We demonstrate that spontaneous transverse polarization of Lambda baryon ($Λ$) production in $e^+e^-$ annihilation can be described using the transverse momentum dependent polarizing fragmentation functions (TMD PFFs). Using a simple Gaussian model, we perform an extraction of the TMD PFFs by fitting the BELLE collaboration's recent measurement of the $Λ$ transverse polarization in back-to-back $Λ+h$ production in $e^+ e^-$ collisions, $e^{-} + e^{+} \rightarrow Λ^{\uparrow}+h+X$. We find that this simple model accurately describes the experimental data for $Λ$ production associated with pions and kaons, and we are able to determine TMD PFFs for different quark flavors. We use these newly extracted TMD PFFs to make predictions for the transverse polarization of $Λ$ produced in semi-inclusive deep inelastic scattering at a future electron-ion collider, and find that such a polarization is around $10\%$ and should be measurable.
Experimental data from Belle Collaboration for the transverse polarization of $Λ$'s measured in $e^+ e^-$ annihilation processes are used to extract the polarizing fragmentation function (FF) within a TMD approach. We consider both associated and inclusive $Λ$ production, showing a quite consistent scenario. Good separation in flavor is obtained, leading to four independent FFs. Predictions for SIDIS processes at the EIC, crucial for understanding their universality and evolution properties, are also presented.
We present the complete structure of the azimuthal dependences and polarization observables for two-hadron production in $e^+e^-$ annihilation processes within a transverse momentum dependent (TMD) approach adopting the helicity formalism. The leading-twist TMD fragmentation functions (TMD-FFs) for spin-1/2 hadrons are fully accounted for. The role of the polarizing FF, together with its extraction from Belle data for the transverse polarization of $Λ$'s, are discussed as well. Finally, predictions for SIDIS processes at EIC are presented.
Data from the Belle Collaboration for associated production (with a light unpolarized hadron) and single-inclusive production of transversely polarized $Λ$-hyperons in $e^+e^-$ annihilation processes allowed to extract within a TMD approach, for the first time, the $Λ$ polarizing fragmentation function. Recent theoretical developments on the computation of cross sections for single-inclusive hadron production in $e^+e^-$ annihilation processes, within a Soft Collinear Effective Theory approach, combined with the CSS formalism for the double-hadron production case, can be used to perform a rene…
We study QCD evolution equations of the first transverse-momentum-moment of the naive-time-reversal-odd fragmentation functions - the Collins function and the polarizing fragmentation function. We find for the Collins function case that the evolution kernel has a diagonal piece same as that for the transversity fragmentation function, while for the polarizing fragmentation function case this piece is the same as that for the unpolarized fragmentation function. Our results might have important implications in the current global analysis of spin asymmetries.
We perform a re-analysis of Belle data for the transverse $Λ$ and $\barΛ$ polarization in $e^+ e^-$ annihilation processes within a transverse momentum dependent (TMD) factorization approach. We consider two data sets, one referring to the associated production of $Λ$'s with a light unpolarized hadron in an almost back-to-back configuration, and one for the inclusive $Λ$ production, with the reconstruction of the thrust axis. We adopt the Collins-Soper-Sterman framework and employ the recent formulation on the factorization of single-inclusive hadron production. This extends a previous phenome…
The concept of spin-directed momentum provides a useful and restrictive framework for describing dynamical mechanisms that can lead to single-spin observables. The value of this framework can be demonstrated by consideration of the polarizing fracture functions that characterize the production of polarized baryons in the target fragmentation region of semi-inclusive deep inelastic scattering from an unpolarized target. When Bjorken x is chosen large enough to indicate a hard scattering from a valence quark, the fracture function formalism dynamically selects a quark-diquark basis for baryon st…
The longstanding problem of explaining the observed polarization of Lambda hyperons inclusively produced in the high energy collisions of unpolarized hadrons is tackled by considering spin and k_T dependent quark fragmentation functions. The data on Lambda's and Lambda-bar's produced in p-N processes are used to determine simple phenomenological expressions for these new "polarizing fragmentation functions", which describe the experiments remarkably well.
