Determination of electroweak parameters in polarised deep-inelastic scattering at HERA
DDESY 18-080 ISSN 0418-9833
Date: May 2018
Determination of electroweak parameters in polariseddeep-inelastic scattering at HERA
H1 Collaboration and H. Spiesberger (Mainz)
Abstract
The parameters of the electroweak theory are determined in a combined electroweak andQCD analysis using all deep-inelastic e + p and e − p neutral current and charged current scat-tering cross sections published by the H1 Collaboration, including data with longitudinallypolarised lepton beams. Various fits to Standard Model parameters in the on-shell schemeare performed. The mass of the W boson is determined as m W = . ± .
115 GeV. Theaxial-vector and vector couplings of the light quarks to the Z boson are also determined.Both results improve the precision of previous H1 determinations based on HERA-I databy about a factor of two. Possible scale dependence of the weak coupling parameters inboth neutral and charged current interactions beyond the Standard Model is also studied.All results are found to be consistent with the Standard Model expectations. Dedicated to the memory of our dear friend and colleague Violette BrissonSubmitted to EPJ C a r X i v : . [ h e p - e x ] S e p . Andreev , A. Baghdasaryan , K. Begzsuren , A. Belousov , A. Bolz , V. Boudry ,G. Brandt , V. Brisson , † , D. Britzger , A. Buniatyan , A. Bylinkin , L. Bystritskaya ,A.J. Campbell , K.B. Cantun Avila , K. Cerny , V. Chekelian , J.G. Contreras ,J. Cvach , J.B. Dainton , K. Daum , C. Diaconu , M. Dobre , G. Eckerlin , S. Egli ,E. Elsen , L. Favart , A. Fedotov , J. Feltesse , M. Fleischer , A. Fomenko , J. Gayler ,L. Goerlich , N. Gogitidze , M. Gouzevitch , C. Grab , A. Grebenyuk , T. Greenshaw ,G. Grindhammer , D. Haidt , R.C.W. Henderson , J. Hladk`y , D. Ho ff mann ,R. Horisberger , T. Hreus , F. Huber , M. Jacquet , X. Janssen , A.W. Jung , H. Jung ,M. Kapichine , J. Katzy , C. Kiesling , M. Klein , C. Kleinwort , R. Kogler , P. Kostka ,J. Kretzschmar , D. Kr¨ucker , K. Kr¨uger , M.P.J. Landon , W. Lange , P. Laycock ,A. Lebedev , S. Levonian , K. Lipka , B. List , J. List , B. Lobodzinski ,E. Malinovski , H.-U. Martyn , S.J. Maxfield , A. Mehta , A.B. Meyer , H. Meyer ,J. Meyer , S. Mikocki , A. Morozov , K. M¨uller , Th. Naumann , P.R. Newman ,C. Niebuhr , G. Nowak , J.E. Olsson , D. Ozerov , C. Pascaud , G.D. Patel , E. Perez ,A. Petrukhin , I. Picuric , D. Pitzl , R. Polifka , V. Radescu , N. Raicevic ,T. Ravdandorj , P. Reimer , E. Rizvi , P. Robmann , R. Roosen , A. Rostovtsev ,M. Rotaru , D. ˇS´alek , D.P.C. Sankey , M. Sauter , E. Sauvan , , S. Schmitt ,L. Schoe ff el , A. Sch¨oning , F. Sefkow , S. Shushkevich , Y. Soloviev , P. Sopicki ,D. South , V. Spaskov , A. Specka , H. Spiesberger , M. Steder , B. Stella ,U. Straumann , T. Sykora , , P.D. Thompson , D. Traynor , P. Tru¨ol , I. Tsakov ,B. Tseepeldorj , , A. Valk´arov´a , C. Vall´ee , P. Van Mechelen , Y. Vazdik , † , D. Wegener ,E. W¨unsch , J. ˇZ´aˇcek , Z. Zhang , R. ˇZlebˇc´ık , H. Zohrabyan , and F. Zomer I. Physikalisches Institut der RWTH, Aachen, Germany School of Physics and Astronomy, University of Birmingham, Birmingham, UK b Inter-University Institute for High Energies ULB-VUB, Brussels and Universiteit Antwerpen,Antwerp, Belgium c Horia Hulubei National Institute for R & D in Physics and Nuclear Engineering (IFIN-HH) ,Bucharest, Romania i STFC, Rutherford Appleton Laboratory, Didcot, Oxfordshire, UK b Institute of Nuclear Physics Polish Academy of Sciences, PL-31342 Krakow, Poland d Institut f¨ur Physik, TU Dortmund, Dortmund, Germany a Joint Institute for Nuclear Research, Dubna, Russia Irfu / SPP, CE Saclay, Gif-sur-Yvette, France DESY, Hamburg, Germany Institut f¨ur Experimentalphysik, Universit¨at Hamburg, Hamburg, Germany a Physikalisches Institut, Universit¨at Heidelberg, Heidelberg, Germany a Department of Physics, University of Lancaster, Lancaster, UK b Department of Physics, University of Liverpool, Liverpool, UK b School of Physics and Astronomy, Queen Mary, University of London, London, UK b Aix Marseille Universit´e, CNRS / IN2P3, CPPM UMR 7346, 13288 Marseille, France Departamento de Fisica Aplicada, CINVESTAV, M´erida, Yucat´an, M´exico g Institute for Theoretical and Experimental Physics, Moscow, Russia h Lebedev Physical Institute, Moscow, Russia Max-Planck-Institut f¨ur Physik, M¨unchen, Germany LAL, Universit´e Paris-Sud, CNRS / IN2P3, Orsay, France LLR, Ecole Polytechnique, CNRS / IN2P3, Palaiseau, France Faculty of Science, University of Montenegro, Podgorica, Montenegro j Institute of Physics, Academy of Sciences of the Czech Republic, Praha, Czech Republic e Faculty of Mathematics and Physics, Charles University, Praha, Czech Republic e Dipartimento di Fisica Universit`a di Roma Tre and INFN Roma 3, Roma, Italy Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria Institute of Physics and Technology of the Mongolian Academy of Sciences, Ulaanbaatar,Mongolia Paul Scherrer Institut, Villigen, Switzerland Fachbereich C, Universit¨at Wuppertal, Wuppertal, Germany Yerevan Physics Institute, Yerevan, Armenia DESY, Zeuthen, Germany Institut f¨ur Teilchenphysik, ETH, Z¨urich, Switzerland f Physik-Institut der Universit¨at Z¨urich, Z¨urich, Switzerland f Universit´e Claude Bernard Lyon 1, CNRS / IN2P3, Villeurbanne, France Now at Lomonosov Moscow State University, Skobeltsyn Institute of Nuclear Physics,Moscow, Russia Now at CERN, Geneva, Switzerland Also at Ulaanbaatar University, Ulaanbaatar, Mongolia Also at LAPP, Universit´e de Savoie, CNRS / IN2P3, Annecy-le-Vieux, France II. Physikalisches Institut, Universit¨at G¨ottingen, G¨ottingen, Germany Now at Institute for Information Transmission Problems RAS, Moscow, Russia k Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, RussianFederation l Department of Physics and Astronomy, Purdue University 525 Northwestern Ave, WestLafayette, IN, 47907, USA Department of Physics, Oxford University, Oxford, UK PRISMA Cluster of Excellence, Institute of Physics, Johannes Gutenberg-Universit¨at,Mainz, Germany † Deceased a Supported by the Bundesministerium f¨ur Bildung und Forschung, FRG, under contractnumbers 05H09GUF, 05H09VHC, 05H09VHF, 05H16PEA b Supported by the UK Science and Technology Facilities Council, and formerly by the UKParticle Physics and Astronomy Research Council c Supported by FNRS-FWO-Vlaanderen, IISN-IIKW and IWT and by Interuniversity AttractionPoles Programme, Belgian Science Policy d Partially Supported by Polish Ministry of Science and Higher Education, grantDPN / N168 / DESY / e Supported by the Ministry of Education of the Czech Republic under the projectINGO-LG14033 f Supported by the Swiss National Science Foundation g Supported by CONACYT, M´exico, grant 48778-F h Russian Foundation for Basic Research (RFBR), grant no 1329.2008.2 and Rosatom i Supported by the Romanian National Authority for Scientific Research under the contract PN09370101 Partially Supported by Ministry of Science of Montenegro, no. 05-1 / k Russian Foundation for Sciences, project no 14-50-00150 l Ministery of Education and Science of Russian Federation contract no 02.A03.21.0003 Introduction
Since the discovery of weak neutral currents in 1973 [1, 2], the Glashow-Weinberg-Salammodel [3–10] has been established as the theory of electroweak (EW) interactions and asthe core of the Standard Model (SM) of particle physics. Already since these early times,deep-inelastic lepton-hadron scattering (DIS) experiments with longitudinally polarised elec-tron beams have provided indispensable results [11, 12] for its great success. Nowadays, EWtheory has been tested in great detail at lower scales with muon life-time measurements [13] andneutrino scattering experiments [14–18], with precision measurements at the Z pole and at evenhigher scales [19–24]. The H1 Collaboration has performed first studies of weak interactionsat the HERA electron-proton collider in 1993: the measurement of the total charged-currentcross section demonstrated for the first time the presence of the W -boson propagator [25]. DISat HERA provides complementary testing ground for studying EW processes at the EW energyscale in the space-like regime. The centre-of-mass energy at HERA nicely fills the gap betweenlow-energy neutrino or muon experiments and high-energy collider experiments, and it o ff ersthe possibility to study neutral and charged currents (NC and CC) on equal footing.The H1 experiment [26–29] at the HERA collider recorded collisions of electrons and positronsof 27.6 GeV and unpolarised protons of up to 920 GeV during the HERA-I running period in theyears 1992 to 2000, and the HERA-II running period in the years 2003 to 2007. These data pro-vide a large set of precise NC and CC cross section measurements. They are an important inputto study Quantum Chromodynamics (QCD), the theory of the strong force, and are indispens-able for exploring the structure of the proton. Furthermore, at the HERA centre-of-mass energyof up to √ s =
319 GeV, EW e ff ects such as γ Z interference significantly contribute to the inclu-sive NC DIS cross sections at high values of negative four-momentum transfers squared ( Q ).The CC interactions are solely mediated by charged W bosons. This allows for a determinationof EW parameters from inclusive NC and CC DIS data at high Q up to 50 000 GeV At HERA, several determinations of the W -boson mass ( m W ) have been performed by the H1and ZEUS experiments based on di ff erent data samples collected during the HERA-I data takingperiod [30–34]. A first EW analysis was performed using the complete HERA-I data collectedby H1 [35], where the weak neutral-current couplings of the light quarks to the Z boson, theaxial-vector ( g u / dA ) and vector ( g u / dV ) couplings, and m W and the top-quark mass ( m t ) were de-termined. Analyses using H1 data from HERA-I and HERA-II cross section measurementstogether with ZEUS data have been reported by the ZEUS Collaboration [36] and by I. Abt etal. [37].In the present analysis, the entire set of inclusive NC and CC DIS cross sections measuredby the H1 Collaboration during the HERA-I and HERA-II running periods is exploited. Thestudies thus benefit from the improved statistical precision of the data samples, as compared tothe previous analysis [35]. In addition, the longitudinal polarisation of the lepton beams in theHERA-II running provides new sensitivity.The EW parameters are determined together with the parameters of parton density functions(PDFs) of the proton in combined fits, thus accounting for their correlated uncertainties. Thecross section predictions used in this analysis include next-to-next-to-leading order (NNLO)QCD corrections at the hadronic vertex and next-to-leading order (NLO) EW corrections.4ithin the SM framework the masses of the W and Z bosons and the couplings of the lightquarks are determined. Potential modifications from physics beyond the SM are explored. EWparameters are tested in DIS at space-like four-momentum transfer. Therefore, the studies pre-sented here are complementary to measurements of EW parameters at e + e − or pp colliders,which