Balitsky-Kovchegov equation

In high-energy particle physics the energy evolution of various quantities can be calculated from the Balitsky-Kovchegov (BK) equation. Depending on the frame that is used to describe the process, the BK equation can be seen to describe either the energy evolution of the virtual photon wave function or the gluon distribution function of a hadron. In this work the BK equation is derived at leading logarithm accuracy from QCD and solved analytically in some special cases. In order to derive it the quantum field theory on the light cone is introduced. Part of the higher order corrections to the BK equation, namely the running strong coupling constant and the kinematical constraint effects, are…

Centrality-dependent forward J/ψ production in high energy proton-nucleus collisions

Forward $J/\psi$ production and suppression in high energy proton-nucleus collisions can be an important probe of gluon saturation. In an earlier work we studied this process in the Color Glass Condensate framework and showed that using the Glauber approach to extrapolate the dipole cross section of a proton to a nucleus leads to results closer to experimental data than previous calculations in this framework. Here we investigate the centrality dependence of the nuclear suppression in this model and show a comparison of our results with recent LHC data.

Exclusive Vector Meson Production at the EIC

We discuss how vector meson production at the future Electron Ion Collider can be used to probe non-linear dynamics in heavy nuclei. Additionally, the potential to study the evolution of proton and nuclear geometries with event-by-event fluctuations is illustrated.

Pohjoismaiden ja Baltian fysiikkaolympialaiset 2021

Tänä keväänä järjestetyt viidennet Pohjoismaiden ja Baltian fysiikkaolympialaiset (NBPhO) toteutettiin viime vuoden tapaan etäkilpailuna [1]. Tämän Suomen ja Viron välisestä yhteistyöstä alkunsa saaneen kilpailun ensiaskeleet voidaan jäljittää aina 1990-luvun alkuun [2]. Viisi vuotta sitten kilpailu laajennettiin koskemaan Suomen ja Viron lisäksi muita Pohjoismaita sekä Baltian maita. Organisaatiovastuu on ollut pääasiassa Virolla, sillä kilpailu järjestetään normaalioloissa Tallinnan Teknillisellä Yliopistolla, mutta kilpailun akateemiseen komiteaan kuuluu Viron lisäksi Suomi, Ruotsi ja Latvia. Nämä neljä maata muodostavat kilpailun niin sanotut päämaat, ja muut kilpailuun osallistuvat maa…

Nuclear modification of forward J/ψ production in proton-nucleus collisions at the LHC

We re-evaluate the nuclear suppression of forward J/ψ production at high energy in the Color Glass Condensate framework. We use the collinear approximation for the projectile proton probed at large x and an up to date dipole cross section fitted to HERA data to describe the target in proton-proton collisions. We show that using the Glauber approach to generalize the proton dipole cross section to the case of a nucleus target leads to a nuclear modification factor much closer to LHC data than previous estimates using the same framework.

Forward J /ψ production in proton-nucleus collisions at high energy

Inclusive production of J/ψ mesons, especially at forward rapidities, is an important probe of small-x gluons in protons and nuclei. In this paper we reevaluate the production cross sections in the color glass condensate framework, where the process is described by a large x gluon from the probe splitting into a quark pair and eikonally interacting with the target proton or nucleus. Using a standard collinear gluon distribution for the probe and an up-to-date dipole cross section fitted to HERA data to describe the target we achieve a rather good description of the cross section in proton-proton collisions, although with a rather large normalization uncertainty. More importantly, we show th…

Ballistic protons in incoherent exclusive vector meson production as a measure of rare parton fluctuations at an Electron-Ion Collider

We argue that the proton multiplicities measured in Roman pot detectors at an electron ion collider can be used to determine centrality classes in incoherent diffractive scattering. Incoherent diffraction probes the fluctuations in the interaction strengths of multi-parton Fock states in the nuclear wavefunctions. In particular, the saturation scale that characterizes this multi-parton dynamics is significantly larger in central events relative to minimum bias events. As an application, we study the centrality dependence of incoherent diffractive vector meson production. We identify an observable which is simultaneously very sensitive to centrality triggered parton fluctuations and insensit…

Single inclusive particle production at high energy from HERA data to proton-nucleus collisions

We study single inclusive hadron production in proton-proton and proton-nucleus collisions in the CGC framework. The parameters in the calculation are determined solely by standard nuclear geometry and by electron-proton deep inelastic scattering data, which is fit using the running coupling BK equation. We show that it is possible to obtain a good fit of the HERA inclusive cross section also without an anomalous dimension in the initial condition. We argue that one must consistently use the proton transverse area as measured by a high virtuality probe in DIS also for the single inclusive cross section in proton-proton and proton-nucleus collisions. We show that this leads to a midrapidity …

Solving the NLO BK equation in coordinate space

We present results from a numerical solution of the next-to-leading order (NLO) BalitskyKovchegov (BK) equation in coordinate space in the large Nc limit. We show that the solution is not stable for initial conditions that are close to those used in phenomenological applications of the leading order equation. We identify the problematic terms in the NLO kernel as being related to large logarithms of a small parent dipole size, and also show that rewriting the equation in terms of the “conformal dipole” does not remove the problem. Our results qualitatively agree with expectations based on the behavior of the linear NLO BFKL equation.

