Parton Model Research Articles

Flow in small and large quark-gluon plasma droplets: the role of nucleon substructure

We study the effects of nucleon substructure on bulk observables in proton-lead collisions at the LHC using Bayesian methodology. Substructure is added to the TRENTo parametric initial condition model using Gaussian nucleons with a variable number of Gaussian partons. We vary the number and width of these partons while recovering the desired inelastic proton-proton cross section and ensemble averaged proton density. We then run the model through a large number of minimum bias hydrodynamic simulations and measure the response of final particle production and azimuthal particle correlations to initial state properties. Once these response functions are determined, we calibrate free parameters of the model using established Bayesian methodology. We comment on the implied viability of the partonic model for describing hydrodynamic behavior in small systems.

Effect of medium recoil and pT broadening on single inclusive jet suppression in high-energy heavy-ion collisions in the high-twist approach

Jet energy loss and single inclusive jet suppression in high-energy heavy-ion collisions are studied within a pQCD parton model that includes both elastic and radiative interactions between jet shower and medium partons as they propagate through the quark-gluon plasma. The collisional energy loss of jets with a given cone-size is found to be relatively small comparing with the radiative energy loss. However the effect of transverse momentum broadening due to elastic scattering is significant in the calculation of radiative energy loss within the higher-twist formalism. The nuclear modification factors for single inclusive jets with different cone-sizes are calculated and compared to experimental data as measured by ALICE and ATLAS experiments in Pb+Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV. Results on jet suppression in Pb+Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV are also presented.

Regge trajectories of excited baryons, quark-diquark models, and quark-hadron duality

The parton model relations in conjunction with quark-hadron duality in deep inelastic scattering suggests an asymptotic dominance of quark-diquark type of baryonic excited states with a radial Regge uniformly distributed mass squared spectrum $M_{n}^2 = \mu^2 n + M_0^2$. We argue that this points to a lineary quark-diquark confining potential. We analyze the radial ($n$) and angular-momentum ($J$) Regge trajectories for all light-quark states with baryon number one listed in the 2016 edition of the Particle Data Tables. The parameters of the mass squared trajectories are obtained by linear regression assuming $\Delta M_n^2 \sim M_n \Gamma_n $ weighted with the width $\Gamma_n$ of the resonance and the error analysis is carried out accordingly.

Modeling of diurnal pattern of air temperature in a tropical environment: Ile-Ife and Ibadan, Nigeria

Modeling of diurnal pattern of air temperature (Ta) is essential in the parameterization of turbulent heat fluxes in climate models. However, climate models still simulate the nocturnal stable boundary layer surface Ta with biases across the globe. This paper therefore validated five different diurnal Ta models (Ephrath, Hirotaka, de Wit, Parton and Fourier series models) used for estimating hourly Ta from daily maximum, daily minimum, and daily mean air temperature. It also developed an improved fourier series parameterization approach for Ta using surface layer observations from Nigerian micrometeorological experimental (NIMEX) site. The overall performance of the Ephrath, Hirotaka, de Wit and Parton models revealed a large deviation from the measured data during the early hours of the morning and late hours of the nighttime. The original fourier series model showed better performance for unstable air temperature parameterizations while the stable Ta was strongly overestimated. The performance of the model was improved with the inclusion of the atmospheric cooling rate that accounts for the temperature inversion which occurs during the nocturnal boundary layer condition. The mean bias error and root mean square error in estimated Ta by the modified fourier series model reduced by 4.13 and 3.01 °C, respectively during the transition period from dry to wet stable atmospheric conditions. The existing models simulated night time Ta with high biases and could not accurately capture the strong cooling inversion associated with a humid tropical region. The modified Fourier series model that incorporated the night time inversion variables gave the best estimation of the diurnal weather patterns of Ta when compared with other existing models for a tropical environment.