are performed in the time-like regime for example at the Z pole or at the WW threshold. NC interactions in the process e ± p → e ± X are mediated by a virtual photon ( γ ) or Z boson inthe t -channel, and the cross section is expressed in terms of generalised structure functions ˜ F ± , x ˜ F ± and ˜ F ± L at EW leading order (LO) as d σ NC ( e ± p ) dxdQ = πα xQ (cid:104) Y + ˜ F ± ( x , Q ) ∓ Y − x ˜ F ± ( x , Q ) − y ˜ F ± L ( x , Q ) (cid:105) , (1)where α is the fine structure constant and x denotes the Bjorken scaling variable (see e.g. [38]).The helicity dependence of the interaction is contained in the terms Y ± = ± (1 − y ) with y being the inelasticity of the process. The generalised structure functions can be separated intocontributions from pure γ - and Z -exchange and their interference [39],˜ F ± = F − ( g eV ± P e g eA ) κ Z F γ Z + (cid:2) ( g eV g eV + g eA g eA ) ± P e g eV g eA (cid:3) κ Z F Z , (2)˜ F ± = − ( g eA ± P e g eV ) κ Z F γ Z + (cid:2) g eV g eA ± P e ( g eV g eV + g eA g eA ) (cid:3) κ Z F Z , (3)and similarly for ˜ F L . The variables g eA and g eV stand for the axial-vector and vector couplingsof the lepton e ± to the Z boson, respectively. The degree of longitudinal polarisation of theincoming lepton is denoted as P e .The Q -dependent coe ffi cient κ Z accounts for the Z -boson propagator, κ Z ( Q ) = Q Q + m Z θ W cos θ W = Q Q + m Z G F m Z √ πα . (4)It can be normalised using the weak mixing angle, sin θ W = − m W / m Z , i.e. using the W and Z boson masses, m W and m Z , or the Fermi coupling constant G F , which is measured withhigh precision in muon-decay experiments [13]. The structure functions are related to linearcombinations of the quark and anti-quark momentum distributions, xq and x ¯ q . For instance, the F and xF structure functions in the naive quark-parton model, i.e. at LO in QCD, are: (cid:104) F , F γ Z , F Z (cid:105) = x (cid:88) q (cid:104) Q q , Q q g qV , g qV g qV + g qA g qA (cid:105) { q + ¯ q } , (5) x (cid:104) F γ Z , F Z (cid:105) = x (cid:88) q (cid:104) Q q g qA , g qV g qA (cid:105) { q − ¯ q } . (6)The axial-vector and vector couplings of the quarks q to the Z boson, g qA and g qV , depend on theelectric charge, Q q , in units of the positron charge, and on the third component of the weak-isospin of the quarks, I , q . In terms of sin θ W , they are given by the standard EW theory: g qA = I , q , (7) g qV = I , q − Q q sin θ W . (8)5he same formulae also apply to the lepton couplings g eA / V .Universal higher-order corrections, to be discussed below, can be taken into account by intro-ducing Q -dependent form factors ρ NC , q and κ NC , q [40], replacing equations (7) and (8) by g qA = √ ρ NC , q I , q , (9) g qV = √ ρ NC , q (cid:16) I , q − Q q κ NC , q sin θ W (cid:17) . (10)The CC cross section at LO is written as d σ CC ( e ± p ) dxdQ = (1 ± P e ) G π x (cid:34) m W m W + Q (cid:35) (cid:16) Y + W ± ( x , Q ) ∓ Y − xW ± ( x , Q ) − y W ± L ( x , Q ) (cid:17) . (11)In the quark-parton model, W ± L =
0, and the structure functions W ± and xW ± are obtainedfrom the parton distribution functions. For electron scattering, only positively charged quarkscontribute: W − = x (cid:16) U + D (cid:17) , xW − = x (cid:16) U − D (cid:17) , (12)while negatively charged quarks contribute to positron scattering: W + = x (cid:16) U + D (cid:17) , xW + = x (cid:16) D − U (cid:17) . (13)Below the top-quark threshold, one has U = u + c , U = ¯ u + ¯ c , D = d + s , D = ¯ d + ¯ s . (14)Higher-order EW corrections are collected in form factors ρ CC , eq / e ¯ q . They modify the LO ex-pressions equations (12) and (13) as W − = x (cid:16) ρ , eq U + ρ , e ¯ q D (cid:17) , xW − = x (cid:16) ρ , eq U − ρ , e ¯ q D (cid:17) , (15) W + = x (cid:16) ρ , eq U + ρ , e ¯ q D (cid:17) , xW + = x (cid:16) ρ , e ¯ q D − ρ , eq U (cid:17) . (16)In the on-shell (OS) scheme [41, 42], the independent parameters of the SM EW theory aredetermined by the fine structure constant α and the masses of the gauge bosons, the Higgsboson m H , and the fermions m f . The weak mixing angle is then fixed, and G F is a prediction,given by G F = πα √ m W θ W − ∆ r ) , (17)where higher-order corrections enter through the quantity ∆ r = ∆ r ( α, m W , m Z , m H , m t , . . . ) [41],which describes corrections to the muon decay beyond the tree-level [43, 44].The ρ NC , κ NC and ρ CC parameters are introduced to cover the universal higher-order EW cor-rections described by loop insertions in the boson propagators. The ρ NC parameters absorb Z -boson propagator corrections combined with higher-order corrections entering the G F - m W -sin θ W relation, equation (17), while the κ NC parameters absorb one-loop γ Z mixing propagatorcorrections. In addition, there are higher-order corrections to the photon propagator which canbe taken into account by using the running fine structure constant. Non-universal corrections6 - - -
10 1 B o r n s / - l oop s = e p, P + NC, e GeV = Q GeV = Q GeV = Q GeV = Q x - - -
10 1 B o r n s / - l oop s = e p, P + CC, e GeV = Q GeV = Q GeV = Q GeV = Q Figure 1: Size of the purely weak one-loop corrections for the e + p unpolarised inclusive NC DIS (left)and CC DIS (right) cross sections at selected values of Q as a function of x . QED corrections due to realand virtual photons and corrections from the vacuum polarisation (the running of α ) are not included.The corrections for electron scattering and for the case of non-vanishing lepton beam polarisation are allvery similar to the positron case, such that they di ff er by less than 0 .
