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- Indico Weeks View
In this talk, I will be discussing recent updates from the JAM collaboration. In addition I will discuss new initiatives funded by SciDAC to build the next generation of phenomenology tools for nuclear tomography.
In this talk, recent results from Compass in the field of hadron structure will be presented.
Parametrizing TMD parton densities and fragmentation functions in ways that consistently match their large transverse momentum behavior in standard collinear factorization has remained notoriously difficult. We show how the problem is solved using a recently introduced set of steps for combining perturbative and nonperturbative transverse momentum in TMD factorization. In this ``hadron structure oriented" approach (HSO), models for intrinsic transverse momentum effects are constrained by integral relations and by the large-$k_T$ behavior predicted by pQCD. We will show an application to semi-inclusive deep inelastic scattering (SIDIS), where we will illustrate how the HSO approach enables the smooth interpolation between the cross section in the TMD region and the large-$q_{\text{T}}$ regime, calculable in collinear factorization.
The transverse momentum dependent (TMD) factorization describes the traverse-momentum differential cross-section in the limit of large virtuality of the probe and fixed other scales. To extend the description to a broader range of scales, one needs to incorporate power corrections. I present an overview of the recent development of power corrections to the TMD factorization, including the factorization at next-to-leading power (at NLO) and the resummation of kinematical power corrections. I demonstrate that the power corrections are essential to account for the data description already at Q~10GeV.
The TMD factorization at the next-to-leading power has an involved structure of singularities.
I discuss the definition and properties of transverse momentum dependent (TMD) distributions of the twist-three including evolution,
symmetry relations, parametrization, interpretation, and singularities.
I demonstrate that the physical TMD distributions (in terms of which observables are written) require an extra subtraction procedure.
As an example of application, I discuss the Drell-Yan/SIDIS processes at the next-to-leading power in terms of physical distributions
and explicitly demonstrate the cancellation of rapidity and end-point divergences.
These results complete the construction of TMD factorization at the next-to-leading power.
In this work we describe how TMD Jet distributions are defined at NLP in a $q_T/Q$ expansion. These distributions are twist-3 distributions that contribute to SIDIS and $e^+e^-$ processes. We find that description of NLP contributions using jets in the large-$R$ limit significantly simplifies the discussion. Here we show what are the LO contributions to the twist-3 jets and cancellation of divergencies. This work is preliminary.
I will report on recent QCD global analyses of single-spin asymmetries involving two different types of observables. On the one hand, measurements of the Sivers, Collins, and sin(phi_S) effects in SIDIS, Collins effect in electron-positron annihilation, Sivers effect in Drell-Yan, and A_N in single-inclusive proton-proton collisions, are sensitive to important TMDs and collinear twist-3 (quark-gluon-quark) functions. On the other hand, measurements where two hadrons are detected in the same parton-initiated jet in SIDIS, electron-positron annihilation, and proton-proton scattering provide information on novel dihadron fragmentation functions. The two different types of observables have overlap in that they both give access to the transversity function, which then can be used to calculate the tensor charges of the nucleon. I will discuss agreements and tensions between the transversity PDFs and tensor charges found from these two methods as well as those computed within lattice QCD.
In this talk we present the latest results of the MAP collaboration about the extraction of Transverse-Momentum-Dependent (TMD) distributions at the N$^3$LL logarithmic accuracy. We discuss the extraction of unpolarized quark TMD Parton Distribution Functions (TMD PDFs) in the proton and in the pion, as well as TMD Fragmentation Functions (TMD FFs), from global fits of Drell-Yan and Semi-Inclusive Deep-Inelastic Scattering (SIDIS) data sets.
In this work, we for the first time extract collinear and transverse momentum dependent (TMD) parton distribution functions (PDFs) in the proton simultaneously from precise high energy Drell-Yan and $Z$-boson production $q_T$-dependent data. We make use of TMD factorization, which is conveniently formulated in $b_T$-space, the Fourier conjugate to intrinsic transverse momentum $k_T$. At collider facilities, the low-$q_T$ data are especially sensitive to the perturbative contributions in small $b_T$ because of the wide availability of phase space and gluon radiations. The perturbative contributions to the cross sections are described by the operator product expansion (OPE) through collinear PDFs. In this way, we are able to study the impacts on the collinear PDFs from transverse-momentum dependent as well as purely collinear data.
