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 distributions, including the distribution of linearly polarized gluons, up to fourth order in $A^+$. The correction due to the quartic correlator provides a transverse momentum scale, $q > 0.5$ GeV, for nearly maximal polarization.
Recently, a measurement of the pressure distribution experienced by the quarks inside the proton has found a strong repulsive (positive) pressure at distances up to 0.6 femtometers from its center and a (negative) confining pressure at larger distances. In this paper we show that this measurement puts significant constraints on modified theories of gravity in which the strength of the gravitational interaction on microscopic scales is enhanced with respect to general relativity. We consider the particular case of Eddington-inspired Born-Infeld gravity, showing that strong limits on $κ$, the on…
A general QCD light front formalism to compute many-body color charge correlation functions due to quarks in the proton was constructed~\cite{Dumitru:2018vpr}. These enable new studies of color charge distributions in the nucleon. The analogies between such correlation functions to electric and magnetization charge densities in the proton and also to nucleon-nucleon correlations in the nucleus are discussed. Including the color charge correlations leads naturally to the removal of infrared divergences that occurs in two- and three-gluon exchange interactions in $q\bar q$-proton scattering. Ext…
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.
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 $J/Ψ$ 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 collis…
Quantum effects inside the chiral bag induce a color anomaly which requires a compensating surface term to prevent breakdown of color gauge invariance. We show that the presence of this surface term first discovered several years ago allows one to derive in a gauge-invariant way a chiral-bag version of the Shore-Veneziano two-component formula for the flavor-singlet axial charge of the proton. This has relevance to what is referred to as the ``proton spin problem" on the one hand and to the Cheshire-Cat phenomenon in hadron structure on the other. We show that when calculated to the leading or…
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 …
In hadronization models with color recombination, partons are allowed to regroup into color singlet structures that are different from those determined by the perturbative parton shower. This aims at modeling the possibility that soft interactions of partons with the underlying event can change color connections. If such an effect is at play in proton-proton collisions, it may be expected to be enhanced in proton-nucleus collisions due to the higher color charge density in the underlying event. Here, we provide a qualitative argument that color recombination effects could lead to a multiplicit…
We calculate the helicity amplitudes for scattering of a quark from both large and small $x$ gluons of a target proton or nucleus using spinor helicity formalism. We show that scattering from large $x$ gluons of the target results in non-zero spin asymmetry at intermediate $p_t$ as well as rapidity loss of the projectile quark. We comment on how this can also generate angular asymmetries in particle production in high energy collisions.
The CMS experiment at the Large Hadron Collider has recently presented data on the average transverse momentum of protons, kaons and pions as a function of particle multiplicity. We relate the particle multiplicity to saturation momentum using recently published computations of the interaction radius determined from the theory of the Color Glass Condensate. We show that the pp and the pA experimental data scale in terms of these saturation momenta. Computing transverse momentum spectra for identified particles using Boltzmann-type distributions and relating different associated multiplicities …
We consider the implications of the Color Glass Condensate for the central region of p+A collisions. We compute the k_t distribution of radiated gluons and their rapidity distribution dN/dy analytically, both in the perturbative regime and in the region between the two saturation momenta. We find an analytic expression for the number of produced gluons which is valid when the saturation momentum of the proton is much less than that of the nucleus. We discuss the scaling of the produced multiplicity with A. We show that the slope of the rapidity density dN/dy provides an experimental measure fo…
