Pomeron Pole Research Articles

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.

Pomeron pole plus grey disk model: Real parts, inelastic cross sections and LHC data

I propose a two component analytic formula $F(s,t)=F^{(1)}(s,t)+F^{(2)}(s,t)$ for $(ab\rightarrow ab) +(a\bar{b}\rightarrow a\bar{b})$ scattering at energies $\ge 100 GeV$ ,where $s,t$ denote squares of c.m. energy and momentum transfer.It saturates the Froissart-Martin bound and obeys Auberson-Kinoshita-Martin (AKM) \cite{AKM1971} scaling. I choose $Im F^{(1)}(s,0)+Im F^{(2)}(s,0)$ as given by Particle Data Group (PDG) fits to total cross sections. The PDG formula is extended to non-zero momentum transfers using partial waves of $Im F^{(1)}$ and $Im F^{(2)}$ motivated by Pomeron pole and 'grey disk' amplitudes . $Re F(s,t)$ is deduced from real analyticity: I prove that $Re F(s,t)/ImF(s,0) \rightarrow (\pi/\ln{s}) d/d\tau (\tau Im F(s,t)/ImF(s,0) )$ for $s\rightarrow \infty$ with $\tau=t (ln s)^2$ fixed, and apply it to $F^{(2)}$.Using also the forward slope fit by Schegelsky-Ryskin , the model gives real parts,differential cross sections for $(-t)<.3 GeV^2$, and inelastic cross sections in good agreement with data at $546 GeV, 1.8 TeV,7 TeV$ and $ 8 TeV $. It predicts for inelastic cross sections for $pp$ or $\bar{p} p$, $\sigma_{inel}=72.7\pm 1.0 mb$ at $7TeV$ and $74.2 \pm 1.0mb$ at $8 TeV$ in agreement with $pp$ Totem experimental values $73.1\pm 1.3 mb $ and $74.7\pm 1.7 mb$ respectively, and with Atlas values $71.3\pm 0.9 mb$ and $71.7\pm 0.7mb$ respectively. The predictions at $546 GeV$ and $1800 GeV$ also agree with $\bar{p} p$ experimental results of Abe et al \cite{Abe} at $546 GeV$ and $1800 GeV$. The model yields for $\sqrt{s}> 0.5 TeV$, with PDG2013 total cross sections , and Schegelsky-Ryskin slopes as input, $\sigma_{inel} (s) =22.6 + .034 ln s + .158 (ln s)^2 mb , and \sigma_{inel} / \sigma_{tot} \rightarrow 0.56, s\rightarrow \infty ,$ where $s$ is in $GeV^2$

Lessons from LHC elastic and diffractive data

We discuss a model which gives a ‘global’ description of the wide variety of high-energy elastic and diffractive data that are presently available, particularly from the LHC experiments. The model is based on only one pomeron pole, but includes multi-pomeron interactions. Significantly, the LHC measurements require that the model includes the transverse momentum dependence of the intermediate partons as a function of their rapidity, which results in a rapidity (or energy) dependence of the multi-pomeron vertices.

Elastic scattering and diffractive dissociation in the light of LHC data

We study the behavior of elastic and diffractive proton dissociation cross sections at high energy. First, we describe what would be expected to be observed at the Large Hadron Collider (LHC) based on conventional Regge theory. We emphasize the tension between these expectations and the recent LHC measurements, and we discuss the possibilty to modify the classic Reggeon Field Theory (RFT) in a physically-motivated way so as to accommodate the tendencies observed at the LHC. As a result, we show that we are able to achieve a "global" description of the wide variety of high energy elastic and diffractive data that are presently available, particularly from the LHC experiments. The model is based on only one pomeron pole, but includes multi-pomeron interactions and, significantly, includes the transverse momentum dependence of intermediate partons as a function of their rapidity, which provides the rapidity dependence of the multi-pomeron vertices. We give predictions for diffractive observables at LHC, and higher, energies.

