Central exclusive diffractive production of $π^{+}π^{-}$ continuum, scalar and tensor resonances in $pp$ and $p \bar{p}$ scattering within tensor pomeron approach
Piotr Lebiedowicz, Otto Nachtmann, Antoni Szczurek
We consider central exclusive diffractive dipion production in the reactions $pp \to pp π^{+} π^{-}$ and $p\bar{p} \to p\bar{p} π^{+} π^{-}$ at high energies. We include the dipion continuum, the dominant scalar $f_{0}(500)$, $f_{0}(980)$, and tensor $f_{2}(1270)$ resonances decaying into the $π^{+} π^{-}$ pairs. The calculation is based on a tensor pomeron model and the amplitudes for the processes are formulated in terms of vertices respecting the standard crossing and charge-conjugation relations of Quantum Field Theory. The formulae for the dipion continuum and tensor meson production are given here for the first time. The theoretical results are compared with existing STAR, CDF, CMS experimental data and predictions for planned or being carried out experiments (ALICE, ATLAS) are presented. We show the influence of the experimental cuts on the integrated cross section and on various differential distributions for outgoing particles. Distributions in rapidities and transverse momenta of outgoing protons and pions as well as correlations in azimuthal angle between them are presented. We find that the relative contribution of resonant $f_2(1270)$ and dipion continuum strongly depends on the cut on proton transverse momenta or four-momentum transfer squared $t_{1,2}$ which may explain some controversial observations made by different ISR experiments in the past. The cuts may play then the role of a $ππ$ resonance filter. We suggest some experimental analyses to fix model parameters related to the pomeron-pomeron-$f_{2}$ coupling.
Results from a phenomenological analysis of dijet and W hard diffractive hadroproduction at Fermilab Tevatron energies are reported. The theoretical framework employed here is a modified version of the Ingelman-Schlein approach which includes DGLAP-evolved structure functions. Different from what has been achieved by the DESY ep HERA reactions, a reasonable overall description of such diffractive hadron processes is obtained only when a complex, quark-rich Pomeron structure function is employed in the calculation.
The study of charge asymmetry of pions in the high-energy process gamma p -> pi+ pi- p (e p -> e pi+ pi- p) at very small dipion momenta offers a method to measure the phase of the forward hadronic (quasi)elastic amplitude gamma p -> rho p. We estimate potential of such measurements at HERA.
Exclusive production of axial-vector $f_{1}(1285)$ meson in proton-proton collisions via pomeron-pomeron fusion within the tensor-pomeron approach is discussed. Two ways to construct the pomeron-pomeron-$f_{1}$ coupling are presented. We adjust the parameters of our model to the WA102 experimental data and compare with predictions of the Sakai-Sugimoto model. Predictions for LHC experiments are given.
The inclusive diffractive quarkonium photoproduction in $pp$ and $pA$ collisions is investigated considering the Resolved Pomeron Model to describe the diffractive interaction. We estimate the rapidity and transverse momentum distributions for the $J/Ψ$, $Ψ(2S)$ and $Υ$ photoproduction in hadronic collisions at the LHC and present our estimate for the total cross sections at the Run 2 energies. A comparison with the predictions associated to the exclusive production also is presented. Our results indicate that the inclusive diffractive production is a factor $\gtrsim 10$ smaller than the exclu…
We present a study of associated jpsi + gamma production through double Pomeron exchange at energies reached at the Fermilab Tevatron and CERN LHC based on the Ingelman-Schlein model for hard diffractive scattering and the factorization formalism of nonrelativistic QCD for quarkonia production. We find that this process (p + pbar \to p + pbar + jpsi + gamma + X) can be used to probe the gluon content of the Pomeron and study the natrue of hard diffractive factorization breaking.
A phenomenological description of diffractive dijet hadroproduction via double Pomeron exchange is presented. This description is based on a modified version of the Ingelman-Schlein model which includes the evolution of the Pomeron structure function and corrections regarding rapidity gap suppression effects. The same quark-dominant Pomeron structure function employed in a previous report to describe diffractive dijet and W production via single Pomeron processes is shown here to yield results consistent with the available data for double Pomeron processes as well.
We calculate the cross section and the $A_{ll}$ asymmetry of the diffractive vector meson leptoproduction for a simple model of the pomeron coupling with the proton. It is found that the sensitivity of the spin--dependent cross section of the diffractive $J/Ψ$ production to the pomeron coupling structure is rather weak. The conclusion is made that it will be difficult to study the structure of the pomeron coupling with the proton in future polarized diffractive experiments on the $J/Ψ$ production.
The dependence of the fractal behaviors of the pomeron induced system in deep inelastic lepton-nucleon scattering upon the diffractive kinematic variables is found rather robust and not sensitive to the distinct parameterization of the pomeron flux factor and structure function. A feasible experimental test of the phenomenological pomeron-exchanged model based on the fractal measurement in DESY $ep$ collider HERA is proposed.
