I consider variations in the definitions, at next-to-leading order (NLO) and at next-to-next-to leading order (NNLO), of a General-Mass Variable Flavour Number Scheme (GM-VFNS) for heavy flavour structure functions. I also define a new "optimal" scheme choice improving the smoothness of the transition from one flavour number to the next. I investigate the variation of the structure function for a fixed set of parton distribution functions (PDFs) and also the change in the PDFs when a new MSTW2008-type global fit to data is performed for each GM-VFNS. At NLO the parton distributions, and predictions using them at hadron colliders, can vary by 2-3% from the mean value. At NNLO there is far more stability with varying GM-VFNS definition, and changes in PDFs and predictions are less than 1%, with most variation at very small x values. Hence, mass-scheme variation is an additional and significant source of uncertainty when considering parton distributions, but as with all perturbative uncertainties, it diminishes quickly as higher orders are included.
Understanding flavor dependence of the parton energy loss is one of key tasks of the jet quenching physics. In these proceedings we provide a summary of recent works on a quantification of the flavor dependence of parton energy loss along with a summary and discussion of a subset of contributions presented at the Hard Probes 2016 conference which are related to the flavor aspects of parton energy loss.
It is argued that while the scale dependence of the parton distributions in the fixed flavor factorization scheme is governed by three active flavors, the scale dependence of the running coupling should nevertheless be better governed by a variable number of active flavors.
We compare `fixed flavor number scheme' (FFNS) and `variable flavor number scheme' (VFNS) parton model predictions at high energy colliders. Based on our recent LO- and NLO-FFNS dynamical parton distributions, we generate radiatively two sets of VFNS parton distributions where also the heavy quark flavors h=c,b,t are considered as massless partons within the nucleon. By studying the role of these distributions in the production of heavy particles (h\bar{h}, t\bar{b}, hW^{+-}, Higgs--bosons, etc.) at high energy ep, p\bar{p} and pp colliders, we show that the VFNS predictions are compatible wit…
A study is made of charm and bottom flavor matching conditions on parton densities. Starting from an $\bar{\rm MS}$ three-flavor density set, where the scale $μ< m_c$, and using the recently derived two-loop matching conditions, we provide a new set of four-flavor parton densities where $ m_c \le μ< m_b$ and five-flavor densities where $μ\ge m_b$. The effect of the next-to-next-to-leading order matching conditions on the evolution equations is important for scales just above the transition regions. This includes the small $x$ and small $Q^2$ domain studied by the H1 and ZEUS experiments at HER…
Recent experimental data on semi-inclusive deep-inelastic scattering from the HERMES collaboration allow us to discuss for the first time the flavor dependence of unpolarized transverse-momentum dependent distribution and fragmentation functions. We find convincing indications that favored fragmentation functions into pions have smaller average transverse momentum than unfavored functions and fragmentation functions into kaons. We find weaker indications of flavor dependence in the distribution functions.
Based on our recent NNLO dynamical parton distributions as obtained in the `fixed flavor number scheme', we generate radiatively parton distributions in the `variable flavor number scheme' where also the heavy quark flavors (c,b,t) become massless partons within the nucleon. Only within this latter factorization scheme NNLO calculations are feasible at present, since the required partonic subprocesses are only available in the approximation of massless initial-state partons. The NNLO predictions for gauge boson production are typically larger (by more than 1 sigma) than the NLO ones, and rates…
We give an interpretation of the $u$ and $d$ quarks contributions to the nucleon electromagnetic form factors for values of the four-momentum transfer in the multi-GeV region where flavor separated data have been recently made available. The data show, in particular, a suppression of $d$ quarks with respect to $u$ quarks at large momentum transfer. %and constant ratios of the flavor dependent Pauli to Dirac form factors ratios. This trend can be explained using a reggeized diquark model calculation of generalized parton distributions, thus providing a correlation between momentum and coordinat…
In order to examine polarized strange quark distribution, semi-inclusive $D/\Dbar$ production in neutrino deep inelastic scattering is studied including ${\cal O}(α_s)$ corrections. Cross section and spin asymmetry are calculated by using various parametrizations of polarized parton distribution functions. It is found that $\Dbar$ production is promising to directly extract the polarized strange sea.