Color charge correlations in the proton at NLO: Beyond geometry based intuition

Color charge correlators provide fundamental information about the proton structure. In this Letter, we evaluate numerically two-point color charge correlations in a proton on the light cone including the next-to-leading order corrections due to emission or exchange of a perturbative gluon. The non-perturbative valence quark structure of the proton is modelled in a way consistent with high-$x$ proton structure data. Our results show that the correlator exhibits startlingly non-trivial behavior at large momentum transfer or central impact parameters, and that the color charge correlation depends not only on the impact parameter but also on the relative transverse momentum of the two gluon pr…

Forward J/ψ production at high energy: Centrality dependence and mean transverse momentum

Forward rapidity $J/\psi$ meson production in proton-nucleus collisions can be an important constraint of descriptions of the small-$x$ nuclear wavefunction. In an earlier work we studied this process using a dipole cross section satisfying the Balitsky-Kovchegov equation, fit to HERA inclusive data and consistently extrapolated to the nuclear case using a standard Woods-Saxon distribution. In this paper we present further calculations of these cross sections, studying the mean transverse momentum of the meson and the dependence on collision centrality. We also extend the calculation to backward rapidities using nuclear parton distribution functions. We show that the parametrization is over…

Forward dihadron correlations in the Gaussian approximation of JIMWLK

We compute forward dihadron azimuthal correlations in deuteron-gold collisions using a Gaussian approximation for the quadrupole operator. The double parton scattering contribution is found to be part of our dihadron calculation. We obtain a good description of the PHENIX data for the azimuthal-angle dependent away side peak and a relatively good estimate for the pedestal contribution.

Impact parameter dependence of color charge correlations in the proton

The impact parameter dependence of color charge correlators in the proton is obtained from the light front formalism in light cone gauge. We include NLO corrections due to the $|qqqg\rangle$ Fock state via light-cone perturbation theory. Near the center of the proton, the $b$-dependence of the correlations is very different from a "transverse profile function". The resulting $t$-dependence of exclusive $J/\Psi$ photoproduction transitions from exponential to power law at $|t| \approx 1$ GeV$^2$. This prediction could be tested at upcoming DIS facilities or in nucleus-proton ultraperipheral collisions (UPCs).

Exclusive production of light vector mesons at next-to-leading order in the dipole picture

Exclusive production of light vector mesons in deep inelastic scattering is calculated at next-to-leading order in the dipole picture in the limit of high photon virtuality. The resulting expression is free of any divergences and suitable for numerical evaluations. The higher-order corrections are found to be numerically important, but they can be mostly captured by the nonperturbative fit parameters describing the initial condition for the small-$x$ evolution of the dipole scattering amplitude. The vector meson production cross section is shown to depend only weakly on the meson distribution amplitude and the factorization scale. We also present phenomenological comparisons of our result t…

Higher-order corrections to exclusive heavy vector meson production

We present results for higher-order corrections to exclusive $\mathrm{J}/\psi$ production. This includes the first relativistic correction of order $v^2$ in quark velocity, and next-to-leading order corrections in $\alpha_s$ for longitudinally polarized production. The relativistic corrections are found to be important for a good description of the HERA data, especially at small values of the photon virtuality. The next-to-leading order results for longitudinal production are evaluated numerically. We also demonstrate how the vector meson production provides complementary information to the structure functions for extracting the initial condition for the small-$x$ evolution of the dipole-pr…

Incoherent diffractiveJ/Ψproduction in high-energy nuclear deep-inelastic scattering

We compute cross sections for incoherent diffractive $J/\ensuremath{\Psi}$ production in lepton-nucleus deep-inelastic scattering (DIS). The cross section is proportional to $A$ in the dilute limit and to ${A}^{1/3}$ in the black disk limit, with a large nuclear suppression due to saturation effects. The $t$ dependence of the cross section, if it can be measured accurately enough, is sensitive to the impact parameter profile of the gluons in the nucleus and their fluctuations, a quantity that determines the initial conditions of a relativistic heavy-ion collision. The nuclear suppression in incoherent diffraction shows how the transverse spatial distribution of the gluons in the nucleus gra…

Diffractive dijet production from the Color Glass Condensate and the small-x gluon distributions

We study exclusive dijet production in electron-proton deep inelastic scattering at a future Electron Ion Collider. We predict the elliptic modulation of the cross section as a function of the angle between the dijet transverse momentum and the recoil momentum, and show that this modulation is due to non-trivial angular correlations between the transverse coordinate and transverse momentum in the Wigner (or Husimi) distribution. The small-$x$ evolution is shown to decrease the elliptic modulation in the EIC kinematics, because of the growth of the proton with decreasing $x$.