We present a formalism for gluon-gluon elastic scattering in the presence of the classical color field of the protons in high energy collision. The classical field is obtained by solving the classical Yang-Mills equation in the covariant gauge and treated as a prescribed background for the quantum gluons involved in the scattering process. The interaction between the classical field and the quantum gluon modifies the gluon propagator, and, in turn, the $gg\rightarrow gg$ amplitude. The modified gluon propagator is derived to the first non-zero order of the classical field using the Gaussian ap…
Forward-backward multiplicity correlations have been studied in electron-positron, proton-proton and more recently in lead-lead collisions. For the proton-proton case, comparison of experimental results to different models reveals an incomplete understanding of the physical phenomenon associated with these correlations. In this work, we present a study of forward-backward multiplicity correlations in proton-proton collisions using the PYTHIA event generator, at LHC energies. A detailed analysis is presented with and without weak decays, splitting data samples into soft and hard QCD processes, …
We show that particle production in proton-nucleus (pA) collisions in the Color Glass Condensate model can be related to Deep Inelastic Scattering of leptons on protons/nuclei (DIS). The common building block is the quark antiquark (or gluon-gluon) dipole cross section which is present in both DIS and pA processes. This correspondence in a sense generalizes the standard leading twist approach to pA collisions based on collinear factorization and perturbative QCD, and allows one to express the pA cross sections in terms of a universal quantity (dipole cross section) which, in principle, can be …
We perform a detailed comparison of long range rapidity correlations in the Color Glass Condensate framework to high multiplicity di-hadron data in proton-proton and proton-lead collisions from the CMS, ALICE and ATLAS experiments at the LHC. The overall good agreement thus far of the non-trivial systematics of theory with data is strongly suggestive of gluon saturation and the presence of subtle quantum interference effects between rapidity separated gluons. In particular, the yield of pairs collimated in their relative azimuthal angle $Δϕ\sim 0$, is sensitive to the shape of unintegrated glu…
We show that in proton-lead (p+Pb) collisions at the LHC, the Color Glass Condensate (CGC) and hydrodynamics lead to qualitatively different behavior of the average transverse momentum, <p_T>, with the particles rapidity. In hydrodynamics, the <p_T> decreases as one goes from zero rapidity, y=0, to the proton fragmentation region since the number of particles decreases. In contrast, in the CGC the saturation momentum increases as one goes from y=0 to the proton fragmentation region, and so the <p_T> increases. At the LHC, the difference between the two models may be large enough to be tested e…
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 modificat…
We construct a general QCD light front formalism to compute many-body color charge correlators in the proton. These form factors can be extracted from deeply inelastic scattering measurements of exclusive final states in analogy to electromagnetic form factors extracted in elastic electron scattering experiments. Particularly noteworthy is the potential to extract a novel Odderon form factor, either indirectly from exclusive $J/Ψ$ measurements, or directly from exclusive measurements of the $η_c$ or tensor mesons at large Bjorken x. Besides the intrinsic information conveyed by these color cha…
We calculate the inclusive heavy quark production cross section for proton-nucleus collisions at high energies. We perform calculation in a quasi-classical approximation (McLerran-Venugopalan model) neglecting all low-x evolution effects. The derived expression for the differential cross section can be applied for studying the heavy quark production in the central rapidity region at RHIC.
Pions and protons production cross-sections are analyzed in proton-proton and proton-nucleus collisions at the RHIC energy at midrapidity. We employ the pQCD factorization scheme supplemented with the color-dipole formalism to investigate the Cronin effect. We calculate the broadening in the color-dipole approach for different centralities. Our main goal is to investigate, in a parameter-free manner within a unified framework, how much of the cronin effect for both pions and baryons comes from the transverse momentum broadening due to initial partons multi-scatterings. We conclude that final-s…
We discuss proton-nucleus collisions in the framework of the color glass condensate. By assuming that the proton can be described as a low density color source, we solve exactly the Yang-Mills equations corresponding to this type of collision, and then use this solution in order to calculate inclusive gluon production or quark-antiquark production. Our result shows that k_T-factorization, while valid for gluon production, is violated for quark pair production in proton-nucleus collisions.
