We show that the diffractive forward production of two quarkonia, especially the $χ_{cJ}$ and $η_c$ states, in proton-proton or proton-ion collisions can access the Weizsäcker-Williams gluon Wigner distribution of the proton. We use the hybrid factorization approach where the collinear, double gluon PDF is applied for one of the protons and the $k_T$-dependent (Wigner or GTMD) distribution for the other. The production of quarkonia is treated in the NRQCD framework. A particularly concise formula is obtained for double $χ_{J=1}$ production.
The appears to exist no detailed calculation of the multiphoton trident process e + n omega_0 -> e' + e+e-, which can occur during the interaction of an electron beam with an intense laser beam. We present a calculation in the Weizsacker-Williams approximation that is in good agreement with QED calculations for the weak-field case.
We compute the quantum corrections to the gluon distribution function in the background of a non--Abelian Weizsäcker--Williams field. These corrections are valid to all orders in the effective coupling $α_s μ$, where $μ^2$ denotes the average valence quark color charge squared per unit area. We find $\ln(1/x)$ logarithmic corrections to the classical gluon distribution function. The one loop corrections to the classical Weizsäcker-Williams field do not contribute to these singular terms in the distribution function. Their effect is to cause the running of $α_s$.
We carefully compute the gluon propagator in the background of a non--Abelian Weizsäcker--Williams field. This background field is generated by the valence quarks in very large nuclei. We find contact terms in the small fluctuation equations of motion which induce corrections to a previously incorrect result for the gluon propagator in such a background field. The well known problem of the Hermiticity of certain operators in Light Cone gauge is resolved for the Weizsäcker--Williams background field. This is achieved by working in a gauge where singular terms in the equations of motion are abse…
We critically examine the validity of the Weizsäcker-Williams approximation in electron-hadron collisions. We show that in its commonly used form it can lead to large errors, and we show how to improve it in order to get accurate results. In particular, we present an improved form that is valid beyond the leading logarithmic approximation in the case when a small-angle cut is applied to the scattered electron. Furthermore we include comparisons of the approximate expressions with the exact electroproduction calculation in the case of heavy-quark production.
We consider the McLerran-Venugopalan model for calculation of the small-$x$ part of the gluon distribution function for a very large ultrarelativistic nucleus at weak coupling. We construct the Feynman diagrams which correspond to the classical Weizsäcker-Williams field found previously [Yu. V. Kovchegov, Phys. Rev. D 54, 5463 (1996)] as a solution of the classical equations of motion for the gluon field in the light-cone gauge. Analyzing these diagrams we obtain a limit for the McLerran-Venugopalan model. We show that as long as this limit is not violated a classical field can be used for cal…
The Weizsaecker-Williams transverse momentum dependent (TMD) gluon distributions can be probed in the production of a hard dijet in semi-inclusive DIS. This process is sensitive not only to the conventional but also to the linearly polarized gluon distribution. The latter gives rise to an azimuthal dependence of the dijet cross section and therefore can be distinguished from the former. Feasibility study of a measurement of these TMDs through dijet production at a future electron-ion collider shows that the extraction of the distribution of linearly polarized gluons with a statistical accuracy…
We consider the collisions of large nuclei using the theory of McLerran and Venugopalan. The two nuclei are ultra-relativistic and sources of non-abelian Weizsäcker-Williams fields. These sources are in the end averaged over all color orientations locally with a Gaussian weight. We show that there is a solution of the equations of motion for the two nucleus scattering problem where the fields are time and rapidity independent before the collision. After the collision the solution depends on proper time, but is independent of rapidity. We show how to extract the produced gluons from the classic…
The conventional and linearly polarized Weizsäcker-Williams gluon distributions at small x are defined from the two-point function of the gluon field in light-cone gauge. They appear in the cross section for dijet production in deep inelastic scattering at high energy. We determine these functions in the small-x limit from solutions of the JIMWLK evolution equations and show that they exhibit approximate geometric scaling. Also, we discuss the functional distributions of these WW gluon distributions over the JIMWLK ensemble at rapidity $Y\sim 1/α_s$. These are determined by a 2d Liouville acti…