Forward dihadron correlations in deuteron-gold collisions with a Gaussian approximation of JIMWLK

We compute dihadron correlations in forward deuteron-gold or proton-gold collisions. The running coupling BK equation is used to calculate the energy dependence of the dipole cross sections and extended to higher point Wilson line correlators using a factorized Gaussian approximation. Unlike some earlier works we include both the "inelastic" and "elastic" contributions to the dihadron cross section. We show that the double parton scattering contribution is included in our calculation and obtain both an away side peak that roughly agrees with experimental observations and an estimate for the azimuthal angle-independent pedestal. We find that nonlinear effects for momenta close to the saturat…

Balitsky-Kovchegov equation at next-to-leading order accuracy with a resummation of large logarithms

We include resummation of large transverse logarithms into the next-to-leading order Balitsky-Kovchegov equation. The resummed NLO evolution equation is shown to be stable, the evolution speed being significantly reduced by higher order corrections. The contributions from $\alpha_s^2$ terms that are not enhanced by large logarithms are found to be numerically important close to phenomenologically relevant initial conditions.

Diffractive scattering at next-to-leading order in the dipole picture

We discuss recent developments towards next-to-leading order (NLO) accuracy in the dipole picture. We review recent NLO results for exclusive vector meson production and diffractive structure functions, and discuss how it is becoming possible to describe both inclusive and exclusive DIS data simultaneously within the Color Glass Condensate framework at NLO accuracy. These developments will make it possible to probe the gluon saturation phenomena in detail especially when nuclear-DIS data from the EIC become available.

Stronger C -odd color charge correlations in the proton at higher energy

The non-forward eikonal scattering matrix for dipole-proton scattering at high energy obtains an imaginary part due to a $C$-odd three gluon exchange. We present numerical estimates for the perturbative Odderon amplitude as a function of dipole size, impact parameter, their relative azimuthal angle, and light-cone momentum cutoff $x$. The proton is approximated as $\psi_\mathrm{qqq}|qqq\rangle + \psi_\mathrm{qqqg}|qqqg\rangle$, where $\psi_\mathrm{qqq}$ is a non-perturbative three quark model wave function while the gluon emission is computed in light-cone perturbation theory. We find that the Odderon amplitude increases as $x$ decreases from 0.1 to 0.01. At yet lower $x$, the reversal of t…

Solving the NLO BK equation in coordinate space

We present results from a numerical solution of the next-to-leading order (NLO) Balitsky-Kovchegov (BK) equation in coordinate space in the large Nc limit. We show that the solution is not stable for initial conditions that are close to those used in phenomenological applications of the leading order equation. We identify the problematic terms in the NLO kernel as being related to large logarithms of a small parent dipole size, and also show that rewriting the equation in terms of the "conformal dipole" does not remove the problem. Our results qualitatively agree with expectations based on the behavior of the linear NLO BFKL equation.

Color glass condensate at next-to-leading order meets HERA data

We perform the first dipole picture fit to HERA inclusive cross section data using the full next-to-leading order (NLO) impact factor combined with an improved Balitsky-Kovchegov evolution including the dominant effects beyond leading logarithmic accuracy at low $x$. We find that three different formulations of the evolution equation that have been proposed in the recent literature result in a very similar description of HERA data, and robust predictions for future deep inelastic scattering experiments. We find evidence pointing towards a significant nonperturbative contribution to the structure function for light quarks, which stresses the need to extend the NLO impact factor calculation t…

Diffractive vector meson production in ultraperipheral heavy ion collisions from the Color Glass Condensate

We compute cross sections for incoherent and coherent diffractive J/$\Psi$ and $\Psi(2S)$ production in ultraperipheral heavy ion collisions. The dipole models used in these calculations are obtained by fitting the HERA deep inelastic scattering data and compared with available electron-proton diffraction measurements. We obtain a reasonably good description of the available ALICE data. We find that the normalization of the ultraperipheral cross section has large model dependence, but the rapidity dependence is more tightly constrained.

Forward J / ψ and D meson nuclear suppression at the LHC

Abstract Using the color glass condensate formalism, we study the nuclear modification of forward J/ψ and D meson production in high energy proton-nucleus collisions at the LHC. We show that relying on the optical Glauber model to obtain the dipole cross section of the nucleus from the one of the proton fitted to HERA DIS data leads to a smaller nuclear suppression than in the first study of these processes in this formalism and a better agreement with experimental data.

Saturation and forward jets in proton-lead collisions at the LHC

We investigate the forward-jet energy spectrum within the Color Glass Condensate framework at 5 TeV center-of-mass energy. In particular, we focus on the kinematic range covered by the CMS-CASTOR calorimeter. We show that our saturation-model calculations are compatible with the CASTOR measurements and that to optimally reproduce the data, effects of multi-parton interactions need to be included. We predict a significant nuclear suppression - reaching down to 50% at the lowest considered jet energies $E_{\rm jet} \sim 500 \, {\rm GeV}$.

