Novel Spin and Statistical Properties of Nonabelian Vortices

We study the statistics of vortices which appear in (2+1)--dimensional spontaneously broken gauge theories, where a compact group G breaks to a finite nonabelian subgroup H. Two simple models are presented. In the first, a quantum state which is symmetric under the interchange of a pair of indistinguishable vortices can be transformed into an antisymmetric state after the passage through the system of a third vortex with an appropriate $H$-flux element. Further, there exist states containing two indistinguishable spinless vortices which obey Fermi statistics. These results generalize to loops of nonabelian cosmic string in 3+1 dimensions. In the second model, fractional analogues of the above behaviors occur. Also, composites of vortices in this theory may possess fractional ``Cheshire spin'' which can be changed by passing an additional vortex through the system.Comment: 11 pages, UICHEP-TH/92-15; FERMILAB-PUB-92/233-T; SLAC-PUB-588

Lepto-mesons, Leptoquarkonium and the QCD Potential

We consider bound states of heavy leptoquark-antiquark pairs (lepto-mesons) as well as leptoquark-antileptoquark pairs (leptoquarkonium). Unlike the situation for top quarks, leptoquarks (if they exist) may live long enough for these hadrons to form. We study the spectra and decay widths of these states in the context of a nonrelativistic potential model which matches the recently calculated two-loop QCD potential at short distances to a successful phenomenological quarkonium potential at intermediate distances. We also compute the expected number of events for these states at future colliders.Comment: 12 pages, 1 figure, 3 tables, plain TeX, requires harvmac. References updated and minor clarifications made. To appear in Physics Letters

Nonabelian Vortices on Surfaces and Their Statistics

We discuss the physics of topological vortices moving on an arbitrary surface M in a Yang-Mills-Higgs theory in which the gauge group G breaks to a finite subgroup H. We concentrate on the case where M is compact and/or nonorientable. Interesting new features arise which have no analog on the plane. The consequences for the quantum statistics of vortices are discussed, particularly when H is nonabelian.Comment: 27 pages, 6 figures, requires harvma

Simple Baryon-Meson Mass Relations For A Logarithmic Interquark Potential

I consider the quantity delta(m_1m_2m_3) = M_{q_1q_2q_3} - [M_{q_1q_2bar} + M_{q_2q_3bar} + M_{q_1q_3bar}]/2, where the M's represent the ground state spin-averaged hadron masses with the indicated quark content and the m's the corresponding constituent quark masses. I assume a logarithmic interquark potential, the validity of a nonrelativistic approach, and various standard potential model inputs. Simple scaling arguments then imply that the quantity R(x)=delta(mmm_3)/delta(m_0m_0m_0) depends only on the ratio x=m/m_3, and is independent of m_0 as well as any parameters appearing in the potential. A simple and accurate analytic determination of delta(mmm_3), and hence R(x), is given using the 1/D expansion where D is the number of spatial dimensions. When applicable, this estimate of R(x) compares very well to experiment -- even for hadrons containing light quarks. A prediction of the above result which is likely to be tested in the near future is M_{Sigma_b^*}/2 + [M_{Lambda_b} + M_{Sigma_b}]/4 = 5774 +/- 4 MeV/c^2.Comment: 13 pages, plain TeX, 1 eps figure, uses harvmac and epsf.st

Resonant Bound State Production at e- e- Colliders

Observation of a sequence of resonances at an e-e- collider would suggest bound states of strongly coupled constituents carrying lepton number. Obvious candidates for these exotic constituents are leptoquarks and leptogluons. We show that under reasonable assumptions, the existence of one leptogluon flavor of appropriate mass can give rise to sizeable ``leptoglueball'' production rates and observable resonance peaks. In contrast, one needs two leptoquark flavors in order to produce the analogous ``leptoquarkonium'' states. Moreover, cross-generational leptoquark couplings are necessary to give observable event rates in many cases, and leptoquarkonium mass splittings are too small to resolve with realistic beam energy resolutions.Comment: 8 pages, 1 table, plain TeX, requires harvmac. Brief comparison to leptoglueball production at e+e- colliders added. Other minor changes. To appear in Physics Letters

Spinning Particles, Braid Groups and Solitons

We develop general techniques for computing the fundamental group of the configuration space of $n$ identical particles, possessing a generic internal structure, moving on a manifold $M$. This group generalizes the $n$-string braid group of $M$ which is the relevant object for structureless particles. In particular, we compute these generalized braid groups for particles with an internal spin degree of freedom on an arbitrary $M$. A study of their unitary representations allows us to determine the available spectrum of spin and statistics on $M$ in a certain class of quantum theories. One interesting result is that half-integral spin quantizations are obtained on certain manifolds having an obstruction to an ordinary spin structure. We also compare our results to corresponding ones for topological solitons in $O(d+1)$-invariant nonlinear sigma models in $(d+1)$-dimensions, generalizing recent studies in two spatial dimensions. Finally, we prove that there exists a general scalar quantum theory yielding half-integral spin for particles (or $O(d+1)$ solitons) on a closed, orientable manifold $M$ if and only if $M$ possesses a ${\rm spin}_c$ structure.Comment: harvmac, 34 pages, HUTP-93/A037; UICHEP-TH/93-18; BUHEP-93-2

Topology Change and theta-Vacua in 2D Yang-Mills Theory

We discuss the existence of $\theta$-vacua in pure Yang-Mills theory in two space-time dimensions. More precisely, a procedure is given which allows one to classify the distinct quantum theories possessing the same classical limit for an arbitrary connected gauge group G and compact space-time manifold M (possibly with boundary) possessing a special basepoint. For any such G and M it is shown that the above quantizations are in one-to-one correspondence with the irreducible unitary representations (IUR's) of $\pi_1(G)$ if M is orientable, and with the IUR's of $\pi_1(G)/2\pi_1(G)$ if M is nonorientable.Comment: 16 pages, 4 figures, uses harvmac and psbo