Color quadrupoles have been found to be important in the proper description of observables sensitive to the small-x regime in nuclei as well as in the operator definition of the Weizsäcker-Williams gluon distribution. In this paper, we derive the small-x evolution equation of the quadrupole and the Weizsäcker-Williams gluon distribution without taking large N_c limit and study the properties of the equation in both dilute and saturation regime. We find that the quadrupole evolution follows the BFKL evolution in the dilute regime and then saturates in the dense region due to nonlinear terms. Th…
The $J/ψ$ production originating from elastic and inelastic photoproduction processes in p-p collisions at LHC energies is investigated, where the fragmentation processes are involved. An exact treatment is performed, which adopts the Martin-Ryskin method to weight the contribution from different channels, and can return to Weizsäcker-Williams approximation (WWA) when $Q^{2}\rightarrow0$. The relevant kinematical relations are also achieved. We present a comprehensive analysis for the feature of WWA by comparing with the exact treatment. The results are expressed in $Q^{2}$, $y$, $z$, $p_{T}$,…
We study the production and signatures of doubly charged Higgs bosons in the process γγH^{- -} H^{++} at the e^-e^+ International Linear Collider and CERN Linear Collider, where the intermediate photons are given by the Weizs[a\ddot]cker-Willians and laser backscattering distributions.
The production of a hard dijet with small transverse momentum imbalance in semi-inclusive DIS probes the conventional and linearly polarized Weizsaecker-Williams (WW) Transverse Momentum Dependent (TMD) gluon distributions. The latter, in particular, gives rise to an azimuthal dependence of the dijet cross-section. In this paper we analyze the feasibility of a measurement of these TMDs through dijet production in DIS on a nucleus at an Electron-Ion Collider. We introduce the MCDijet Monte-Carlo generator to sample quark-antiquark dijet configurations based on leading order parton level cross-…
Beam dump experiments have been used to search for new particles with null results interpreted in terms of limits on masses $m_ϕ$ and coupling constants $ε$. However these limits have been obtained by using approximations [including the Weizsäcker-Williams (WW) approximation] or Monte-Carlo simulations. We display methods, using a new scalar boson as an example, to obtain the cross section and the resulting particle production numbers without using approximations or Monte-Carlo simulations. We show that the approximations cannot be used to obtain accurate values of cross sections. The correspo…
Beam dump experiments have been used to search for new particles, $ϕ$, with null results interpreted in terms of limits on masses $m_ϕ$ and coupling constants $ε$. However these limits have been obtained by using approximations [including the Weizsäcker-Williams (WW) approximation] or Monte-Carlo simulations. We display methods to obtain the cross section and the resulting particle production rates without using approximations on the phase space integral or Monte-Carlo simulations. In our previous work we examined the case of the new scalar boson production; in this paper we explore all possib…
Considering very high energy peripheral electron-hadron scattering with a production of hadronic state X moving closely to the direction of initial hadron the Weizsäcker-Williams like expression, relating the difference of q^2-dependent differential cross-sections of DIS processes to the convergent integral over the difference of the total hadron photo-production cross-sections on hadros, is derived. Then, exploiting analytic properties of the forward retarded Compton scattering amplitude on the same hadrons, first, the sum rules are derived bringing into relation hadron electromagnetic form f…
We systematically study dijet production in various processes in the small-$x$ limit and establish an effective $k_t$-factorization for hard processes in a system with dilute probes scattering on a dense target. We find that the well-known Weizsäcker-Williams gluon distribution can be directly probed in the quark-antiquark jet correlation in deep inelastic scattering and the dipole gluon distribution can be directly measured in the direct photon-jet correlation in $pA$ collisions. In the large-$N_c$ limit, the unintegrated gluon distributions involved in other different dijet channels in pA co…
We propose a novel way of studying the gluon number density (the so-called Weizsäcker-Williams gluon distribution) using the planned Electron Ion Collider. Namely, with the help of the azimuthal correlations between the total transverse momentum of the dijet system and the scattered electron, we examine an interplay between the effect of the soft gluon emissions (the Sudakov form factor) and the gluon saturation effects. The kinematic cuts are chosen such that the dijet system is produced in the forward direction in the laboratory frame, which provides an upper bound on the probed longitudinal…
The distribution of linearly polarized gluons inside a large nucleus is studied in the framework of the color glass condensate. We find that the Weizsäcker-Williams distribution saturates the positivity bound at large transverse momenta and is suppressed at small transverse momenta, whereas the dipole distribution saturates the bound for any value of the transverse momentum. We also discuss processes in which both distributions of linearly polarized gluons can be probed.
