Regge Analysis Research Articles

Probing the Pomeron spin structure with Coulomb-nuclear interference

Polarized pp elastic scattering at small angles in the Coulomb-nuclear interference (CNI) region offers a unique opportunity to study the spin structure of the Pomeron. Electromagnetic effects in elastic amplitude can be equivalently treated either as Coulomb corrections to the hadronic amplitude (Coulomb phase), or as absorption corrections to the Coulomb scattering amplitude. We perform the first calculation of the Coulomb phase for the spin-flip amplitude and found it significantly exceeding the widely used non-flip Coulomb phase. The alternative description in terms of absorption corrections, though equivalent, turned out to be a more adequate approach for the Coulomb corrected spin-flip amplitude. Inspired by the recent high statistics measurements of single-spin asymmetry with the HJET polarimeter at the BNL, we also performed a Regge analysis of data, aiming at disentangling the Pomeron contribution. However, in spite of an exceptional accuracy of the data, they do not allow to single out the Pomeron term, which strongly correlates with the major sub-leading Reggeons. A stable solution can be accessed only by making additional ad hoc assumptions, e.g. assuming the Pomeron to be a simple Regge pole, or fixing some unknown parameters. Otherwise, in addition to the STAR data at s=200GeV new measurements, say at 100GeV or 500GeV, could become decisive.

Regge limit of gauge theory amplitudes beyond leading power approximation

We study the high-energy small-angle Regge limit of the fermion-antifermion scattering in gauge theories and consider the part of the amplitude suppressed by a power of the scattering angle. For abelian gauge group all-order resummation of the double-logarithmic radiative corrections to the leading power-suppressed term is performed. We find that when the logarithm of the scattering angle is comparable to the inverse gauge coupling constant the asymptotic double-logarithmic enhancement overcomes the power suppression, a formally subleading term becomes dominant, and the small-angle expansion breaks down. In QCD we show that in the color-singlet channel for sufficiently small scattering angles the abelian power-suppressed contribution becomes comparable to the one of BFKL pomeron. Possible role of the subleading-power effects for the solution of the unitarity problem of perturbative Regge analysis in QED and QCD is discussed. An intriguing relation between the asymptotic behavior of the power-suppressed amplitudes in Regge and Sudakov limits is discovered.

Exclusiveπ0electroproduction atW>2 GeV with CLAS

Exclusive neutral-pion electroproduction ($ep\to e^\prime p^\prime \pi^0$) was measured at Jefferson Lab with a 5.75-GeV electron beam and the CLAS detector. Differential cross sections $d^4\sigma/dtdQ^2dx_Bd\phi_\pi$ and structure functions $\sigma_T+\epsilon\sigma_L, \sigma_{TT}$ and $\sigma_{LT}$ as functions of $t$ were obtained over a wide range of $Q^2$ and $x_B$. The data are compared with Regge and handbag theoretical calculations. Analyses in both frameworks find that a large dominance of transverse processes is necessary to explain the experimental results. For the Regge analysis it is found that the inclusion of vector meson rescattering processes is necessary to bring the magnitude of the calculated and measured structure functions into rough agreement. In the handbag framework, there are two independent calculations, both of which appear to roughly explain the magnitude of the structure functions in terms of transversity generalized parton distributions.

Regge analysis of the ππ scattering amplitude

The theoretical predictions for the subtraction constants lead to a very accurate dispersive representation of the ππ scattering amplitude below 0.8 GeV. The extension of this representation up to the maximum energy of validity of the Roy equations (1.15 GeV) requires a more precise input at high energies. In this paper we determine the trajectories and residues of the leading Regge contributions to the ππ amplitude (Pomeron, f and ρ), using factorization, phenomenological parametrizations of the πN and NN total cross sections at high energy, and a set of sum rules which connect the high and low energy properties of ππ scattering. We find that nonleading Regge terms are necessary in order to achieve a smooth transition from the partial waves to the Regge representation at or below 2 GeV. We obtain thus a Regge representation consistent both with the experimental information at high energies and the Roy equations for the partial waves with ℓ≤4. The uncertainties in our result for the Regge parameters are sizable, but in the solutions of the Roy equations these only manifest themselves above the $K\hspace {0.03cm}\overline {\rule [0.7em]{0.6em}{0em}}\hspace {-0.8em}K$ threshold.

