Nonperturbative Sudakov Research Articles

The Non-perturbative Sudakov Form Factor and the Role of Soft Gluons

The Non-perturbative Sudakov Form Factor and the Role of Soft Gluons

The Sivers asymmetry in charged Kaon and Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} hyperon produced SIDIS process at electron ion colliders

We investigate the single transverse-spin asymmetry with a sin(ϕh-ϕS)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sin (\\phi _h-\\phi _S)$$\\end{document} modulation in the charged Kaon produced and in Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} hyperon produced SIDIS process within the theoretical framework of transverse momentum dependent (TMD) factorization at the next-to-leading-logarithmic order. The asymmetry is contributed by the convolution of Sivers function and the unpolarized fragmentation function D1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_1$$\\end{document} for the produced hadron. The parametrization for the proton Qiu–Sterman function, which is closely related to the Sivers function, is adopted to numerically estimate the Sivers asymmetry at the kinematical region of Electron Ion Collider (EIC) and Electron Ion Collider in China (EicC). The TMD evolution of the TMD parton distribution functions are considered by employing the non-perturbative Sudakov form factor. It is found that the predicted Sivers asymmetries AUTsin(ϕh-ϕS)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A_{UT}^{\\sin (\\phi _h-\\phi _S)}$$\\end{document} as functions of x, z and PhT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{hT}$$\\end{document} are sizable at the kinematical configurations of both EIC and EicC. The strange constituent of the produced charged Kaon and Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} hyperon in the final state can be a promising probe of the sea quark Sivers function as well as the flavor dependence in the proton target. Therefore, it is important to utilize the future EIC facilities to constrain the sea quark distribution functions as well as the validity of the generalized universality of the Sivers function.

The Collins Asymmetry in Λ Hyperon Produced SIDIS Process at Electron–Ion Colliders

We investigate Collins asymmetry in the Λ hyperon produced semi-inclusive deep inelastic scattering (SIDIS) process based on the kinematical region of Electron-ion collider in China (EicC) and Electron–ion collider (EIC) within the transverse momentum dependence (TMD) factorization framework at next-to-leading-logarithmic order. The asymmetry is contributed by the convolution of the target proton transversity distribution function and the Collins function of the final-state Λ hyperon. The TMD evolution effect of the corresponding parton distribution functions (PDFs) and fragmentation functions (FFs) is considered with the help of parametrization of the non-perturbative Sudakov form factors for the proton PDFs and Λ fragmentation functions. We apply the parametrization of the collinear proton transversity distribution function and the model results of Λ Collins function from the diquark spectator model as the inputs of the TMD evolution to numerically calculate Collins asymmetry in Λ produced SIDIS process at the kinematical configurations of EIC and EicC. It can be shown that the asymmetry is significant and can be measured at EIC and EicC. The flavor dependence of transversity distribution functions could be further constrained by studying the Λ hyperon produced SIDIS process in the future to improve our understanding of the spin structure within nucleons.

The sin 2phi _h azimuthal asymmetry of pion production in SIDIS within TMD factorization

We study the sin 2phi _h azimuthal asymmetry of charged and neutral pion productions off the longitudinally polarized nucleon targets in semi-inclusive deeply inelastic scattering (SIDIS) process within the transverse momentum dependent (TMD) factorization. The asymmetry is contributed by the convolution of the TMD distribution h_{1L}^{perp } and the Collins fragmentation function H_{1}^perp . We adopt the Wandzura–Wilczek-type (WW-type) approximation for h_{1L}^{perp } and two different parametrizations on the nonperturbative Sudakov form factor for h_{1L}^{perp } and H_{1}^perp . We estimate the sin 2phi _h asymmetry at HERMES and CLAS and compare them with the corresponding experimental data. We also provide the prediction at kinematical configuration of CLAS12. It is shown that our theoretical calculation can describe the HERMES and CLAS data, except the asymmetry of the pi ^- production off proton target at HERMES and CLAS. We also find that different choices of the nonperturbative part of TMD evolution lead qualitatively similar results.

