Parton Transverse Momentum Research Articles

What are the low- Q and large- x boundaries of collinear QCD factorization theorems?

Familiar factorized descriptions of classic QCD processes such as deeply-inelastic scattering (DIS) apply in the limit of very large hard scales, much larger than nonperturbative mass scales and other nonperturbative physical properties like intrinsic transverse momentum. Since many interesting DIS studies occur at kinematic regions where the hard scale, $Q \sim$ 1-2 GeV, is not very much greater than the hadron masses involved, and the Bjorken scaling variable $x_{bj}$ is large, $x_{bj} \gtrsim 0.5$, it is important to examine the boundaries of the most basic factorization assumptions and assess whether improved starting points are needed. Using an idealized field-theoretic model that contains most of the essential elements that a factorization derivation must confront, we retrace the steps of factorization approximations and compare with calculations that keep all kinematics exact. We examine the relative importance of such quantities as the target mass, light quark masses, and intrinsic parton transverse momentum, and argue that a careful accounting of parton virtuality is essential for treating power corrections to collinear factorization. We use our observations to motivate searches for new or enhanced factorization theorems specifically designed to deal with moderately low-$Q$ and large-$x_{bj}$ physics.

Nonperturbative-transverse-momentum effects and evolution in dihadron and direct photon-hadron angular correlations in p+p collisions at s=510 GeV

Dihadron and isolated direct photon-hadron angular correlations are measured in $p$$+$$p$ collisions at $\sqrt{s}=510$ GeV. Correlations of charged hadrons of $0.7<p_T<10$ GeV/$c$ with $\pi^0$ mesons of $4<p_T<15$ GeV/$c$ or isolated direct photons of $7<p_T<15$ GeV/$c$ are used to study nonperturbative effects generated by initial-state partonic transverse momentum and final-state transverse momentum from fragmentation. The nonperturbative behavior is characterized by measuring the out-of-plane transverse momentum component $p_{\rm out}$ perpendicular to the axis of the trigger particle, which is the high-$p_T$ direct photon or $\pi^0$. Nonperturbative evolution effects are extracted from Gaussian fits to the away-side inclusive-charged-hadron yields for different trigger-particle transverse momenta ($p_T^{\rm trig}$). The Gaussian widths and root mean square of $p_{\rm out}$ are reported as a function of the interaction hard scale $p_T^{\rm trig}$ to investigate possible transverse-momentum-dependent evolution differences between the $\pi^0$-h$^\pm$ and direct photon-h$^\pm$ correlations and factorization breaking effects. The widths are found to decrease with $p_T^{\rm trig}$, which indicates that the Collins-Soper-Sterman soft factor is not driving the evolution with the hard scale in nearly back-to-back dihadron and direct photon-hadron production in $p$$+$$p$ collisions. This behavior is in contrast to Drell-Yan and semi-inclusive deep-inelastic scattering measurements.

Unintegrated double parton distributions

We present the construction of unintegrated double parton distribution functions which include dependence on transverse momenta of partons. We extend the formulation which was used to obtain the single unintegrated parton distributions from the standard, integrated parton distribution functions. Starting from the homogeneous part of the evolution equations for the integrated double parton distributions, we construct the unintegrated double parton distributions as the convolutions of the integrated double distributions and the splitting functions, multiplied by the Sudakov form factors. We show that there exist three domains of external hard scales which require three distinct forms of the unintegrated double distributions. The additional transverse momentum dependence which arises through the Sudakov form factors leads to non-trivial correlations in the parton momenta. We also discuss the non-homogeneous contribution to the unintegrated double parton distributions, which arises due to the splitting of a single parton into daughter partons with high transverse momenta. We analyze two cases, the unfolding of the transverse momenta dependence from the last step of the evolution of two partons, and the case where the transverse momenta are generated directly from the single parton splitting.

Single-diffractive production of charmed mesons at the LHC within the kt-factorization approach

We discuss the single-diffractive production of cc pairs and charmed mesons at the LHC. For a first time we propose a kt-factorization approach to the diffractive processes. The transverse momentum dependent diffractive parton distributions are obtained from standard (collinear) diffractive parton distributions used in the literature. In this calculation the transverse momentum of the pomeron is neglected with respect to transverse momentum of partons entering the hard process. We also perform a first evaluation of the cross sections at the LHC using the diffractive transverse momentum dependent parton distributions. The results of the new approach are compared with those of the standard collinear one. Significantly larger cross sections are obtained in the kt-factorization approach in which some parts of higher-order effects is effectively included. The differences between corresponding differential distributions are discussed. Finally, we present a feasibility study of the process at the LHC using proton tagging technique. The analysis suggests that the measurement of single-diffractive charm production is possible using ATLAS and CMS/TOTEM detectors.