Nuclear modification factors of single hadrons and dihadrons at large transverse momentum ($p_{\rm T}$) in high-energy heavy-ion collisions are studied in a next-to-leading-order (NLO) perturbative QCD parton model. Parton fragmentation functions (FFs) in $A+A$ collisions are modified due to jet energy loss which is proportional to the jet transport coefficient $\hat{q}$ characterizing the interaction between the parton jet and the produced medium. By confronting 6 current sets of NLO parton FFs for large $p_{\rm T}$ hadron productions, we extract $\hat{q}$ quantitatively via a global fit to d…
Simplified approach to extracting nucleon transversity in collinear factorization using near-side energy-energy correlators
University of California, Los Angeles（加州大学洛杉矶分校）；Mani L. Bhaumik Institute for Theoretical Physics, University of California, Los Angeles（加州大学洛杉矶分校马尼·L·巴乌米克理论物理研究所）；Center for Frontiers in Nuclear Science, Stony Brook University（石溪大学核科学前沿中心）；Temple University（天普大学）；Lebanon Valley College（黎巴嫩谷学院）
We investigate the $\sin (ϕ_Λ-ϕ_S)$ single-spin asymmetry in the transversely polarized $Λ$ production in semi-inclusive deeply inelastic scattering process within the framework of the transverse momentum dependent~(TMD) factorization. The asymmetry is contributed by the convolution of the polarizing TMD fragmentation function $D_{1T}^\perp$ of the $Λ$ hyperon and the unpolarized TMD distribution function $f_1$ of the target nucleon. We apply two sets of $D_{1T}^{\perp,Λ^\uparrow/q}$, the spectator diquark model result and available parametrization, to numerically estimate the $\sin (ϕ_Λ-ϕ_S)$…
The fractured Boer-Mulders functions describe an inriguing class of polarization effects for the production of baryons in the target fragmentation region of deep-inelastic processes. These functions characterize transverse momentum asymmetries related to the spin orientation for different flavors of axial vector diquarks in an unpolarized ensemble of protons just as the familiar Boer-Mulders functions characterize transverse momentum asymmetries connected to the spin orientation of quarks in unpolarized targets. The asymmetries of the fractured Boer-Mulders effect originating in the proton dis…
The transverse polarization observed in the inclusive production of Lambda hyperons in the high energy collisions of unpolarized hadrons is tackled by considering a new set of spin and kT dependent quark fragmentation functions. Simple phenomenological expressions for these new ``polarizing fragmentation functions'' are obtained by a fit of the data on Lambda's and Lambdabar's produced in p-N processes.
Current all-orders proofs of factorization of hard processes are made by extracting the leading power behavior of Feynman graphs, i.e., by extracting asymptotics strictly order-by-order in perturbation theory. The resulting parton densities and fragmentation functions include non-perturbative effects. I show how there are missing elements in the proofs; these are related to and exemplified by string and cluster models of hadronization. The proofs rely on large rapidity differences between different parts of graphs for the process; but in reality large rapidity gaps are filled in
The long-standing problem of transverse Lambda polarization in high-energy collisions of unpolarized hadrons can be tackled by considering new, spin and k_T-dependent quark fragmentation functions for an unpolarized quark into a polarized, spin-1/2 hadron. Simple phenomenological parameterizations of these new "polarizing fragmentation functions", which describe quite well the experimental data on Lambda and Lambda-bar hyperons produced in p-A processes, are utilized and extended here to give predictions for transverse Lambda polarization in semi-inclusive DIS
Determination of Fragmentation Functions from Charge Asymmetries in Hadron Production
State Key Laboratory of Dark Matter Physics, Shanghai Key Laboratory for Particle Physics and Cosmology, Key Laboratory for Particle Astrophysics and Cosmology (MOE), School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院，粒子天体物理与宇宙学教育部重点实验室，暗物质物理全国重点实验室，粒子物理与宇宙学上海市重点实验室）
We present an update to the QCD global analysis of single transverse-spin asymmetries presented in Cammarota, et al., PRD 102, 054002 (2020) (JAM3D-20). JAM3D-20 simultaneously included transverse momentum dependent and collinear twist-3 observables, both of which are sensitive to quark-gluon-quark correlations in hadrons. In this study we extract for the first time the twist-3 chiral odd fragmentation function $\tilde{H}$ by incorporating the $\sinϕ_s$ modulation data from SIDIS along with its contribution to the single transverse-spin asymmetry in pion production from proton-proton collision…
We investigate the transverse polarization of the $Λ$ hyperon in the processes $e^+e^-\toΛ^\uparrow π^\pm X$ and $e^+e^-\toΛ^\uparrow K^\pm X$ 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 $e^+e^-\toΛ^\uparrow h X$ process at…
In this paper we study transverse polarization of $Λ$ hyperons in single-inclusive leptonic annihilation. We show that when the transverse momentum of the $Λ$ baryon is measured with respect to the thrust axis, a transverse momentum dependent (TMD) factorization formalism is required and the polarization is generated by the TMD polarizing fragmentation function (TMD PFF), $D_{1T}^\perp$. However, when the transverse momentum of the $Λ$ baryon is measured with respect to the momentum of the initial leptons, a collinear twist-3 formalism is required and the polarization is generated by the intri…
We reconsider the option of extracting the transversity distribution by using interference fragmentation functions into two leading hadrons inside the same current jet. To this end, we perform a new study of two-hadron fragmentation functions. We derive new positivity bounds on them. We expand the hadron pair system in relative partial waves, so that we can naturally incorporate in a unified formalism specific cases already studied in the literature, such as the fragmentation functions arising from the interference between the s- and p-wave production of two mesons, as well as the production o…
We explore the feasibility of directly extracting the large-x valence d/u ratio through a measurement of pions in the current fragmentation region of semi-inclusive deep-inelastic scattering from protons.
