Precision determination of the strong coupling constant within a global PDF analysis
Richard D. Ball, Stefano Carrazza, Luigi Del Debbio, Stefano Forte, Zahari Kassabov, Juan Rojo, Emma Slade, Maria Ubiali
备注：
23 pages, 10 figures.Final version, published in EPJC. New plots added to figs 3.5 and 3.6 and improved discussion of the d'Agostini bias. Discussion of ABMP clarified. Some references added
We present a determination of the strong coupling constant $α_s(m_Z)$ based on the NNPDF3.1 determination of parton distributions, which for the first time includes constraints from jet production, top-quark pair differential distributions, and the $Z$ $p_T$ distributions using exact NNLO theory. Our result is based on a novel extension of the NNPDF methodology - the correlated replica method - which allows for a simultaneous determination of $α_s$ and the PDFs with all correlations between them fully taken into account. We study in detail all relevant sources of experimental, methodological and theoretical uncertainty. At NNLO we find $α_s(m_Z) = 0.1185 \pm 0.0005^\text{(exp)}\pm 0.0001^\text{(meth)}$, showing that methodological uncertainties are negligible. We conservatively estimate the theoretical uncertainty due to missing higher order QCD corrections (N$^3$LO and beyond) from half the shift between the NLO and NNLO $α_s$ values, finding $Δα^{\rm th}_s =0.0011$.
We present a first global determination of spin-dependent parton distribution functions (PDFs) and their uncertainties using the NNPDF methodology: NNPDFpol1.1. Longitudinally polarized deep-inelastic scattering data, already used for the previous NNPDFpol1.0 PDF set, are supplemented with the most recent polarized hadron collider data for inclusive jet and $W$ boson production from the STAR and PHENIX experiments at RHIC, and with open-charm production data from the COMPASS experiment, thereby allowing for a separate determination of the polarized quark and anti-quark PDFs, and an improved de…
We present the first unbiased determination of parton distribution functions (PDFs) with electroweak corrections. The aim of this thesis is to provide an exhaustive description of the theoretical framework and the technical implementation which leads to the determination of a set of PDFs which includes the photon PDF and quantum electrodynamics (QED) contributions to parton evolution. First, we introduce and motivate the need of including electroweak corrections to PDFs, providing phenomenological examples and presenting an overview of the current state of the art in PDF fits. The theoretical …
We present {\tt GKG18-DPDFs}, a next-to-leading order (NLO) QCD analysis of diffractive parton distribution functions (diffractive PDFs) and their uncertainties. This is the first global set of diffractive PDFs determined within the {\tt xFitter} framework. This analysis is motivated by all available and most up-to-date data on inclusive diffractive deep inelastic scattering (diffractive DIS). Heavy quark contributions are considered within the framework of the Thorne-Roberts (TR) general mass variable flavor number scheme (GM-VFNS). We form a mutually consistent set of diffractive PDFs due to…
We discuss the determination of electroweak parameters from hadron collider observables, focusing on the $W$ boson mass measurement. We revise the procedures adopted in the literature to include in the experimental analysis the uncertainty due to our imperfect knowledge of the proton structure. We show how the treatment of the proton parton density functions (PDFs) uncertainty as a source of systematic error, leads to the automatic inclusion in the fit of the bin-bin correlation of the kinematic distributions with respect to PDF variations. In the case of the determination of $M_W$ from the ch…
We discuss the recent results obtained in the context of PDF determination with the inclusion of logarithmic resummations and their phenomenological applications.
We study the impact of the inclusion of Neutral Current (NC) DY data from LHC mapped in the Forward-Backward Asymmetry ($A_{\rm FB}$) observable on PDF uncertainties, using the open source platform \texttt{xFitter}. We find that $A_{\rm FB}$ enables new PDF sensitivity at current and future luminosity stages of LHC.
