Yu. M. Shabelski, A. G. Shuvaev
High energy (CERN SPS and LHC) $pp$ ($p\bar p$) scattering is treated in the framework of Additive Quark Model together with Pomeron exchange theory. The reasonable agreement with experimental data is achieved both for the elastic scattering and for the diffractive dissociation with natural parameters for the strong matter distribution inside proton.
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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 present main ideas and obtained results of our recent calculations of Coulomb and QCD contribution to the pion diffractive dissociation into two jets.
We calculate the cross section for the production of two jets with large transverse momenta $\kf^2$ in DIS diffractive dissociation for both transverse and longitudinally polarized photons. The scale which defines the hardness of the pomeron is found to be $\kf^2\frac{Q^2+M^2}{M^2}$. We present analytic expressions and discuss numerical results relevant for the diffractive dissociation at HERA.
We describe a QCD based model which incorporates the main properties of the inclusive particle distributions expected for diffractive processes, including the diffractive dissociation at high energies. We study, in turn, the total cross section, $σ_{tot}$, the differential elastic, $dσ_{el}/dt$, cross section, the dependence of the single proton dissociation cross section, $ξd^{SD}/dξ$, on the momentum fraction, $ξ= 1-x_L$, lost by the leading proton, the multiplicity distributions in inelastic (non-diffractive) collisions and in the processes of dissociation. Besides this we calculate the mea…
We summarize the results of including running coupling corrections into the nonlinear evolution equation for diffractive dissociation. We also document a prediction that the NLO QCD odderon intercept is zero resulting from a discussion at the Diffraction 2012 Workshop.
The fundamental relations in the dynamics of single diffraction dissociation and elastic scattering at high energies are discussed.
We discuss the high energy diffractive dissociation in DIS at the Next to Leading Order. In the large $N_c$ dipole limit we derive the NLO version of the Kovchegov-Levin equation. We argue that the original structure of the equation is preserved, that is it coincides with the Balitsky-Kovchegov equation at NLO.
We have extended the Interacting Gluon Model (IGM) to calculate diffractive mass spectra generated in hadronic collisions. We show that it is possible to treat both diffractive and non-diffractive events on the same footing, in terms of gluon-gluon collisions. A systematic analysis of available data is performed. The energy dependence of diffractive mass spectra is addressed. They show a moderate narrowing at increasing energies. Predictions for LHC energies are presented.
We report on investigations concerning the production of large transverse momentum jets in DIS diffractive dissociation. These processes constitute a new class of events that allow for a clean test of perturbative QCD and of the hard (perturbative) pomeron picture. The measurement of the corresponding cross sections might possibly serve to determine the gluon density of the proton.
We study diffractive scattering cross sections, focusing on the rapidity gap distribution in realistic kinematics at future electron-ion colliders. Our study consists in numerical solutions of the QCD evolution equations in both fixed and running coupling frameworks. The fixed and the running coupling equations are shown to lead to different shapes for the rapidity gap distribution. The obtained distribution when the coupling is fixed exhibits a shape characteristic of a recently developed model for diffractive dissociation, which indicates the relevance of the study of that diffractive observ…
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.
We calculate the cross sections for both electromagnetic and diffractive dissociation of protons for semiexclusive production of $J/ψ$ mesons in proton-proton collisions at the LHC. Several differential distributions in missing mass ($M_X$), or single-particle variables related exclusively to the $J/ψ$ meson are calculated for $\sqrt{s}$ = 7 TeV as an example. The cross sections and distributions are compared to the cross section of the purely exclusive reaction $p p \to p p J/ψ$. We show the corresponding ratio as a function of $J/ψ$ meson rapidity. We compare the distributions for purely ele…
We report a study of the processes of coherent a pion and a photon diffraction dissociation into two jets. The structure of non-factorizable contributions in these reactions is discussed. We argue that production of hard dijets by real photons can provide direct evidence for chirality violation in hard processes and the first measurement of the magnetic susceptibility of the quark condensate.
