Regge Exchange Research Articles

Triple Regge exchange and transverse single-spin asymmetries of the very forward neutral pion production in polarized p+p collisions

Recently, the RHICf Collaboration measured the transverse single-spin asymmetries of the very forward neutral pion in polarized $p+p$ collisions at $\sqrt{s}=510$ GeV, produced at large pseudorapidity ($\eta\gtrsim 6$). The data show large asymmetries both in longitudinal momentum fraction $x_F$ and transverse momentum $p_T$ at $p_T<1\,\mathrm{GeV}/c$. Employing baryonic triple Regge exchanges, we describe the complete RHICf data for the first time and show that the neutral pion production at low $p_T$ can be interpreted as a diffractive one.

Exclusive photoproduction of π0 up to large values of Mandelstam variables s,t, and u with CLAS

Exclusive photoproduction cross sections have been measured for the process $\gamma p \rightarrow p\pi^0(e^+e^-(\gamma))$ with the Dalitz decay final state using tagged photon energies in the range of $E_{\gamma} = 1.275-5.425$ GeV. The complete angular distribution of the final state $\pi^0$, for the entire photon energy range up to large values of $t$ and $u$, has been measured for the first time. The data obtained show that the cross section $d\sigma/dt$, at mid to large angles, decreases with energy as $s^{-6.89\pm 0.26} $. This is in agreement with the perturbative QCD quark counting rule prediction of $s^{-7} $. Paradoxically, the size of angular distribution of measured cross sections is greatly underestimated by the QCD based Generalized Parton Distribution mechanism at highest available invariant energy $s=11$ GeV$^2$. At the same time, the Regge exchange based models for $\pi^0$ photoproduction are more consistent with experimental data.

Triple Regge exchange mechanisms of four-pion continuum production in the pp→ppπ+π−π+π− reaction

We consider exclusive multi-peripheral production of four charged pions in proton-proton collisions at high energies with simultaneous exchange of three pomerons/reggeons. The amplitude(s) for the genuine $2 \to 6$ process are written in the Regge approach. The calculation is performed with the help of the GenEx Monte Carlo code. Some corrections at low invariant masses in the two-body subsystems are necessary for application of the Regge formalism. We estimate the corresponding cross section and present differential distributions in rapidity, transverse momenta and two- and four-pion invariant masses. The cross section and the distributions depend on the value of the cut-off parameter of a form factor correcting amplitudes for off-shellness of $t$-channel pions. Rather large cross section is found for the whole phase space ($\sigma \sim$ 1-5 $\mu$b, including absorption corrections). Relatively large four-pion invariant masses are populated in the considered diffractive mechanism compared to other mechanisms discussed so far in the context of four-pion production. We investigate whether the triple Regge exchange processes could be identified with the existing LHC detectors. We consider the case of ATLAS and ALICE cuts. The ATLAS (or CMS) has better chances to identify the process in the region of large invariant masses $M_{4 \pi} > 10$ GeV. In the case of the ALICE experiment the considered mechanism competes with other mechanisms (production of $\sigma \sigma$, $\rho \rho$ pairs or single resonances) and cannot be unambiguously identified.

Preserving local gauge invariance witht-channel Regge exchange

Considering single-meson photo- and electroproduction off a baryon, it is shown how to restore local gauge invariance that was broken by replacing standard Feynman-type meson exchange in the t-channel by exchange of a Regge trajectory. This is achieved by constructing a contact current whose four-divergence cancels the gauge-invariance-violating contributions resulting from all states above the base state on the Regge trajectory. To illustrate the procedure, modifications necessary for the process $\gamma +p \to K^+ + \Sigma^{*0}$ are discussed in some detail. We also provide the general expression for the contact current for an arbitrary reaction.