Recent LHC W/Z vector boson production data in proton-lead collisions are quite sensitive to the heavier flavors (especially the strange PDF), and this complements the information from neutrino-DIS data. As the proton flavor determination is dependent on nuclear corrections (from heavy target DIS, for example), LHC heavy ion measurements can also help improve proton PDFs. We introduce a new implementation of the nCTEQ code (nCTEQ++) based on C++ which has a modular strucure and enables us to easily integrate programs such as HOPPET, APPLgrid, and MCFM. Using ApplGrids generated from MCFM, we u…
We present a new software package designed to reduce the computational burden of hadron collider measurements in Parton Distribution Function (PDF) fits. The APFELgrid package converts interpolated weight tables provided by APPLgrid files into a more efficient format for PDF fitting by the combination with PDF and $α_s$ evolution factors provided by APFEL. This combination significantly reduces the number of operations required to perform the calculation of hadronic observables in PDF fits and simplifies the structure of the calculation into a readily optimised scalar product. We demonstrate t…
We investigate the impact of high-statistics Drell-Yan (DY) measurements at the LHC on the study of non-perturbative QCD effects from parton distribution functions (PDF). We present the results of a PDF profiling analysis based on the neutral-current DY forward-backward asymmetry, using the open source fit platform xFitter.
We evaluate the uncertainties due to nuclear effects in global fits of proton parton distribution functions (PDFs) that utilise deep-inelastic scattering and Drell-Yan data on deuterium targets. To do this we use an iterative procedure to determine proton and deuteron PDFs simultaneously, each including the uncertainties in the other. We apply this procedure to determine the nuclear uncertainties in the SLAC, BCDMS, NMC and DYE866/NuSea fixed target deuteron data included in the NNPDF3.1 global fit. We show that the effect of the nuclear uncertainty on the proton PDFs is small, and that the in…
The goal of this study is to determine a set of diffractive parton distribution function (diffractive PDFs) from a QCD analysis of all available and up-to-date diffractive deep inelastic scattering (diffractive DIS) data sets from HERA $ep$ collider, including the most recent H1 and ZUES combined inclusive diffractive cross section measurements. This extraction of diffractive PDFs, referred to as {\tt HK19-DPDF}, is performed at next-to-leading (NLO) and next-to-next-to-leading (NNLO) in perturbative QCD. This new determination of diffractive PDFs is based on the fracture functions methodology…
Parton distributions are an essential ingredient of the LHC program. PDFs are relevant for precision Standard Model measurements, for Higgs boson characterization as well as for New Physics searches. In this contribution I review recent progress in the determination of the parton distributions of the proton during the last year. Important developments include the impact of new LHC measurements to pin down poorly known PDFs, studies of theoretical uncertainties, higher order calculations for processes relevant for PDF determinations, PDF benchmarking exercises with LHC data, as well as methodol…
We study several sources of theoretical uncertainty in the determination of parton distributions (PDFs) which may affect current PDF sets used for precision physics at the Large Hadron Collider, and explain discrepancies between them. We consider in particular the use of fixed-flavor versus variable-flavor number renormalization schemes, higher twist corrections, and nuclear corrections. We perform our study in the framework of the NNPDF2.3 global PDF determination, by quantifying in each case the impact of different theoretical assumptions on the output PDFs. We also study in each case the im…
We present an unbiased determination of the charm content of the proton, in which the charm parton distribution function (PDF) is parametrized on the same footing as the light quarks and the gluon in a global PDF analysis. This determination relies on the calculation of deep-inelastic structure functions in the FONLL scheme, generalized to account for massive charm-initiated contributions. In contrast to the usual situation in which the charm PDF is assumed to be generated perturbatively by pair radiation off gluons and light quarks, vanishing at a scale set by the value of the charm mass m_c,…
The determination of Parton Distribution Functions from a finite set of data is a typical example of an inverse problem. Inverse problems are notoriously difficult to solve, in particular when a robust determination of the uncertainty in the result is needed. We present a Bayesian framework to deal with this problem and discuss first results from a closure test.
We discuss how the experimental information from longitudinal single-spin asymmetries for $W^{\pm}$ boson production in polarised proton-proton collisions can be included in a polarised parton determination by Bayesian reweighting of a Monte Carlo set of polarised PDF replicas. We explicitly construct a prior ensemble of polarised parton distributions using available fits to inclusive and semi-inclusive DIS data and we discuss the potential impact of existing and future RHIC measurements on it.