Recent experimental measurements of the Gottfried Sum Rule, and pp and pD Drell-Yan processes, suggest significant violation of flavor symmetry in the proton sea. This interpretation rests on the assumption of parton charge symmetry. Our model calculations suggest charge symmetry violation [CSV] for parton valence distributions of a few percent. Precision measurements of structure functions in muon and neutrino experiments allow us to set rather stringent experimental limits on CSV in certain kinematic regions. In another region, these experiments suggest substantial CSV effects. We suggest ex…
Precision measurements of heavy-flavor hadroproduction at the Large Hadron Collider (LHC) have the ability to probe heavy-flavor parton distribution functions (PDFs) in the proton. Sensitivity of inclusive $B^\pm$ meson production cross section measurements at LHCb 13 TeV to the bottom-quark PDF is illustrated by using theory predictions obtained with a the S-ACOT-MPS general mass variable flavor number (GMVFN) scheme within the QCD factorization formula. This approach can easily be extended to other heavy-flavor production processes, such as $Z$ boson production in association with a bottom- …
A new code for the scale evolution of modified-minimal-subtraction-scheme parton densities is described. Through next-to-leading order the program uses exact splitting functions. In next-to-next-to-leading order approximate splitting functions are used. For efficiency the program includes analytical results for the evaluation of the weights required for the integrations over the longitudinal momentum fractions of the partons. It also incorporates the operator matrix elements required for the matching conditions across heavy flavor thresholds in higher order perturbation theory. The more effici…
The systematic treatment of heavy quark mass effects in DIS in current CTEQ global analysis is summarized. Applications of this treatment to the comparison between theory and experimental data on DIS charm production are described. The possibility of intrinsic charm in the nucleon is studied. The issue of determining the charm mass in global analysis is discussed.
Polarized deep inelastic scattering (DIS) data are analyzed in leading and next-to-leading order of QCD within the common `standard' scenario of polarized parton distributions with a flavor-symmetric light sea (antiquark) distribution $δ\bar{q}$, and a completely SU(3)$_f$ broken `valence' scenario with totally flavor-asymmetric light sea densities $(δ\bar{u}\neqδ\bar{d}\neqδ\bar{s})$. The latter flavor-broken light sea distributions are modelled with the help of a Pauli-blocking ansatz at the low radiative/dynamical input scales of $μ_{\rm LO(NLO)}^2=0.26$ (0.40) GeV$^2$ which complies with p…
Using a physically motivated parameterization based on the reggeized diquark model we perform a flavor separation of the chiral-odd generalized parton distributions obtained from both $π^0$ and $η$ exclusive electroproduction. In our approach we exploit a connection between the chiral-even and chiral-odd reduced helicity amplitudes using Parity transformations that are relevant for a class of models that includes two-component models. We compare our results for $η$ production to the previously obtained $π^0$ results, and we make predictions for the transverse single spin asymmetry components w…
This paper describes salient features of new sets of parton distributions obtained by the CTEQ Collaboration based on a comprehensive QCD global analysis of all available data. The accuracy of the new data on deep inelastic scattering structure functions obtained by the very high statistics NMC and CCFR experiments provides unprecedented sensitivity to the flavor dependence of the sea-quark distributions. In addition to much better determination of the small x dependence of all parton distributions, we found: (i) the strange quark distribution is much softer than the non-strange sea quarks and…
An intuitive definition of the partonic flavor of a jet in quantum chromodynamics is often only well-defined in the deep ultraviolet, where the strong force becomes a free theory and a jet consists of a single parton. However, measurements are performed in the infrared, where a jet consists of numerous particles and requires an algorithmic procedure to define their phase space boundaries. To connect these two regimes, we introduce a novel and simple partonic jet flavor definition in the infrared. We define the jet flavor to be the net flavor of the partons that lie exactly along the direction …
The analysis of deeply virtual meson production is extended to neutrino-production of the pseudo-Goldstone mesons (pions, kaons, eta-mesons) on nucleons, with the flavor content of the recoil baryon either remaining intact, or changing to a hyperon from the SU(3) octet. We rely on the SU(3) relations and express all the cross-sections in terms of the proton generalized parton distributions (GPDs). The corresponding amplitudes are calculated at the leading twist level and in the leading order in α_{s}, using a phenomenological parametrization of GPDs. We provide a computational code, which can …
The Parton Branching (PB) Method describes the evolution of transverse momentum dependent parton densities (TMDs). The obtained TMDs can be used in Monte Carlo generators to describe physical observables. We give an overview of recent developments, in particular the new application of PB TMDs in Drell-Yan + jets production, the four-flavor and five-flavor schemes for heavy quark contributions, and the inclusion of QED corrections in the PB evolution.
