Dynamic versus Static Structure Functions and Novel Diffractive Effects in QCD
Stanley J. Brodsky
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8 pages, 1 figure. Presented at Diffraction 2008: International Workshop On Diffraction In High Energy Physics 9-14 Sep 2008, La Londe-les-Maures, France
Initial- and final-state rescattering, neglected in the parton model, have a profound effect in QCD hard-scattering reactions, predicting single-spin asymmetries, diffractive deep inelastic scattering, diffractive hard hadronic reactions, the breakdown of the Lam Tung relation in Drell-Yan reactions, and nuclear shadowing and non-universal antishadowing--leading-twist physics not incorporated in the light-front wavefunctions of the target computed in isolation. I also discuss the use of diffraction to materialize the Fock states of a hadronic projectile and test QCD color transparency, and anomalous heavy quark effects. The presence of direct higher-twist processes where a proton is produced in the hard subprocess can explain the large proton-to-pion ratio seen in high centrality heavy ion collisions. I emphasize the importance of distinguishing between static observables such as the probability distributions computed from the square of the light-front wavefunctions versus dynamical observables which include the effects of rescattering.
A new method of extracting diffractive parton distributions is presented which avoids the use of Regge theory ansatz and is in much closer relation with the factorisation theorem for diffractive hard processes.
A new method of extracting diffractive parton distributions is presented which avoids the use of Regge theory ansatz and is in much closer relation with the factorization theorem for diffarctive hard processes.
We review the application of perturbative QCD to diffractive processes. We introduce the two gluon exchange model to describe diffractive qq(bar) and qq(bar)g production in deep inelastic scattering. We study the triple Regge limit and briefly consider multiple gluon exchange. We discuss diffractive vector meson production at HERA both at t = 0 and large |t|. We demonstrate the non-factorization of diffractive processes at hadron colliders.
We discuss recent theoretical results on diffractive deeply inelastic scattering, focusing on the partonic picture of diffraction in configuration space and the predictions for the beta behavior and the scaling violation.
Experimental results from HERA on diffractive vector meson production and their theoretical interpretation within microscopic QCD are reviewed with an emphasis on the BFKL color dipole and kt-factorization approaches.
The exclusive reaction $pp \to pp (K^{*0} \bar{K}^{*0} \to K^{+}π^{-}K^{-}π^{+})$ for the LHC experiments is discussed. The amplitudes for the reaction are formulated within the tensor-pomeron approach. We consider two diffractive mechanisms: the $f_{2}(1950)$ $s$-channel exchange mechanism and the $K^{*0}$-exchange mechanism. First mechanism is a candidate for central diffractive production of tensor glueball and the second one is an irreducible continuum. Comparison with data from WA102 experiment are made and predictions for LHC experiments are given. We find that including the continuum co…
We show that AdS/QCD generates predictions for the rate of diffractive rho meson electroproduction that are in agreement with data collected at the HERA electron-proton collider.
The HERA diffractive structure function data are interpreted in terms of `diffractive parton distributions' which satisfy DGLAP evolution. These distributions are modeled assuming that the scattering takes place off a colour singlet `pomeron' target. A quantitative test of the universality of diffractive parton distributions is proposed.
The QCD analysis of deep inelastic diffractive scattering at HERA is performed assuming the dominance of the "soft" pomeron exchange and simple, physically motivated parametrization of parton distributions in the pomeron. Both the LO and NLO approximations are considered and the theoretical predictions concerning the quantity $R=F_L^D/F_T^D$ for diffractive structure functions are presented.
I review the modern status of QCD theory of diffractive vector meson production with the focus on shrinkage of photons with Q2 and (Q2+mV2)$scaling, j-plane properties of the QCD pomeron and Regge shrinkage of diffraction cone, $s$-channel helicity non-conservation and sensitivity to spin-orbital properties of vector mesons.
We demonstrate another success of the AdS/QCD correspondence by showing that an AdS/QCD holographic light-front wavefunction for the $ρ$ meson generates predictions for the cross-sections of diffractive $ρ$ production that are in agreement with data collected at the HERA electron-proton collider.
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.
