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# NNLO constraints on proton PDFs from the SeaQuest and STAR experiments and other developments in the CTEQ-TEA global analysis

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## Abstract

We review progress in the global QCD analysis by the CTEQ-TEA group since the publication of CT18 parton distribution functions (PDFs) in the proton. Specifically, we discuss comparisons of CT18 NNLO predictions with the LHC 13 TeV measurements as well as with the FNAL SeaQuest and BNL STAR data on lepton pair production. The specialized CT18X PDFs approximating saturation effects are compared with the CT18sx PDFs obtained using NLL/NLO small-$x$ resummation. Short summaries are presented for the special CT18 parton distributions with fitted charm and with lattice QCD inputs. A recent comparative analysis of the impact of deuteron nuclear effects on the parton distributions by the CTEQ-JLab and CTEQ-TEA groups is summarized.

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The separation of the connected and disconnected sea partons, which were uncovered in the Euclidean path-integral formulation of the hadronic tensor, is accommodated with the CT18 parametrization of the global analysis of the parton distribution functions (PDFs). This is achieved with the help of the distinct small x x behaviors of these two sea parton components and the constraint from the lattice calculation of the ratio of the strange momentum fraction to that of the {\bar u} u ‾ or {\bar d} d ‾ in the disconnected insertion. This allows lattice calculations of separate flavors in both the connected and disconnected insertions to be directly compared with the global analysis results term by term.
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We report on the W and Z/γ* differential and total cross sections as well as the W+/W− and (W++W−)/(Z/γ*) cross section ratios measured by the STAR experiment at RHIC in p+p collisions at s=500 GeV and 510 GeV. The cross sections and their ratios are sensitive to quark and antiquark parton distribution functions. In particular, at leading order, the W cross section ratio is sensitive to the d¯/u¯ ratio. These measurements were taken at high Q2∼MW2,MZ2 and can serve as input into global analyses to provide constraints on the sea quark distributions. The results presented here combine three STAR datasets from 2011, 2012, and 2013, accumulating an integrated luminosity of 350 pb−1. We also assess the expected impact that our W+/W− cross section ratios will have on various quark distributions, and find sensitivity to the u¯−d¯ and d¯/u¯ distributions.
Article
Parton distribution functions (PDFs) describe the structure of hadrons as composed of quarks and gluons. They are needed to make predictions for short-distance processes in high-energy collisions and are determined by fitting to cross-section data. Definitions of the PDFs and their relations to high-energy cross sections are reviewed. The focus is on the PDFs in protons, but PDFs in nuclei are also discussed. The standard statistical treatment needed to fit the PDFs to data using the Hessian method is reviewed in some detail. Tests are discussed that critically examine whether the needed assumptions are indeed valid. Also presented are some ideas of what one can do in case tests indicate that the assumptions fail.
Article
The light-quark flavor dependence of the proton sea has been of great interest for many years because of its close connection with non-perturbative effects. One hypothesis is that the sea arises from the pion cloud of the proton. We make precise predictions based on the pion cloud idea for an anticipated future measurement. This is achieved by applying light cone perturbation theory and experimental constraints to a chiral Lagrangian so that the relevant Fock-space components of the nucleon wave function are computed with reasonable accuracy. Existing experimental information regarding the light flavor sea is studied, and predictions, including uncertainties, for future experimental results are provided. Future experiments will either confirm or rule out the idea that the pion cloud provides the flavor dependence of the proton's sea quark distribution, and have profound implications for understanding the nucleon-nucleon force.
Article
We determine a new set of parton distribution functions (ABMP16), the strong coupling constant $\alpha_s$ and the quark masses $m_c$, $m_b$ and $m_t$ in a global fit to next-to-next-to-leading order (NNLO) in QCD. The analysis uses the $\overline{\mathrm{MS}}$ scheme for $\alpha_s$ and all quark masses and is performed in the fixed-flavor number scheme for $n_f=3, 4, 5$. Essential new elements of the fit are the combined data from HERA for inclusive deep-inelastic scattering (DIS), data from the fixed-target experiments NOMAD and CHORUS for neutrino-induced DIS, and data from Tevatron and the LHC for the Drell-Yan process and the hadro-production of single-top and top-quark pairs. The theory predictions include new improved approximations at NNLO for the production of heavy quarks in DIS and for the hadro-production of single-top quarks. The description of higher twist effects relevant beyond the leading twist collinear factorization approximation is refined. At NNLO we obtain the value $\alpha_s^{(n_f=5)}(M_Z) = 0.1147 \pm 0.0008$.
