Searcharxiv⌕ Search

arXiv subjects

Robert Shrock

Publications and source records attributed to Robert Shrock.

At least 73 records · Page 4Linked to original sources
arXiv2015

Renormalization-Group Evolution and Nonperturbative Behavior of Chiral Gauge Theories with Fermions in Higher-Dimensional Representations

We study the ultraviolet to infrared evolution and nonperturbative behavior of a simple set of asymptotically free chiral gauge theories with an SU($N$) gauge group and an anomaly-free set of $n_{S_k}$ copies of chiral fermions transforming as the symmetric rank-$k$ tensor representation, $S_k$, and $n_{\bar A_\ell}$ copies of fermions transforming according to the conjugate antisymmetric rank-$\ell$ tensor representation, $\bar A_\ell$, of this group with $k, \ \ell \ge 2$. As part of our study, we prove a general theorem guaranteeing that a low-energy effective theory resulting from the dynamical breaking of an anomaly-free chiral gauge theory is also anomaly-free. We analyze the theories with $k=\ell=2$ in detail and show that there are only a finite number of these. Depending on the specific theory, the ultraviolet to infrared evolution may lead to a non-Abelian Coulomb phase, or may involve confinement with massless composite fermions, or fermion condensation with dynamical gauge and global symmetry breaking. We show that $S_k \bar A_k$ chiral gauge theories with $k \ge 3$ are not asymptotically free. We also analyze theories with fermions in $S_k$ and $\bar A_\ell$ representations of SU($N$) with $k \ne \ell$ and $k, \ \ell \ge 2$.

hep-th↗
arXiv2015

Exact Partition Functions for the $q$-State Potts Model with a Generalized Magnetic Field on Lattice Strip Graphs

We calculate the partition function of the $q$-state Potts model on arbitrary-length cyclic ladder graphs of the square and triangular lattices, with a generalized external magnetic field that favors or disfavors a subset of spin values $\{1,...,s\}$ with $s \le q$. For the case of antiferromagnet spin-spin coupling, these provide exactly solved models that exhibit an onset of frustration and competing interactions in the context of a novel type of tensor-product $S_s \otimes S_{q-s}$ global symmetry, where $S_s$ is the permutation group on $s$ objects.

cond-mat.stat-mech↗
arXiv2015

Analysis of a Zero of a Beta Function Using All-Orders Summation of Diagrams

Conventionally, one calculates a zero in a beta function by computing this function to a given loop order and solving for the zero. Here we discuss a different method which is applicable in theories where one can perform a partial diagrammatic summation to infinite-loop order. We show that this method, compared with the conventional method, yields much better agreement with exact results in the case of an asymptotically free gauge theory with ${\cal N}=1$ supersymmetry. Applications to other field theories are also discussed.

hep-th↗
arXiv2015

A facility to Search for Hidden Particles at the CERN SPS: the SHiP physics case

This paper describes the physics case for a new fixed target facility at CERN SPS. The SHiP (Search for Hidden Particles) experiment is intended to hunt for new physics in the largely unexplored domain of very weakly interacting particles with masses below the Fermi scale, inaccessible to the LHC experiments, and to study tau neutrino physics. The same proton beam setup can be used later to look for decays of tau-leptons with lepton flavour number non-conservation, $τ\to 3μ$ and to search for weakly-interacting sub-GeV dark matter candidates. We discuss the evidence for physics beyond the Standard Model and describe interactions between new particles and four different portals - scalars, vectors, fermions or axion-like particles. We discuss motivations for different models, manifesting themselves via these interactions, and how they can be probed with the SHiP experiment and present several case studies. The prospects to search for relatively light SUSY and composite particles at SHiP are also discussed. We demonstrate that the SHiP experiment has a unique potential to discover new physics and can directly probe a number of solutions of beyond the Standard Model puzzles, such as neutrino masses, baryon asymmetry of the Universe, dark matter, and inflation

hep-ph↗
arXiv2015

Determination of SU(4)$_{TC}$ Technicolor Gauge Group from Embedding in Extended Technicolor

In technicolor theories using an SU($N_{TC}$) gauge group, the value of $N_{TC}$ is not, {\it a priori}, determined and is typically chosen by phenomenological criteria. Here we present a novel way to determine $N_{TC}$ from the embedding of a one-family technicolor model, with fermions in the fundamental represention of SU($N_{TC}$), in an extended technicolor theory, and use it to deduce that $N_{TC}=4$ in this framework.

hep-ph↗
arXiv2014

New Scheme Transformations and Application to Study Scheme Dependence of an Infrared Zero of the Beta Function in Gauge Theories

We present two new one-parameter families of scheme transformations and apply these to study the scheme dependence of the infrared zero in the beta function of an asymptotically free non-Abelian gauge theory up to four-loop order. Our results provide a further quantitative measure of this scheme dependence, showing that for moderate values of the gauge coupling and the parameter specifying the scheme transformation, this dependence is relatively mild. We also remark on a generalized multi-parameter family of rational scheme transformations.

