Secondary Reggeons Research Articles

Soft-photon radiation in high-energy proton-proton collisions within the tensor-Pomeron approach: Bremsstrahlung

We discuss diffractive processes in proton-proton collisions at small momentum transfers without and with photon radiation. We consider the soft exclusive reactions $pp\ensuremath{\rightarrow}pp$, $p\overline{p}\ensuremath{\rightarrow}p\overline{p}$, and $pp\ensuremath{\rightarrow}pp\ensuremath{\gamma}$ within the tensor-Pomeron and vector-odderon approach. We compare our results with the data for $pp$ and $p\overline{p}$ total cross sections, for the ratio of real to imaginary parts of the forward scattering amplitude, and for the elastic $pp$ cross sections, especially those from TOTEM. To describe the low-energy data more accurately, the secondary reggeons must be included. We write down the amplitudes for the photon bremsstrahlung in high-energy proton-proton collisions using the tensor-Pomeron model. These results are relevant for the c.m. energies presently available at the Relativistic Heavy Ion Collider and at the LHC. We present predictions for the proposed measurements of soft photons with the planned future upgrade of the ALICE experiment at the LHC. We investigate the limits of applicability of the soft-photon approximation (SPA) based on Low's theorem. The corresponding SPA results are compared to those obtained from our complete model. The regions of phase space are given quantitatively where SPA and our complete tensor-Pomeron results are close to each other. As an example, let ${k}_{\ensuremath{\perp}}$, $\mathrm{y}$, and $\ensuremath{\omega}$, be the absolute value of the transverse momentum, the rapidity, and the energy of the photon, respectively, in the overall c.m. system. For the region $1\text{ }\text{ }\mathrm{MeV}<{k}_{\ensuremath{\perp}}<100\text{ }\text{ }\mathrm{MeV}$ and $3.5<|\mathrm{y}|<5.0$, we find that the SPA Ansatz with only the pole terms $\ensuremath{\propto}{\ensuremath{\omega}}^{\ensuremath{-}1}$ agrees at the percent level with our complete model result up to $\ensuremath{\omega}\ensuremath{\cong}2\text{ }\text{ }\mathrm{GeV}$.

Isolating the Odderon in central production in high energy pA and AA collisions

We study the rapidity dependence of the central exclusive production cross sections of C-even mesons in pA and AA collisions, where A is a heavy ion. We observe qualitatively different behaviour of the contributions arising from gamma -Odderon and Pomeron–Pomeron fusion mechanisms. This can be used to extract the Odderon signal from the events of f_2 mesons exclusively produced in the forward region. Estimates, obtained using expected values of the Odderon cross section, indicate that the gamma -Odderon contribution may exceed by a few times the Pomeron-induced background in Pb–Pb collisions. Moreover, the Odderon effect can be clearly seen in terms of the asymmetry in pA and AA collisions with the beam and target reversed. It is particularly interesting to note that the asymmetry for gamma -Odderon fusion reaches its maximum value close to 1 in the forward direction, whereas the asymmetry for the Pomeron–Pomeron fusion contribution is small. The role of additional interactions of the f_2 meson with nucleons in the heavy ion, and also the contributions from secondary Reggeons, are estimated. The photon–Odderon contribution has a large normalisation uncertainty but the enhanced cross-section in the forward region combined with a large asymmetry increases the chance of experimentally detecting the Odderon.

The odderon: myths and reality

In the framework of a Regge-pole model, we discussthe forward phase of the proton-proton elastic scattering amplitude (ρ(13 TeV) = 0.1 ± 0.01), recently measured at the LHC. Our model includesa dipole pomeron, odderon and secondary reggeon exchanges. It accommodetes forthe low- |t| «break» (departure from the exponential behavior of the diffraction cone), the accelerating rise with energy of the forward slope B(s, t = 0) and absence of secondary dips and bumps. Contrary to the majority of Regge-pole models, our approach is based on he use of a dipole (double pole) pomeron (DP). It has a number of advantages over the conventional simple pole pomeron: DP generates rising cross sections even at unit pomeron intercept and, what is even more important, it produces a single diffraction minimum and maximum in the differential cross section, in accord with the experimental data. Relative contributions from different components to the scattering amplitude are evaluated from the fitted model.

CGC/saturation approach: Secondary Reggeons and [formula omitted] dependence on energy

In this letter we demonstrate that a model based on the CGC/saturation approach, successfully describes soft interaction collisions for the wide range of W=s=30GeV÷13TeV including the new TOTEM data at 13 TeV. We have now incorporated the secondary Reggeons in our approach this enables us to describe the complete set of the soft data, including the energy behavior of ρ the ratio of the real to imaginary parts of the elastic scattering amplitude. We argue that it is premature to claim that an odderon contribution is necessary, but estimate its possible strength as 1 mb to the real part of the amplitude at W=13 TeV. We show that the odderon contribution depends on the value of energy leading to ReA(s,t=0)=8 mb at W=21.2 GeV. Bearing this in mind we do not believe that ρ at high energies is the appropriate observable for detecting the odderon contribution. The successful description of the soft data in the wide range of energy strengthens our claim that the CGC/saturation approach is the only viable candidate for an effective theory for high energy QCD.