The factorization theorem plays an important role in the analysis of high energy quantum chromodynamic (QCD) processes, separating the nonperturbative hadronic interaction into the universal parton distribution functions (PDFs) and fragmentation functions (FFs) and the process-dependent interactions into short distance perturbative calculations, with any interference power suppressed. With a virtual photon exchange, lepton-hadron deep inelastic scattering (DIS) provides an electromagnetic hard probe for the partonic structure of colliding hadron and has played an important role in the development of QCD factorization. However, the collision induced QED radiation can change the momentum of the exchanged but unobserved virtual photon, making the photon-hadron frame, where the factorization formalism for DIS and semi-inclusive DIS (SIDIS) was derived, ill defined. An new analogous factorization approach has been introduced to separate the leading power process-independent QED radiative contributions to the single photon exchange by introducing lepton distribution functions (LDFs) and lepton fragmentation functions (LFFs), while process-dependent effects are perturbatively calculated with large logarithms removed [J. High Energ. Phys. 2021, 157 (2021)]. These LDFs and LFFs are considered global, as they appear in many different interactions, such as $e^+ e^-$, DIS and SIDIS, so data from experiments can be used to fit and describe these functions across a wide range of lepton scattering. In this talk, I will apply this new factorization approach to lepton-hadron SIDIS to study the cross-section in two different kinematic regions: (1) the scattered lepton and observed hadron are not near back-to-back, and (2) they are close to back-to-back, where collinear QCD factorization works for (1) and TMD QCD factorization for (2) while collinear QED factorization works for both, in a newly introduced hybrid factorization approach. As part of this work, I show the effects on the SIDIS cross section using fixed order calculations for the unpolarized structure function by first showing the effect of the radiative corrections on the main kinematic variables, especially how the internal transverse momentum is significantly correlated to the external angular dependence, and then the unpolarized structure function (or cross section) with matching between the descriptions for low and high transverse momentum.
In this talk, we will present a recent re-analysis of Belle data for the transverse $\Lambda$ and $\bar{\Lambda}$ polarization in $e^+e^-$ annihilation processes within a TMD factorization approach and adopting the CSS framework.
We will also discuss the issue of isospin symmetry and the role of the charm quark contribution, with their impact on the description of the experimental data as well as on the extraction of the polarizing fragmentation function.
Estimates for the transverse $\Lambda$ polarization in SIDIS processes, at typical energies of the future EIC, will be presented.
In global extractions of transverse momentum dependent (TMD) distributions, the TMDs match the collinear parton density functions (PDF) in the limit of small transverse distances. The use of different PDF sets is one of the sources of discrepancy among TMD sets available. In this talk we discuss the influence of the PDF choice on the determination of unpolarized TMDPDFs and the description of TMD Drell-Yan-pair and Z-boson production data. To this end we perform the fit with the same functional form for the non-perturbative components of the TMDPDFs and CS kernel, matched to different sets of collinear PDFs. We find that the PDF choice biases the extraction of TMDPDF; however this bias is alleviated once the PDF uncertainty is taken into account, and if we allow the non-perturbative TMD profile to be flavour-dependent. Taking into account these two features improve the agreement between theory and experiment, provide a more realistic uncertainty for TMD distributions than previously extracted, and should be consiedered in future global analyses
Extending the TMD factorization to thrust-dependent observables entails difficulties ultimately associated with the behavior of soft radiation.
In this talk, the factorization properties of the thrust distribution of $e^+e^−$ annihilation into a single hadron are discussed and their peculiarities with respect to standard TMD factorization are highlighted.
I present the phenomenological extraction of the unpolarized TMD Fragmentation Function for pions, for the first time based on a sound factorization theorem that correctly takes into account the thrust dependence in the 2-jet region.
The DGLAP evolution equations are arguably the most important evolution equations for collider physics applications. However, DGLAP doesn’t capture correlations in fragmentation, which e.g. enter in dihadron fragmentation or the study of energy flow within jets. In this talk I present a general non-linear collinear evolution equation, that accounts for these correlations. We have calculated the next-to-leading order evolution kernels and shown that they reproduce DGLAP for single hadron fragmentation. Furthermore, the (so far unknown) next-to-leading order evolution of N-hadron fragmentation functions can be directly obtained from our results. Finally, the full evolution equations are needed for track functions, which can be applied to calculations of track-based observables.