The method of equivalent quanta is applied both to photon-photon and, by analogy, to double pomeron exchange in heavy-ion collisions. This Weizsäcker-Williams approach is used to calculate production cross sections for the glueball candidate $f_J(1710)$ meson via photon-photon and pomeron-pomeron fusion in peripheral heavy-ion collisions at both RHIC and LHC energies. The impact-parameter dependence for total and elastic cross sections are presented, and are compared to results for proton-proton collisions.
Quark and gluon distributions in the light-cone wavefunction of a high energy hadron or nucleus are calculated in the saturation regime. One loop calculations are performed explicitly using the equivalence between the parton distribution in the light-cone wavefunction and the production distribution of that parton in a current-nucleon (nucleus) scattering. We argue that, except for some overall numerical factors, the Weizsacker- Williams wavefunction correctly gives the physics of the gluon distribution in a light-cone wavefunction.
The process of two pion production in the electron-polarized proton scattering is investigated. In the Weizsäcker-Williams approximation the differential spectral distributions and the spin-momentum correlations are considered. The spin correlation effects caused by $ρ$-meson widths are estimated to be of an order of several per cent. Both channels of the $π^+π^-$ and $π^+π^0$ creation are considered. The effects of intermediate excited baryons are not considered. The spectral distributions on pion energy fractions in polarized and unpolarized cases are presented analytically and numerically.
We determine the first correction to the quadrupole operator in high-energy QCD beyond the TMD limit of Weizsaecker-Williams and linearly polarized gluon distributions. These functions give rise to isotropic resp. ~ cos 2 phi angular distributions in DIS dijet production. On the other hand, the correction produces a ~ cos 4 phi angular dependence which is suppressed by one additional power of the dijet transverse momentum scale (squared) P^2.
Experiments using proton beams at high luminosity colliders and fixed target facilities provide impressive sensitivity to new light weakly coupled degrees of freedom. With these experiments in mind, we revisit the production of dark vectors and scalars via proton bremsstrahlung, making use of a model that describes the underlying nucleon scattering cross-section in the forward direction due to pomeron exchange. We compare the resulting distributions and rates with those obtained via variants of the Fermi-Weizsacker-Williams approximation, and provide production rate distributions for a range o…
Presented here is a calculation of inelastic $J/ψ$ production in polarized photon-hadron collisions under the framework of NRQCD factorization formalism. We consider the photoproduction of $\jpsi$ in the energy range relevant to HERA. The Weizsäcker-Williams approximation is adopted in the evaluation of the cross sections for $ep$ collisions. We found that this process can give another independent test for the color-octet mechanism, and the different features for the two color-octet processes may provide further informations on the mechanism for inelastic $\jpsi$ photoproduction. And the discr…
Quark-antiquark pair (or dijet) production at the electron-ion collider (EIC) has been argued to be one of most important processes that allowing to access the Weizsäcker-Williams (WW) gluon distributions at small $x$ limit. Within the framework of Color Glass Condensate (CGC) effective field theory (EFT), we calculated the dijet cross sections and the azimuthal correlations by including the Sudakov resummations, numerical results shown that the back-to-back correlations are significantly suppressed when the Sudakov resummations are taken into account. In addition, by using the solutions of ru…
