arXiv subjects

Robert Shrock

Publications and source records attributed to Robert Shrock.

At least 145 records · Page 8Linked to original sources

arXiv2004

Flavor-Changing Processes in Extended Technicolor

We analyze constraints on a class of extended technicolor (ETC) models from neutral flavor-changing processes induced by (dimension-six) four-fermion operators. The ETC gauge group is taken to commute with the standard-model gauge group. The models in the class are distinguished by how the left- and right-handed $(L,R)$ components of the quarks and charged leptons transform under the ETC group. We consider $K^{0} - \bar K^0$ and other pseudoscalar meson mixings, and conclude that they are adequately suppressed if the $L$ and $R$ components of the relevant quarks are assigned to the same (fundamental or conjugate-fundamental) representation of the ETC group. Models in which the $L$ and $R$ components of the down-type quarks are assigned to relatively conjugate representations, while they can lead to realistic CKM mixing and intra-family mass splittings, do not adequately suppress these mixing processes. We identify an approximate global symmetry that elucidates these behavioral differences and can be used to analyze other possible representation assignments. Flavor-changing decays, involving quarks and/or leptons, are adequately suppressed for any ETC-representation assignment of the $L$ and $R$ components of the quarks, as well as the leptons. We draw lessons for future ETC model building.

hep-ph↗

arXiv2004

Transfer Matrices for the Zero-Temperature Potts Antiferromagnet on Cyclic and Mobius Lattice Strips

We present transfer matrices for the zero-temperature partition function of the $q$-state Potts antiferromagnet (equivalently, the chromatic polynomial) on cyclic and Möbius strips of the square, triangular, and honeycomb lattices of width $L_y$ and arbitrarily great length $L_x$. We relate these results to our earlier exact solutions for square-lattice strips with $L_y=3,4,5$, triangular-lattice strips with $L_y=2,3,4$, and honeycomb-lattice strips with $L_y=2,3$ and periodic or twisted periodic boundary conditions. We give a general expression for the chromatic polynomial of a Möbius strip of a lattice $Λ$ and exact results for a subset of honeycomb-lattice transfer matrices, both of which are valid for arbitrary strip width $L_y$. New results are presented for the $L_y=5$ strip of the triangular lattice and the $L_y=4$ and $L_y=5$ strips of the honeycomb lattice. Using these results and taking the infinite-length limit $L_x \to \infty$, we determine the continuous accumulation locus of the zeros of the above partition function in the complex $q$ plane, including the maximal real point of nonanalyticity of the degeneracy per site, $W$ as a function of $q$.

cond-mat.stat-mech↗

arXiv2004

Exact Results for Average Cluster Numbers in Bond Percolation on Lattice Strips

We present exact calculations of the average number of connected clusters per site, $ $, as a function of bond occupation probability $p$, for the bond percolation problem on infinite-length strips of finite width $L_y$, of the square, triangular, honeycomb, and kagomé lattices $Λ$ with various boundary conditions. These are used to study the approach of $ $, for a given $p$ and $Λ$, to its value on the two-dimensional lattice as the strip width increases. We investigate the singularities of $ $ in the complex $p$ plane and their influence on the radii of convergence of the Taylor series expansions of $ $ about $p=0$ and $p=1$.

cond-mat.stat-mech↗

arXiv2004

Quark Dipole Operators in Extended Technicolor Models

We study diagonal and transition quark dipole operators in a class of extended technicolor (ETC) models, taking account of the multiscale nature of the ETC gauge symmetry breaking and of the mixing among ETC interaction eigenstates. Because of this mixing, terms involving the lowest ETC scale can play an important role in dipole operators, and we focus on these terms. We derive from experiment new correlated constraints on the quark mixing angles and phases. Our bounds yield information on mixing angles individually in the up- and down-sectors, for both left- and right-handed quark fields and thus constrain even quark mixing parameters that do not enter in the CKM matrix. With phases of order unity, we conclude that these mixing angles are small, constraining future ETC model building, but plausibly in the range suggested by the size of the CKM elements. These values still allow substantial deviations from the standard model predictions, in particular for several CP violating quantities, including the asymmetries in $b \to s γ$ and $B_{d} \to ϕK_S$, $Re(ε^\prime/ε)$, and the electric dipole moments of the neutron and the ${}^{199}$Hg atom.

