Regge couplings and intercepts from the planar dual bootstrap

Planar unitarization of dual models is examined in terms of renormalized diagrams. The shift of the Reggeon intercept 1 ? α(0) and the renormalized coupling $\text{g}{}^2\text{N}\text{16π}$ are both expected of order unity in a model with SU(N) Chan-Paton factors. In four space-time dimensions Regge behaviour makes the shift of the dual photon mass reminiscent of Schwinger's mechanism.     

Apparent spin-dependent forces in QCD or the quantum chemistry of hadrons

Mesons in QCD are viewed as $\text{q}\text{q}$ pairs at the ends of a string (electric flux line). The (mass)² spectrum is approximately linear in the number of nodes, ν, in the wave function ψ(x), x being the fraction of total momentum carried by one quark. For the equal mass case ψ is even (odd) under reflection x ? (1 ? x) for ν even (odd). Thus this reflection symmetry is to be interpreted as charge conjugation where C = +1 (?1) respectively, and hence by Fermi statistics, singlets (triplets) in spin. Since the spectrum of (mass)² is evenly spaced in ν, one can represent the even and odd states by two Regge trajectories separated by intercept $\text{1}\text{2}$, thereby explaining the famous $\text{1}\text{2}$ intercept difference for the π, ρ system. The argument generalizes to K, K¹ as well, but must be further analyzed before we generalize it to baryons.     

Predictions on the couplings of f- and ϱ- trajectories to mesons from chiral symmetry

We employ a chiral saturation scheme involving 15, $\text{L = 0,}\text{and}\text{15}\text{, L = 1}$ mesons in a classification according to SU(4) ? O(3) (i.e. the mesonns π, ?, ω, A₁, A₂, f, A₀ (δ), B, D and σ) and calculate all f and ? Regge couplings between these mesons via a matrix version of finite-energy sum rules. In addition the size of exotic exchanges is evaluated and found to be small. The results are compared with experimental numbers and other models as far as available.     

Backward meson-baryon scattering and geometrical properties of baryonic exchanges

On the basis of the “b universality” hypothesis, Regge behaviour and SU(3) symmetry, we discuss processes of the type $\text{0?}\text{1+}\text{2}\text{→ 0?}\text{1+}\text{2}$ at backward angles when significant data are available. Related annihilation processes by line-reversal are also studied and duality constraints are taken into account. On the whole a satisfactory scheme seems to emerge.     

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.     

Baryon exchange effects in dual unitarisation

The effects of baryon exchanges in the renormalisation of Regge trajectories are studied in the dual unitarisation scheme. The main results are that: (i) the pomeron is boosted above α = 1, giving rising total cross sections beyond baryon-antibaryon thresholds, and (ii) the ω trajectory remains approximately at α = 0.5 but acquires a sizeable admixture of the exotic $\text{q}\text{q}\text{qq}$ state, which enhances its coupling to baryons. There are in addition a number of other interesting predictions.     

Strings with dimension-dependent intercept

By changing the boundary conditions of the relativistics string in extra dimensions, the intercept α(0) is lowered to $\text{1 ?}\text{1}\text{16}\text{(26 ?D}{}_0\text{)}$ in the modified orbital model, where D₀ is the dimensionality of the Poincaré-invariant subspace of space-time. In the modified model of the spinning string, the boson intercept becomes $\text{1}\text{2}\text{?}\text{1}\text{8}\text{(10 ? D}{}_{\mathrm{o}}\text{)}$, while the fermion intercept stays at zero. The projective invariance of the ground state is broken, giving the “photon” mass by a Higgs-like mechanism. Unfortunately, the strings have a negative “G parity”, so the usual, unshifted strings appear as intermediate states in the scattering amplitudes. Also, some of the amplitudes are not dual.     

Bound state models for fermion Regge poles

Trajectories of fermion Regge poles are calculated in a model in which a spin $\text{1}\text{2}$ particle is bound to a spin 0 core. The leading trajectory with parity $\text{(?1)}{}^{\mathrm{<mtext>j?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ is much like the boson trajectory generated by similar interactions. The opposite parity trajectory satisfies the constraints of MacDowell symmetry, yet is totally distinct for s>0. The model produces a trajectory which above the elastic threshold has a small negative Im α and an increasing Re α. Such a trajectory produces poles on the physical sheet of the energy plane.     