We present a computation of one- and two-jet cross sections in polarized photon-hadron collisions, which is accurate to next-to-leading order in QCD. Our results can be used to compute photoproduction cross sections in electron-proton scattering. To this purpose, we investigate the structure of the polarized Weizsaecker-Williams function, where we include a universal, non-logarithmic term, neglected in the literature. We construct a Monte Carlo code, within the framework of the subtraction method, and we use it to study the phenomenology of jet production in the energy range relevant to HERA. …
Differential cross section of processes with high energy $p(\bar p)p$ collisions in frames of QED: creation of scalar, pseudoscalar and lepton pair - are considered in Weizsäcker - Williams approximation. In frames of QCD processes with conversion of initial proton (antiproton) to fermionic jets accompanied with one gluon jet as well as the state of two gluons and quark-antiquark pair (with out rapidity gap) are considered in frames of effective Reggion action of theory of Lipatov. Process of creation of a Higgs boson accompanied with two fermionic jets is considered. The azimuthal correlation…
We compute the distribution functions for gluons at very small x and not too large values of transverse momenta. We extend the McLerran-Venugopalan model by using renormalization group methods to integrate out effects due to those gluons which generate an effective classical charge density for Weizsäcker-Williams fields. We argue that this model can be extended from the description of nuclei at small x to the description of hadrons at yet smaller values of x. This generates a Lipatov like enhancement for the intrinsic gluon distribution function and a non-trivial transverse momentum dependence…
It has been shown recently that there exist analytical solutions of the Yang-Mills equations for non-Abelian Weizsäcker-Williams fields which describe the distribution of gluons in large nuclei at small x. These solutions however depend on the color charge distribution at large rapidities. We here construct a model of the color charge distribution of partons in the fragmentation region and use it to compute the boost covariant momentum distributions of wee gluons. The phenomenological applications of our results are discussed.
We study the feasibility of producing the graviton of the novel Kaluza-Klein theory in which there are d large compact dimensions in addition to the 4 dimensions of Minkowski spacetime. We calculate the cross section for producing such a graviton in nucleus-nucleus collisions via t-channel photon-photon fusion using the semiclassical Weizsacker-Williams method and show that it can exceed the cross section for graviton production in electron-positron scattering by several orders of magnitude.
Heavy nuclei at collider energies are a source of high energy Weizsaecker-Williams photons. This photon flux may be utilized to study high energy photon-nucleus interactions. Here we concentrate on the coherent diffractive production of heavy vector mesons on nuclear targets and show how it probes the unintegrated glue of the nucleus in the saturation domain. We present predictions for rapidity distributions of exclusive coherent J/Psi and Upsilon mesons which can be measured by the ALICE experiment at the LHC.
We manifest the origin of the wrong conclusion made by several groups of authors on the absence of Coulomb corrections to the cross section of the e^+e^- pair production in ultrarelativistic heavy-ion collisions. The source of the mistake is connected with an incorrect passage to the limit in the expression for the cross section. When this error is eliminated, the Coulomb corrections do not vanish and agree with the results obtained within the Weizsäcker-Williams approximation.