Sivers effect and the spin asymmetry in meson production

The transverse polarization of nucleon and the transverse momentum of its unpolarized constituent partons are correlated with each other. This can be fairly described by the Sivers effect. In recent years this effect is cynosure and produces privilege aspects from both theoretical and experimental views. To extend our knowledge from nucleon structure, this effect has an outstanding role. One way to obtain the Sivers function which is essentially depends on transverse momentum of partons, is to employ the Semi inclusive DIS (SIDIS) process. In this article a new parametrization for the concerned piece of Sivers function is used which is different with respect to what has been done in [M. Anselmino et al., Phys. Rev. D 72 (2005) 094007]. The required collinear PDF is getting from HERAPDF parametrization group. The unknown parameters which exist in Sivers function can be extracted, fitting the available experimental data for single spin asymmetry (SSA) in π+π− production. The final analytical results for SSA are in good agreement with the HERMES experimental data.

Polarized $$^{\varvec{3}}$$ 3 He Target and Final State Interactions in SiDIS

Jefferson Lab (JLab) is starting a wide experimental program aimed at studying the neutron's structure, with a great emphasis on the extraction of the parton transverse-momentum distributions (TMDs). To this end, Semi-inclusive deep-inelastic scattering (SiDIS) experiments on polarized $^3$He will be carried out, providing, together with proton and deuteron data, a sound flavor decomposition of the TMDs. Given the expected high statistical accuracy, it is crucial to disentangle nuclear and partonic degrees of freedom to get an accurate theoretical description of both initial and final states. In this contribution, a preliminary study of the Final State Interaction (FSI) in the standard SiDIS, where a pion (or a Kaon) is detected in the final state is presented, in view of constructing a realistic description of the nuclear initial and final states.

Wigner Distributions of Quark

Wigner distribution functions are the quantum analogue of the classical phase space distribution and being quantum implies that they are not genuine phase space distribution and thus lack any probabilistic interpretation. Nevertheless, Wigner distributions are still interesting since they can be related to both generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs) under some limit. We study the Wigner distribution of quarks and also the orbital angular momentum (OAM) of quarks in the dressed quark model.

The 3D structure of QCD and the roots of the Standard Model

For many phenomenological applications involving hadrons in high energy processes the hadronic structure can be taken care of by parton distribution functions (PDFs), in which only the collinear momenta of quarks and gluons are important. In principle the transverse structure, however, provides interesting new phenomenology. Taking into account transverse momenta of partons one works with transverse momentum dependent PDFs (TMDs), These allow all spin-spin correlations and also spin-orbit correlations that have a time reversal odd character and lead to new observables. In many theoretical developments the link to the collinear treatment is used. In this talk I will speculate on a novel view of the 3-dimensional (3D) structure of QCD, which fits in a broader study looking at the roots of the Standard Model of particle physics.

Key Future Measurements of TMDs at Jefferson Lab and Other Facilities

Transverse-momentum dependent parton distribution functions (TMDs) provide a description of nucleon structure in terms of the parton transverse momentum and its transverse spin. At leading twist there are eight TMDs, each offering a unique feature of quarks in a polarized or an unpolarized nucleon. The Sivers distribution is one of the most interesting TMD due to its non-universality. It has been extracted using the data from semi-inclusive deep-inelastic scattering (SIDIS), but there is no data yet from spin-dependent Drell-Yan (DY) process. Such measurement will provide a crucial test of TMD formalism which predicts an equal magnitude and opposite sign for the Sivers function extracted from SIDIS and DY process. We will discuss key future measurements of TMDs using both SIDIS and DY process with a focus on Hall A SoLID SIDIS program at Jefferson Lab.

Predictions for Sivers single spin asymmetries in one- and two-hadron electroproduction at CLAS12 and EIC

The study of the Sivers effect, describing correlations between the transverse polarization of the nucleon and its constituent (unpolarized) parton's transverse momentum, has been the topic of a great deal of experimental, phenomenological and theoretical effort in recent years. Semi-inclusive deep inelastic scattering measurements of the corresponding single spin asymmetries (SSA) at the upcoming CLAS12 experiment at JLab and the proposed Electron-Ion Collider will help to pinpoint the flavor structure and the momentum dependence of the Sivers parton distribution function describing this effect. Here we describe a modified version of the $\tt{PYTHIA}$ Monte Carlo event generator that includes the Sivers effect. Then we use it to estimate the size of these SSAs, in the kinematics of these experiments, for both one and two hadron final states of pions and kaons. For this purpose we utilize the existing Sivers parton distribution function (PDF) parametrization extracted from HERMES and COMPASS experiments. Using this modified version of $\tt{PYTHIA}$, we also show that the the leading order approximation commonly used in such extractions may provide significantly underestimated values of Sivers PDFs, as in our Monte Carlo simulations the omitted parton showers and non-DIS processes play an important role in these SSAs, for example in the COMPASS kinematics.

