We present a study in which the possibility of a (sizable) nonperturbative contribution to the charm parton distribution function (PDF) in a nucleon is investigated together with theoretical issues arising in its interpretation. The separation of the universal component of the nonperturbative charm from the rest of the radiative contributions is also discussed. We illustrate the potential impact of a nonperturbative charm PDF on LHC scattering processes. An estimate of nonperturbative charm magnitude in the CT14 and CT14HERA2 global QCD analyses at the next-to-next-to leading order (NNLO) in the QCD coupling strength is given by including the latest experimental data from HERA and the Large Hadron Collider. We show a comparison between different models of intrinsic charm and illustrate prospects for standard candle observables at the LHC

Dulat, Sayipjamal

Gao, Jun

Guzzi, Marco

Hou, Tie-Jiun

Huston, Joey

Nadolsky, Pavel

Schmidt, Carl

Winter, Jan

Xie, Keping

Yuan, C.-P.

English

DigitalCommons@Kennesaw State University

Kennesaw State University DigitalCommons@Kennesaw State University Faculty Publications Faculty Works Hub Fall 11-14-2018 CTEQ-TEA parton distribution functions with intrinsic charm Marco Guzzi Kennesaw State University, mguzzi@kennesaw.edu Tie-Jiun Hou National Taiwan Normal University Sayipjamal Dulat Xinjiang University Jun Gao Shanghai Jiaotong University Joey Huston Michigan State University See next page for additional authors Follow this and additional works at: https://digitalcommons.kennesaw.edu/facpubs  Part of the Elementary Particles and Fields and String Theory Commons Recommended Citation Guzzi, Marco; Hou, Tie-Jiun; Dulat, Sayipjamal; Gao, Jun; Huston, Joey; Nadolsky, Pavel; Schmidt, Carl; Winter, Jan; Xie, Keping; and Yuan, C.-P., "CTEQ-TEA parton distribution functions with intrinsic charm" (2018). Faculty Publications. 6506. https://digitalcommons.kennesaw.edu/facpubs/6506 This Article is brought to you for free and open access by the Faculty Works Hub at DigitalCommons@Kennesaw State University. It has been accepted for inclusion in Faculty Publications by an authorized administrator of DigitalCommons@Kennesaw State University. For more information, please contact digitalcommons@kennesaw.edu. Authors Marco Guzzi, Tie-Jiun Hou, Sayipjamal Dulat, Jun Gao, Joey Huston, Pavel Nadolsky, Carl Schmidt, Jan Winter, Keping Xie, and C.-P. Yuan This article is available at DigitalCommons@Kennesaw State University: https://digitalcommons.kennesaw.edu/facpubs/6506 © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/).EPJ Web of Conferences 192, 00003 (2018) https://doi.org/10.1051/epjconf/201819200003QCD@Work  2018CTEQ-TEA parton distribution functions with intrinsiccharmMarco Guzzi1,∗, Tie-Jiun Hou2,6, Sayipjamal Dulat3, Jun Gao4, Joey Huston5, PavelNadolsky6, Carl Schmidt5, JanWinter5, Keping Xie6, and C.-P. Yuan51Department of Physics, Kennesaw State University, 370 Paulding Ave., 30144 Kennesaw, GA, U.S.A.2National Tsing Hua University, Hsinchu City, Taiwan.3School of Physics Science and Technology & Center for Theoretical Physics, Xinjiang University,Urumqi, Xinjiang 830046 China.4INPAC, Shanghai Key Laboratory for Particle Physics and Cosmology& School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.5Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 U.S.A.6Department of Physics, Southern Methodist University, Dallas, TX 75275-0181, U.S.A.Abstract. We present a study in which the possibility of a (sizable) nonpertur-bative contribution to the charm parton distribution function (PDF) in a nucleonis investigated together with theoretical issues arising in its interpretation. Theseparation of the universal component of the nonperturbative charm from therest of the radiative