Single-spin asymmetry ATsin(2ϕ−ϕS) in π−p Drell-Yan process within TMD factorization

We study the single-spin asymmetry ATsin(2ϕ−ϕS) in the pion-induced Drell-Yan process within the transverse momentum dependent factorization (TMD factorization). The asymmetry can be expressed as the convolution of the Boer-Mulders function and the transversity function. We numerically estimate the asymmetry ATsin(2ϕ−ϕS) at the COMPASS kinematics with the model results for the pion meson distributions from the light-cone wave function approach and the available parametrization for the proton distributions. We also include the TMD evolution formalism both proton and pion parton distribution functions by using two different parametrizations on nonperturbative Sudakov form factor. We find that the asymmetry ATsin(2ϕ−ϕS) as functions of xp, xπ, xF and q⊥ is qualitatively consistent with the recent COMPASS measurement.

Sin(ϕΛ−ϕS) azimuthal asymmetry in transversely polarized Λ production in SIDIS within TMD factorization at the EIC

We investigate the $\mathrm{sin}({\ensuremath{\phi}}_{\mathrm{\ensuremath{\Lambda}}}\ensuremath{-}{\ensuremath{\phi}}_{S})$ single-spin asymmetry in the transversely polarized $\mathrm{\ensuremath{\Lambda}}$ production in semi-inclusive deeply inelastic scattering process within the transverse momentum dependent (TMD) factorization. The asymmetry is contributed by the convolution of the polarizing TMD fragmentation function ${D}_{1T}^{\ensuremath{\perp}}$ of the $\mathrm{\ensuremath{\Lambda}}$ hyperon and the unpolarized TMD distribution function ${f}_{1}$ of the proton target. We adopt the spectator diquark model result and the available parametrization for ${D}_{1T}^{\ensuremath{\perp},{\mathrm{\ensuremath{\Lambda}}}^{\ensuremath{\uparrow}}/q}$ to numerically estimate the $\mathrm{sin}({\ensuremath{\phi}}_{\mathrm{\ensuremath{\Lambda}}}\ensuremath{-}{\ensuremath{\phi}}_{S})$ asymmetry at the kinematical region of the electron ion collider (EIC). To implement the TMD evolution formalism, we apply two different parametrizations on the nonperturbative Sudakov form factors associated with the distribution function of the proton and the fragmentation function of the $\mathrm{\ensuremath{\Lambda}}$. It is found that the two sets of ${D}_{1T}^{\ensuremath{\perp},{\mathrm{\ensuremath{\Lambda}}}^{\ensuremath{\uparrow}}/q}$ lead to different $\mathrm{sin}({\ensuremath{\phi}}_{\mathrm{\ensuremath{\Lambda}}}\ensuremath{-}{\ensuremath{\phi}}_{S})$ asymmetry, particularly in sign. We also discuss the impact of the assumptions and approximations applied in the calculations, which may bring large uncertainties to the results in the EIC. Future measurements on the $\mathrm{sin}({\ensuremath{\phi}}_{\mathrm{\ensuremath{\Lambda}}}\ensuremath{-}{\ensuremath{\phi}}_{S})$ asymmetry with high precision at the EIC can provide important cross checks on the available $\mathrm{\ensuremath{\Lambda}}$ polarizing fragmentation functions, as well as constrain them more stringently.

Exploring the non-perturbative Sudakov factor via Z0-boson production in pp collisions

Z0-boson production at low transverse momentum offers a unique opportunity to explore the non-perturbative Sudakov factor. In this paper, we employ three parameterizations of the non-perturbative Sudakov factor to calculate the ϕ⁎-distribution and compare our results with the ultra-precise experimental data. We extract the free parameters in each parameterization with a χ2 analysis. The parton-momentum-fraction dependence of these free parameters is also studied by comparing the values extracted at different collision energies and different rapidity ranges.

The transverse polarization of Lambda hyperons in e^+e^-rightarrow Lambda ^uparrow h X processes within TMD factorization

We investigate the transverse polarization of the Lambda hyperon in the processes e^+e^-rightarrow Lambda ^uparrow pi ^pm X and e^+e^-rightarrow Lambda ^uparrow K^pm X within the framework of the transverse momentum dependent (TMD) factorization. The transverse polarization is contributed by the convolution of the transversely polarizing fragmentation function (PFF) D_{1T}^perp of the lambda hyperon and the unpolarized fragmentation function D_1 of pion/kaon. We adopt the spectator diquark model result for D_{1T}^{perp } to numerically estimate the transverse polarization in e^+e^-rightarrow Lambda ^uparrow h X process at the kinematical region of Belle Collaboration. To implement the TMD evolution formalism of the fragmentation functions, we apply two different parametrizations on the nonperturbative Sudakov form factors associated with the fragmentation functions of the Lambda , pion and kaon. It is found that our prediction on the polarization in the Lambda pi ^+ production and {bar{Lambda }} pi ^- is consistent with the recent Belle measurement in size and sign, while the model predictions on the polarizations in Lambda pi ^- and Lambda K^pm productions show strong disagreement with the Belle data. The reason for the discrepancies is discussed and possible approaches to improve the calculation in the future are also discussed.