hep-ph↗

arXiv2004

Exact Potts Model Partition Functions for Strips of the Triangular Lattice

We present exact calculations of the Potts model partition function Z(G,q,v) for arbitrary q and temperature-like variable v on n-vertex strip graphs G of the triangular lattice for a variety of transverse widths equal to L vertices and for arbitrarily great length equal to m vertices, with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These have the form Z(G,q,v)=\sum_{j=1}^{N_{Z,G,λ}} c_{Z,G,j}(λ_{Z,G,j})^{m-1}. We give general formulas for N_{Z,G,j} and its specialization to v=-1 for arbitrary L. The free energy is calculated exactly for the infinite-length limit of the graphs, and the thermodynamics is discussed. It is shown how the internal energy calculated for the case of cylindrical boundary conditions is connected with critical quantities for the Potts model on the infinite triangular lattice. Considering the full generalization to arbitrary complex q and v, we determine the singular locus {\cal B}, arising as the accumulation set of partition function zeros as m\to\infty, in the q plane for fixed v and in the v plane for fixed q.

cond-mat.stat-mech↗

arXiv2004

Transfer Matrices for the Partition Function of the Potts Model on Cyclic and Mobius Lattice Strips

We present a method for calculating transfer matrices for the $q$-state Potts model partition functions $Z(G,q,v)$, for arbitrary $q$ and temperature variable $v$, on cyclic and Möbius strip graphs $G$ of the square (sq), triangular (tri), and honeycomb (hc) lattices of width $L_y$ vertices and of arbitrarily great length $L_x$ vertices. For the cyclic case we express the partition function as $Z(Λ,L_y \times L_x,q,v)=\sum_{d=0}^{L_y} c^{(d)} Tr[(T_{Z,Λ,L_y,d})^m]$, where $Λ$ denotes lattice type, $c^{(d)}$ are specified polynomials of degree $d$ in $q$, $T_{Z,Λ,L_y,d}$ is the transfer matrix in the degree-$d$ subspace, and $m=L_x$ ($L_x/2$) for $Λ=sq, tri (hc)$, respectively. An analogous formula is given for Möbius strips. We exhibit a method for calculating $T_{Z,Λ,L_y,d}$ for arbitrary $L_y$. Explicit results for arbitrary $L_y$ are given for $T_{Z,Λ,L_y,d}$ with $d=L_y$ and $d=L_y-1$. In particular, we find very simple formulas the determinant $det(T_{Z,Λ,L_y,d})$, and trace $Tr(T_{Z,Λ,L_y})$. Corresponding results are given for the equivalent Tutte polynomials for these lattice strips and illustrative examples are included. We also present formulas for self-dual cyclic strips of the square lattice.

cond-mat.stat-mech↗

arXiv2004

Lepton Dipole Moments in Extended Technicolor Models

We analyze the diagonal and transition magnetic and electric dipole moments of charged leptons in extended technicolor (ETC) models, taking account of the multiscale nature of the ETC gauge symmetry breaking, conformal (walking) behavior of the technicolor theory, and mixing in the charged-lepton mass matrix. We show that mixing effects dominate the ETC contributions to charged lepton electric dipole moments and that these can yield a value of |d_e| comparable to the current limit. The rate for mu to e gamma can also be close to its limit. From these and other processes we derive constraints on the charged lepton mixing angles. The constraints are such that the ETC contribution to the muon anomalous magnetic moment, which includes a significant lepton mixing term, can approach, but does not exceed, the current sensitivity level.

hep-ph↗

arXiv2003

On a Neutrino Electroweak Radius

We study a combination of amplitudes for neutrino scattering that can isolate a (gauge-invariant) difference of chirality-preserving neutrino electroweak radii for $ν_μ$ and $ν_τ$. This involves both photon and $Z_μ$ exchange contributions. It is shown that the construction singles out the contributions of the hypercharge gauge field $B_μ$ in the standard model. We comment on how gauge-dependent terms from the charge radii cancel with other terms in the relative electroweak radii defined.

hep-ph↗

arXiv2003

Fermion Masses and Mixing in Extended Technicolor Models

We study fermion masses and mixing angles, including the generation of a seesaw mechanism for the neutrinos, in extended technicolor (ETC) theories. We formulate an approach to these problems that relies on assigning right-handed $Q=-1/3$ quarks and charged leptons to ETC representations that are conjugates of those of the corresponding left-handed fermions. This leads to a natural suppression of these masses relative to the $Q=2/3$ quarks, as well as the generation of quark mixing angles, both long-standing challenges for ETC theories. Standard-model-singlet neutrinos are assigned to ETC representations that provide a similar suppression of neutrino Dirac masses, as well as the possibility of a realistic seesaw mechanism with no mass scale above the highest ETC scale of roughly $10^3$ TeV. A simple model based on the ETC group SU(5) is constructed and analyzed. This model leads to non-trivial, but not realistic mixing angles in the quark and lepton sectors. It can also produce sufficiently light neutrinos, although not simultaneously with a realistic quark spectrum. We discuss several aspects of the phenomenology of this class of models.