contributions is also discussed. We illustrate the poten-tial impact of a nonperturbative charm PDF on LHC scattering processes. Anestimate of nonperturbative charm magnitude in the CT14 and CT14HERA2global QCD analyses at the next-to-next-to leading order (NNLO) in the QCDcoupling strength is given by including the latest experimental data from HERAand the Large Hadron Collider. We show a comparison between different mod-els of intrinsic charm and illustrate prospects for standard candle observables atthe LHC.1 IntroductionThe principle of the global analysis is to use QCD theory to analyze a broad range of exper-imental data, including precision data from HERA, the Tevatron, and the Large Hadron Col-lider (LHC). In particular, theoretical predictions for short-distance scattering processes al-low the measurement, within some approximations, of universal parton distribution functions(PDFs) for the proton. As new experimental measurements from the LHC grow increasinglyprecise, novel challenges arise in extracting accurate predictions for the parton content of theproton in global QCD analysis of PDFs needed for advanced tests of the Standard Model andpossible physics beyond the Standard Model. A recently published CTEQ-TEA (CT) globalanalysis of experimental data [1] produced the CT14NNLO PDFs, referred to as the CT14PDFs. The analysis is based on the next-to-next-to-leading order (NNLO) approximation forperturbative QCD.∗e-mail: mguzzi@kennesaw.edu2EPJ Web of Conferences 192, 00003 (2018) https://doi.org/10.1051/epjconf/201819200003QCD@Work  20181.1 The perturbative charm PDFIn global PDF analyses, all QCD parameters, such as αs and the quark masses, are correlatedwith the PDFs. The determination of the PDFs depends not only on the data sample includedin the fits, but also on the specific theory assumptions and underlying physics models. Asone such choice made in the standard CT PDF sets, the charm quark and antiquark PDFs aretaken to be zero below a low energy scale Qc = Q0 of order of the charm mass. In the CT14analysis, the charm quark and antiquark PDFs were turned on at the scale Qc = Q0 = mc =1.3 GeV, with an initial O(α2s) distribution consistent with NNLOmatching [2, 3] to the three-flavor result. At higher Q, most of the charm PDF is generated from the DGLAP evolutionthat proceeds through perturbative splittings of gluons and light-flavor quarks. Hence, thecharm PDF from a standard global analysis is called “perturbative” and it is obtained byperturbatively evolving the PDFs from the initial scale Qc to the experimental data scale Q.1.2 A nonperturbative component for the charm PDFIn addition to the perturbative charm production mechanism, it is believed that “intrinsiccharm quarks” may emerge from the nonperturbative structure of the hadronic bound state.The plausibility of the intrinsic charm (IC) component, its dynamical origin, and its actualmagnitude have been a subject of a long-standing debate. Indeed, QCD theory rigorously pre-dicts existence of power-suppressed (higher-twist) channels for charm quark production thatare independent of the leading-power (twist-2, or perturbative) production of charm quarks.The IC quarks have been associated with the excited |uudcc〉 Fock state of the proton wavefunction [4–9] and predicted by meson-baryon models [10–13]. The range of validity of thePDFmodels with nonperturbative charm has been appraised in a recent CT analysis publishedin Ref. [14] and in other recent studies [15–19].1.3 Fitted charm and nonperturbative charm parametrizationsStarting from the factorization theorem for DIS cross sections with massive fermions, that is afundamental QCD result, one can draw a consequential distinction between the “fitted” charmPDF parametrization and the nonperturbative charm PDF. The