Measurements of the forward-backward asymmetry in neutral-current Drell-Yan di-lepton production have primarily been used for determinations of the weak mixing angle $θ_W$. We observe that, unlike the case of Run-I of the Large Hadron Collider (LHC Run-I), for the first time at the LHC Run-II the reconstructed forward-backward asymmetry has the capability of placing useful constraints on the determination of the parton distribution functions (PDFs). By examining the statistical and the PDF uncertainties on the reconstructed forward-backward asymmetry, we investigate its potential for disentang…
The xFitter project (former HERAFitter project) is an open-source package that provides a framework for the determination of the parton distribution functions (PDFs) of the proton for many different kinds of analyses in Quantum Chromodynamics (QCD). xFitter version 2.0.0 has recently been released, and offers an expanded set of tools and options. It incorporates experimental data from a wide range of experiments including fixed-target, Tevatron, HERA, and LHC. xFitter can analyze this data up to next-to-next-to-leading-order (NNLO) in perturbation theory with a variety of theoretical calculati…
Impact of Z-boson transverse-momentum resummation on PDF determination
Universidad de Sevilla（塞维利亚大学）；Università di Torino, and INFN, Sezione di Torino（都灵大学和意大利国家核物理研究所都灵分部）；Università di Milano-Bicocca, and INFN, Sezione di Milano-Bicocca（米兰比可卡大学和意大利国家核物理研究所米兰比可卡分部）
We show how theoretical uncertainties due to nuclear effects may be incorporated into global fits of proton parton distribution functions (PDFs) that include deep-inelastic scattering and Drell-Yan data on nuclear targets. We specifically consider the CHORUS, NuTeV and E605 data included in the NNPDF3.1 fit, which used Pb, Fe and Cu targets, respectively. We show that the additional uncertainty in the proton PDFs due to nuclear effects is small, as expected, and in particular that the effect on the $\bar{d}/\bar{u}$ ratio, the total strangeness $s+\bar{s}$, and the strange valence distribution…
We provide a discussion of the impact of a subset of Drell-Yan data from LHC on the determination of the photon parton distribution function (PDF), using the NNPDF methodology. In previous work we have shown that the photon PDF determined from deep-inelastic scattering (DIS) data only has large uncertainties, suggesting the need for more data from other processes such as Drell-Yan, which unlike DIS, includes photon-induced contributions at leading order in QED. We describe the inclusion of ATLAS Drell-Yan W, Z data, which is a subset of the LHC data used in a final photon PDF determination, by…
The precision measurement of the W boson mass allows to perform stringent consistency tests of the Standard Model by means of global electroweak fits. The accurate determination of the W boson mass is one of the legacy results of the Tevatron, where the experimental accuracy is such that $M_W$ is now limited by theoretical uncertainties related to the parton distributions of the proton. In this contribution, we show how to quantify the impact of PDF uncertainties in the measurement of $M_W$ at the Tevatron and the LHC by means of a template method, and study both the use of the W transverse ma…
We study the correlation between different sets of parton distributions (PDFs). Specifically, viewing different PDF sets as distinct determinations, generally correlated, of the same underlying physical quantity, we examine the extent to which the correlation between them is due to the underlying data. We do this both for pairs of PDF sets determined using a given fixed methodology, and between sets determined using different methodologies. We show that correlations have a sizable component that is not due to the underlying data, because the data do not determine the PDF uniquely. We show that…
The LHC has recently released precise measurements of the transverse momentum distribution of the Z-boson that provide a unique constraint on the structure of the proton. Theoretical developments now allow the prediction of these observables through next-to-next-to-leading order (NNLO) in perturbative QCD. In this work we study the impact of incorporating these latest advances into a determination of parton distribution functions (PDFs) through NNLO including the recent ATLAS and CMS 7 TeV and 8 TeV $p_T^Z$ data. We investigate the consistency of these measurements in a global fit to the avail…