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 study large-distance contributions to the nucleon parton densities in the transverse coordinate (impact parameter) representation based on generalized parton distributions (GPDs). Chiral dynamics generates a distinct component of the partonic structure, located at momentum fractions x ~< M_pi/M_N and transverse distances b ~ 1/M_pi. We analyze the phenomenological "pion cloud" model of the flavor asymmetry dbar(x) - ubar(x) and quantify what fraction of the calculated asymmetry results from the universal large-distance region. Our findings indicate that a two-component picture of the nucleo…
Recent measurements of the Gottfried sum rule have focused attention on the possibility of substantial flavor symmetry breaking in the proton sea. This is confirmed by pp and pD Drell-Yan processes measured at FNAL. Theoretical models used to `prove' flavor symmetry breaking rely on the assumption of charge symmetric parton distributions. Substantial charge symmetry violation [CSV] could affect current tests of flavor symmetry. In this review we examine the possibility of CSV for parton distributions. We first give definitions for structure functions without making the usual assumption of char…
Previously published CTEQ6 parton distributions adopt the conventional zero-mass parton scheme; these sets are most appropriate for use with massless hard-scattering matrix elements commonly found in most physics applications. For precision observables which are sensitive to charm and bottom quark mass effects, we provide in this paper an additional CTEQ6HQ parton distribution set determined in the more general variable flavor number scheme which incorporates heavy flavor mass effects. The results are obtained by combining these parton distributions with consistently matched DIS structure func…
We present the CTEQ6HQ parton distribution set which is determined in the general variable flavor number scheme which incorporates heavy flavor mass effects; hence, this set provides advantages for precision observables which are sensitive to charm and bottom quark masses. We describe the analysis procedure, examine the predominant features of the new distributions, and compare with previous distributions. We also examine the uncertainties of the strange quark distribution and how the the recent NuTeV dimuon data constrains this quantity.
We examine the flavor dependence of the nuclear modification factor $R_{AA}$ in the pQCD calculations at LHC energies. The computations are performed accounting for radiative and collisional parton energy loss with running coupling constant. Our results show that the recent LHC data on the $R_{AA}$ for charged hadrons, D-mesons and non-photonic electrons agree reasonably with the pQCD picture of the parton energy loss with the dominating contribution from the radiative mechanism.
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…
Determination of proton parton distribution functions is present under the dynamical parton model assumption by applying DGLAP equations with GLR-MQ-ZRS corrections. We provide two data sets, referred as IMParton16, which are from two different nonperturbative inputs. One is the naive input of three valence quarks and the other is the input of three valence quarks with flavor-asymmetric sea components. Basically, both data sets are compatible with the experimental measurements at high scale ($Q^2>2$ GeV$^2$). Furthermore, our analysis shows that the input with flavor-asymmetric sea components …
We present the first exact analytic result for all partonic channels contributing to the total cross section for the production of a pair of heavy flavors in hadronic collisions in NLO QCD. Our calculation is an essential step in the derivation of the top quark pair production cross section at NNLO in QCD, which is a cornerstone of the precision LHC program. Our results uncover the analytical structures behind observables with heavy flavors at higher orders. They also reveal surprising and non-trivial implications for kinematics close to partonic threshold.
