Comparison of Some Exact and Perturbative Results for a Supersymmetric SU(NcN_c) Gauge Theory

We consider vectorial, asymptotically free ${\cal N}=1$ supersymmetric SU($N_c$) gauge theories with $N_f$ copies of massless chiral super fields in various representations and study how perturbative predictions for the lower boundary of the infrared conformal phase, as a function of $N_f$, compare with exact results. We make use of two-loop and three-loop calculations of the beta function and anomalous dimension of the quadratic chiral super field operator product for this purpose. The specific chiral superfield contents that we consider are $N_f$ copies of (i) $F+\bar F$, (ii) $Adj$, (iii) $S_2+\bar S_2$, and (iv) $A_2 + \bar A_2$, where $F$, $Adj$, $S_2$, and $A_2$ denote, respectively, the fundamental, adjoint, and symmetric and antisymmetric rank-2 tensor representations. We find that perturbative results slightly overestimate the value of $N_{f,cr}$ relative to the respective exact results for these representations, i.e., slightly underestimate the interval in $N_f$ for which the theory has infrared conformal behavior. Our results provide a measure of how closely perturbative calculations reproduce exact results for these theories.Comment: 16 pages, 3 figure

Microwave and Millimeter Wave Techniques

Contains reports on one research project.Joint Services Electronics Program (Contract DAAB07-71-C-0300

Extracting the rho meson wavefunction from HERA data

We extract the light-cone wavefunctions of the rho meson using the HERA data on diffractive rho photoproduction. We find good agreement with predictions for the distribution amplitude based on QCD sum rules and from the lattice. We also find that the data prefer a transverse wavefunction with enhanced end-point contributions.Comment: 13 pages, 7 figures, significant improvements over the original version with a new section on distribution amplitudes adde

Extracting the Distribution Amplitudes of the rho meson from the Color Glass Condensate

We extract the leading twist-2 and subleading twist-3 Distribution Amplitudes (DAs) of the rho meson using the HERA data on diffractive rho photoproduction. We do so using several Colour Glass Condensate (CGC) inspired and a Regge inspired dipole models. We find that our extracted twist-2 DA is not much model dependent and is consistent with QCD Sum Rules and lattice predictions. The extracted twist-3 DA is more model dependent but is still consistent with the Sum Rules prediction.Comment: 21 pages, 10 figures, 3 tables. Section 6 revised, figures 8 and 9 and table 3 updated. Conclusions essentially unchange

Baryon-Baryon Interactions

After a short survey of some topics of interest in the study of baryon-baryon scattering, the recent Nijmegen energy dependent partial wave analysis (PWA) of the nucleon-nucleon data is reviewed. In this PWA the energy range for both pp and np is now 0 < Tlab < 350 MeV and a chi^2_{d.o.f.}=1.08 was reached. The implications for the pion-nucleon coupling constants are discussed. Comments are made with respect to recent discussions around this coupling constant in the literature. In the second part, we briefly sketch the picture of the baryon in several, more or less QCD-based, quark-models that have been rather prominent in the literature. Inspired by these pictures we constructed a new soft-core model for the nucleon-nucleon interaction and present the first results of this model in a chi^2 -fit to the new multi-energy Nijmegen PWA. With this new model we succeeded in narrowing the gap between theory and experiment at low energies. For the energies Tlab = 25-320 MeV we reached a record low chi^2_{p.d.p.} = 1.16. We finish the paper with some conclusions and an outlook describing the extension of the new model to baryon-baryon scattering.Comment: 12 pages LaTeX and one postscript figure included. Invited talk presented at the XIVth European Conference of Few-Body Problems in Physics, Amsterdam, August 23-28, 199

Nonperturbative Renormalization in Light-Cone Quantization

Two approaches to nonperturbative renormalization are discussed for theories quantized on the light cone. One is tailored specifically to a calculation of the dressed-electron state in quantum electrodynamics, where an invariant-mass cutoff is used as a regulator and a Tamm-Dancoff truncation is made to include no more than two photons. The other approach is based on Pauli-Villars regulators and is applied to Yukawa theory and a related soluble model. In both cases discretized light-cone quantization is used to obtain a finite matrix problem that can be solved nonperturbatively.Comment: 10 pages, LaTeX/RevTex, no figures, to appear in the proceedings of Orbis Scientiae 1997: Twenty-Five Coral Gables Conferences and their Impact on High Energy Physics and Cosmology, B.N. Kursunoglu, e

Next-to-leading and resummed BFKL evolution with saturation boundary

We investigate the effects of the saturation boundary on small-x evolution at the next-to-leading order accuracy and beyond. We demonstrate that the instabilities of the next-to-leading order BFKL evolution are not cured by the presence of the nonlinear saturation effects, and a resummation of the higher order corrections is therefore needed for the nonlinear evolution. The renormalization group improved resummed equation in the presence of the saturation boundary is investigated, and the corresponding saturation scale is extracted. A significant reduction of the saturation scale is found, and we observe that the onset of the saturation corrections is delayed to higher rapidities. This seems to be related to the characteristic feature of the resummed splitting function which at moderately small values of x possesses a minimum.Comment: 34 page

Holographic Approach to Regge Trajectory and Rotating D5 brane

We study the Regge trajectories of holographic mesons and baryons by considering rotating strings and D5 brane, which is introduced as the baryon vertex. Our model is based on the type IIB superstring theory with the background of asymptotic $AdS_5\times S^5$. This background is dual to a confining supersymmetric Yang-Mills theory (SYM) with gauge condensate, $$, which determines the tension of the linear potential between the quark and anti-quark. Then the slope of the meson trajectory ($\alpha'_{M}$) is given by this condensate as $\alpha'_{M}=1/\sqrt{\pi }$ at large spin $J$. This relation is compatible with the other theoretical results and experiments. For the baryon, we show the importance of spinning baryon vertex to obtain a Regge slope compatible with the one of $N$ and $\Delta$ series. In both cases, mesons and baryons, the trajectories are shifted to large mass side with the same slope for increasing current quark mass.Comment: 28 pages, 7 figure

The "recoil" correction of order mα6m \alpha^6 to hyperfine splitting of positronium ground state

The "recoil" correction of order $m \alpha^6$ to the hyperfine splitting of positronium ground state was found. The formalism employed is based on the noncovariant perturbation theory in QED. Equation for two-particle component of full (many-body) wave function is used, in which effective Hamiltonian depends on the energy of a system. The effective Hamiltonian is not restricted to the nonrelativistic region, so there is no need in any regularization. To evaluate integrals over loop momenta, they are divided into "hard" and "soft" parts, coming from large and small momenta respectively. Soft contributions were found analytically, and hard ones are evaluated by numerical integration. Some soft terms due to the retardation cancel each other. To calculate the "hard" contributions, a great number of noncovariant graphs is replaced by only a few covariant ones. The hard contribution was found in two ways. The first way is to evaluate contributions of separate graphs, using the Coulomb gauge. The second one is to calculate full hard contribution as a whole using the Feynman gauge. The final result for the "recoil" correction is 0.381(6) m\al^6 and agrees with those of previous papers. Diagram-to-diagram comparison with the revised results of Adkins&Sapirstein was done. All the results agree, so the "recoil" correction is now firmly established. This means a considerable disagreement with the experimental data.Comment: 28 pages, latex including latex figure