We calculate the $O(α_s^2)$ massive operator matrix elements for the twist--2 operators, which contribute to the heavy flavor Wilson coefficients in unpolarized deeply inelastic scattering in the region $Q^2 \gg m^2$, up to the $O(ε)$ contributions. These terms contribute through the renormalization of the $O(α_s^3)$ heavy flavor Wilson coefficients of the structure function $F_2(x,Q^2)$. The calculation has been performed using light--cone expansion techniques without using the integration-by-parts method. We represent the individual Feynman diagrams by generalized hypergeometric structures, the $ε$--expansion of which leads to infinite sums depending on the Mellin variable $N$. These sums are finally expressed in terms of nested harmonic sums using the general summation techniques implemented in the {\tt Sigma} package.
Recent data from semi-inclusive deep inelastic scattering collected by the HERMES collaboration allow for the first time to discuss how the transverse-momentum dependence of unpolarized distribution and fragmentation functions is affected by the flavor of the involved partons. A model built with flavor-dependent Gaussian transverse-momentum distributions fits data better than the same flavor-independent model. The current analysis is performed for totally unpolarized scattering of leptons off protons and deuterons, with detected pions in the final state. There are convincing indications of fla…
A survey is given on the new 2- and 3-loop results for the heavy flavor contributions to deep-inelastic scattering in the unpolarized and the polarized case. We also discuss related new mathematical aspects applied in these calculations.
We show that measuring the $\cos 2ϕ$ angular dependence in unpolarized Drell-Yan processes with $π^-$ beams colliding on proton and deuteron targets can determine the ratio of the Boer-Mulders functions for $d$ and $u$ quarks inside the proton $h_1^{\perp,d}/h_1^{\perp,u}$, which is still lack of theoretical constraint. The comparison of the $\cos 2 ϕ$ asymmetries measured in unpolarized $π^- p$ and $π^- D$ Drell-Yan processes, which are accessible at CERN by the COMPASS collaboration, can help to discriminate whether $h_1^\perp$ effects or QCD vacuum effects are preferred by data.
We calculate the $O(α_s^2)$ massive operator matrix elements for the twist--2 operators, which contribute to the heavy flavor Wilson coefficients in unpolarized deeply inelastic scattering in the region $Q^2 \gg m^2$. The calculation has been performed using light--cone expansion techniques. We confirm an earlier result obtained in \cite{Buza:1995ie}. The calculation is carried out without using the integration-by-parts method and in Mellin space using harmonic sums, which lead to a significant compactification of the analytic results derived previously. The results allow to determine the heav…
We perform a new extraction for unpolarized and polarized parton distribution functions considering a flavor decompositions for sea quarks and applying very recent deep inelastic scattering (DIS) and semi inclusive deep inelastic scattering (SIDIS) data in the fixed flavor number scheme (FFNS) framework. In the new symmetry breaking scenario the light quark and antiquark densities are extracted separately and new parametrization forms are determined for them. The heavy flavors contribution, including charm and bottom quarks, are also taken to be account for unpolarized distributions.