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 investigate the azimuthal distribution of quark-antiquark jets in DIS diffractive dissociation with large transverse momentum. In this kinematical region the matrix element is expressed in terms of the gluon structure function. For the transverse part of the cross section we find a $\cos(2 ϕ)$-distribution with the maximum at $ϕ= \pm π/2$, i.e.\ the jets prefer a direction perpendicular to the electron plane. This is in contrast to boson gluon fusion where the $q\bar{q}$ jet cross section for transversely polarized bosons peaks at $ϕ=0$ and $ϕ=π$. We discuss the origin of this striking diff…
We study the diffractive production of $q\bar{q}g$ jets with large transverse momenta in the region of large diffractive masses (small $β$). Cross sections for transverse and longitudinal photons are obtained in the leading log $1/x_{\fP}$ and log $1/β$ approximation, keeping all powers in log $k_t^2/Q^2$. We perform a numerical study and illustrate the angular distribution of the three jets. We also estimate the integrated diffractive three jet cross section and compare with the dijet cross section obtained before.
We show that eikonal corrections imposed on diffraction dissociation processes calculated in the triple Regge limit, produce a radical change in the energy dependence of the predicted cross section. The induced correction is shown to be in general agreement with the new experimental data measured at the Tevatron.
We present a calculation of open charm quark production in diffractive deep inelastic electron-proton scattering in a perturbative QCD framework. The cross section is proportional to the square of the gluon density and explicitly displays breaking of Regge factorization. Jet cross sections as well as the charm contribution to the diffractive structure function are calculated. As a consequence of the steep rise of the gluon density at small x the charm contribution to $F_2^{D}$ rises with decreasing x_P.
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 …
We present predictions for the distribution of rapidity gaps in realistic kinematics of future electron-ion colliders, based on numerical solutions of the original Kovchegov-Levin equation and of its next-to-leading extension taking into account the running of the strong coupling. We find that for the rapidities we have considered, the fixed and the running coupling equations lead to different distributions, rather insensitive to the chosen prescription in the running coupling case. The obtained distributions for the fixed coupling framework exhibit a shape characteristic of a recently propose…
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)
It is shown that in a supercritical pomeron model the contribution of the tirple-pomeron diagrams violates the unitarity bound for cross-section even with account of the multiple pomeron exchanges between the initial hadrons. Asymptotic behaviour of the single diffractive dissoci\-ation cross-section is calculated in the approximation where every pomeron in the $3P$-diagram is eikonalized as well as an elastic interaction of initial hadrons is taken into account. In this approximation $σ^{SD}/σ_{tot}\rightarrow 0$ at $s\rightarrow \infty.$
The diffraction dissociation of virtual photons is considered in the framework of conventional Regge theory. It is shown that the recent HERA data on large rapidity gap events can be successfully described in terms of the Pomeron structure function. Using Regge factorization, the latter can be related to the deuteron structure function. The parameters which relate these two structure functions are determined from soft hadronic diffraction data. The size of the shadowing corrections at low x and large Q**2 is also obtained.
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, …
We present a partonic picture for diffractive onium-nucleus scattering in the large-number-of-color limit from which the distribution of rapidity gaps in a certain kinematic region can be deduced. This picture allows us to draw a parallel between diffractive dissociation and the genealogy of partonic evolution, the latter being essentially similar to a branching-diffusion process in which the branching is the parton splitting, and the diffusion occurs in the transverse momenta of the partons. In particular, we show that the rapidity gap distribution corresponds to the distribution of the split…
The small-$t$ behaviour of the deep inelastic diffractive dissociation cross section in the triple Regge region is investigated, using the BFKL approximation in perturbative QCD. We show that the cross section is finite at $t=0$, but the diffusion in $\ln{k_t^2}$ leads to a large contribution of small momenta at the triple Pomeron vertex. We study the dependence upon the total energy and the invariant mass. At $t=0$, there is a decoupling of the three BFKL singularities which is a consequence of the conservation of the conformal dimension. For large invariant masses, the four gluon state in th…
We determine running coupling corrections to the kernel of the non-linear evolution equation for the cross section of single diffractive dissociation in high energy DIS. The running coupling kernel for diffractive evolution is found to be exactly the same as the kernel of the rcBK evolution equation.