Using DGLAP evolution equation with the corrections of parton recombinations, the flavor asymmetric sea quark distributions in the proton are first extracted from the available experimental data with the global QCD analysis method. Comparisons of our predictions to the CTEQ, MRS, and GRV parton distribution functions for sea quarks are presented. Based on the separation of the flavor symmetric and asymmetric sea, the possible relations between strange quark distribution and symmetric light quark distribution are discussed. The results are used to explain the recent HERMES result of the strange…
We present an initiatory study of quark helicity flip generalized parton distributions (GPDs) in n_f=2 lattice QCD, based on clover-improved Wilson fermions for a large number of coupling constants and pion masses. Quark helicity flip GPDs yield essential information on the transverse spin structure of the nucleon. In this work, we show first results on their lowest moments and dipole masses and study the corresponding chiral and continuum extrapolations.
We consider the production of $Z$ bosons associated with heavy (charm and beauty) jets at the LHC energies using two scenarios based on the transverse momentum dependent (TMD) parton densities in a proton. The first of them employs the Catani-Ciafaloni-Fiorani-Marchesini gluon evolution and is implemented in the Monte-Carlo event generator PEGASUS. Here, the heavy quarks are always produced in the hard partonic scattering. The second scheme is based on the parton branching approach, currently implemented into the Monte-Carlo event generator CASCADE. In this scenario, the $Z$ + jets sample is g…
We apply the Meson Cloud Model to the calculation of nonsinglet parton distributions in the nucleon sea, including the octet and the decuplet cloud baryon contributions. We give special attention to the differences between nonstrange and strange sea quarks, trying to identify possible sources of SU(3) flavor breaking. A analysis in terms of the $κ$ parameter is presented, and we find that the existing SU(3) flavor asymmetry in the nucleon sea can be quantitatively explained by the meson cloud. We also consider the $Σ^+$ baryon, finding similar conclusions.
1) We discuss a sum rule of the tensor structure function $b_1(x)$ for spin-one hadrons along with the Gottfried sum rule. Both sum rules are similar in the sense that they are phenomenological ones based on a naive parton model. As the Gottfried sum rule became useful for studying SU(2)$_{flavor}$ breaking in antiquark distributions, the $b_1$ sum rule could provide important information on sea-quark tensor polarization. 2) Pionic contributions to the antiquark distribution $\bar u-\bar d$ and violation of the Gottfried sum rule are discussed. We find that the contributions account for about …
The consequences of a flavor broken SU(3)_f dynamical parton model are studied in the context of the elastic scattering of supersymmetric dark matter off nucleons. It is shown that the predictions of this model differ considerably from those of the commonly applied `standard' parton model. Some notable properties of the dynamical parton model are finally presented and discussed.
