It is known the single transverse spin asymmetry in semi-inclusive deep inelastic scattering can be factorized by a twist-3 distribution function $T_F$, which contains a gluon field strength tensor. With transverse gluon included in the power expansion, we find the gluon field strength tensor can be recovered definitely in soft-gluon-pole contribution at leading order of $α_s$ expansion. This conclusion holds in Feynman and light-cone gauges.
The twist-3 gluon contribution to $A_N$ in $J/ψ$ production in $pp$ collisions
Institute of Nuclear Physics Polish Academy of Sciences（波兰科学院核物理研究所）；State Key Laboratory of Nuclear Physics and Technology, Institute of Quantum Matter, South China Normal University（华南师范大学量子物质研究院核物理与技术国家重点实验室）；Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, Guangdong Provincial Key Laboratory of Nuclear Science（广东省核科学广东省基础研究中心与前沿相互作用卓越中心、广东省核科学重点实验室）
We investigate the emergence of single spin asymmetries (SSA) in hard processes using transverse momentum dependent (TMD) distribution and fragmentation functions. Specifically, the description of SSA involves time reversal-odd functions. Process-dependence (non-universality) in measurements of SSA can be attributed to the non-trivial gauge link structure in the TMD correlator. Finding the appropriate gauge links, however, also enables us to characterize the non-universality
We investigate the relative size of various twist-3 quark-gluon correlation functions relevant to single transverse spin asymmetries (SSAs) in a quark-diquark model of the nucleon. We calculate the quark-gluon correlation function $T_{q,F}(x, x)$ that is responsible for the gluonic pole contribution to the SSAs, as well as $T_{q,F}(0, x)$ and $T_{Δ{q}, F}(0, x)$ responsible for the fermionic pole contributions. We find in both cases of a scalar diquark and an axial-vector diquark that at the first nontrivial order only the $\tq(x, x)$ is finite while all other quark-gluon correlation functions…
Recently, it has been shown, contrary to previous beliefs, that the k_T distribution of quarks in a transversely polarized proton can be asymmetric. This ``Sivers effect'' had already been used to explain transverse single spin asymmetries (SSA) observed in inclusive pion production, p(transv. polarized) p --> pion + X and p-bar(transv. polarized) p --> pion + X. In such channels, however, other mechanisms, like the ``Collins effect'' (a k_T asymmetric fragmentation of a transversely polarized quark into pions), may generate SSA. The Sivers asymmetry is used here to compute SSA in Drell-Yan pr…
Generalized parton distributions involving transverse polarization are transversely deformed. The deformation of chirally odd GPDs is related to a transversity decomposition of the quark angular momentum. Potential consequences for T-odd single-spin asymmetries (Sivers and Boer-Mulders effects) are discussed.
We discuss the possibility of using electroproduction of $J/ψ$ as a probe of gluon Sivers function by measuring single spin asymmetry (SSA) in experiments with transversely polarized protons and electron beams. We estimate SSA for JLab, HERMES, COMPASS and eRHIC energies using the color evaporation model of charmonium production and find asymmetry up to 25% for certain choices of model parameters which have been used earlier for estimating SSA in the SIDIS and Drell-Yan processes.
Within the collinear twist-3 framework, we study the single-spin asymmetry (SSA) in collisions between unpolarized protons and transversely polarized protons with focus on the fragmentation term. The fragmentation mechanism must be analyzed in detail in order to unambiguously determine the impact of various contributions to SSAs in hadron production. Such a distinction may also settle the "sign mismatch" between the transverse SSA in proton-proton collisions and the Sivers effect in semi-inclusive deep inelastic scattering. We calculate terms involving quark-quark and quark-gluon-quark correla…
Sivers asymmetry, adopted to explain transverse single spin asymmetries (SSA) observed in inclusive pion production, p(transv. polarized) p --> pion + X and p-bar(transv. polarized) p --> pion + X is used here to compute SSA in Drell-Yan processes; in this case, by considering the differential cross section in the lepton-pair invariant mass, rapidity and transverse momentum, other mechanisms which may originate SSA cannot contribute. Estimates for RHIC experiments are given.