Azimuthal correlations in diffractive scattering at the Electron-Ion Collider

We calculate azimuthal correlations between the exclusively produced vector meson and the scattered electron in Deep Inelastic Scattering processes at the future Electron-Ion Collider (EIC). We identify "kinematical" and "intrinsic" contributions to these correlations, and show that the correlations are sensitive to the non-trivial correlations in the gluon distribution of the target. Realistic predictions at the EIC kinematics are provided using two different approaches to describe the dipole-proton interaction at relatively small xx. peerReviewed

Signatures of gluon saturation from structure-function measurements

We study experimentally observable signals for nonlinear QCD dynamics in deep inelastic scattering (DIS) at small Bjorken variable $x$ and moderate virtuality $Q^2$, by quantifying differences between the linear Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution and nonlinear evolution with the Balitsky-Kovchegov (BK) equation. To remove the effect of the parametrization freedom in the initial conditions of both equations, we first match the predictions for the DIS structure functions $F_2$ and $F_{\rm L}$ from both frameworks in a region in $x,Q^2$ where both frameworks should provide an accurate description of the relevant physics. The differences in the dynamics are then quanti…

Relativistic corrections to the vector meson light front wave function

We compute a light front wave function for heavy vector mesons based on long distance matrix elements constrained by decay width analyses in the Non Relativistic QCD framework. Our approach provides a systematic expansion of the wave function in quark velocity. The first relativistic correction included in our calculation is found to be significant, and crucial for a good description of the HERA exclusive $\mathrm{J}/\psi$ production data. When looking at cross section ratios between nuclear and proton targets, the wave function dependence does not cancel out exactly. In particular the fully non-relativistic limit is found not to be a reliable approximation even in this ratio. The important…

Bayesian inference of the fluctuating proton shape in DIS and hadronic collisions

We determine the likelihood distribution for the model parameters describing the event-by-event fluctuating proton geometry at small $x$ by performing a Bayesian analysis within the Color Glass Condensate framework. The exclusive $\mathrm{J}/\psi$ production data from HERA is found to constrain the model parameters well, and we demonstrate that complementary constraints can be obtained from simulations of Pb+Pb collisions at the LHC.

Multi-scale Imaging of Nuclear Deformation at the Electron Ion Collider

We show within the Color Glass Condensate framework that exclusive vector meson production at high energy is sensitive to the geometric deformation of the target nucleus at multiple length scales. Studying $e+$U collisions and varying the deformation of the uranium target, we demonstrate that larger deformations result in enhanced incoherent vector meson production cross sections. Further, different multipole deformation parameters affect different regions of transverse momentum transfer. Employing JIMWLK evolution to study the Bjorken-$x$ dependence of our results, we find that the ratio of incoherent to coherent cross sections decreases with decreasing $x$, largely independently of the qu…

Including resummation in the NLO BK equation

We include a resummation of large transverse momentum logarithms in the next-to-leading order (NLO) Balitsky-Kovchegov equation. The resummed evolution equation is shown to be stable, the evolution speed being significantly reduced by NLO corrections. The contributions from NLO terms that are not enhanced by large logarithms are found to be numerically important close to phenomenologically relevant initial conditions. We numerically determine the value for the constant in the resummed logarithm that includes a maximal part of the full NLO terms in the resummation.

Review of proton and nuclear shape fluctuations at high energy

Determining the inner structure of protons and nuclei in terms of their fundamental constituents has been one of the main tasks of high energy nuclear and particle physics experiments. This quest started as a mapping of the (average) parton densities as a function of longitudinal momentum fraction and resolution scale. Recently, the field has progressed to more differential imaging, where one important development is the description of the event-by-event quantum fluctuations in the wave function of the colliding hadron. In this Review, recent developments on the extraction of proton and nuclear transverse geometry with event-by-event fluctuations from collider experiments at high energy is …

Nuclear geometry at high energy from exclusive vector meson production

We show that when saturation effects are included one obtains a good description of the exclusive $\mathrm{J}/\psi$ production spectra in ultra peripheral lead-lead collisions as recently measured by the ALICE Collaboration at the LHC. As exclusive spectra are sensitive to the spatial distribution of nuclear matter at small Bjorken-$x$, this implies that gluon saturation effects modify the impact parameter profile of the target as we move towards small $x$. In addition to saturation effects, we find a preference for larger nuclear strong-interaction radii compared to the typical charge radius. We demonstrate the role of finite photon transverse momentum and the interference between the case…

Fysiikan kehityshanke 2021

Opetushallitus myönsi marraskuussa 2020 MAOLille valtionavustuksen, jonka tavoitteena oli “kasvattaa tiedeolympialaistoiminnan vaikuttavuutta ja kattavuutta kansallisella tasolla ja lisätä toimijoiden välistä yhteistyötä sekä hyvien käytänteiden levittämistä” [1]. Avustuksen viimeiseksi päiväksi määrättiin 31. joulukuuta 2021, joten fysiikan valmennustiimissä aloimme luonnollisesti kutsua vuotta 2021 kehitysvuodeksi. Tällaiselle kehitysvuodelle olikin ollut jo pitkään tarvetta. nonPeerReviewed

Imaging the nucleus with high-energy photons

In the 1930's, nuclear physicists developed the first realistic atomic models, showing that nuclei were made up of protons and neutrons. In the 1960's, Deep Inelastic Scattering experiments showed that protons and neutrons had internal structure: quarks and gluons (collectively, partons), and later experiments showed that the parton momentum distributions are different in heavy nuclei, compared to those in free nucleons. This difference is not surprising; partons are sensitive to their environment, and two gluons from different nucleons may fuse together, for example. Understanding how quarks and gluons behave in the nuclear environment is a significant focus of modern nuclear physics. Rece…

Accessing the gluonic structure of light nuclei at a future electron-ion collider