Measurements in heavy flavor azimuthal angular correlation provide insight into the production, propagation, and hadronization of heavy flavor jets in ultra-relativistic hadronic and heavy-ion collisions. These measurements across different colliding systems, like p--A and A--A, help us isolate the possible modification in particle production due to cold nuclear matter (CNM) effects and the formation of Quark-Gluon Plasma (QGP), respectively. Jet correlation studies give direct access to the initial parton dynamics produced in these collisions. This article studies the azimuthal angular correl…
Multiple scattering and induced parton splitting lead to a medium modification of the QCD evolution for jet fragmentation functions and the final hadron spectra. Medium-induced parton splittings not only lead to energy loss of leading partons and suppression of leading hadron spectra, but also modify the flavor composition of a jet due to induced flavor conversion via gluon emission, quark pair production and annihilation. Through a numerical study of the medium-modified QCD evolution, leading $K^-$ strange meson spectra are found to be particularly sensitive to the induced flavor conversion i…
We show that the well-known obstacle for working with the zero-mass variable flavor number scheme, namely, the omission of O(1) mass power corrections close to the conventional heavy flavor matching point (HFMP) mu_b=m, can be easily overcome. For this it is sufficient to take advantage of the freedom in choosing the position of the HFMP. We demonstrate that by choosing a sufficiently large HFMP, which could be as large as 10 times the mass of the heavy quark, one can achieve the following improvements: 1) above the HFMP the size of missing power corrections O(m) is restricted by the value of …
We present a new global QCD analysis of nuclear parton distribution functions and their uncertainties. In addition to the most commonly analyzed data sets for the deep-inelastic scattering of charged leptons off nuclei and Drell-Yan di-lepton production, we include also measurements for neutrino-nucleus scattering and inclusive pion production in deuteron-gold collisions. The analysis is performed at next-to-leading order accuracy in perturbative QCD in a general mass variable flavor number scheme, adopting a current set of free nucleon parton distribution functions, defined accordingly, as re…
We compute the distribution amplitudes of the pion and kaon in the light-front constituent quark model with the symmetric quark-bound state vertex function. In the calculation we explicitly include the flavor-SU(3) symmetry breaking effect in terms of the constituent quark masses of the up (down) and strange quarks. To calculate the kaon parton distribution functions~(PDFs), we use both the conditions in the light-cone wave function, i.e., when $\bar{s}$ quark is on-shell, and when $u$ quark is on-shell, and make a comparison between them. The kaon PDFs calculated in the two different conditio…
Double parton scattering is sensitive to correlations between the two partons in the hadron, including correlations in flavor, spin, color, momentum fractions and transverse separation. We obtain a first estimate of the size of these correlations by calculating the corresponding double parton distribution functions in a bag model of the proton. We find significant correlations between momentum fractions, spin and flavor, but negligible correlations with transverse separation. The model estimates of the relative importance of these correlations will help experimental studies disentangle them.
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.…
We present a next-to-next-to-leading order (NNLO) calculation of the quasi parton distribution functions (Quasi-PDFs) in the large momentum effective theory (LaMET). We focus on the flavor non-diagonal quark-quark channel and demonstrate the LaMET factorization at the NNLO accuracy in the modified minimal subtraction scheme. The matching coefficient between the quasi-PDF and the light-cone PDF is derived. This provides a first step towards a complete NNLO analysis of quasi-PDFs and to better understand the nucleon structures from the first principle of QCD.
The Linear Boltzmann Transport (LBT) model coupled to hydrodynamical background is extended to include transport of both light partons and heavy quarks through the quark-gluon plasma (QGP) in high-energy heavy-ion collisions. The LBT model includes both elastic and inelastic medium-interaction of both primary jet shower partons and thermal recoil partons within perturbative QCD (pQCD). It is shown to simultaneously describe the experimental data on heavy and light flavor hadron suppression in high-energy heavy-ion collisions for different centralities at RHIC and LHC energies. More detailed in…
Taking proton as an ensemble of quark-gluon Fock states and using the principle of detailed balance, we construct a simple statistical model for parton distribution of proton. The recent observed Bjorken-$x$ dependent light flavor sea quark asymmetry $\bar{d}(x)-\bar{u}(x)$ can be well reproduced by Monte Carlo simulation as a pure statistical effect.
We calculate the transverse momentum dependence in the production of two back-to-back hadrons in electron-positron annihilations at the medium/large energy scales of BES-III and BELLE experiments. We use the parameters of the transverse-momentum-dependent (TMD) fragmentation functions that were recently extracted from the semi-inclusive deep-inelastic-scattering multiplicities at low energy from HERMES. TMD evolution is applied according to different approaches and using different parameters for the nonperturbative part of the evolution kernel, thus exploring the sensitivity of our results to …
The extension of the method [arXiv:hep-ph/0503109] for solving the leading order evolution equation for Generalized Parton Distributions (GPDs) is presented. We obtain the solution of the evolution equation both for the flavor nonsinglet quark GPD and singlet quark and gluon GPDs. The properties of the solution and, in particular, the asymptotic form of GPDs in the small x and ξregion are discussed.
