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Robert Shrock

Publications and source records attributed to Robert Shrock.

At least 109 records · Page 6Linked to original sources
arXiv2010

Essence of the vacuum quark condensate

We show that the chiral-limit vacuum quark condensate is qualitatively equivalent to the pseudoscalar meson leptonic decay constant in the sense that they are both obtained as the chiral-limit value of well-defined gauge-invariant hadron-to-vacuum transition amplitudes that possess a spectral representation in terms of the current-quark mass. Thus, whereas it might sometimes be convenient to imagine otherwise, neither is essentially a constant mass-scale that fills all spacetime. This means, in particular, that the quark condensate can be understood as a property of hadrons themselves, which is expressed, for example, in their Bethe-Salpeter or light-front wavefunctions.

nucl-th↗
arXiv2010

Study of an Alternate Mechanism for the Origin of Fermion Generations

In usual extended technicolor (ETC) theories based on the group ${\rm{SU}(N_{ETC}})_{ETC}$, the quarks of charge 2/3 and -1/3 and the charged leptons of all generations arise from ETC fermion multiplets transforming according to the fundamental representation. Here we investigate a different idea for the origin of SM fermion generations, in which quarks and charged leptons of different generations arise from ETC fermions transforming according to different representations of ${\rm{SU}(N_{ETC}})_{ETC}$. Although this mechanism would have the potential, {\it a priori}, to allow a reduction in the value of $N_{ETC}$ relative to conventional ETC models, we show that, at least in simple models, it is excluded by the fact that the technicolor sector is not asymptotically free or by the appearance of fermions with exotic quantum numbers which are not observed.

hep-ph↗
arXiv2010

Upper Limits on a Possible Gluon Mass

We analyze upper limits on a possible gluon mass, $m_g$. We first discuss various ways to modify quantum chromodynamics to include $m_g \ne 0$, including a bare mass, a Higgs mechanism, and dynamical breaking of color SU(3)$_c$. From an examination of experimental data, we infer an upper limit $m_g < O(1)$ MeV. We discuss subtleties in interpreting gluon mass limits in view of the fact that at scales below $Λ_{QCD}$, quantum chromodynamics is strongly coupled, perturbation theory is not reliable, and the physics is not accurately described in terms of the Lagrangian degrees of freedom, including gluons. We also point out a fundamental difference in the behavior of quantum chromodynamics with a nonzero gluon mass and a weakly coupled gauge theory with a gauge boson mass.

hep-ph↗
arXiv2010

Generational Structure of Models with Dynamical Symmetry Breaking

In models with dynamical electroweak symmetry breaking, this breaking is normally communicated to quarks and leptons by a set of vector bosons with masses generated via sequential breaking of a larger gauge symmetry. In reasonably ultraviolet-complete theories of this type, the number of stages of breaking of the larger gauge symmetry is usually equal to the observed number of quark and lepton generations, $N_{gen.}=3$. Here we investigate the general question of how the construction and properties of these models depend on $N_{gen.}$, regarded as a variable. We build and analyze models with illustrative values of $N_{gen.}$ different from 3 (namely, $N_{gen.}=1,2,4$) that exhibit the necessary sequential symmetry breaking down to a strongly coupled sector that dynamically breaks electroweak symmetry. Our results for variable $N_{gen.}$ show that one can robustly obtain, for this latter sector, a theory with a gauge coupling that is large but slowly running, controlled by an approximate infrared fixed point of the renormalization group. Owing to this, we find that for all of the values of $N_{gen.}$ considered, standard-model fermions of the highest generation have masses that can be comparable to the electroweak-symmetry breaking scale. We also study the interplay of multiple strongly coupled gauge symmetries in these models.

hep-ph↗
arXiv2010

Lower Bounds on the Ground State Entropy of the Potts Antiferromagnet on Slabs of the Simple Cubic Lattice

We calculate rigorous lower bounds for the ground state degeneracy per site, $W$, of the $q$-state Potts antiferromagnet on slabs of the simple cubic lattice that are infinite in two directions and finite in the third and that thus interpolate between the square (sq) and simple cubic (sc) lattices. We give a comparison with large-$q$ series expansions for the sq and sc lattices and also present numerical comparisons.