Previous Lattice QCD calculations of nucleon transverse momentum-dependent parton distributions (TMDs) focused on the case of transversely polarized nucleons, and thus did not encompass two leading-twist TMDs associated with longitudinal polarization, namely, the helicity TMD $g_1 $ and the worm-gear TMD $h_{1L}^{\perp } $ corresponding to transversely polarized quarks in a longitudinally polarized nucleon. Based on a definition of TMDs via hadronic matrix elements of quark bilocal operators containing staple-shaped gauge connections, TMD observables characterizing the aforementioned two TMDs are evaluated, utilizing a RBC/UKQCD domain wall fermion ensemble at the physical pion mass. The results suggest that $h_{1L}^{\perp } $ is significantly suppressed in magnitude compared to its counterpart, the worm-gear TMD $g_{1T} $, deviating from the generic prediction of quark models, and thus indicating the influence of strong gluonic dynamical effects.
Typically, a production of a particle with a small transverse momentum in hadron-hadron collisions is described
by CSS-based TMD factorization at moderate Bjorken $x_B\sim 1$ and by $k_T$-factorization at small $x_B$.
A uniform description valid for all $x_B$ is provided by rapidity-only TMD factorization developed in a series
of recent papers at the tree level. In this paper the rapidity-only TMD factorization for particle production by
gluon fusion is extended to the one-loop level.
The ”tomography” of the proton and heavy nuclei, which refers to the three-dimensional imaging of elementary quarks and gluons in these QCD bound states, is one the primary goal of the future Electron-Ion Collider (EIC). Gluon tomography is mathematically encoded into the gluon Weizs̈acker-Williams (WW) transverse momentum dependent (TMD) distribution which, in light cone gauge, represents the light cone quantized number distribution of gluons as function of their transverse momenta in a proton or nucleus at small $x_{\rm Bj}$. A "golden process" to extract the gluon WW distribution is the inclusive production of a pair of back-to-back jets, or back-to-back hadrons, in deep inelastic electron-proton or electron-nucleus scattering (DIS).
In this talk, I will show that for dijets with relative transverse momenta $P_\perp$ and transverse momentum imbalance $q_\perp$, to leading power in $q_\perp/P_\perp$, the cross-section for longitudinally and transversely polarized virtual photons to NLO can be fully factorized into a product of a perturbative hard factor and the non-perturbative Weizsäcker-Williams TMD. This factorization formula is valid to all orders in $Q_s/q_\perp$ for $q_\perp, Q_s\ll P_\perp$, where $Q_s$ is the CGC saturation scale. The hard factor and the soft factor, which resums Sudakov double and single logs in $P_\perp/q_\perp$, are given by remarkably compact analytic expressions while the WW TMD satisfies a kinematically constrained JIMWLK renormalization group evolution in rapidity.
I will finally present results of a numerical study that explores the relative importance of gluon saturation, Sudakov effects and genuine $\mathcal{O}(\alpha_s)$ corrections on the inclusive back-to-back dijet cross-section in DIS at small $x_{\rm Bj}$.
Refs:
[1] Caucal, Salazar, Schenke, Venugopalan, JHEP 11 (2022) 169, arXiv:2208.13872.
[1] Caucal, Salazar, Schenke, Stebel, Venugopalan, to appear.
Using the colour dipole picture and the colour glass condensate (CGC) framework, we systematically study the diffractive production of two (quark-antiquark) and three (quark, antiquark, and gluon) jets via coherent photon-nucleus interactions at high energy. We focus on the hard scattering regime where at least one of the transverse momentum scales in the problem (the photon virtuality and/or the relative transverse momentum of two of the produced jets) is much larger than the saturation momentum $Q_s$ of the nuclear target. We argue that, despite this hardness, the cross-sections for all these processes are controlled by large dipole configurations, with transverse size $R\sim 1/Q_s$, which undergo strong scattering. We demonstrate that these dominant contributions admit factorisations in terms of the quark or gluon diffractive transverse-momentum dependent distributions (TMDs) of the Pomeron. These diffractive TMDs have support at transverse momenta $k_\perp\le Q_s$ and vanish as a power of $1-x$ when the parton splitting fraction $x$ approaches to unity. Their dependence upon the longitudinal momentum fraction of the Pomeron $x_{\mathbb{P}}$ is controlled by the BK/JIMWLK equations of the CGC. By integrating over $k_\perp$ up to the hard scale, we deduce explicit results for the respective diffractive PDFs and structure functions.