We summarize recent attempts to calculate the flavor asymmetry of the nucleon's sea quark distributions in the large-$N_c$ limit, where the nucleon can be described as a soliton of an effective chiral theory. We discuss the leading-twist longitudinally polarized and transversity antiquark distributions, $Δ\bar u (x) - Δ\bar d (x)$ and $δ\bar u (x) - δ\bar d (x)$, as well as the unpolarized one, $\bar u (x) - \bar d (x)$, which appears only in the next-to-leading order of the $1/N_c$-expansion. Results for $\bar u (x) - \bar d (x)$ are in good agreement with the recent Drell-Yan data from the F…
It is now widely recognized that a key to unravel the nonperturbative chiral-dynamics of QCD hidden in the deep-inelastic-scattering observables is the flavor structure of sea-quark distributions in the nucleon. We analyze the flavor structure of the nucleon sea in both of the unpolarized and longitudinally polarized parton distribution functions (PDFs) within a single theoretical framework of the flavor SU(3) chiral quark soliton model (CQSM), which contains only one adjustable parameter $Δm_s$, the effective mass difference between the strange and nonstrange quarks. A particular attention is…
We calculate the gluonic massive operator matrix elements in the unpolarized and polarized cases, $A_{gg,Q}(x,μ^2)$ and $ΔA_{gg,Q}(x,μ^2)$, at three-loop order for a single mass. These quantities contribute to the matching of the gluon distribution in the variable flavor number scheme. The polarized operator matrix element is calculated in the Larin scheme. These operator matrix elements contain finite binomial and inverse binomial sums in Mellin $N$-space and iterated integrals over square root-valued alphabets in momentum fraction $x$-space. We derive the necessary analytic relations for the…
We discuss the dependence on the flavor of the intrinsic transverse momentum in unpolarized transverse-momentum-dependent distribution functions (TMD PDFs) and fragmentation functions (TMD FFs) analyzing data of semi-inclusive deep-inelastic scattering (SIDIS) released by the HERMES collaboration. Adopting a flavor-dependent Gaussian model in the transverse momentum and neglecting QCD evolution, we find interesting evidences concerning the flavor dependence in TMD FFs, whereas the indications are weaker in TMD PDFs and deserve further investigations. Inclusions of new data sets of SIDIS, elect…
A phenomenological ansatz for the flavor-asymmetry of the light sea distributions of the nucleon, based on the Pauli exclusion principle, is proposed. This ansatz is compatible with the measured flavor-asymmetry of the unpolarized sea distributions, $\bar{d}>\bar{u}$, of the nucleon. A prediction for the corresponding polarized flavor-asymmetry is presented and shown to agree with predictions of (chiral quark--soliton) models which successfully reproduced the flavor-asymmetry of the unpolarized sea.
We present results on the quark unpolarized, helicity and transversity parton distributions functions of the nucleon. We use the quasi-parton distribution approach within the lattice QCD framework and perform the computation using an ensemble of twisted mass fermions with the strange and charm quark masses tuned to approximately their physical values and light quark masses giving pion mass of 260 MeV. We use hierarchical probing to evaluate the disconnected quark loops. We discuss identification of ground state dominance, the Fourier transform procedure and convergence with the momentum boost.…
Lattice QCD Benchmark of Proton Helicity and Flavor-Dependent Unpolarized Transverse Momentum-Dependent Parton Distribution Functions at Physical Quark Masses
We investigate the heavy quark mass effects on the parton distribution functions in the unpolarized virtual photon up to the next-to-leading order in QCD. Our formalism is based on the QCD-improved parton model described by the DGLAP evolution equation as well as on the operator product expansion supplemented by the mass-independent renormalization group method. We evaluate the various components of the parton distributions inside the virtual photon with the massive quark effects, which are included through the initial condition for the heavy quark distributions, or equivalently from the matri…
We calculate the $O(α_s^3)$ heavy flavor contributions to the Wilson coefficients of the structure function $F_2(x,Q^2)$ and the massive operator matrix elements (OMEs) for the twist--2 operators of unpolarized deeply inelastic scattering in the region $Q^2 \gg m^2$. The massive Wilson coefficients are obtained as convolutions of massive OMEs and the known light flavor Wilson coefficients. We also compute the massive OMEs which are needed to evaluate heavy flavor parton distributions in the variable flavor number scheme (VFNS) to 3--loop order. All contributions to the Wilson coefficients and …