We test the hypothesis that diffractive scattering in the perturbative and non-perturbative domain is determined by the exchange of a single pomeron with a scale dependent trajectory. Present data on diffractive vector meson production are well compatible with this model and recent results for $J/ψ$ photoproduction at LHC strongly support it. The model is inspired by concepts of gauge/string duality applied to the pomeron.
Central diffractive production of heavy states (massive dijets, Higgs boson) is studied in the exclusive mode using a new Hybrid Pomeron Model (HPM). Built from Hybrid Pomerons defined by the combination of one hard and one soft color exchanges, the model describes well the centrally produced diffractive dijet data at the Tevatron. Predictions for the Higgs boson and dijet exclusive production at the LHC are presented.
This study focuses on hard diffractive events produced in proton-proton collision at LHC exhibiting one intact proton in the final state which can be tagged by forward detectors. We report prospective results on the W boson charge asymmetry measured for such events, which allow to constrain the quark diffractive density functions in the Pomeron.
We review the recent progress in the theory of diffractive DIS, focusing on predictions of strong breaking of the Ingelman-Schlein-Regge factorization and the related breaking of the GLDAP evolution for the diffractive structure function.
Pomeron non factorization for the diffractive scattering is considered and an analysis of experimental data is performed with different cuts in the momentum fraction $ξ$. The results of the analysis are compared with the breaking predicted in the Genovese-Nikolaev-Zakharov model.
By using Monte Carlo simulation of pomeron exchange model, the dependence of the fractal behavior of the pomeron induced system in deep inelastic lepton-nucleon scattering upon the diffractive kinematic variables is found rather robust and not sensitive to the distinct parameterization of the pomeron flux factor and structure function. Based on this characteristic fractal plot, a feasible experimental test of the phenomenological pomeron-exchange model in DESY $ep$ collider HERA is proposed.
We present a study of diffractive associated jpsi + gamma production at the Fermilab Tevatron and LHC based on the Ingelman-Schlein model for hard diffractive scattering and the factorization formalism of NRQCD for quarkonia production. We find that this process (p + pbar to p + jpsi + gamma + X) can be used to probe the gluon content of the Pomeron and test the assumption of diffractive hard scattering factorization. Using the renormalized Pomeron flux factor D simeq 0.11 (0.052), the single diffractive jpsi + gamma production cross section at 4<P_T< 10 GeV, -1<eta<1 region is found to be of …
We study the contribution of diffractive $Q \bar Q$ production to the $F_2^D$ proton structure function and the longitudinal double-spin asymmetry in polarized deep--inelastic $lp$ scattering. We show the strong dependence of the $F_2^D$ structure function and the $A_{ll}$ asymmetry on the quark--pomeron coupling structure.
Large-distance effects, which lead to the spin-flip part of the hadron -pomeron coupling in QCD -models, are discussed. We study spin asymmetries in exclusive reactions and in diffractive $Q \bar Q$ and vector meson production which are sensitive to the spin-dependent part of the pomeron coupling.
Presented here is a study of the large p_T J/psi production in hard diffractive process by the pomeron exchange at the Fermilab Tevatron. We find that this process (p\bar p \to p+J/psi+X) can be used to probe the gluon content of the pomeron and to measure the gluon fraction of the pomeron. And the diffractive direct J/psi production can also provide another crucial test for the color-octet fragmentation mechanism. Using the renormalised pomeron flux factor D\approx 1/9, the single diffractive J/psi production cross section at large p_T (\geq 8GeV) is found to be of order of 0.01 nb, and the r…
We analyze contributions to the heavy vector meson production with large transverse momentum in proton--proton and diffractive photon--proton scattering driven by an exchange of two Balitsky--Fadin--Kuraev--Lipatov Pomerons in the squared amplitudes. The Pomerons couple to a single parton and form a Pomeron loop closed by the vector meson impact factors. For the photon--proton case the diffractive cut of the Pomeron loop contributes, and for the inclusive hadroproduction one finds the loop with two cut Pomerons. We compute both of these Pomeron loop contributions and study in detail their prop…
We have recently studied the QCD pomeron loop evolution equations in zero transverse dimensions [Shoshi:2005pf]. Using the techniques developed in [Shoshi:2005pf] together with the AGK cutting rules, we present a calculation of single, double and central diffractive cross sections (for large diffractive masses and large rapidity gaps) in zero transverse dimensions in which all dominant pomeron loop graphs are consistently summed. We find that the diffractive cross sections unitarise at asymptotic energies and that they are suppressed by powers of alpha_s. Our calculation is expected to expose …
The role of the QCD vacuum effects in high energy diffractive quark-quark and quark-antiquark scattering is studied with the Instanton Liquid Model. The special attention is given to the problem of formation of the soft Pomeron. We show that in the leading approximation in instanton density the $C-$odd instanton contribution to the diffractive amplitude is suppressed as $1/s$ compared to the $C-$even one.