Radial and Regge excitations in unified,grand unified and subconstituent models

Necessary group theoretic conditions for all elementary gauge bosons and fermions of an arbitrary renormalizable gauge theory to lie on Regge trajectories are reviewed. It is then argued that in properly unified gauge theories all particles of a given spin lie on Regge trajectories. This then implied that a properly unified gauge theory has no local U(1) factor groups, and no massive fermion singlets. A consideration of the general pattern of Regge and radial recurrences to be expected in quantum field theories suggests that the presence or absence of spin $\text{3}\text{2}$ quarks and/or leptons in the TeV region will provide crucial clues to enable one to distinguish between various classes of unified, grand unified, and subconstituent models. The correct interpretation of such excited fermions will require correlation with the Higgs boson mass and possible radial and Regge excitations of the weak vector bosons.     

Ambiguities in Regge analyses of backward scattering

Ambiguities in Regge analyses of backward scattering due to the possibility of $\text{u}$ dependence in trajectory and residue functions of fermion Regge poles are investigated. Experiments to clarify the ambiguities are suggested. Also an intrinsic difficulty in separating exchanges of opposite parity is discussed.     

Proton-proton scattering and the pomeron

We describe various attempts to fit the data on pp and $\text{p}\text{p}$ elastic scattering and total cross sections, including the recent ISR data, with a variety of Regge pole and cut models. Only two types of model are able to explain the data over the whole energy range satisfactorily. The simplest of these has no cuts, but a pomeron pole with trajectory αp(0) = 1.06 + 0.25 t, and a non-shrinking “core” term at large |t|. The other has a flat trajectory, αp(t) = 1.06 for all t, and strong eikonal-model cuts which explain both the shrinkage at low |t|, and the lack of it at larger |t|. We also briefly review various speculations which relate the fact that αp(0) > 1 to the small triple-pomeron coupling.     

Phenomenological characteristics of absorption in charge- and hypercharge-exchange reactions

We try to explain in a unique framework charge- and hypercharge-exchange reactions above 3 GeV/c. Our approach is based on exchange degenerate and SU(3) symmetric Regge poles to which absorption corrections are applied.In the absence of a firm theoretical basis for these corrections we adopt the approach of fixing the Regge poles through theoretical and phenomenological considerations; we then determine what kind of absorption we should apply. At intermediate energy (around 5 GeV/c our results indicate complete absorption of the s-wave amplitude. Of the two terms 1 and e^?iπα of the Reggesignature factor, the latter should be more strongly absorbed. This effect may explain especially the breaking of line-reversal symmetry for hypercharge-exchange reactions, π^?p→π⁰n polarization data, and the difference of peripherality of ??ω and A₂?f₀ contributions.In addition, K-exchange in $\text{p}\text{p}\text{→}\text{Λ}\text{Λ}$ has been studied.     

Relativistic spin selection rules obtained by SL(3, R) symmetry

All irreducible (unitary or not) ray representations of SL(3, R) obeying the Δj = 2 selection rule imposed by Regge trajectories are constructed. They provide irreducible ray representations of $\text{SL(4,}\text{R}\text{) · T}{}^4$ which restricted to the Poincaré subgroup yield unitary representation of real mass and of spin spectrum which statisfies the Δj = 2 selection rule.     

Operator formulation of Regge asymptotic behavior

If the appropriate high-energy limits of the amplitudes $\text{W ≡ ?}\text{d}\text{x}\text{e}{}^{\mathrm{<mtext>i</mtext><mtext>q\; ·\; x</mtext>}}\text{<b|j(x)j′(0)|b′ >}$ are Regge pole dominated, then the large distance (x₀ → ∞, x²fixed) behavior of the current product is completely characterized by an operator expression $\text{R}\text{(x : 0)}$, involving only local operators at 0, which is such that $\text{R ≡ ?}\text{d}\text{x}\text{e}{}^{\mathrm{<mtext>i</mtext><mtext>q\; ·\; x</mtext>}}\text{<b|}\text{R}\text{|b′ >}$ and W have the same high-energy behavior. In the only case (|b> a single particle stateand |b′> the vacuum) where W is not Regge behaved, it is shown that R is identical to W, and so the relation $\text{jj′ →}\text{R}$ is established as a large distance operator expansion, valid between all states. $\text{R}$ is expressed as a differential operation B(□_x, ?_x · ?₀, □₀) on the light-cone expansion and some of its properties are deduced by carrying out the differentiations. A second form of $\text{R}$ is given in terms of non-local “reggeon” field operators R_αm(0) (α is a (fixed) spin index and m is a (variable) helicity index) which might be useful coordinate in reggeon field theories. These operators can be used to define reggeon-particle amplitudes and if conventional double-Regge and triple-Regge behaviors are further assumed, the large distance behaviors of the current-reggeon and reggeon-reggeon field products are specified in terms of other reggeon fields.     