We calculate the isovector (flavor-nonsinglet) unpolarized quark- and antiquark distributions in the nucleon at a low normalization point in the large-N_c limit. The nucleon is described as a soliton of the effective chiral theory. The isovector distribution appears in the next-to-leading order of the 1/N_c-expansion. Numerical results for the quark- and antiquark distributions compare well with the parametrizations of the data at a low normalization point. This large-N_c approach gives a flavor asymmetry of the antiquark distribution (violation of the Gottfried sum rule) in good agreement wit…
We study the azimuthal $\cos φ$ and $\cos 2φ$ asymmetries in heavy-quark pair leptoproduction, $lN\rightarrow l^{\prime}Q\bar{Q}X$, as probes of linearly polarized gluons inside unpolarized proton, where the azimuth $φ$ is the angle between the lepton scattering plane $(l,l^{\prime})$ and the heavy quark production plane $(N,Q)$. First, we determine the maximal values for the $\cos φ$ and $\cos 2φ$ asymmetries allowed by the photon-gluon fusion with unpolarized gluons; these predictions are large, $(\sqrt{3}-1)/2$ and $1/3$, respectively. Then we calculate the contribution of the transverse-mo…
We propose and discuss a numerical use of our previous precision results for the radiative corrections to unpolarized spin one-half baryon semileptonic decays, which is not compromised to fixing the form factors at prescribed values. We present various crosschecks and comparisons with other results available in the literature of such analytical radiative corrections. Our analysis, however, is general and applies to all charge assignments to the baryons allowed by heavy quarks. The procedure is exemplified with the processes Ξ^0 \to Σ^+ e\barν and Λ_c^+ \to Λe^+ ν.
The theoretical predictions of the chiral quark soliton model for the unpolarized and longitudinally polarized structure functions of the nucleon are compared with recent high energy data. The theory is shown to explain all the qualitatively noticeable features of the existing experiments, including the light flavor sea-quark asymmetry for the unpolarized distribution functions established by the NMC measurement as well as very small quark spin fraction of the nucleon indicated by the EMC measurement. Another unique feature of the model is that it predicts sizably large isospin asymmetry also …
We calculate the universal flavor-singlet radiative QED corrections to unpolarized lepton scattering applicable to general differential scattering cross sections, involving charged fermions or photons in initial or final states. The radiators are derived to $O((α\ln(Q^2/m_f^2))^5)$ in analytic form. Numerical illustrations are given.
In recent papers [1,2], two new ways have been proposed to probe the linear polarization of gluons in unpolarized proton: using the azimuthal asymmetries and Callan-Gross ratio in heavy-quark pair leptoproduction, $lN\rightarrow l^{\prime}Q\bar{Q}X$. In this talk, we discuss in details the sensitivity of the QCD predictions for the azimuthal $\cos φ$ and $\cos 2φ$ asymmetries to the contribution of linearly polarized gluons inside unpolarized proton, where the azimuth $φ$ is the angle between the lepton scattering plane $(l,l^{\prime})$ and the heavy quark production plane $(N,Q)$. Our analysi…
We consider the azimuthal $\cos φ$ and $\cos 2φ$ distributions and the Callan-Gross ratio $R={\rm d}σ_L/{\rm d}σ_T$ in heavy-quark pair electroproduction, $lN\rightarrow l^{\prime}Q\bar{Q}X$, as probes of linearly polarized gluons in unpolarized nucleons. Our analysis shows that the azimuthal asymmetries and Callan-Gross ratio are predicted to be large and very sensitive to the contribution of the gluonic counterpart of the Boer-Mulders function, $h_{1}^{\perp g}$, describing the linear polarization of gluons inside unpolarized nucleon. In particular, the maximum values of the azimuthal distri…
The $O(α_s^2)$ massive operator matrix elements for unpolarized and polarized heavy flavor production at asymptotic values $Q^2 >> m^2$ are calculated in Mellin space without applying the integration-by-parts method. We confirm previous results given in Refs. \cite{BU1,BU2}, however, obtain much more compact representations.
Complete analytical results for the production of heavy-quark pairs by polarized and unpolarized photons in next-to-leading order are presented. Two-, three- and two plus three-jet cross sections for total photon spin $J_z=0,\pm 2$ are presented for $b\bar{b}(g)$ production. The 2-jet cross sections are considered as a background to $γγ\rightarrow H^* \rightarrow b\bar{b}$ (standard model). Top production, not too far above threshold, is also considered for $J_z=0,\pm 2$. For both $b$- and $t$-quark production, the higher order QCD corrections are found to be significant.