Double-Regge exchange limit for theγp→K+K−preaction

We apply the generalized Veneziano model ($B_5$ model) in the double-Regge exchange limit to the $\gamma p \to K^+ K^- p$ reaction. Four different cases defined by the possible combinations of the signature factors of leading Regge exchanges (($K^*,a_2/f_2$), ($K^*,\rho/\omega$), ($K_2^*,a_2/f_2$), and ($K_2^*,\rho/\omega$)) have been simulated through the Monte Carlo method. Suitable event candidates for the double-Regge exchange high-energy limit were selected employing \textit{Van Hove} plots as a better alternative to kinematical cuts in the $K^+ K^- p$ Dalitz plot. In this way we predict and analyze the double-Regge contribution to the $K^+ K^- p$ Dalitz plot, which constitutes one of the major backgrounds in the search for strangeonia, hybrids and exotics using $\gamma p\rightarrow K^+K^-p$ reaction. We expect that data currently under analysis, and that to come in the future, will allow verification of the double-Regge behavior and a better assessment of this component of the amplitude.

Form factors of pseudoscalar mesons in a model with unitarity and Regge exchanges

We consider the transition and electromagnetic pseudoscalar form factors in a wide range of energy-momentum transfer, s. We employ dispersion relations to connect the time-like and space-like region. We find that hadronic resonances give sizable contributions in the currently available range of s. For the asymptotic contribution, we propose a model that operates with reggeized fermion exchanges.

Quark-nucleon dynamics and deep virtual Compton scattering

We consider deeply virtual Compton scattering and deep inelastic scattering in presence of Regge exchanges that are part of the non-perturbative quark-nucleon amplitude. In particular we discuss contribution from the Pomeron exchange and demonstrate how it leads to Regge scaling of the Compton amplitude. Comparison with HERA data is given.

Nucleon tensor charge from exclusiveπ0electroproduction

Exclusive ${\ensuremath{\pi}}^{o}$ electroproduction from nucleons is suggested for extracting the tensor charge and other quantities related to transversity from experimental data. This process isolates C-parity odd and chiral-odd combinations of t-channel exchange quantum numbers. In a hadronic picture it connects the meson production amplitudes to C-odd Regge exchanges with final state interactions. In a description based on partonic degrees of freedom, the helicity structure for this C-odd process relates to the quark helicity flip, or chiral-odd generalized parton distributions. This differs markedly from deeply virtual Compton scattering, and both vector meson and charged $\ensuremath{\pi}$ electroproduction, where the axial charge can enter the amplitudes. Contrarily, the tensor charge enters the ${\ensuremath{\pi}}^{o}$ process. The connection through the helicity description of the process to both the partonic and hadronic perspectives is studied and exploited in model calculations to indicate how the tensor charge and other transversity parameters can be related to cross section and spin asymmetry measurements over a broad range of kinematics.

Pomeron structure functions from HERA to Tevatron and LHC

The proton diffractive structure function F 2 D ( 3 ) measured in the H1 and ZEUS experiments at HERA are analysed in terms of perturbative QCD in the perspective of the QCD extrapolation to the Tevatron and the LHC. It is shown that both data sets can be well described by a QCD analysis in which point-like parton distributions, evolving according to the next-leading DGLAP equations, are assigned to the leading and sub-leading Regge exchanges. For present data from H1 and ZEUS the gluon distributions are found to be quite different and we give the corresponding sets of quark and gluon parton distributions for the Pomeron, extracted from the two experiments. An extrapolation to the Tevatron range is compared with CDF data on single diffraction. Conclusions on factorization breaking between HERA and Tevatron critically depend on whether H1 (strong violation) or ZEUS (compatibility at low β) fits are taken into account. Using the double pomeron formulation in central diffractive dijet production we show that the Tevatron mass fraction is much sensitive to the high β tail of the gluon in the pomeron, suggesting a new way of handling the otherwise badly known gluon distribution in the pomeron. Extrapolation of the fits to very high Q 2 are given since they will be relevant for QCD and diffraction studies at the LHC.

Renormalization scale-fixing for complex scattering amplitudes

We show how to fix the renormalization scale for hard-scattering exclusive processes such as deeply virtual meson electroproduction by applying the BLM prescription to the imaginary part of the scattering amplitude and employing a fixed-t dispersion relation to obtain the scale-fixed real part. In this way, we resolve the ambiguity in BLM renormalization scale-setting for complex scattering amplitudes. We illustrate this by computing the H generalized parton distribution at leading twist in an analytic quark-diquark model for the parton-proton scattering amplitude that can incorporate Regge exchange contributions characteristic of the deep inelastic structure functions.

