Log-normal distribution for correlators in lattice QCD?
Many hadronic correlators used in spectroscopy calculations in lattice QCD simulations appear to show a log-normal distribution at intermediate time separations.
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arXiv subjects
Thomas DeGrand
Publications and source records attributed to Thomas DeGrand.
SU(4) lattice gauge theory with decuplet fermions: Schrödinger functional analysis
We complete a program of study of SU(N) gauge theories coupled to two flavors of fermions in the two-index symmetric representation by performing numerical simulations in SU(4). The beta function, defined and calculated via the Schrödinger functional, runs more slowly than the two-loop perturbative result. The mass anomalous dimension levels off in strong coupling at a value of about 0.45, rendering this theory unsuitable for walking technicolor. A large-N comparison of this data with results from SU(2) and SU(3) reveals striking regularities.
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Gauge theories with fermions in the two-index symmetric representation
We summarize our recent work on gauge theories with two flavors of fermions in the two-index symmetric representation: SU(2) gauge theory with adjoint fermions, SU(3) with sextets, and SU(4) with ten-dimensional-representation fermions. All three systems have beta functions smaller than their perturbative value, approaching a fixed point near the expected two-loop zero. In all cases the mass anomalous dimension is small, under 0.5.
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Finite-size scaling tests for spectra in SU(3) lattice gauge theory coupled to 12 fundamental flavor fermions
I carry out a finite-size scaling study of the correlation length in SU(3) lattice gauge theory coupled to 12 fundamental flavor fermions, using recent data published by Fodor, Holland, Kuti, Nogradi and Schroeder. I make the assumption that the system is conformal in the zero-mass, infinite volume limit, that scaling is violated by both nonzero fermion mass and by finite volume, and that the scaling function in each channel is determined self-consistently by the data. From several different observables I extract a common exponent for the scaling of the correlation length xi with the fermion mass m_q, xi proportional to m_q to the power -1/y_m, with y_m ~ 1.35. Shortcomings of the analysis are discussed.
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Infrared fixed point in SU(2) gauge theory with adjoint fermions
We apply Schrodinger-functional techniques to the SU(2) lattice gauge theory with N_f=2 flavors of fermions in the adjoint representation. Our use of hypercubic smearing enables us to work at stronger couplings than did previous studies, before encountering a critical point and a bulk phase boundary. Measurement of the running coupling constant gives evidence of an infrared fixed point g* where 1/g*^2 = 0.20(4)(3). At the fixed point, we find a mass anomalous dimension gamma_m(g*) = 0.31(6).
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Lattice studies of QCD-like theories with many fermionic degrees of freedom
I give an elementary introduction to the study of gauge theories coupled to fermions with many degrees of freedom. Besides their intrinsic interest, these theories are candidates for nonperturbative extensions of the Higgs sector of the Standard Model. While related to QCD, these systems can exhibit very different behavior from it: they can possess a running gauge coupling with an infrared attractive fixed point (IRFP). I briefly survey recent lattice work in this area.
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Sextet QCD: slow running and the mass anomalous dimension
I report the results of Schroedinger functional calculations in the SU(3) gauge theory with two flavors of color sextet fermions, defined with the Wilson-clover action using nHYP fat links. While we cannot confirm the infrared fixed point seen with thin links, we find very slow evolution of the coupling constant, so slow that extraction of the mass anomalous dimension is straightforward.
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Running coupling and mass anomalous dimension of SU(3) gauge theory with two flavors of symmetric-representation fermions
We have measured the running coupling constant of SU(3) gauge theory coupled to Nf=2 flavors of symmetric representation fermions, using the Schrodinger functional scheme. Our lattice action is defined with hypercubic smeared links which, along with the larger lattice sizes, bring us closer to the continuum limit than in our previous study. We observe that the coupling runs more slowly than predicted by asymptotic freedom, but we are unable to observe fixed point behavior before encountering a first order transition to a strong coupling phase. This indicates that the infrared fixed point found with the thin-link action is a lattice artifact. The slow running of the gauge coupling permits an accurate determination of the mass anomalous dimension for this theory, which we observe to be small, gamma_m < 0.6, over the range of couplings we can reach. We also study the bulk and finite-temperature phase transitions in the strong coupling region.
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Oblique correction in a walking lattice theory
I compute the difference of vector and axial vector current correlators in the weak coupling phase of (lattice-regulated) SU(3) gauge theory with two flavors of symmetric-representation dynamical fermions. This is a walking theory at the bare parameter values chosen for the simulation. Otherwise, it is not a conventional technicolor candidate. The correlator difference shows scaling behavior in the fermion mass, and vanishes in the fermion zero mass limit. Consequences for the phenomenology of similar systems which might be candidates for beyond Standard Model physics are discussed. I check my methodology against ordinary QCD, by computing the Gasser-Leutwyler coefficient L_10 and the charged - neutral pion mass difference from an approximate parameterization of the correlator.