cond-mat.stat-mech↗
arXiv2009

Weighted-Set Graph Colorings

We study a weighted-set graph coloring problem in which one assigns $q$ colors to the vertices of a graph such that adjacent vertices have different colors, with a vertex weighting $w$ that either disfavors or favors a given subset of $s$ colors contained in the set of $q$ colors. We construct and analyze a weighted-set chromatic polynomial $Ph(G,q,s,w)$ associated with this coloring. General properties of this weighted-set chromatic polynomial are proved, and illustrative calculations are presented for various families of graphs. This study extends a previous one for the case $s=1$ and reveals a number of interesting new features.

math-ph↗
arXiv2009

Weighted Graph Colorings

We study two weighted graph coloring problems, in which one assigns $q$ colors to the vertices of a graph such that adjacent vertices have different colors, with a vertex weighting $w$ that either disfavors or favors a given color. We exhibit a weighted chromatic polynomial $Ph(G,q,w)$ associated with this problem that generalizes the chromatic polynomial $P(G,q)$. General properties of this polynomial are proved, and illustrative calculations for various families of graphs are presented. We show that the weighted chromatic polynomial is able to distinguish between certain graphs that yield the same chromatic polynomial. We give a general structural formula for $Ph(G,q,w)$ for lattice strip graphs $G$ with periodic longitudinal boundary conditions. The zeros of $Ph(G,q,w)$ in the $q$ and $w$ planes and their accumulation sets in the limit of infinitely many vertices of $G$ are analyzed. Finally, some related weighted graph coloring problems are mentioned.

math-ph↗
arXiv2009

Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on Lattice Strips

We determine the general structure of the partition function of the $q$-state Potts model in an external magnetic field, $Z(G,q,v,w)$ for arbitrary $q$, temperature variable $v$, and magnetic field variable $w$, on cyclic, Möbius, and free strip graphs $G$ of the square (sq), triangular (tri), and honeycomb (hc) lattices with width $L_y$ and arbitrarily great length $L_x$. For the cyclic case we prove that the partition function has the form $Z(Λ,L_y \times L_x,q,v,w)=\sum_{d=0}^{L_y} \tilde c^{(d)} Tr[(T_{Z,Λ,L_y,d})^m]$, where $Λ$ denotes the lattice type, $\tilde c^{(d)}$ are specified polynomials of degree $d$ in $q$, $T_{Z,Λ,L_y,d}$ is the corresponding transfer matrix, and $m=L_x$ ($L_x/2$) for $Λ=sq, tri (hc)$, respectively. An analogous formula is given for Möbius strips, while only $T_{Z,Λ,L_y,d=0}$ appears for free strips. We exhibit a method for calculating $T_{Z,Λ,L_y,d}$ for arbitrary $L_y$ and give illustrative examples. Explicit results for arbitrary $L_y$ are presented for $T_{Z,Λ,L_y,d}$ with $d=L_y$ and $d=L_y-1$. We find very simple formulas for the determinant $det(T_{Z,Λ,L_y,d})$. We also give results for self-dual cyclic strips of the square lattice.

cond-mat.stat-mech↗
arXiv2009

Some Exact Results on the Potts Model Partition Function in a Magnetic Field

We consider the Potts model in a magnetic field on an arbitrary graph $G$. Using a formula of F. Y. Wu for the partition function $Z$ of this model as a sum over spanning subgraphs of $G$, we prove some properties of $Z$ concerning factorization, monotonicity, and zeros. A generalization of the Tutte polynomial is presented that corresponds to this partition function. In this context we formulate and discuss two weighted graph-coloring problems. We also give a general structural result for $Z$ for cyclic strip graphs.

cond-mat.stat-mech↗
arXiv2009

Gluon-Glueball Duality and Glueball Searches

We discuss a notion of gluon-glueball duality analogous to quark-hadron duality. We apply this idea to the radiative decay of heavy orthoquarkonium, $Q\bar Q \to γg g$, which has been used to search for glueballs. The duality is first introduced in two simplified contexts: (i) a hypothetical version of QCD without any light quarks and (ii) QCD in the large-$N_c$ limit. We then discuss how an approximate form of this duality could hold in real QCD, based on a hierarchy of time scales in the temporal evolution of the $gg$ subsystem in radiative orthoquarkonium decay. We apply this notion of gluon-glueball duality to suggest a method that could be useful in experimental searches for glueballs.

