arXiv subjects
Publications and source records attributed to Thomas DeGrand.
I review the physics of lattice fermions obeying the Ginsparg-Wilson relation. I describe their relation to domain wall fermions. I give a description of methodology for performing numerical simulations with overlap fermions. This is a chapter contributed to the on-line book ``Lattice QCD at 50 years,'' (LQCD@50), edited by Tanmoy Bhattacharya, Maarten Golterman, Rajan Gupta, Laurent Lellouch, and Steve Sharpe.
I show comparisons of the pseudoscalar meson vector form factor from simulations of QCD with $N_c = 3$, 4 and 5 colors and $N_f = 2$ flavors of degenerate mass fermions at a common (matched) fermion mass, lattice spacing, and simulation volume. The dependence of the form factor on the momentum transfer is nearly independent of the number of colors, and is consistent with the expectations of vector meson dominance.
I show comparisons of the pion - pion scattering length in the isospin - two channel from simulations of of QCD with $N_c = 3$, 4 and 5 colors and $N_f = 2$ flavors of degenerate mass fermions. The scattering length varies as $1/N_c$, as expected from large $N_c$ counting arguments.
We present a lattice calculation of the low energy constants of QCD with $N_c=3$, 4 and 5 colors and $N_f=2$ flavors of degenerate mass fermions. We fit data for the pseudoscalar meson mass, the pseudoscalar decay constant, and the Axial Ward Identity fermion mass to formulas from next to next to leading order chiral perturbation theory. We extract the next to leading order low energy constants and study their behavior as a function of $N_c$. Pre-existing analyses of $N_c=3$ inform our fitting strategies.
Contribution from the USQCD Collaboration to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021).
Lattice quantum chromodynamics has proven to be an indispensable method to determine nonperturbative strong contributions to weak decay processes. In this white paper for the Snowmass community planning process we highlight achievements and future avenues of research for lattice calculations of weak $b$ and $c$ quark decays, and point out how these calculations will help to address the anomalies currently in the spotlight of the particle physics community. With future increases in computational resources and algorithmic improvements, percent level (and below) lattice determinations will play a central role in constraining the standard model or identifying new physics.
I make some simple observations about the calculation of weighted averages over energy of Minkowski space spectral densities from weighted averages over time of Euclidean space correlation functions, measured in latice simulations. The correlator of two vector currents is used as an example, where it appears that a determination of a weighted average of the spectral function near the rho pole at the five per cent level is possible from lattice simulations.
We present preliminary results from our calculation of the low energy constants (LECs) of the chiral effective theory for 3, 4 and 5 color QCD with $N_f=2$ dynamical fermion flavors. We simulate with clover fermions over a range of lattice couplings and quark masses. We observe the expected $N_c$ scaling for the LECs appropriate to the condensate $B$ and pseudoscalar decay constant $F$. The range of quark masses over which leading order chiral perturbation theory describes the data grows as $N_c$ rises.
It is well known that the deconfinement transition temperature for $SU(N_c)$ gauge theory is almost independent of $N_c$, and the transition is first order for $N_c \ge 3$. In the real world ($N_c=3$, light quarks) it is a crossover located far away from the pure gauge value. What happens to the transition temperature at fixed fermion mass if the number of fermion flavors is held constant ($N_f=2$) and $N_c$ is varied? There are multiple plausible stories, only one of which appears to be true when the systems are simulated on the lattice. I describe the physics issues which surround the question and my lattice - based answer to it.
I present a numerical study of the crossover between the low temperature chirally broken phase and the high temperature chirally restored phase in $SU(N_c)$ gauge theory with $N_c=3-5$ colors and $N_f=2$ degenerate fermion flavors. Fermion masses span a range of intermediate values (represented by the squared ratio of pseudoscalar to vector meson masses $(m_{PS}/m_V)^2\sim 0.25$ to 0.63). Observables include the temperature dependent chiral condensate and screening masses. At each fermion mass these quantities show nearly identical temperature dependence across $N_c$.