hep-th↗
arXiv2014

Renormalization-Group Evolution of Chiral Gauge Theories

We calculate the ultraviolet to infrared evolution and analyze possible types of infrared behavior for several asymptotically free chiral gauge theories with gauge group SU($N$) and massless chiral fermions transforming according to a symmetric rank-2 tensor representation $S$ and $N+4$ copies (flavors) of a conjugate fundamental representation $\bar F$, together with a vectorlike subsector with chiral fermions in higher-dimensional representation(s). We construct and study three such chiral gauge theories. These have respective vectorlike subsectors comprised of (a) $p$ copies of fermions in the adjoint representation, (b) $N = 2k$ even and $p$ copies of fermions in the antisymmetric rank-$k$ tensor representation, and (c) $p$ copies of $\{S + \bar S\}$ fermions. Results are presented for beta functions, their infrared zeros, and predictions from the most-attractive-channel approach for the formation of bilinear fermion condensates. Importantly, we show that for these theories, the expected ultraviolet to infrared evolution obeys a conjectured inequality concerning the field degrees of freedom for all values of the parameters $N$ and $p$ characterizing each theory.

hep-th↗
arXiv2014

On the Question of an Ultraviolet Zero of the Beta Function of the $λ(\vecϕ^2)^2_4$ Theory

We investigate the possibility of an ultraviolet (UV) zero in the $n$-loop beta function of a $λ(\vecϕ^2)^2$ field theory with an $N$-component scalar field, $\vecϕ$, in four spacetime dimensions, up to the level of $n=5$ loops. Although the two-loop beta function has a UV zero, we find that the $n$-loop beta function for $n=3, \ 4, \ 5$ either does not have a UV zero or does not have one at a value of $λ$ in approximate agreement with the two-loop calculation. Similar results are obtained after application of scheme transformations to the beta function and via calculation of Padé approximants. We thus conclude that in the range of $λ$ where the perturbative calculation of the $n$-loop beta function is reliable, the theory does not exhibit robust evidence of a UV zero up to the level of $n=5$ loops.

hep-th↗
arXiv2014

Generalized Scheme Transformations for the Elimination of Higher-Loop Terms in the Beta Function of a Gauge Theory

We construct and study a generalized one-parameter class of scheme transformations, denoted $S_{R,m,k_1}$ with $m \ge 2$, with the property that an $S_{R,m,k_1}$ scheme transformation eliminates the $\ell$-loop terms in the beta function of a gauge theory from loop order $\ell=3$ to order $\ell=m+1$, inclusive. These scheme transformations are applied to the higher-loop calculation of the infrared zero of the beta function of an asymptotically free gauge theory with multiple fermions. We show that scheme transformations in this generalized class satisfy a set of criteria for physical acceptability over a larger range of numbers of fermions than previously studied scheme transformations. We also present an interesting modification of a different type of scheme transformation that removes the three-loop term in the beta function.

hep-th↗
arXiv2014

Study of Possible Ultraviolet Zero of the Beta Function in Gauge Theories with Many Fermions

We study the possibility of an ultraviolet (UV) zero in the $n$-loop beta function of U(1) and non-Abelian gauge theories with $N_f$ fermions for large $N_f$. The effect of scheme transformations on the coefficients of different powers of $N_f$ in the $n$-loop term in the beta function is calculated. A general scheme-independent criterion is given for determining whether or not the $n$-loop beta function has a UV zero for large $N_f$. We compare the results with exact integral representations of the leading terms in the beta functions for the respective Abelian and non-Abelian theories in the limit $N_f \to \infty$ limit with $N_f α$ finite. As part of this study, new analytic and numerical results are presented for certain coefficients, denoted $b_{n,n-1}$, that control the large-$N_f$ behavior at $n$-loop order in the beta function. We also investigate various test functions incorporating a power-law and essential UV zero in the beta function and determine their manifestations in series expansions in powers of coupling and in powers of $1/N_f$.

hep-th↗
arXiv2014

Renormalization-Group Flows and Fixed Points in Yukawa Theories

We study renormalization-group flows in Yukawa theories with massless fermions, including determination of fixed points and curves that separate regions of different flow behavior. We assess the reliability of perturbative calculations for various values of Yukawa coupling $y$ and quartic scalar coupling $λ$ by comparing the properties of flows obtained with the beta functions of these couplings calculated to different orders in the loop expansion. The results provide a determination of the region in $y$ and $λ$ where calculations up to two loops can yield reasonably reliable results.

hep-th↗
arXiv2013

On the Ultraviolet to Infrared Evolution of Chiral Gauge Theories

We discuss the ultraviolet (UV) to infrared (IR) evolution of asymptotically free chiral gauge theories. Various types of IR behavior are considered, including confinement without spontaneous chiral symmetry breaking, and formation of bilinear fermion condensates that preserve or dynamically break the chiral gauge invariance. We compare different schemes for the study of this evolution and the resultant IR structure of the theories, including a conjectured inequality based on the counting of degrees of freedom. We note some new patterns of UV to IR evolution.