We discuss the observed scaling of the small-x diffractive and total deep-inelastic structure functions at HERA. We argue that the parton interpretation of Buchmüller and Hebecker can be understood within QCD as the appearance of the Pomeron in a Super-Critical phase. In diffractive hard scattering, the Pomeron appears as reggeized gluon exchange in a color-compensating background field. The formalism can also be applied to diffractive $W$ production at the Tevatron. If the scaling is a true asymptotic property then it should anticipate the appearance of a further massive sector of QCD and ass…
Exclusive and semi-exclusive processes, the diffractive dissociation of hadrons into jets, and hard diffractive processes such as vector meson leptoproduction provide new testing grounds for QCD and essential information on the structure of light-cone wavefunctions of hadrons, particularly the pion distribution amplitude. I review the basic features of the leading-twist QCD predictions and the problems and challenges of studying QCD at the amplitude level. The application of the light-cone formalism to the exclusive semi-leptonic decay of heavy hadrons is also discussed.
We discuss single diffractive gauge bosons ($γ^*,\,W^{\pm},\,Z$) production in proton-proton collisions at different (LHC and RHIC) energies within the color dipole approach. The calculations are performed for gauge bosons produced at forward rapidities. The diffractive cross section is predicted as function of fractional momentum and invariant mass of the lepton pair. We found a dramatic breakdown of the diffractive QCD factorisation caused by an interplay of hard and soft interactions. Data from the CDF experiment on diffractive production of $W$ and $Z$ are well explained in a parameter fre…
We present a combined QCD analysis of recent data produced by the H1 and ZEUS collaborations on the diffractive and leading-proton deep inelastic positron--proton scattering structure functions, $F_2^{D(3)}$ and $F_2^{LP(3)}$, respectively. It is shown that the QCD framework for semi-inclusive processes, based on fracture functions, allows a unified treatment of both diffractive and leading-proton processes, and offers a precise perturbative QCD description for them, alternative to those that rely on model-dependent assumptions, such as Regge factorization, or other non-perturbative approaches
The AdS/QCD holographic wave function of basis light-front quantization (BLFQ) for vector meson $J/ψ$ is applied in this manuscript. The exclusive production of $J/ψ$ in diffractive process is computed in dipole model with AdS/QCD holographic wave function. We use IP-Sat and IIM model in the calculation of the differential cross section of the dipole scattering off the proton. The prediction of AdS/QCD holographic wave function in BLFQ gives a good agreement to the experimental data.
The most important results on subnuclear diffractive phenomena obtained at HERA and Tevtaron are reviewed and new issues in nucleon tomography are discussed. Some challenges for understanding diffraction at the LHC, including the discovering of the Higgs boson, are outlined.
The QCD analysis of deep inelastic diffractive scattering is performed assuming the dominance of the "soft" pomeron exchange and simple, physically motivated parametrization of parton distributions in a pomeron. Results of the analysis are compared with the recent data obtained by the H1 collaboration at HERA. Both the LO and NLO approximations are considered and the theoretical predictions concerning the quantity $R=F_L^D/F_T^D$ for diffractive structure functions are presented.
An effective field theory describing the QCD diffraction scattering is constructed. The constituent quarks interacting with multiperi- pheral gluons and Goldstone bosons are described by impact- parameter two-dimensional sigma models for the color and the flavor degrees of freedom. The elastic scattering amplitude is then shown to factorize into the hard and the soft pomeron contributions (talk at 5th Blois Workshop on Elastic and Diffractive Scattering Workshop, June 8 - 12, 1993, Providence RI USA)
We discuss diffractive photon-production of vector mesons in holographic QCD. At large $\sqrt{s}$, the QCD scattering amplitudes are reduced to the scattering of pair of dipoles exchanging a closed string or a pomeron. We use the holographic construction in AdS$_5$ to describe both the intrinsic dipole distribution in each hadron, and the pomeron exchange. Our results for the heavy meson photon-production are made explicit and compared to some existing experiments.
The asymptotic collinear factorisation theorem, which holds for diffractive deep-inelastic scattering, has important modifications in the sub-asymptotic HERA regime. We use perturbative QCD to quantify these modifications. The diffractive parton distributions are shown to satisfy an inhomogeneous evolution equation. We emphasise that it is necessary to include both the gluonic and sea-quark t-channel components of the perturbative Pomeron. The corresponding Pomeron-to-parton splitting functions are derived in the Appendix.