Using QCD motivated and phenomenological considerations, we construct x- dependent polarized parton distributions, which evolve under GLAP evolution, satisfy DIS data and are within positivity constraints. Each flavor is done separately and the overall set can be used to predict polarization asymmetries for various processes. We perform our NLO analysis strictly in x space, avoiding difficulties in moment inversion. Small-x results and other physical considerations are discussed.
We present, for the first time, an \textit{ab initio} calculation of the individual up, down and strange quark helicity parton distribution functions for the proton. The calculation is performed within the twisted mass clover-improved fermion formulation of lattice QCD using one ensemble of dynamical up, down, strange and charm quarks with a pion mass of 260 MeV. The lattice matrix elements are non-perturbatively renormalized and the final results are presented in the $\overline{ \rm MS}$ scheme at a scale of 2 GeV. We give results on the $Δu^+(x)$ and $Δd^+(x)$, including disconnected quark l…
We determine the parton distribution functions (PDFs) in a next-to-next-to-leading order (NNLO) QCD-analysis of the inclusive neutral-current deep-inelastic-scattering (DIS) world data combined with the neutri{-}no-nucleon DIS di-muon data and the fixed-target Drell-Yan data. The PDF-evolution is performed in the $N_f = 3$ fixed-flavor scheme and supplementary sets of PDFs in the 4- and 5-flavor schemes are derived from the results in the 3-flavor scheme using matching conditions. The charm-quark DIS contribution is calculated in a general-mass variable-flavor-number (GMVFN) scheme interpolati…
We present a phenomenological study of charm quark photoproduction in longitudinally polarized lepton-hadron collisions at next-to-leading order accuracy of QCD. Our results are based on a recently developed, flexible parton-level Monte Carlo program for spin-dependent heavy flavor hadroproduction, which we extend to deal also with both direct and resolved photon contributions. The subsequent hadronization into charmed mesons is modeled in our calculations, which allows us to compare with data on double-spin asymmetries for D0 meson production taken by the COMPASS collaboration. In general, ne…
We show that when Bjorken $x_B$ is large, the leading order twist-four contributions to the structure functions can be expressed in terms of the derivatives of the normal twist-two parton distributions. Our analytical results are not only consistent with the parameterized power corrections extracted from the data, but also predict the flavor dependence of the power corrections. We also discuss the impact of our analytical results on the extraction and the flavor separation of the parton distributions at large $x$.
We determine at NNLO (3-loop) of QCD the dynamical parton distributions of the nucleon generated radiatively from valencelike positive input distributions at an optimally chosen low resolution scale (Q_0^2<1 GeV^2) by employing the "fixed flavor number factorization scheme" (FFNS). These are compared with "standard" NNLO distributions, generated at some fixed and higher resolution scale (Q_0^2>1 GeV^2). The NNLO corrections imply in both approaches an improved value of χ^2, typically χ^2_{NNLO} \sim 0.9χ^2_{NLO}. The dynamical NNLO uncertainties are somewhat smaller than the NLO ones and both …
Working in the hybrid high-energy/collinear factorization, where the next-to-leading resummation of energy logarithms is combined with collinear parton densities and fragmentation functions, we study observables sensitive to high-energy dynamics in the context of heavy-flavor physics.
We study photoproduction of jets and heavy flavors in a polarized collider mode of HERA and in polarized $ep$ collisions at $\sqrt{S}\approx 30$ GeV. We examine the sensitivity of the cross sections and their asymmetries to the proton's polarized gluon distribution and to the completely unknown parton distributions of longitudinally polarized photons.