Factorization theorems have long been a successful and elegant tool to describe and interpret hadronic structure. The early parton model picture, first developed by Feynman, has now been generalized past the leading power description of inclusive processes like deep inelastic scattering (DIS) to semi-inclusive ones like SIDIS and much more. However, a consistent description of both collinear and TMD distribution functions is still not agreed upon along with the limits of the factorization program. The inherent complexity of QCD prohibits a direct test of factorization but any other simpler renormalizable theory can be adopted to stress-test its validity and the schemes regularly used to describe physical observables like cross sections and structure functions.
A scalar Yukawa model, free of gauge degrees of freedom, can be studied as toy-model to quantitatively tackle issues such as the positivity of collinear PDFs (and FFs) and their possible definitions as the integrated versions of TMD distributions. The performance of the well known $b_*$ prescription can also be compared directly along with quantitative results on the role of the W and Y term in the description of TMD observables.
The information obtained by studying a simpler model that still retains some of the features of QCD could shed light onto many of the standard schemes employed in regular QCD and cast some doubts on the various assumptions that are made.
Pseudo- and quasi-parton distribution functions (PDFs) defined through space-like bilocal operators allow for direct access to the PDFs from first principles in lattice gauge theory. However, this formalism currently leaves the small Bjorken $x$ regime inaccessible. With the future Electron-Ion Collider in mind, it is timely to study the PDFs at small-$x$. In a previous calculation, we showed that the gluon pseudo and quasi PDFs have distinct behavior at small-$x$. It is known that the behavior of the quark distribution at small-$x$ is not directly related to that of the gluon PDF, as previous research has shown. In this talk, I will present the calculation of the quark pseudo- and quasi-PDFs in the high-energy limit, and show that they too have distinct behavior at small-$x$.
We calculate the Next-to-Leading Order (NLO) virtual correction to the Higgs-induced DIS coefficient function in the infinite top-mass limit. Since we want to use this result in the framework of kt-factorization to resum small-$x$ logarithms up to Next-to-Leading-Logarithm (NLL), we work in light-cone gauge and we keep the incoming gluon off-shell. This choice raises many challenging points like the presence of spurious singularities and a different definition for the UV-counterterms. This calculation is a necessary ingredient for the coefficient function that will be used to resum up to NLL small-$x$ logarithms for this process.
Double-spin asymmetry in particle and jet productions in longitudinally polarized proton-proton collisions is one of the flagship measurements at RHIC, with the aim of determining the spin fraction of gluons within the proton. Although current next-to-leading order perturbative QCD predictions, based on collinear factorization, have been quite successful in explaining experimental data and extracting gluon helicity distribution within the RHIC kinematics, there is a need for predictions that take into account the small x evolution and gluon saturation effect in order to better understand gluons at smaller x. In this talk, I will discuss our efforts to directly calculate the longitudinal double-spin asymmetry in the small x limit, particularly for the gluon production at midrapidity. Our findings show that, in the pure glue case, the double-spin asymmetry depends on a new twist-3 transverse momentum-dependent gluon distribution, in addition to the transverse-momentum dependent gluon helicity distribution. These results suggest that extracting gluon helicity distribution at small $x$ from the double-spin asymmetry using the collinear factorization formalism might overestimate the contribution.
QCD multiple scattering plays an essential role in explaining the observed nontrivial phenomena in high energy nuclear collisions. In cold nuclear medium, there are two extensively used theoretical frameworks for describing QCD multiple scatterings, i.e. the high-twist approach and the color glass condensate (gluon saturation) framework that resums multiple eikonal scattering. In this talk, we explore for the first time the relation between these two well-known formalisms. In particular, we use direct photon production in proton-nucleus collisions as an example to show the consistency between these two formalisms.
I discuss a determination of unpolarised charged pion and kaon fragmentation functions from a set of single-inclusive electron-positron annihilation and lepton-nucleon semi-inclusive deep-inelastic scattering data. The determination includes next-to-next-to-leading order QCD corrections to both processes, and is carried out in a framework that combines a neural-network parametrisation of fragmentation functions with a Monte Carlo representation of their uncertainties. I discuss the quality of the determination, in particular its dependence on higher order corrections, and an application to a companion determination of helicity parton distribution functions.