Two widely proposed kt-dependent gluon distributions in the small-x saturation regime are investigated using two particle back-to-back correlations in high energy scattering processes. The Weizsacker-Williams gluon distribution, interpreted as the number density of gluon inside the nucleus, is studied in the quark-antiquark jet correlation in deep inelastic scattering. On the other hand, the unintegrated gluon distribution, defined as the Fourier transform of the color-dipole cross section, is probed in the direct photon-jet correlation in pA collisions. Dijet-correlation in pA collisions depe…
We use the Color Glass Condensate (CGC) framework to study the production of forward heavy quark-antiquark pairs in unpolarized proton-nucleus or proton-proton collisions in the small-x regime. In the limit of nearly back-to-back jets, the CGC result simplifies into the transverse-momentum dependent (TMD) factorization approach. For massless quarks, the TMD factorization formula involves three unpolarized gluon TMDs: the Weizsäcker-Williams gluon distribution, the adjoint-dipole gluon distribution, and an additional one. When quark masses are kept non-zero, three new gluon TMDs appear -- each …
Dilepton production from two photon interactions $γγ\rightarrow l^+l^-$ are studied in semi-central and peripheral nuclear collisions. Based on Weizsäcker-Williams approach, it is shown that the dilepton photoproduction is proportional to the electromagnetic (EM) fields $\sim E^2B^2$ and therefore sensitive to the magnitude and lifetime of initial EM fields which last only for a short time and are hard to be measured in experiments directly. We propose dilepton photoproduction as a probe for the nuclear charge fluctuations, which are crucial for the electric/magnetic field induced chiral and c…
We use a diagrammatic approach to study color-neutral heavy particle production in nucleus-nucleus collisions in a quasi-classical approximation without small-$x$ evolution. In order to treat the two nuclei symmetrically, we use the Coulomb gauge which gives the appropriate light cone gauge for each nucleus. The resulting cross section is factorized into a product of two Weizsäcker-Williams gluon distributions of the two nuclei when the transverse momentum of the produced scalar particle is around the saturation momentum. We confirm our results in covariant gauge where the transverse momentum …
We studied single $W$ boson production in high energy $eγ$ collisions and the sensitivity of various observables to the $WWγ$ gauge boson coupling by evaluating the helicity amplitudes of all Feynman diagrams which contribute to the final state being studied, including the $W$ decay to final state fermions. We examined $W$ production at 500 GeV and 1 TeV $e^+e^-$ colliders, comparing results for photon spectra obtained from a backscattered laser and from beamstrahlung radiation. Here we found that the couplings could best be measured using the backscattered laser photons with $|δκ_γ|\leq 0.07$…
Color charge correlations in the proton at moderately small $x\sim 0.1$ are extracted from its light-cone wave function. The charge fluctuations are far from Gaussian and they exhibit interesting dependence on impact parameter and on the relative transverse momentum (or distance) of the gluon probes. We provide initial conditions for small-$x$ Balitsky-Kovchegov evolution of the dipole scattering amplitude with impact parameter and $\hat r \cdot \hat b$ dependence, and with non-zero $C$-odd component due to three-gluon exchange. Lastly, we compute the (forward) Weizsaecker-Williams gluon distr…
Transverse-momentum-dependent (TMD) gluon distributions have different operator definitions, depending on the process under consideration. We study that aspect of TMD factorization in the small-x limit, for the various unpolarized TMD gluon distributions encountered in the literature. To do this, we consider di-jet production in hadronic collisions, since this process allows to be exhaustive with respect to the possible operator definitions, and is suitable to be investigated at small x. Indeed, for forward and nearly back-to-back jets, one can apply both the TMD factorization and Color Glass …
The exclusive $Z^0$ photoproduction at high energies in $γp (A)$, $p p$ and $AA$ collisions is investigate within the color dipole formalism. We generalize the description of the deeply virtual compton scattering (DVCS) process, which describe quite well the HERA data, for the production of $Z^0$ bosons and estimate the total cross section for the exclusive process $γ^* h\to Z^0 h$ ($h=p,A$) for different energies, photon virtualities and atomic numbers. As hadrons at collider energies are a source of Weizsäcker - Williams photons, we consider electromagnetic interactions in hadron-hadron coll…
