High energy proton-proton cross-section and Froissart bound

A model for high energy proton-proton system is developed which obeys several asymptotic bounds including Froissart bound. The amplitude taken has two parts, a Regge part and a pomeron part. The Regge part is described by the exchange degenerate pairw andP′. To calculate the pomeron part the Freund-Harari duality is invoked which states that the pomeron is dual to thes-channel background. Thes-channel background is estimated by parametrising the branch cuts inS through a conformal mapping method. Expressions for total cross-section, ratio of real-to-imaginary parts of forward amplitude and the slope parameter are presented. The corresponding quantities for are also evaluated. Our analysis favours strong exchange degeneracy.     

Absorptive corrections to multihadron production and the unit intercept of the Pomeron

We propose a simple absorptive model for multihadron production in which the zero strength limit (g → 0) of the strong interactions is a vector theory, the Pomeron intercept is predicted to be at α_p=1 for any value of g, and the leading non-Pomeron singularity is at $\text{α}{}_{\mathrm{<mtext>R</mtext>}}\text{=1?}\text{g}\text{2}$. Themodel can accommodate correlations and incorporates the unitarity (Froissart) bound. Other properties of the model are discussed.     

The s-channel dual absorptive model as a consequence also of t-channel absorption

The dual absorptive model applied to t-channel predicts that Regge residues above threshold are I_n-functions which for t ? 0, for the leading trajectory, are simply J_n(R_o√−t). Thus s-channel absorptive models can be expressed entirely in terms of t-channel quantities. Implications to complex Regge poles is discussed.     

f-pole corrections to the critical parameters of the pomeron

A reggeon field theory with two vacuum quantum numbers Regge poles, the pomeron and the f-reggeon is presented. In such a theory only one stable fixed point appears which is sensibly different from that governing a RFT with the pomeron alone. This fact is responsible for the modifications of the critical parameters of the pomeron. In particular, the intercept of the bare pomeron increases and approaches the phenomenological value.     

General features of the reggeon calculus with α > 1

We discuss some general properties of the reggeon calculus with input intercept greater than one, in an attempt to formulate a model yielding indefinitely rising cross sections which is consistent with t-channel unitarity. In general the leading behaviour of the amplitude always factorises. If interactions between reggeons are ignored the scattering is equivalent to that from a grey absorbing disk of radius O (ln s). Diagrams involving such interactions are subject to large-scale cancellations. These enable the model to give sensible results for inclusive cross sections. In quantum number exchange reactions, factorisation of the Regge pole residues is weakly broken in the model.     

Possible Odderon exchange in pp and ■p elastic collisions at the TOTEM experiment

Based on the Froissart-Martin theorem,the Regge theory and the possible Odderon exchange,the total cross-sectionσtot and the ratio of the real to imaginary parts of the forward scattering amplitude p in the pp and pp elastic collisions in the TOTEM energy region are studied in the FPO model.We consider the contributions of the Froissart bound and of the Pomeron,Reggeon and Odderon exchange terms in the scattering amplitude of the pp and pp elastic collisions.Using the Odderon interceptαo(0)=0.5,our theoretical predictions are in good agreement with the recent results of the TOTEM experiment.These results show that the Odderon,corresponding to the odd elastic scattering amplitude,is likely to exist.     

Bound states in N = 8 supergravity and N = 4 supersymmetric Yang-Mills theories

We present a study of possible bound states in N = 8 supergravity. We find evidence for the existence of multiplets of two-body bound states and expect that many-body bound states may exist as well. Our study is based on a calculation of Regge trajectories in the two-body scattering amplitudes of the lagrangian field theory. We also study Regge trajectories in N = 4 Yang-Mills theory and find evidence for a possible spin zero, SU(4) and gauge singlet, massless bound state. If such a state actually exists and supersymmetry is not broken, it may be a member of a supersymmetric multiplet which includes the graviton.     

Reggeon field theory: Formulation and use

We formulate and discuss Reggeon field theory, which enables one to systematically analyze the exchange of Regge poles and associated branch points in high energy hardron scattering. The field theory is first motivated by a consideration of hybrid Feynman graphs, and then a more general derivation from crossed-channel multiparticle unitarity relations is given. Rules for Reggeon interaction and propagation are formulated. We treat in some detail the problem of the Pomeron or vacuum pole which has α(0) = 1 and is responsible for diffractive processes. In particular the renormalization group analysis of Reggeon field theory is presented and the structure of Pomeron partial wave amplitudes is elucidated. Also the question of Pomeron or absorptive corrections to secondary trajectories (both fermion and boson) is considered. We make some comments on important problems yet remaining in Reggeon field theory; in particular, we stress the study of its s-channel content.     