fitted charm PDF accountsfor the nonperturbative charm plus other (possibly not universal) higher O(αs) higher powersuppressed terms. Since the perturbative charm PDF component cancels near the thresholdup to a higher order, the fitted charm component may approximate for a missing higher-orderterm or a power-suppressed nonperturbative component. The genuine nonperturbative charmPDF instead, is defined by the means of power counting of radiative contributions to DIS.Assuming that this additional nonperturbative charm component can be factorized like theperturbative charm component, one is able to examine how it differs from the perturbativecharm, and how it depends on theoretical inputs in a global QCD analysis of PDFs. Inprinciple, the intrinsic charm content would be suppressed by powers of (Λ2QCD/m2c), but,since this ratio is not very small, it may be relevant in some processes such as precise DIS. Fora more detailed description of QCD factorization with power suppressed charm contributions,we refer the reader to the recent CTEQ-TEA analysis of Ref. [14].1.4 Valence-like and sea-like models for the charm PDF parametrizationVarious model estimates suggest a power-suppressed charm cross section of a modest size:of order of a fraction of the α2s component in DIS charm production, carrying less than abouta percent of the proton’s momentum. We examine a more extensive list of nonperturbative3EPJ Web of Conferences 192, 00003 (2018) https://doi.org/10.1051/epjconf/201819200003QCD@Work  2018models, fit the most complete set of DIS data from HERA as well as the data from the LHCand (optionally) the EMC experiment [20], and utilize a PDF parametrization that results ina more physical behavior. Given that several mechanisms may give rise to the fitted charm,we will parametrize it by two generic shapes, a “valence-like” and a “’sea-like” shape. Thetwo shapes arise in a variety of dynamical models.A valence-like shape has a local maximum at x above 0.1 and satisfies fq/p(x,Qc) ∼x−a1 with a1  1/2 for x → 0 and fq/p(x,Qc) ∼ (1 − x)a2 with a2  3 for x → 1. Thedistributions for valence u and d quarks fall into this broad category, as well as the “intrinsic”sea-quark distributions that can be naturally generated in several ways [6], e.g., for all flavors,nonperturbatively from a |uudQQ〉 Fock state in light-cone [4, 5, 7–9] and meson-baryonmodels [10–13]; for ū and d̄, from connected diagrams in lattice QCD [21].1 The approximateBrodsky-Hoyer-Peterson-Sakai (BHPS) model [4, 5] parametrizes the charm PDF at Q0 by avalence-like nonperturbative functionĉ(x) =12A x2[13(1 − x)(1 + 10x + x2) − 2x(1 + x) ln (1/x)]. (1)This function is obtained from a light-cone momentum distribution by taking the charm massto be much heavier than the masses of the proton and light quarks: mc  Mp,mu,md. A isthe normalization factor that is to be determined from the fit. The BHPS1 and BHPS2 globalfits are obtained with this parametrization choice and are illustrated in Sec. 2 below.Instead of approximating the probability integral as in the original BHPS model, the ĉ(x)can also be obtained by solving the BHPS model for the |uudcc̄〉 Fock state numericallyand keeping the exact dependence on Mp,mu, and md. In this BHPS model, the intrinsicquark distributions are determined by starting from a |uudqq̄〉 proton Fock state, where theprobability differential for a quark i to carry a momentum fraction xi is given bydP(x1, . . . , x5) = A dx1 . . . dx5 δ(1 −5∑i=1xi)1[M2p −∑5i=1m2ix2i]2 . (2)This generalized BHPS model, used in the context of the CT14HERA fit with IC, is namedBHPS3. We do not, however, include the intrinsic contribution to the s quark PDF, becauseit is overwhelmed by the very large strange PDF uncertainty. The presence of an intrinsiccomponent for the strange