Diffractive excitation is usually described by the Good--Walker formalism for low masses, and by the triple-Regge formalism for high masses. In the Good--Walker formalism the cross section is determined by the fluctuations in the interaction. In this paper we show that by taking the fluctuations in the BFKL ladder into account, it is possible to describe both low and high mass excitation by the Good--Walker mechanism. In high energy $pp$ collisions the fluctuations are strongly suppressed by saturation, which implies that pomeron exchange does not factorise between DIS and $pp$ collisions. The Dipole Cascade Model reproduces the expected triple-Regge form for the bare pomeron, and the triple-pomeron coupling is estimated.
We review QCD based descriptions of diffractive deep inelastic scattering emphasizing the role of models with parton saturation. These models provide natural explanation of such experimentally observed facts as the constant ratio of diffractive and total DIS cross sections as a function of the Bjorken variable x and Regge factorization of diffractive parton distributions.
Using the Good and Walker picture, we derive a simple formula for diffractive dissociation that can apply to recent data collected at HERA in the low Q2 regime.
We analyse the dissociation of a photon in diffractive deep inelastic scattering in the kinematic regime where the diffractive mass is much bigger than the photon virtuality. We consider the dominant q\bar{q}g component keeping track of the transverse momentum of the gluon which can be measured as a final-state jet. We show that the diffractive gluon-jet production cross-section is strongly sensitive to unitarity constraints. In particular, in a model with parton saturation, this cross-section is sensitive to the scale at which unitarity effects become important, the saturation scale. We argue…
We review diffractive deep inelastic scattering (DIS) in the light of the collinear factorization theorem. This theorem allows to define diffractive parton distributions in the leading twist approach. Due to its selective final states, diffractive DIS offers interesting insight into the form of the diffractive parton distributions which we explore with the help of the saturation model. We find Regge-like factorization with the correct energy dependence measured at HERA. A remarkable feature of diffractive DIS is the dominance of the twist-4 contribution for small diffractive masses. We quantif…
In the framework of the QCD shock-wave approach, we review our results on the description of diffractive production of various final states (jets, meson) at next-to-leading order. This is applied to exclusive diffractive dijet electroproduction at HERA.
We successfully describe the HERA-data on diffractive deep inelastic scattering using a saturation model which has been applied in our earlier analysis of the inclusive $ep$-scattering data. No further parameters are needed. Saturation already turned out to be essential in describing the transition from large to small values of $Q^2$ in inclusive scattering. It is even more important for diffractive processes and naturally leads to a constant ratio of the diffractive versus inclusive cross sections. We present an extensive discussion of our results as well as detailed comparison with data.
Combining the QCD dipole model with the Good and Walker picture, we formulate diffractive dissociation of a photon of virtuality Q^2 off a hadronic target, in the kinematical regime in which Q is close to the saturation scale and much smaller than the invariant mass of the diffracted system. We show how the obtained formula compares to the HERA data and discuss what can be learnt from such a phenomenology. In particular, we argue that diffractive observables in these kinematics provide useful pieces of information on the saturation regime of QCD.
We propose a new description of inclusive diffraction in deep inelastic scattering (DIS). The diffractive structure functions are expressed in the dipole picture and contain heavy-quark contributions. The dipole scattering amplitude, a saturation model fitted on inclusive DIS data, features a saturation scale Q_s(x) larger than 1 GeV for x=10^{-5}. The q\bar{q}g contribution to the diffractive final state is modeled in such a way that both the large-Q^2 and small-beta limits are implemented. In the regime xpom<0.01 in which saturation is expected to be relevant, we obtain a parameter-free desc…
The logarithmic slope of the diffractive structure function is a potential observable scanning the hard and soft contributions in diffraction, allowing to disentangle the QCD dynamics. We report our calculations concerning this quantity, in particular the estimates emerging from the saturation model applied to diffraction dissociation.