01 units. due to vertex one-loop Feynman graphs and box diagrams are added separately to the NC crosssections. For the CC cross sections, both universal and non-universal corrections can be com-bined into the form factors ρ CC , eq / e ¯ q . The dominating corrections in this case are due to loopinsertions in the W -boson propagator.One-loop EW corrections have been calculated in refs. [45–47] for NC and in refs. [48, 49] forCC scattering (see also ref. [50] for a study of numerical results). The present analysis uses theimplementation of EW higher-order corrections in the program EPRC described in ref. [51].The size of the purely weak one-loop corrections to the di ff erential cross sections is displayedin figure 1 for selected values of Q for e + p scattering. It includes the ρ NC / CC and κ NC formfactors, as well as contributions from vertex and box graphs. The corresponding higher ordercorrections for electron scattering or for non-zero lepton beam polarisation di ff er by less than0 .
01 units from the corrections shown in figure 1. Higher-order QED corrections due to realand virtual emission of photons, as well as vacuum polarisation, i.e. the running of the finestructure constant, also have to be taken into account [52, 53]. These e ff ects, however, had beenconsidered for the cross section measurement and are therefore not included here.In the OS scheme, used in this analysis, the higher-order correction factors ρ NC , κ NC and ρ CC are calculated as a function of α and the input mass values. They depend quadratically onthe top-quark mass through ∆ ρ t ∼ m t , and logarithmically on the Higgs-boson mass, ∆ ρ H ∼ ln (cid:16) m H / m W (cid:17) . On the Z pole they amount to about 4%. For DIS at HERA they are of similarsize, but they exhibit a non-negligible Q -dependence [54]. In a modified version of the OSscheme [55], commonly used in QCD analyses of DIS data, the Fermi constant can be used tofix the input parameters replacing the W -boson mass as an input parameter. In that case theone-loop corrections are very small, i.e. ρ CC , eq / e ¯ q deviate from 1 by a few per mille.7any extensions of the SM predict modifications of the weak NC couplings. They can bedescribed conveniently by introducing additional parameters ρ (cid:48) NC and κ (cid:48) NC , thus modifying theSM corrections. Also for charged current cross sections, similar ρ (cid:48) CC parameters describingnon-standard modifications of the CC couplings can be introduced. The ρ (cid:48) NC , κ (cid:48) NC and ρ (cid:48) CC areintroduced through the following replacements in equations (9), (10), (15) and (16): ρ NC → ρ (cid:48) NC ρ NC , (18) κ NC → κ (cid:48) NC κ NC , (19) ρ CC → ρ (cid:48) CC ρ CC . (20)In the SM, the parameters ρ (cid:48) NC , κ (cid:48) NC and ρ (cid:48) CC are defined to be 1. Various models with physicsbeyond the SM predict typical flavour-dependent deviations from 1 and therefore distinct para-meters for quarks ( ρ (cid:48) NC , q and κ (cid:48) NC , q ) and for leptons ( ρ (cid:48) NC , e and κ (cid:48) NC , e ) are considered. These para-meters may also depend on the energy scale. Precision EW measurements on the Z resonanceare sensitive to the NC couplings at m Z [19], while DIS is also probing their Q dependence. ForCC there could be independent modifications ( ρ (cid:48) CC ) for the lepton and quark couplings for eachgeneration. However, only the product of lepton times quark couplings appears in the final ex-pression for the cross section and therefore the same non-standard coupling for all generationsis assumed here. Nonetheless, new 4-fermion operators can introduce a di ff erence betweenelectron-quark and electron-antiquark scattering, and thus two distinct parameters ρ (cid:48) CC , eq and ρ (cid:48) CC , e ¯ q are considered. These possibly scale-dependent parameters allow for additional tests ofthe SM couplings. This study is based on the entire set of measurements of inclusive NC and CC DIS cross sectionsby the H1 Collaboration, using data samples for e + p and e − p taken in HERA-I and HERA-II. The measurements are subdivided into two kinematic ranges, corresponding to di ff erentsubdetectors where the leptons with small and large scattering angles are identified: low- andmedium- Q for values of Q typically smaller than 150 GeV and high- Q for larger values upto 50 000 GeV . A summary of the data sets used is given in table 1.The low- and medium- Q data sets (data sets 1 and 2) [56] are combined data sets, and theyrepresent all corresponding NC DIS measurements at di ff erent beam energies and during di ff er-ent data taking periods published by H1 [56, 60–63]. For these data photon exchange dominatesover electroweak e ff ects, but they are important in this analysis to constrain the proton PDFswith high precision.Cross section measurements at high Q are published separately for the individual data takingperiods (data sets: 3–4 [32], 5–7 [33, 57], 8–9 [57], 10–19 [58]). The HERA-II data weretaken with longitudinally polarised lepton beams and exhibit smaller statistical uncertaintiesdue to the increased integrated luminosity, as compared to HERA-I. The high- Q data provide The numerical values of the HERA-II cross sections [58] are corrected to the luminosity measurement erra-tum [59], by applying the factor 1.018. ata set Q -range √ s L No. of Polarisation Ref.[GeV ] [GeV] [pb − ] data points [%]1 e + combined low- Q (0.5) 8.5 – 150 301,319 20, 22, 97.6 94 (262) – [56]2 e + combined low- E p (1.5) 8.5 – 90 225,252 12.2, 5.9 132 (136) – [56]3 e + NC 94–97 150 – 30 000 301 35.6 130 – [32]4 e + CC 94–97 300 – 15 000 301 35.6 25 – [32]5 e − NC 98–99 150 – 30 000 319 16.4 126 – [33]6 e − CC 98–99 300 – 15 000 319 16.4 28 – [33]7 e − NC 98–99 high- y
100 – 800 319 16.4 13 – [57]8 e + NC 99–00 150 – 30 000 319 65.2 147 – [57]9 e + CC 99–00 300 – 15 000 319 65.2 28 – [57]10 e + NC L HERA-II 120 – 30 000 319 80.7 136 − . ± . e + CC L HERA-II 300 – 15 000 319 80.7 28 − . ± . e + NC R HERA-II 120 – 30 000 319 101.3 138 + . ± . e + CC R HERA-II 300 – 15 000 319 101.3 29 + . ± . e − NC L HERA-II 120 – 50 000 319 104.4 139 − . ± . e − CC L HERA-II 300 – 30 000 319 104.4 29 − . ± . e − NC R HERA-II 120 – 30 000 319 47.3 138 + . ± . e − CC R HERA-II 300 – 15 000 319 47.3 28 + . ± . e + NC HERA-II high- y