Forward dispersion relations and Roy equations in ππ scattering

We first review the results of an analysis of ππ interactions in S, P and D waves for the two-pion effective mass from threshold to about 1.4 GeV. In particular, we show a recent improvement of this analysis above the K \( \bar K \) threshold using more data for phase shifts and including the S0-wave inelasticity from ππ → K \( \bar K \). In addition, we have improved the fit to the f 2(1270)-resonance and used a more flexible P-wave parametrization above the K \( \bar K \) threshold and included an estimation of the D2-wave inelasticity. The better accuracy thus achieved also required a refinement of the Regge analysis above 1.42 GeV. Finally, in this work we check that the ππ scattering amplitudes obtained in this approach satisfy remarkably well forward dispersion relations and Roy’s equations.

Erratum: Pion-pion scattering amplitude. II. Improved analysis aboveK¯Kthreshold [Phys. Rev. D74, 014001 (2006)

We improve, in the energy region between $\bar{K}K$ threshold and $\sim~1.4$ GeV, the energy-dependent phase shift analysis of $\pi\pi$ scattering presented in a previous paper. For the S0 wave we have included more data above $\bar{K}K$ threshold and we have taken into account systematically the elasticity data on the reaction $\pi\pi\to\bar{K}K$. We here made a coupled channel fit. For the D0 wave we have considered information on low energy parameters, and imposed a better fit to the $f_2$ resonance. For both waves the expressions we now find are substantially more precise than the previous ones. We also provide slightly improved D2 and P waves, including the estimated inelasticity for the first, and a more flexible parametrization between 1 and 1.42 GeV for the second. The accuracy of our amplitudes is now such that it requires a refinement of the Regge analysis, for $s^{1/2}\geq1.42$ GeV, which we also carry out. We show that this more realistic input produces $\pi\pi$ scattering amplitudes that satisfy better forward dispersion relations, particularly for $\pi^0\pi^0$ scattering.

Pion-pion scattering amplitude. II. Improved analysis aboveK¯Kthreshold

We improve, in the energy region between the KK threshold and ~ 1.4 GeV, the energy-dependent phase shift analysis of π π scattering presented in a previous paper. For the S0 wave, we have included more data above the KK threshold and we have taken into account systematically the elasticity data on the reaction π π →KK. We here made a coupled channel fit. For the D0 wave, we have considered information on low energy parameters, and imposed a better fit to the f_2 resonance. For both waves the expressions we now find are substantially more precise than the previous ones. We also provide slightly improved D2 and P waves, including the estimated inelasticity for the first, and a more flexible parametrization between 1 and 1.42 GeV for the second. The accuracy of our amplitudes is now such that it requires a refinement of the Regge analysis, for^(1/2) ≥ 1.42 GeV, which we also carry out. We show that this more realistic input produces π π scattering amplitudes that satisfy better forward dispersion relations, particularly for π^0 π^0 scattering.

Comparative Regge analysis of Λ,ΣΛ(1520) and Θ+ production in γp,πp and pp reactions

Using the Quark-Gluon Strings Model --combined with Regge phenomenology-- we perform a comparative analysis of Λ, Σ0, Λ(1520) and Θ+ production in binary reactions induced by photon, pion and proton beams on the nucleon. We find that the existing experimental data on the γp↦K+Λ differential and total cross-sections can be described very well by the model for photon energies 1-16 GeV and - t < 2 GeV2 assuming a dominant contribution of the K* Regge trajectory. Moreover, using the same parameters we also reproduce the total γp↦K+Σ0 and γp↦K+Λ(1520) cross-sections suggesting a “universality” of the Regge model. In order to check the consistency of the approach we evaluate the differential and total cross-sections for the reaction π-p↦K0Λ which is also found to be dominated by the K* Regge trajectory. Using the apparent “universality” of the Regge model we extend our scheme to the analysis of the binary reactions γp↦¯0Θ+, π-p↦K-Θ+ and pp↦Σ+Θ+ as well as the exclusive and inclusive Θ+ production in the reactions pp↦p¯0Θ+ and pp↦Θ+X. Our detailed studies demonstrate that Θ+ production does not follow the “universality” principle, thus suggesting an essentially different internal structure of the exotic baryon relative to conventional hyperons or hyperon resonances.

Regge analysis of pion-pion (and pion-kaon) scattering for energy s1/2&amp;gt;1.4 GeV

