Unusual High-Energy Phenomenology of Lorentz-Invariant Noncommutative Field Theories

It has been suggested that one may construct a Lorentz-invariant noncommutative field theory by extending the coordinate algebra to additional, fictitious coordinates that transform nontrivially under the Lorentz group. Integration over these coordinates in the action produces a four-dimensional effective theory with Lorentz invariance intact. Previous applications of this approach, in particular to a specific construction of noncommutative QED, have been studied only in a low-momentum approximation. Here we discuss Lorentz-invariant field theories in which the relevant physics can be studied without requiring an expansion in the inverse scale of noncommutativity. Qualitatively, we find that tree-level scattering cross sections are dramatically suppressed as the center-of-mass energy exceeds the scale of noncommutativity, that cross sections that are isotropic in the commutative limit can develop a pronounced angular dependence, and that nonrelativistic potentials (for example, the Coloumb potential) become nonsingular at the origin. We consider a number of processes in noncommutative QED that may be studied at a future linear collider. We also give an example of scattering via a four-fermion operator in which the noncommutative modifications of the interaction can unitarize the tree-level amplitude, without requiring any other new physics in the ultraviolet.Comment: 24 pages LaTeX, 4 eps figures (v2: reference added, v3: minor clarifications

Scalar radius of the pion in the Kroll-Lee-Zumino renormalizable theory

The Kroll-Lee-Zumino renormalizable Abelian quantum field theory of pions and a massive rho-meson is used to calculate the scalar radius of the pion at next to leading (one loop) order in perturbation theory. Due to renormalizability, this determination involves no free parameters. The result is $_s = 0.40 {fm}^2$. This value gives for $\bar{\ell}_4$, the low energy constant of chiral perturbation theory, $\bar{\ell}_4 = 3.4$, and $F_\pi/F = 1.05$, where F is the pion decay constant in the chiral limit. Given the level of accuracy in the masses and the $\rho\pi\pi$ coupling, the only sizable uncertainty in this result is due to the (uncalculated) NNLO contribution

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.Comment: 20 pages, no figures, uses RevTeX; typos correcte

Quarkonium Wave Functions at the Origin

We tabulate values of the radial Schr\"{o}dinger wave function or its first nonvanishing derivative at zero quark-antiquark separation, for $c\bar{c}$, $c\bar{b}$, and $b\bar{b}$ levels that lie below, or just above, flavor threshold. These quantities are essential inputs for evaluating production cross sections for quarkonium states.Comment: 9 pages, RevTeX, no figure

Skew Category Algebras Associated with Partially Defined Dynamical Systems

We introduce partially defined dynamical systems defined on a topological space. To each such system we associate a functor $s$ from a category $G$ to \Top^{\op} and show that it defines what we call a skew category algebra $A \rtimes^{\sigma} G$. We study the connection between topological freeness of $s$ and, on the one hand, ideal properties of $A \rtimes^{\sigma} G$ and, on the other hand, maximal commutativity of $A$ in $A \rtimes^{\sigma} G$. In particular, we show that if $G$ is a groupoid and for each e \in \ob(G) the group of all morphisms $e \rightarrow e$ is countable and the topological space $s(e)$ is Tychonoff and Baire, then the following assertions are equivalent: (i) $s$ is topologically free; (ii) $A$ has the ideal intersection property, that is if $I$ is a nonzero ideal of $A \rtimes^{\sigma} G$, then $I \cap A \neq \{0\}$; (iii) the ring $A$ is a maximal abelian complex subalgebra of $A \rtimes^{\sigma} G$. Thereby, we generalize a result by Svensson, Silvestrov and de Jeu from the additive group of integers to a large class of groupoids.Comment: 16 pages. This article is an improvement of, and hereby a replacement for, version 1 (arXiv:1006.4776v1) entitled "Category Dynamical Systems and Skew Category Algebras

Spacings of Quarkonium Levels with the Same Principal Quantum Number

The spacings between bound-state levels of the Schr\"odinger equation with the same principal quantum number $N$ but orbital angular momenta $\ell$ differing by unity are found to be nearly equal for a wide range of power potentials $V = \lambda r^\nu$, with $E_{N \ell} \approx F(\nu, N) - G(\nu,N) \ell$. Semiclassical approximations are in accord with this behavior. The result is applied to estimates of masses for quarkonium levels which have not yet been observed, including the 2P $c \bar c$ states and the 1D $b \bar b$ states.Comment: 20 pages, latex, 3 uuencoded figures submitted separately (process using psfig.sty