Coherently diffractive dissociation in electron-hadron collisions: from HERA to the future EIC
该研究利用含跑动耦合的非线性 Kovchegov-Levin 方程计算电子-强子相干衍射解离，以 HERA 数据约束质子初始条件，并通过光学 Glauber 模型推广到核靶，预言未来 EIC 能区存在显著核修正。
We present the cross sections for both electromagnetic and diffractive dissociation of protons for semiexclusive production of $J/ψ$ mesons in proton-proton collisions at the LHC. Differential distributions in missing mass ($M_X$), as well as distributions in rapidity and transverse momentum of the $J/ψ$ are calculated for $\sqrt{s} = 7$ TeV and 13 TeV proton proton collisions. We compare the distributions for purely electromagnetic and purely diffractive proton excitations/dissociation. We predict cross sections for electromagnetic and diffractive excitations of similar order of magnitude.
We study the behaviour of elastic and diffractive proton dissociation cross sections at high energy. First, we describe what would be expected to be observed at the 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 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 prese…
We calculate spectra of secondary particles produced in process of single diffraction dissociation in the Model of Quark-Gluon Strings. For description of diffractive dissociation process we use the reggeon model where all legs of triple-reggeon diagrams are eikonalized. Numerical calculation shows that the model gives a good description of data on charged particles pseudorapidity distribution in $p\bar{p}$ single diffractive dissociation.
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…
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 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.
We describe the formalism, and present the results, for a triple-Regge analysis of the available pp and p\bar{p} high-energy data which explicitly accounts for absorptive corrections. In particular, we allow for the gap survival probability, S^2, in single proton diffractive dissociation. Since for pp scattering the value of S^2 is rather small, the triple-Pomeron vertex obtained in this analysis is larger than that obtained in the old analyses where the suppression caused by the absorptive corrections was implicitly included in an effective vertex. We show that the bare triple-Pomeron couplin…
We calculate the cross section of a pion diffraction dissociation in two jets with large transverse momenta originating from a hard gluon exchange between the pion constituents. To the leading logarithmic accuracy (in energy), the contribution coming from small transverse separations between the quark and the antiquark in the pion acquires the expected factorized form, the longitudinal momentum distribution of the jets being proportional to the pion distribution amplitude. The hard gluon exchange can in this case be considered as a part of the unintegrated gluon distribution. Beyond the leadin…
The excitation of the proton into undetected multiparticle states (double diffraction dissociation) is an important background to single diffractive deep-inelastic processes $ep \rightarrow e'p'ρ^{0}, ~e'p'J/Ψ, ~e'p'X$ at HERA. We present estimates of the admixture of the double diffraction dissociation events in all diffractive events. We find that in the $J/Ψ$ photoproduction, electroproduction of the $ρ^0$ at large $Q^2$ and diffraction dissociation of real and virtual photons into high mass states $X$ the contamination of the double diffraction dissociation can be as large as $\sim 30\%$, …
We consider angular dependence of the diffractive dissociation processes at high energies. It appeared that angular dependence of the diffractive dissociation has no dip and bump structure at the LHC energies and would show a smooth power-like decrease with $t$. The normalized differential cross-section has a scaling behavior and depends on the ratio $-t/M^2$ only. These results reflect general trends of unitarity limitations at high energies and are realized within the chiral quark model with unitarization performed through the generalized reaction matrix.
Diffractive events at hadron colliders are typically characterised by a region of the detector without particles, known as a rapidity gap. In order to observe diffractive events in this way, we consider the pseudorapidity acceptance in the forward region of the ATLAS and CMS detectors at the Large Hadron Collider (LHC) and discuss the methods to select soft diffractive dissociation for pp collisions at sqrt(s) = 7 TeV. We showed that in the limited detector rapidity acceptance, it is possible to select diffractive dissociated events by requiring a rapidity gap in the event, however, it is not …
We explore the possibility whether the gluon helicity distribution $ΔG(x)$ can be extracted from a comparison of experimental data on the longitudinal spin-spin asymmetry $A_{LL}$ in $γp$ diffractive deep inelastic scattering with calculations performed within the framework of perturbative QCD (pQCD). The data could be obtained at the future HERA collider in scattering of polarized electrons/positrons off polarized protons. In this paper we look for such kinematical regions where contributions to $A_{LL}$ from soft processes (reggeon exchanges) are suppressed to guarantee an applicability of p…
A selected review of topics at the border of hard and soft physics is given. Particular emphasis is a placed on diffraction dissociation at Fermilab and HERA. Recently, significant differences between diffraction dissociation at HERA and at Fermilab have become apparent. This may suggest that one already is reaching nonlinear (unitarity) effects which are extending from the soft physics region into the semihard regime of QCD.