High-energy single diffractive dissociation of nucleons and the 3P-model applicability range

The adequacy of the triple-Pomeron interaction approximation (the 3P-model) for description of the high-energy single diffractive dissociation of nucleons is analyzed via application to the available experimental data on nucleon–nucleon scattering, including the recent results produced by CMS Collaboration which allow to estimate reliably the triple-Pomeron coupling value. It is argued that the total contribution of secondary Reggeon exchanges is not negligible up to the Tevatron energy.

Nonlinearity of Regge trajectories in the scattering region

The nonlinearity of Regge trajectories at real negative values of the argument is discussed as their general QCD-inspired property. The processes of elastic diffractive scattering $p+p\to p+p$ and $\bar p+p\to\bar p+p$ at collision energies $\sqrt{s}>23 GeV$ and transferred momenta squared $0.005 GeV^2<-t<3 GeV^2$ are considered in the framework of the Regge-eikonal model \cite{arnold}. By comparison of phenomenological estimates with available experimental data on angular distributions it is demonstrated that in this kinematical range the data can be satisfactorily described as if taking into account only three nonlinear Regge trajectories with vacuum quantum numbers (``soft'' pomeron, C-even $f_2/a_2$-reggeon and $C$-odd $\omega/\rho$-reggeon). It is also shown that their nonlinearity is essential and not to be ignored. The correspondence of the Kwiecinski $q\bar q$-pole \cite{kwiecinski} to the secondary reggeons and the relevance of the Kirschner-Lipatov ``hard'' pomeron pole \cite{kirschner} to elastic diffraction are discussed.

An analysis on extrema and constrained bounds for the soft pomeron intercept

We investigate some aspects and consequences of the extrema bounds for the soft pomeron intercept, recently determined by means of global fits to pp and p ¯ p total cross section data at both accelerator and cosmic-ray energy regions (scattering data). We also examine the effects of the secondary reggeons by introducing fitted trajectories from Chew–Frautschi plots (spectroscopy data) and determining new constrained bounds for the pomeron intercept. In both cases we extend the analysis to baryon– p, meson– p, baryon– n, meson– n, gamma– p and gamma– gamma scattering, presenting tests on factorization and quark counting rules. We show that in all the cases investigated, the bounds lead to good descriptions of the bulk of experimental data on the total cross sections, but with different extrapolations to higher energies. Our main conclusion is that the experimental information presently available on the above quantities is not sensitive to an uncertainty of 2% in the value of the soft pomeron intercept. At 14 TeV (CERN LHC) the extrema and constrained bounds allow to infer σ tot = 114 ± 25 mb and 105 ± 10 mb , respectively.

γ*γ* SCATTERING VIA SECONDARY REGGEON EXCHANGE IN QCD

We summarize the results on the high energy behavior of quark–antiquark exchange in γ*γ* elastic scattering. The ladder diagrams, summed in the double logarithmic approximation, provide a perturbative QCD model for secondary reggeon exchange.

Quark-antiquark exchange in γ* γ* scattering

We calculate the high energy behavior of quark-antiquark exchange in $\gamma^* \gamma^*$ elastic scattering by summing, to all orders, the leading double logarithmic contributions of the QCD ladder diagrams. Motivation comes from the LEP data for $\sigma_{tot}^{\gamma^* \gamma^*}$ which indicate the need for secondary reggeon exchange. We show that, for large photon virtualities, this exchange is calculable in pQCD. This applies, in particular, to parts of the LEP kinematic region.

Secondary reggeons in perturbative QCD

Using the Kirschner-Lipatov equation as a basis, we study high energy elastic quark-quark amplitudes, which correspond to secondary Reggeons and pion exchange in the double-logarithmic approximation of perturbative QCD.

Mechanism for the double-spin asymmetry in electromagnetic ρ production at HERMES

We calculate the contribution of meson and Pomeron exchanges to the double-spin asymmetry in \ensuremath{\rho}-meson electromagnetic production at HERMES energies. We show that the observed double-spin asymmetries, which are large, can be explained by the interference between the natural parity ${f}_{2}$-secondary Reggeon and the unnatural parity anomalous ${f}_{1}$ exchanges.