We show how exclusive vector meson production off light ions can be used to probe the spatial distribution of small-$x$ gluons in the deuteron and $^3$He wave functions. In particular, we demonstrate how short range repulsive nucleon-nucleon interactions affect the predicted coherent $J/\Psi$ production spectra. Fluctuations of the nucleon substructure are shown to have a significant effect on the incoherent cross section above $|t|\gtrsim 0.2\,\mathrm{GeV}^2$. By explicitly performing the JIMWLK evolution, we predict the $x$-dependence of coherent and incoherent cross sections in the EIC energy range. Besides the increase of the average size of the nucleus with decreasing $x$, both the gro…

Energy and system size dependence of subnucleonic fluctuations

The energy evolution of the fluctuating proton structure is studied by solving the JIMWLK renormalization group equation. The initial condition at moderate $x$ is obtained by fitting the charm reduced cross section data from HERA, requiring that the proton size remains compatible with the diffractive vector meson production measurements. Additionally, we show that the nucleon shape fluctuations are visible in exclusive vector meson production off nuclei.

Predictions for cold nuclear matter effects in p+Pb collisions at s N N = 8.16 TeV

Impact parameter dependent JIMWLK evolution meets HERA data

We calculate the small-$x$ evolution of protons with finite size by solving numerically the JIMWLK evolution equation. The initial condition is constrained by the HERA measurements of charm reduced cross section and of exclusive vector meson production. We compute the energy dependence of diffractive cross sections in order to access the energy evolution of the event-by-event fluctuating proton density profile. The fundamental problems arising from the regime sensitive to non-perturbatively large dipoles are also discussed.

Gluon imaging using azimuthal correlations in diffractive scattering at the Electron-Ion Collider

We study coherent diffractive photon and vector meson production in electron-proton and electron-nucleus collisions within the Color Glass Condensate effective field theory. We show that electron-photon and electron-vector meson azimuthal angle correlations are sensitive to non-trivial spatial correlations in the gluon distribution of the target, and perform explicit calculations using spatially dependent McLerran-Venugopalan initial color charge configurations coupled to the numerical solution of small $x$ JIMWLK evolution equations. We compute the cross-section differentially in $Q^2$ and $|t|$ and find sizeable anisotropies in the electron-photon and electron-$\mathrm{J}/��$ azimuthal co…

Next-to-leading order Balitsky-Kovchegov equation with resummation

We solve the Balitsky-Kovchegov evolution equation at next-to-leading order accuracy including a resummation of large single and double transverse momentum logarithms to all orders. We numerically determine an optimal value for the constant under the large transverse momentum logarithm that enables including a maximal amount of the full NLO result in the resummation. When this value is used the contribution from the $\alpha_s^2$ terms without large logarithms is found to be small at large saturation scales and at small dipoles. Close to initial conditions relevant for phenomenological applications these fixed order corrections are shown to be numerically important.

Forward rapidity isolated photon production in proton-nucleus collisions

We calculate isolated photon production at forward rapidities in proton-nucleus collisions in the Color Glass Condensate framework. Our calculation uses dipole cross sections solved from the running coupling Balitsky-Kovchegov equation with an initial condition fit to deep inelastic scattering data and extended to nuclei with an optical Glauber procedure that introduces no additional parameters beyond the basic nuclear geometry. We present predictions for future forward RHIC and LHC measurements. The predictions are also compared to updated results for the nuclear modification factors for pion production, Drell-Yan dileptons and $J/\psi$ mesons in the same forward kinematics, consistently c…

Diffractive dijet production and Wigner distributions from the color glass condensate

Experimental processes that are sensitive to parton Wigner distributions provide a powerful tool to advance our understanding of proton structure. In this work, we compute gluon Wigner and Husimi distributions of protons within the Color Glass Condensate framework, which includes a spatially dependent McLerran-Venugopalan initial configuration and the explicit numerical solution of the JIMWLK equations. We determine the leading anisotropy of the Wigner and Husimi distributions as a function of the angle between impact parameter and transverse momentum. We study experimental signatures of these angular correlations at a proposed Electron Ion Collider by computing coherent diffractive dijet p…

In depth analysis of the combined HERA data in the dipole models with and without saturation

We present an updated impact parameter dependent saturation model (IPsat) determined trough a fit to the combined HERA I and I+II reduced cross section data. The same HERA data are used to fit the linearized (IPnonsat) version of the applied dipole amplitude, which makes it possible to estimate the magnitude of the saturation effects in various experiments. We find that both parametrizations provide comparable descriptions of the considered data when an effective confinement scale dynamics is incorporated with quark masses. Moreover, it is possible to consistently determine the light and charm quark masses. The role of potentially non-perturbatively large dipoles is examined in detail, with…

Cubic color charge correlator in a proton made of three quarks and a gluon

The three point correlation function of color charge densities is evaluated explicitly in light cone gauge for a proton on the light cone. This includes both $C$-conjugation even and odd contributions. We account for perturbative corrections to the three-quark light cone wave function due to the emission of an internal gluon which is not required to be soft. We verify the Ward identity as well as the cancellation of UV divergences in the sum of all diagrams so that the correlator is independent of the renormalization scale. It does, however, exhibit the well known soft and collinear singularities. The expressions derived here provide the $C$-odd contribution to the initial conditions for hi…

Small-x physics at the LHeC

The Large Hadron-electron Collider LHeC is a proposed upgrade of the LHC. It would add an electron beam to the LHC, and make it possible to study electron-proton and electron-nucleus collisions at very high energies. We present some of the highlights of the LHeC physics program related to the studies of partonic structure of protons and nuclei, and to the non-linear QCD phenomena visible at small $x$.