Bounds for Regge slopes and intercepts for ordinary and new hadrons

We have derived a constraint $\text{2α}{}_{\mathrm{<mtext>i</mtext><mtext>j</mtext>}}\text{(0) + α}{}_{\mathrm{<mtext>i</mtext><mtext>i</mtext>}}\text{(0) + α}{}_{\mathrm{<mtext>j</mtext><mtext>j</mtext><mtext>(0)</mtext>}}$ form the einequality for he unitarity relation. This constraint, combined with slope factorization leads to bounds for Regge slopes and intercepts. Bottom cases are also argued.     

Non-diffractive Pomeron renormalization,multiplicities, and the topological expansion

The renormalization of the Pomeron due to nondiffractive K$\text{K}$, B$\text{B}$ production thresholds is considered within a simple generalization of the Chew-Rosenzweig multiperipheral realization of Veneziano's topological expansion. The results are consistent with the existence of both the “low-energy” bare Pomeron with intercept $\text{α=0.85}$ and Gribov bare Pomeron with intercept above one. The vacuum exchange part of 2σ_KN?σ_πN basically rises with energy. Qualitatively correct features of shrinkage and breaks of $\text{d}\text{σ}\text{d}\text{t}$ emerge. The multiplicity of product clusters (n) increases with energy faster than 1ns and agrees with experiment for an average number of particles per cluster of 3–4. Independently of our model the Harari-Freund multiperipheral realization of the topological expansion is shown to be in serious difficulty with multiplicities, requiring around 20 particles per cluster.     

Deviation from scaling in the triple-regge region of pp→ pX and fP universality

By generalizing $\text{f}\text{P}$ universality to Regge-particle “scattering” we obtain $\text{s}\text{d}\text{σ}\text{d}\text{t}\text{d}\text{M}{}^2\text{= F(}\text{s}\text{M}{}^2\text{,t)}$$\text{[1 +}\text{M}{}^{\mathrm{?1}}\text{b}{}_{\mathrm{<mtext>f</mtext>}}\text{(0)}\text{b}{}_{\mathrm{<mtext>P</mtext>}}\text{(0)}\text{]}$ for pp → pX, where b_f(t) and b_P(t) are the f and P Regge residues for, say, pp → pp. This agrees with the recent NAL data.     

Quarks and reggeons

We propose a new algebra which will hopefully contribute to the joint understanding of electromagnetic and weak structure functions and of Regge couplings. It involves an infinite number of form factors of arbitrary complex spin J (with Re(J?1) > 0) and definite signature. The algebra holds exactly in a quark-gluon model when quantized canonically on equal light fronts. If all form factors have k = 0 and J = 1, the algebra closes and becomes U(6) × U(6), with the connecting subgroups being associated with pure quarks and pure antiquark currents, respectively. This doubling of the group leads to exact exchange degeneracy if baryons and mesons consist of qqq and q$\text{q}$ wave functions only.To some lowest approximation, Regge couplings can be calculated by representing U(6) × U(6) on properly mixed quark wave functions. With the mixing parameters fixed by the chiral subgroup, these couplings are determined up to an overall normalization.As an illustration, the coupling of the trajectories ?, ω; A₂, f; A₁, D; Z, Z_sg; π, η; B, H trajectories are estimated for the meson resonances ?, ω; π, η; A₂, f; A₁, D; B, H; A₀, σ. The trajectories π, η; B, H are not in the algebra initially but can be inferred from an extension of PCAC to the bilocal currents (“PCBC”).     

Regeneration amplitude of KS0 from KL0 in carbon

We have measured the transmission regeneration amplitude for carbon. The invariant amplitude $\text{[?(0) ?}\text{?}\text{(0)]/P}$ varies from 5.909 ± 0.066 mb at 4.5 GeV/c to 3.933 ± 0.152 mb at 9.5 GeV/c. The results agree with optical model calculations using measured kaon-nucleon total cross sections. The data also provide a value for the ω trajectory intercept α_ω(0) = 0.42 ± 0.04.     

Predictions of duality for the charmed meson masses

The constraints of duality via FESR's are applied to the processes P+P→P+V, using particles with a new quantum number (charm) as both external and internal (resonance saturation) states. The results are independent of any detailed dynamics or symmetry schemes, as well as independent of coupling strengths. We use the masses of the recently-discovered D and D¹ to set the scale. We predict , m_F = 1938 ± 33 MeV, . Thus slopes of Regge trajectories for charmed mesons are predicted to be substantially smaller than those for ordinary mesons.