Modern parton distribution function (PDF) determinations either neglect higher-order corrections in the electroweak (EW) coupling or implement them approximately for a subset of PDF processes. We present a new tool, PineAPPL, which supports perturbative correction in arbitrary powers of the EW and strong coupling constant, and stores theoretical predictions independently of the used PDFs in so-called interpolation grids. These are the foundation of any PDF determination, and will allow us to perform a PDF fit taking into account EW corrections for all processes consistently. Apart from PDF det…
The parton distribution functions (PDFs) which characterize the structure of the proton are currently one of the dominant sources of uncertainty in the predictions for most processes measured at the Large Hadron Collider (LHC). Here we present the first extraction of the proton PDFs that accounts for the missing higher order uncertainty (MHOU) in the fixed-order QCD calculations used in PDF determinations. We demonstrate that the MHOU can be included as a contribution to the covariance matrix used for the PDF fit, and then introduce prescriptions for the computation of this covariance matrix u…
The current analysis aims to present the results of a QCD analysis of diffractive parton distribution functions (diffractive PDFs) at next-to-leading order (NLO) accuracy in perturbative QCD. In this new determination of diffractive PDFs, we use all available and up-to-date diffractive deep inelastic scattering (diffractive DIS) datasets from H1 and ZEUS Collaborations at HERA including the most recent H1/ZEUS combined measurements. In this analysis, we consider the heavy quark contributions to the diffractive DIS in the so-called framework of {\tt FONLL} general mass variable flavor number sc…
Determination of Nuclear PDFs using Markov Chain Monte Carlo Methods
Institute of Nuclear Physics Polish Academy of Sciences（波兰科学院核物理研究所）；Southern Methodist University（南方卫理公会大学）；Jefferson Lab（杰斐逊实验室）；Westfälische Wilhelms-Universität Münster（明斯特西法利亚威廉大学）
The determination of the $W$-boson mass through an analysis of the decay charged-lepton transverse momentum distribution has a sizable uncertainty due to the imperfect knowledge of the relevant parton distribution functions (PDFs). In this paper, a quantitative assessment of the $W$-boson mass uncertainty at the LHC resulting from the PDF uncertainty is examined. We use the CT14 NNLO PDFs with a NNLL + NNLO calculation (ResBos) to simulate the $W$-boson production and decay kinematics. The uncertainty of the $W$-boson mass determination is then determined as a function of the boson and lepton …
Without proper control of numerical and methodological errors in theoretical predictions at the per mille level it is not possible to study the effect of input parameters in current hadron-collider measurements at the required precision. We present a new version of the parton-level code MCFM that achieves this requirement through its highly-parallelized nature, significant performance improvements and new features. An automatic differential cutoff extrapolation is introduced to assess the cutoff dependence of all results, thus ensuring their reliability and potentially improving fixed-cutoff r…
We propose a new observable for the measurement of the forward-backward asymmetry $(A_{FB})$ in Drell-Yan lepton production. At hadron colliders, the $A_{FB}$ distribution is sensitive to both the electroweak (EW) fundamental parameter $\sin^2 θ_{W}$, the weak mixing angle, and the parton distribution functions (PDFs). Hence, the determination of $\sin^2 θ_{W}$ and the updating of PDFs by directly using the same $A_{FB}$ spectrum are strongly correlated. This correlation would introduce large bias or uncertainty into both precise measurements of EW and PDF sectors. In this article, we show tha…
We consider some trends, achievements and a series of remaining problems in the precision determination of parton distribution functions. For the description of the scaling violations of the deep-inelastic scattering data, forming the key ingredients to all PDF fits, a solid theoretical framework is of importance. It is provided by the fixed flavor number scheme in describing the heavy-quark contributions which is found in good agreement with the present experimental data in a very wide range of momentum transfers. In this framework also a consistent determination of the heavy-quark masses is …
We present a discussion on the methods for extracting a given parameter from measurements of hadronic data, with particular focus on determinations of the strong coupling constant. We show that when the PDF dependency on the determination is adequately taken into account, the dispersion between the results from different measurements is significantly reduced. We speculatively propose the concept of preferred value of a parameter from a particular dataset.
