arXiv subjects
Publications and source records attributed to R. L. Jaffe.
We study scattering theory identities previously obtained as consistency conditions in the context of one-loop quantum field theory calculations. We prove the identities using Jost function techniques and study applications.
I review what is known about the quark and gluon spin distributions in the nucleon. I discuss in some detail (a) the existence of sum rules for angular momentum; (b) the interpretation and possible measurement of the nucleon's transversity distributions; and (c) the uses of spin-dependent fragmentation functions.
We compute fractional and integer fermion quantum numbers of static background field configurations using phase shifts and Levinson's theorem. By extending fermionic scattering theory to arbitrary dimensions, we implement dimensional regularization in a 1+1 dimensional gauge theory. We demonstrate that this regularization procedure automatically eliminates the anomaly in the vector current that a naive regulator would produce. We also apply these techniques to bag models in one and three dimensions.
I discuss two topics of current interest in the study of the spin structure of the nucleon. First, I discuss whether there is a sum rule for the components of the nucleon's angular moments. Second, I discuss the measurement of the nucleon's transversity distribution in light of recent results reported by the HERMES collaboration at DESY.
We discuss speculative disaster scenarios inspired by hypothetical new fundamental processes that might occur in high energy relativistic heavy ion collisions. We estimate the parameters relevant to black hole production; we find that they are absurdly small. We show that other accelerator and (especially) cosmic ray environments have already provided far more auspicious opportunities for transition to a new vacuum state, so that existing observations provide stringent bounds. We discuss in most detail the possibility of producing a dangerous strangelet. We argue that four separate requirements are necessary for this to occur: existence of large stable strangelets, metastability of intermediate size strangelets, negative charge for strangelets along the stability line, and production of intermediate size strangelets in the heavy ion environment. We discuss both theoretical and experimental reasons why each of these appears unlikely; in particular, we know of no plausible suggestion for why the third or especially the fourth might be true. Given minimal physical assumptions the continued existence of the Moon, in the form we know it, despite billions of years of cosmic ray exposure, provides powerful empirical evidence against the possibility of dangerous strangelet production.
We find static solitons stabilized by quantum corrections in a (1+1)-dimensional model with a scalar field chirally coupled to fermions. This model does not support classical solitons. We compute the renormalized energy functional including one-loop quantum corrections. We carry out a variational search for a configuration that minimizes the energy functional. We find a nontrivial configuration with fermion number whose energy is lower than the same number of free fermions quantized about the translationally invariant vacuum. In order to compute the quantum corrections for a given background field we use a phase-shift parameterization of the Casimir energy. We identify orders of the Born series for the phase shift with perturbative Feynman diagrams in order to renormalize the Casimir energy using perturbatively determined counterterms. Generalizing dimensional regularization, we demonstrate that this procedure yields a finite and unambiguous energy functional.
We consider one-loop quantum corrections to soliton energies and central charges in the supersymmetric $ϕ^4$ and sine-Gordon models in 1+1 dimensions. In both models, we unambiguously calculate the correction to the energy in a simple renormalization scheme and obtain $ΔH = - m/(2π)$, in agreement with previous results. Furthermore, we show that there is an identical correction to the central charge, so that the BPS bound remains saturated in the one-loop approximation. We extend these results to arbitrary 1+1 dimensional supersymmetric theories.
We show that quantum effects can stabilize a soliton in a model with no soliton at the classical level. The model has a scalar field chirally coupled to a fermion in 1+1 dimensions. We use a formalism that allows us to calculate the exact one loop fermion contribution to the effective energy for a spatially varying scalar background. This energy includes the contribution from counterterms fixed in the perturbative sector of the theory. The resulting energy is therefore finite and unambiguous. A variational search then yields a fermion number one configuration whose energy is below that of a single free fermion.
We study the possibility that the light scalar mesons are (qbar qbar q q) states rather than (qbar q). We perform a lattice QCD calculation of pseudoscalar meson scattering amplitudes, ignoring quark loops and quark annihilation, and find indications that for sufficiently heavy quarks there is a stable four-quark bound state with J^{PC}=0^{++} and non-exotic flavor quantum numbers.
A simple generalization of the Breit Interaction explains many qualitative features of the spectrum of hadrons.
The Casimir energy is the first-order-in-\hbar correction to the energy of a time-independent field configuration in a quantum field theory. We study the Casimir energy in a toy model, where the classical field is replaced by a separable potential. In this model the exact answer is trivial to compute, making it a good place to examine subtleties of the problem. We construct two traditional representations of the Casimir energy, one from the Greens function, the other from the phase shifts, and apply them to this case. We show that the two representations are correct and equivalent in this model. We study the convergence of the Born approximation to the Casimir energy and relate our findings to computational issues that arise in more realistic models.
We consider the production and decay of the $χ_2$ charmonium state in polarized and unpolarized $pp$ collisions at RHIC in the framework of an effective theory based on the QCD multipole expansion. We find that the angular distribution in the decay of the produced charmonium, $χ_2 \to J/ψ+ γ$, in the unpolarized case allows us to distinguish clearly between the color singlet and color octet production mechanisms. Once the production mechanism is known, the angular distribution in the polarized case can be used to measure the polarized gluon distribution in the proton, $ΔG(x)$.
We consider the dynamics of a relativistic Dirac particle constrained to move in the interior of a twisted tube by confining boundary conditions, in the approximation that the curvature of the tube is small and slowly varying. In contrast with the nonrelativistic theory, which predicts that a particle's spin does not change as the particle propagates along the tube, we find that the angular momentum eigenstates of a relativistic spin-1/2 particle may behave nontrivially. For example, a particle with its angular momentum initially polarized in the direction of propagation may acquire a nonzero component of angular momentum in the opposite direction on turning through 2 πradians. Also, the usual nonrelativistic effective potential acquires an additional factor in the relativistic theory.
A transcription with minor alterations of the talk presented to honor Sid Drell on the occasion of his retirement.
We suggest a method of constructing gauge invariant quark and gluon distributions that describe an abstract QCD observable and apply this method to analyze angular momentum of a hadron. In addition to the known quark and gluon polarized structure functions, we obtain gauge invariant distributions for quark and gluon orbital angular momenta, and consider some basic properties of these distributions and their moments.
We explore further applications of the twist-two quark interference fragmentation functions introduced earlier. We show that semi-inclusive production of two pions in the current fragmentation region in deep inelastic scattering of a longitudinally polarized electron on a longitudinally polarized nucleon can provide a probe of the valence quark spin (or helicity difference) distribution in the nucleon.
We introduce twist-two quark interference fragmentation functions in helicity density matrix formalism and study their physical implications. We show how the nucleon's transversity distribution can be probed through the final state interaction between two mesons ($π^+π^-$, $K\bar K$, or $πK$) produced in the current fragmentation region in deep inelastic scattering on a transversely polarized nucleon.
We study the tensor structure function $b_1\xq$ in deep inelastic scattering (DIS) of an electron from a polarized deuteron target. We model the electron-nucleon cross section at the starting point for $Q^2$ evolution by vector-meson-dominance (VMD). Shadowing due to the double-scattering of vector mesons, along with the presence of a d-state admixture in ground state deuteron wave function gives rise to a non-vanishing contribution to $b_1\xq$. Although significant at large Bjorken $x$, the restoration of rotational symmetry for small $x$ ($\leq10^{-3}$) requires that $b_1^{(2)}\xq$ approach zero as $x\to 0$ in this model. If the model is valid, it should apply within the range of present fixed target experiments.