The Odderon state in perturbative QCD is briefly reviewed. Recent calculations devoted to estimate the diffrative eta_c production at high energies from the leading known Odderon states are discussed.
We present the microscopic QCD evaluation of the secondary reggeon contribution to diffractive DIS. It is shown that the interference between Pomeron and Reggeon enters in the maximal possible way. In the region of large $β\simeq 1$ it is shown, that the structure functions of the Reggeon and Pomeron as well as the Reggeon-Pomeron interference SF have a universal $\sim (1-β)^2$ behaviour.
It is argued that the QCD dipole picture allows to build an unified theoretical description -based on BFKL dynamics- of the total and diffractive nucleon structure functions. This description is in qualitative agreement with the present collection of data obtained by the H1 collaboration. More precise theoretical estimates, in particular the determination of the normalizations and proton transverse momentum behaviour of the diffractive components, are shown to be required in order to reach definite conclusions.
We perform a novel type of analysis of diffractive deep-inelastic scattering data, in which the input parton distributions of the Pomeron are parameterised using the perturbative QCD expressions. In particular, we treat individually the components of the Pomeron of different size. We are able to describe simultaneously both the recent ZEUS and H1 diffractive data. In addition to the usual two-gluon model for the perturbative Pomeron, we allow for the possibility that it may be made from two sea quarks.
The $F_{2}$, $F_{G}$, $R=F_{L}/F_{T}$ proton structure functions are derived in the QCD dipole picture of BFKL dynamics. We get a three parameter fit describing the 1994 H1 proton structure function $F_{2}$ data in the low $x$, moderate $Q^{2}$ range. Without any additional parameter, the gluon density and the longitudinal structure functions are predicted.The diffractive dissociation processes are also discussed, and a new prediction for the proton diffractive structure function is obtained.
Following recent progresses in the understanding of high-energy scattering in QCD, we derive the first phenomenological consequences of Pomeron loops, in the context of both inclusive and diffractive deep inelastic scattering. In particular, we discuss diffusive scaling, a new scaling law that emerges for sufficiently high energies and up to very large values of $Q^2,$ well above the proton saturation momentum.
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…
Using a set of new odderon states, we calculate their contribution to the diffractive eta_c photo- and electroproduction process. Compared to previous simple 3-gluon exchange calculations we find an enhancement of about one order of magnitude in the cross section. The t-dependence of the cross section exhibits a dip structure in the small t region.
We report on the results of our recent research published in [1] that shows that AdS/QCD generates predictions for the rate of diffractive ρ-meson electroproduction that are in agreement with data collected at the HERA electron-proton collider [2,3]. Preliminary results of this research were presented in [4].
The 1994 data published by the H1 collaboration are compared with models based on Regge phenomenology. The $x_{\PO}$ dependence of the data can be described in a model based on the exchange of a dominant diffractive (pomeron) trajectory with additional sub-leading reggeon contributions. The dynamics of the Pomeron structure is studied within the framework of perturbative QCD and new parton distributions are obtained. These parton distributions will allow a direct test of factorisation breaking at Tevatron.
In the context of both inclusive and diffractive deep inelastic scattering, we derive the first phenomenological consequences of the inclusion of Pomeron loops in the QCD evolution equations towards high energy. We discuss the transition between the well-known geometric scaling regime and the new diffusive scaling, that emerges for sufficiently high energies and up to very large values of Q^2, well above the proton saturation momentum.
We compute the rate for diffractive $ϕ$ electro-production using the Color Glass Condensate dipole model. The model parameters are obtained from fits to the most recent combined HERA data on inclusive deep inelastic scattering. As for the $ϕ$ meson, we use an AdS/QCD holographic light front wavefunction. Our predictions are compared to the available data collected at the HERA collider.
We examine a model of hadronic diffractive scattering which interpolates between perturbative QCD and non-perturbative fits. We restrict the perturbative QCD resummation to the large transverse momentum region, and use a simple Regge-pole parametrization in the infrared region. This picture allows us to account for existing data, and to estimate the size of the perturbative contribution to future diffractive measurements. At LHC and SSC energies, we find that a cut-off BFKL equation can lead to a measurable perturbative component in traditionally soft processes. In particular, we show that the…
Charge asymmetries in diffractive electroproduction of two mesons are proportional to the interference of Pomeron and Odderon exchange amplitudes. We calculate in the framework of QCD and in the Born approximation a forward-backward charge asymmetry which turns out to be sizable in a kinematical domain accessible to HERA experiments. We predict a distinctive dependence of this asymmetry on the invariant mass of the two pions. Testing this prediction is a crucial step in the discovery of the QCD-Odderon.
