arXiv subjects

Thomas Schaefer

Publications and source records attributed to Thomas Schaefer.

At least 127 records · Page 7Linked to original sources

arXiv2003

Patterns of Symmetry Breaking in QCD at High Baryon Density

We study the structure of QCD at very large baryon density for an arbitrary number of flavors $N_f$. We provide evidence that for any number of flavors larger than $N_f=2$ chiral symmetry remains broken at asymptotically large chemical potential. For $N_c=N_f=3$, chiral symmetry breaking follows the standard pattern $SU(3)_L\times SU(3)_R\to SU(3)$, but for $N_f>3$ unusual patterns emerge. We study the case $N_f=3$ in more detail and calculate the magnitude of the chiral order parameters $<\barψψ>$ and $<(\barψψ)^2>$ in perturbative QCD. We show that, asymptotically, $<\barψψ>^{1/3}$ is much smaller than $<(\barψψ)^2>^{1/6}$. The result can be understood in terms of an approximate discrete symmetry.

hep-ph↗

arXiv2002

Instanton contribution to scalar charmonium and glueball decays

We study instanton contributions to hadronic decays of the scalar glueball, the pseudoscalar charmonium state $η_c$, and the scalar charmonium state $χ_c$. Hadronic decays of the $η_c$ are of particular interest. The three main decay channels are $K\bar{K}π$, $ηππ$ and $η'ππ$, each with an unusually large branching ratio $\sim 5%$. On the quark level, all three decays correspond to an instanton type vertex $(\bar{c}c)(\bar{s}s)(\bar{d}d)(\bar{u}u)$. We show that the total decay rate into three pseudoscalar mesons can be reproduced using an instanton size distribution consistent with phenomenology and lattice results. Instantons correctly reproduce the ratio $B(ππη)/B(ππη')$ but over-predict the ratio $B(K\bar{K}π)/B(ππη(η'))$. We consider the role of scalar resonances and suggest that the decay mechanism can be studied by measuring the angular distribution of decay products.

hep-ph↗

arXiv2002

QCD and the eta prime Mass: Instantons or Confinement?

We argue that lattice calculations of the $η'$ mass in QCD with $N_c=2$ colors performed at non-zero baryon chemical potential can be used to study the mechanism responsible for the mass of the $η'$. QCD with two colors is an ideal laboratory because it exhibits confinement, chiral symmetry breaking and a would-be $U(1)_A$ Goldstone boson at all densities. Since the instanton density and the confinement scale vary with density in a very different way, instantons are clearly distinguishable from other possible mechanisms. There is an instanton prediction for the $η'$ mass at large density that can be compared to lattice results. The density dependence of the instanton contribution is a simple consequence of the integer topological charge carried by the instanton. We also argue that $N_c=3$ color QCD at finite isospin density can be used in order to study the origin of OZI-violation in the scalar sector.

hep-lat↗

arXiv2002

Instantons in QCD with Many Colors

We study instantons in QCD with many colors. We first discuss a number of qualitative arguments concerning the large N_c scaling behavior of a random instanton ensemble. We show that most hadronic observables are compatible with standard large N_c counting rules provided the average instanton size is O(1) and the instanton density is O(N_c) in the large N_c limit. This is not the case for the topological susceptibility and the mass of the eta'. For these observables consistency with conventional large N_c counting requires that fluctuations in the instanton liquid are suppressed compared to Poissonian fluctuations. Using mean field estimates and numerical simulations we show that the required scaling behavior of the instanton density is natural in models in which the instanton density is regularized in terms of a classical repulsive core. We also show that in these models fluctuations of the topological charge are suppressed and that m^2_eta'=O(1/N_c). We conclude that the instanton liquid model is not necessarily in conflict with the 1/N_c expansion.

hep-ph↗

arXiv2002

Effective Theory of the Color-Flavor-Locked Phase

We explain how an effective theory of the CFL phase can be used to study the effect of the strange quark mass on the ground state and the excitation spectrum. We also apply the effective theory to the problem of neutrino emission from a CFL quark core inside a neutron star.