In nucleus-nucleus collisions at RHIC and LHC, partons produced at high transverse momentum can undergo multiple scattering within the collision region prior to fragmenting into hadrons. We have studied the resulting medium-modified fragmentation function based on a calculation of the BDMPS-Z medium-induced gluon radiation for a dense, expanding medium of small finite extension. Here we explain how the BDMPS transport coefficient which measures the energy density attained in the collision, can be extracted from the observed modification of high-pt hadroproduction. We also comment on the signif…
We provide a comprehensive overview of transversely polarized $Λ$ production at the future Electron-Ion Collider (EIC). In particular, we study both spontaneous transverse $Λ$ polarization as well as the transverse spin transfer within the Transverse Momentum Dependent (TMD) factorization region. To describe spontaneous $Λ$ polarization, we consider the contribution from the TMD Polarizing Fragmentation Function (TMD PFF). Similarly, we study the contribution of the transverse spin transfer originating from the transversity TMD Fragmentation Function (TMD FF). We provide projections for the st…
I present new results on the quark distribution in an on-shell heavy quark in perturbative QCD and explore its all-order relations with heavy-quark fragmentation. I first compute the momentum distribution function to all orders in the large-beta_0 limit and show that it is identical to the perturbative heavy-quark fragmentation function in the same approximation. I then analyze the Sudakov limit of the distribution and the fragmentation functions using Wilson lines and prove that the corresponding Sudakov exponents in the non-Abelian theory are the same to any logarithmic accuracy. The anomalo…
We study the dihadron fragmentation functions (DiFF) of longitudinally polarized quarks into pion pairs. The quark-jet framework is used to model the sequential hadronization of a polarized quark into hadrons, where the polarization transfer to the remnant quark in each hadron emission step is calculated using the spin density matrix formalism. Using Monte Carlo (MC) simulations of the hadronization process, we find a nonvanishing helicity dependent DiFF, $G_1^\perp$ , which is also related to the longitudinal jet handedness. A method is developed for extracting the angular moments of this DiF…
We study the production of transversely polarized Lambda hyperons in high-energy collisions of protons with large nuclei. The large gluon density of the target at saturation provides an intrinsic semi-hard scale which should naturally allow for a weak-coupling QCD description of the process in terms of a convolution of the quark distribution of the proton with the elementary quark-nucleus scattering cross section (resummed to all twists) and a fragmentation function. In this case of transversely polarized Lambda production we employ a so-called polarizing fragmentation function, which is an od…
We investigate the properties of interference fragmentation functions arising from the emission of two leading hadrons inside the same jet for inclusive lepton-nucleon deep-inelastic scattering. Using an extended spectator model for the mechanism of the hadronization, we give a complete calculation and numerical estimates for the examples of a proton-pion pair produced with invariant mass on the Roper resonance, and of two pions produced with invariant mass close to the $ρ$ mass. We discuss azimuthal angular dependence of the leading order cross section to point up favourable conditions for ex…
The fragmentation of a light parton i to a jet containing a light energetic hadron h, where the momentum fraction of this hadron as well as the invariant mass of the jet is measured, is described by "fragmenting jet functions". We calculate the one-loop matching coefficients J_{ij} that relate the fragmenting jet functions G_i^h to the standard, unpolarized fragmentation functions D_j^h for quark and gluon jets. We perform this calculation using various IR regulators and show explicitly how the IR divergences cancel in the matching. We derive the relationship between the coefficients J_{ij} an…
Following a previous description of Lambda and Lambda-bar polarization in unpolarized p-p interactions, within a perturbative QCD factorization scheme with new polarizing fragmentation functions, here we investigate the transverse polarization of Lambda's and Lambda-bar's produced in semi-inclusive DIS. Analytical expressions for both neutral and charged current exchange are given. Since quantitative predictions cannot be given at this stage and comparison with existing data are not yet significant, we present the general formalism and a qualitative analysis displaying generic features of the …