Confronting the impact parameter dependent JIMWLK evolution with HERA data

The small-$x$ evolution of protons is determined from numerical solutions of the JIMWLK equations, starting from an initial condition at moderate $x$ for a finite size proton. The resulting dipole amplitude is used to calculate the total reduced cross section $\sigma_r$ and charm reduced cross section $\sigma_{rc}$, as well as diffractive vector meson production. We compare results to experimental data from HERA and discuss fundamental problems arising from the regime sensitive to non-perturbative physics. We emphasize that information on the gluonic content of the proton, gluon spatial distributions and correlations over wide ranges in $x$, which can in principle be constrained by our stud…

Dipole amplitude with uncertainty estimate from HERA data and applications in Color Glass Condensate phenomenology

We determine the initial condition for the small-x evolution equation (BK) from the HERA deep inelastic scattering data using a new parametrization that also keeps the unintegrated gluon distribution positive. The obtained dipole amplitude and its uncertainty estimate can be used to compute single inclusive particle production in proton-proton and proton-nucleus collisions. We argue that one has to use consistently the proton transverse area measured in DIS and the total inelastic cross section when calculating the single inclusive cross section. This leads to a midrapidity nuclear modification factor RpA that approaches unity at large transverse momentum, independently of the center-of-mas…

Solving the Balitsky-Kovchegov equation at next to leading order accuracy

We solve the Balitsky-Kovchegov small-x evolution equation in coordinate space. We find that the solution to the equation is unstable when using an initial condition relevant for phenomenological applications at leading order. The problematic behavior is shown to be due to a large double logarithmic contribution. The same problem is found when the evolution of the “conformal dipole” is solved, even though the double logarithmic term is then absent from the evolution equation.

Complete calculation of exclusive heavy vector meson production at next-to-leading order in the dipole picture

Exclusive production of transversely polarized heavy vector mesons in deep inelastic scattering at high energy is calculated at next-to-leading order accuracy in the Color Glass Condensate framework. In addition to the first QCD correction proportional to the strong coupling constant $\alpha_s$, we systematically also include the first relativistic correction proportional to the heavy quark velocity squared $v^2$. When combined with our previously published results for longitudinal vector meson production at next-to-leading order accuracy, these results make phenomenological calculations of heavy vector meson production possible at the order $\mathcal{O}(\alpha_s v^0, \alpha_s^0 v^2)$. When…

Proposal for a running coupling JIMWLK equation

In the CGC framework the initial stages of a heavy ion collision at high energy are described as "glasma" field configurations. The initial condition for these evolving fields depends, in the CGC effective theory, on a probability distribution for color charges. The energy dependence of this distribution can be calculated from the JIMWLK renormalization group equation. We discuss recent work on a practical implementation of the running coupling constant in the Langevin method of solving the JIMWLK equation.

Particle Production in the Color Class Condensate: from electron-proton DIS to proton-nucleus collisions

We study single inclusive hadron production in proton-proton and proton-nucleus collisions in the CGC framework. The parameters in the calculation are obtained by fitting electron-proton deep inelastic scattering data. The obtained dipole-proton amplitude is generalized to dipole-nucleus scattering without any additional nuclear parameters other than the Woods-Saxon distribution. We show that it is possible to use an initial condition without an anomalous dimension and still obtain a good description of the HERA inclusive cross section and LHC single particle production measurements. We argue that one must consistently use the proton transverse area as measured by a high virtuality probe in…

Centrality dependence of forward J/ψ suppression in high energy proton–nucleus collisions

The production of forward $J/\psi$ mesons in proton-nucleus collisions can provide important information on gluon saturation. In a previous work we studied this process in the Color Glass Condensate framework, describing the target using a dipole cross section fitted to HERA inclusive data and extrapolated to the case of a nuclear target using the optical Glauber model. In this work we study the centrality dependence of the nuclear suppression in this model and compare our results with recent LHC data for this observable.

Bayesian inference of the fluctuating proton shape

Using Bayesian inference, we determine probabilistic constraints on the parameters describing the fluctuating structure of protons at high energy. We employ the color glass condensate framework supplemented with a model for the spatial structure of the proton, along with experimental data from the ZEUS and H1 Collaborations on coherent and incoherent diffractive $\mathrm{J}/\psi$ production in e+p collisions at HERA. This data is found to constrain most model parameters well. This work sets the stage for future global analyses, including experimental data from e+p, p+p, and p+A collisions, to constrain the fluctuating structure of nucleons along with properties of the final state.