We discuss the single transverse-spin asymmetry (SSA) to be observed in the $D$-meson production with large transverse-momentum in semi-inclusive DIS (SIDIS), $e p^\uparrow \rightarrow e D X$. This contribution is embodied as a twist-3 mechanism in the collinear factorization, which is induced by purely gluonic correlation inside the transversely-polarized nucleon, in particular, by the three-gluon correlation effects. We derive the first complete formula for the corresponding SSA in the leading-order QCD, revealing the five independent structures with respect to the dependence on the azimutha…
The role of intrinsic transverse momentum both in unpolarized and polarized processes is discussed. We consider inclusive cross sections for pion production in hadronic collisions and for Drell-Yan processes. We reanalyze transverse single spin asymmetries (SSA) in inclusive pion production, p(transv. polarized) p --> pion + X, in terms of Sivers effect and show its contribution to A_{UL} in semi-inclusive DIS (SIDIS).
The prediction of single spin asymmetry (SSA) in double $\rm J/ψ$ production in proton-proton collision is given out within the framework of non-relativistic QCD, using the recently obtained best fit parameters for the gluon Sivers function extracted from PHENIX data in $\rm p+p^\uparrow\toπ^0+X$. The color singlet state $\rm ^3 S_1^{(1)}$ and color octet state $\rm ^3 S_1^{(8)}$ are considered to the SSA contribution in the double $\rm J/ψ$ hadroproduction. Our result shows that a sizable asymmetry can be estimated as functions of different kinematic variables.
We discuss the role of gluon poles and the gauge invariance for the hadron tensors of Drell-Yan and direct photon production processes with the transversely polarized hadron. These hadron tensors are needed to construct the corresponding single spin asymmetries. For the Drell-Yan process, we perform our analysis within both the Feynman and axial-type (contour) gauges for gluons. In both the Feynman and contour gauges, we demonstrate that the gauge invariance leads to the need of the new (non-standard) diagrams. Moreover, in the Feynman gauge, we argue the absence of gluon poles in the correlat…
We disscuss a new nonperturbative mechanism for spin effects in high energy reactions with hadrons. This mechanism is based on the existence of a large anomalous quark chromomagnetic moment (AQCM) induced by the nontrivial topological structure of QCD vacuum. As an example, we estimate the contribution of this interaction to the single spin asymmetry (SSA) in the inclusive pion production in the proton-proton scattering. We show that SSA induced by AQCM is large and its value is in qualitative agreement with experimental data.
We study the single spin asymmetry (SSA) for the pion production with large transverse momentum p_T in semi-inclusive deep inelastic scattering $ep^\uparrow\to eπX$. We derive the twist-3 cross section formula for SSA, focussing on the soft-gluon-pole contributions associated with the twist-3 distribution for the nucleon and with the twist-3 fragmentation function for the pion. We present a simple estimate of the asymmetries due to each twist-3 effect from nucleon and pion, respectively, by fixing the overall strength of the relevant nonperturbative quantities by the data on the SSA A_N in $p^…
Transverse single-spin asymmetries (SSA) in inclusive reactions are now considered to be directly related to the transverse momentum $k_{T}$ of the fundamental partons involved in the process. Several possible leading-twist QCD mechanisms have been proposed to explain the available data, in particular the Sivers effect which was resurrected recently. We show that from the measurement of transverse SSA in inclusive production of gauge bosons, one can learn more about the Sivers functions and possibly to achieve a reliable flavor separation.