I present a calculation of the topological susceptibility $χ_T$ in $SU(N_c)$ gauge theory with $N_c=3-5$ colors and $N_f=2$ degenerate flavors of fermions. The results lie on a common curve when expressed in terms of the combination $N_c m_{PS}^2 t_0$ where $m_{PS}$ is the pseudoscalar meson mass and $t_0$ is the flow parameter. $χ_T$ approaches its quenched value as the pseudoscalar mass becomes large. The lattice simulations use clover fermions. They are done at a single lattice spacing, roughly matched across $N_c$, and over a restricted range of fermion masses.
A number of proposed extensions of the Standard Model include new strongly interacting dynamics, in the form of SU(N) gauge fields coupled to various numbers of fermions. Often, these extensions allow N = 3 as a plausible choice, or even require N = 3, such as in twin Higgs models, where the new dynamics is a "copy" of QCD. However, the fermion masses in such a sector are typically different from (often heavier than) the ones of real-world QCD, relative to the confinement scale. Many of the strong interaction masses and matrix elements for SU(3) at heavy fermion masses have already been computed on the lattice, typically as a byproduct of the approach to the physical point of real QCD. We provide a summary of these relevant results for the phenomenological community.
These lectures about lattice field theory were written for, and given at, TASI 2019, ``The many dimensions of quantum field theory.'' The students at this TASI were mostly interested in formal things, and so these are slightly unusual lattice lectures: I wanted to give the physical motivation behind lattice calculations rather than describe all the technical details. A quick outline: (1) The really big picture: lattice basics, lattice confinement, getting rid of the lattice. (2) A walk through the parts of a lattice calculation -- an overview, to show what's involved. (3) Chiral fermions on the lattice. (This part might be interesting to lattice people.) (4) Case studies: the three dimensional Ising model, and QCD.
Partial compositeness is a mechanism for the generation of fermion masses which replaces a direct Higgs coupling to the fermions by a linear mixing with heavy composite partners. We present the first calculation of the relevant matrix element in a lattice model which is very close to a candidate theory containing a composite Higgs boson and a partially composite top quark. Specifically, our model is an SU(4) gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations. The matrix element we obtain is small and hence our result disfavors the scenario of obtaining a realistic top mass in this model.
We present a progress report on our investigation of the thermodynamics of QCD with $N_f=2$ flavors of dynamical Wilson fermions in the limit of a large number of colors $N_c$. To date, studies of the thermodynamics of QCD at large $N_c$ have been limited to the quenched approximation, i.e., to the behavior of pure $\mathrm{SU}(N_c)$ gauge theory at large $N_c$. This is the first study of thermodynamics at large $N_c$ using dynamical fermions, and thus the first study able to test whether the quenched approximation is a valid way to investigate large $N_c$ thermodynamics. After reviewing 't Hooft's large $N_c$ limit, we discuss the automation we use to make this study feasible, and finally compare our preliminary physics results for $\mathrm{SU}(3-5)$ with large $N_c$ expectations.
Some recent beyond Standard Model phenomenology is based on new strongly interacting dynamics of $SU(N)$ gauge fields coupled to various numbers of fermions. When $N=3$ these systems are analogues of QCD, although the fermion masses are typically different from -- and heavier than -- the ones of real world QCD. Many quantities needed for phenomenology from these models have been computed on the lattice. We are writing a guide for these phenomenologists, telling them about lattice results. We'll tell you (some of) what they are interested in knowing.
We have simulated the SU(4) lattice gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations simultaneously. Such theories arise naturally in the context of composite Higgs models that include a partially composite top quark. We describe the low-lying meson spectrum of the theory and fit the pseudoscalar masses and decay constants to chiral perturbation theory. We infer as well the mass and decay constant of the Goldstone boson corresponding to the non-anomalous U(1) symmetry of the model. Our results are broadly consistent with large-Nc scaling and vector-meson dominance.
We investigate the phase structure of SU(4) gauge theory with the gauge field simultaneously coupled to two flavors of fermion in the fundamental representation and two flavors of fermion in the two-index antisymmetric representation. We find that the theory has only two phases, a low-temperature phase with both species of fermion confined and chirally broken, and a high-temperature phase with both species of fermion deconfined and chirally restored. The single phase transition in the theory appears to be first order, in agreement with theoretical predictions.