Consequences of Crossed Channel Structure for High Energy Elastic Scattering

This review describes a field in the S-matrix theory of elastic stattering. Analyticity and elastic unitarity in the crossed t-channel are shown in a rigorous manner to yield constraints on s-channel quantities. Strong restrictions on s-channel partial wave with angular momenta l ⩾√s/2(b₀ + λ In s) follow from realistic assumptions on the amplitude in the unphysical domain (Mandelstam analyticity and Regge behaviour). The possibility of phenomenological application of these results is discussed.     

Impact parameter analysis of KN and πN scattering in the intermediate energy region

We have evaluated the s-channel-helicity partial-wave amplitudes for $\text{K}\text{N and πN}$ scattering as functions of the impact parameter using partial-wave data in the energy range P_L≈1.0–2.0 GeV/c. We find that the $\text{K}\text{N}$ background and resonance amplitudes exhibit features consistent with the dual absorptive picture for pomeron and f + ω and A₂ + ? exchanges. Comparison of the πN low-energy amplitude with the partial-wave decomposition of a quantitative Regge model gives evidence for local duality between the s-channel resonance and t- and u-channel Regge exchanges.     

Kaon-nucleon finite energy sum rules revisited

Kaon-nucleon finite energy and continuous moment sum rule integrals are evaluated using recent phase-shift solutions to extract the t-channel exchange amplitudes and the results are compared with Regge pole models. The exchange degeneracy breaking previously observed in the ? and A₂ amplitudes is confirmed, and it is suggested that this may be due to an exotic P₀₁ KN resonance. Regge trajectories are extracted from the integrals and are in good agreement with those found from direct fits to high-energy data.     

Upper bound on the slope parameter

We find the axiomatic upper bound on the slope parameter of the scattering amplitude, which is logarithmically divergent with respect to energies in the region 0 < t < 4m²_π. This upper bound is realized in Regge-pole theory. We also obtain explicitly the numerical upper bound on the slope parameter of the linear Regge trajectory.     

Determination of valley splitting in (100) Si inversion layers

An experimental method is presented to determine the valley splitting in n-channel Si inversion layers. The method is an extension of the “tilted field” experiment under conditions, where the valley splitting is resolved at all tilt angles. In the framework of Ohkawa and Uemura's theory, the bare splitting as well as the effective exchange interaction are obtained directly from the angles of coincidence. The bare valley splitting in the samples investigated is 0.15 meV/10¹² cm^-2 ·n_s. Using experimentally determined parameters we have calculated the oscillatory conductivity σ_xx in a simplified version of Ohkawa and Uemura's model. The calculated curves reproduce the detailed structure of the experimental data for the various tilt angles of the experiment.     

Rigorous lower and upper bounds for the slope parameter

It is proved within the framework of axiomatic field theory that the logarithmic derivative of the absorptive part of the scattering amplitude with respect to momentum transfer is bounded from above by $\text{(15}\text{log}\text{s)}\text{[4√t(2 ? √t)]}$ for a sequence of s→+∞, and from below either in the s-channel by const. × s^?5 log^?4s or in the u-channel by const. × u^?5 log^?4u for at least one sequence of s or u →+∞, respectively. In the particular case of the s?u even-symmetric amplitude, a stronger lower bound is obtained; namely, const. × s^?5 log^?4s for at least one sequence of s→+∞. Here s, t, and u are the usual Mandelstam variables, and all bounds are obtained in the forward and the unphysical regions: 0?t<4 (in units of pion mass).It is observed that the Regge amplitude β(t)s^α(t) of high-energy scattering gives the same energy dependence as the above upper bound, and, furthermore, that the slope of the Regge trajectory is bounded from above by $\text{15}\text{[4√t(2 ? √t)]}\text{for}\text{0 < t < 4}$.     

Non-vanishing of the bare triple-Pomeron coupling from s-channel unitarity

In the crossing symmetric Reggeon calculus based on the $\text{1}\text{N}$ expansion, s-channel unitarity sum rules are written down explicitly to each order in $\text{1}\text{N}$. Some of the lowest order sum rules are shown to imply a non-vanishing bare triple-Pomeron coupling at t = 0, irrespectively of the bare Pomeron intercept.     

Production properties of A1 in πp interactions at 5.45 GeV/c

The production of the peripheral 3π mass enhancement in the A₁ region is described. The differential cross section and its variation with 3π mass is studied and the spin density matrix elements are given for the t-channel and s-channel helicity frames. As observed in π⁻p interactions t channel but not s channel helicity is conserved. A Deck type double Regge trajectory exchange amplitude gives good fits to the experimental distributions. Its use is supported by the equality of ?_{0 0} for the A₁ and ?00 for the ? in the t-channel, as noted by Donohue.