Jan W. Dash

TheO(ɛ2) scaling law fordσ/dt in the Reggeon Field Theory

We calculate the two loop contributions within the ε-expansion to the Reggeon Field Theory scaling law fordσ/dt, derived using the renormalization group and a general renormalization point for the Pomeron propagator. This generalizes theO(ε) work of Abarbanel, Bartels, Bronzan, and Sidhu. The invariance of the results under certain coupling constant rescalings is demonstrated. We also make some qualitative comments regarding phenomenological applications. Our amplitude in a certain limit approximates the form of the low energy diffractive amplitude advocated by Kane.

Large-N universality of variant actions

Abstract Corrections to large- N universality in mixed action lattice gauge theories imply constraints on the cut-off dependence. We state the form of these constraints and show that they are satisfied up to and including two loops (weak coupling). This implies that the second coefficient of the β function on the lattice is indeed universal as expected. We then evaluate the complete form of the corrections to large- N universality up to and including two loops. They give a sizeable contribution and determine qualitative aspects of equal string tension data like the bending seen for SU(2).

The complete O(ɛ2) reggeon field theory scaling law dσel/dt and its applications at collider energies

Abstract We give the complete asymptotic reggeon field theory (RFT) scaling law for the elastic cross section in O(ɛ2), extending previous results to include the 3-pomeron cut. This provides the most detailed realistic test of this theory. Numerically we find the encouraging result that the small-t SPS collider data for dσel/dt are in agreement with these new asymptotic RFT predictions. However, ISR data are not compatible with this theory, either in s or t dependence. Previous positive ISR results were largely due to the existence of a j = 1 fixed cut which is not present here. Our results, coupled with the observation that critical RFT fits to σtot require large non-leading terms, imply that a lower bound for the RFT asymptotic scale in single renormalized propagator processes (σtot,dσel/dt) lies around SPS-collider energies. The asymptotic scale for multi-propagator processes (the rapidity plateau, ab→aX reactions, multiplicity distributions etc.) is expected to be well beyond the SPS collider. A possible global RFT picture is them that perturbation theory (including finite rapidity scale effects due to the excitation of new quantum numbers) is applicable through ISR and up to the SPS collider, consistent with recent observations. The critical RFT can become the relevant diffractive theory for σtot and dσel/dt at larger t at and above the SPS collider. Predictions for dσel/dt at larger t at the SPS collider are given in this paper and we urge experimentalists to test them.

Higher order reggeon field theory results for dσ/dt

Abstract The critical reggeon field theory (RFT) asymptotic scaling law for d σ /d t can be evaluated using the e expansion for renormalization group (RG) quaatities at t ≠ 0 along with the two variable RG equations found by Abarbanel, Bartels, Bronzan and Sidhu (ABBS). The amplitude thus obtained has an e-exponentiated form. Interestingly, it reduces in a certain limit to the Bessel function pomeron model advocated by Kane. We perform a systematic numerical study here. Our results are as follows. Although the asymptotic RFT scaling is violated by the data, introduction of a mild external particle vertex with one parameter improvesthe situation considerably at current energies. Moreover, the shape of the ABBS scaling curve predicted by the O(e 2 ) results of Dash and Grandou is in at least qualitative agreement with the data, including the absence of a second dip. Two additional parameters (the t = 0 normalization and the scale in t ) have to be fixed by hand. The overall conclusion is that in spite of many a priori objections the asymptotic RFT does a surprisingly good job of describing both the s and t dependence of d σ /d t at current energies.

Flavor and baryon quantum number renormalizations in the P + f model

Abstract Flavoring renormalization of the pomeron (i.e., the non-diffractive renormalization due to s,c, … quarks and baryons) can correct the failure of standard P + f models to satisfy f poleresonances duality, when rising π N cross sections are accounted for. We present the P + f + flavoring phenomenology of t = 0 NN, π N, and KN scattering. Some absorption is needed. The unflavored pomeron intercept is 0.91 and the flavored pomeron intercept is 1.1.Flavoring thus appears to be an important ingredient in both the P-f identify and P + f models of diffraction, and renders experimental distinction between them rather vague.

Universality for a three-parameter mixed action

We calculate the bare effective Wilson coupling as a function of the three couplings in the mixed SU(2) lattice gauge theory (without fermions), including Tr Up in the three lowest (spin12, 1, 32) representations, complete to two loops and including some higher-order graphs. The calculation is compatible with the N → ∞ limit. We also examine the phase structure of the theory qualitatively using mean-field techniques. We conjecture that a specific constraint among the couplings provides an improved action, and we present some evidence from Monte Carlo renormalization group results in its favour.

Color, flavor, duality, and the pomeron

AtNc/Nf=∞ such that quark loops are absent the Harari-Freund (HF)P+f model of diffraction can be motivated through the identification Pomeron ≈ glueball,f≈leading planar trajectory. AtNc=3, the presence of confinement-related mass scales introduced by quark loops is a basic complication that can easily change this situation to, e.g., a dominantP−f identity structure. Aurenche and Gonzales Mestres (AGM) have argued that diffraction is essentially identical atNc/Nf=∞ and atNc=3. They further claim to have generated the HF scheme directly atNc=3 through the novel mechanism of a multiperipheral iteration of daughters that becomes theP. We respond to these arguments. We give a general qualitative discussion of changes expected in theNc/Nf=∞ toNc=3 transition. Important hadron scattering quantities like particle multiplicities are very different in dynamics dominated by glue and atNc=3, unlike other quantities like resonance width to mass ratios. We argue that the weak coupling dual model is not a reliable guide toNc=3 dynamics. We criticize AGMs “daughter generated Pomeron”, and we close with a brief summary of other attempts to generate theP+f model.

The P-f: Resolution of the “Identity crisis”

Pennington, Schrempp, and Schrempp have argued that there is a “crisis” for theP-f identity hypothesis because the difference Δα(t) between theP-f trajectory and the leading planar trajectory violates a simple dispersion relation. We show why one should not expect such a dispersion relation to hold within and even independent of theP-f identity hypothesis. We conclude that there is no “identity crisis”.

The Reggeon Field Theory and finite scales at collider energies

The Reggeon Field Theory (RFT) with attention paid to finite “flavoring” rapidity scales is considered in the light of emerging SPS collider data. Predictions from a simple RFT perturbative model made in 1978 are shown to be consistent with σtot and other data, in both theP−f identity andP+f versions. The RFT scaling laws are judged not applicable without large non-leading terms, implying an asymptotic region beyond the collider.