arXiv subjects
Publications and source records attributed to Richard F. Lebed.
The 1/N_c expansion (N_c being the number of QCD colors) has been applied in recent papers to the phenomenology of excited baryon resonances. This talk surveys the work done to date, and discusses its successes and remaining challenges.
We show that excited baryons in large N_c QCD form multiplets, within which masses are first split at O(1/N_c). The dominant couplings of resonances to various mesons are highly constrained: The N(1535) decays at leading 1/N_c order exclusively to eta-N rather than pi-N, and vice versa for the N(1650). This multiplet structure is reproduced by a simple large N_c quark model, well studied in the literature, that describes resonances as single-quark excitations.
We consider Lorentz-violating operators induced at the loop level in softly-broken supersymmetric noncommutative QED. Dangerous operators forbidden in the supersymmetric limit are generated via finite corrections, with the scale of supersymmetry breaking serving as a gauge-invariant regulator. We compare the most dangerous loop effects to those obtained in noncommutative theories truncated by a momentum-space cutoff, and find significantly improved bounds.
We develop a straightforward method to compute charge radii and quadrupole moments for baryons both with and without strangeness, when the number of QCD color charges is N_c. The minimal assumption of the single-photon exchange ansatz implies that only two operators are required to describe these baryon observables. Our results are presented so that SU(3) flavor and isospin symmetry breaking can be introduced according to any desired specification, although we also present results obtained from two patterns suggested by the quark model with gluon exchange interactions. The method also permits to extract a number of model-independent relations; a sample is r^2_Lambda / r_n^2 = 3/(N_c+3), independent of SU(3) symmetry breaking.
We calculate expressions for the quadrupole moments of nonstrange baryons in which the number of QCD color charges is N_c. Using only the assumption of single-photon exchange, we obtain 4 relations among the 6 moments, and show how all of them may be obtained from Q_{Δ^+ p} up to O(1/N_c^2) corrections. We compare to the N_c=3 case, and obtain relations between the neutron charge radius and quadrupole moments. We also discuss prospects for the measurement of these moments.
We demonstrate a concise method to enumerate the number of generalized polarizabilities---quantities characterizing the independent observables in singly-virtual Compton scattering---for a target particle of arbitrary spin s. By using crossing symmetry and J^{PC} conservation, we show that this number is (10s+1+delta_{s,0}).
Jurco, Moller, Schraml, Schupp, and Wess have shown how to construct noncommutative SU(N) gauge theories from a consistency relation. Within this framework, we present the Feynman rules for noncommutative QCD and compute explicitly the most dangerous Lorentz-violating operator generated through radiative corrections. We find that interesting effects appear at the one-loop level, in contrast to conventional noncommutative U(N) gauge theories, leading to a stringent bound. Our results are consistent with others appearing recently in the literature that suggest collider limits are not competitive with low-energy tests of Lorentz violation for bounding the scale of spacetime noncommutativity.
We discuss a little-studied class of weak decay modes sensitive to only one quark topology at leading order in G_F: M --> m gamma, where M,m are mesons with completely distinct flavor quantum numbers. Specifically, they proceed via the annihilation of the valence quarks through a W and the emission of a single hard photon, and thus provide a clear separation between CKM and strong interaction physics. We survey relevant calculations performed to date, discuss experimental discovery potential, and indicate interesting future directions.
We present a simple method to count the number of hadronic form factors based on the partial wave formalism and crossing symmetry. In particular, we show that the number of independent nucleon form factors of spin-n, twist-2 operators (the vector current and energy-momentum tensor being special examples) is n+1. These generalized form factors define the generalized (off-forward) parton distributions that have been studied extensively in the recent literature. In proving this result, we also show how the J^{PC} rules for onium states arise in the helicity formalism.
Recent neutrino parameter measurements place increasingly stringent constraints on acceptable supersymmetric theories of flavor. A very fruitful approach is the application of non-Abelian discrete gauged flavor symmetries G_f. We discuss a highly successful model using G_f = T' x Z_3, where T' is a non-Abelian group based on the symmetries of a tetrahedron. This model reproduces the basic features of the U(2) model, and also predicts neutrino masses and mixing angles consistent with either the SMA or LMA solutions.
