549 research outputs found
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 . This value gives for , the low energy constant of
chiral perturbation theory, , and , where F
is the pion decay constant in the chiral limit. Given the level of accuracy in
the masses and the 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 ,
, and 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 from a category to
\Top^{\op} and show that it defines what we call a skew category algebra . We study the connection between topological freeness of
and, on the one hand, ideal properties of and, on
the other hand, maximal commutativity of in . In
particular, we show that if is a groupoid and for each e \in \ob(G) the
group of all morphisms is countable and the topological space
is Tychonoff and Baire, then the following assertions are equivalent:
(i) is topologically free; (ii) has the ideal intersection property,
that is if is a nonzero ideal of , then ; (iii) the ring is a maximal abelian complex subalgebra of . 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 but orbital angular momenta
differing by unity are found to be nearly equal for a wide range of power
potentials , with . 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 states and the 1D
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 (g_\rpp^2).Comment: Revised version corrects a misprint in Eq.(1
Recommended from our members
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
Evaluation of the implementation of the Time Matters programme
Merseyside is one of the 18 areas allocated funding since 2019 by the UK government to establish a Violence Reduction Unit. To inform the continued development of the Merseyside Violence Reduction Partnership (VRP), since its inception in the Merseyside Academics’ Violence Prevention Partnership (MAVPP) led by LJMU have been commissioned to evaluate the Merseyside VRP as a whole, and selected work programme. In addition, the 22/23 LJMU were commissioned to implement additional research to fill gaps in local knowledge. This report forms one of a suite of outputs from the 2022/23 evaluation and research work programme, and specifically presents an evaluation of the Time Matters Programme. All Merseyside VRP research and evaluation outputs are available on the LJMU1 and Merseyside VRP2 websites, or via the work programme lead, Prof Zara Quigg ([email protected])
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