The diffractive dissociation of a hadron at high energies, by either Coulomb or Pomeron exchange, has a natural description in QCD as the materialization of the projectile's light-cone wavefunctions; in particular, the diffractive dissociation of a meson, baryon, or photon into high transverse momentum jets measures the shape and other features of the projectile's distribution amplitude. Diffractive dissociation can thus test fundamental properties of QCD, including color transparency and intrinsic charm. All of these effects have an impact on exclusive decays of $B$ mesons and the study of $C…
Diffractive dissociation processes are analysed in the framework of covariant reggeization. We have considered the general form of hadronic tensor and its asymptotic behaviour for $t\rightarrow 0$ in the case of conserved tensor currents before reggeization. Resulting expressions for differential cross-section of single dissociation (SD) process ($pp \rightarrow p M$), double dissociation (DD) ($pp\rightarrow M_1 M_2$) and for the proton-Pomeron cross-section are given in detail, and corresponding problems of the approach are discussed.
We demonstrate that study of large t vector meson photoproduction with rapidity gaps in ultraperipheral proton-ion and ion-ion collisions at LHC would allow to investigate the energy dependence of cross section of elastic scattering of a small dipole off the parton over a wide range of energies $10^3 < s_{dipole - parton} < 10^6 GeV^2$ where this cross section is expected to change by a factor $\ge 20$. The accessible energy range exceeds the one reached at HERA by a factor of 10 both in $γp$ and in $γA$ scattering. In addition, study of A-dependence of this process will allow to determine the…
We explore the possibility to observe hard exclusive three-jet production in early LHC runs, corresponding to diffractive dissociation of the incident proton into three jets with large but compensating transverse momenta. This process is sensitive to the proton unintegrated gluon distribution at small x and to the distribution of the three valence quarks in the proton at small transverse distances. The corresponding cross section is calculated using an approach based on k_t factorization. According to our estimates, observation of hard diffractive three-jet production at LHC is feasible for je…
We evaluate the large momentum transfer $J/ψ$ photoproduction with rapidity gaps in ultraperipheral proton-ion collisions at the LHC which provides an effective method of probing dynamics of large t elastic hard QCD Pomeron interactions. It is shown that the experimental studies of this process would allow to investigate the energy dependence of cross section of elastic scattering of a small $c\bar c$ dipole off the gluon over a wide range of invariant energies 10^3 < s_{c\bar c - gluon} < 10^6 GeV^2. The accessible energy range exceeds the one reached in γp at HERA by a factor of 10 and allow…
Dip-Bump Structure in Proton's Single Diffractive Dissociation at the Large Hadron Collider
本文扩展偶极子 Pomeron 模型至质子单衍射解离，预测了 LHC 能量下 $t$ 分布中的偶极子-凸起结构，并引入了与缺失质量相关的直接道 Regge 轨迹。
We discuss diffractive dissociation of gluons into heavy quark pairs. The particular mechanism is similar to the diffractive dissociation of virtual photons into quarks. The amplitude for the $g p \to Q \bar Q p$ is derived in the impact parameter and momentum space. The cross section for single diffractive $p p \to Q \bar Q p X$ is calculated as a convolution of the elementary cross section and gluon distribution in the proton. Integrated cross section and differential distributions in transverse momentum and rapidity of the charm and bottom quark and antiquark, etc. are calculated for the no…
Contribution of the gluon distribution in the nucleon to the cross section for the pion diffractive dissociation into two jets has been calculated recently. In addition, we present here calculation of contribution of the quark distributions to this process. It is expected usually that the quark contributions are much smaller than the gluon one at high energies. We show that, under the conditions of the E791 experiment, the quark contributions are as significant as the gluon one, so that the total cross section exceeds several times those with only gluon contribution. Nevertheless, the distribu…
A large correlation of production and decay planes of (π^-π^+π^-)-system in dissociation of $π^-$-beam 40 GeV/c on nuclear targets was observed. The dependence of the correlation on atomic number, Feynmann variable and transversal momentum as well as on invariant mass of the pion triple and neutral pion pair were investigated. It was shown that the phenomenon has a clear dynamic origin and resembles the single spin asymmetry behavior.