Transverse-momentum-dependent wave functions with Glauber gluons inB→ππ,ρρdecays

We investigate the Glauber-gluon effect on the $B \to \pi \pi$ and $\rho \rho$ decays, which is introduced via a convolution of a universal Glauber phase factor with transverse-momentum-dependent(TMD) meson wave functions in the $k_T$ factorization theorem. For an appropriate parametrization of the Glauber phase, it is observed that a TMD wave function for the pion ($\rho$ meson) with a weak (strong) falloff in parton transverse momentum $k_T$ leads to significant (moderate) modification of the $B^0 \to \pi^0 \pi^0$ ($B^0 \to \rho^0 \rho^0$) branching ratio: the former (latter) is enhanced (reduced) by about a factor of 2 (15\%). This observation is consistent with the dual role of the pion as a massless Nambu-Goldstone boson and as a $q \bar q$ bound state, which requires a tighter spatial distribution of its leading Fock state relative to higher Fock states. The agreement between the theoretical predictions and the data for all the $B \to \pi \pi$ and $\rho^0 \rho^0$ branching ratios is then improved simultaneously, and it is possible to resolve the $B \to \pi \pi$ puzzle.

Exclusive processes at JLab at 6 GeV

Deeply virtual exclusive reactions provide a unique opportunity to probe the complex internal structure of the nucleon. They allow to access information about the correlations between parton transverse spatial and longitudinal momentum distributions from experimental observables. Dedicated experiments to study Deeply Virtual Compton Scattering (DVCS) and Deeply Virtual Meson Production (DVMP) have been carried out at Jefferson Lab using continuous electron beam with energies up to 6 GeV. Unpolarized cross sections, beam, target and double spin asymmetries have been measured for DVCS as well as for π 0 exclusive electroproduction. The data from Hall B provide a wide kinematic coverage with Q 2 =1-4.5 GeV 2 , xB=0.1-0.5, and −t up to 2 GeV 2 . Hall A data have limited kinematic range partially overlapping with Hall B kinematics but provide a high accuracy measurements. Scaling tests of the DVCS cross sections provide solid evidence of twist-2 dominance, which makes chiral-even GPDs accessible even at modest Q 2 . We will discuss the interpretation of these data in terms of Generalized Parton Distributions (GPDs) model. Successful description of the recent CLAS π 0 exclusive production data within the framework of the GPD-based model provides a unique opportunity to access the chiral-odd GPDs.

Wigner Functions and Quark Orbital Angular Momentum

Wigner distributions contain combined position and momentum space information of the quark distributions and are related to both generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs). We report on a recent model calculation of the Wigner distributions for the quark and their relation to the orbital angular momentum.

Color Entanglement in Hadronic Processes for Transverse Momentum Dependent Parton Distribution Functions

In the description of protons, we go beyond the ordinary collinear parton distribution functions (PDFs), by including transverse momentum dependent PDFs (TMDs). As such, we become sensitive to polarization modes of the partons and protons that one cannot probe without accounting for transverse momenta of partons, in particular when looking at azimuthal asymmetries. Hadronic processes require the inclusion of gluon contributions forming the gauge links, which are path-ordered exponentials tracing the color flow. In processes with two hadrons in the initial state, such as Drell-Yan (DY), the gauge links from different parts of the process get entangled. We show that in color disentangling this gauge link structure, one becomes sensitive to this color flow. After disentanglement, particular combinations of TMDs will require a different numerical color factor than one naively might have expected. Such color factors will even play a role for azimuthal asymmetries in the simplest hadronic processes such as DY.