We study the Callan-Gross ratio $R={\rm d}σ_L/{\rm d}σ_T$ in heavy-quark pair leptoproduction, $lN\rightarrow l^{\prime}Q\bar{Q}X$, as a probe of linearly polarized gluons inside unpolarized proton, where ${\rm d}σ_T$ (${\rm d}σ_L$) is the differential cross section of the $γ^*N\rightarrow Q\bar{Q}X$ process initiated by a transverse (longitudinal) virtual photon. Note first that the maximal value for the quantity $R$ allowed by the photon-gluon fusion with unpolarized gluons is large, about 2. We calculate the contribution of the transverse-momentum dependent gluonic counterpart of the Boer-M…
The flavor dependence of the naive time reversal odd (``T-odd'') parton distributions for $u$- and $d$-quarks are explored in the spectator model. The flavor dependence of $h_{1}^{\perp}$ is of significance for the analysis of the azimuthal $\cos(2ϕ)$ asymmetries in unpolarized SIDIS and DY-processes, as well as for the overall physical understanding of the distribution of transversely polarized quarks in unpolarized nucleons. As a by-product of the formalism, we calculate the chiral-odd but ``T-even'' function $h_{1L}^{\perp}$ which enables us to present a prediction for the single spin asymm…
It is shown that neutrino and antineutrino deep inelastic scattering of unpolarized and polarized $Λ$ and $\barΛ$ productions, can provide a clean separation of unpolarized and polarized fragmentation functions of a quark into a $Λ$, for both light-flavor quarks and antiquarks and also for strange quarks. Combining with $Λ$ and $\barΛ$ productions in polarized electron deep inelastic scattering, one can systematically measure or check the various flavor and spin dependent fragmentation functions. Such measurements can provide crucial tests of different predictions concerning the spin structure…
We present the results of our QCD analysis for nonsinglet unpolarized quark distributions and structure function $F_2(x,Q^2)$. New parameterizations are derived for the nonsinglet quark distributions for the kinematic wide range of $x$ and $Q^2$. The analysis is based on the Jacobi polynomials expansion of the structure function. The higher twist contributions of proton and deuteron structure function are obtained in the large $x$ region. Our calculations for nonsinglet unpolarized quark distribution functions based on the Jacobi polynomials method are in good agreement with the other theoreti…
We study azimuthal asymmetries in heavy quark pair production in unpolarized electron-proton and proton-proton collisions, where the asymmetries originate from the linear polarization of gluons inside unpolarized hadrons. We provide cross section expressions and study the maximal asymmetries allowed by positivity, for both charm and bottom quark pair production. The upper bounds on the asymmetries are shown to be very large depending on the transverse momentum of the heavy quarks, which is promising especially for their measurements at a possible future Electron-Ion Collider or a Large Hadron …
We present a recent calculation of $J/ψ$ and $Υ$ production in unpolarized $pp$ collision and show that this can be used to probe the unpolarized gluon as well as the linearly polarized gluon transverse momentum dependent parton distributions (TMDs). We use the color evaporation model for the heavy quarkonium production and use a generalized factorized form of the cross section. We compare the results with experimental data.
New insights from the flavor dependence of quark transverse momentum distributions in the pion
Università di Milano（米兰大学）；INFN, Sezione di Milano（意大利国家核物理研究所米兰分部）；Università di Pavia（帕维亚大学）；INFN, Sezione di Pavia（意大利国家核物理研究所帕维亚分部）；IRFU, CEA, Université Paris-Saclay（巴黎萨克雷大学CEA IRFU）
The flavor structure of the nucleon sea provides unique information to test the statistical parton distributions approach, which imposes strong relations between quark and antiquarks. These properties for unpolarized and helicity distributions have been verified up to now by recent data. We will present here some new results which are a real challenge, also for forthcoming accurate experimental results, mainly in the high Bjorken-$x$ region.