In this paper we investigate the saturation physics in diffractive deep inelastic electron-ion scattering. We estimate the energy and nuclear dependence of the ratio $σ^{diff}/σ^{tot}$ and predict the $x_{\pom}$ and $β$ behavior of the nuclear diffractive structure function $F_{2,A}^{D(3)}(Q^2, β, x_{IP})$. Moreover, we analyze the ratio $R^{diff}_{A1,A2}(Q^2, β, x_{IP}) = F_{2,A1} ^{D(3)}/F_{2,A2} ^{D(3)}$, which probes the nuclear dependence of the structure of the Pomeron. We show that saturation physics predicts that approximately 37 % of the events observed at eRHIC should be diffractive.
We construct diffractive parton distributions in the model of DIS diffraction in which the diffractive state is formed by the $q\bar{q}$ and $q\bar{q}g$ components. The interaction of such systems with the proton is described by the dipole cross section given by the saturation model. We find Regge factorization property with the measured at HERA depenedence on energy. The found parton distributions are evolved with the DGLAP evolution equations to make a comparison with the data.
Unitarization schemes can be reduced to non-linear equations which saturate at small $b$ the evolution of the elastic amplitude with $s$, and which mimic parton saturation in the non-perturbative regime. These equations enable us to study the effect of saturation on total and elastic cross sections for various models, and to evaluate the uncertainties on $σ_{tot}$ and $ρ(s,t)$ at the LHC in the presence of a hard pomeron.
We present two NLO exclusive impact factors computed in the QCD shock wave approach. These are the very first steps towards precision studies of a wide range of high energy exclusive processes with saturation effects in $ep$, $eA$, $pp$ and $pA$ collisions.
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.
As Glauber has shown in 1959, the spin-flip phenomena caused by the conventional spin-orbit interaction do vanish in the scattering off heavy, strongly absorbing nuclei. On the other hand, the origin of the s-channel helicity nonconservation (SCHNC) in diffractive DIS is of the origin different from simple spin-orbit interaction, and here we demonstrate that SCHNC in vector meson production survives strong absorption effects in nuclear targets. The intranuclear absorption often discussed in terms of the saturation effects introduces a new large scale $Q_A^2$ into the calculation of diffractive…
Through a direct implementation of the saturation regime resulting from the unitarity limit in the impact parameter representation, we explore various possibilities for the energy dependence of hadronic scattering. We show that it is possible to obtain a good description of the scattering amplitude from a hard pomeron provided one includes non-linear effects.
We perform the first next-to-leading order computation of the $γ^{(*)} \to V$ ($ρ, ϕ, ω$) impact factor in the QCD shockwave approach and in the most general kinematics. This paves the way to the very first quantitative study of high-energy nucleon and nucleus saturation beyond the leading order, in various processes to be measured in $ep$, $eA$, $pp$ and $pA$ collisions at existing and future colliders.
Diffractive excitation is usually described by the Good--Walker formalism for low masses, and by the triple-Regge formalism for high masses. In the Good-Walker formalism the cross section is determined by the fluctuations in the interaction. By taking the fluctuations in the BFKL ladder into account, it is possible to describe both low and high mass excitation in the Good-Walker formalism. In high energy pp collisions the fluctuations are strongly suppressed by saturation, which implies that pomeron exchange does not factorise between DIS and pp collisions. The Dipole Cascade Model reproduces …
This paper presents the first numerical solution to the non-linear evolution equation for diffractive dissociation processes in deep inelastic scattering. It is shown that the solution depends on one scaling variable $τ= Q^2/Q^{D 2}_s(x,x_0)$, where $Q^D_s(x,x_0)$ is the saturation scale for the diffraction processes. The dependence of the saturation scale $Q^D_s(x,x_0)$ on both $x$ and $x_0$ is investigated, ($Y_0 = \ln(1/x_0)$ is a minimal rapidity gap for the diffraction process). The $x$ - dependence of $Q^D_s$ turns out to be the same as of the saturation scale in the total inclusive DIS …
The geometric scaling property observed in the HERA data at small x, that the deep inelastic scattering (DIS) total cross-section is a function of only the variable Q^2*x^λ, has been argued to be a manifestation of the saturation regime of QCD and of the saturation scale Q^2_s(x) x^{-λ}. We show that this implies a similar scaling in the context of diffractive DIS and we observe, for several diffractive observables, that the experimental data from HERA confirm the expectations of this scaling.
