arXiv subjects
Publications and source records attributed to Richard C. Brower.
This document is one of a series of whitepapers from the USQCD collaboration. Here, we discuss opportunities for lattice field theory research to make an impact on models of new physics beyond the Standard Model, including composite Higgs, composite dark matter, and supersymmetric theories.
We present our lattice studies of SU(3) gauge theory with $N_f$ = 8 degenerate fermions in the fundamental representation. Using nHYP-smeared staggered fermions we study finite-temperature transitions on lattice volumes as large as $L^3 \times N_t = 48^3 \times 24$, and the zero-temperature composite spectrum on lattice volumes up to $64^3 \times 128$. The spectrum indirectly indicates spontaneous chiral symmetry breaking, but finite-temperature transitions with fixed $N_t \leq 24$ enter a strongly coupled lattice phase as the fermion mass decreases, which prevents a direct confirmation of spontaneous chiral symmetry breaking in the chiral limit. In addition to the connected spectrum we focus on the lightest flavor-singlet scalar particle. We find it to be degenerate with the pseudo-Goldstone states down to the lightest masses reached so far by non-perturbative lattice calculations. Using the same lattice approach, we study the behavior of the composite spectrum when the number of light fermions is changed from eight to four. A heavy flavor-singlet scalar in the 4-flavor theory affirms the contrast between QCD-like dynamics and the low-energy behavior of the 8-flavor theory.
We present a method for defining a lattice realization of the $ϕ^4$ quantum field theory on a simplicial complex in order to enable numerical computation on a general Riemann manifold. The procedure begins with adopting methods from traditional Regge Calculus (RC) and finite element methods (FEM) plus the addition of ultraviolet counter terms required to reach the renormalized field theory in the continuum limit. The construction is tested numerically for the two-dimensional $ϕ^4$ scalar field theory on the Riemann two-sphere, $\mathbb{S}^2$, in comparison with the exact solutions to the two-dimensional Ising conformal field theory (CFT). Numerical results for the Binder cumulants (up to 12th order) and the two- and four-point correlation functions are in agreement with the exact $c = 1/2$ CFT solutions.
Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a multi-grid algorithm for the Kogut-Susskind (or staggered) fermion discretization which has proven difficult relative to Wilson multigrid due to its first-order anti-Hermitian structure. The solution is to introduce a novel spectral transformation by the Kähler-Dirac spin structure prior to the Galerkin projection. We present numerical results for the two-dimensional, two-flavor Schwinger model, however, the general formalism is agnostic to dimension and is directly applicable to four-dimensional lattice QCD.
The lattice Dirac equation is formulated on a simplicial complex which approximates a smooth Riemann manifold by introducing a lattice vierbein on each site and a lattice spin connection on each link. Care is taken so the construction applies to any smooth D-dimensional Riemannian manifold that permits a spin connection. It is tested numerically in 2D for the projective sphere ${\mathbb S}^2$ in the limit of an increasingly refined sequence of triangles. The eigenspectrum and eigenvectors are shown to converge rapidly to the exact result in the continuum limit. In addition comparison is made with the continuum Ising conformal field theory on ${\mathbb S}^2$. Convergence is tested for the two point, $\langle ε(x_1) ε(x_2) \rangle$, and the four point, $\langle σ(x_1) ε(x_2) ε(x_3 )σ(x_4) \rangle $, correlators for the energy, $ε(x) = i \bar ψ(x)ψ(x)$, and twist operators, $σ(x)$, respectively.
We present results for the spectrum of a strongly interacting SU(3) gauge theory with $N_f = 8$ light fermions in the fundamental representation. Carrying out non-perturbative lattice calculations at the lightest masses and largest volumes considered to date, we confirm the existence of a remarkably light singlet scalar particle. We explore the rich resonance spectrum of the 8-flavor theory in the context of the search for new physics beyond the standard model at the Large Hadron Collider (LHC). Connecting our results to models of dynamical electroweak symmetry breaking, we estimate the vector resonance mass to be about 2 TeV with a width of roughly 450 GeV, and predict additional resonances with masses below ~3 TeV.