Predictions for cold nuclear matter effects in p+Pb collisions at sNN=8.16 TeV

Predictions for cold nuclear matter effects on charged hadrons, identified light hadrons, quarkonium and heavy flavor hadrons, Drell–Yan dileptons, jets, photons, gauge bosons and top quark pairs produced in p +Pb collisions at sNN=8.16 TeV are compiled and, where possible, compared to each other. Predictions of the normalized ratios of p +Pb to p+p cross sections are also presented for most of the observables, providing new insights into the expected role of cold nuclear matter effects. In particular, the role of nuclear parton distribution functions on particle production can now be probed over a wider range of phase space than ever before.

Exclusive Vector Meson Production at the EIC

We discuss how vector meson production at the future Electron Ion Collider can be used to probe non-linear dynamics in heavy nuclei. Additionally, the potential to study the evolution of proton and nuclear geometries with event-by-event fluctuations is illustrated. nonPeerReviewed

The importance of kinematic twists and genuine saturation effects in dijet production at the Electron-Ion Collider

We compute the differential yield for quark anti-quark dijet production in high-energy electron-proton and electron-nucleus collisions at small $x$ as a function of the relative momentum $\boldsymbol{P}_\perp$ and momentum imbalance $\boldsymbol{k}_\perp$ of the dijet system for different photon virtualities $Q^2$, and study the elliptic and quadrangular anisotropies in the relative angle between $\boldsymbol{P}_\perp$ and $\boldsymbol{k}_\perp$. We review and extend the analysis in [1], which compared the results of the Color Glass Condensate (CGC) with those obtained using the transverse momentum dependent (TMD) framework. In particular, we include in our comparison the improved TMD (ITMD…

Exclusive heavy vector meson production at next-to-leading order in the dipole picture

We calculate exclusive production of a longitudinally polarized heavy vector meson at next-to-leading order in the dipole picture. The large quark mass allows us to separately include both the first QCD correction proportional to the coupling constant $\alpha_s$, and the first relativistic correction suppressed by the quark velocity $v^2$. Both of these corrections are found to be numerically important in $\mathrm{J}/\psi$ production. The results obtained are directly suitable for phenomenological calculations. We also demonstrate how vector meson production provides complementary information to structure function analyses when one extracts the initial condition for the energy evolution of …

Dipole model at Next-to-Leading Order meets HERA data

Deep inelastic scattering (DIS) total cross section data at small-x as measured by the HERA experiments is well described by Balitsky-Kovchegov (BK) evolution in the leading order dipole picture. Recently the full Next-to-Leading Order (NLO) dipole picture total cross sections have become available for DIS, and a working factorization scheme has been devised which subtracts the soft gluon divergence present at NLO. We report our recently published work in which we make the first comparisons of the NLO DIS total cross sections to HERA data. The non-perturbative initial condition to BK evolution is fixed by fitting the HERA reduced cross section data. As the NLO results for the DIS total cros…

Proton Structure Functions at Next-to-Leading Order in the Dipole Picture with Massive Quarks

We predict heavy quark production cross sections in deep inelastic scattering at high energy by applying the color glass condensate effective theory. We demonstrate that, when the calculation is performed consistently at next-to-leading order accuracy with massive quarks, it becomes possible, for the first time in the dipole picture with perturbatively calculated center-of-mass energy evolution, to simultaneously describe both the light and heavy quark production data at small xBj. Furthermore, we show how the heavy quark cross section data provides additional strong constraints on the extracted nonperturbative initial condition for the small-xBj evolution equations.

Proton shape fluctuation and its relation to DIS

We review the recent progress in extracting the proton fluctuating substructure by studying exclusive processes at HERA, and the applications of these developments in the interpretation of the LHC heavy ion data. The possibilities to extract the proton geometry directly from the LHC high-multiplicity proton-nucleus and proton-proton collision data is also discussed. peerReviewed

Particle production from the Color Glass Condensate: proton-nucleus collisions in light of the HERA data

We compute single inclusive hadron production in proton-proton and proton-nucleus collisions consistently within the CGC framework. The parameters in the calculations are obtained from electron-proton DIS and standard nuclear geometry. We obtain a good description of the DIS data without an anomalous dimension in the initial condition of the BK evolution and get a good agreement with the available single inclusive proton-proton and proton-nucleus data.

Scattering off the color glass condensate

In this thesis the Color Glass Condensate (CGC) framework, which describes quantum chromodynamics (QCD) at high energy, is applied to various scat- tering processes. Higher order corrections to the CGC evolution equations, known as the BK and JIMWLK equations, are also considered. It is shown that the leading order CGC calculations describe the experimen- tal data from electron-proton deep inelastic scattering (DIS), proton-proton and proton-nucleus collisions. The initial condition for the BK evolution equation is obtained by performing a fit to deep inelastic scattering data. The fit result is used as an input to calculations of single particle spectra and nuclear suppression in proton-prot…

Systematics of strong nuclear amplification of gluon saturation from exclusive vector meson production in high energy electron–nucleus collisions

We show that gluon saturation gives rise to a strong modification of the scaling in both the nuclear mass number $A$ and the virtuality $Q^2$ of the vector meson production cross-section in exclusive deep-inelastic scattering off nuclei. We present qualitative analytic expressions for how the scaling exponents are modified as well as quantitative predictions that can be tested at an Electron-Ion Collider.