Article
We present a new set of leading twist parton distribution functions, referred to as "CJ15", which take advantage of developments in the theoretical treatment of nuclear corrections as well as new data. The analysis includes for the first time data on the free neutron structure function from Jefferson Lab, and new high-precision charged lepton and W-boson asymmetry data from Fermilab. These significantly reduce the uncertainty on the d/u ratio at large values of x and provide new insights into the partonic structure of bound nucleons.
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Filling a gap in the current literature, this book is the first entirely dedicated to high energy QCD including parton saturation. It presents groundbreaking progress on the subject and describes many of the problems at the forefront of research, bringing postgraduate students, theorists and advanced experimentalists up to date with the current status of the field. A broad range of topics in high energy QCD are covered, most notably on the physics of parton saturation and the Color Glass Condensate (CGC). The material is presented in a pedagogical way, with numerous examples and exercises. Discussion ranges from the quasi-classical McLerran-Venugopalan model to the linear and non-linear BFKL/BK/JIMWLK small-x evolution equations. The authors adopt both a theoretical and experimental outlook and present the physics of strong interactions in a universal way, making it useful to physicists from various sub-communities and applicable to processes studied at high energy accelerators around the world. A selection of color figures is available online at www.cambridge.org/9780521112574.
Article
Quantum electrodynamics and electroweak corrections are an important ingredient for many theoretical predictions at the LHC. This paper introduces APFEL, a new PDF evolution library which allows for the first time to perform DGLAP evolution up to NNLO in QCD and to LO in QED, in the variable-flavor-number scheme and with either pole or MSbar heavy quark masses. APFEL consistently accounts for the QED corrections to the evolution of quark and gluon PDFs and for the contribution from the photon PDF in the proton. The coupled QCD+QED equations are solved in x-space by means of higher order interpolation, followed by Runge-Kutta solution of the resulting discretized evolution equations. APFEL is based on an innovative methodology for the sequential solution of the QCD and QED evolution equations and their combination, leading to a flexibility that allows to explore different options for the treatment of subleading terms. APFEL has been validated by means of detailed benchmark comparisons with other publicly available QCD and QED PDF evolution tools. Written in Fortran77, APFEL can also be easily used via the C/C++ and Python interfaces, and is publicly available from the HepForge repository.
Article
Heavy flavour production is an important quantum chromodynamics (QCD) process both in its own right and as a key component of precision global QCD analysis. Apparent disagreements between fixed-flavour scheme calculations of b-production rate with experimental measurements in hadro-, lepto- and photo-production provide new impetus for a thorough examination of the theory and phenomenology of this process. We review existing methods of calculation and place them in the context of the general perturbative QCD framework of Collins. A distinction is drawn between scheme dependence and implementation issues related to quark mass effects near threshold. We point out a so far overlooked kinematic constraint on the threshold behaviour, which greatly simplifies the variable flavour number scheme. This obviates the need for the elaborate existing prescriptions and leads to robust predictions. It can facilitate the study of current issues on heavy flavour production as well as precision global QCD analysis.
Article
A method to facilitate the consistent inclusion of cross-section measurements based on complex final-states from HERA, TEVATRON and the LHC in proton parton density function (PDF) fits has been developed. This can be used to increase the sensitivity of LHC data to deviations from Standard Model predictions. The method stores perturbative coefficients of NLO QCD calculations of final-state observables measured in hadron colliders in look-up tables. This allows the aposteriori inclusion of parton density functions (PDFs), and of the strong coupling, as well as the aposteriori variation of the renormalisation and factorisation scales in cross-section calculations. The main novelties in comparison to original work on the subject are the use of higher-order interpolation of Lagrangian form, which substantially improves the trade-off between accuracy and memory use, and a CPU and computer memory optimised way to construct and store the look-up table using modern software tools. It is demonstrated that a sufficient accuracy on the cross-section calculation can be achieved with reasonably small look-up table size by using the examples of jet production and electro-weak boson (Z,W) production in proton-proton collisions at a center-of-mass energy of 14TeV at the LHC. The use of this technique in PDF fitting is demonstrated in a PDF-fit to HERA data and simulated LHC jet cross-sections as well as in a study of the jet cross-section uncertainties at various centre-of-mass energies.