We analyze the single transverse-spin asymmetry (SSAs) for inclusive hadron production in the $pp$ collision at RHIC based on the twist-3 mechanism in QCD. As an origin of SSAs, we take into account of all kinds of pole contributions associated with the twist-3 quark-gluon correlation functions in the polarized proton. By the inclusion of the soft-fermion-pole contribution in addition to the soft-gluon-pole contribution, we find SSAs observed at RHIC are better described for all kinds of mesons. $P_T$-dependence of the asymmetry and the comparison with the FNAL data are also presented.
We calculate the contribution of the non-perturbative Pauli couplings in the quark-photon and quark-gluon vertices to the single-spin asymmetries (SSAs) in semi-inclusive deep inelastic scattering (SIDIS). We describe the nucleon using the spectator model with scalar and axial-vector diquarks. Both of the new couplings can cause the helicity flip of the struck quark. The helicity flip and the rescattering induced by the non-perturbative gluon exchange between the struck quark and diquark lead to the SSAs. Their azimuthal dependencies are the same as that usually ascribed to the Collins and Siv…
We study the single spin asymmetry (SSA) induced by purely gluonic correlation inside a nucleon, in particular, by the three-gluon correlation functions in the transversely polarized nucleon, $p^\uparrow$. This contribution is embodied as a twist-3 mechanism in the collinear factorization framework and controls the SSA to be observed in the $D$-meson production with large transverse-momentum in semi-inclusive DIS (SIDIS), $ep^\uparrow \rightarrow eDX$. We define the relevant three-gluon correlation functions in the nucleon, and determine their complete set at the twsit-3 level taking into acco…
We study the scattering of a single parton state with a multi-parton state to derive the complete results of perturbative coefficient functions at leading order, which appear in the collinear factorization for Single transverse-Spin Asymmetry(SSA) in Drell-Yan processes with a transversely polarized hadron in the initial state. We find that the factorization formula of SSA contains hard-pole-, soft-quark-pole- and soft-gluon-pole contributions. It is interesting to note that the leading order perturbative coefficient functions of soft-quark-pole- and soft-gluon-pole contributions are extracted…
In this paper, we propose a new calculation method for the twist-3 gluon Sivers effect within the collinear factorization approach. The method called pole calculation has been used to derive the cross section formula for the single transverse-spin asymmetry(SSA) as a standard method. We point out that we encounter a problem when we try to apply the pole calculation to the SSA in the heavy quarkonium production whose hadronization mechanism is described by non-relativistic QCD(NRQCD) framework. We show that the new calculation method solves this problem and successfully reproduces known results…
Transverse single-spin asymmetries (SSA) in inclusive reactions are now considered to be directly related to the transverse momentum ${\bf k}_{T}$ of the fundamental partons involved in the process. We find that the ideal probe to extract information on the gluon Sivers function is the transverse SSA of prompt photon production $p p^{\uparrow} \to γX$, at large $p_T$. The following related processes, $p p^{\uparrow} \to γ+ jet + X$, $p p^{\uparrow} \to γ^* + X \to μ^+ μ^- + X$ and $\bar{p} p^{\uparrow} \to γ+ X$ are also briefly discussed.
We find a novel mechanism for generating transverse single-spin asymmetry (SSA) in semi-inclusive deep inelastic scattering, distinct from the known ones which involve the Sivers and Collins functions, or their collinear twist-three counterparts. It is demonstrated that a phase needed for SSA can be produced purely within a parton-level cross section starting at two loops. We identify the complete set of two-loop diagrams for SSA, and discuss their gauge invariance and collinear factorization which features the $g_T$ distribution function. In the $k_T$ factorization framework, many more source…
We propose measurement of transverse single spin asymmetry (SSA) in charmonium production as a probe of gluon Sivers function. We estimate SSA in low virtuality electroproduction of $J/ψ$ using color evaporation model of charmonium production and existing models of the gluon Sivers function and find sizable asymmetry at JLab, HERMES, COMPASS and eRHIC energies.
Transverse single-spin asymmetries (SSA) are expected to be small in perturbative QCD because of the chiral nature of the theory. Experiment shows large transverse SSA for particle produced in special kinematics. This contribution reviews the experimental situation and provide an outlook for future measurements.