hep-th↗
arXiv2013

Study of Scheme Transformations to Remove Higher-Loop Terms in the $β$ Function of a Gauge Theory

Since three-loop and higher-loop terms in the $β$ function of a gauge theory are scheme-dependent, one can, at least for sufficiently small coupling, carry out a scheme transformation that removes these terms. A basic question concerns the extent to which this can be done at an infrared fixed point of an asymptotically free gauge theory. This is important for quantitative analyses of the scheme dependence of such a fixed point. Here we study a scheme transformation $S_{R,m}$ with $m \ge 2$ that is constructed so as to remove the terms in the beta function at loop order $\ell=3$ to $\ell=m+1$, inclusive. Starting from an arbitrary initial scheme, we present general expressions for the coefficients of terms of loop order $\ell$ in the beta function in the transformed scheme from $\ell=m+2$ up to $\ell=8$. Extending a previous study of $S_{R,2}$, we investigate the range of applicability of the $S_{R,3}$ scheme transformation in an asymptotically free SU($N_c$) gauge theory with an infrared zero in $β$ depending on the number, $N_f$, of fermions in the theory. We show that this $S_{R,3}$ scheme transformation can only be applied self-consistently in a restricted range of $N_f$ with a correspondingly small value of infrared fixed-point coupling. We also study the effect of higher-loop terms on the beta function of a U(1) gauge theory.

hep-ph↗
arXiv2013

Studies on the UV to IR Evolution of Gauge Theories and Quasiconformal Behavior

We describe recent results from our studies of the UV to IR evolution of asymptotically free vectorial gauge theories and quasiconformal behavior. These include higher-loop calculations of the IR zero of the beta function and of the anomalous dimension of the fermion bilinear. Effects of scheme-dependence of higher-loop results are assessed in detail. Applications to models with dynamical electroweak symmetry breaking are discussed.

hep-ph↗
arXiv2013

Higher-Loop Calculations of the Ultraviolet to Infrared Evolution of a Vectorial Gauge Theory in the Limit $N_c \to \infty$, $N_f \to \infty$ with $N_f/N_c$ Fixed

We consider an asymptotically free vectorial SU($N_c$) gauge theory with $N_f$ fermions in the fundamental representation and analyze higher-loop contributions to the evolution of the theory from the ultraviolet to the infrared in the limit where $N_c \to \infty$ and $N_f \to \infty$ with $r=N_f/N_c$ a fixed, finite constant. We focus on the case where the $n$-loop beta function has an infrared zero, at $ξ=ξ_{IR,n\ell}$, where $ξ=αN_c$. We give results on $ξ_{IR,n\ell}$, the anomalous dimension of the fermion bilinear evaluated at $ξ_{IR,n\ell}$, denoted $γ_{IR,n\ell}$, and certain structural properties of the beta function, $β_ξ$. The approach to this limit is investigated, and it is shown that the leading correction terms are strongly suppressed, by the factor $1/N_c^2$. This provides an understanding of a type of approximate universality in calculations for moderate values of $N_c$ and $N_f$, namely that $α_{IR,n\ell}N_c$, $γ_{IR,n\ell}$, and structural properties of the beta function are similar in theories with different values of $N_c$ and $N_f$ provided that they have similar values of $N_f/N_c$. We give results up to four loops for nonsupersymmetric theories and up to three loops for supersymmetric theories.

hep-th↗
arXiv2013

Higher-Loop Structural Properties of the $β$ Function in Asymptotically Free Vectorial Gauge Theories

We investigate some higher-loop structural properties of the $β$ function in asymptotically free vectorial gauge theories. Our main focus is on theories with fermion contents that lead to an infrared (IR) zero in $β$. We present analytic and numerical calculations of the value of the gauge coupling where $β$ reaches a minimum, the value of $β$ at this minimum, and the slope of $β$ at the IR zero, at two-, three-, and four-loop order. The slope of $β$ at the IR zero is relevant for estimates of a dilaton mass in quasiconformal gauge theories. Some inequalities are derived concerning the dependence of the above quantities on loop order. A general inequality is derived concerning the dependence of the shift of the IR zero of $β$, from the $n$-loop to the $(n+1)$-loop order, on the sign of the $(n+1)$-loop coefficient in $β$. Some results are also given for gauge theories with ${\cal N}=1$ supersymmetry.

hep-th↗
arXiv2012

Zeros of the Potts Model Partition Function on Sierpinski Graphs

We calculate zeros of the $q$-state Potts model partition function on $m$'th-iterate Sierpinski graphs, $S_m$, in the variable $q$ and in a temperature-like variable, $y$. We infer some asymptotic properties of the loci of zeros in the limit $m \to \infty$ and relate these to thermodynamic properties of the $q$-state Potts ferromagnet and antiferromagnet on the Sierpinski gasket fractal, $S_\infty$.

cond-mat.stat-mech↗