High-energy elastic and diffractive cross sections

We present a `global' description of the wide variety of high energy elastic and diffractive data that are presently available, particularly from the LHC experiments. The model is based on only one pomeron pole, but includes multi-pomeron interactions and, significantly, includes the transverse momentum dependence of intermediate partons as a function of their rapidity, which provides the rapidity dependence of the multi-pomeron vertices. We give predictions for diffractive observables at LHC energies.

Proton (antiproton) elastic scattering at energies from FNAL to the LHC in the tripole Pomeron-Odderon model

The model of elastic scattering amplitudes dominated by the triple (at $t=0$) pomeron pole suggested earlier is modified to confront to existing experimental data on $pp$ and $\bar pp$ total and differential cross sections at $\sqrt{s}\geq 19$ GeV and $|t|\leq 14.2$ GeV$^{2}$ including the newest TOTEM data. Predictions for the future TOTEM measurements at 13 and 14 TeV are given.

Pomeron loops in the perturbative QCD with large N c

The lowest order pomeron loop is calculated for the leading conformal weight with full dependence of the triple-pomeron vertex on intermediate conformal weights. The loop is found to be convergent. Its contribution to the pomeron Green function begins to dominate already at rapidities 10–15. The pomeron pole renormalization is found to be quite small due to a rapid fall of the triple-pomeron vertex with rising conformal weights.

Evidence for the discrete asymptotically-free BFKL Pomeron from HERA data

We show that the next-to-leading-order renormalization-group-improved asymptotically-free BFKL Pomeron provides a good fit to HERA data on virtual photoproduction at small x and large Q2. The leading discrete Pomeron pole reproduces qualitatively the Q2 dependence of the HERA data for x∼10−3, and a fit using the three leading discrete singularities reproduces quantitatively the Q2 and x dependence of the HERA data for x<10−2. This fit fixes the phase for all the BFKL wavefunctions at a chosen infrared scale.

Unitarisation and black-disk limit at the LHC in the presence of a hard pomeron

Recent models of soft diffraction include a hard pomeron pole besides the usual soft term. Such models violate the black-disk limit around Tevatron energies, so that they need to be supplemented by a unitarisation scheme. Two standard schemes are considered in this Letter, and we show that they lead to an uncertainty at the LHC much larger than previously estimated. We also examine the signature of unitarisation on various small-t observables, the slope in t of the elastic cross section, or the ratio of the real to imaginary parts of the scattering amplitude, and show that the existence of a unitarised hard pomeron in soft scattering may be confirmed by LHC data.

Elasticppandp¯pscattering in models with a unitarized Pomeron

Elastic scattering amplitudes dominated by the Pomeron singularity which obey the principal unitarity bounds at high energies are constructed and analyzed. Confronting the models of double and triple (at $t=0$) Pomeron pole (supplemented by some terms responsible for the low energy behavior) with existing experimental data on $pp$ and $\overline{p}p$ total and differential cross sections at $\sqrt{s}\ensuremath{\ge}5\text{ }\text{ }\mathrm{GeV}$ and $|t|\ensuremath{\le}6\text{ }\text{ }{\mathrm{GeV}}^{2}$ we are able to tune the form of the Pomeron singularity. Actually the good agreement with the data is received for both models though the behavior given by the dipole model is more preferable in some aspects. The predictions made for the LHC energy values display, however, the quite noticeable difference between the predictions of models at $t\ensuremath{\approx}\ensuremath{-}0.4\text{ }\text{ }{\mathrm{GeV}}^{2}$. Apparently the future results of TOTEM experiment will be more conclusive to make a true choice.

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.