Differential cross sections forγ+p→K++Yfor Λ andΣ0hyperons

High-statistics cross sections for the reactions gamma + p --> K^+ + Lambda and gamma + p --> K^+ + Sigma^0 have been measured using CLAS at Jefferson Lab for center-of-mass energies W between 1.6 and 2.53 GeV, and for -0.85 < cos theta_{K^+}^{c.m.}< +0.95. In the K^+ Lambda channel we confirm a resonance-like structure near W=1.9 GeV at backward kaon angles. The position and width of this structure change with angle, indicating that more than one resonance is likely playing a role. The K^+ Lambda channel at forward angles and all energies is well described by a t-channel scaling characteristic of Regge exchange, while the same scaling applied to the K^+ Sigma^0 channel is less successful. Several existing theoretical models are compared to the data, but none provide a good representation of the results.

Photoproduction of theΘ+resonance on the nucleon in a Regge model

We estimate the reaction mechanisms for the photoproduction of the ${\ensuremath{\Theta}}^{+}(1540)$ resonance on the nucleon, through $K$ and ${K}^{*}$ Regge exchanges. We compare the size of the cross sections for the $\ensuremath{\gamma}n\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\Theta}}^{+}$ and $\ensuremath{\gamma}p\ensuremath{\rightarrow}{\overline{K}}^{0}{\ensuremath{\Theta}}^{+}$ reactions and investigate their sensitivity to the spin-parity assignments ${J}^{P}={\frac{1}{2}}^{\ifmmode\pm\else\textpm\fi{}},{\frac{3}{2}}^{\ifmmode\pm\else\textpm\fi{}}$ for the ${\ensuremath{\Theta}}^{+}$ resonance. The model allows one to estimate the cross sections corresponding with a given upper bound on the width of the ${\ensuremath{\Theta}}^{+}$. Within this model, the cross sections on the neutron are found to be around a factor of 5 larger than the ones on the proton, due to the presence of charged $K$ exchange for the reaction on a neutron target. Furthermore, the photon asymmetry is found to display a pronounced sensitivity to the parity of the ${\ensuremath{\Theta}}^{+}$, making it a very promising observable to help determine the quantum numbers of the ${\ensuremath{\Theta}}^{+}$ resonance.

Final state interactions for B→VV charmless decays

We estimate final state interactions in the $B$-meson decays into two light vector mesons by the Regge model. We consider Pomeron exchange and charmed Regge trajectories that can relate intermediate charmed particles to the final state. The Regge poles have various helicity-flip residues, which allows a change from the longitudinal to transverse polarization. In this way a significant reduction of the longitudinal polarization fraction can be produced. In the factorization approximation we find agreement with recent data from the BABAR and Belle Collaborations in the $B\ensuremath{\rightarrow}{K}^{*}\ensuremath{\phi}$ decay channel, as a result of an appropriate choice of semileptonic form factors and Regge exchanges. On the other hand, data for the ${K}^{*}\ensuremath{\rho}$ decay channels appear more elusive. The soft effects discussed in the present paper are based on a model of Regge trajectories that is shown to reproduce correctly in the noncharmed case the Regge phenomenology of light mesons.

The process $\gamma(^*) + p \to \eta_c + X$ : a test for the perturbative QCD odderon

The rates of inclusive photo- and electroproduction of the eta_c meson: gamma* + p -> eta_c + X are calculated in the triple Regge region, integrated over the diffractive mass X. For the Regge exchanges we use the hard Pomeron and Odderon, both being calculated in the framework of perturbative QCD. The integrated cross-section depends upon the coupling of the BFKL pomeron to two $C=-1$ odderons, and it is found to be of the order 60 pb for photoproduction and 1.5 pb at Q^2=25 GeV^2.

MULTIPARTICLE PHASE SHIFT ANALYSIS IN PERIPHERAL PRODUCTION EXPERIMENTS: LESSONS FROM THE PAST

We recall some of our understanding of meson resonance production in high energy collisions from 20 years ago and its implications for a new generation of high statistics experiments. We discuss S-matrix theory, duality and Regge exchanges. We briefly mention some computing issues.

Resonance-reggeon and parton-hadron duality in strong interactions

By using the concept of duality between direct channel resonances and Regge exchanges we relate the small- and large-$x$ behavior of the structure functions. We show that even a single resonance exhibits Bjorken scaling at large $Q^2$.

