Extent of sensitivity of single photon production to parton distribution functions

We have studied the production of single isolated prompt photons in high-energy proton–proton collisions at the RHIC ( \(\sqrt {s}\) = 200 GeV) and the LHC ( \(\sqrt {s}\) = 7 TeV) energies within the framework of perturbative QCD upto next-to leading order of strong coupling (α _s). We have used five different parametrizations of parton distribution function (PDF) starting from the old CTEQ4M to the new CT10 distributions and compared our results with the recent single-prompt photon data from the PHENIX and the CMS Collaborations. The prompt photon cross-section is found to be described equally well by all the PDFs within the experimental errors at the RHIC and the LHC energies. The deviation in the single-prompt photon yield for different PDF sets is within ±20% when compared to CTEQ4M, indicating the upper bound of uncertainty in determining the gluon density. The diphoton measurement could be a potential candidate to constrain the gluon distribution inside the proton.     

Factorization scheme and parton distributions in the polarized virtual photon target

We investigate spin-dependent parton distributions in the polarized virtual photon target in perturbative QCD up to the next-to-leading order (NLO). In the case , where is the mass squared of the probe (target) photon, the parton distributions can be predicted completely up to NLO, but they are factorization-scheme dependent. We analyze the parton distributions in six different factorization schemes and discuss their scheme dependence. We study, in particular, the QCD and QED axial anomaly effects on the first moments of the parton distributions to see the interplay between the axial anomalies and factorization schemes. We also show that the factorization-scheme dependence is characterized by the large-x behaviors of the quark distributions in the virtual photon. The gluon distribution is predicted to be the same up to NLO among the six factorization schemes examined. In particular, the first moment of the gluon distribution is found to be factorization-scheme independent up to NLO. Received: 24 January 2001 / Published online: 18 May 2001     

Quantifying uncertainties in the high-energy neutrino cross-section

The predictions for high-energy neutrino and antineutrino deep inelastic scattering cross-sections are compared within the conventional DGLAP formalism of next-to-leading order QCD, using the latest parton distribution functions (PDF) such as CT10, HERAPDF1.5 and MSTW08 and taking account of PDF uncertainties. From this, a benchmark cross-section and uncertainty are derived which is consistent with the results obtained earlier using the ZEUS-S PDFs. The use of this is advocated for analysing data from neutrino telescopes, in order to facilitate comparison between their results.     

Dynamical parton distributions from DGLAP equations with nonlinear corrections

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(Q~2 2 GeV~2).Furthermore,our analysis shows that the input with flavor-asymmetric sea components better reproduces the structure functions at high Q~2.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 GeV~2,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 Q~2.     

Transversity and its accompanying T-odd distribution from Drell–Yan processes with pion-proton collisions

This paper studies the possibility of direct extraction of the transversity and its accompanying T-odd parton distribution function (PDF) from Drell–Yan (DY) processes with unpolarized pion beam and with both unpolarized and transversely polarized proton targets. At present, such an extraction can be performed with the COMPASS experiment at CERN. The preliminary estimations performed for the COMPASS kinematic region demonstrate that it is quite realistic to extract both transversity and its accompanying T-odd PDF under COMPASS conditions. PACS 13.60.Hb, 13.88.+e     

Resummation of large logarithms in the heavy-quark effects on the parton distributions inside the virtual photon

We discuss the resummation of the large logarithmic terms appearing in the heavy-quark effects on parton distribution functions inside the virtual photon. We incorporate heavy-quark mass effects by changing the initial condition of the leading-order DGLAP evolution equation. In a certain kinematical limit, we recover the logarithmic terms of the next-to-leading order heavy-quark effects obtained in the previous work. This method enables us to resum the large logarithmic terms due to heavy-quark mass effects on the parton distributions in the virtual photon. We numerically calculate parton distributions using the formulae derived in this work, and we discuss the property of the resummed heavy-quark effects.     

x-distribution of non-singlet structure function at low and high x

In recent years, study of parton distribution function (PDF) has itself become a topic of significant interest. To overcome the shortcoming of the conventional PDF, several alternative methods have been proposed in recent years like neural network formalism. In the present work, x distribution of the non-singlet structure function is obtained using the recently reported complete solution of Taylor-approximated DGLAP equation. The results are compared with exact results as well as CCFR data.     

