The content of unitarity constraints on a pomeron pole of intercept one

We present a consistent picture of a pomeron pole with intercept one, together with its cuts, which evades the decoupling arguments. We use the reggeon cut discontinuity formulae to introduce Gribov's reggeon calculus as an exact solution of multiparticle t-channel unitarity. We show how, within the calculus, two-pomeron iterations of a singular kernel can be responsible for the zero in the triple-pomeron vertex. Using the concept of a bare pomeron pole as a multiperipheral production process which is subsequently renormalised by other effects, we apply the reggeon calculus analysis to inclusive cross sections. We find that the inclusive sum rule decoupling arguments are avoided because of the addition of enhanced absorptive corrections to the conventional Regge pole contributions. However, we show that in this picture the combined pole and two-pomeron cut contribution to the total cross section factories to order (ln s)^?2.We also show that, when the correct helicity structure of the pomeron is taken into account, the s-channel unitarity condition for pomeron scattering amplitudes does not lead to any serious decouplings.     

General description of new physics in t,b and boson interactions and its unitarity constraints

We list all possible dim = 6 CP conserving and SU(3) × SU(2) × U(1) gauge invariant interactions, which could be generated in case no new particles would be reachable in the future Colliders, and the only observable New Physics would be in the form of new interactions affecting the scalar sector and the quarks of the third family. These interactions are described by operators involving the standard model scalar field, the quarks of the third family and the gauge bosons. Subsequently, we identify those operators which do not contribute to LEP1 (and lower energy) observables at tree level and are not purely gluonic. Since present measurements do not strongly constrain the couplings of these operators, we derive here the unitarity bounds on them. Finally, in order to get a feeling on the possible physical meaning of the appearance of any of these operators, we identify the operators generated in a class of renormalizable dynamical models which at the TeV scale, are fully described by the SU(3) × SU(2) × U(1) gauge group.     

Generalized eikonalization and unitarity

In the literature, the notion of eikonalization is often used as synonymous of unitarization or, at least, as implying that unitarity is not violated. This, to the very least, appears to be wishful thinking. We discuss the properties of various types of eikonalization within a unified treatment. Linear trajectories with intercept larger than unity (so popular nowadays) lead to small asymptotic violations of unitarity even after eikonalization. Classes of eikonalizations in which the Odderon could dominate over the Pomeron are given; even so the maximal Odderon is still excluded by eikonalization.     

Fragmentation models and unitarity

We use the diffractive excitation model to evaluate the inelastic part of the proton-proton unitarity equation. Conventional assumptions about the phase of the vacuum singularity, and an experimentally motivated choice of mass dependence for the diffractive slope, lead to an upper bound for the proportion of diffractively excited inelastic processes. We also discuss the apparent breakdown of factorization.     

Stringent constraints on the scalar K$ \pi$ form factor from analyticity,unitarity and low-energy theorems

We investigate the scalar K p \pi form factor at low energies by the method of unitarity bounds adapted so as to include information on the phase and modulus along the elastic region of the unitarity cut. Using at input the values of the form factor at t = 0 and the Callan-Treiman point, we obtain stringent constraints on the slope and curvature parameters of the Taylor expansion at the origin. Also, we predict a quite narrow range for the higher-order ChPT corrections at the second Callan-Treiman point.     

Multiparticle unitarity and diffractive amplitudes

Generalizing the results of previous work, an explicit construction of elastic and inelastic diffractive amplitudes through multiparticle unitarity is given starting from a simple parametrization of non-diffractive production amplitudes. The energy dependent interference mechanism which has been previously shown to be essential to produce the diffraction peak in the elastic process is now seen to be also responsible, in a natural way, for the leading particle effect which dominates production yields.     

Gluon shadowing and unitarity effects

New data from HERA experiment on deep inelastic scattering have been used to parametrize nucleon and Pomeron structure functions. Within the Gribov theory, the parameterizations were employed to calculate gluon shadowing for various heavy ions. The latter was compared with predictions from other models. Calculations of multiplicity reduction due to gluon shadowing for d+Au collisions at forward rapidities at √s _NN =200 GeV are in good agreement with BRAHMS data on the nuclear modification factor.     

Inequalities based on unitarity and duality

Two sets of inequalities, one based on unitarity and the other on duality, are derived. From them we obtain useful constraints on various Regge couplings involving the Pomeron. The constraints are particularly powerful if the Pomeron is a pole with unit intercept. Interesting relationships among the intercepts of the leading Reggeons of different quantum number are also obtained; all agree with the experemental observation.     

Quark mixing,CKM unitarity

In the Standard Model of elementary particles, quark-mixing is expressed in terms of a 3 x 3 unitary matrix V, the so called Cabibbo-Kobayashi-Maskawa (CKM) matrix. Significant unitarity checks are so far possible for the first row of this matrix. This article reviews the experimental and theoretical information on these matrix elements. On the experimental side, we find a 2.2 to 2.7 deviation from unitarity, which conflicts with the Standard Model.Received: 25 October 2003, Published online: 29 January 2004F. Glück: Present address: Johannes Gutenberg University Mainz, Inst. Physics, WA EXAKT, 55099 Mainz, GermanyA. Serebrov: Also: Paul Scherrer Institut, 5232 Villigen PSI, Switzerland     

Estimates of the unitarity integral

The elastic unitarity integral is studied for amplitudes which satisfy a Mandelstam representation without subtraction. The double spectral functions are taken to belong to function spaces which allow local, even non-integrable, singularities. The existence of fixed point solutions is derived and the additional restrictions due to inelastic unitarity are discussed.     

Experimental disagreements with extended unitarity

In production processes, e.g. J/Ψ→ωππ or p̄p→3π, the σ and f₀(980) overlap in the same partial wave. The conjecture of extended unitarity (EU) states that the ππ pair should have the same phase variation as ππ elastic scattering. This is an extension of Watson’s theorem beyond its original derivation, which stated only that the s-dependence of a single resonance should be universal. The prediction of EU is that the deep dip observed in ππ elastic scattering close to 1 GeV should also appear in production data. Four sets of data disagree with this prediction. All require different relative magnitudes of σ and f₀(980). That being so, a fresh conjecture is to rewrite the 2-body unitarity relation for production in terms of observed magnitudes. This leads to a prediction different to EU. Central production data from the AFS experiment fit naturally to this hypothesis. PACS 13.25.-k; 13.25.Gv; 13.75.Lb