Mapping jet substructure in heavy-ion collisions with track functions
CERN（欧洲核子研究中心）；Brookhaven National Laboratory（布鲁海文国家实验室）；Universidad de Oviedo（奥维耶多大学）；Instituto Universitario de Ciencias y Tecnologías Espaciales de Asturias (ICTEA)（阿斯图里亚斯宇宙科学与技术大学研究所）
The most recent data on the weighted transverse single spin asymmetry $A_{UT}^{\sin(ϕ_h-ϕ_S)}$ from HERMES and COMPASS collaborations are analysed within LO parton model with unintegrated parton distribution and fragmentation functions; all transverse motions are taken into account, with exact kinematics, in the elementary interactions. The overall quality of the data is such that, for the first time, a rather well constrained extraction of the Sivers function for $u$ and $d$ quarks is possible and is performed. Comparisons with models are made. Based on the extracted Sivers functions, predict…
We extend the analysis of two-hadron fragmentation functions to the subleading twist, discussing also the issue of color gauge invariance. Our results can be used anywhere two unpolarized hadrons are semi-inclusively produced in the same fragmentation region, also at moderate values of the hard scale Q. Here, we consider the example of polarized deep-inelastic production of two hadrons and we give a complete list of cross sections and spin asymmetries up to subleading twist. Among the results, we highlight the possibility of extracting the transversity distribution with longitudinally polarize…
I present some results about transverse momentum dependent distribution and fragmentation functions. Firstly I illustrate a simple model, with predictive power about the energy behavior, for T-odd, chiral odd functions. Moreover I propose a slight modification in extracting transversity from HERMES data, so as to apply correctly factorization. Lastly I suggest a method for determining the quark transverse polarization in an unpolarized or spinless hadron.
We propose a new formula for extracting the polarized gluon distribution from the large-$p_T$ light hadron pair production for semi-inclusive processes in polarized deep inelastic scattering. In general, a large-$p_T$ hadron pair is produced via photon-gluon fusion(PGF) and QCD Compton at the lowest order of QCD. The PGF gives us a direct information on $Δg$ in the nucleon, while QCD Compton becomes background to the signal process for extracting $Δg$. We show that the contribution from this background, i.e. the QCD Compton process, can be removed by using symmetry relation among fragmentation…
We present the complete twist-4 results for the semi-inclusive annihilation process $e^+ +e^- \to h+ \bar q+X$ at the tree level of perturbative quantum chromodynamics. The calculations are carried out by using the formalism obtained by applying the collinear expansion to this process where the multiple gluon scattering is taken into account and gauge links are obtained systematically and automatically. We present the results for structure functions in terms of gauge invariant fragmentation functions up to twist-4 and the corresponding results for the azimuthal asymmetries and polarizations of…
We calculate the transverse polarizations of the produced hyperons in the semi-inclusive deep inelastic scattering of unpolarized lepton beam on transversely polarized nucleon, since these polarizations provide a potential method for extracting the transversity distribution h1(x) of the nucleon. In this calculation we use the SU(6) wavefunctions of the octet baryons and the spectator model for the distribution functions of nucleons and the fragmentation functions of hyperons. We find that that H1(z) of the Sigma hyperons are much larger than that of the Lambda hyperon. Therefore, when one trie…
We discuss the possibility of extracting ${\mid}V_{cb}{\mid}$ from the future measurement at LHC of the $B_c\ {\rightarrow}\ J/ψ μ^+\ ν$ decay rate followed by the leptonic decay $J/ψ {\rightarrow}\ μ^+μ^-$. We examine in detail the influence of the measurement of the muons' momenta and vertex reconstruction in the final uncertainty of ${\mid}V_{cb}{\mid}$, as well as the required theoretical inputs at both the production and weak decay level, and their reliability in this regard. We stress the relevance of a rigorous description of the fragmentation contributions to inclusive production at la…