Integral and derivative dispersion relations, analysis of the forward scattering data

Integral and derivative dispersion relations (DR) are considered for the forward scattering $pp$ and $\bar pp$ amplitudes. A new representation for the derivative DR, valid not only at high energy, is obtained. The data on the total cross sections for $pp (\bar pp)$ interaction as well as the data on the parameter $\rho $ are analyzed within the various forms of the DR and high-energy Regge models. It is shown that three models for the Pomeron, Simple pole Pomeron, Tripole Pomeron and Dipole Pomeron (the both with the intercept equal unit) lead to practically equivalent description of the data at $\sqrt{s}>$5 GeV. It is also shown that the correctly calculated low-energy part of the dispersion integral (from the two-proton threshold up to $\sqrt{s}=$5 GeV) allows to reproduce well the $\rho $ data at low energies without additional free parameters.

DGLAP evolution extends the triple pole Pomeron fit

We show that the triple pole pomeron model \cite{CMS} provides an initial condition for a DGLAP evolution \cite{DGLAP} that produces a fit to high $Q^2$ experimental DIS data. We obtain good $\chi^2$ for initial scales down to 3 GeV$^2$. Values of the initial scale smaller than 1.45 GeV$^2$ are ruled out at the 90% confidence level.

Coherent and incoherent particle production off nuclei at high energies

The Glauber-Gribov model for hadronnucleus scattering is extended to multiproduction processes by supplimenting it with the AGK cutting rules. In contrast to the standard Glauber approach neither smallness of the interaction radius compared to the nuclear radii nor Gaussian form of theh-N-interaction profile function are assumed. We consistently use the theory of superciritical Pomeron. However all the results are more general and do not depend on the specific parametrization of the Pomeron pole amplitude. The inelastic screening due to the low mass diffractive excitations is also included. The cross-sections of coherent and incoherent diffractive production of the low mass hadronic states are calculated. We comment on the novel features of particle-nucleus interactions at superhigh energies when the interaction region blows up to the nucleus size. Specifically, one encounters here the rapid rise of the coherent interaction cross-sections and strong suppression of incoherent quasielastic processes.

Topological cross-section in hadron-nucleus collisions and multiple scattering theory

The multiple scattering theory supplemented with AGK cutting rules is applied to calculation of the hadron-nucleus interaction cross-sections. In contrast to standard Glauber approach neither smallness of the interaction radius compared to the nuclear radii nor Gaussian form of thehN-interaction profile function are assumed. We consistently use the theory of the supercritical Pomeron. However all the results are more general and do not depend on the specific parametrization of the Pomeron pole ampletude. The region of validity of the widely used approximate formulae for topological and totalhA-interaction cross sections are discussed. It is discussed the novel features of particle-nucleus interactions at superhigh energies.

High-energy pp elastic scattering and evidence for a nucleon core of valence quarks

High-energy pp elastic scattering is analyzed in a model that incorporates a hard mechanism besides diffraction. The hard process is responsible for large-momentum-transfer scattering, while diffraction dominates the small-momentum-transfer region. Orear fall-off (dσ/dt∼exp[−bp⊥]) is taken as the basic characteristic behavior of the large-t scattering. The origin of this behavior is explored and is attributed to a smoothed Yukawa potential. The form of this potential indicates that each nucleon has a core and the two cores interact via meson exchange. The model provides an overall quantitative picture of pp elastic scattering that extends over the energy rangeEL≅(15÷1500) GeV and |t|≅(0÷15) (GeV)2, where dσ/dt drops more than ten decades. This is regarded as evidence for the existence of the nucleon core. Diffraction, as a by-product, is found to be well represented by as-channel pomeron pole. Physical implications of the core are explored. The core is interpreted as originating from the distribution of valence quarks in a nucleon. The valence quarks, being confined in a small region, are found to have large average transverse momentum consistent with the values indicated by large-p⊥ inelastic processes. The core is also identified with the repulsive nucleon core known in low-energyNN interaction. The model is found to join smoothly with the quark interchange model of pp high-energy large-angle scattering.