We study the single spin asymmetry (SSA) for the pion production in semi-inclusive deep inelastic scattering, $ep^\uparrow\to eπX$, in the framework of the collinear factorization. We derive the complete cross section formula associated with the twist-3 quark-gluon correlation functions for the transversely polarized nucleon, including all types of pole (hard-pole, soft-fermion-pole and soft-gluon-pole) contributions which produce the strong interaction phase necessary for SSA. We prove that the partonic hard part from each pole contribution satisfies certain constraints from Ward identities f…
Perturbative QCD relates the single transverse-spin asymmetries (SSAs) for hard processes at large transverse-momentum of produced particle to partonic matrix elements that describe interference between scattering from a coherent quark-gluon pair and from a single quark, generated through twist-3 quark-gluon correlations inside a hadron. When the coherent gluon is soft at the gluonic poles, its coupling to partonic subprocess can be systematically disentangled, so that the relevant interfering amplitude can be derived entirely from the Born diagrams for the scattering from a single quark. We e…
The observed results for the azimuthal single spin asymmetries (SSAs) of the proton, measured in the semi-inclusive deep inelastic scattering (SIDIS), can be explained by the final-state interaction (FSI) from the gluon exchange between the outgoing quark and the target spectator system. SSAs require a phase difference between two amplitudes coupling the target with opposite spins to the same final state. We have used the model of light front wave functions (LFWFs) consisting of a spin-$\frac{1}{2}$ system as a composite of a spin-$\frac{1}{2}$ fermion and a spin-1 vector boson to estimate the…
We extend our analysis of transverse single spin asymmetry (SSA) in electroproduction of $J/ψ$ to include the effect of the scale evolution of the transverse momentum dependent (TMD) parton distribution functions and gluon Sivers function. We estimate SSA for JLab, HERMES, COMPASS, and eRHIC energies using the color evaporation model of charmonium production, using an analytically obtained approximate solution of TMD evolution equations discussed in the literature. We find that there is a reduction in the asymmetry compared with our predictions for the earlier case considered by us, wherein th…
We present our recent analysis on the transverse single-spin asymmetry (SSA) in inclusive pion and direct-photon production in pp collisions for RHIC kinematics. The analysis includes the contributions from twist-3 quark-gluon-quark correlations in the proton and twist-3 fragmentation effects for the pion. Some of the functions appearing in the formula for the SSA, such as the soft-gluon-pole Qiu-Sterman function, the nucleon transversity, and the Collins function were fixed consistently with the SSA data in semi-inclusive DIS and in e+e- annihilation, so that our analysis is free from the sig…
We compute the twist-three fragmentation contribution to the transverse single spin asymmetry (SSA) in light hadron production $p^\uparrow p\to hX$ and $p^\uparrow A\to hX$ including the gluon saturation effect in the unpolarized nucleon/nucleus. Together with the results in our previous paper, this completes the full evaluation of the SSA in this process in the "hybrid" formalism. We argue that the dependence of SSAs on the atomic mass number in the forward region can elucidate the relative importance of the soft gluon pole contribution from the twist-three quark-gluon-quark correlation in th…
We consider the recent RHIC data on the transverse single spin asymmetry (SSA) A_N, measured in p(transv. polarized) p -> pi^0 X processes at mid-rapidity by the PHENIX collaboration. The measurement is consistent with a vanishing SSA. We analyze this experimental information within a hard scattering approach based on a generalized QCD factorization scheme, with unintegrated, transverse momentum dependent (TMD), parton distribution and fragmentation functions. It turns out that, in the kinematical region of the data, only the gluon Sivers effect could give a large contribution to A_N; its vani…