Diffractive hard scattering is interpreted as the effect of soft gluon exchanges between the emerging energetic quarks and the nucleon's color field, resulting in an overall color singlet exchange. Summing multiple gluon exchanges to all orders leads to exponentiation and an amplitude in analytic form. Numerical evaluation reproduces the precise HERA data and gives new insights on the density of gluons in the proton.
We present a QCD-based model where rescattering between final state partons in deep inelastic scattering leads to events with large rapidity gaps and a leading proton. In the framework of this model the amplitude for multiple gluon exchanges is calculated in the eikonal approximation to all orders in perturbation theory. Both large and small invariant mass M_X limits are considered. The model successfully describes the precise HERA data on the diffractive deep inelastic cross section in the whole available kinematical range and gives new insight into the density of gluons at very small momentu…
We examine diffractive proton-proton scattering. Using a functional integral approach we derive the scattering amplitudes, which are governed by the expectation value of lightlike Wegner-Wilson loops. This expectation value is then evaluated using a cumulant expansion and the model of the stochastic vacuum. From the scattering amplitudes we calculate total and differential cross sections for high centre of mass energy and small momentum transfer and compare with experiments.
We demonstrate that the distinctive features of the forward differential cross section of diffractive leptoproduction of a vector meson can be legitimately calculated in perturbative QCD in terms of the light-cone $q \bar q$ wave function of the vector meson and the gluon distribution of the target. In particular, we calculate the $Q^2$ and nuclear dependence of the diffractive leptoproduction of vector mesons and estimate the cross section. The production of longitudinally polarized vector mesons by longitudinally polarized virtual photons is predicted to be the dominant component, yielding a…
Hard diffractive electroproduction of longitudinally polarized vector mesons is calculated within the leading $α_s\ln{Q^2\overΛ_{QCD}^2}$ approximation of QCD using the leading order parton densities within the nucleon. Novel QCD features of the production of excited states and of the restoration of flavor symmetry are analyzed. At the onset of the asymptotic regime, our analysis finds an important role of quark Fermi motion within the diffractively produced vector mesons, and we suggest to use this effect to measure the high momentum tail of the wave function of the vector mesons. We deduce a…
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.
We study the impact of the "intrinsic" hadron transverse momentum on the pre-asymptotic behavior of the diffractive electroproduction of longitudinally polarized $ ρ$-meson. Surprisingly, we find the onset of the asymptotic regime in this problem to be rather low, Q^2 ~ 10 GeV^2 where power corrections due to the transverse momentum do not exceed 20 % in the amplitude. This drastically contrasts with exclusive amplitudes where the asymptotics starts at much higher Q^2 = 50 - 100 GeV^2. The sources of such unexpected behavior are traced back to some general (the quark-hadron duality) as well as…
The diffractive open charm production is computed in perturbative QCD formalism and in the Regge approach. The results are compared with recent data on charm diffractive structure function measured at DESY-HERA. Our results demonstrate that this observable can be useful to discriminate the QCD dynamics.
We perform a NLO QCD analysis of deep-inelastic scattering data, in which we account for absorptive corrections. These corrections are determined from a simultaneous analysis of diffractive deep-inelastic data. The absorptive effects are found to enhance the size of the gluon distribution at small x, such that a negative input gluon distribution at Q^2 = 1 GeV^2 is no longer required. We discuss the problem that the gluon distribution is valence-like at low scales, whereas the sea quark distribution grows with decreasing x. Our study hints at the possible importance of power corrections for Q^…
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…
We review a consistent description of the fusion and saturation of partons in the Lorentz-contracted ultrarelativistic nuclei in terms of a nuclear attenuation of color dipole states of the photon and collective Weizsäcker-Williams (WW) gluon structure function of a nucleus. Diffractive DIS provides a basis for the definition of the WW nuclear glue. The point that all observables for DIS off nuclei are uniquely calculable in terms of the nuclear WW glue amounts to a new form of factorization in the saturation regime.