We apply our recently formulated Gluon Exchange Model (GEM) to baryon production in proton-nucleus reactions involving N>1 proton-nucleon collisions. We propose a description scheme for the process of soft color octet (gluon) exchange, based on the assumption that probabilities to form an effective diquark are equal for all allowed pairs of quarks. The latter effective diquark can form either from two valence, one valence and one sea, or from two sea quarks. Consequently we calculate the probabilities for different color configurations involving diquarks of valence-valence, valence-sea and sea…
In this thesis the Color Glass Condensate (CGC) framework, which describes quantum chromodynamics (QCD) at high energy, is applied to various scattering 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 experimental 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 u…
A recent experiment [{\bf Phys. Rev. Lett. 126,082301 (2021)}] used the $(e,e'p)$ reaction on $^{12}$C to search for the effects of color transparency (the absence of final state interactions). Color transparency was said to be ruled out. The ability to observe the effects of color transparency depends on the ability of a putative point-like-configuration (PLC), formed in a high-momentum transfer coherent reaction, to escape the nucleus without expanding its size. We study the expansion aspect of color transparency using superconformal baryon-meson symmetry and light-front holographic QCD. A n…
Based on PYTHIA6.428, event-by-event fluctuations of the mean transverse momentum in proton- proton collisions at sqrt_s = 7 TeV are studied using several measures of the fluctuations. The study compares results of the fluctuations for events where color reconnection is turned on, with those where color reconnection is turned off. The comparison reveals that some of the fluctuation measures are much more sensitive to color reconnection than others. Through the comparison it is demonstrated for the first time that for proton-proton collisions at the Large Hadron Collider, these sensitive measur…
We compute the inclusive cross-section of $f_{2}$ tensor mesons production in proton-proton collisions at high-energy. We use an effective theory inspired from the tensor meson dominance hypothesis that couples gluons to $f_{2}$ mesons. We compute the differential cross-section in the $k_{\perp}$-factorization and in the Color Glass Condensate formalism in the low density regime. We show that the two formalisms are equivalent for this specific observable. Finally, we study the phenomenology of $f_{2}$ mesons by comparing theoretical predictions of different parameterizations of the unintegrate…
Color fluctuations in hadron-hadron collisions are responsible for the presence of inelastic diffraction and lead to distinctive differences between the Gribov picture of high energy scattering and the low energy Glauber picture. We find that color fluctuations give a larger contribution to the fluctuations of the number of wounded nucleons than the fluctuations of the number of nucleons at a given impact parameter. The two contributions for the impact parameter averaged fluctuations are comparable. As a result, standard procedures for selecting peripheral (central) collisions lead to selectio…
The power-law tail of high-pt pi^\pm spectra observed in forward d+Au collisions at RHIC can be attributed to the power-law decrease of the dipole forward scattering amplitude appearing in the color glass condensate (CGC) approach. Forward particle production probes the small-x gluon distribution of the target nucleus where its anomalous dimension is rather flat (gamma = 0.6 \sim 0.8) for moderately high pt (\lsim 5 GeV), and where the leading-twist DGLAP approximation is not valid. In the same framework, we examine p and \bar{p} production using baryon fragmentation functions parameterized in…
We employ a small $x$ Color Glass Condensate (CGC)+ Non-Relativistic QCD (NRQCD) formalism to compute $J/ψ$ production at low $p_\perp$ in proton-proton collisions at collider energies. Very good agreement is obtained for total cross-sections, rapidity distributions and low momentum $p_\perp$ distributions. Similar agreement is obtained for $ψ^\prime$ production. We observe an overlap region in $p_\perp$ where our results match smoothly to those obtained in a next-to-leading order (NLO) collinearly factorized NRQCD formalism. The relative contribution of color singlet and color octet contribut…
In this work we estimate the heavy quark production in proton-proton and proton-nucleus collisions at LHC energies using the color dipole formalism and the solution of the running coupling Balitsky-Kovchegov equation. Nuclear effects are considered in the computation of the total cross sections and rapidity distributions for scattering on protons and nuclei.
Proton-nucleus collisions (p+A) at LHC energies provide a rigorous test of the Color Glass Condensate (CGC), a model proposed to describe the high energy limit of Quantum Chromodynamics. In the CGC the average multiplicity of charged particles at midrapidity in p+A collisions depends logarithmically on the number of participants, $N_{part}$. In contrast, the Wounded Nucleon Model (WNM) of independent nucleon-nucleon scatterings, verified at RHIC energies, predicts that multiplicity in p+A depends linearly on $N_{part}$. We argue that for the first time, the dependence of mean multiplicity on $…
While the form factors and parton distributions provide separately the shape of the proton in coordinate and momentum spaces, a more powerful imaging of the proton structure can be obtained through phase-space distributions. Here we introduce the Wigner-type quark and gluon distributions which depict a full-3D proton at every fixed light-cone momentum, like what seen through momentum("color")-filters. After appropriate phase-space reductions, the Wigner distributions are related to the generalized parton distributions (GPD's) and transverse-momentum dependent parton distributions which are mea…
We study exclusive dijet production in electron-proton deep inelastic scattering at a future Electron Ion Collider. We predict the elliptic modulation of the cross section as a function of the angle between the dijet transverse momentum and the recoil momentum, and show that this modulation is due to non-trivial angular correlations between the transverse coordinate and transverse momentum in the Wigner (or Husimi) distribution. The small-$x$ evolution is shown to decrease the elliptic modulation in the EIC kinematics, because of the growth of the proton with decreasing $x$.