Experimental rates of W and dijets diffractively produced at the Tevatron Collider have recently become available. We use parametrizations of the pomeron structure function obtained from HERA data by two different schemes to compare theoretical expectations with the measured rates.
We study Pomeron-Odderon interference effects giving rise to charge and single-spin asymmetries in diffractive electroproduction of a $π^+ π^-$ pair. The final state interactions and the role of $f_0$ meson are discussed. The absence of $f_0$ signal in the charge asymmetry observed by HERMES may be due to the smalness of its quark component.
The most important consequence of Pomeron being a pole is the factorization property. However, due to Pomeron intercept being greater than 1, the extrapolated single diffraction dissociation cross section based on a classical triple-Pomeron formula is too large leading to a potential unitarity violation at Tevatron energies. It is our desire here to point out that the "flavoring" of Pomeron plays the dominant role in resolving this apparent "paradox".
In this paper we discuss the processes of diffractive production in the framework of the BFKL Pomeron calculus in zero transverse dimension. Considering the diffractive production of a bunch of particles with not very large masses, namely, $\ln\Lb M^2/m^2 \Rb \ll \frac{1}{\bas} \ln\Lb \frac{N^2_c}{\bas^2}\Rb$, we found explicit formulae for calculation of the cross sections for the single and double diffractive production as well as for the value of the survival probability for the diffractive central production. These formulae include the influence of the correlations due to so called Pomeron…
The diffractive 2-jet production reactions in the proton-proton and lepton-proton processes are discussed. It is shown that they may be very suitable for studying the properties of the pomeron couplings with quarks and hadrons in future polarized experiments at HERA, especially for HERA-$\vec N$ project.
We present predictions for the diffractive production of heavy quarks in deep-inelastic scattering and hadron-hadron collisions and for double diffractive dijet production in hadron-hadron collisions. With the assumption of hard scattering factorization, the predictions are made using diffractive parton densities that we have previously fitted to HERA data. Comparisons of our predictions with preliminary data from HERA and the Tevatron indicate that factorization is obeyed in diffractive DIS but fails in hadron-induced processes.
The double diffractive Higgs production at central rapidity is formulated in terms of the fusion of two AdS gravitons/Pomerons first introduced by Brower, Polchinski, Strassler and Tan in elastic scattering. Here we propose a simple self-consistent holographic framework capable of providing phenomenologically compelling estimates of diffractive cross sections at the LHC. As in the traditional weak coupling approach, we anticipate that several phenomenological parameters must be tested and calibrated through factorization for a self-consistent description of other diffractive process such as to…
In this paper, the inclusive Pomeron-Pomeron, Reggeon-Reggeon, Pomeron-Reggeon as well as gluon-Pomeron(-Reggeon) and photon-Pomeron(-Reggeon) interactions for the $\rm η_{c}$ at the LHC energies have been examined in proton-proton, proton-nucleus and nucleus-nucleus collision modes. The cross section has been computed based on the NRQCD factorization and Regge theory formalism. The cross exchange of Pomeron-Reggeon contribution is important in $\rm pp$ and $\rm pA$ modes. The Pomeron-Pomeron contribution is significant in $\rm AA$ mode. The Pomeron contribution is considerable for $\rm AA$ an…
We discuss consequences of the models of "tensorial pomeron" and "vectorial pomeron" for exclusive diffractive production of scalar and pseudoscalar mesons in proton-proton collisions. Diffractive production of $f_{0}(980)$, $f_{0}(1370)$, $f_{0}(1500)$, $η$, and $η'(958)$ mesons is discussed. Different pomeron-pomeron-meson tensorial coupling structures are possible in general. In most cases two lowest orbital angular momentum - spin couplings are necessary to describe experimental differential distributions. For $f_{0}(980)$ and $η$ production reggeon-pomeron, pomeron-reggeon, and reggeon-re…
The production of the $W$ and $Z$ bosons in single diffractive processes at the LHC is investigated taking into account the ATLAS, CMS and LHCb acceptances and considering different assumptions for the flavour content of the Pomeron. The total cross sections and pseudorapidity distributions are estimated for $pp$ collisions at $\sqrt{s} = 13$ TeV. Our results indicate that a future experimental analysis of the ratio between the $W$ and $Z$ cross sections can be used to probe the flavour content of the Pomeron.
Measurements of the diffractive structure function, $F_2^D$, of the proton at HERA are used to extract the partonic structure of the Pomeron. Regge Factorization is tested and is found to describe well the existing data within the selected kinematic range. The analysis is based on the next to leading order QCD evolution equations. The results obtained from various data sets are compared. An analysis of the uncertainties in determining the parton distributions is provided. The probability of diffraction is calculated using the obtained results.