We use the Color Glass Condensate (CGC) framework to study the production of forward heavy quark-antiquark pairs in unpolarized proton-nucleus or proton-proton collisions in the small-x regime. In the limit of nearly back-to-back jets, the CGC result simplifies into the transverse-momentum dependent (TMD) factorization approach. For massless quarks, the TMD factorization formula involves three unpolarized gluon TMDs: the Weizsäcker-Williams gluon distribution, the adjoint-dipole gluon distribution, and an additional one. When quark masses are kept non-zero, three new gluon TMDs appear -- each …
We investigate the inclusive emission in unpolarized proton collisions of a charm-flavored hadron in association with a Higgs boson, featuring large transverse momenta and produced with a large rapidity distance. Taking advantage of a narrow timing coincidence between the ATLAS detector and the future FPF ones, we study the behavior of cross sections and azimuthal correlations for ultraforward rapidities of the detected hadron. We provide evidence that the hybrid high-energy and collinear factorization, encoding the BFKL resummation of large energy logarithms and supplemented by collinear dens…
The high energy Operator Product Expansion for the product of two electromagnetic currents is extended to the sub-eikonal level in a rigorous way. I calculate the impact factors for polarized and unpolarized structure functions, define new distribution functions, and derive the evolution equations for unpolarized and polarized structure functions in the flavor singlet and non-singlet case.
Simple experimental tests are proposed which can clarify the origin for the anomalously high $η'$ appearance in charmless strange final states in $B$ decays and can investigate the the nature of SU(3) symmetry-breaking in weak heavy flavor decays.
Heavy flavour production like $J/ψ$ and $D$- meson production in scattering of electrons/unpolarized protons off polarized proton target offer promising probes to investigate gluon Sivers function. In this talk, I will summarize our recent work on trasverse single spin asymmetry in $J/ψ$ -production and $D$ - meson production in $p p^\uparrow$ scattering using a generalized parton model approach. We compare predictions obtained using different models of gluon Sivers function within this approach and then, taking into account the transverse momentum dependent evolution of the unpolarized parton…
We calculate $O(α_s)$ corrections to inclusive and isolated double prompt photon production, both for the unpolarized case, and for longitudinal polarization of the incoming hadrons. The calculation is performed using purely analytical techniques for the inclusive case, and a combination of analytical and Monte Carlo techniques to perform the phase space integration in the isolated case. A brief phenomenological study is made of the process $pp\rightarrow γγX$ at CMS energies appropriate for the RHIC heavy ion collider.
An introduction to the heavy quark effective theory and its symmetries is given. Some implications of the heavy quark spin and flavor symmetries are discussed. Recent results on fragmentation to quarkonium states are reviewed.
Some aspects of heavy flavor probes of quark-gluon plasma (QGP) including quarkonia and open heavy flavor D- and B-mesons, aimed to study the properties of QGP, are discussed in this lecture note.
The spectrum of the doubly heavy baryons is estimated with respect to the new observation from the LHCb collaboration [Aaij:2017ueg] by using the chiral partner structure and heavy quark spin-flavor symmetry. The effects of heavy quark flavor symmetry breaking and light quark flavor symmetry are considered. The mass splitting of doubly heavy baryons with the same spin but opposite parity arises from the generalized Goldberger-Treiman relation. The intermultiplet one-pion transition and intramultiplet radiative transitions are also be estimated.
We argue that the color deconfinement in heavy ion collisions may lead to enhanced production of hadrons with open heavy flavor (charm or bottom). We estimate the upper bound of this enhancement.
We discuss heavy-flavor production at hadron colliders in recent global QCD analyses to determine parton distribution functions (PDFs) in the proton. We discuss heavy-flavor treatments in precision theory predictions at the LHC. In particular, we discuss factorization schemes in presence of heavy flavors in proton-proton collisions, as well as the impact of heavy-flavor production at the LHC on PDFs. We show results of recent updates beyond CT18, the latest global QCD analysis from the CTEQ-TEA group.