QCD analysis of the diffractive structure functionF2D(3)

The proton diffractive structure function $F_2^{D(3)}$ measured in the H1 and ZEUS experiments at HERA is analyzed in terms of both Regge phenomenology and perturbative QCD evolution. A new method determines the values of the Regge intercepts in ``hard'' diffraction, confirming a higher value of the Pomeron intercept than for soft physics. The data are well described by a QCD analysis in which point-like parton distributions, evolving according to the DGLAP equations, are assigned to the leading and sub-leading Regge exchanges. The gluon distributions are found to be quite different for H1 and ZEUS. A {\it global fit} analysis, where a higher twist component is taken from models, allows us to use data in the whole available range in diffractive mass and gives a stable answer for the leading twist contribution. We give sets of quark and gluon parton distributions for the Pomeron, and predictions for the charm and the longitudinal proton diffractive structure function from the QCD fit. An extrapolation to the Tevatron range is compared with CDF data on single diffraction. Conclusions on factorization breaking depend critically whether H1 (strong violation) or ZEUS (compatibility at low $\beta$) fits are taken into account.

Contribution of inelastic rescattering toB→ππ,KK¯decays

We discuss multichannel inelastic rescatterring effects in B decays into a pair $PP$ of pseudoscalar mesons ($PP = \pi \pi$ or $K\bar{K}$). In agreement with short-distance models it is assumed that initially $B$ meson decays dominantly into jet-like states composed of two flying-apart low-mass resonances $M_1 M_2$ which rescatter into $PP$. Since from all S-matrix elements $<i|S|PP>$ involving $PP$ only some ($i = M_1 M_2$) contribute to the final state rescatterring, the latter is treated as a correction only. The rescatterring of resonance pair $M_1 M_2$ into the final $PP$ state is assumed to proceed through Regge exchange. Although effects due to a single intermediate state $M_1 M_2$ are small, it is shown that the combined effect of all such states should be large. In particular, amplitudes of B decays into $K\bar{K}$ become significantly larger than those estimated through short-distance penguin diagrams, to the point of being comparable to the $B\to \pi \pi$ amplitudes.

Λ polarization in associated K+– Λ electro-production

The result of a feasibility study to measure the Λ polarization in associated K +– Λ electro-production is presented. This measurement was performed in the experimental Hall C at Jefferson Lab. The scattered electron was detected in the HMS spectrometer, and the electro-produced kaon and the proton from the Λ→ pπ − decay were both detected in the SOS spectrometer. This quantity is very sensitive to the elementary p( e, e′ K) Λ process and gives information on resonance production, and Regge exchange, among others. The result presented was measured at Q 2=1.50 (GeV/c) 2 and cos θ Kγ CM=14°. The limits of the Λ polarization, with respect to the p γ× p K axis, were found to be −0.21 and +0.89 with a confidence level of 68%. The result is compared to theoretical predictions based on an effective hadronic field Lagrangian model and a Regge framework model.

Long-range two-body final-state interactions and directCPasymmetry inB+→π+K0decay

We present a calculation of the direct $\mathrm{CP}$ asymmetry ${A}_{\mathrm{CP}}^{\mathrm{dir}}$ for the process ${B}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{K}^{0}$ including the effects of long-range two-body inelastic final-state interactions (FSI). We admit four two-body channels in our calculation: ${B}^{+}\ensuremath{\rightarrow}({\ensuremath{\pi}}^{+}{K}^{0}),(\ensuremath{\eta}{K}^{+}),$ ${(D}_{s}^{+}{D}^{0})$ and the charge-exchange channel ${\ensuremath{\pi}}^{0}{K}^{+}.$ The strong scattering is described in terms of Pomeron and Regge exchanges. We find that the direct $\mathrm{CP}$ asymmetry is enhanced by a factor of $\ensuremath{\sim}3$ as a result of FSI, but remains well short of the claims of (10--20)% in recent literature. A critical assessment of papers claiming large $\mathrm{CP}$ asymmetries is also presented. Many-body decay channels could play an important role in direct $\mathrm{CP}$ asymmetry; however, their contribution is hard to estimate.