quark does not affect our conclusions about the nonperturbativecharm.A sea-like component is usually monotonic in x and satisfies fq/p(x,Qc) ∼ x−a1 for x → 0and fq/p(x,Qc) ∼ (1 − x)a2 for x → 1, with a1 slightly above 1, and a2  5. This behavioris typical for the leading-power, or “extrinsic” production. For example, an (anti)quark PDFwith this behavior originates from g → qq̄ splittings in perturbative QCD, or from discon-nected diagrams in lattice QCD (see Ref. [21] for details). Even a missing next-to-next-to-next-to-leading order (N3LO) leading-power correction may produce a sea-like contributionat x  0.1, where the valence-like components are suppressed. In the SEA model, the charmPDF is parametrized by a “sea-like” nonperturbative function that is proportional to the lightquark distributions:ĉ(x) = A(d(x,Q0) + u(x,Q0)). (3)This model is assumed with the SEA1 and SEA2 PDF sets which are illustrated in Sec. 2below. Finally, the normalization coefficient A in the models described above can be derived1In contrast to the light flavors, in lattice QCD a charm PDF arises exclusively from disconnected diagrams [22].This suggests that c and c̄ contributions in DIS are connected to the hadron target by gluon insertions.4EPJ Web of Conferences 192, 00003 (2018) https://doi.org/10.1051/epjconf/201819200003QCD@Work  2018∆χ2<x>ICBHPS1BHPS2SEA1SEA2CT14  Q0=1.3GeVBHPSBHPS + Tier-2SEASEA + Tier-2-40-20 0 20 40 60 80 100 120 0  0.01  0.02  0.03∆χ2<x>ICBHPS3CT14HERA2  Q0=1.3GeVBHPSBHPS + Tier-2SEASEA + Tier-2-40-20 0 20 40 60 80 100 120 0  0.01  0.02  0.03Figure 1. The change ∆χ2 in the goodness of fit to the CT14 (left) and CT14HERA2 (right) data setsas a function of the charm momentum fraction 〈x〉IC for the BHPS (blue) and SEA (red) models. Solid(dashed) lines represent the total χ2 and the partial χ2global, as defined in Sec. 2.from the charm momentum fraction (first moment) at scale Q:〈x〉IC =∫ 10x [c(x,Q0) + c̄(x,Q0)] dx. (4)By its definition, 〈x〉IC is evaluated at the initial scale Q0. It is to be distinguished from thefull charm momentum fraction 〈x〉c+c̄(Q) at Q > Qc, which rapidly increases with Q becauseof the admixture of the twist-2 charm component.2 Results of the global analysisIn this section we illustrate the main findings of our global analysis in which we assume thatthe additional nonperturbative charm component can be factorized in a similar fashion to theperturbative one. To gauge the preference of the global QCD data to a specific 〈x〉IC, weexamine the goodness-of-fit function χ2 ≡ χ2global + P, constructed in the CT14 method fromthe global χ2global and a “tier-2” statistical penalty P [1]. It is convenient to compare each fitwith an 〈x〉IC  0 to the “null-hypothesis” fit obtained assuming 〈x〉IC = 0. Thus, we start bycomputing ∆χ2 ≡ χ2−χ20,where χ2 and χ20 are given for 〈x〉IC  0 and 〈x〉IC = 0, respectively,at 50 values of 〈x〉IC and default Q0 = mpolec = 1.3 GeV. We plot the resulting ∆χ2 behaviorin Fig. 1. The CT14 (CT14HERA2) data sets are compared against the approximate (exact)solution of the BHPS model, respectively. The SEA charm parametrizations are constructedas in Eq. (3) in terms of the respective CT14 or CT14HERA2 light-antiquark parametriza-tions. We see from Fig. 1 that large amounts of intrinsic charm are disfavored for all modelsunder scrutiny. A mild reduction in χ2, however, is observed for the BHPS fits, roughly at〈x〉IC = 1%, both in the CT14 and CT14HERA2 frameworks. The significance of this re-duction and the upper limit on 〈x〉IC depends on the assumed criterion. In CTEQ practice, aset of PDFs with ∆χ2 smaller (larger) than 100 units is deemed to be accepted (disfavored)at about 90% C.L. Thus, a reduction of χ2 by less than forty units for the BHPS curves hassignificance roughly of order one standard