60 – 800 319 182.0 11 – [58, 59]19 e − NC HERA-II high- y
60 – 800 319 151.7 11 – [58, 59]
Table 1: Data sets used in the combined EW and QCD fits. For each of the data sets, the correspondingrange in Q , the centre-of-mass energy √ s , the corresponding integrated luminosity values, the numberof measured data points, and the average longitudinal polarisation values of the lepton beam are given.During the HERA-I running period data were taken with unpolarised lepton beams. The numbers inbrackets denote the respective quantities for the full data set, i.e. without the selection of Q ≥ . .The low- and medium- Q data sets for √ s = highest sensitivity for the determination of the EW parameters. The availability of longitudi-nally polarised lepton beams at HERA-II further improves the sensitivity to the vector couplings g qV , as compared to unpolarised data. The data are restricted to Q ≥ . , for which quarkmass e ff ects are expected to be small, and NNLO QCD predictions [64, 65] are expected toprovide a good description of the data [66, 67].All the data samples (data sets 1–19) had been corrected for higher-order QED e ff ects due tothe emission of photons from the lepton line, photonic lepton vertex corrections, self-energycontributions at the external lepton lines, and fermionic contributions to the running of the finestructure constant (c.f. ref. [32]). QED radiative corrections due to the exchange of two or morephotons between the lepton and the quark lines are small compared to the quoted errors of theQED corrections and had been neglected (c.f. ref. [33]). In the case of CC cross sections, thedata had been corrected for O ( α ) QED e ff ects at the lepton line (c.f. ref. [32]).9n order to ensure that all first order EW corrections are considered fully and consistently in thisanalysis, the applied QED corrections to the input data are revisited in detail. In the formulae forthe cross section derivation [58], the QED corrections are applied together with acceptance, res-olution, and bin-centre corrections, using two independent implementations of the cross sectioncalculations. It turns out that for the HERA-II data (data sets 10–19, ref. [58]), these two imple-mentations have employed slightly di ff erent numerical values for the input EW parameters, andfurthermore have considered di ff erent components of the higher-order EW corrections. The cor-rections are therefore re-evaluated and updated values of the previously published cross sectionsare obtained for this analysis. The procedure is equivalent to the initial cross section determi-nation and therefore does not introduce additional uncertainties. The updated cross sections forthe data sets 10–17, as used in this analysis, are provided in the appendix A. The di ff erencesto the published cross sections are significantly smaller than the statistical uncertainties for anydata point. The data sets 18 and 19 are at lower values of Q and remain unchanged, as well asthe HERA-I data (data sets 1–9). The e ff ect of these updates is expected to be small for QCDanalyses [58, 66, 67]. As a cross check, fits similar to H1PDF2012 [58] were performed usingeither previously published data [58, 59] or the corrected data given in the appendix. The twofits are in agreement within experimental uncertainties, where the largest deviations of size onestandard deviation are observed for the down-valence contribution at low factorisation scales.In the present analysis the impact is also found to be insignificant, but the updated cross sectionsare nevertheless applied in order to have best consistency between data and the predictions usedin the fits described below. The EW parameters are determined in fits of the predictions to data, where in addition to the EWparameters of interest also parameters of the PDFs are determined in order to account for PDFuncertainties. The fits are denoted according to their fit parameters, for instance ‘ m W + PDF’denotes a determination of m W together with the parameters of the PDFs.A dedicated determination of the PDFs in this analysis is important, since all state-of-the-artPDF sets were determined using H1 data, while assuming that the EW parameters take theirSM values. Hence, the use of such PDF sets could bias the results. Furthermore, PDF setswhich include the H1 data su ff er from the additional complication that the same data were to beused twice, thus leading to underestimated uncertainties.The parameterisation of the PDFs follows closely the approach of ref. [66], where the PDF setHERAPDF2.0 was obtained, using EW parameters determined from other experiments. Theparameterisation uses five functional forms with altogether 13 fit parameters, defined at thestarting scale Q = . . The scale dependence of the PDFs is evaluated using the DGLAPformalism.As opposed to the HERAPDF2.0 analysis, the A lpos fitting framework [67] is used in thepresent analysis. The cross section predictions have been validated against the xFitter frame- HERAPDF2.0 is determined from combined inclusive NC and CC data from the H1 and ZEUS experimentsassuming unpolarised lepton beams. ff ects, as outlined in section 3.The goodness of fit, χ , is derived from a likelihood function assuming the quantitites to benormal distributed in terms of relative uncertainties [67, 71], which is equivalent to log-normaldistributed quantities in terms of absolute uncertainties. The log-normal distribution is strictlypositive and a good approximation of a Poisson distribution. The latter is important, since inthe kinematic domain where the data exhibit the highest sensitivity to the EW parameters, thestatistical uncertainties may become sizeable and dominating. The χ is calculated as χ = (cid:88) i j log ς i ˜ σ i V − i j log ς j ˜ σ j , (21)where the sum runs over all data points with measured cross sections ς i and the correspondingtheory predictions, ˜ σ i . The covariance matrix V i j is constructed from all relative uncertainties,taking also correlated uncertainties between the data sets into account [58]. The beam polar-isation measurements provide four additional data points, included in the vector ς , with theiruncertainties [72] and four corresponding parameters in the fit.The PDF fit alone, i.e. all EW parameters set to their SM values [40], yields a fit quality of χ / n dof = / (1414 − = .