通过基矢光前量子化方法研究K介子

为研究K介子的性质,通过基矢光前量子化(BLFQ)方法获得K介子的光前波函数(LFWF)。使用的光前哈密顿量中包含了动能项、横向与纵向禁闭势以及夸克-胶子相互作用,其中横向禁闭势借鉴了光前全息量子色动力学(LFHQCD)模型的禁闭势。基矢空间包括领头阶与次领头阶的Fock空间。在前期工作的基础上,只引入了奇异夸克的质量作为唯一额外参数,使K>介子的质量与实验值相匹配。基于K介子领头阶Fock空间的LFWF,计算了K介子的部分子分布振幅(PDA),其结果与量子色动力学(QCD)微扰论在零夸克质量近似下计算的结果相近。本工作得到的K介子的电磁形状因子(FF)与欧洲核子中心(CERN)超级质子同步加速器 (SPS)以及费米国家加速器实验室(FNAL)的实验结果一致。从领头阶Fock空间的LFWF计算出的电磁半径与粒子物理数据表(PDG)的实验值相近。计算出的K介子部分子分布函数(PDF),QCD演化后,在实验能标下的K介子和$ \pi $介子中价夸克u的PDF之比与CERN-NA-003的实验数据在整体趋势上大体相符。此外,在计算出的K介子PDF中,价夸克携带的纵向动量之比,$ \langle x_{uv}\rangle/\langle x_{sv}\rangle $,约为$ 2/3 $,这个数值与Bethe-Salpeter equation(BSE)模型以及密西根州立大学格点QCD(MSULat)模型的计算结果相近。还计算了K介子的结构函数,发现与BLFQ考虑有效 Nambu–Jona-Lasinio相互作用(BLFQ-NJL)模型的结果有显著差别。K介子的结构函数有望在将来的电子离子对撞机(EIC)实验中得到观测与检验。     

Parton distribution functions and nuclear EMC effect in a statistical model

A new and simple statistical approach is performed to calculate the parton distribution functions (PDFs) of the nucleon in terms of light-front kinematic variables.Analytic expressions of x-dependent PDFs are obtained in the whole x region.And thereafter,we treat the temperature T as a parameter of the atomic number A to explain the nuclear EMC effect in the region x ∈ [0.2,0.7].We give the predictions of PDF ratios,and they are very different from those by other models,thus experiments aiming at measuring PDF ratios are suggested to provide a discrimination of different models.     

Dynamics of the Landau–Pomeranchuk–Migdal effect in Au + Au collisions at s=200AGeV

We study the role played by the Landau–Pomeranchuk–Migdal (LPM) effect in relativistic collisions of hadrons and heavy nuclei, within a parton cascade model. We find that the LPM effect strongly affects the gluon multiplication due to radiation and considerably alters the spacetime evolution of the dynamics of the collision. It ensures a multiplicity distribution of hadrons in agreement with the experimental proton–proton data. We study the production of single photons in relativistic heavy ion collisions and find that the inclusion of LPM suppression leads to a reduction in the single photon yield at small and intermediate transverse momenta. The parton cascade calculation of the single photon yield including the LPM effect is shown to be in good agreement with the recent PHENIX data taken at the Relativistic Heavy-Ion Collider.     

Parton distribution functions at LO,NLO and NNLO with correlated uncertainties between orders

Sets of parton distribution functions (PDFs) of the proton are reported for the leading (LO), next-to-leading (NLO) and next-to-next-to-leading-order (NNLO) QCD calculations. The parton distribution functions are determined with the HERAFitter program using the data from the HERA experiments and preserving correlations between uncertainties for the LO, NLO and NNLO PDF sets. The sets are used to study cross-section ratios and their uncertainties when calculated at different orders in QCD. A reduction of the overall theoretical uncertainty is observed if correlations between the PDF sets are taken into account for the ratio of \(WW\) di-boson to \(Z\) boson production cross sections at the LHC.     

Photon structure functions beyond the SUSY threshold

We evolve virtual photon parton densities up to the SUSY threshold and higher using coupled inhomogeneous DGLAP differential equations. Reliable input parameterizations were available from the c-quark threshold. Limited (target photon virtuality) dependence is observed. The difference to the photon structure function is shown to be significant with the introduction of SUSY dependent splitting functions. A negligible difference is observed by letting the gluino mass enter after the squark mass. An effort is made to include the squark threshold effect in such a way that both the renormalization group equations are satisfied and the perturbative calculation is reproduced. Received: 25 August 2000 / Revised version: 1 November 2000 / Published online: 21 December 2000     