We perform a detailed Regge analysis of NN, $\ensuremath{\pi}N,$ KN, \ensuremath{\pi}\ensuremath{\pi}, and $\ensuremath{\pi}K$ scattering. From it, we find expressions that represent the \ensuremath{\pi}\ensuremath{\pi} scattering amplitudes with an accuracy of a few percent for exchange of isospin zero and \ensuremath{\sim}15% for exchange of isospin 1, and this for energies ${s}^{1/2}&gt;1.4\mathrm{GeV}$ and for momentum transfers $|t{|}^{1/2}\ensuremath{\lesssim}0.4\mathrm{GeV}.$ These Regge formulas are perfectly compatible with the low energy ${(s}^{1/2}\ensuremath{\sim}1.4\mathrm{GeV})$ scattering amplitudes deduced from \ensuremath{\pi}\ensuremath{\pi} phase shift analyses as well as with higher energy ${(s}^{1/2}\ensuremath{\gtrsim}1.4\mathrm{GeV})$ experimental \ensuremath{\pi}\ensuremath{\pi} cross sections. They are also compatible with NN, KN, and $\ensuremath{\pi}N$ experimental cross sections using factorization, a property that we check with precision. This contrasts with results from current phase shift analyses of the \ensuremath{\pi}\ensuremath{\pi} scattering amplitude, which bear little resemblance to reality in the region $1.4&lt;{s}^{1/2}&lt;2\mathrm{GeV},$ as they are not well defined and increasingly violate a number of physical requirements when the energy grows. $\ensuremath{\pi}K$ scattering is also considered, and we present a Regge analysis for these processes valid for energies ${s}^{1/2}&gt;1.7\mathrm{GeV}.$ As a by-product of our analysis, we obtain also a fit of NN, $\ensuremath{\pi}N,$ and KN cross sections valid from c.m. kinetic energy ${E}_{\mathrm{kin}}\ensuremath{\simeq}1\mathrm{GeV}$ to multi-TeV energies.

Exclusive electromagnetic production of strangeness on the nucleon: Regge analysis of recent data

In view of the numerous experimental results recently released, we provide in this paper an update on the performance of our simple Regge model for strangeness electroproduction on the nucleon. Without refitting any parameters, a decent description of all measured observables and channels is achieved. We also give predictions for spin transfer observables, recently measured at Jefferson Lab, which have high sensitivity to discriminate between different theoretical approaches.

Regge analysis of diffractive and leading baryon structure functions from deep inelastic scattering

In this paper we present a combined analysis of the H1 data on leading baryon and diffractive structure functions from DIS, which are handled as two components of the same semi-inclusive process. The available structure function data are analyzed in a series of fits in which three main exchanges are taking into account: pomeron, reggeon and pion. For each of these contributions, Regge factorization of the correspondent structure function is assumed. By this procedure, we extract information about the interface between the diffractive, pomeron-dominated, region and the leading proton spectrum, which is mostly ruled by secondary exchanges. One of the main results is that the relative reggeon contribution to the semi-inclusive structure function is much smaller than the one obtained from a analysis of the diffractive structure function alone.

Photoproduction with a leading proton at HERA

The total cross section for the photoproduction process with a leading proton in the final state has been measured at γp centre-of-mass energies W of 91, 181 and 231 GeV. The measured cross sections apply to the kinematic range with the transverse momentum of the scattered proton restricted to p T ⩽0.2 GeV and 0.68⩽ z⩽0.88, where z= E p ′/ E p is the scattered proton energy normalised to the beam energy. The cross section d σ γp→ Xp′ ( W, z)/d z is observed to be independent of W and z within the measurement errors and amounts to (8.05±0.06 ( stat)±0.89 ( syst)) μb on average. The data are well described by a Triple Regge model in which the process is mediated by a mixture of exchanges with an effective Regge trajectory of intercept α i(0)=0.33±0.04 ( stat)±0.04 ( syst) . The total cross section for the interaction of the photon with this mixture ( γα i → X) can be described by an effective trajectory of intercept α k(0)=0.99±0.01 ( stat)±0.05 ( syst) . Predictions based on previous triple Regge analyses of pp→ pX data assuming vertex factorisation are broadly consistent with the γp data. The measured cross sections are compared with deep inelastic scattering leading proton data in the same region of z and p T for photon virtuality Q 2>2.5 GeV 2 . The ratio of the cross section for leading proton production to the total cross section is found to rise with Q 2.

Triple Regge analysis of inclusiveΛ production inK + p and π+ p interactions at 250 GeV/c

A triple Regge analysis is performedof inclusive Λ production in the proton fragmentation region ofK+→Λ+X and π+→Λ+X at 250 GeV/c. Slope and intercept of the leading strange meson trajectory are determined. The results obtained here are compared with those of other experiments.

Study of Λ-production in target fragmentation region frompp interactions at 360 GeV/c in the triple regge framework

A study of Λ production has been made in the target fragmentation region frompp interactions at 360 GeV/c. The triple Regge analysis of the double differential distributiond2N/d(M2/s)dt led to an estimate of the kaon trajectory intercept as ≈-−0.6. Comparison of the double and single inclusive distributions supports the idea of Pomeron factorization. The charged multiplicities and moments from virtual ‘K+’p interactions have been studied as a function ofM, the c.m. energy of the virtual ‘K+’p system. The results agree reasonably well with the on shellK+p data.