nucl-th↗

arXiv2002

Neutrino Emission from Goldstone Modes in Dense Quark Matter

We calculate neutrino emissivities from the decay and scattering of Goldstone bosons in the color-flavor-locked (CFL) phase of quarks at high baryon density. Interactions in the CFL phase are described by an effective low-energy theory. For temperatures in the tens of keV range, relevant to the long-term cooling of neutron stars, the emissivities involving Goldstone bosons dominate over those involving quarks, because gaps in the CFL phase are $\sim 100$ MeV while the masses of Goldstone modes are on the order of 10 MeV. For the same reason, the specific heat of the CFL phase is also dominated by the Goldstone modes. Notwithstanding this, both the emissivity and the specific heat from the massive modes remain rather small, because of their extremely small number densities. The values of the emissivity and the specific heat imply that the timescale for the cooling of the CFL core in isolation is $\sim 10^{26}$ y, which makes the CFL phase invisible as the exterior layers of normal matter surrounding the core will continue to cool through significantly more rapid processes. If the CFL phase appears during the evolution of a proto-neutron star, neutrino interactions with Goldstone bosons are expected to be significantly more important since temperatures are high enough ($\sim 20-40$ MeV) to admit large number densities of Goldstone modes.

astro-ph↗

arXiv2002

Gluino Condensation in an Interacting Instanton Ensemble

We perform a semi-classical study of chiral symmetry breaking and of the spectrum of the Dirac operator in QCD with adjoint fermions. For this purpose we calculate matrix elements of the adjoint Dirac operator between instanton zero modes and study their symmetry properties. We present simulations of the instanton ensemble for different numbers of Majorana fermions in the adjoint representation. These simulations provide evidence that instantons lead to gluino condensation in supersymmetric gluodynamics.

hep-ph↗

arXiv2002

Instantons and the Large N_c Limit of QCD

We summarize our current understanding of instantons in the large N_c limit of QCD. We also present some recent results from simulations of the instanton liquid in QCD for N_c>3.

hep-ph↗

arXiv2002

Instanton Effects in QCD at High Baryon Density

We study instanton effects in QCD at very high baryon density. In this regime instantons are suppressed by a large power of $(Λ_{QCD}/μ)$, where $Λ_{QCD}$ is the QCD scale parameter and $μ$ is the baryon chemical potential. Instantons are nevertheless important because they contribute to several physical observables that vanish to all orders in perturbative QCD. We study, in particular, the chiral condensate and its contribution $m_{GB}^2\sim m<\barψψ>$ to the masses of Goldstone bosons in the CFL phase of QCD with $N_f=3$ flavors. We find that at densities $ρ\sim (5-10) ρ_0$, where $ρ_0$ is the density of nuclear matter, the result is dominated by large instantons and subject to considerable uncertainties. We suggest that these uncertainties can be addressed using lattice calculations of the instanton density and the pseudoscalar diquark mass in QCD with two colors. We study the topological susceptibility and Witten-Veneziano type mass relations in both $N_c=2$ and $N_c=3$ QCD.

hep-ph↗

arXiv2002

Superdense Matter

We review recent work on the phase structure of QCD at very high baryon density. We introduce the phenomenon of color superconductivity and discuss the use of weak coupling methods. We 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 study the possibility of kaon condensation at very large baryon density.

nucl-th↗

arXiv2001

Strange Goings on in Quark Matter

We review recent work on how the superfluid state of three flavor quark matter is affected by non-zero quark masses and chemical potentials.