Implications of CMS analysis of photon-photon interactions for photon PDFs

As part of a recent analysis of exclusive two-photon production of W+W-pairs at the LHC, the CMS experiment used di-lepton data to obtain an "effective" photon-photon luminosity. We show how the CMS analysis on their 8 TeV data, along with some assumptions about the likelihood for events in which the proton breaks up to pass the selection criteria, can be used to significantly constrain the photon parton distribution functions, such as those from the CTEQ, MRST, and NNPDF collaborations. We compare the data with predictions using these photon distributions, as well as the new LUXqed photon distribution. We study the impact of including these data on the NNPDF2.3 QED, NNPDF3.0 QED and CT14 QEDinc fits. We find that these data place a useful and complementary cross-check on the photon distribution, which is consistent with the LUXqed prediction while suggesting that the NNPDF photon error band should be significantly reduced. Additionally, we propose a simple model for describing the two-photon production of W+W-at the LHC. Using this model, we constrain the number of inelastic photons that remain after the experimental cuts are applied.     

Cold Nuclear Matter Effects on Isolated Prompt Photon and Isolated Prompt Photon+Jet Productions in Relativistic Heavy-Ion Collisions

We investigate the cold nuclear matter(CNM) effects on isolated prompt photon and isolated prompt photon associated jet productions in nuclear collisions at the NLO accuracy by using the EPS09 NLO nuclear parton distribution functions and their error sets.Nuclear modification factors of isolated prompt photon and isolated prompt photon+jet productions due to CNM effects in p+A and A+A reactions at the RHIC and the LHC are provided with varying rapidity and transverse momentum of the final state photon.It is shown that the CNM effects on isolated prompt photon and photon+jet are modest,which give a small enhancement at low pT region and a more obvious suppression at large pT at central rapidity.At forward rapidity a pronounced suppression of γ as well as γ+jet is always observed.     

Parton distributions for LO generators

We present a study of the results obtained by combining LO partonic matrix elements with either LO or NLO parton distributions. These are compared to the best prediction using NLO for both matrix elements and parton distributions. The aim is to determine which parton distributions are most appropriate to use in those cases where only LO matrix elements are available, e.g. as in many Monte Carlo generators. Both LO and NLO parton distributions have flaws, sometimes serious, for some processes, so a modified optimal LO set is suggested. We investigate a wide variety of processes, and the new modified LO* PDF works at least as well as, and often better than, both LO and NLO PDFs in nearly all cases.     

Resummation of the jet broadening in DIS

We calculate the leading and next-to-leading logarithmic resummed distribution for the jet broadening in deep inelastic scattering, as well as the power correction for both the distribution and mean value. A truncation of the answer at NLL accuracy, as is standard, leads to unphysical divergences. We discuss their origin and show how the problem can be resolved. We then examine DIS specific procedures for matching to fixed order calculations and compare our results to the data. One of the tools developed for the comparison is an NLO parton distribution evolution code. When compared to PDF sets from MRST and CTEQ it reveals limited discrepancies in both. Received: 16 October 2001 / Published online: 12 April 2002     

A parton shower model for hadronic two-photon process in e+e− scattering

A new model of QCD parton shower is proposed which is dedicated to two-photon processes in e⁺e^? scattering. When hadron jets are produced, the photon may resolve into quark-antiquark pairs so that the structure functions of the photon should be introduced. Based on the Altarelli-Parisi equation for these functions, an algorithm is formulated that allows us to construct a model for parton showers for the photon. Our model consists of two parts, one of which describes the deep inelastic scattering of the photon and the other one the scattering of two quasi-real photons. Using the model some results are presented on parton distributions and jet production.     

Generalized parton distributions of the photon

We present a first calculation of the generalized parton distributions of the photon (both polarized and unpolarized) using overlaps of light-front wave functions at leading order in α and zeroth order in αs; for non-zero transverse momentum transfer and zero skewness. We present the novel parton content of the photon in transverse position space.     

Measurement of dijet cross-sections in low {\rm Q}^2 ep collisions and the extraction of an effective parton density for the virtual photon

The triple-differential dijet cross-section, , is measured with the H1 detector at HERA as a function of the photon virtuality , the fraction of the photon's momentum carried by the parton entering the hard scattering, , and the square of the mean transverse energy, , of the two highest jets. Jets are found using a longitudinal boost-invariant clustering algorithm in the center of mass frame. The measurements cover the ranges GeV in virtuality and in inelasticity y. The results are well described by leading order QCD models which include the effects of a resolved component to the virtual photon. Models which treat the photon as point-like fail to describe the data. An effective leading order parton density for the virtual photon is extracted as a function of the photon virtuality, the probing scale and the parton momentum fraction. The and probing scale dependences of the parton density show characteristic features of photon structure, and a suppression of this structure with increasing is seen. Received: 18 December 1998 / Published online: 25 February 2000