Mapping the 3D structure of the proton in terms of its spinning quark and gluon constituents is one of the main goals of current hadronic physics investigations. Generalized parton distributions can provide part of the solution, connecting through Fourier transformation to the single particle spatial density of quarks and gluons with a given longitudinal momentum fraction, x. The physical properties derived from GPDs are the average radius of each partonic component of the proton/neutron and quantities derived from it. A fuller dynamical picture of the proton's interior can be, however, captured by introducing two-particle spatial density distributions. The latter
render the relative position of quarks and gluons with respect to one another in the transverse plane, providing a measure of the amount of correlations in the particles' motion. We show that two-particle densities can be de?ned in QCD introducing the concept of generalized double parton distributions (GDPDs) and provide data informed scenarios on the geometric structure of the proton including the relative positions of gluons around valence quarks inside the proton.
We show that the momentum sum rule is a necessary condition for factorization of double parton distributions into a product of two single parton distributions for small values of the parton momentum fractions $x$ and large enough values of the evolution scale $Q^2$. This is a somewhat surprising result since the momentum sum rule involves integration over all values of the momentum fraction. In essence, the momentum sum rule provides a proper relation between the double and single parton distributions, which is necessary for the small $x$ factorization at large $Q^2$.
Precise theoretical predictions at the LHC require a thorough understanding of double parton scattering (DPS), a simplest form of multiparton interactions. Due to high abundance of jet events in pp collisions, multiple jet production plays a special role among various processes where DPS can occur. In this talk we discuss the status of DPS studies for this class of processes, focusing in particular on four-jet final states.
In this talk, I will introduce the concept of the nucleon energy-energy correlator (NEEC). I will argue how NEEC can be measured in the DIS process and present the NLL+NLO results. Its physical meaning and possible application to the nucleon/nucleus structure studies will also be discussed.
In this talk I will summarise the development of NLL accurate parton shower algorithms from the study of amplitude evolution. I will give particular focus to recent work on generalising the coherent branching framework.
The Parton Branching (PB) approach provides evolution equations for transverse momentum dependent parton densities (TMDs). It is an angular ordered evolution that keeps track of the transverse momentum throughout the whole evolution chain and has equations that are structured such that they can be solved with Monte Carlo (MC) techniques. The obtained TMDs can be used in MC generators to describe physical observables.
I will give an overview of recent predictions obtained with the method, as well as the progress in terms of the evolution equations, such as the first steps to extend the approach towards small-x.
In the coming years, the Electron-Ion-Collider (EIC) in the United States will enable researchers to study lepton-hadron collisions with unprecedented precision. To consolidate figures of merit of a variety of measurements at the EIC, it is essential to include radiative corrections in simulations of electron-proton and electron-nucleus collisions. For the time being, there do not exist any automated simulation tools for such reactions, including even only next-to-leading order (NLO) radiative corrections.
In this talk, I will present our recent progress in the implementation of photoproduction, where the photon is either coming from an electron or from a proton in an ultra-peripheral collision at the LHC. We perform the calculations at NLO in the fixed-order mode within MadGraph5_aMC@NLO, a framework for (N)LO computation, intensively used at the LHC. In addition, I will also present the development for asymmetric hadron collisions in order to provide predictions e.g. for proton-nucleus collisions.
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The almost-11 GeV polarised electron beam scattering from polarised and unpolarised fixed targets at Jefferson Lab (JLab), USA, enables measurements of deep inelastic scattering in the valence quark regime. A range of exclusive and semi-inclusive processes give access to three-dimensional structure of the nucleon through, respectively, the frameworks of Generalised Parton Distributions (GPDs) and Transverse Momentum-dependent Distributions (TMDs). This talk will review the relevant results from experiments conducted at JLab.
Transverse-momentum distributions inside hadrons have been a very active topic in hadron physics for the past three decades. An important ingredient to this endeavour is hadronization (or fragmentation), the formation of hadrons from partons. Belle was a pioneer in employing electron-positron annihilation data to constrain the Collins fragmentation function for charged pions and various other related fragmentation functions, providing data at a scale larger than that available at fixed-target lepton-scattering experiments. In this talk, among others, recent results on the transverse-momentum dependence of spin-averaged and transverse-spin dependent fragmentation will be discussed, including the first Belle measurement of the explicit transverse-momentum dependence of the pion and eta Collins fragmentation.
We report on recent results on extraction of generalized parton distributions and relevant form factors from deeply virtual Compton scattering (DVCS) and deeply virtual meson production (DVMP) data. Using the more recent proton DVCS data, we extract the set of leading Compton form factors (CFFs) with uncertainties and, by adding neutron DVCS data, we separate the contributions of up and down quarks to the CFFs H and E utilizing neural networks. We make simultaneous fits to high energy DVCS and DVMP data and demonstrate that extraction of unique GPDs becomes possible at next-to-leading order.