We discuss the single transverse-spin asymmetry (SSA) to be observed in the $D$-meson production with large transverse-momentum in semi-inclusive deep inelastic scattering, $e p^\uparrow \rightarrow e D X$. This contribution is embodied as a twist-3 mechanism in the collinear factorization, which is induced by purely gluonic correlation inside the transversely-polarized nucleon, in particular, by the three-gluon correlation effects. The complete formula for the corresponding SSA in the leading-order QCD is expressed in terms of the four independent gluonic correlation functions and reveals the…
We present a study of transverse single-spin asymmetries (SSAs) in $p^\uparrow p\to J/ψ\,X$ and $p^\uparrow p\to D X$ within the framework of the generalized parton model (GPM), which includes both spin and transverse momentum effects, and show how they can provide useful information on the still almost unknown gluon Sivers function. Moreover, by adopting a modified version of this model, named color gauge invariant (CGI) GPM, we analyze the impact of the initial- and final-state interactions on our predictions. As a consequence, we find that these two processes are sensitive to different gluo…
We discuss some experimental and theoretical results on single spin asymmetries (SSA) in high energy lepton-hadron and hadron-hadron reactions. In particular, recent results on meson SSA obtained by HERMES are considered in detail. We also discuss the SSA results obtained recently by COMPASS, as well as those from BRAHMS, PHENIX and STAR. Special attention is paid to a possible nonperturbative QCD mechanism that might be responsible for the observed meson SSA. This mechanism originates from the spin-flip quark-gluon chromomagnetic interaction induced by the complex topological structure of the…
Using the latest quark Sivers functions extracted from the global analysis of available data on single transverse spin asymmetry (SSA), we calculate the SSA of Drell-Yan inclusive production of lepton pairs of invariant mass $Q$ at both $4<Q<9$ GeV and $Q\sim M_Z$ in $p^\uparrow p$ collisions at RHIC energies. We find that the features of the asymmetry $A_N$ for $Q\sim M_Z$ are significantly different from that when $4<Q<9$ GeV. The $A_N$ near $Z^0$ pole is positive and sizable in the central rapidity region while the $A_N$ at low $Q$ is negative and only sizable in the forward rapidity region…
Our understanding of the transverse spin structure of hadrons might definitely get improved by the information we gather on transverse momentum dependent (TMD) distributions. These new functions could also be crucial for a description of the observed transverse single spin asymmetries (SSA). In a hard scattering model for inclusive hadronic reactions, based on a generalized QCD factorization scheme, many mechanisms - namely the Sivers, Collins, Boer-Mulders effects - might contribute to a SSA. We show how the k_T dependent phases arising from the partonic kinematics together with a suitable ch…
We present a new analysis for the single-transverse spin asymmetry (SSA) for the inclusive pion and kaon productions in the proton-proton collisions measured at RHIC. The framework we use is the collinear factorization in which SSA appears as a twist-3 observable resulting from the multiparton correlations in the hadrons. As a relevant multiparton correlation, we include all the contributions associated with the quark-gluon correlation functions in the transversely polarized proton, i.e., those from the soft-gluon-pole (SGP) and the soft-fermion-pole (SFP). We have found that the SGP contribut…
We show that in the Mclerran-Venugopalan model, an axial asymmetrical valence quark distributions in the transverse plane of a transversely polarized proton can give rise to a spin dependent odderon. Such polarized odderon is responsible for the transverse single spin asymmetries(SSAs) for jet production in the backward region of pp collisions and open charm production in semi-inclusive DIS process.