Testing the universality of the Collins function in pion-jet production at RHIC

By adopting a generalised parton model approach at leading order in QCD, including spin and intrinsic parton motion effects, we study the Collins azimuthal asymmetries for pions within a large-pT jet produced at mid-rapidity in polarised hadronic collisions. Using available information on the quark transversity distributions and the pion Collins functions, as extracted from semi-inclusive deeply inelastic scattering and e+e−→h1h2X processes, we compute estimates for the Collins asymmetries in kinematical configurations presently investigated at RHIC by the STAR Collaboration. Collins-like asymmetries, involving linearly polarised gluons, are also considered. Our predictions, compared against available preliminary data, show a very good agreement, even if some discrepancies, to be further scrutinized both theoretically and experimentally, appear in the transverse momentum dependence of the Collins asymmetry. These results are in favour of the predicted universality of the Collins function and of a mild, if any, evolution with the hard scale of the asymmetries.

Probing the gluon Sivers function in p↑p→J/ψ X and p↑p→DX

We present a study of transverse single-spin asymmetries (SSAs) in $p^\uparrow p\to J/\psi\,X$ and $p^\uparrow p\to D X$ within the framework of the generalized parton model (GPM), which includes both spin and transverse momentum effects, and show how they can provide useful information on the still almost unknown gluon Sivers function. Moreover, by adopting a modified version of this model, named color gauge invariant (CGI) GPM, we analyze the impact of the initial- and final-state interactions on our predictions. As a consequence, we find that these two processes are sensitive to different gluon Sivers functions, which can be expressed as linear combinations of two distinct, universal gluon distributions. We therefore define proper observables which could allow for a separate extraction of these two independent Sivers functions. At the same time, we show how it would be possible to discriminate between the GPM and the CGI-GPM approaches by comparing the corresponding estimates of SSAs with present and future experimental results at RHIC.

Nuclear suppression of the phi meson yields with large p_T at the RHIC and the LHC

We calculate phi meson transverse momentum spectra in mathrm{p}+mathrm{p} collisions as well as their nuclear suppressions in central mathrm{A}+mathrm{A} collisions both at the RHIC and the LHC in LO and NLO with the QCD-improved parton model. We have included the parton energy loss effect in a hot/dense QCD medium with the effectively medium-modified phi fragmentation functions in the higher-twist approach of jet quenching. The nuclear modification factors of the phi meson in central mathrm{Au}+mathrm{Au} collisions at the RHIC and central mathrm{Pb}+mathrm{Pb} collisions at the LHC are provided, and nice agreement of our numerical results at NLO with the ALICE measurement is observed. Predictions of the yield ratios of neutral mesons such as phi /pi ^0, phi /eta and phi /rho ^0 at large p_T in relativistic heavy-ion collisions are also presented for the first time.

Extracting jet quenching parameters from large pT hadron suppression at RHIC/LHC

The large pT hadron suppression in high-energy heavy-ion collisions at RHIC/LHC is studied in a NLO pQCD parton model in which the fragmentation function is modified due to jet quenching. The energy loss of the energetic parton jets is incorporated in the modified fragmentation functions which utilize two important parameters to characterize the jet transport properties, the jet transport parameter qˆ0 and the mean free path λ0, both at the initial time τ0 in the center of the fireball created in central AA collisions. We performed a phenomenological study of simultaneous χ2/d.o.f fits to RHIC as well as LHC data to constrain the two parameters for energetic quarks, qˆ0≈1.1±0.2 GeV2/fm and λ0≈0.4±0.03 fm in central Au+ Au collisions at sNN=200 GeV, while qˆ0≈1.7±0.3 GeV2/fm, and λ0≈0.5±0.05 fm in central Pb + Pb collisions at sNN=2.76 TeV. Numerical results for the best fit give a multiple scattering picture for the hard jets with a moderate averaged number of gluon emissions. Based on the best constraints for λ0 and τ0, the estimated value for the mean-squared transverse momentum broadening is moderate which implies that the hard jets go through the medium with small reflection.

Dynamical parton distributions from DGLAP equations with nonlinear corrections**Supported by National Basic Research Program (973 Program 2014CB845406) and Century Program of Chinese Academy of Sciences (Y101020BR0)

Determination of proton parton distribution functions is presented under the dynamical parton model assumption by applying DGLAP equations with GLR-MQ-ZRS corrections. We provide two data sets, referred to 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 (Q2 > 2 GeV2). Furthermore, our analysis shows that the input with flavor-asymmetric sea components better reproduces the structure functions at high Q2. Generally, the parton distribution functions obtained, especially the gluon distribution function, are good options for inputs to simulations of high energy scattering processes. The analysis is performed under the fixed-flavor number scheme for nf = 3, 4, 5. Both data sets start from very low scales, around 0.07 GeV2, where the nonperturbative input is directly connected to the simple picture of the quark model. These results may shed some lights on the origin of the parton distributions observed at high Q2.