The Collins asymmetry in electroproduction of Kaon at the electron ion colliders within TMD factorization

We apply the transverse momentum dependent factorization formalism to investigate the transverse single spin dependent Collins asymmetry with a sin (phi _h+phi _s) modulation in the semi-inclusive production of Kaon meson in deep inelastic scattering process. The asymmetry is contributed by the convolutions of the transversity distribution function h_1(x) of the target proton and the Collins function of the Kaon in the final state. We adopt the available parametrization of h_1(x) as well as the recent extracted result for the Kaon Collins function. To perform the transverse momentum dependent evolution, the parametrization of the nonperturbative Sudakov form factor of the proton and final state Kaon are utilized. We numerically predict the Collins asymmetry for charged Kaon production at the electron ion colliders within the accuracy of next-to-leading-logarithmic order. It is found that the asymmetry is sizable and could be measured. We emphasize the importance of planned electron ion colliders in the aspect of constraining sea quark distribution functions as well as accessing the information of the nucleon spin structure and the hadronization mechanism.

Non-perturbative contributions to vector-boson transverse momentum spectra in hadronic collisions

Experimental measurements of Drell-Yan (DY) vector-boson production are available from the Large Hadron Collider (LHC) and from lower-energy collider and fixed-target experiments. In the region of low vector-boson transverse momenta qT, which is important for the extraction of the W-boson mass at the LHC, QCD contributions from non-perturbative Sudakov form factors and intrinsic transverse momentum distributions become relevant. We study the potential for determining such contributions from fits to LHC and lower-energy experimental data, using the framework of low-qT factorization for DY differential cross sections in terms of transverse momentum dependent (TMD) distribution functions. We investigate correlations between different sources of TMD non-perturbative effects, and correlations with collinear parton distributions. We stress the relevance of accurate DY measurements at low masses and with fine binning in transverse momentum for improved determinations of long-distance contributions to Sudakov evolution processes and TMDs.

Sin(2ϕ−ϕS) azimuthal asymmetry in the pion induced Drell-Yan process within TMD factorization

We investigate the single transverse-spin asymmetry with a $\sin (2\phi-\phi_S)$ modulation in the pion-induced Drell-Yan process within the theoretical framework of the transverse momentum dependent factorization. The asymmetry is contributed by the convolution of the Boer-Mulders function and the transversity. We adopt the model results for the distributions of the pion meson from the light-cone wavefunction approach and the available parametrization for the distributions of the proton to numerically estimate the $\sin (2\phi-\phi_S)$ asymmetry in $\pi^- p$ Drell-Yan at the kinematics of the COMPASS at CERN. To implement the TMD evolution formalism of parton distribution functions, we apply the recently extracted nonperturbative Sudakov form factor associated with the distribution functions of the proton and the pion. It is found that our prediction on the single transverse-spin dependent asymmetry ${\sin (2\phi-\phi_S)}$ as functions of $x_p$, $x_\pi$, $x_F$ and $q_\perp$ is qualitatively consistent with the recent COMPASS measurement in both sign and magnitude.

Boer-Mulders effect in the unpolarized pion induced Drell\u2013Yan process at COMPASS within TMD factorization

We investigate the theoretical framework of the cos 2phi azimuthal asymmetry contributed by the coupling of two Boer-Mulders functions in the dilepton production unpolarized pi p Drell–Yan process by applying the transverse momentum dependent factorization at leading order. We adopt the model calculation results of the unpolarized distribution function f_1 and Boer-Mulders function h_1^perp of pion meson from the light-cone wave functions. We take into account the transverse momentum dependent evolution effects for both the distribution functions of pion and proton by adopting the existed extraction of the nonperturbative Sudakov form factor for the pion and proton distribution functions. An approximate kernel is included to deal with the energy dependence of the Boer-Mulders function related twist-3 correlation function T_{q,F}^{(sigma )}(x,x) needed in the calculation. We numerically estimate the Boer-Mulders asymmetry nu _{BM} as the functions of x_p, x_pi , x_F and q_T considering the kinematics at COMPASS Collaboration.