nucl-th↗

arXiv2001

Mass Terms in Effective Theories of High Density Quark Matter

We study the structure of mass terms in the effective theory for quasi-particles in QCD at high baryon density. To next-to-leading order in the $1/p_F$ expansion we find two types of mass terms, chirality conserving two-fermion operators and chirality violating four-fermion operators. In the effective chiral theory for Goldstone modes in the color-flavor-locked (CFL) phase the former terms correspond to effective chemical potentials, while the latter lead to Lorentz invariant mass terms. We compute the masses of Goldstone bosons in the CFL phase, confirming earlier results by Son and Stephanov as well as Bedaque and Schäfer. We show that to leading order in the coupling constant $g$ there is no anti-particle gap contribution to the mass of Goldstone modes, and that our results are independent of the choice of gauge.

hep-ph↗

arXiv2001

Possible Color Octet Quark-Anti-Quark Condensate in the Instanton Model

Inspired by a recent proposal for a Higgs description of QCD we study the possible formation of a color-octet/flavor-octet quark-anti-quark condensate in the instanton liquid model. For this purpose we calculate two-point correlation functions of color-singlet and octet quark-anti-quark operators. We find long range order in the standard $<\barψψ>$ channel, but not in the color-octet channel. We emphasize that similar calculations in lattice QCD can check whether or not a color-flavor locked Higgs phase is realized in QCD at zero temperature and baryon density.

hep-lat↗

arXiv2000

Phases of QCD at High Baryon Density

We review recent work on the phase structure of QCD at very high baryon density. We introduce the phenomenon of color superconductivity and discuss how the quark masses and chemical potentials determine the structure of the superfluid quark phase. We comment on the possibility of kaon condensation at very high baryon density and study the competition between superfluid, density wave, and chiral crystal phases at intermediate density.

nucl-th↗

arXiv2000

Implications of the ALEPH tau-Lepton Decay Data for Perturbative and Non-Perturbative QCD

We use ALEPH data on hadronic $τ$ decays in order to calculate Euclidean coordinate space correlation functions in the vector and axial-vector channels. The linear combination $V-A$ receives no perturbative contribution and is quantitatively reproduced by the instanton liquid model. In the case of $V+A$ the instanton calculation is in good agreement with the data once perturbative corrections are included. These corrections clearly show the evolution of $α_s$. We also analyze the range of validity of the Operator Product Expansion (OPE). In the $V-A$ channel we find a dimension $d=6$ contribution which is comparable to the original SVZ estimate, but the instanton model provides a different non-singular term of the same magnitude. In the $V+A$ case both the OPE and the instanton model predict the same $d=4$ power correction induced by the gluon condensate, but it is masked by much larger perturbative contributions. We conclude that the range of validity of the OPE is limited to $x\lsim0.3$ fm, whereas the instanton model describes the data over the entire range.

hep-ph↗

arXiv2000

Quark Hadron Continuity in QCD with one Flavor

We study QCD with one flavor at finite baryon density. In the limit of very high baryon density the system is expected to be a color superconductor. In the case of one flavor, the order parameter is in a $\bar 3$ of color and has total angular momentum one. We show that in weak coupling perturbation theory, the energetically preferred phase exhibits ``color-spin-locking'', i.e. the color and spin direction of the condensate are aligned. We discuss the properties of this phase and argue that it shares important features of the hadronic phase at low density. In particular, we find an unbroken rotational symmetry, spin 3/2 quasiparticles, and an unusual mechanism for quark-anti-quark condensation. Our results are relevant to three flavor QCD in the regime where the strange quark mass is bigger than the critical value for color-flavor-locking. We find that the gaps in this case are on the order of one MeV.

hep-ph↗

arXiv2000

Kaon Condensation in High Density Quark Matter

We point out that the problem of kaon condensation in dense hadronic matter can be addressed in perturbative QCD. Indeed, perturbative calculations suggest that negative kaons are condensed in high density quark matter if the electroweak interaction is taken into account. This observation sheds new light on the proposal that the low density hyperon and high density quark phase of QCD are continuously connected.

nucl-th↗

arXiv1999

Color Superconductivity

We discuss recent results on color superconductivity in QCD at large chemical potential.

nucl-th↗