Large - distance effects in the hadron wave function for the hadron-Pomeron vertex in the QCD -model are discussed. It is shown that they lead to the spin-flip part of the Pomeron coupling which can reach $10 ÷20 %$ with respect to the non-flip part. The obtained structure of the Pomeron coupling modifies spin asymmetries in high--energy diffractive reactions where the Pomeron structure becomes determinative. We study spin asymmetries in exclusive reactions and in the diffractive $Q \bar Q$ and $J/Ψ$ production. We have found that spin effects in these diffractive processes are sensitive to th…
The holographic approach to double diffractive Higgs production is presented for the AdS graviton/Pomeron. The goal is to provide a predictive phenomenology for the strong coupling expansion of QCD. This is the first step to set up the framework for the double diffractive Higgs production in anticipation of experimental observations at the LHC. Comparisons are made with the weak coupling approach based on the BFKL Pomeron models and soft Regge parameterizations.
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.
Recent results by the authors on proton diffractive dissociation (single, double and central) in the low-mass resonance region with emphasis on the LHC kinematics are reviewed and updated. Based on the previous ideas that the contribution of the inelastic proton-Pomeron vertex can be described by the proton structure function, the contribution of the inelastic Pomeron-Pomeron vertex appearing in central diffraction is now described by a Pomeron structure function.
The diffractive heavy quark cross sections are estimated considering photon-Pomeron ($γ\pom$) interactions in hadron - hadron at RHIC, Tevatron, and CERN LHC energies. We assume the validity of the hard diffractive factorization and calculate the charm and bottom total cross sections and rapidity distributions using the diffractive parton distribution functions of the Pomeron obtained by the H1 Collaboration at DESY-HERA. Moreover, we compare our predictions with those obtained using the dipole model. We verify that this process is a good test of the different mechanisms for diffractive heavy …
We analyse the momentum space triple Pomeron vertex in perturbative QCD. In addition to the standard form of this vertex which is used in the context of total cross-sections at high energies and in the QCD reggeon field theory, there exists an alternative form which has to be used in the study of high-mass diffraction. We review and analyse the relation between these two versions. We discuss some implications for the BK-equation. In the second part of our paper we extend this analysis to the Pomeron-Odderon-Odderon vertex.
The interference of Pomeron and Odderon amplitudes gives rise to a charge asymmetry in the diffractive electroproduction of a pi+pi- -pair. We calculate this charge asymmetry in perturbative QCD in the Born approximation and on the leading Q^2-level. The numerical evaluation shows a sizeable asymmetry in an experimentally accessible kinematical region. We find a characteristic m_{pi+pi} -dependence mainly dictated by the relevant Breit-Wigner-amplitudes and the corresponding phase-shifts.
In this Letter we study the double diffractive vector meson production in $e^+e^-$ collisions assuming the dominance of the BFKL pomeron exchange. We consider the non-forward solution of the BFKL equation at high energy and large momentum transfer and estimate the total cross section for the process $e^+e^- \to e^+e^- V_1 V_2$ with antitagged $e^+$ and $e^-$, where $V_1$ and $V_2$ can be any two vector mesons ($V_i = ρ, ω, ϕ, J/Ψ, Υ$). The event rates for the future linear colliders are given.
We have calculated the mass distribution ($dσ/dM_X$) as observed by UA8 Collaboration in the inclusive reaction $p \bar p \to p X \bar p$ at $\sqrt s = 630 GeV$, using the Interacting Gluon Model (IGM) with Double Pomeron Exchange included. The only new parameter is the $IP IP$ cross section, which we can extract from fitting experimental data. We compare our results with the values obtained in the UA8 study. Assuming a constant Pomeron-Pomeron total cross section ($σ_{IP IP} = 1 mb$), we make predictions for $dσ/dM_X$ at Tevatron and LHC energies.
Predictions of the elastic scattering, total-inetastic, and total proton-proton cross sections, based on a Regge theory inspired tensor-Pomeron implementation of the RENORM model for hadronic diffraction, are compared to the latest experimental measurements at the LHC. The measured cross sections are in good agreement within the experimental uncertainties of the data and the theoretical uncertainties of the model, reaching down to the ~1% level.
A model for exclusive diffractive resonance production in proton-proton collisions at high energies is presented. This model is able to predict double differential distributions with respect to the mass and the transverse momentum of the produced resonance in the mass region $\sqrt{M^2}\le$5 GeV. The model is based on convoluting the Pomeron distribution in the proton with the Pomeron-Pomeron-meson total cross section. The Pomeron-Pomeron-meson cross section is saturated by direct-channel contributions from the Pomeron as well as from two different $f$ trajectories, accompanied by the isolated…