Triple Regge analysis of the reactionπp→Λ+X at 16 GeV/c

The inclusive reactionπp→Λ+X at 16 GeV/c beam momentum has been analysed in terms of the triple Regge formalism. Assuming Pomeron dominance the effective trajectory obtained from a fit to theM 2 distribution in differentt-bins is compatible with that of theK *-trajectory. The description of the data for $$p\xrightarrow{{\pi ^ - }}\Lambda $$ at 16 GeV/c offered by this simple model is found to be remarkably good over a large region of phase space.

Elastic scattering ofC12bySi28

$^{12}\mathrm{C}$ + $^{28}\mathrm{Si}$ elastic scattering angular distributions have been measured at twenty-three bombarding energies over a range $19 \mathrm{MeV}\ensuremath{\le}{E}_{\mathrm{lab}}\ensuremath{\le}48 \mathrm{MeV}$. At energies below 30 MeV the angular distributions are smooth and can be reproduced with a wide variety of optical potentials; similarly, above 40 MeV the angular distributions exhibit diffraction oscillations which optical potentials can rather easily reproduce. Irregular structure is observed in the cross sections for angles larger than 50\ifmmode^\circ\else\textdegree\fi{} in the bombarding energy range 30-40 MeV. No optical potential has been found to give a good account of all the data; the best potential is a surface transparent Woods-Saxon potential which has energy dependences for both real and imaginary well depths. Examination of potentials which give reasonably good fits to the 36 MeV data shows that, although these potentials agree on a real well depth at a reasonable strong absorption radius, they can have quite different Argand diagrams---even in the range of the most sensitive partial waves. A Regge analysis finds several equally good families of Regge parameters for the same choice of background potential, but larger angle data might allow this ambiguity to be lifted. A Breit-Wigner analysis gives results which are at least partially consistent with the resonance parameters reported by Ost et al. Coupled-channel calculations with a 20% reduction of real and imaginary optical model well depths give a good account of inelastic scattering to the $^{28}\mathrm{Si}$ ${2}^{+}$ state while leaving the elastic scattering essentially unchanged from the predictions of the unmodified one-channel optical model. In the energy range of this study the grazing partial wave is found to be the same as the most important exit channel partial wave of the $^{24}\mathrm{Mg}$($^{16}\mathrm{O}$, $^{12}\mathrm{C}$)$^{28}\mathrm{Si}$ ground state transition.NUCLEAR REACTIONS $^{28}\mathrm{Si}$($^{12}\mathrm{C}$, $^{12}\mathrm{C}$)$^{28}\mathrm{Si}$, measured $\ensuremath{\sigma}(E,\ensuremath{\theta})$ $E=19\ensuremath{-}48$ MeV deduced optical model parameters.

A Regge analysis of np and [formula omitted]p charge exchange scattering at 8 GeV/ c

A phenomenological analysis of np and p p charge exchange scattering at 8 GeV/ c is presented and a simple model is formulated to account for the data. This model is compared to one of KN → K ∗ N and it is speculated that the model could be used to describe the reaction pp → Δ ++n.

On the parametrization of the Δ residue function

The complex residues at the Δ(1236) and Δ(1950) poles in the relevant partial-wave amplitudes provide information on the behaviour of the Δ Regge residue function in the resonance region u > 0. Attempts to incorporate this information in parametrizations of the residue by functions that are real on the real u-axis result in residues which have unsatisfactory behaviour in the region u < 1 GeV 2. The choice of complex functions for the trajectory and residue removes this undesirable feature and provides a better representation of the residue in the resonance region, suggesting that complex parametrizations would be better suited to Regge analyses of near-backward scattering.

Lepton pair production by hadronic collisions in the Regge limit

We present a refined and corrected version of our Regge analysis of inelastic muon pair production by proton-proton collision. The role of the different high-energy limits (fragmentation, pionization) is studied in full detail, both for the amplitude and for the structure functions. The possibility of Bjorken-scaling is discussed. We succeeded in giving a very simple physical interpretation of the results of the BNL-Columbia experiment.

Regge analysis of deep-inelastic lepton-nucleon scattering

The asymptotic behavior of the structure functions ${F}_{2}^{\mathrm{ep}}(x)$ and ${F}_{2}^{\ensuremath{\nu}p}(x)$ is studied in a quark-parton model. It is shown that the structure functions have the expected Regge behavior. The calculated Regge residues agree well with those obtained from pion-nucleon cross sections by an extrapolation in ${Q}^{2}$ via a weak form of generalized scaling. The total photoabsorption cross section is also reproduced in this scheme, once the over-all scale is fixed.