We present a combined QCD analysis of diffractive and leading proton deep inelastic scattering data using the framework of fracture functions. It is shown that this framework allows a precise and unified perturbative QCD description for the data, alternative to those that relay on Regge factorization.
The elastic leptoproduction of $ϕ$ measured by the H1 collaboration at HERA is described by a perturbative QCD model, based on open $s\bar{s}$ production and parton hadron duality, proposed by Martin et al. We observe that both the total cross section and the ratio of the longitudinal and transverse cross sections are well reproduced with an effective strange-quark mass $m_s \sim 320- 380 $ MeV for various gluon distribution functions. Possible connection of the effective mass and the momentum dependent dynamical mass associated with dynamical breaking of chiral symmetry is also discussed.
ZEUS inclusive diffractive cross-section measurements have been used in a next-to-leading-order QCD analysis to extract the diffractive parton distribution functions. Data on diffractive dijet production in deep inelastic scattering have also been used to constrain the gluon density. Predictions based on the extracted parton densities are able to describe measurements of dijet photoproduction.
We present a novel analysis of diffractive DIS data, in which the input parton distributions of the Pomeron are parameterised using perturbative QCD expressions. In addition to the usual two-gluon model for the perturbative Pomeron, we allow for the possibility that it may be made from two sea quarks. In particular, we treat individually the components of the Pomeron of different size. This property allows the absorptive corrections to the inclusive DIS structure function F_2 to be calculated using the AGK cutting rules. The absorptive effects are found to enhance the size of the gluon distrib…
We present first predictions of the cross sections and differential distributions for the exclusive reaction $pp \to pp K^{*0} \bar{K}^{*0}$ contributing to the $K^{+} K^{-} π^{+} π^{-}$ channel. The amplitudes for the reaction are formulated within the nonperturbative tensor-pomeron approach. We consider separately the $f_{2}(1950)$ $s$-channel exchange mechanism and the $K^{*0}$ $t/u$-channel exchange mechanism, focusing on their specificities. First mechanism is a candidate for the central diffractive production of tensor glueball and the second one is an irreducible continuum. We adjust pa…
We use an anti-de Sitter/Quantum Chromodynamics (AdS/QCD) holographic light-front wavefunction for the $ρ$ and $ϕ$ mesons, in conjunction with the Color Glass Condensate (CGC) dipole cross-section whose parameters are fitted to the most recent 2015 high precision HERA data on inclusive Deep Inelastic Scattering (DIS), in order to predict the cross-sections for diffractive $ρ$ and $ϕ$ electroproduction. Our results suggest that the holographic meson light-front wavefunction is able to give a simultaneous description of the $ρ$ and $ϕ$ production data provided we use a set of light quark masses …
We report a detailed study of the process of pion diffraction dissociation into two jets with large transverse momenta. We find that the standard collinear factorization does not hold in this reaction. The structure of non-factorizable contributions is discussed and the results are compared with the experimental data. Our conclusion is that the existing theoretical uncertainties do not allow, for the time being, for a quantitative extraction of the pion distribution amplitude. (Talk presented at the Workshop on Exclusive Processes at High Momentum Transfer, Jefferson News, VA, May 15-18, 2002)
A new NLO DGLAP QCD fit to recent inclusive diffractive DIS data from the H1 collaboration is presented. Diffractive parton distributions are extracted, including their experimental and theoretical uncertainties. The parton distributions are used for comparisons with recent diffractive final state data from HERA and the TEVATRON.
We derive an evolution equation describing the high energy behavior of the cross section for the single diffractive dissociation in deep inelastic scattering on a hadron or a nucleus. The evolution equation resums multiple BFKL pomeron exchanges contributing to the cross section of the events with large rapidity gaps. Analyzing the properties of an approximate solution of the proposed equation we point out that at very high energies there is a possibility that for a fixed center of mass energy the cross section will reach a local maximum at a certain intermediate size of the rapidity gap, or, …
In view of future phenomenological applications, we study the impact factor for the photon to quark, antiquark and gluon transition within Balitsky's shock-wave formalism. The aim of the present program is to extend existing results beyond approximations discussed in the literature. We present our results of the real contribution, and report on recent progress in calculating the virtual contributions for the photon to quark, antiquark transition.