Article
We discuss a general framework for the inclusion of heavy quark mass contributions to deep-inelastic structure functions and their perturbative matching to structure functions computed in variable-mass schemes. Our approach is based on the so-called FONLL method, previously introduced and applied to heavy quark hadroproduction and photoproduction. We define our framework, provide expressions up to second order in the strong coupling, and use them to construct matched expressions for structure functions up to NNLO. After checking explicitly the consistency of our results, we perform a study of the phenomenological impact of heavy quark terms, and compare results obtained at various perturbative orders, and with various prescriptions for the treatment of subleading terms, specifically those related to threshold behaviour. We also consider the heavy quark structure function F2c and discuss issues related to the presence of mass singularities in their coefficient functions.
Article
Recent data give unexpectedly large cross-sections for charmed particle production at high xF in hadron collisions. This may imply that the proton has a non-negligible uudc Fock component. The interesting consequences of such a hypothesis are explored.
Article
We present the program Top++ for the numerical evaluation of the total inclusive cross-section for producing top quark pairs at hadron colliders. The program calculates the cross-section in a) fixed order approach with exact NNLO for $q\bar q\to t\bar t+X, qq\to t\bar t+X, q\bar q'\to t\bar t+X, qq'\to t\bar t+X$ and through approximate NNLO for $gg\to t\bar t+X$ and b) by including soft-gluon resummation for the hadronic cross-section in Mellin space with full next-to-next-to-leading logarithmic accuracy. The program offers the user significant flexibility through the large number (31) of available options. Top++ is written in C++. It has a very simple to use interface that is intuitive and directly reflects the physics. The running of the program requires no programing experience from the user.
Article
The existence of the five-quark Fock states for the intrinsic charm quark in the nucleons was suggested some time ago, but conclusive evidence is still lacking. We generalize the previous theoretical approach to the light-quark sector and study possible experimental signatures for such five-quark states. In particular, we compare the d-ū and ū + d-s-s data with the calculations based on the five-quark Fock states. The qualitative agreement between the data and the calculations is interpreted as evidence for the existence of the intrinsic light-quark sea in the nucleons. The probabilities for the |uuduū and |uuddd Fock states are also extracted.
Article
A detailed proof of hard scattering factorization is given with the inclusion of heavy quark masses. Although the proof is explicitly given for deep-inelastic scattering, the methods apply more generally The power-suppressed corrections to the factorization formula are uniformly suppressed by a power of \Lambda/Q, independently of the size of heavy quark masses, M, relative to Q. Comment: 56 pages, 13 figures; RevTeX & epsf
Article
A unified QCD formulation of leptoproduction of massive quarks in charged current and neutral current processes is described. This involves adopting consistent factorization and renormalization schemes which encompass both vector-boson-gluon-fusion (flavor creation) and vector-boson-massive-quark-scattering (flavor excitation) production mechanisms. It provides a framework which is valid from the threshold for producing the massive quark (where gluon-fusion is dominant) to the very high energy regime when the typical energy scale \mu is much larger than the quark mass m_Q (where the quark-scattering should be prevalent). This approach effectively resums all large logarithms of the type (alpha_s(mu) log(mu^2/m_Q^2)^n which limit the validity of existing fixed-order calculations to the region mu ~ O(m_Q). We show that the (massive) quark-scattering contribution (after subtraction of overlaps) is important in most parts of the (x, Q) plane except near the threshold region. We demonstrate that the factorization scale dependence of the structure functions calculated in this approach is substantially less than those obtained in the fixed-order calculations, as one would expect from a more consistent formulation. Comment: LaTeX format, 29 pages, 11 figures. Revised to make auto-TeX-able
Article
Existing calculations of heavy quark production in charged-current and neutral current lepton-hadron scattering are formulated differently because of the artificial distinction of light'' and heavy'' quarks made in the traditional approach. A proper QCD formalism valid for a wide kinematic range from near threshold to energies much higher then the quark mass should treat these processes in a uniform way. We formulate a unified approach to both types of leptoproduction processes based on the conventional factorization theorem. In this paper, we present the general framework with complete kinematics appropriate for arbitrary masses, emphasizing the simplifications provided by the helicity formalism. We illustrate this approach with an explicit calculation of the leading order contribution to the quark structure functions with general masses. This provides the basis for a complete QCD analysis of charged current and neutral current leptoproduction of charm and bottom quarks to be presented in subsequent papers. Comment: LaTeX format, 28 pages, 7 figures. Revised to make auto-TeX-able
Article
We investigate a simplified version of the ACOT prescription for calculating deeply inelastic scattering from Q^2 values near the squared mass M_H^2 of a heavy quark to Q^2 much larger than M_H^2.