove that the energy of any three-nucleon state is bounded below by the average energy of the lowest two-nucleon and four-nucleon states. We show how this is modified by lowest-order terms breaking Wigner symmetry and prove general energy convexity results for SU(N). We also discuss the inclusion of Wigner-symmetric three and four-nucleon force terms.

nucl-th↗
arXiv2004

An Effective Theory for Baryons in the CFL Phase

We study the effective field theory for fermions in the color-flavor locked (CFL) phase of high density QCD. The effective theory contains a flavor nonet of baryons interacting with a nonet of pseudoscalar Goldstone bosons as well as a singlet scalar Goldstone boson. The theory is similar to chiral perturbation theory in the one-baryon sector. We explain how to incorporate quark mass terms and study the spectrum as a function of the strange quark mass. Without meson condensation gapless baryon modes appears if the strange quark mass exceeds a critical value m_s^2/(2p_F)=Delta, where p_F is the Fermi momentum and Delta is the gap in the chiral limit. We show that kaon condensation leads to a rearrangement of the baryon spectrum and shifts the critical strange quark mass for the appearance of a gapless mode to higher values.

hep-ph↗
arXiv2004

Non-Fermi Liquid Effects in QCD at High Density

We study non-Fermi liquid effects due to the exchange of unscreened magnetic gluons in high density QCD by using an effective field theory. A one-loop calculation gives the well known result that magnetic gluons lead to a logarithmic enhancement in the fermion self energy near the Fermi surface. The self energy is of the form $Σ(ω)\sim ωγ\log(ω)$, where $ω$ is the energy of the fermion, $γ=O(g^2)$, and $g$ is the coupling constant. Using an analysis of the Dyson-Schwinger equations we show that, in the weak coupling limit, this result is not modified by higher order corrections even in the regime where the logarithm is large, $γ\log(ω)\sim 1$. We also show that this result is consistent with the renormalization group equation in the high density effective field theory.

hep-ph↗
arXiv2004

New phases in CFL quark matter

We consider order $α_s$ corrections to the squared masses of the pseudo-Goldstone excitations about the ground state of dense quark matter. We show that these contributions tend to destabilize the vacuum, leading to a surprisingly complex phase structure for quark matter as a function of quark mass, even for small $α_s$. In particular we find two new phases of CFL quark matter possibly relevant for the real world, for which the QCD angle theta-bar equals pi/2.

hep-ph↗
arXiv2004

Nuclear Lattice Simulations with Chiral Effective Field Theory

We study nuclear and neutron matter by combining chiral effective field theory with non-perturbative lattice methods. In our approach nucleons and pions are treated as point particles on a lattice. This allows us to probe larger volumes, lower temperatures, and greater nuclear densities than in lattice QCD. The low energy interactions of these particles are governed by chiral effective theory and operator coefficients are determined by fitting to zero temperature few-body scattering data. Any dependence on the lattice spacing can be understood from the renormalization group and absorbed by renormalizing operator coefficients. In this way we have a realistic simulation of many-body nuclear phenomena with no free parameters, a systematic expansion, and a clear theoretical connection to QCD. We present results for hot neutron matter at temperatures 20 to 40 MeV and densities below twice nuclear matter density.

nucl-th↗
arXiv2004

Effective Theory of Superfluid Quark Matter

We provide a brief introduction to the high density effective theory of QCD. As an application, we consider the instanton correction to the perturbatively generated gap in the color superconducting phase. We show that the instanton correction becomes large for mu = 1.25 GeV in N_f=2 QCD, and for mu = 750 MeV in N_f=3 QCD with a massive strange quark. We also study some other numerical issues related to the magnitude of the gap. We find, in particular, that a renormalization group improved gap equation does not give results that are substantially different from a gap equation with a fixed coupling.

hep-ph↗
arXiv2003

Instantons and Scalar Multiquark States: From Small to Large N_c

We study scalar quark-anti-quark and two-quark-two-anti-quark correlation functions in the instanton liquid model. We show that the instanton liquid supports a light scalar-isoscalar (sigma) meson, and that this state is strongly coupled to both $(\bar{q}q)$ and $(\bar{q}q)^2$. The scalar-isovector $a_0$ meson, on the other hand, is heavy. We also show that these properties are specific to QCD with three colors. In the large $N_c$ limit the scalar-isoscalar meson is not light, and it is mainly coupled to $(\bar{q}q)$.

hep-ph↗
arXiv2003

Hard Loops, Soft Loops, and High Density Effective Field Theory

We study several issues related to the use of effective field theories in QCD at large baryon density. We show that the power counting is complicated by the appearance of two scales inside loop integrals. Hard dense loops involve the large scale $μ^2$ and lead to phenomena such as screening and damping at the scale $gμ$. Soft loops only involve small scales and lead to superfluidity and non-Fermi liquid behavior at exponentially small scales. Four-fermion operators in the effective theory are suppressed by powers of $1/μ$, but they get enhanced by hard loops. As a consequence their contribution to the pairing gap is only suppressed by powers of the coupling constant, and not powers of $1/μ$. We determine the coefficients of four-fermion operators in the effective theory by matching quark-quark scattering amplitudes. Finally, we introduce a perturbative scheme for computing corrections to the gap parameter in the superfluid phase

hep-ph↗
arXiv2003

Quark Matter

In these lectures we provide an introduction to the theory of QCD at very high baryon density. We begin with a review of some aspects of quantum many-body system that are relevant in the QCD context. We also provide a brief review of QCD and its symmetries. The main part of these lectures is devoted to the phenomenon of color superconductivity. We discuss the use of weak coupling methods and study the phase structure as a function of the number of flavors and their masses. We also introduce effective theories that describe low energy excitations at high baryon density. Finally, we use effective field theory methods in order to study the effects of a non-zero strange quark mass.

hep-ph↗