hep-ph↗

arXiv2003

Comment on "Observability of the Neutrino Charge Radius"

In Phys. Rev. Lett. 89, 101802 (2002); erratum, ibid. 89, 229902(E) (2002), Bernabeu, Papavassiliou, and Vidal claim that they can extract a gauge-independent neutrino charge radius (NCR) which is, therefore, a physical observable. We show here that this claim is incorrect by demonstrating that the NCR is, in general, gauge-dependent.

hep-ph↗

arXiv2003

Reliability Polynomials and their Asymptotic Limits for Families of Graphs

We present exact calculations of reliability polynomials $R(G,p)$ for lattice strips $G$ of fixed widths $L_y \le 4$ and arbitrarily great length $L_x$ with various boundary conditions. We introduce the notion of a reliability per vertex, $r(\{G\},p) = \lim_{|V| \to \infty} R(G,p)^{1/|V|}$ where $|V|$ denotes the number of vertices in $G$ and $\{G\}$ denotes the formal limit $\lim_{|V| \to \infty} G$. We calculate this exactly for various families of graphs. We also study the zeros of $R(G,p)$ in the complex $p$ plane and determine exactly the asymptotic accumulation set of these zeros ${\cal B}$, across which $r(\{G\})$ is nonanalytic.

cond-mat.stat-mech↗

arXiv2003

Dynamical Symmetry Breaking of Extended Gauge Symmetries

We construct asymptotically free gauge theories exhibiting dynamical breaking of the left-right, strong-electroweak gauge group $G_{LR} = {\rm SU}(3)_c \times {\rm SU}(2)_L \times {\rm SU}(2)_R \times {\rm U}(1)_{B-L}$, and its extension to the Pati-Salam gauge group $G_{422}={\rm SU}(4)_{PS} \times {\rm SU}(2)_L \times {\rm SU}(2)_R$. The models incorporate technicolor for electroweak breaking, and extended technicolor for the breaking of $G_{LR}$ and $G_{422}$ and the generation of fermion masses, including a seesaw mechanism for neutrino masses. These models explain why $G_{LR}$ and $G_{422}$ break to ${\rm SU}(3)_c \times {\rm SU}(2)_L \times {\rm U}(1)_Y$, and why this takes place at a scale ($\sim 10^3$ TeV) which is large compared to the electroweak scale.

hep-ph↗

arXiv2002

Neutrino Masses in Theories with Dynamical Electroweak Symmetry Breaking

We address the problem of accounting for light neutrino masses in theories with dynamical electroweak symmetry breaking. We discuss this in the context of a class of (extended) technicolor (ETC) models and analyze the full set of Dirac and Majorana masses that arise in such theories. As a possible solution, we propose a combination of suppressed Dirac masses and a seesaw involving dynamically generated $|ΔL|=2$ condensates of standard-model singlet, ETC-nonsinglet fermions. We show how this can be realized in an explicit ETC model. An important feature of this proposal is that, because of the suppression of Dirac neutrino mass terms, a seesaw yielding realistic neutrino masses does not require superheavy Majorana masses; indeed, these Majorana masses are typically much smaller than the largest ETC scale.

hep-ph↗

arXiv2002

Flow Polynomials and their Asymptotic Limits for Lattice Strip Graphs

We present exact calculations of flow polynomials $F(G,q)$ for lattice strips of various fixed widths $L_y$ and arbitrarily great lengths $L_x$, with several different boundary conditions. Square, honeycomb, and triangular lattice strips are considered. We introduce the notion of flows per face $fl$ in the infinite-length limit. We study the zeros of $F(G,q)$ in the complex $q$ plane and determine exactly the asymptotic accumulation sets of these zeros ${\cal B}$ in the infinite-length limit for the various families of strips. The function $fl$ is nonanalytic on this locus. The loci are found to be noncompact for many strip graphs with periodic (or twisted periodic) longitudinal boundary conditions, and compact for strips with free longitudinal boundary conditions. We also find the interesting feature that, aside from the trivial case $L_y=1$, the maximal point, $q_{cf}$, where ${\cal B}$ crosses the real axis, is universal on cyclic and Möbius strips of the square lattice for all widths for which we have calculated it and is equal to the asymptotic value $q_{cf}=3$ for the infinite square lattice.