Dual unitarization scheme with several trajectories

Consequences of bootstrap with several input Regge trajectories are investigated. We find that in a general (without the duality-diagrams constraints) treatment of bootstrap, consistency requires the intercept of the output Pomeron pole in the one-dimensional case to be larger than one: ${\ensuremath{\alpha}}_{P}(0)&gt;1$, a situation reminiscent of the one in Reggeon field theory. Symmetry breakings of the Pomeron couplings are discussed. These couplings coincide with those of the $f$-dominated Pomeron model of Carlitz, Green, and Zee (CGZ). The case when in the unitarity loops all possible trajectories are exchanged is also considered. Predictions of the dual unitary model for the slopes of differential cross sections for diffractive scattering are made which differ from those of the CGZ model. A comparison with the experimentally available data is performed.

Flavor and baryon quantum numbers and their nondiffractive renormalizations of the Pomeron

We present a theoretical review and a detailed phonomenological description of the ''flavoring'' of the bare Pomeron pole at t = 0 (i.e., the nondiffractive renormalization of its multiperipheral unitarity sum by strange quarks, charmed quarks, diquarks,...) from an ''unflavored'' intercept alpha-circumflex = 0.85 to a ''flavored'' intercept ..cap alpha.. approx. = 1.08. Experimentally, flavoring effects seem to converge rapidly; hence this number is probably close to the bare intercept of the Reggeon field theory. We treat NN, ..pi..N, and KN total cross sections and real to imaginary amplitude ratios. We do not observe oscillations. We pay particular attention to 2sigma/sub K/N - sigma/sub piN/ which rises monotonically. We present a closely related combination of inelastic diffraction cross sections which decreases monotonically, indicating that vacuum amplitudes are not simply the sum of a Pomeron pole and an ideally mixed f. In fact we argue that a Pomeron + f structure is neither compatible with flavoring nor with schemes in which flavoring is somehow absorbed away. In contrast, flavoring is required for consistency with experiment by the Chew-Rosenzweig hypothesis of the Pomeron-f identity. We close with a description of flavoring threshold effects on the Reggeon field theory at current energies.

Regge cuts and large-| t| pp scattering

It is shown that recent measurements of the large-| t| pp elastic-scattering differential cross section at FNAL and CERN-ISR agree with earlier predictions based on the dominance of a pomeron pole(P) with αp( t) = 1.067 + 0.10 t, and a P ⊗ P cut, out to the largest measured | t| values (12 GeV 2). Some of the problems raised by this success are discussed.

Universality of the clothed, physical pomeron

Cosmic-ray da t a hint the possible b reakdown of the s t ra igh t forward ex t rapola t ion of the I n s physics to beyond 100 TeV (1). In any case, the na ive phenomenology based on the idea of the bare simple pole pomeron will sooner or la te r become i r re levant at ex t r eme ly high energies, bu t ins tead the concept of the c lo thed physical pomeron wil l t u rn out to be more and more i m p o r t a n t at least for the self-consistent in te rp re ta t ion of diffract ive phenomena at a sympto t i ca l ly high energies (2.4). The clothed pomeron is of ten referred to as the geometr ica l pomeron (GP) (4). The GP is universal in the sense tha t the c lothed pomeron is a lmost independen t of the detai led dynamics bui ld ing up and uni tar iz ing the bare pomeron. All unusual features of the physical pomeron are inheren t in universa l i ty of the GP. Accordingly the concept of universa l i ty plays the role of the most impor t an t guiding principle in pomeron physics (:.4). I t is then na tu ra l to ask how the GP universa l i ty is dynamica l ly guaran teed and how the universal GP affects no rma l reggeons under reggeon-pomeron interact ions . Solutions to these key questions are seeked in this short note. Pr incipal consequences of the GP universa l i ty in reggeon-pomeron in teract ions are discussed from the t -channel point of view. In addi t ion the responsibi l i ty of the so-called hiding cut mechanism (HCM) (5) of 0 e h m e type for un iversa l i ty of the GP is clarified. Le t us recap i tu la te the GP pa ramet r i za t ion which furnishes the most perspicacious subs tant ia t ion of universa l i ty of the physical pomeron. The GP par t ia l -wave amplitude IF(t, J ) is expressed by (2,4)