We study coherent and incoherent diffractive hadron production in high energy quarkonium--heavy nucleus collisions as a probe of the gluon saturation regime of QCD. Taking this process as a model for pA collisions, we argue that the coherent diffractive gluon production, in which the target nucleus states intact, exhibits a remarkable sensitivity to the energy, rapidity and atomic number dependence. The incoherent diffractive gluon production is less sensitive to the details of the low-x dynamics but can serve as a probe of fluctuations in the color glass condensate. As a quantitative measure …
We calculate the cross section for diffractive hadron production in deep inelastic scattering off heavy nuclei in the framework of gluon saturation/color glass condensate. We analyze the kinematic region of the future Electron-Ion Collider. We argue that coherent and incoherent diffractive channels are very sensitive to the structure of the nuclear matter at low $x$. This expresses itself in a characteristic dependence of the cross sections on rapidity and transverse momentum of the produced hadron and on the nuclear weight. We also discuss dependence on the scattering angle and argue that bot…
Through a determination of the $S$-matrix element for the scattering of a localized colour dipole on a proton, we show that saturation effects can already be sizable at HERA. The saturation scale is found to be around 1-1.5 $GeV^2$ for the highest available energies and for central collisions, and is a decreasing function of the impact parameter.
We study coherent diffractive dijet production in electron-hadron and electron-nucleus collisions within the dipole picture. We provide semi-analytic results for the differential cross section and elliptic anisotropy in the angle between dijet transverse momentum and hadron recoil momentum. We demonstrate the direct relation between angular moments of the dipole amplitude in coordinate space and angular moments of the diffractive dijet cross sections. To perform explicit calculations we employ two different saturation models, extended to include the target geometry. In the limit of large photo…
In this paper we describe a formalism for generating exclusive final states in diffractive excitation, based on the optical analogy where diffraction is fully determined by the absorption into inelastic channels. The formalism is based on the Good--Walker formalism for diffractive excitation, and it is assumed that the virtual parton cascades represent the diffractive eigenstates defined by a definite absorption amplitude. We emphasize that, although diffractive excitation is basically a quantum-mechanical phenomenon with strong interference effects, it is possible to calculate the different i…
Following recent predictions that the geometric scaling properties of deep inelastic scattering data in inclusive gamma*-p collisions are expected also in exclusive diffractive processes, we investigate the diffractive production of vector mesons. Using analytic results in the framework of the BK equation at non-zero momentum transfer, we extend to the non-forward amplitude a QCD-inspired forward saturation model including charm, following the theoretical predictions for the momentum transfer dependence of the saturation scale. We obtain a good fit to the available HERA data and make predictio…
We estimate the value of the survival probability for central exclusive production, in a model, which is based on the CGC/saturation approach. Hard and soft processes are described in the same framework. At LHC energies, we obtain a small value for the survival probability. The source of the small value, is the impact parameter dependence of the hard amplitude. Our model has successfully described a large body of soft data: elastic, inelastic and diffractive cross sections,inclusive production and rapidity correlations, as well as the $t$-dependence of deep inelastic diffractive production of …
We expect to observe parton saturation in a future electron - ion collider. In this letter we discuss this expectation in more detail considering two different models which are in good agreement with the existing experimental data on nuclear structure functions. In particular, we study the predictions of saturation effects in electron - ion collisions at high energies, using a generalization for nuclear targets of the b-CGC model, which describes the $ep$ HERA quite well. We estimate the total, longitudinal and charm structure functions in the dipole picture and compare them with the predictio…
In this note we analyse the relation between the triple-pomeron and Good-Walker formalisms for diffractive excitation in DIS and hadronic collisions. In both approaches gap events are interpreted as the shadow of absorption into inelastic channels. We here argue that the two formalisms are just different views of the same phenomenon. We first demonstrate how this relation works in a simple toy model, and then show how the relevant features of the toy model are also realized in real perturbative QCD.