hep-ph↗
arXiv2009

Gedanken Worlds without Higgs: QCD-Induced Electroweak Symmetry Breaking

To illuminate how electroweak symmetry breaking shapes the physical world, we investigate toy models in which no Higgs fields or other constructs are introduced to induce spontaneous symmetry breaking. Two models incorporate the standard SU(3)_c x SU(2)_L x U(1)_Y gauge symmetry and fermion content similar to that of the standard model. The first class--like the standard electroweak theory--contains no bare mass terms, so the spontaneous breaking of chiral symmetry within quantum chromodynamics is the only source of electroweak symmetry breaking. The second class adds bare fermion masses sufficiently small that QCD remains the dominant source of electroweak symmetry breaking and the model can serve as a well-behaved low-energy effective field theory to energies somewhat above the hadronic scale. A third class of models is based on the left-right--symmetric SU(3)_c x SU(2)_L x SU(2)_R x U(1)_{B-L} gauge group. In a fourth class of models, built on SU(4)_{PS} x SU(2)_L x SU(2)_R gauge symmetry, lepton number is treated as a fourth color. Many interesting characteristics of the models stem from the fact that the effective strength of the weak interactions is much closer to that of the residual strong interactions than in the real world. The Higgs-free models not only provide informative contrasts to the real world, but also lead us to consider intriguing issues in the application of field theory to the real world.

hep-ph↗
arXiv2008

Variants of the Standard Model with Electroweak-Singlet Quarks

The successful description of current data provided by the Standard Model includes fundamental fermions that are color-singlets and electroweak-nonsinglets, but no fermions that are electroweak-singlets and color-nonsinglets. In an effort to understand the absence of such fermions, we construct and study {\it gedanken} models that do contain electroweak-singlet chiral quark fields. These models exhibit several distinctive properties, including the absence of any neutral lepton and the fact that both the $(uud)$ and $(ddu)$ nucleons are electrically charged. We also explore how such models could arise as low-energy limits of grand unified theories and, in this more restrictive context, we show that they exhibit further exotic properties.

hep-ph↗
arXiv2008

On Condensates in Strongly Coupled Gauge Theories

We present a new perspective on the nature of quark and gluon condensates in quantum chromodynamics. We suggest that the spatial support of QCD condensates is restricted to the interiors of hadrons, since these condensates arise due to the interactions of confined quarks and gluons. An analogy is drawn with order parameters like the Cooper pair condensate and spontaneous magnetization experimentally measured in finite samples in condensed matter physics. Our picture explains the results of recent studies which find no significant signal for the vacuum gluon condensate. We also give a general discussion of condensates in asymptotically free vectorial and chiral gauge theories.

hep-th↗
arXiv2008

Light-Front Holography and Hadronization at the Amplitude Level

The correspondence between theories in anti-de Sitter space and conformal field theories in physical space-time leads to an analytic, semiclassical model for strongly-coupled QCD which has scale invariance at short distances and color confinement at large distances. Light-front holography is a remarkable feature of AdS/CFT: it allows hadronic amplitudes in the AdS fifth dimension to be mapped to frame-independent light-front wavefunctions of hadrons in physical space-time, thus providing a relativistic description of hadrons at the amplitude level. Some novel features of QCD are discussed, including the consequences of confinement for quark and gluon condensates and the behavior of the QCD coupling in the infrared. We suggest that the spatial support of QCD condensates is restricted to the interior of hadrons, since they arise due to the interactions of confined quarks and gluons. Chiral symmetry is thus broken in a limited domain of size of the inverse pion mass in analogy to the limited physical extent of superconductor phases. A new method for computing the hadronization of quark and gluon jets at the amplitude level, an event amplitude generator, is outlined.

hep-ph↗
arXiv2008

Maximum Wavelength of Confined Quarks and Gluons and Properties of Quantum Chromodynamics

Because quarks and gluons are confined within hadrons, they have a maximum wavelength of order the confinement scale. Propagators, normally calculated for free quarks and gluons using Dyson-Schwinger equations, are modified by bound-state effects in close analogy to the calculation of the Lamb shift in atomic physics. Because of confinement, the effective quantum chromodynamic coupling stays finite in the infrared. The quark condensate which arises from spontaneous chiral symmetry breaking in the bound state Dyson-Schwinger equation is the expectation value of the operator $\bar q q$ evaluated in the background of the fields of the other hadronic constituents, in contrast to a true vacuum expectation value. Thus quark and gluon condensates reside within hadrons. The effects of instantons are also modified. We discuss the implications of the maximum quark and gluon wavelength for phenomena such as deep inelastic scattering and annihilation, the decay of heavy quarkonia, jets, and dimensional counting rules for exclusive reactions. We also discuss implications for the zero-temperature phase structure of a vectorial SU($N$) gauge theory with a variable number $N_f$ of massless fermions.

hep-th↗