Isolated photon production in proton-nucleus collisions at forward rapidity

We calculate isolated photon production at forward rapidities in proton-nucleus collisions in the Color Glass Condensate framework. Our calculation uses dipole cross sections solved from the running coupling Balitsky-Kovchegov equation with an initial condition fit to deep inelastic scattering data. For comparison, we also update the results for the nuclear modification factor for pion production in the same kinematics. We present predictions for future forward RHIC and LHC measurements at $\sqrt{s_{NN}}=200$ GeV and $\sqrt{s_{NN}}=8$ TeV.

Lukiolaisten kansainväliset fysiikkakilpailut

Vuosittain järjestettävät Kansainväliset fysiikkaolympialaiset (International Physics Olympiad, IPhO) tarjoaa lukiolaisille ympäri maailmaa mahdollisuuden kamppailla fysiikan hallinnassa, ja verkostoitua muiden samanhenkisten nuorten kanssa. Kansainvälisiä fysiikkaolympialaisia on järjestetty vuodesta 1967 lähtien, ja Suomi osallistui niihin ensimmäisen kerran vuonna 1977. Ensimmäisten kisojen joukkueesta Jukka Pekola ja Kari Kujansuu palasivat kotiin olympiamitalit kaulassaan. Siitä lähtien suomalaiset kilpailijat ovat saavuttaneet mitaleja ja kunniamainintoja säännöllisen vaihtelevaan tahtiin. Kultaa ovat voittaneet Heikki Tuuri ja Aleksi Kononen. Suomalaiset fyysikot järjestivät kilpailu…

Electron-Ion Collisions at the LHeC and FCC-he

The LHeC and the FCC-he will open a new realm in our understanding of nuclear structure and the dynamics in processes involving nuclei, in an unexplored kinematic domain. We review some of the recent studies as shown in the update of the 2012 LHeC CDR, including the determination of nuclear parton densities in the framework of global fits and for a single nucleus, inclusive and exclusive diffraction and the unique capabilies of these high-energy colliders for probing QCD in the non-linear regime of phase space.

Suomalaisnuoret menestyivät 46. kansainvälisissä fysiikkaolympialaisissa Intiassa

Next-to-leading order Balitsky-Kovchegov equation beyond large Nc

We calculate finite-Nc corrections to the next-to-leading order (NLO) Balitsky-Kovchegov (BK) equation. We find analytical expressions for the necessary correlators of six Wilson lines in terms of the two-point function using the Gaussian approximation. In a suitable basis, the problem reduces from the diagonalization of a six-by-six matrix to the diagonalization of a three-by-three matrix, which can easily be done analytically. We study numerically the effects of these finite-Nc corrections on the NLO BK equation. In general, we find that the finite-Nc corrections are smaller than the expected 1/N2c∼10%. The corrections may be large for individual correlators, but have less of an influence…

Multigluon Correlations and Evidence of Saturation from Dijet Measurements at an Electron-Ion Collider.

We study inclusive and diffractive dijet production in electron-proton and electron-nucleus collisions within the Color Glass Condensate effective field theory. We compute dijet cross sections differentially in both mean dijet transverse momentum $\mathbf{P}$ and recoil momentum $\mathbf{\Delta}$, as well as the anisotropy in the relative angle between $\mathbf{P}$ and $\mathbf{\Delta}$. We use the nonlinear Gaussian approximation to compute multiparticle correlators for general small $x$ kinematics, employing running coupling Balitsky-Kovchegov evolution to determine the dipole amplitude at small $x$. Our results cover a much larger kinematic range than accessible in previous computations …

Forward J/ψ production at high energy: Centrality dependence and mean transverse momentum

Forward rapidity J=ψ meson production in proton-nucleus collisions can be an important constraint of descriptions of the small-x nuclear wave function. In an earlier work we studied this process using a dipole cross section satisfying the Balitsky-Kovchegov equation, fit to HERA inclusive data and consistently extrapolated to the nuclear case using a standard Woods-Saxon distribution. In this paper we present further calculations of these cross sections, studying the mean transverse momentum of the meson and the dependence on collision centrality. We also extend the calculation to backward rapidities using nuclear parton distribution functions. We show that the parametrization is overall ra…

Finite Nc corrections in the Balitsky-Kovchegov equation at next-to-leading order

Publisher Copyright: © owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). We study the finite-Nc corrections to the next-to-leading order (NLO) Balitsky-Kovchegov (BK) equation. This contains correlators of six Wilson lines, which we express in terms of the two-point function using the Gaussian approximation. Numerically, the effects of these finite-Nc corrections on the NLO BK equation are found to be smaller than the expected 1/Nc2 ∼ 10%. Corrections may be large for individual correlators, but have less of an influence on the shape of the amplitude as a function of the dipole size. There is a…

Forward particle correlations in the color glass condensate

Multiparticle correlations, such as forward dihadron correlations in pA collisions, are an important probe of the strong color fields that dominate the initial stages of a heavy ion collision. We describe recent progress in understanding two-particle correlations in the dilute-dense system, e.g. at forward rapidity in deuteron-gold collisions. This requires evaluating higher point Wilson line correlators from the JIMWLK equation, which we find well described by a Gaussian approximation. We then calculate the dihadron correlation, including both the "elastic" and "inelastic" contributions, and show that our result includes the double parton scattering contribution.