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…
The flavor singlet axial charge has been a source of study in the last years due to its relation to the so called {\it Proton Spin Problem}. The relevant flavor singlet axial current is anomalous, i.e., its divergence contains a piece which is the celebrated $U_A(1)$ anomaly. This anomaly is intimately associated with the $η^\prime$ meson, which gets its mass from it. When the gauge degrees of freedom of QCD are confined within a volume as is presently understood, the $U_A(1)$ anomaly is known to induce color anomaly leading to "leakage" of the color out of the confined volume (or bag). For co…
The dilepton production is investigated in proton-nucleus collisions in the forward region using the Color Glass Condensate approach. The transverse momentum distribution ($p_T$), more precisely the low $p_T$ region, where the saturation effects are expected to increase, is analyzed. The ratio between proton-nucleus and proton-proton differential cross section for RHIC and LHC energies is evaluated, showing the effects of saturation at small $p_T$, and presenting a Cronin type peak at moderate $p_T$. These features indicate the dilepton as a most suitable probe to study the properties of the s…
The flavor singlet axial charge has been a source of study in the last years due to its relation to the so called {\it Proton Spin Problem}. The relevant flavor singlet axial current is anomalous, i.e., its divergence contains a piece which is the celebrated $U_A(1)$ anomaly. This anomaly is intimately associated with the $η^\prime$ meson, which gets its mass from it. When the gauge degrees of freedom of QCD are confined within a volume as is presently understood, the $U_A(1)$ anomaly is known to induce color anomaly leading to "leakage" of the color out of the confined volume (or bag). For co…
Simple power counting arguments in the dilute-dense framework of the Color Glass Condensate (CGC) Effective Field Theory predict that even and odd azimuthal anisotropy harmonics of two-particle correlations in proton-nucleus collisions at the LHC will respectively satisfy v^2_{2n} ~ N_{ch}^0 and v^2_{2n+1} ~ N_{ch}, where N_{ch} denotes the number of charged particles. We show that these expectations are borne out qualitatively, and even quantitatively, within systematic uncertainties, for v_2 and v_4 in comparisons with data from the ATLAS collaboration. We also observe that ATLAS data for th…
We propose a new model for a homogeneous description of hadron-hadron and hadron-nucleus collisions, the Gluon Exchange Model, fundamentally based on color octet (gluon) exchange. In proton-proton collisions we provide an exact description of the final state proton and neutron spectrum including the proton diffractive peak. In proton-nucleus reactions we find that the projectile proton diquark cannot survive in more than about half of multiple proton-nucleon processes and consequently must be very frequently disintegrated, leading to long transfers of baryon number over rapidity space.
I present an overview of the ridge phenomenon in proton-proton and proton-lead collisions. This novel collimation between rapidity separated hadron pairs is a consequence of non-linear gluon dynamics within the small-x wave-function of the colliding hadrons.
In order to get information about the polarized gluon distribution in a proton, we studied the electroproduction of ψ' in polarized electron and polarized proton collisions in the framework of the NRQCD factorization approach. The value of the cross section dΔσ/ dp_T^2 for color-octet mechanism is about 5 times larger than that for color-singlet one, and it might be another test of the color-octet model if the polarized gluon distribution Δg(x) is well known. Furthermore, we found that this reaction is quite effective for testing the model of gluon polarization by measuring the double spin asy…
We calculate total hadron-hadron cross sections at high energies using the Low-Nussinov two-gluon model of the Pomeron. The gluon exchange is represented by a phenomenological potential including screened color-Coulomb, screened confining, and spin-spin interactions. We use bound-state wave functions obtained from a potential model for mesons, and a Gaussian wave function for a proton. We evaluate total cross sections for collisions involving pion, kaon, rho, phi, D, J/psi, psi', Upsilon, Upsilon', and the proton. We find that the total cross sections increase with the square of the sum of the…
We consider dilepton production in high energy proton-nucleus (and very forward nucleus-nucleus) collisions. Treating the target nucleus as a Color Glass Condensate and describing the projectile proton (nucleus) as a collection of quarks and gluons as in the parton model, we calculate the differential cross section for dilepton production in quark-nucleus scattering and show that it is very sensitive to the saturation scale characterizing the target nucleus.