Protons and antiprotons at collider energies are a source of high energy Weizsäcker--Williams photons. This may open a possibility to study exclusive photoproduction of heavy vector mesons at energies much larger than possible at the HERA accelerator. Here we present a detailed investigation of the exclusive $J/ψ$ photoproduction in proton-proton (RHIC, LHC) and proton-antiproton (Tevatron) collisions. We calculate several differential distributions in $t_1, t_2, y, ϕ$, as well as transverse momentum distributions of $J/Ψ$'s. We discuss correlations in the azimuthal angle between outgoing prot…
We show that the linearly polarized gluon distributions appear in the color dipole model as we derive the full cross sections of the DIS dijet production and the Drell-Yan dijet ($γ^*$ jet correlation) process. Together with the normal Weizsäcker-Williams gluon distribution, the linearly polarized one will contribute to the DIS dijet production cross section as the coefficient of the $\cos(2 Δϕ) $ term in the correlation limit. We also derive the exact results for the cross section of the Drell-Yan dijet process, and find that the linearly polarized dipole gluon distribution which is identical…
We studied single $W$ boson production in high energy $eγ$ collisions and the sensitivity of various observables to the $WWγ$ gauge boson coupling. We evaluated the helicity amplitudes including the $W$ decay to final state fermions and all Feynman diagrams which give the same final state. At high energy, the non-resonant diagrams give significant contributions to the cross sections and should not be neglected. We first considered a $\sqrt{s}=120$~GeV $e^+e^-$ collider converted to an $eγ$ collider by backscattering a low energy laser off of one of the original electron beams. Such a collider …
The contribution of the QCD Pomeron to the process AA -> AA J/Psi J/Psi is discussed. We focus on the photon-photon collision, with the quasi-real photon coming from the Weizsacker - Williams spectrum of the nuclei. We calculate the cross section for this process considering the solution of the LLA BFKL equation at zero momentum transfer using a small-t approximation for the differential cross section of the subprocess. Furthermore, the impact of non-leading corrections to the BFKL equation is also analyzed. In both cases the cross section is found to increase with the energy, predicting consi…
In relativistic heavy ion collisions, top quarks can be produced by photon-gluon fusion when a photon from the Weizsäcker-Williams virtual photon field of one nucleus interacts with a gluon in the other nucleus. Photoproduction with heavy ions at the Large Hadron Collider (LHC) will be the first accessible non-hadronic top production channel. We calculate the $t \bar t$ photoproduction cross sections, pair mass and top quark rapidity distributions in peripheral heavy ion collisions. The cross sections are sensitive to the top quark charge and the large-$Q^2$ gluon distribution in the nucleus. …
The Lam-Tung relation breaking coefficient $A_{\mathrm{LT}} = A_0 - A_2$ in the Drell-Yan dilepton angular distributions in the $Z^0$ boson mass region at the LHC is analyzed in the $k_T$-factorization approach. This observable was recently measured with high precision by ATLAS collaboration. Within the $k_T$-factorization approach we perform an approximate ${\cal O}(α_{\mathrm{em}}α_s^2)$ calculation of the off-shell parton hard matrix elements in which we include the leading tree level contributions of valence quarks and off-shell gluons: the $q_{\mathrm{val}} g^* \to qZ^0$ channel and the $…
The STAR collaboration has observed an excess production of $e^+e^-$ pairs in relativistic heavy ion collisions, over the expectations from hadronic production models. The excess pairs have transverse momenta $p_T < 150\ {\rm MeV}/c$ and are most prominent in peripheral gold-gold and uranium-uranium collisions. The pairs exhibit a peak at the $J/ψ$ mass, but include a wide continuum, with pair invariant masses from 400 MeV/c$^2$ up to 2.6 GeV/c$^2$. The ALICE Collaboration observes a similar excess in peripheral lead-lead collisions, but only at the $J/ψ$ mass, without a corresponding continuu…
Quarkonium production offers good possibilities to study gluon TMDs. In this proceedings contribution this topic is explored for the linearly polarized gluons inside unpolarized hadrons and unpolarized gluons inside transversely polarized hadrons. It is argued that $χ_{b0/2}$ and $η_b$ production at LHC are best to study the effects of linearly polarized gluons in hadronic collisions, by means of angular independent ratios of ratios of cross sections. This can be directly compared to $\cos 2ϕ$ asymmetries in heavy quark pair and dijet production in DIS at a future high-energy Electron-Ion Coll…