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Finite-size scaling tests for SU(3) lattice gauge theory with color sextet fermions
The observed slow running of the gauge coupling in SU(3) lattice gauge theory with two flavors of color sextet fermions naturally suggests it is a theory with one relevant coupling, the fermion mass, and that at zero mass correlation functions decay algebraically. I perform a finite-size scaling study on simulation data at two values of the bare gauge coupling with this assumption and observe a common exponent for the scaling of the correlation length with the fermion mass, y_m ~ 1.5. An analysis of the scaling of valence Dirac eigenvalues at one of these bare couplings produces a similar number.
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Comments on lattice gauge theories with infrared-attractive fixed points
Theories of interacting gauge fields and fermions can possess a running gauge coupling with an infrared attractive fixed point (IRFP). We present a minimal description of the physics of these systems and comment on some simple expectations for results from lattice simulations done within the basin of attraction of the IRFP in these theories.
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Volume scaling of Dirac eigenvalues in SU(3) lattice gauge theory with color sextet fermions
I observe a rough volume-dependent scaling of the low eigenvalues of a chiral Dirac operator in lattice studies of SU(3) lattice gauge theory with two flavors of color sextet fermions, in its weak-coupling phase. The mean value of the ith eigenvalue scales with the simulation volume V=L^4 as L^p ~zeta_i, where zeta_i is a volume-independent constant. The exponent p is about 1.4. A possible explanation for this phenomenon is that p is the leading relevant exponent associated with the fermion mass dependence of correlation functions in a theory whose zero-mass limit is conformal.
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Phase structure of SU(3) gauge theory with two flavors of symmetric-representation fermions
We have performed numerical simulations of SU(3) gauge theory coupled to Nf=2 flavors of symmetric representation fermions. The fermions are discretized with the tadpole-improved clover action. Our simulations are done on lattices of length L=6, 8, and 12. In all simulation volumes we observe a crossover from a strongly coupled confined phase to a weak coupling deconfined phase. Degeneracies in screening masses, plus the behavior of the pseudoscalar decay constant, indicate that the deconfined phase is also a phase in which chiral symmetry is restored. The movement of the confinement transition as the volume is changed is consistent with avoidance of the basin of attraction of an infrared fixed point of the massless theory.
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Reweighting QCD simulations with dynamical overlap fermions
I apply a recently developed algorithm for reweighting simulations of lattice QCD from one quark mass to another to simulations performed with overlap fermions in the epsilon regime. I test it by computing the condensate from distributions of the low lying eigenvalues of the Dirac operator. Results seem favorable.
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Nonperturbative infrared fixed point in sextet QCD
The SU(3) gauge theory with fermions in the sextet representation is one of several theories of interest for technicolor models. We have carried out a Schrodinger functional (SF) calculation for the lattice theory with two flavors of Wilson fermions. We find that the discrete beta function changes sign when the SF renormalized coupling is in the neighborhood of g^2 = 2.0, showing a breakdown of the perturbative picture even though the coupling is weak. The most straightforward interpretation is an infrared-stable fixed point.
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Exploring the phase diagram of sextet QCD
As a follow up to the previous talk about the beta function of SU(3) gauge theory with Nf=2 symmetric representation (clover) fermions [arXiv:0809.2885 [hep-lat]], we describe our explorations of the beta-kappa plane, away from the massless limit. Our simulations are mostly done on lattices of length L=8 and 12. We observe a phase transition from a strong coupling confined phase to a deconfined, chirally restored phase. The line of transitions avoids (so far) the location of the infrared fixed point discussed in the last talk.
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Finite-volume Correction to the Pion Decay Constant in the Epsilon-Regime
In the chiral limit of QCD, the pion decay constant F can be extracted from lattice gauge theory by means of a coupling to isospin chemical potential. Here we compute the leading correction due to finite volume in the epsilon-expansion of chiral perturbation theory. A comparison is made to recent Monte Carlo data.
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Zero of the discrete beta function in SU(3) lattice gauge theory with color sextet fermions
We have carried out a Schrodinger functional (SF) calculation for the SU(3) lattice gauge theory with two flavors of Wilson fermions in the sextet representation of the gauge group. We find that the discrete beta function, which governs the change in the running coupling under a discrete change of spatial scale, changes sign when the SF renormalized coupling is in the neighborhood of g^2=2.0. The simplest explanation is that the theory has an infrared-attractive fixed point, but more complicated possibilities are allowed by the data. While we compare rescalings by factors of 2 and 4/3, we work at a single lattice spacing.
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