03, where the number of degrees of freedom, n dof , is calculatedfrom 1410 cross section data points plus 4 measurements of the polarisation, and considering13 PDF and 4 fit polarisation parameters. This indicates an overall good description of the databy the employed model. More detailed studies of the QCD analysis with the given data sampleshave been presented previously [58, 67]. This section reports the results of di ff erent fits, starting with mass determinations in section 5.1,followed by weak NC coupling determinations in section 5.2 and the study of ρ (cid:48) NC , κ (cid:48) NC and ρ (cid:48) CC parameters in section 5.3. The masses of the W and Z bosons, as well as the top-quark mass are determined using di ff erentprescriptions to fix the fit parameters of the EW theory in the OS scheme. The di ff erent prescrip-tions lead to di ff erent sensitivities of the measured cross sections to the EW parameters [73].The results are summarised in table 2.In the combined m W + PDF fit, where α , m Z , m t , m H and m f are taken as external input val-ues [40], the EW parameter m W is determined to be m W = . ± . stat ± . syst ± . PDF = . ± . tot GeV . (22)11 it parameters Result Independent input parameters m W + PDF m W = . ± . stat ± . syst ± . PDF
GeV α , m Z , m t , m H , m f m prop W + PDF m prop W = . ± . stat ± . syst ± . PDF
GeV α , m W , m Z , m t , m H , m f m ( G F , m W ) W + PDF m ( G F , m W ) W = . ± . stat ± . syst ± . PDF
GeV α , G F , m t m H , m f m Z + PDF m Z = . ± . stat ± . syst ± . PDF
GeV α , m W , m t , m H , m f m t + PDF m t = ± stat ± syst ± PDF ± m W GeV α , m W , m Z , m H , m f Table 2: Results for five combined fits of mass parameters together with PDFs. The multiple uncer-tainties correspond to statistical (stat), experimental systematic (syst) and PDF uncertainties. The m t determination also includes an uncertainty due to the uncertainty of the W mass. The most-right columnlists further input parameters not varied in the fit. and the expected uncertainty is 0.118 GeV. The total (tot) uncertainty is improved by abouta factor of two in comparison to the earlier result based on HERA-I data only [35]. The un-certainty decomposition is derived by switching o ff the uncertainty sources subsequently orrepeating the fit with fixed PDF parameters . Other uncertainties due to the input masses ( m Z , m t , m H ) and theoretical uncertainties, e.g. from incompletely known higher-order terms in ∆ r ,or model and parameterisation uncertainties of the PDF fit, are all found to be negligible withrespect to the experimental uncertainty. The correlation of m W with any of the PDF parametersis weak, with absolute values of the correlation coe ffi cients below 0.2. The global correlationcoe ffi cient [75] of m W in the EW + PDF analysis is 0.64. The m W sensitivity arises predomi-nantly from the CC data, with the most important constraint being the normalisation through G F (see equations (11) and (17)). The highest sensitivity of the H1 data to m W is at a Q valueof about 3800 GeV . The result for m W is compared to determinations from other single exper-iments [76–83] in figure 2, and is found to be consistent with these as well as with the worldaverage value of 80 . ± .
015 GeV [40, 84]. The W -mass determination in the space-likeregime at HERA can be interpreted as an indirect constraint on G F through equation (17), how-ever in a process at large momentum transfer. Using the world average value of m Z [19, 40],the result obtained here, m W = . ± .
115 GeV, represents an indirect determination of theweak mixing angle in the OS scheme as sin θ W = . ± . m W determination matches the anticipated HERA results in [73] and in [38, 85].Alternative determinations of m W are also explored. One option is to use exclusively the de-pendence of the CC cross section on the propagator mass σ CC ∝ (cid:16) m W / ( m W + Q ) (cid:17) . The resultis m prop W = . ± .
79 GeV, with an expected uncertainty of 0.80 GeV. This improves theprecision of the corresponding fit to HERA-I data [35] by more than a factor of two. The valueis consistent with the world average value and with the result of the m W + PDF fit.Another m W determination is based on the high precision measurement of G F [13], which isperformed at low energy, together with α as main external input. For this fit, m Z is a predic-tion and is given by the G F - m W - m Z relation in equation (17). With the precise knowledge of G F , the normalisations of the CC predictions are known, and therefore the predominant sensi-tivity to m W arises from the W -boson propagator, and the m W dependence through m Z in the The expected uncertainty is obtained from a re-fit using the Asimov data set and the data uncertainties [74]. The PDF uncertainty contains both a statistical and a systematic component, but the systematic componentdominates. W m PDG
H1OPALL3DELPHID0CDFATLAS ALEPH
W-boson mass H1 Figure 2: Value of the W -boson mass compared to results obtained by the ATLAS, ALEPH, CDF, D0,DELPHI, L3 and OPAL experiments, and the world average value. The inner error bars indicate statisti-cal uncertainties and the outer error bars full uncertainties. NC normalisation is small. In this fit, the value of m W , denoted as m ( G F , m W ) W , is determined as m ( G F , m W ) W = . ± .
