Studies of pentaquarks and of noncommutative field theory

Several experiments reported seeing evidence in their data of a new particle, the strangeness +1 Theta+ pentaquark made of four quarks and an antiquark. In the first few chapters of this dissertation we study four-quark-antiquark systems within the framework of a constituent quark model. We describe the Theta+ as a member of a spin-½ pentaquark antidecuplet. For both parity-odd, and parity-even antidecuplets we derive useful decompositions of the quark model wave functions that allow for easy computation of color-flavor-spin-orbital matrix elements, and we compute mass splittings within the antidecuplet. We study parity-even antidecuplet in an effective theory with dominant flavor-spin interactions. We predict narrow strangeness -2 cascade pentaquarks at about 1900 MeV in this framework. The wave function for the positive parity Theta+ has a small overlap with the kinematically allowed final states, and naturally explains the observed narrowness of the state. In this dissertation we also study noncommutative field theories. Specifically, we study phenomenology of Lorentz-conserving noncommutative QED developed by Carlson, Carone, and Zobin. We obtain bounds on the energy scale of noncommutativity Lambda by calculating modifications to dilepton and diphoton production, and comparing our results to LEP 2 data. We find that Lambda is greater than 160 GeV at 95% C.L., and we make predictions for what may be seen in future collider experiments. We also present a way to extend the discussion of nontrivial commutators to include nonvanishing anticommutation relations among spinor coordinates theta and theta-bar in N = 1 superspace. We present a consistent algebra for the supercoordinates, and find a star-product. We give the Wess-Zumino Lagrangian within our model. It is manifestly Hermitian, with Lorentz-invariant modifications due to non (anti)commutativity

Positive Parity Pentaquarks Pragmatically Predicted

We consider the possibility that the lightest pentaquark is a parity even state, with one unit of orbital angular momentum. Working within the framework of a constituent quark model, we show that dominant spin-flavor interactions render certain parity-even states lighter than any pentaquark with all quarks in the spatial ground state. For such states, we focus on predicting the mass and decays of other members of the same SU(3) flavor multiplet. Specifically, we consider the strangeness -2 cascade pentaquarks, which are relatively immune to mixing. We take into account flavor SU(3) breaking effects originating from the strange quark mass as well as from the structure of the spin-flavor exchange interactions themselves. We predict the lightest cascade pentaquarks at approximately 1906 MeV, with a full width about 3 times larger than that of the Theta^+.Comment: 13 pages, 1 figure, 4 tables, Revtex

Proton structure corrections to hyperfine splitting in muonic hydrogen

We present the derivation of the formulas for the proton structure-dependent terms in the hyperfine splitting of muonic hydrogen. We use compatible conventions throughout the calculations to derive a consistent set of formulas that reconcile differences between our results and some specific terms in earlier work. Convention conversion corrections are explicitly presented, which reduce the calculated hyperfine splitting by about 46 ppm. We also note that using only modern fits to the proton elastic form factors gives a smaller than historical spread of Zemach radii and leads to a reduced uncertainty in the hyperfine splitting. Additionally, hyperfine splittings have an impact on the muonic hydrogen Lamb shift/proton radius measurement, however the correction we advocate has a small effect there.Comment: 6 pages, 3 figure

Proton structure corrections to electronic and muonic hydrogen hyperfine splitting

We present a precise determination of the polarizability and other proton structure dependent contributions to the hydrogen hyperfine splitting, based heavily on the most recent published data on proton spin dependent structure functions from the EG1 experiment at the Jefferson Laboratory. As a result, the total calculated hyperfine splitting now has a standard deviation slightly under 1 part-per-million, and is about 1 standard deviation away from the measured value. We also present results for muonic hydrogen hyperfine splitting, taking care to ensure the compatibility of the recoil and polarizability terms.Comment: 9 pages, 1 figur

Evaluating matrix elements relevant to some Lorenz violating operators

Carlson, Carone and Lebed have derived the Feynman rules for a consistent formulation of noncommutative QCD. The results they obtained were used to constrain the noncommutativity parameter in Lorentz violating noncommutative field theories. However, their constraint depended upon an estimate of the matrix element of the quark level operator (gamma.p - m) in a nucleon. In this paper we calculate the matrix element of (gamma.p - m), using a variety of confinement potential models. Our results are within an order of magnitude agreement with the estimate made by Carlson et al. The constraints placed on the noncommutativity parameter were very strong, and are still quite severe even if weakened by an order of magnitude.Comment: 4 pages, 3 figures, RevTex, minor change

Phenomenology of the Pentaquark Antidecuplet

We consider the mass splittings and strong decays of members of the lowest-lying pentaquark multiplet, which we take to be a parity-odd antidecuplet. We derive useful decompositions of the quark model wave functions that allow for easy computation of color-flavor-spin matrix elements. We compute mass splittings within the antidecuplet including spin-color and spin-isospin interactions between constituents and point out the importance of hidden strangeness in rendering the nucleon-like states heavier than the S=1 state. Using recent experimental data on a possible S=1 pentaquark state, we make decay predictions for other members of the antidecuplet.Comment: 12 pages LaTeX, 1 eps figur

Field Theory in Noncommutative Minkowski Superspace

There is much discussion of scenarios where the space-time coordinates x^\mu are noncommutative. The discussion has been extended to include nontrivial anticommutation relations among spinor coordinates in superspace. A number of authors have studied field theoretical consequences of the deformation of N=1 superspace arising from nonanticommutativity of coordinates \theta, while leaving \bar{theta}'s anticommuting. This is possible in Euclidean superspace only. In this note we present a way to extend the discussion by making both \theta and \bar{theta} coordinates non-anticommuting in Minkowski superspace. We present a consistent algebra for the supercoordinates, find a star-product, and give the Wess-Zumino Lagrangian L_{WZ} within our model. It has two extra terms due to non(anti)commutativity. The Lagrangian in Minkowski superspace is always manifestly Hermitian and for L_{WZ} it preserves Lorentz invariance.Comment: 8 pages, added references, two-column format, published in PR

A Naturally Narrow Positive Parity Theta^+

We present a consistent color-flavor-spin-orbital wave function for a positive parity Theta^+ that naturally explains the observed narrowness of the state. The wave function is totally symmetric in its flavor-spin part and totally antisymmetric in its color-orbital part. If flavor-spin interactions dominate, this wave function renders the positive parity Theta^+ lighter than its negative parity counterpart. We consider decays of the Theta^+ and compute the overlap of this state with the kinematically allowed final states. Our results are numerically small. We note that dynamical correlations between quarks are not necessary to obtain narrow pentaquark widths.Comment: 10 pages, 1 figure, Revtex4, two-column format, version to be published in Phys. Rev. D, includes numerical estimates of decay width