deviation. The new upper limits on 〈x〉IC in theCT14 and CT14HERA2 analyses at the 90% C.L.: 〈x〉IC  0.021 for CT14 BHPS; 〈x〉IC 0.024 for CT14HERA2 BHPS; 〈x〉IC  0.016 for CT14 and CT14HERA2 SEA.5EPJ Web of Conferences 192, 00003 (2018) https://doi.org/10.1051/epjconf/201819200003QCD@Work  2018H(gluon fustion) [pb]Z [pb]LHC 13 TeV1603.09222ATLAS-CONF-2016-081CT14 NNLO 90% C.L., mpolec    =1.3 GeVBHPS1BHPS2BHPS3SEA1SEA2 40 45 50 1850  1900  1950  2000  2050W-  [nb]W+ [nb]LHC 13 TeV1603.09222CT14 NNLO 90% C.L., mpolec    =1.3 GeVBHPS1BHPS2BHPS3SEA1SEA28.08.59.09.511.0 11.5 12.0Figure 2. CT14 NNLO H (gluon-gluon fusion), Z, W+, and W− production cross sections with an ICPDF component at the LHC√s = 13 TeV, with pole mass mpolec = 1.3 GeV. The 90% C.L. uncertaintyregions for CT14 at NNLO and experimental points from ATLAS [23, 24] are also shown.2.1 Impact of IC on the electroweak Z and H boson production cross sections atthe LHCFigure 2 illustrates predictions of the total cross sections for inclusive production of elec-troweak bosons W±, Z0, and H (via gluon-gluon fusion) for the BHPS and SEA models atthe LHC√s = 13 TeV with charm quark mass mc = 1.3 GeV. To provide a visual measureof the CT14NNLO uncertainty, each figure shows an error ellipse corresponding to CT14NNLO at the 90% C.L. and experimental data points relative to measurements from the AT-LAS collaboration [23, 24]. The W and Z inclusive cross sections (multiplied by branchingratios for the decay into one charged lepton flavor), are calculated by using the Vrap v0.9program [25, 26] at NNLO in QCD, with the renormalization and factorization (µR and µF)scales set equal to the invariant mass of the vector boson. The Higgs boson cross sections viagluon-gluon fusion are calculated at NNLO in QCD by using the iHixs v1.3 program [27], inthe heavy-quark effective theory (HQET) with finite top quark mass correction, and with theQCD scales set equal to the invariant mass of the Higgs boson. The central value predictionsfor the BHPS and SEA models are all within the CT14 NNLO uncertainties, with BHPS veryclose to the CT14 nominal fit. The impact of IC on these key LHC observables is mild.3 ConclusionsWe explored the possibility of sizeable nonperturbative contribution to charm PDF assumingthat factorization for such contributions exists. We have determined the magnitude of theIC component of the proton that is consistent with the CT14 global QCD analysis of hardscattering data: 〈x〉 < 2% for BHPS IC and 〈x〉 <1.6% for SEA IC at 90% C.L.. As of today,the experimental confirmation of the IC component in the proton is still missing, and datafrom far more sensitive measurements are required.Acknowledgments. This work was supported in part by the U.S. Department of Energyunder Grant No. DESC0010129; by the U.S. National Science Foundation under Grant No.PHY-1417326; by the National Natural Science Foundation of China under the Grant No.11465018; and by the Lancaster-Manchester-Sheffield Consortium for Fundamental Physicsunder STFC Grant No. ST/L000520/1. The work of J.G. is sponsored by Shanghai PujiangProgram.6EPJ Web of Conferences 192, 00003 (2018) https://doi.org/10.1051/epjconf/201819200003QCD@Work  2018References[1] S. Dulat et al., Phys. Rev. D93 (2016) 033006, 1506.07443.[2] M. Buza et al., Nucl. Phys. B472 (1996) 611, hep-ph/9601302.[3] M. Buza et al., Eur. Phys. J. C1 (1998) 301, hep-ph/9612398.[4] S.J. Brodsky et al., Phys. Lett. B93 (1980) 451.[5] S.J. Brodsky, C. Peterson and N. Sakai, Phys. Rev. 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CTEQ-TEA parton distribution functions with intrinsic charm

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CTEQ-TEA parton distribution functions with intrinsic charm

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