We study at a quantitative level the impact of the uncertainties on the value of the W boson mass measured at hadron colliders due to: the proton parton distribution functions (PDFs), the value of the strong coupling constant alpha_S and the value of the charm mass used in the PDF determination. The value of the W boson mass is extracted, by means of a template fit technique, from the lepton-pair transverse mass distribution measured in the charged current Drell-Yan process. We study the determination of M_W at the Tevatron and at the LHC with 7 and 14 TeV of center-of-mass energy in a realist…
Resummation-scale uncertainties in PDF determinations
School of Physics, Institute for Research in Fundamental Sciences (IPM)（基础科学研究所）；Department of Physics, Malayer University（马拉耶尔大学物理系）；IRFU, CEA, Université Paris-Saclay（巴黎萨克雷大学CEA IRFU）；Dipartimento di Fisica, Universitá di Cagliari（卡利亚里大学物理系）；INFN, Sezione di Cagliari（意大利国家核物理研究院卡利亚里分部）；Universitá degli Studi Link（林克大学）；INFN Sezione di Roma Tor Vergata（意大利国家核物理研究院罗马托维加塔分部）；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器）；Physik-Institut, Universität Zürich（苏黎世大学物理学院）；Theoretical Physics Department, University of Oxford（牛津大学理论物理系）；SMU Physics（南卫理公会大学物理系）；University of Sharjah（沙迦大学）；II. Institut für Theoretische Physik, Universität Hamburg（汉堡大学第二理论物理研究所）
We discuss the impact of EW corrections on differential distributions in top-quark pair production at the LHC and future hadron colliders, focusing on the effects of initial-state photons. Performing a calculation at Next-to-Leading Order QCD+EW accuracy, we investigate in detail the impact of photon-initiated channels on central values as well as PDF and scale uncertainties, both at order $α_sα$ and $α_s^2α$. We present predictions at 13 and 100 TeV, and provide results for the 8 TeV differential measurements performed by ATLAS and CMS. A thorough comparison of results obtained with the NNPDF…
In this QCD analysis, we investigate the impact of recent measurements of heavy-flavor charm and beauty cross sections data sets on the simultaneous determination of Parton Distribution Functions (PDFs) and the strong coupling, $α_s(M^2_Z)$. We perform three different fits based on Variable-Flavour Number Scheme (VFNS) at the Leading Order (LO) and Next-to-Leading Order (NLO) and choose the full HERA run I and II combined data as a new measurement of inclusive Deep Inelastic Scattering (DIS) cross sections for our base data set. We show that including charm and beauty cross sections data reduc…
The parton distribution functions (PDFs) of the proton, a necessary input to almost all theory predictions for hadron colliders, are reviewed in this document. An introduction to the PDF determination by global analyses of the main PDF fitting groups with an emphasis on HERA PDFs is presented. Finally, theory predictions based on different PDFs are compared to some recent relevant LHC and Tevatron measurements.
The Fortran LHAPDF library has been a long-term workhorse in particle physics, providing standardised access to parton density functions for experimental and phenomenological purposes alike, following on from the venerable PDFLIB package. During Run 1 of the LHC, however, several fundamental limitations in LHAPDF's design have became deeply problematic, restricting the usability of the library for important physics-study procedures and providing dangerous avenues by which to silently obtain incorrect results. In this paper we present the LHAPDF 6 library, a ground-up re-engineering of the PDFL…
The precision measurement of the W boson mass is an important milestone for the LHC physics program in the coming years. An accurate measurement of $M_W$ allows to perform stringent consistency tests of the Standard Model by means of global electroweak fits, which in turn are sensitive to New Physics at scales potentially higher than the ones explored in direct searches. From the theoretical point of view, our limited knowledge of PDFs will be one of the dominant sources of uncertainty in ongoing and future LHC determinations of $M_W$. In this whitepaper, we have quantified the impact of PDF u…
The method of closure testing for analysing the effectiveness of a PDF fitting procedure is discussed. In order to pass a closure test, a fitting methodology must be able to reproduce a known generating function in a fit to an ideal pseudo-dataset generated by that PDF up to the level of experimental uncertainty in the data. Here we present an initial study of the closure property of the NNPDF fitting methodology. An idealised pseudo-dataset is generated by a set of toy PDFs that differ substantially from previous NNPDF determinations. In a fit to this pseudodata, the NNPDF methodology is show…
I present a determination of the photon PDF from a fit to the recent ATLAS measurements of high-mass Drell-Yan lepton-pair production at $\sqrt{s} = 8$ TeV. This analysis is based on the {\tt xFitter} framework interfaced to the {\tt APFEL} program, that accounts for NLO QED effects, and to the {\tt aMCfast} code to account for the photon-initiated contributions within {\tt MadGraph5\_aMC@NLO}. The result is compared with other recent determinations of the photon PDF finding a general good agreement.