In this talk, we give a short review of our recent works on studying the singly heavy baryon, doubly heavy baryon, and triply heavy baryon spectra from QCD sum rules.
SU(3) flavor dependence of the leading and subleading parameters appeared in the heavy quark expansion of the heavy-light mesons are systematically analyzed by using QCD sum rules.
Recent theoretical results on heavy flavor production and decay in the framework of perturbative QCD are reviewed. This includes calculations for top production at hadron colliders, inclusive charmonium production and the comparison between the singlet and octet mechanisms. Predictions for heavy flavor production in $e^+e^-$ annihilation will be discussed in some detail, covering both the threshold and the high energy region. The first results in NLO for heavy flavor decays will also be reviewed.
The phenomenology of flavor mixing of heavy Majorana neutrinos is studied. The physical degrees of freedom, which propagate like free particles until they decay in the presence of flavor mixing, are identified by diagonalizing the resummed propagator. It is shown that they should be interpreted as quasiparticles which lose Majorana nature.
We review the status of hard interactions, in particular of jet and heavy flavor production, at HERA and LEP. Emphasis is given to recent theoretical developments. Instantons, event shapes, and prompt photons are also briefly discussed.
In a previous work, we proposed an extended Nambu--Jona-Lasinio (NJL) model including heavy quark flavors. In this work, we will calculate strong and radiative decays of vector mesons in this extended NJL model, including light $ρ$, $ω$, $K^*$, $ϕ$ and heavy $D^*$, $D^*_s$, $B^*$, $B^*_s$.
We describe a light-cone wave function formalism for hadroproduction of heavy-flavors via gluon-gluon fusion. The developed approach is well suited to address coherence effects in heavy-quark production on nuclei at small $x_{2} \lsim 0.1\cdot A^{-1/3}$. Nuclear attenuation in hadroproduction of heavy-flavors is found to be similar to shadowing effects for heavy-flavor structure functions in deep-inelastic scattering from nuclei. Nevertheless, remaining differences in the theoretical formulation of both processes imply corrections to factorization theorems.
We investigate the possible existence of multibaryons with heavy flavor quantum numbers using the bound state approach to the topological soliton model and the recently proposed approximation for multiskyrmion fields based on rational maps. We use an effective interaction lagrangian which consistently incorporates both chiral symmetry and the heavy quark symmetry including the corrections up to order 1/m_Q. The model predicts some narrow heavy flavored multibaryon states with baryon number four and seven.
The couplings and interactions of baryons containing a heavy quark are related by light quark spin-flavor symmetry in the large $N$ limit. The single pion coupling constant which determines all heavy quark baryon-pion couplings is equal to the pion coupling constant for light quark baryons. Light quark symmetry relations amongst the baryon couplings are violated at order $1/N^2$. Heavy quark spin-flavor symmetry is used in conjunction with large $N$ light quark spin-flavor symmetry to determine the couplings of the degenerate doublets of heavy quark baryons.
We report on the calculation of the three-loop polarized and unpolarized flavor non-singlet and the polarized singlet anomalous dimensions using massless off-shell operator matrix elements in a gauge-variant framework. We also reconsider the unpolarized two-loop singlet anomalous dimensions and correct errors in the foregoing literature.
Spin dependent fragmentation functions for heavy flavor quarks to fragment into heavy baryons are calculated in a quark-diquark model. The production of intermediate spin 1/2 and 3/2 excited states is explicity included. $Λ_b$ , $Λ_c$ and $Ξ_c$ production rate and polarization at LEP energies are calculated and, where possible, compared with experiment. A different approach, also relying on a heavy quark-diquark model, is proposed for the small momentum transfer inclusive production of polarized heavy flavor hyperons. The predicted $Λ_c$ polarization is roughly in agreement with experiment.