Viable non-perturbative methods for lattice quantum field theories on curved manifolds are difficult. By adapting features from the traditional finite element methods (FEM) and Regge Calculus, a new simplicial lattice Quantum Finite Element (QFE) Lagrangian is constructed for fields on a smooth Riemann manifold. To reach the continuum limit additional counter terms must be constructed to cancel the ultraviolet distortions. This is tested by the comparison of phi 4-th theory at the Wilson-Fisher fixed point with the exact Ising (c =1/2) CFT on a 2D Riemann sphere. The Dirac equation is also constructed on a simplicial lattice approximation to a Riemann manifold by introducing a lattice vierbein and spin connection on each link. Convergence of the QFE Dirac equation is tested against the exact solution for the 2D Riemann sphere. Future directions and applications to Conformal Field Theories are suggested.
We present a multiscale thermalization algorithm for lattice gauge theory, which enables efficient parallel generation of uncorrelated gauge field configurations. The algorithm combines standard Monte Carlo techniques with ideas drawn from real space renormalization group and multigrid methods. We demonstrate the viability of the algorithm for pure Yang-Mills gauge theory for both heat bath and hybrid Monte Carlo evolution, and show that it ameliorates the problem of topological freezing up to controllable lattice spacing artifacts.
We focus on a holographic approach to DIS at small-x in high energy where scattering is dominated by exchanging a Reggeized Graviton in $AdS_5$. We emphasize the importance of confinement, which corresponds to a deformation of $AdS_5$ geometry in the IR. This approach provides an excellent fit to the combined HERA data at small $x$. We also discuss the connection of Pomeron/Odderon intercepts in the conformal limit with anomalous dimensions in strong coupling.
We present a new model of "Stealth Dark Matter": a composite baryonic scalar of an $SU(N_D)$ strongly-coupled theory with even $N_D \geq 4$. All mass scales are technically natural, and dark matter stability is automatic without imposing an additional discrete or global symmetry. Constituent fermions transform in vector-like representations of the electroweak group that permit both electroweak-breaking and electroweak-preserving mass terms. This gives a tunable coupling of stealth dark matter to the Higgs boson independent of the dark matter mass itself. We specialize to $SU(4)$, and investigate the constraints on the model from dark meson decay, electroweak precision measurements, basic collider limits, and spin-independent direct detection scattering through Higgs exchange. We exploit our earlier lattice simulations that determined the composite spectrum as well as the effective Higgs coupling of stealth dark matter in order to place bounds from direct detection, excluding constituent fermions with dominantly electroweak-breaking masses. A lower bound on the dark baryon mass $m_B \gtrsim 300$ GeV is obtained from the indirect requirement that the lightest dark meson not be observable at LEP II. We briefly survey some intriguing properties of stealth dark matter that are worthy of future study, including: collider studies of dark meson production and decay; indirect detection signals from annihilation; relic abundance estimates for both symmetric and asymmetric mechanisms; and direct detection through electromagnetic polarizability, a detailed study of which will appear in a companion paper.
We calculate the spin-independent scattering cross section for direct detection that results from the electromagnetic polarizability of a composite scalar baryon dark matter candidate -- "Stealth Dark Matter", that is based on a dark SU(4) confining gauge theory. In the nonrelativistic limit, electromagnetic polarizability proceeds through a dimension-7 interaction leading to a very small scattering cross section for dark matter with weak scale masses. This represents a lower bound on the scattering cross section for composite dark matter theories with electromagnetically charged constituents. We carry out lattice calculations of the polarizability for the lightest baryons in SU(3) and SU(4) gauge theories using the background field method on quenched configurations. We find the polarizabilities of SU(3) and SU(4) to be comparable (within about 50%) normalized to the baryon mass, which is suggestive for extensions to larger SU(N) groups. The resulting scattering cross sections with a xenon target are shown to be potentially detectable in the dark matter mass range of about 200-700 GeV, where the lower bound is from the existing LUX constraint while the upper bound is the coherent neutrino background. Significant uncertainties in the cross section remain due to the more complicated interaction of the polarizablity operator with nuclear structure, however the steep dependence on the dark matter mass, $1/m_B^6$, suggests the observable dark matter mass range is not appreciably modified. We briefly highlight collider searches for the mesons in the theory as well as the indirect astrophysical effects that may also provide excellent probes of stealth dark matter.