77 GeV. The value is consistent at about 2 standard deviations with theworld average value and with the result of the m W + PDF fit above. The larger uncertainty com-pared to the fit described above is expected. This indirect determination of the W -boson massassumes the validity of the SM [38].A simultaneous determination of m W and m Z is also performed. The 68 % and 95 % confidencelevel contours of that m W + m Z + PDF fit are displayed in figure 3 (left). Sizeable uncertainties ∆ m W = . ∆ m Z = . θ W = − m W / m Z instead of m Z (figure 3, right). Amild tension of less than 3 standard deviations between the world average values for m W and m Z and the fit result is observed. The very strong correlation prevents a meaningful simultaneousdetermination of the two boson masses from the H1 data alone.In such a simultaneous determination of two mass parameters, the precise measurement of G F can be taken as additional input. Due to its great precision it e ff ectively behaves like a constraint,as was proposed earlier [54,86]. The 68% confidence level contours of the m W + m Z + PDF fit with G F as one additional input data [13], is further displayed in figure 3. As expected, the resultingvalue of m W is equivalent to the value obtained in the m ( G F , m W ) W + PDF fit. The 68% confidencelevel contour is very shallow due to the high precision of G F . The mild tension with the worldaverage values of m W and m Z is reduced in comparison to the fit without G F constraint. In the m W - m Z plane the G F constraint corresponds to a thin band. The orientation of the m W + m Z + PDFcontour is similar to the slope of the G F band, because the predominant sensitivity to m W and m Z of the H1 data arises through terms proportional to G F and sin θ W rather than the propagatorterms. This explains the large uncertainty observed in the m ( G F , m W ) W + PDF fit as compared to thenominal m W + PDF fit.The value of m Z is determined in the m Z + PDF fit to m Z = . ± .
11 GeV, to be compared13 [GeV] W m80 82 84 86 88 [ G e V ] Z m ,PDF) Z ,m W (m H1 C.L. ,PDF) 95% Z ,m W (m H1 as input F ,PDF) with G Z ,m W (m H1 ) W ,m F GW (m H1PDG 2017 -2 GeV -5 = 1.1663787(6) x 10 F G = 0.22336(10) W Q sin H1 [GeV] W m80 82 84 86 88 Z m W m - = W q s i n +PDF) Z +m W (m H1 C.L. +PDF) 95% Z +m W (m H1 as input F ,PDF) with G Z +m W (m H1 ) W ,m F GW (m H1PDG 2017 -2 GeV -5 = 1.1663787(6) x 10 F G GeV = 91.1876(21) Z m H1 Figure 3: Results of the m W + m Z + PDF fit, and the m W + m Z + PDF fit with G F as additional input. Forbetter visibility, the right panel displays the quantity sin θ W = − m W / m Z on the vertical axis andidentical results as the left panel. The 68 % confidence level (C.L.) contour of the fit including the G F measurement is very shallow. The result of the m ( G F , m W ) W fit is further indicated but without uncertainties. with the measurements at the Z pole of m Z = . ± . W -mass determination, as can be expected from figure 3.The value of m t is determined in the m t + PDF fit, where m W and m Z are taken as external input,yielding m t = ± stat ± syst ± PDF ± m W GeV. The last uncertainty accounts for the W -mass uncertainty of 15 MeV [40]. The result is consistent with direct measurements at theLHC [87–91] and Tevatron [92]. At HERA, the top quark mass contributes only through loope ff ects, this explains the moderate sensitivity and the strong dependence on the W mass.Higher-order corrections to G F (see equation (17), ∆ r ) include bosonic self-energy correc-tions [55] with a logarithmic dependence on the Higgs-boson mass, m H , and thus could, inprinciple, allow for constraints on m H [73]. At HERA, however, the Higgs-boson mass depen-dent contribution is too small and no meaningful constraints on m H can be obtained with theHERA data.A further study on the determination of EW parameters is performed, by considering the pre-cision measurements of m Z [19], G F [13], m t [40] and m H [93] as experimental input data inaddition to the H1 data. In this simplified global fit, it is observed that the H1 data cannotprovide significant constraints, for instance on the W -boson mass or its correlation to any otherparameter. This is because a precision of 7 MeV on m W is already achieved through indirectconstraints [40, 94, 95]. The weak NC couplings, defined in equations (9) and (10), enter the calculation of the structurefunctions in equations (5) and (6). They are scale dependent beyond the tree-level approxima-14 it parameters Result Correlations g uA g uV g dA g dV g uA + g uV + g dA + g dV + PDF g uA = . ± g uV = . ± − .
10 1.00 g dA = − . ± − .
10 1.00 g dV = − . ± .
13 0.70 − .
09 1.00 g uA + g uV + PDF g uA = ± g uV = ± − .
18 1.00 g dA + g dV + PDF g dA = − . ± g dV = − . ± − .
68 1.00
Table 3: Results of the fitted weak neutral-current couplings of the u - and d -type quarks. The other para-meters α , m W , m Z , m t , m H and m f are taken as external input [40]. The uncertainties quoted correspondto the total uncertainties. tion. The fit parameters for the axial-vector and vector couplings considered here are definedas the tree-level parameters, given in equations (7) and (8). The one-loop corrections are takeninto account through multiplicative factors. Results of the fits thus are compared with the SMtree-level predictions for the axial-vector and vector coupling constants. The axial-vector andvector couplings of the u - and d -type quarks, g u / dA and g u / dV , are determined in a combined fittogether with the PDF parameters and the results are presented in table 3. The two-dimensionalcontours representing the 68% confidence level for two fit parameters are displayed and com-pared with results from other experiments in figure 4 (left). The results are consistent with theSM expectation. The sensitivity on g uA and g uV is similar to LEP and D0 measurements. TheHERA measurements do not exhibit sign ambiguities or ambiguities between axial-vector andvector couplings, which are for example present in determinations from Z -decays at the pole.The results for g u / dA and g u / dV obtained from this analysis are found to be compatible withfits, where alternatively external PDFs, such as ABMP16 [97], CT14 [98], H1PDF2017 [67],MMHT14 [99] or NNPDF3.0 [100], are used and the corresponding PDF uncertainties are con-sidered in the χ definition. As explained in Section 4, this approach yields underestimateduncertainties, but provides a valuable cross check.By extracting the couplings of the u - and d -type quarks separately, i.e. fixing the couplings of theother quark type to their SM expectations and performing a g uA + g uV + PDF or g dA + g dV + PDF fit, theuncertainties reduce significantly due to weaker correlations between the fitted quark couplings.The 68% confidence level contours are also displayed in figure 4 (right), and numerical valuesare listed in table 3. It is worth to note that the results are corrected to the Born-level, whereas other experiments often considere ff ective couplings defined at the Z pole [19, 96]. Such a fixed-scale definition of couplings is not suitable forDIS, where data cover a wide range of Q values. On the other hand, the relation between tree-level and e ff ective Z -pole couplings is well known (see for example [19]), and the di ff erences of corresponding numerical values aresignificantly smaller than the achieved precision. A g1 - - q V g - - H1 (d=s,u) SLD & LEP = cD ( D0 SM
C.L. % ud H1 qA g1 - - q V g - - ) +PDF dV +g dA +g uV +g uA g ( H1 ) +PDF uV +g uA g ( H1 ) +PDF dV +g dA g ( H1 SM
C.L. % ud H1 Figure 4: Results for the weak neutral-current couplings of the u - and d -type quarks at the 68% confi-dence level (C.L.) obtained with the g uA + g uV + g dA + g dV + PDF fit. The left panel shows a comparison withresults from the D0, LEP and SLD experiments (the mirror solutions are not shown). The 68% C.L.contours of the H1 results correspond to ∆ χ = .