Traditionally, lattice QCD computations of generalized parton distributions (GPDs) have been carried out in a symmetric frame, where the transferred momentum is symmetrically distributed between the incoming and outgoing hadrons. Such frames require a separate calculation for each value of the momentum transfer, increasing significantly the computational cost. I will present a newly developed Lorentz covariant framework for faster and more accurate lattice QCD calculations of GPDs exploiting asymmetric momentum transfer between the incoming and outgoing hadrons. By Taking advantage of this new framework, I will present recent lattice QCD results on some of the valance GPDs of proton. I will also present lattice QCD results for first few Mellin moments of these GPDs, obtained from the short-distance expansion of the lattice QCD matrix elements.
Conformal symmetry of QCD is restored at the Wilson-Fisher critical point in noninteger space-time dimensions. Correlation functions of multiplicatively renormalizable operators with different anomalous dimensions at the critical point vanish identically.
We show that this property allows one to calculate off-diagonal parts of the anomalous dimension matrices for leading-twist operators from a set of two-point correlation functions of gauge-invariant operators which can be evaluated using standard computeralgebra techniques. As an illustration, we present the results for the NNLO anomalous dimension matrix for flavor-singlet QCD operators for spin N ≤ 8.
I derive an all-order resummation formula for the logarithmically enhanced contributions proportional to αsnx±ξ \frac{\alpha_s^n}{x\pm \xi } x±ξαsn log (ξ±x2ξ)k {\left(\frac{\xi \pm x}{2\xi}\right)}^k (2ξξ±x)k in the quark coefficient function of deeply-virtual-Compton scattering and the pion-photon transition form factor in momentum space. The resummation is performed at the next-to-next-to-leading logarithmic accuracy. The key observation is that the quark coefficient function itself factorizes in the x → ±ξ limit, which allows for a resummation using renormalization group equations. A preliminary numerical analysis suggests that the corrections due to resummation for the quark contribution might be small.
We will discuss the gluon GPD from moderate to small x using partial twist expansion.
Generalized Transverse Momentum Dependent (GTMD) distributions provide the most complete information on the structure of hadrons one can hope to constrain via experiments described in perturbative QCD. Using their Fourier transforms, Wigner distributions, it is possible to write very intuitive definitions for some physical properties inside hadrons such as the decomposition of its spin between its constituent helicities and orbital angular momenta.
In this talk we will first discuss the theoretical definition, properties and limits of GTMD distributions. Then we will consider the prospects for phenomenology where these distributions are involved, and what we can learn about GTMDs in different processes.
Both deeply-virtual and photoproduction of mesons offer promising access
to generalized parton distributions and complementary description of different kinematical regions. Higher-twist effects have been identified as especially important in the case of the production of pseudo-scalar mesons. This was confirmed by recent evaluation of the complete twist-3 contribution to π production and its confrontation with experimental data.
We discuss the photoproduction of a photon-meson pair in the collinear factorisation framework as a channel for the extraction of GPDs. What makes this channel interesting, from among the family of $2 \to 3$ processes, is that depending on the chosen meson (and its polarisation) in the final state, one is able to probe chiral-even and chiral-odd GPDs, as well as gluonic GPDs, all at the leading twist. More specifically, we consider the case where the outgoing meson is a pion or rho meson (with any charge). In fact, choosing a transversely-polarised rho meson in the final state allows us to access chiral-odd quark GPDs at the leading twist, which are not known experimentally. Working at leading order in QCD, we compute the cross sections and polarisation asymmetries (wrt the incoming photon) for the various final state mesons, and we discuss the prospects of measuring them at various experiments, namely JLab-12, COMPASS, future EIC, and ultra-peripheral collisions at LHC.
We calculate the one-loop corrections to single and double inclusive hadron production in DIS at small x using the Color Glass Condensate effective theory of QCD at small x. We show that all divergences either cancel or are absorbed into DGLAP evolution of the parton-hadron fragmentation functions and JIMWLK evolution of dipoles and quadrupoles describing the dynamics of the target proton or nucleus. We discuss the applications of our results to the future Electron Ion Collider (EIC) and the Ultra-peripheral heavy ion collisions at RHIC and the LHC.