The modified additive quark model applied to the elastic and charge exchange pion proton reaction

The modified additive quark model (MAQM) successfully used in pp and p p elastic scattering and also in pion proton total cross section is applied to the description of differential cross section in pion proton scattering (elastic and charge exchange). The spin-flip components of pomeron and secondary reggeons are included permitting to describe polarization.

The role of secondary reggeons in central meson production

We estimate the contribution of f_2 trajectory exchange to the central \eta and \eta^\prime production. It is shown that secondary Reggeons may give a large contribution to processes of double diffractive meson production at high energy.

Leading baryon production in deep inelastic scattering at HERA

Deep-inelastic scattering events with a leading baryon have been detected by the H1 experiment at HERA using a forward proton spectrometer and a forward neutron calorimeter. Semi-inclusive cross sections have been measured in the kinematic region 2 ⩽ Q 2 ⩽ 50 GeV 2, 6·10 −5 ⩽ x ⩽ 6·10 −3 and baryon p T ⩽ 200 MeV. A Regge model of leading baryon production which consists of pion, pomeron and secondary reggeon exchanges gives an acceptable description of both semi-inclusive cross sections in the region 0.1 ⩽ x P ⩽ 0.3. The leading neutron data are used to estimate the structure function of the pion at small Bjorken- x.

The additive quark model revisited: Hadron- and photon-induced cross sections

The standard additive quark model and the ensuing counting rules are modified to take into account not only the quark–gluonic content of the Pomeron but also of the secondary Reggeons, as well as the fact that the soft Pomeron is not just a gluonic ladder. A much-improved description of pp, $\pi p$ , $\gamma p$ and $\gamma \gamma$ cross sections is obtained.

The additive quark model revisited: Hadron- and photon-induced cross sections

The standard additive quark model and the ensuing counting rules are modified to take into account not only the quark–gluonic content of the Pomeron but also of the secondary Reggeons, as well as the fact that the soft Pomeron is not just a gluonic ladder. A much-improved description of pp, $\pi p$ , $\gamma p$ and $\gamma \gamma$ cross sections is obtained.

Measurement of leading proton and neutron production in deep-inelastic scattering at HERA

Deep--inelastic scattering events with a leading baryon have been detected by the H1 experiment at HERA using a forward proton spectrometer and a forward neutron calorimeter. Semi--inclusive cross sections have been measured in the kinematic region 2 = 160 GeV. The measurements are used to test production models and factorization hypotheses. A Regge model of leading baryon production which consists of pion, pomeron and secondary reggeon exchanges gives an acceptable description of both semi-inclusive cross sections in the region 0.7 <= E'/E_p <= 0.9, where E_p is the proton beam energy. The leading neutron data are used to estimate for the first time the structure function of the pion at small Bjorken--x.

Hard diffraction at HERA in the dipole model of BFKL dynamics

Using the QCD dipole picture of the hard BFKL pomeron, we derive the general expressions of the elastic and inelastic components of the proton diffractive structure functions. We obtain a good seven-parameter fit (including a secondary reggeon contribution) to data taken at HERA by the H1 and ZEUS Collaborations. The main characteristic features of the model in reproducing the data are discussed, namely the effective pomeron intercept, the scaling violations and the β-dependence. A difference obtained in the separate H1 and ZEUS fits leads us to analyze directly the differences between both measurements. Predictions on R, the ratio of longitudinal to transverse photon cross sections are performed and lead to very large values at high beta and large virtuality Q which may lead to a discrimination between models.

Pomeron and odderon in high energypp and $$p\bar p$$ elastic scattering

High energypp and\(p\bar p\) data on elastic scattering and total cross sections are analyzed in a model including the pomeron, odderon and secondary reggeons. A dipole model is used for the pomeron and for the odderon. By construction, our (bare) pomeron ansatz produces a single dip, as observed experimentally. The model reproduces the logarithmically rising cross sections with a unit pomeron intercept, but better fits are obained when a small non-zero value of the parameter δ = αp (0) is allowed for. Predictions for the future accelerators (UNK, LHC, SSC) are given.

The Pomeron from dual models: beyond the naive geometrical picture

A generalization of the geometrical model of Chou and Yang incorporating energy dependence and analyticity is suggested. It is based on a Pomeron exchange with a trajectory αP(t)=α0 − γ ln(1−βt) suggested by suitably approximating analyticity preserving dual models. Various limits and approximations are discussed and it is shown how, naturally, one is lead to energy dependent form factors. An explicit Born approximation to the Pomeron is constructed, the secondary reggeons are properly added and the eikonalization procedure is carried out. The description of the high energypp\(\bar p\)p data is shown to improve considerably not only when the radii increase with energy but even more so when this increase is different for protons and antiprotons. Taken at face value, our analysis implies that thepp interaction size increases faster than the\(\bar p\)p one with increasing energy. LHC energies would prove or disprove quite clearly our claim.