We show how one may define baryon constituent quarks in a rigorous manner, given physical assumptions that hold in the large-N_c limit of QCD. This constituent picture gives rise to an operator expansion that has been used to study large-N_c baryon observables; here we apply it to the case of charge radii of the N and Delta states, using minimal dynamical assumptions. For example, one finds the relation r_p^2 - r_{Delta^+}^2 = r_n^2 - r_{Delta^0}^2 to be broken only by three-body, O(1/N_c^2) effects for any N_c.
We address numerical aspects of local quark-hadron duality using the example of the exactly solvable 't Hooft model, two-dimensional QCD with N_c --> infinity. The primary focus of these studies is total semileptonic decay widths relevant for extracting |V_{cb}| and |V_{ub}|. We compare the exact channel-by-channel sum of exclusive modes to the corresponding rates obtained in the standard 1/m_Q expansion arising from the Operator Product Expansion. An impressive agreement sets in unexpectedly early, immediately after the threshold for the first hadronic excitation in the final state. Yet even at higher energy release it is possible to discern the seeds of duality-violating oscillations. We find the ``Small Velocity'' sum rules to be exceptionally well saturated already by the first excited state. We also obtain a convincing degree of duality in the differential distributions and in an analogue of R_{e^+e^-}(s). Finally, we discuss possible lessons for semileptonic decays of actual heavy quarks in QCD.
A new measurement of the Xi^0 mass verifies the accuracy of the Coleman-Glashow relation at the level predicted by the 1/N_c expansion. Values for other baryon isospin mass splittings are updated, and continue to agree with the 1/N_c hierarchy.
We study a number of models, based on a non-Abelian discrete group, that successfully reproduce the simple and predictive Yukawa textures usually associated with U(2) theories of flavor. These models allow for solutions to the solar and atmospheric neutrino problems that do not require altering successful predictions for the charged fermions or introducing sterile neutrinos. Although Yukawa matrices are hierarchical in the models we consider, the mixing between second- and third-generation neutrinos is naturally large. We first present a quantitative analysis of a minimal model proposed in earlier work, consisting of a global fit to fermion masses and mixing angles, including the most important renormalization group effects. We then propose two new variant models: The first reproduces all important features of the SU(5)xU(2) unified theory with neither SU(5) nor U(2). The second demonstrates that discrete subgroups of SU(2) can be used in constructing viable supersymmetric theories of flavor without scalar universality even though SU(2) by itself cannot.
We present a model of fermion masses based on a minimal, non-Abelian discrete symmetry that reproduces the Yukawa matrices usually associated with U(2) theories of flavor. Mass and mixing angle relations that follow from the simple form of the quark and charged lepton Yukawa textures are therefore common to both theories. We show that the differing representation structure of our horizontal symmetry allows for new solutions to the solar and atmospheric neutrino problems that do not involve modification of the original charged fermion Yukawa textures, or the introduction of sterile neutrinos.
A class of meson decay modes sensitive to only one quark topology at leading G_F order (annihilation of valence quarks through a W) is described. No experimental observations, nor even upper limits, have been reported for these decays. This work presents a simpleminded (order-of-magnitude) calculation of their branching fractions, and compares to results of previous calculations where available. Although rare, one of these modes (D_s^+ --> rho^+ gamma) might already be observable at charm experiments, two others (D^+ --> K^{*+} gamma, B^+ --> D_s^{*+} gamma) should appear at the B factories, and the rest at hadron colliders.
This talk presents an introduction to the use of dispersion relations to constrain the shapes of hadronic form factors consistent with QCD. The applications described include methods for studying |V_{cb}| and |V_{ub}|, the strange quark mass, and the pion charge radius.
We construct a supersymmetric theory of flavor based on the discrete gauge group (D_6)^2, where D_6 describes the symmetry of a regular hexagon under proper rotations in three dimensions. The representation structure of the group allows one to distinguish the third from the lighter two generations of matter fields, so that in the symmetry limit only the top quark Yukawa coupling is allowed and scalar superpartners of the first two generations are degenerate. Light fermion Yukawa couplings arise from a sequential breaking of the flavor symmetry, and supersymmetric flavor-changing processes remain adequately suppressed. We contrast our model with others based on non-Abelian discrete gauge symmetries described in the literature, and discuss the challenges in constructing more minimal flavor models based on this approach.