We investigate the resonant production of color octet muons in order to explore the discovery potential of the FCC-based μp colliders. It is shown that search potential of μp colliders essentially surpass potential of the LHC and would exceed that of FCC pp collider.
The forthcoming LHC measurement of hadron multiplicity in proton-nucleus collisions is a crucial test of the k_t factorization and gluon saturation based models. Here, we provide quantitative predictions for the pseudorapidity distribution of charged particles produced in minimum bias proton-nucleus collisions at the LHC based on the idea of gluon saturation in the color-glass condensate framework. Our formulation gives good descriptions of the LHC and RHIC data for the charged-hadron multiplicities in both proton-proton and nucleus-nucleus collisions, and also the deep inelastic scattering at…
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 $\mathrm{J}/ψ$ 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.
The unification of gauge interactions in the context of Adjoint SU(5) and its phenomenological consequences are investigated. We show the allowed mass spectrum of the theory which is compatible with proton decay, and discuss the possibility to have a cold dark matter candidate. Due to the upper bounds on the proton decay partial lifetimes, tau (p --> K^+ nubar) < 9.3 10^{36} years and tau(p --> pi^+ nubar) < 3.0 10^{35} years, the theory could be tested at future proton decay experiments. The theory predicts also light scalar color octets which could be produced at the Large Hadron Collider.
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 depend…
We develop a Monte-Carlo event generator based on combination of a parton production formula including the effects of parton saturation (called the DHJ formula) and hadronization process due to the Lund string fragmentation model. This event generator is designed for the description of hadron productions at forward rapidities and in a wide transverse momentum range in high-energy proton-proton collisions. We analyze transverse momentum spectra of charged hadrons as well as identified particles; pion, kaon, (anti-)proton at RHIC energy, and ultra-forward neutral pion spectra from LHCf experimen…
We present studies that show how multi-parton interaction and color reconnection affect the hadro-chemistry in proton-proton (pp) collisions with special focus on the production of resonances using the PYTHIA8 event generator. We find that color reconnection suppresses the relative production of meson resonances such as $ρ_{0}$ and K*, providing an alternative explanation for the K*/K decrease observed in proton-proton collisions as a function of multiplicity by the ALICE collaboration. Detailed studies of the underlying mechanism causing meson resonance suppression indicate that color reconne…
We explore consequences of the existence of gluonic hot spots inside the proton for coherent and incoherent exclusive vector meson production cross sections in deep inelastic scattering. By working in the dilute limit of the Color Glass Condensate framework to compute the cross sections for Gaussian hot spots of fluctuating color charges and employing a non-relativistic vector meson wave function, we are able to perform large parts of the calculation analytically. We find that the coherent cross section is sensitive to both the size of the target and the structure of the probe. The incoherent …
We argue that the large suppression of the $ψ(2S)$ inclusive cross-section relative to the $J/ψ$ inclusive cross-section in proton-nucleus (p+A) collisions can be attributed to factorization breaking effects in the formation of quarkonium. These factorization breaking effects arise from soft color exchanges between charm-anticharm pairs undergoing hadronization and comoving partons that are long-lived on time scales of quarkonium formation. We compute the short distance pair production of heavy quarks in the Color Glass Condensate (CGC) effective field theory and employ an improved Color Evapo…
We review the theoretical interpretation of deep-inelastic electron-proton scattering at low values of the Bjorken variable $x \simeq Q^2/W^2 \lsim 0.1$. The process proceeds via the interaction of quark-antiquark $(q \bar q)$ color-dipole fluctuations of the (virtual) photon with the proton. In terms of the forward Compton scattering amplitude, two reaction channels contribute to the interaction of the $q \bar q$ color dipole with the gluon field in the proton. Dependent on the kinematics, there is either {\it color transparency}, corresponding to a cancellation of the amplitudes for the two …
We introduce a data analysis procedure for color transparency experiments which is considerably less model dependent than the transparency ratio method. The new method is based on fitting the shape of the A dependence of the nuclear cross section at fixed momentum transfer to determine the effective attenuation cross section for hadrons propagating through the nucleus. The hard scattering cross section is then determined directly from the data. We apply this procedure to the Brookhaven experiment of Carroll et al and find that it clearly shows color transparency: the effective attenuation cros…