We show that soft-gluon twist-3 contributions to single-spin asymmetries (SSA) in hard processes may be expressed in the form of effective T-odd Sivers distributions, whose signs and scales are modified by process-dependent colour factors. We thus prove that the Sivers mechanism may also be applied at large transverse momenta. We stress that twist-3 SSA in semi-inclusive deeply inelastic scattering and Drell-Yan processes are suppressed by transverse momentum rather than a virtual-photon momentum transfer and thus naively correspond to twist two at the hadronic level. More rigorously, the tran…
We consider the transverse single-spin asymmetry (SSA) for $J/ψ$ production in $p^\uparrow p \to J/ψ+ X$ within a TMD approach in non-relativistic QCD. Extending a previous study [1], we employ here the color-gauge invariant generalized parton model (CGI-GPM), in which spin and intrinsic transverse momentum effects are taken into account, together with leading-order initial- and final-state interactions (ISIs and FSIs). We find that, even when the heavy-quark pair is produced in a color-octet state, ISIs and FSIs lead to a nonvanishing SSA, allowing, in principle, to test the process dependenc…
We analyze the possibility of measuring the single spin asymmetry (SSA) in open charm production by linearly polarized photons in the planned E160/E161 experiments at SLAC using the inclusive spectra of secondary (decay) leptons. In leading order pQCD, the SSA in the azimuthal distribution of the charged decay lepton is predicted to be about 0.2 for SLAC kinematics. Our calculations show that the SSA in the decay lepton distribution is well defined in pQCD: it is stable both perturbatively and parametrically, and practically insensitive to theoretical uncertainties in the charm semileptonic de…
The transverse momentum dependent gluon density obtained with CCFM evolution is determined from a fit to the latest combined HERA structure function measurements.
We study the transverse single spin asymmetry (SSA), A_N, for the single inclusive process l p (transv. polarized) --> h + X, in a perturbative QCD factorization scheme with inclusion of spin and transverse momentum dependent (TMD) distributions. By adopting the relevant TMDs (Sivers and Collins functions) as extracted from semi-inclusive deep inelastic scattering (SIDIS) and e+e- data, predictions for these SSAs are given. A measurement of A_N for this process could then provide a direct test of the validity of the TMD factorization.
We prove that twist-3 soft-gluon-pole (SGP) cross section for single spin asymmetries (SSA) is determined by a certain ``primordial'' twist-2 cross section up to kinematic and color factors in the leading order perturbative QCD. In particular, for the processes in which the partonic hard scattering occurs among massless partons, the invariance of the ``primordial'' partonic cross section under scale transformation leads to remarkable simplification of the SGP cross section, reproducing compact form that was recently observed for pion production $p^\uparrow p\to πX$ and direct-photon production…
We calculate the q q correlation function associated to transverse target lepton-nucleon inclusive deep-inelastic scattering by direct evaluation of the corresponding matrix element. We use the electromagnetic impact parameter potential for a transversely polarized nucleon to define the q q correlation function for each avor in terms of the field components of that avor. The results are compared with the two existing models for the q q correlator. Using the calculated q q correlation function, we estimated the transverse target SSA in IDIS process.
We combine soft and collinear matrix elements to define transverse momentum dependent parton distributions (TMDs) for gluons, free from rapidity divergences. We establish a factorization theorem at next-to-leading order for the Higgs boson transverse momentum ($q_T$) spectrum, and use it to derive evolution equations for gluon TMDs. The evolution for all gluon TMDs is driven by a universal kernel, i.e. the same for all polarizations. In the region of intermediate $q_T$ we match the unpolarized, helicity and linearly polarized gluon distributions onto PDFs. We calculate the resummed Higgs trans…
We calculate the transverse single-spin asymmetry (SSA) for $J/ψ$ production in proton-proton collisions, within non-relativistic QCD, employing the transverse momentum dependent, generalized parton model, which includes both spin and intrinsic motion effects. In particular, we study the role of the color octet mechanism in accessing the gluon Sivers function. In doing that, we also show, within this approach, how the singularities coming from color octet terms in the low-$P_T$ region can be handled, leading to finite cross sections. Predictions for both unpolarized cross sections and SSAs are…
We derive the analog of the Wandzura-Wilczek relation for the light-cone distributions of polarized gluons in a transversely polarized nucleon. The short distance cross-section is entirely due to the intrinsic transverse momenta of gluon in the nucleon, in complete analogy to the quark case. Numerical estimate for the double spin transverse asymmetries at RHIC are presented.