The accurate determination of the Parton Distribution Functions (PDFs) of the proton is an essential ingredient of the Large Hadron Collider (LHC) program. PDF uncertainties impact a wide range of processes, from Higgs boson characterisation and precision Standard Model measurements to New Physics searches. A major recent development in modern PDF analyses has been to exploit the wealth of new information contained in precision measurements from the LHC Run I, as well as progress in tools and methods to include these data in PDF fits. In this report we summarise the information that PDF-sensit…
Determination of proton PDF uncertainties with Markov chain Monte Carlo
Institut für Theoretische Physik, Universität Münster（明斯特大学理论物理研究所）；Department of Physics, Southern Methodist University（南方卫理公会大学物理系）；Theory Center, Jefferson Lab（杰弗逊实验室理论中心）；Institute of Nuclear Physics Polish Academy of Sciences（波兰科学院核物理研究所）
Measurement at Hadron colliders of neutral- and charged-current Drell-Yan production provide essential constraints in the determination of parton distribution functions. Experimentally, they have reached percent level precision, challenging the accuracy of the theoretical predictions. In this work we benchmark the novel implementation in $\texttt{DYTurbo}$ of linear fiducial power corrections in the $q_T$-subtraction formalism at NLO and NNLO in QCD. We illustrate how the inclusion of linear fiducial power corrections impacts predictions for precise $W$ and $Z$ measurements from the LHC and af…
We address the impact of future measurements of charged and neutral current Drell-Yan (DY) asymmetries and their combination on Parton Distribution Functions (PDFs) uncertainties. We quantify the reduction of PDF uncertainties using the QCD tool xFitter. We examine the effects of such reduced PDF errors on both Standard Model (SM) and Beyond SM (BSM) observables.
We formulate a general approach to the inclusion of theoretical uncertainties, specifically those related to the missing higher order uncertainty (MHOU), in the determination of parton distribution functions (PDFs). We demonstrate how, under quite generic assumptions, theory uncertainties can be included as an extra contribution to the covariance matrix when determining PDFs from data. We then review, clarify, and systematize the use of renormalization and factorization scale variations as a means to estimate MHOUs consistently in deep inelastic and hadronic processes. We define a set of presc…
We present a new procedure to determine Parton Distribution Functions (PDFs), based on Markov Chain Monte Carlo (MCMC) methods. The aim of this paper is to show that we can replace the standard $χ^2$ minimization by procedures grounded on Statistical Methods, and on Bayesian inference in particular, thus offering additional insight into the rich field of PDFs determination. After a basic introduction to these technics, we introduce the algorithm we have chosen to implement -- namely Hybrid (or Hamiltonian) Monte Carlo. This algorithm, initially developed for Lattice QCD, turns out to be very i…
We discuss a conceptual issue concerning the neutrino velocity measurement, in connection with the statistical method employed by the OPERA collaboration for the inference of the neutrino time of flight. We expound the theoretical framework that underlies the delicate statistical procedure illustrating its salient aspects. In particular, we show that the order of the two operations of sum and normalization used to combine the single waveforms so as to build the global PDF is a crucial point. We also illustrate how a consistency check able to test the correctness of the PDF-composing procedure …