The cross-sections of diffractive double hadron photo- or electroproduction with large pT, on a nucleon or a nucleus, are calculated to NLO accuracy.
A hybrid formalism mixing collinear factorization and high energy kt factorization, more precisely the shockwave formalism, is used to derive the results.
The cancellation of divergences is explicitly shown, and the finite parts of the NLO differential cross-section are found. We work in arbitrary kinematics such that both photoproduction and leptoproduction are considered, making the results usable in order to detect saturation at both the future EIC or already at LHC, using UPC
Precision physics in the Higgs sector has been one of the main challenges in recent years. The pure fixed-order calculations, entering the collinear factorization framework, in particular conditions, must be supplemented by all-order resummations. In this talk, we consider the production of a Higgs boson in association with a jet at large rapidity separation. When the two detected objects are widely separated in rapidity, the hard scattering cross section gets large logarithmic corrections that can be resummed through the Balitsky-Fadin-Kuraev-Lipatov (BFKL) approach.
We present the full next-to-leading order resummation for the aformentioned process and discuss preliminary phenomenological results for the LHC kinematical configurations.
$J/\psi$-pair production at the LHC is currently the most promising tool to probe the unknown gluon transverse momentum distributions (TMDs). Data from LHCb at low transverse momenta are already available and more are expected soon from CMS and LHCb. Such data in the collider mode should soon allow one to probe the evolution of the unpolarised-gluon TMDs and to measure, for the first time, the distribution of the linearly polarised gluon in unpolarised protons. In addition, data in the fixed-target mode will give us some handle to measure the momentum-fraction dependence of the TMDs.
In this talk, I will revise previous results obtained for the collider mode and present first results for the fixed-target mode. After showing a comparison with the existing LHCb data, I will discuss predictions of transverse-momentum distributions at different invariant masses that could be measured by LHCb and CMS in the collider mode. I will then present predictions for azimuthal modulations of the cross section that arise from linearly polarised gluons.
I will show that the azimuthal modulations are reduced when the momentum fractions of the two colliding gluons are different, $x_1 \neq x_2$. In general, the azimuthal modulations are found significantly larger for $x_1 = x_2$, which is then likely the most favourable region to set constraints on the linearly polarised gluon TMDs.
We present a calculation of the azimuthal asymmetries in back-to-back production of J/psi-jet and J/psi-photon at the future electron-ion collider (EIC). We use NRQCD to estimate the J/psi production, and assume TMD factorization for the back-to-back kinematics. We show that these asymmetries will be useful for probing the the gluon TMDs, like the linearly polarizaed gluon TMD, in unpolarized scattering, and gluon Sivers function, when the proton is transversely polarized. We give estimates of the upper bound of the asymmetries, as well as using different parametrizations of the gluon TMDs. We investigate the effect of TMD evolution on the asymmetry.
Quarkonia are very important tools to probe gluon transverse momentum dependent (TMD) distributions at lower energies as compared, for instance, to Higgs production. Among them, the $J/\psi$ meson is one of the most studied, since it frequently decays into lepton pairs, making its detection easier with respect to other quarkonia. Thus, describing observables that involve $J/\psi$ production within a proper theoretical formalism is highly valuable.
Adopting the non-relativistic QCD approach, the evaluation of these observables at low transverse momentum is achieved by combining the TMD distribution(s) for the initial state(s) and the long-distance matrix elements for the J/ψ meson in the final state. However, it has been shown that the correct TMD factorisation requires a generalisation of the latter, the so-called TMD shape functions, which include smearing effects. Observables are then written in terms of TMD parton distribution(s) and shape functions, assuming both colour-singlet and colour-octet production mechanisms for the $J/\psi$ meson.
In this talk, I will discuss the derivation of the TMD shape functions for semi-inclusive deep-inelastic scattering. I will then propose a new TMD factorized formula and a procedure to extract these new universal functions, taking into account their evolution with respect to the factorisation scale. The phenomenological studies presented in this talk could be performed at the future Electron-Ion Collider.