Phenomenology from SIDIS ande+e−multiplicities: multiplicities and phenomenology - part I

This study is part of a project to investigate the transverse momentum dependence in parton dis- tribution and fragmentation functions, analyzing (semi-)inclusive high-energy processes within a proper QCD framework. We calculate the transverse-momentum-dependent (TMD) multiplicities for e + e − annihilation into two hadrons (considering different combinations of pions and kaons) aiming to investigate the impact of in- trinsic and radiative partonic transverse momentum and their mixing with flavor. Different descriptions of the non-perturbative evolution kernel (see, e.g., Refs. (1-5)) are available on the market and there are 200 sets of flavor configurations for the unpolarized TMD fragmentation functions (FFs) resulting from a Monte Carlo fit of Semi-Inclusive Deep-Inelastic Scattering (SIDIS) data at Hermes (see Ref. (6)). We build our predictions of e + e − multiplicities relying on this rich phenomenology. The comparison of these calculations with future experimental data (from Belle and BaBar collaborations) will shed light on non-perturbative aspects of hadron structure, opening important insights into the physics of spin, flavor and momentum structure of hadrons.

Partonic transverse momenta in soft collisions

The partonic transverse momentum, $$k_t$$ , distribution plays a crucial role in driving high-energy hadron interactions. If $$k_t$$ is limited we have old fashioned Regge theory. If $$k_t$$ increases with energy the interaction may be described by perturbative QCD. We use BFKL diffusion in $$\ln k_t$$ , supplemented by a stronger absorption of low $$k_t$$ partons, to estimate the growth of the mean transverse momenta $$\langle k_t\rangle $$ with energy. This growth reveals itself in the distribution of secondaries produced at the collider energies. We present a simple, BFKL-based, model to demonstrate the possible size of the effect. Moreover, we propose a way to evaluate experimentally the shape of the parton transverse momenta distribution by studying the spectra of the ( $$D$$ or $$B$$ ) mesons which contain one heavy quark.

Sivers effect in dihadron semi-inclusive deep inelastic scattering

The Sivers effect describes the correlation of the unpolarized parton's transverse momentum with the transverse spin of the nucleon. It manifests as a sine modulation of the cross section for single hadron semi-inclusive deep inelastic scattering (SIDIS) on a transversely polarized nucleon with the azimuthal angle between the produced hadron's transverse momentum and the nucleon spin ($\varphi_h$ and $\varphi_S$, respectively). It has been recently suggested that the Sivers effect can also be measured in two hadron SIDIS process as sine modulations involving the azimuthal angles $\varphi_T$ and $\varphi_R$ of both the total and the relative transverse momenta of the hadron pair. Here we present the detailed derivation of the two hadron SIDIS cross section using simple parton-model inspired functional forms for both the parton distribution and the fragmentation functions. We show explicitly that the terms corresponding to the $\sin(\varphi_R-\varphi_S)$ and $\sin(\varphi_T-\varphi_S)$ modulations are non-zero. Further, we derive the cross section expressions for single hadron production in the two hadron sample. Finally, we employ a modified version of the $\tt{LEPTO}$ Monte Carlo event generator that includes the Sivers effect to estimate the size of single spin asymmetries corresponding to these modulations independent of the formalism developed.

EXPERIMENTAL DATA ON TRANSVERSE-MOMENTUM DISTRIBUTIONS FROM SEMI-INCLUSIVE DEEP-INELASTIC SCATTERING

The exploration of the structure of the nucleon reaches a new level of sophistication when explicit dependences on transverse momenta of partons in both parton distributions and fragmentation functions are included. These dependences lead to a manifold of new correlations between the nucleon and quark spin as well as their momenta and thus a wealth of experimental observables. A particular example is the novel Sivers function that—according to firm QCD predictions—has to change sign when going from the Drell-Yan process to semi-inclusive deep-inelastic scattering. Here a review is given on which knowledge has been gathered about transverse-momentum-dependent (TMD) distribution and fragmentation functions from semi-inclusive deep-inelastic scattering experiments.

Measurement of TMD observables at COMPASS

COMPASS is a fixed target experiment at the CERN SPS taking data since 2002. An important part of the physics programme is the study of the spin structure of the nucleon by measuring deep inelastic scattering of high energy muons off polarized or unpolarized nucleons. In particular COMPASS has given and is giving an important contribution to understand the role of parton transverse spin and transverse momentum, a recent topic on which a large international community is working. The most recent COMPASS measurements in this field and their relevance are here reviewed.

Investigations into the flavor dependence of partonic transverse momentum

Recent experimental data on semi-inclusive deep-inelastic scattering from the HERMES collaboration allow us to discuss for the first time the flavor dependence of unpolarized transverse-momentum dependent distribution and fragmentation functions. We find convincing indications that favored fragmentation functions into pions have smaller average transverse momentum than unfavored functions and fragmentation functions into kaons. We find weaker indications of flavor dependence in the distribution functions.