Sivers asymmetry in the pion induced Drell-Yan process at COMPASS within transverse momentum dependent factorization

We investigate the Sivers asymmetry in the pion-induced single polarized Drell-Yan process in the theoretical framework of the transverse momentum dependent factorization up to next-to-leading logarithmic order of QCD. Within the TMD evolution formalism of parton distribution functions, the recently extracted nonperturbative Sudakov form factor for the pion distribution functions as well as the one for the Sivers function of the proton are applied to numerically estimate the Sivers asymmetry in the $\pi^- p$ Drell-Yan at the kinematics of the COMPASS at CERN. In the low $b$ region, the Sivers function in $b$-space can be expressed as the convolution of the perturbatively calculable hard coefficients and the corresponding collinear correlation function, of which the Qiu-Sterman function is the most relevant one. The effect of the energy-scale dependence of the Qiu-Sterman function to the asymmetry is also studied. We find that our prediction on the Sivers asymmetries as functions of $x_p$, $x_\pi$, $x_F$ and $q_\perp$ is consistent with the recent COMPASS measurement.

Transverse momentum spectrum of dilepton pair in the unpolarized \u03c0\u2212N Drell-Yan process within TMD factorization

We study the transverse momentum spectrum of dilepton produced in the unpolarized π−N Drell-Yan process, using transverse momentum dependent factorization up to next-to-logarithmic order of QCD. We extract the nonperturbative Sudakov form factor for the pion in the evolution formalism of the unpolarized TMD distribution function, by fitting the experimental data collected by the E615 Collaboration at Fermilab. With the extracted Sudakov factor, we calculate the normalized differential cross section with respect to transverse momentum of the dimuon and compare it with the recent measurement by the COMPASS Collaboration.

Heavy quarkonium production at lowP⊥in nonrelativistic QCD with soft gluon resummation

We extend the non-relativistic QCD (NRQCD) prediction for the production of heavy quarkonium with low transverse momentum in hadronic collisions by taking into account effects from all order soft gluon resummation. Following the Collins-Soper-Sterman formalism, we resum the most singular terms in the partonic subprocesses. The theoretical predictions of $J/\psi$ and $\Upsilon$ productions are compared to the experimental data from the fixed target experiments (E866) and the collider experiments (RHIC, Tevatron, LHC). The associated non-perturbative Sudakov form factor for the gluon distributions is found to be different from the previous assumption of rescaling the quark form factor by the ratio of color factors. This conclusion should be further checked by future experiments on Higgs boson and/or di-photon production in $pp$ collisions. We also comment on the implication of our results on determining the color-octet matrix elements associated with the $J/\psi$ and $\Upsilon$ productions in the NRQCD factorization formalism.

Evidence for infrared-finite coupling in Sudakov resummation

New arguments are presented in favor of the infrared finite coupling approach to power corrections in the context of Sudakov resummation. The more regular infrared behavior of some peculiar combinations of Sudakov anomalous dimensions, free of Landau singularities at large Nf, is pointed out. A general conflict between the infrared finite coupling and infrared renormalon approaches to power corrections is explained, and a possible resolution is proposed, which makes use of the arbitrariness of the choice of constant terms in the Sudakov exponent. A simple ansatz for a `universal' non-perturbative Sudakov effective coupling at large Nf emerges naturally from these considerations. An alternative evidence for an infrared finite {\em perturbative} effective coupling in the Drell-Yan process at large Nf (albeit at odds with the infrared renormalon argument) is found within the framework of Sudakov resummation for eikonal cross sections of Laenen, Sterman and Vogelsang.

Sudakov suppression in azimuthal spin asymmetries

It is shown that transverse momentum dependent azimuthal spin asymmetries suffer from suppression due to Sudakov factors, in the region where the transverse momentum is much smaller than the large energy scale Q2. The size and Q2 dependence of this suppression are studied numerically for two such asymmetries, both arising due to the Collins effect. General features are discussed of how the fall-off with Q2 is affected by the nonperturbative Sudakov factor and by the transverse momentum weights and angular dependences that appear in different asymmetries. For a subset of asymmetries the asymptotic Q2 behavior is calculated analytically, providing an upper bound for the decrease with energy of other asymmetries. The effect of Sudakov factors on the transverse momentum distributions is found to be very significant already at present-day collider energies. Therefore, it is essential to take into account Sudakov factors in transverse momentum dependent azimuthal spin asymmetries.