We study transverse-momentum-dependent (TMD) gluon distributions and factorization theorems for the gluon-initiated semi-inclusive processes at hadron colliders. Gauge-invariant TMD gluon distributions are defined, and their relations to the integrated (Feynman) parton distributions are explored when the transverse momentum is large. Through explicit calculations, soft-collinear factorization is verified at one-loop order for scalar particle production. Summation over large double logarithms is made through solving the Collins-Soper equation. We reproduce the known result in the limit that the…
We consider the production of high transverse momentum gluons in the McLerran-Venugopalan model of nuclear structure functions. We explicitly compute the high momentum component in this model. We compute the nuclear target size $A$ dependence of the distribution of produced gluons.
We investigate the gluon distribution functions and their contributions to the Higgs boson production in pp collisions in the transverse momentum dependent factorization formalism. In addition to the usual azimuthal symmetric transverse momentum dependent gluon distribution, we find that the azimuthal correlated gluon distribution also contributes to the Higgs boson production. This explains recent findings on the additional contribution in the transverse momentum resummation for the Higgs boson production as compared to that for electroweak boson production processes. We further examine the s…
We present a simple gluon production picture which is based on the McLerran-Venugopalan model and gluon BFKL evolution in relativistic heavy ion collision. Results for the multiplicity and transverse energy distribution in both the central and forward rapidity regions for gluon production in early stages of heavy ion collisions at the LHC are given. Finally, we provide a general qualitative discussion of the consequences of the forward rapidity behavior of produced gluons.
The transverse symmetry transformations associated with the normal symmetry transformations in gauge theories are introduced, which at first are used to reproduce the transverse Ward-Takahashi identities in the Abelian theory QED. Then the transverse symmetry transformations associated with the BRST symmetry and chiral transformations in the non-Abelian theory QCD are used to derive the transverse Slavnov-Taylor identities for the vector and axial-vector quark-gluon vertices, respectively. Based on the set of normal and transverse Slavnov-Taylor identities, an expression of the quark-gluon ver…
We study how gluons carrying linear polarization inside an unpolarized hadron contribute to the transverse momentum distribution of Higgs bosons produced in hadronic collisions. They modify the distribution produced by unpolarized gluons in a characteristic way that could be used to determine whether the Higgs boson is a scalar or a pseudoscalar particle.
We study resummation of transverse-momentum-related large logarithms generated from soft-gluon radiations in soft-collinear effective field theory. The anomalous dimensions of the effective quark and gluon currents, an important ingredient for the resummation, are calculated to two-loop order. the result at next-to-leading-log reproduces that obtained using the standard method for deep-inelastic scattering, Drell-Yan process, and Higgs production through gluon-gluon fusion. We comment on the extension of the calculation to next-to-next-to-leading logarithms.
We present estimates of Single Spin Asymmetry(SSA) in the electroproduction of J/ψ taking into account the transverse momentum dependent(TMD) evolution of the Sivers function. We estimate SSA for JLab, HERMES, COMPASS and eRHIC energies using color evaporation model of J/ψ. We have calculated the asymmetry using recent parameters extracted by Echevarria et al. using the CSS approach to TMD evolution. These recent TMD evolution fits are based on the evolution kernel in which the perturbative part is resummed up to NLL accuracy. We have also estimated the asymmetry by using parameters which had …
We utilise the fact that the CCFM equation in the single loop approximation can be diagonalised by the Fourier-Bessel transform. The analytic solution of the CCFM equation for the moments $f_ω(b,Q)$ of the scale dependent gluon distribution is obtained, where $b$ is the transverse coordinate conjugate to the transverse momentum of the gluon. The unintegrated gluon distributions obtained from this solution are analysed. It is shown how the approximate treatment of the exact solution makes it possible to express the unintegrated gluon distributions in terms of the integrated ones. The correspond…