cond-mat.stat-mech↗

arXiv2002

On the Large-$N_c$ Limit and Electroweak Interactions: Some Properties of the $N_c$-Extended Standard Model

We discuss properties of QCD with variable and large $N_c$, taking into account electroweak interactions; i.e., we analyze the generalization of the standard model based on the gauge group $G={\rm SU}(N_c) \times {\rm SU(2)}_L \times {\rm U(1)}_Y$. General classes of solutions to anomaly constraints are given, and it is shown that these allow a $T_3 = \pm 1/2$ quark or $T_3=-1/2$ lepton rather than the neutrino as an electrically neutral fermion. The issue of grand unification is addressed, and it is shown that $G$ cannot be embedded in the usual way in a simple SO($N$) or SU($N$) gauge group unless $N_c=3$. The ratio of strengths of QCD and electroweak interactions is discussed.

hep-ph↗

arXiv2002

Exact Potts Model Partition Function for Strips of the Square Lattice

We present exact calculations of the Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature-like variable $v$ on $n$-vertex square-lattice strip graphs $G$ for a variety of transverse widths $L_t$ and for arbitrarily great length $L_\ell$, with free longitudinal boundary conditions and free and periodic transverse boundary conditions. These have the form $Z(G,q,v)=\sum_{j=1}^{N_{Z,G,λ}} c_{Z,G,j}(λ_{Z,G,j})^{L_\ell}$. We give general formulas for $N_{Z,G,j}$ and its specialization to $v=-1$ for arbitrary $L_t$ for both types of boundary conditions, as well as other general structural results on $Z$. The free energy is calculated exactly for the infinite-length limit of the graphs, and the thermodynamics is discussed. It is shown how the internal energy calculated for the case of cylindrical boundary conditions is connected with critical quantities for the Potts model on the infinite square lattice. Considering the full generalization to arbitrary complex $q$ and $v$, we determine the singular locus ${\cal B}$, arising as the accumulation set of partition function zeros as $L_\ell \to \infty$, in the $q$ plane for fixed $v$ and in the $v$ plane for fixed $q$.

cond-mat.stat-mech↗

arXiv2002

General Structural Results for Potts Model Partition Functions on Lattice Strips

We present a set of general results on structural features of the $q$-state Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature Boltzmann variable $v$ for various lattice strips of arbitrarily great width $L_y$ vertices and length $L_x$ vertices, including (i) cyclic and Möbius strips of the square and triangular lattice, and (ii) self-dual cyclic strips of the square lattice. We also present an exact solution for the chromatic polynomial for the cyclic and Möbius strips of the square lattice with width $L_y=5$ (the greatest width for which an exact solution has been obtained so far for these families). In the $L_x \to \infty$ limit, we calculate the ground-state degeneracy per site, $W(q)$ and determine the boundary ${\cal B}$ across which $W(q)$ is singular in the complex $q$ plane.

cond-mat.stat-mech↗

arXiv2002

Tutte Polynomials and Related Asymptotic Limiting Functions for Recursive Families of Graphs

We prove several theorems concerning Tutte polynomials $T(G,x,y)$ for recursive families of graphs. In addition to its interest in mathematics, the Tutte polynomial is equivalent to an important function in statistical physics, the Potts model partition function of the $q$-state Potts model, $Z(G,q,v)$, where $v$ is a temperature-dependent variable. We determine the structure of the Tutte polynomial for a cyclic clan graph $G[(K_r)_m,L=jn]$ comprised of a chain of $m$ copies of the complete graph $K_r$ such that the linkage $L$ between each successive pair of $K_r$'s is a join $jn$, and $r$ and $m$ are arbitrary. The explicit calculation of the case $r=3$ (for arbitrary $m$) is presented. The continuous accumulation set of the zeros of $Z$ in the limit $m \to \infty$ is considered. Further, we present calculations of two special cases of Tutte polynomials, namely, flow and reliability polynomials, for cyclic clan graphs and discuss the respective continuous accumulation sets of their zeros in the limit $m \to \infty$. Special valuations of Tutte polynomials give enumerations of spanning trees and acyclic orientations. Two theorems are presented that determine the number of spanning trees on $G[(K_r)_m,jn]$ and $G[(K_r)_m,id]$, where $L=id$ means that the identity linkage. We report calculations of the number of acyclic orientations for strips of the square lattice and use these to obtain an improved lower bound on the exponential growth rate of the number of these acyclic orientations.

math-ph↗