James Watson Cronin

James Watson Cronin

Heavy Flavour Production as Probe of Gluon Sivers Function

Heavy flavour production like $J/\psi$ 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/\psi $ -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 distribution functions and gluon Sivers function, we study the effect of evolution on asymmetry.

A ‘soft + hard’ model for heavy-ion collisions

We describe the spectra of neutral pions stemming from AuAu collisions at in a ‘soft + hard’ model. The model is based on the assumptions that hadrons stemming from hard processes are described via perturbative quantum chromodynamics improved parton model calculations, while those stemming from the Quark-Gluon Plasma (we refer to as soft yields) can be described in a super-statistical model induced by multiplicity uctuations. The obtained dependence of the parameters of the model on the event centrality is compared to what is observed in PbPb collisions at .

DIS structure functions in the NLO approximation of the Parton Reggeization Approach

The main ideas of the NLO calculations in Parton Reggeization Approach are illustrated on the example of the simplest NLO subprocess, which contributes to DIS: $\gamma^\star+R\to q + \bar{q}$. The double counting with the LO contribution $\gamma^\star + Q \to q$ is resolved. The problem of matching of the NLO results for single-scale observables in the Parton Reggeization Approach on the corresponding NLO results in the Collinear Parton Model is considered. In the developed framework, the usual NLO PDFs in the $\overline{MS}$-scheme can be consistently used as the collinear input for the NLO calculation in the Parton Reggeization Approach.

Transverse single spin asymmetry inp+p↑→D+X

We present expected values of the Single Spin Asymmetry (SSA) in $D$-meson production in the process $p+p^\uparrow \rightarrow D^0 + X $ at RHIC energy $(\sqrt{s}=200\text{ GeV})$ using a generalized parton model approach. We use fits to the gluon Sivers function obtained recently by D'Alesio {\it et al.,} by fitting to the asymmetry data for the process $p+p^\uparrow \rightarrow \pi^0+ X$ measured by the PHENIX collaboration at RHIC. These fits give peak asymmetry predictions which lie in a broad range, $0.5\%\lesssim A_N\lesssim10\%$ for the kinematic regions considered. This is to be compared with the upper bound of 18\% expected for the maximal gluon Sivers function. We extend our analysis to two other centre of mass energies of proposed experiments - AFTER@LHC $(\sqrt{s}=115\text{ GeV})$ and a future RHIC run $(\sqrt{s}=500\text{ GeV})$. We further investigate (at $\sqrt{s}=200$ GeV) the effect of the transverse momentum dependent (TMD) evolution of the unpolarized parton distribution functions (pdf's) and of the gluon Sivers function on the asymmetry predictions. We perform this study using an evolution setup given by Anselmino {\it et al}. We find that the effect of evolution is an overall reduction of the asymmetry predictions. For example, for the saturated gluon Sivers function, upon taking into account TMD evolution, peak asymmetry predictions reduce by a factor 3 or more. This decrease is similar to that noticed earlier for Single Spin Asymmetries (SSA) in the electroproduction of $J/\psi$.

Parton Distribution Functions and models of proton structure functions with self-similarity

Sometime back, a self-similarity based model of the proton structure function at small [Formula: see text] was proposed by Lastovicka. We make reanalysis of this model with most recent HERA data. No significance difference with the earlier analysis is found. Both the analyses have singularity within the kinematical range of [Formula: see text]: [Formula: see text]. We therefore study the model with the additional assumption that it should be singularity free, imposing positivity conditions on the model parameters. This results in a new model which is, however, phenomenologically valid only in a limited low [Formula: see text] range. We therefore make further generalization of the defining self-similar unintegrated Parton Density Function (uPDF) and show that the with proper generalizations and initial conditions on them not only remove the undesired singularity but also results in a structure function with logarithmic growth in [Formula: see text] closer to QCD. The phenomenological range of validity is then found to be much larger than the earlier versions. We also extrapolate the models to large [Formula: see text] in a parameter-free way. The possibility of incorporation of Transverse Momentum Dependent (TMD) PDF in this approach is explored as well.