Impact of the $f$-Reggeon exchanges on the observables of the single diffractive dissociation of nucleon at ultrahigh energies
本文提出具有非线性 Regge 轨迹的双 Reggeon 模型，研究高能碰撞中核子单衍射解离，证明考虑 $f$-Reggeon 交换不可忽略，并在统一唯象方案内描述了弹性衍射散射与 SDD。
The cross section for the nuclear diffractive dissociation in proton-lead collisions at the LHC is estimated. Based on the current theoretical uncertainties for the single (target) diffactive cross section in hadron-hadron reactions one obtains sigma_SD(5.02 TeV) = 19.67 \pm 5.41 mb and sigma_SD(8.8 TeV) = 18.76 \pm 5.77 mb, respectively. The invariant mass M_X for the reaction pPb -> pX is also analyzed. Discussion is performed on the main theoretical uncertainties associated to the calculations.
We propose a partonic picture for high-mass diffractive dissociation events in onium-nucleus scattering, which leads to simple and robust predictions for the distribution of the sizes of gaps in diffractive dissociation of virtual photons off nuclei at very high energies. We show that the obtained probability distribution can formally be identified to the distribution of the decay time of the most recent common ancestor of a set of objects generated near the edge of a branching random walk, and explain the physical origin of this appealing correspondence. We then use the fact that the diffract…
We discuss diffractive dissociation of gluons into heavy quark pairs. The particular mechanism is similar to the diffractive dissociation of virtual photons into quarks, which drives diffractive deep inelastic production of charm in the low-mass diffraction, or large $β$-region. There, it can be understood, with some reservations, in terms of a valence heavy quark content of the Pomeron. The amplitude for the $g p \to Q \bar Q p$ is derived in the impact parameter and momentum space. The cross section for single diffractive $p p \to Q \bar Q p X$ is calculated as a convolution of the elementar…
We calculate $p_T$-dependences of diffractive vector meson photo- and electroproduction in electron-proton collisions with and without proton dissociation at small momenta transfers. The calculated slopes are in good agreement with the data.
The model of soft diffractive dissociation proposed some time ago by Miettinen and Pumplin is shown to describe correctly the data at FERMILAB energies. The comparison with Goulianos model of renor malized pomeron flux is also presented.
The method used and results obtained are described for calculation of the cross section for the pion diffractive dissociation into two jets. The main new qualitative result is that the distribution of longitudinal momenta for jets is not simply proportional to the profile of the pion wave function $ϕ_π(x)$, but depends on it in a complicated way. In particular, it is shown that under conditions of the E791 experiment, the momentum distribution of jets is similar in its shape for the asymptotic and CZ wave functions. It is concluded therefore that, unfortunately, the process considered is reall…
The background due to the direct diffractive dissociation of the photon into the $π^+π^-$-pair to the "elastic" diffractive $ρ^0$-meson production in electron-proton collisions is calculated. At large $Q^2$ the interference between resonant and non-resonant $π^+ π^-$ production changes the $σ^L/σ^T$ ratio with the mass of the $2π$ (i.e. $ρ^0$-meson) state.
We present an evolution equation for the Bjorken x dependence of diffractive dissociation on hadrons and nuclei at high energies. We extend the formulation of Kovchegov and Levin by relaxing the factorization assumption used there. The formulation is based on a technique used by Weigert to describe interjet energy flow. The method can be naturally extended to other exclusive observables.
In this thesis, we study the detailed partonic content of the quantum states of a quark-antiquark color dipole subject to high-energy evolution, which are represented by a set of dipoles generated by a stochastic binary branching process, in the scattering off a large nucleus, and produce predictions for diffractive dissociation in electron-ion collisions, based on the dipole picture of QCD. Our main results are as follows. First, the scattering events of a color dipole, when parameters are set in such a way that the total cross section is small, are triggered by rare partonic fluctuations, wh…
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