We explore the possibility to use ultra-peripheral proton-lead collisions at the LHC to study inclusive $J/\psi$ photoproduction, namely when a quasi-real photon emitted by the fully stripped lead ion breaks a proton to produce the $J/\psi$. Owing to the extremely large energies of the colliding hadrons circulating in the LHC, the range of accessible $W_{\gamma p}$ largely exceed what has been and will be studied at lepton-hadron colliders like HERA and the EIC. We obtain a leading-order inclusive-photoproduction cross section of order 50 $\mu$b, which we find large enough to be measured by CMS and LHCb. In addition, we find that inclusive-photoproduction can be isolated from possible hadroproduction processes by imposing the absence of significant activity in the lead-going direction, and may be further isolated by imposing rapidity-gap based cuts on detector activity. We estimate the background-to-signal ratio to be of order 0.001 and 0.01 at CMS and LHCb, respectively. In addition, we propose a method similar to the Jacquet-Blondel Method to reconstruct $W_{\gamma p}$ and the elasticity ($z$). Reconstructing these variables will allow kinematic regions to be defined that minimise theoretical uncertainty. We find that $z$ can be reconstructed with a resolution of 0.1, 0.15, and 0.2 in LHCb Pb$p$, CMS, and LHCb $p$Pb, respectively, where Pb$p$ and $p$Pb imply opposite beam directions.
This talk reexamines the running coupling prescription for the small x evolution equations. Our analysis is based on the NLO JIMWLK, which enabled us to identify potentially large logarithms associated with the running coupling contributions. We show that past analyses performed in the framework of BK and JIMWLK attributed several DGLAP-like logarithms to the running coupling corrections. We discuss the DGLAP-like contribution and its resumation; we also propose a resumed expression for the running coupling. The resulting prescription significantly differs from those put forward by Balitsky, and Kovchegov/Weigert. We comment on the phenomenological implications of our studies.
It is well known that the evolution in the limit of small Bjorken x acquires large corrections at NLO order. These corrections needs to be resummed by taking into account kinematical constraints and the matching to the DGLAP evolution. This is known as the collinear resummation. In order for the physical cross sections to be consistent with resummation, the impact factors entering them also need to be resummed. In this work we perform the resummation of the photon-gluon impact factor. We analyze the gamma-gamma cross section, and perform the consistent matching of the resummed gluon Green's function to the resummed impact factors. We illustrate our the results and their uncertainties numerically by calculating the effects of the resummation on the energy dependence of the cross section.
The $p_T$-integrated cross section of inclusive hadro and photo-production of heavy quarkonia when computed up to NLO in Collinear Factorisation(CF) shows a perturbative instability at high hadronic or photon-hadron collision energies -- the cross section could turn negative for reasonable factorisation/renormalisation scale-choices. We solve this problem by resummation of the subset of LLA higher-order corrections $\sim \alpha_s^n \ln^{n-1}(\hat{s}/M^2)$, where $\hat{s}$ is the partonic center of mass energy squared, using High-Energy Factorisation(HEF) formalism. We use doubly-logarithmic approximation for the resummation factors $\sim \alpha_s^n[\ln(\hat{s}/M^2)\ln(q_T/\mu_F)]^{n-1}$, for consistency with NLO DGLAP evolution of PDFs. The DLA HEF result is then matched with the full NLO CF calculation to provide uniformly accurate description at low and high collision energies.
The phenomenological results for $\eta_c$ total and rapidity-differential cross sections will be presented, as well as for $J/\psi$ inclusive photoproduction will be presented. The calculation of loop corrections to $\gamma+R(q_T)\to c\bar{c}[{}^1S_0^{[8]}]$ coefficient function of HEF, which is necessary to go beyond the DLA, will be discussed.
The production of $\eta_c$ in diffractive $ep$ and $eA$ collisions has been suggested as a golden probe of the C-odd QCD interaction, the odderon. Previous studies of this process have considered a linearised Bartels-Kwiecinski-Praszalowicz odderon [1-3], which is appropriate in the dilute regime where the x region probed in the proton is not too small. In this work [4], we explore this process in the dense regime, i.e., at low-x values in the proton or in large nuclei where effects of gluon saturation may become important. We treat the energy evolution of the odderon using the running coupling Balitsky-Kovchegov equation which incorporates saturation effects and present numerical estimates for eta_c production in diffractive ep and eA (Au, Cu, Al) at the Electron-Ion Collider (EIC). As the initial condition for odderon evolution, we adopt a Jeon-Venugopalan model [5] based odderon, with the overall normalisation being fixed by a group theoretic constraint [6,7] which gives us an upper bound for the size of the odderon, as well as the cross-section. By studying the dependence of eta_c production on different kinematics and nuclear size, and the relative sizes of the QCD and QED contributions, we aim to identify the ideal scenario to get a signal for the odderon at the EIC.
References:
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