Diffractive production of heavy flavors is calculated within the light-cone dipole approach. Novel leading twist mechanisms are proposed, which involve both short and long transverse distances inside the incoming hadron. Nevertheless, the diffractive cross section turns out to be sensitive to the primordial transverse momenta of projectile gluons, rather than to the hadronic size. Our calculations agree with the available data for diffractive production of charm and beauty, and with the observed weak variation of the diffraction-to-inclusive cross section ratios as function of the hard scale.
We use perturbative QCD and parton-hadron duality to estimate the cross sections for the diffractive electroproduction of rhoprime(1-) and rho(3-) resonances which occur in the 1.3-1.8 GeV mass interval. We present the cross sections and the ratios sigma_L/sigma_T as a function of Q^2. We compare the predictions with those for the diffractive electroproduction of rho mesons. We show how such diffractive electroproduction measurements at HERA can probe features of the perturbative QCD 'Pomeron'.
We confront saturation-based results for diffractive $ψ(2s)$ and $ρ$ production at HERA and $J/ψ$ photoproduction with all available data including recent ones from HERA, ALICE and LHCb, finding a good agreement. We show that the $t$-distribution of differential cross-section of photoproduction of vector mesons offers a unique opportunity to discriminate among saturation and non-saturation models. This is due to emergence of a pronounced dip (or multiple dips) in the $t$-distribution of diffractive photoproduction of vector mesons at relatively large, but potentially accessible $|t|$ that can …
We calculate the diffraction slope $B_{D}$ for diffractive DIS. We find a counterintuitive rise of $B_{D}$ from exclusive diffractive excitation of vector mesons to excitation of continuum states with $M^{2} \sim Q^{2}$. For the small-mass continuum we predict a rapid variation of $B_{D}$ with $M^{2}$ on the scale $m_{V}^{2}$ and a sharp drop of $B_{D}$ for a small-mass continuum above the vector meson excitation.
Saturation effects in diffractive deep inelastic scattering
University of California, Los Angeles（加州大学洛杉矶分校）；Mani L. Bhaumik Institute for Theoretical Physics, University of California, Los Angeles（加州大学洛杉矶分校马尼·L·巴乌米克理论物理研究所）；The University of Kansas（堪萨斯大学）；The University of Helsinki（赫尔辛基大学）
The process of single diffractive dissociation off nuclei is considered on a basis of solutions to the nonlinear evolution equation. The relevant saturation scales $Q_{s A}^D(x,x_0)$ are determined and their dependences on Bjorken $x$, atomic number $A$, and minimal rapidity gap $Y_0\equiv \ln 1/x_0$ are investigated. The solutions are shown to posses the geometrical scaling in a broad kinematic region for $x$ well below $x_0$. A detailed theoretical discussion of saturation scale and scaling is presented. The ratio $σ^{diff}/σ^{tot}$ is computed for several nuclei. We predict that at $x\simeq…
We present our study of the diffraction in charged current DIS. We analyse the perturbatively tractable excitation of heavy quarks, emphasizing the peculiarities of the Regge factorization breaking in excitation of open charm.
Within the k_t-factorization framework, we study diffractive production of orbitally excited vector mesons and compare it with the production of radial excitations, focusing on the rho(1450)/rho(1700) case. At small Q^2, orbital excitation of light quarkonia is found to dominate over radial excitations in diffractive production. We predict strong suppression of the production of orbital excitations by longitudinal photons, which leads to very small sigma_L/sigma_T ratio. At small Q^2, the s-channel helicity violating transitions contribute \sim 10-15% of the transverse cross section and \sim 5…
Revisiting the role of saturation in diffractive vector meson production
University of Jyväskylä（于韦斯屈莱大学）；Helsinki Institute of Physics（赫尔辛基物理研究所）；Brookhaven National Laboratory（布鲁克海文国家实验室）；Wayne State University（韦恩州立大学）；Central China Normal University（华中师范大学）
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.