Pion form factor in the Kroll-Lee-Zumino model

The renormalizable Abelian quantum field theory model of Kroll, Lee, and Zumino is used to compute the one-loop vertex corrections to the tree-level, Vector Meson Dominance (VMD) pion form factor. These corrections, together with the known one-loop vacuum polarization contribution, lead to a substantial improvement over VMD. The resulting pion form factor in the space-like region is in excellent agreement with data in the whole range of accessible momentum transfers. The time-like form factor, known to reproduce the Gounaris-Sakurai formula at and near the rho-meson peak, is unaffected by the vertex correction at order $\cal{O}$(g_\rpp^2).Comment: Revised version corrects a misprint in Eq.(1

Decays of neutral pseudoscalar mesons into lepton pairs

The authors calculate the branching ratio {Lambda}(P {yields} {ell}{sup +}{ell}{sup -})/{Lambda}(P {yields} {gamma}{gamma}) to lowest contributing order in quantum electrodynamics, with a vector meson model for the pseudoscalar meson form factor. They treat the processes {eta} {yields} {mu}{sup +}{mu}{sup -}; {eta} {yields} e{sup +}e{sup -}; K{sub 2}{sup 0} {yields} {mu}{sup +}{mu}{sup -}; K{sub 2}{sup 0} {yields} e{sup +}e{sup -}; {pi}{sup 0} {yields} e{sup +}e{sup -}. Results are compared with those of previous calculations

Singularity Structures in Coulomb-Type Potentials in Two Body Dirac Equations of Constraint Dynamics

Two Body Dirac Equations (TBDE) of Dirac's relativistic constraint dynamics have been successfully applied to obtain a covariant nonperturbative description of QED and QCD bound states. Coulomb-type potentials in these applications lead naively in other approaches to singular relativistic corrections at short distances that require the introduction of either perturbative treatments or smoothing parameters. We examine the corresponding singular structures in the effective potentials of the relativistic Schroedinger equation obtained from the Pauli reduction of the TBDE. We find that the relativistic Schroedinger equation lead in fact to well-behaved wave function solutions when the full potential and couplings of the system are taken into account. The most unusual case is the coupled triplet system with S=1 and L={(J-1),(J+1)}. Without the inclusion of the tensor coupling, the effective S-state potential would become attractively singular. We show how including the tensor coupling is essential in order that the wave functions be well-behaved at short distances. For example, the S-state wave function becomes simply proportional to the D-state wave function and dips sharply to zero at the origin, unlike the usual S-state wave functions. Furthermore, this behavior is similar in both QED and QCD, independent of the asymptotic freedom behavior of the assumed QCD vector potential. Light- and heavy-quark meson states can be described well by using a simplified linear-plus-Coulomb-type QCD potential apportioned appropriately between world scalar and vector potentials. We use this potential to exhibit explicitly the origin of the large pi-rho splitting and effective chiral symmetry breaking. The TBDE formalism developed here may be used to study quarkonia in quark-gluon plasma environments.Comment: 23 pages, 4 figure

Gang membership and sexual violence: associations with childhood maltreatment and psychiatric morbidity.

BACKGROUND: Gang members engage in many high-risk sexual activities that may be associated with psychiatric morbidity. Victim-focused research finds high prevalence of sexual violence towards women affiliated with gangs. AIMS: To investigate associations between childhood maltreatment and psychiatric morbidity on coercive and high-risk sexual behaviour among gang members. METHOD: Cross-sectional survey of 4665 men 18-34 years in Great Britain using random location sampling. The survey oversampled men from areas with high levels of violence and gang membership. Participants completed questionnaires covering violent and sexual behaviours, experiences of childhood disadvantage and trauma, and psychiatric diagnoses using standardised instruments. RESULTS: Antisocial men and gang members had high levels of sexual violence and multiple risk behaviours for sexually transmitted infections, childhood maltreatment and mental disorders, including addictions. Physical, sexual and emotional trauma were strongly associated with adult sexual behaviour and more prevalent among gang members. Other violent behaviour, psychiatric morbidity and addictions accounted for high-risk and compulsive sexual behaviours among gang members but not antisocial men. Gang members showed precursors before age 15 years of adult preference for coercive rather than consenting sexual behaviour. CONCLUSIONS: Gang members show inordinately high levels of childhood trauma and disadvantage, sexual and non-sexual violence, and psychiatric disorders, which are interrelated. The public health problem of sexual victimisation of affiliated women is explained by these findings. Healthcare professionals may have difficulties promoting desistance from adverse health-related behaviours among gang members whose multiple high-risk and violent sexual behaviours are associated with psychiatric morbidity, particularly addictions