From the perspective of AdS/CFT the Pomeron is identified with a Reggeized Graviton, while the Odderons correspond to Reggeized anti-symmetric $AdS_5$ Kalb-Ramond tensor-fields. In this paper, we consider the strong coupling expansion of the dimension of the leading twist operators dual to these Regge trajectories, $Δ(j)$, to determine its analytic continuation in $j$ beyond the diffusion limit. In particular, we compute the strong coupling expansion of the intercept to order $λ^{-3}$, where $λ$ is the t'Hooft coupling, for both the Pomeron, which is $C=+1$ crossing-even, and the "Odderons", which are the leading $C=-1$ crossing-odd Regge singularities. We discuss the spectral curves of the class of single-trace operators to which these string modes couple.
We present a review of the properties of generalized domain wall Fermions, based on a (real) Möbius transformation on the Wilson overlap kernel, discussing their algorithmic efficiency, the degree of explicit chiral violations measured by the residual mass ($m_{res}$) and the Ward-Takahashi identities. The Möbius class interpolates between Shamir's domain wall operator and Boriçi's domain wall implementation of Neuberger's overlap operator without increasing the number of Dirac applications per conjugate gradient iteration. A new scaling parameter ($α$) reduces chiral violations at finite fifth dimension ($L_s$) but yields exactly the same overlap action in the limit $L_s \rightarrow \infty$. Through the use of 4d Red/Black preconditioning and optimal tuning for the scaling $α(L_s)$, we show that chiral symmetry violations are typically reduced by an order of magnitude at fixed $L_s$. At large $L_s$ we argue that the observed scaling for $m_{res} = O(1/L_s)$ for Shamir is replaced by $m_{res} = O(1/L_s^2)$ for the properly tuned Möbius algorithm with $α= O(L_s)$
Lattice radial quantization was proposed in a recent paper by Brower, Fleming and Neuberger[1] as a nonperturbative method especially suited to numerically solve Euclidean conformal field theories. The lessons learned from the lattice radial quantization of the 3D Ising model on a longitudinal cylinder with 2D Icosahedral cross-section suggested the need for an improved discretization. We consider here the use of the Finite Element Methods(FEM) to descretize the universally-equivalent $ϕ^4$ Lagrangian on $\mathbb R \times \mathbb S^2$. It is argued that this lattice regularization will approach the exact conformal theory at the Wilson-Fisher fixed point in the continuum. Numerical tests are underway to support this conjecture.
We present the spectrum of baryons in a new SU(4) gauge theory with fundamental fermion constituents. The spectrum of these bosonic baryons is of significant interest for composite dark matter theories. Here, we compare the spectrum and properties of SU(3) and SU(4) baryons, and then compute the dark-matter direct detection cross section via Higgs boson exchange for TeV-scale composite dark matter arising from a confining SU(4) gauge sector. Comparison with the latest LUX results leads to tight bounds on the fraction of the constituent-fermion mass that may arise from electroweak symmetry breaking. Lattice calculations of the dark matter mass spectrum and the Higgs-dark matter coupling are performed on quenched $16^{3} \times 32$, $32^{3} \times 64$, $48^{3} \times 96$, and $64^{3} \times128$ lattices with three different lattice spacings, using Wilson fermions with moderate to heavy pseudoscalar meson masses. Our results lay a foundation for future analytic and numerical study of composite baryonic dark matter.
We discuss how exact conformal invariance in the strong coupling leads naturally through AdS/CFT correspondence to a systematic expansion for the Pomeron and Odderon intercepts in power of $λ^{-1/2}$, with $λ=g^2N_c$ the 't Hooft coupling. We also point out the importance of confinement for a realistic treatment of DIS in the HERA energy range.
We consider radial quantization for conformal quantum field theory with a lattice regulator. A Euclidean field theory on $\mathbb R^D$ is mapped to a cylindrical manifold, $\mathbb R\times \mathbb S^{D-1}$, whose length is logarithmic in scale separation. To test the approach, we apply this to the 3D Ising model and compute $η$ for the first $Z_2$ odd primary operator.
In the past decade overwhelming evidence has emerged for a conjectured duality between a wide class of gauge theories in d dimensions and string theories on asymptotically AdS_{d+1} spaces. We apply this duality to scattering processes that occur via Pomeron exchange. First we develop the Pomeron in string theory, as done by Brower, Polchinski, Strassler and Tan, showing that it naturally emerges as the Regge Trajectory of the AdS graviton. Next we apply the AdS Pomeron to the study of Deeply Virtual Compton Scattering (DVCS), and see that our model gives good results when compared to HERA data. We then show how we can extend our results to double Pomeron exchange, and apply it to developing a formalism for the study of double diffractive Higgs production.