Through an analysis of diffractive vector meson production, we show that the proton appears quite dense to a small size probe at present HERA energies. This means that saturation effects are already important.
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.
In the paper we discussed the evolution equations for diffractive production in the framework of CGC/saturation approach, and found the analytical solutions for several kinematic regions. The most impressive features of these solutions are, that diffractive production does not exibit geometric scaling behaviour i.e. being a function of one variable. Based on these solutions, we suggest an impact parameter dependent saturation model, which is suitable for describing diffraction production both deep in the saturation region, and in the vicinity of the saturation scale. Using the model we attempt…
In this letter we demonstrate that our dipole model is successful in describing the inclusive production within the same framework as diffractive physics. We believe that this achievement stems from the fact that our approach incorporates the positive features of the Reggeon approach and CGC/saturation effective theory, for high energy QC
We discuss a phenomenological model that describes results on diffractive pp and pbar-p cross sections and event final states up to the Fermilab Tevatron collider energy of 1.96 TeV and use it to make predictions for Large Hadron Collider (LHC) collision energies up to 14 TeV and asymptotically as the pp collision energy goes to infinity. The model is anchored in a saturation effect observed in single diffraction dissociation that explains quantitatively the factorization breaking observed in soft and hard pp and pbar-p diffractive processes and in diffractive photoproduction and low Q-square …
We demonstrate that hard dijet production via coherent inelastic diffraction is a promising channel for probing gluon saturation at the Electron-Ion Collider. By $inelastic$ diffraction we mean a process in which the two hard jets - a quark-antiquark pair generated by the decay of the virtual photon - are accompanied by a softer gluon jet, emitted by the quark or the antiquark. This process can be described as the elastic scattering of an effective gluon-gluon dipole. The cross section takes a factorised form, between a hard factor and a unintegrated ("Pomeron") gluon distribution describing t…
The Lund dipole model DIPSY is based on BFKL evolution and saturation. It can be applied to collisions between electrons, protons, and nuclei. In this talk I present some recent results for exclusive final states in inelastic collisions, a method to generate final states in diffractive excitation, and some results for collisions with nuclei.
We present various aspects of the saturation model which provides good description of inclusive and diffractive DIS at small x. The model uses parton saturation ideas to take into account unitarity requirements. A new scaling predicted by the model in the small x domain is successfully confronted with the data.
We describe the most recent data on the diffractive structure functions from the H1 and ZEUS Collaborations at HERA using four models. First, a Pomeron Structure Function (PSF) model, in which the Pomeron is considered as an object with parton distribution functions. Then, the Bartels Ellis Kowalski Wusthoff (BEKW) approach is discussed, assuming the simplest perturbative description of the Pomeron using a two-gluon ladder. A third approach, the Bialas Peschanski (BP) model, based on the dipole formalism is then described. Finally, we discuss the Golec-Biernat-Wüsthoff (GBW) saturation model w…
We study exclusive dijet production in coherent diffractive processes in deep inelastic scattering and real (and virtual) photon-hadron ($γ^{(*)}$-h) collisions in the Color Glass Condensate formalism at leading order. We show that the diffractive dijet cross section is sensitive to the color-dipole orientation in the transverse plane, and is a good probe of possible correlations between the $q\bar{q}$-dipole transverse separation vector $\r$ and the dipole impact parameter $\b$. We also investigate the diffractive dijet azimuthal angle correlations and $t$-distributions in $γ^{(*)}$-h collisi…
With the imminent construction of an electron-ion collider in the USA, both saturation physics and nuclear shadowing physics will be important for the same processes for the first time. In particular for exclusive production of vector mesons, such as the J/$ψ$. In this paper we investigate the underlying assumptions commonly made when phenomenologically investigating this process from a shadowing and saturation perspective respectively. We use the bSat model which is commonly used to describe saturation physics, and a calculation by M.G. Ryskin which is commonly used when describing nuclear sh…