Tensor polarization dependent fragmentation functions ande+e−→VπXat high energies

We present the systematic results for three dimensional fragmentation functions of spin one hadrons defined via quark-quark correlator. There are totally 72 such fragmentation functions, among them 18 are twist-2, 36 are twist-3 and 18 are twist-4. We also present the relationships between the twist-3 parts and those defined via quark-gluon-quark correlator obtained from the QCD equation of motion. We show that two particle semi-inclusive hadron production process $e^+e^-\to V\pi X$ at high energies is one of the best places to study the three-dimensional tensor polarization dependent fragmentation functions. We present the general kinematic analysis of this process and show that the cross section should be expressed in terms of 81 independent structure functions. After that we present parton model results for the hadronic tensor, the structure functions, the azimuthal and spin asymmetries in terms of these gauge invariant fragmentation functions at the leading order pQCD up to twist-3.

TMDs and SSAs in hadronic interactions

We present an overview on the current experimental and phenomenological status of transverse single spin asymmetries (tSSAs) in proton-proton collisions. In particular, we focus on large-$p_T$ inclusive pion, photon, jet, pion-jet production and Drell-Yan processes. For all of them theoretical estimates are given in terms of a generalised parton model (GPM) based on a transverse momentum dependent (TMD) factorisation scheme. Comparisons with the corresponding results in a collinear twist-3 formalism and in a modified GPM approach are also made. On the experimental side, a selection of the most interesting and recent results from RHIC is presented.

Two-photon dilepton production in proton-proton collisions: Two alternative approaches

We investigate different methods to incorporate the effect of photons in hard processes. We compare two different approaches used for calculating cross sections for two-photon $p p \to l^+ l^- X$ process. In one of the approaches photon is treated as a collinear parton in the proton. In the second approach recently proposed a $k_T$-factorization method is used. We discuss how results of the collinear parton model depend on the initial condition for the QCD evolution and discuss an approximate treatment where photon is excluded from the combined QCD-QED evolution. We demonstrate that it is not necessary to put photon into the evolution equation as often done recently but it is sufficient to use a simplified approach in which photon couples to quarks and antiquarks which by themselves undergo DGLAP evolution equations. We discuss sensitivity of the results to the choice of structure function parametrization and experimental cuts in the $k_T$-factorization approach. A new optimal structure function parametrization is proposed. We compare results of our calculations with recent experimental data for dilepton production and find that in most cases the contribution of the photon-photon mechanism is rather small. We discuss how to enhance the photon-photon contribution. We also compare our results to those of recent measurements of exclusive and semi-exclusive $e^+ e^-$ pair production with certain experimental data by the CMS collaboration.

Strange particle production in relativistic nucleus-nucleus collisions in the RHIC BES energy region**Supported by National Natural Science Foundation of China (11475068, 11247021), Excellent Youth Foundation of Hubei Scientific Committee (2006ABB036) and Key Laboratory foundation of Quark and Lepton Physics (Hua-Zhong Normal University)(QLPL2014P01)

The parton and hadron cascade model PACIAE is used to investigate strange particle production in Au + Au collisions at in different centralities and at , 11.5 and 7.7 GeV in the most central collision, respectively. It is shown that the transverse momentum distributions of strange particles by the PACIAE model fit the RHIC Beam Energy Scan experimental results well.

Nonperturbative approach to the parton model

In this paper, the nonperturbative parton distributions, obtained from the Lorentz contracted wave functions, are analyzed in the formalism of many-particle Fock components and their properties are compared to the standard perturbative distributions. We show that the collinear and IR divergencies specific for perturbative evolution treatment are absent in the nonperturbative version, however for large momenta [Formula: see text] (string tension), the bremsstrahlung kinematics is restored. A preliminary discussion of possible nonperturbative effects in DIS and high energy scattering is given, including in particular a possible role of multihybrid states in creating ridge-type effects.