3, where at the contour all other fit parameters areminimised. The SM expectation is displayed as a star. The right panel shows a comparison of resultsfrom fits where the couplings of one quark type are fit parameters, and the couplings of the other quarktype are fixed, i.e. the g uA + g uV + PDF and g dA + g dV + PDF fits. ρ (cid:48) NC , κ (cid:48) NC and ρ (cid:48) CC parameters The values of the ρ (cid:48) NC , f and κ (cid:48) NC , f parameters (c.f. equations (18) and (19)) are deter-mined for u - and d -type quarks and for electrons in ρ (cid:48) NC , u + κ (cid:48) NC , u + PDF, ρ (cid:48) NC , d + κ (cid:48) NC , d + PDF and ρ (cid:48) NC , e + κ (cid:48) NC , e + PDF fits, respectively. In these fits, the respective ρ (cid:48) NC and κ (cid:48) NC parameters are freefit parameters, while the other ρ (cid:48) and κ (cid:48) NC parameters are set to one and the SM EW parametersare fixed. Scale-dependent quantities such as ρ NC , f , κ NC , f , ρ CC , f are calculated in the OS schemeas outlined in section 2. The results are presented in table 4 and the 68% confidence level con-tours for the individual light quarks and for electrons are shown in figure 5. The results arecompatible with the SM expectation at 1–2 standard deviations. The parameters of the d -typequarks exhibit larger uncertainties than those of the u -type quarks. This is due to the smallelectric charge of the d quark in the leading γ Z -interference term (see equations (5) and (6)),and also in g dV (see equation (10)). Furthermore, the d -valence component of the PDF is smallerthan the u -valence component.The results of the ρ (cid:48) NC , u + κ (cid:48) NC , u + PDF and ρ (cid:48) NC , d + κ (cid:48) NC , d + PDF fits (table 4) are equivalent to the val-ues determined for the NC couplings in g uA + g uV + PDF and g dA + g dV + PDF fits, as presented above.The results can be compared to the combined results for sin θ ( u , d )e ff and ρ ( u , d ) from the LEP + SLDexperiments [19]: while the uncertainties are of similar size, the present determinations considerdata from a single experiment only.A simultaneous determination of ρ (cid:48) NC , u , ρ (cid:48) NC , d , κ (cid:48) NC , u and κ (cid:48) NC , d is performed, i.e. a ρ (cid:48) NC , u + ρ (cid:48) NC , d + κ (cid:48) NC , u + κ (cid:48) NC , d + PDF fit, and the results are given in the appendix B. The results are16 it parameters Result Correlation ρ (cid:48) NC , u + κ (cid:48) NC , u + PDF ρ (cid:48) NC , u = . ± . κ (cid:48) NC , u = . ± .
12 0.61 ρ (cid:48) NC , d + κ (cid:48) NC , d + PDF ρ (cid:48) NC , d = . ± . κ (cid:48) NC , d = . ± .
85 0.92 ρ (cid:48) NC , e + κ (cid:48) NC , e + PDF ρ (cid:48) NC , e = . ± . κ (cid:48) NC , e = . ± .
06 0.74 ρ (cid:48) NC , d + κ (cid:48) NC , d + ρ (cid:48) NC , u + κ (cid:48) NC , u + PDF see appendix B ρ (cid:48) NC , q + κ (cid:48) NC , q + PDF ρ (cid:48) NC , q = . ± . κ (cid:48) NC , q = . ± .
11 0.69 ρ (cid:48) NC , q + κ (cid:48) NC , q + ρ (cid:48) NC , e + κ (cid:48) NC , e + PDF see appendix B ρ (cid:48) NC , f + κ (cid:48) NC , f + PDF ρ (cid:48) NC , f = . ± . κ (cid:48) NC , f = . ± .
05 0.83
Table 4: Results for ρ (cid:48) NC and κ (cid:48) NC parameters and their correlation coe ffi cients. The parameters α , m W , m Z , m t , m H and m f are set to their SM values. The uncertainties quoted correspond to the total uncertainties. NC,f ' r NC ,f ' k )PDF+ NC,u ' k + NC,u ' r ( u )PDF+ NC,d ' k + NC,d ' r ( d )PDF+ NC,q ' k + NC,q ' r ( u=d )PDF+ NC,e ' k + NC,e ' r ( e SM C.L. % H1 Figure 5: Results for the ρ (cid:48) NC , f and κ (cid:48) NC , f parameters for u - and d -type quarks and electrons at 68% con-fidence level (C.L.), obtained with the ρ (cid:48) NC , u + κ (cid:48) NC , u + PDF, ρ (cid:48) NC , d + κ (cid:48) NC , d + PDF and ρ (cid:48) NC , e + κ (cid:48) NC , e + PDF fits,respectively. The SM expectation is displayed as a star. The contour of the d -type quark is truncated dueto the limited scale of the panel. For comparison, also the result of the ρ (cid:48) NC , q + κ (cid:48) NC , q + PDF fit is displayed,where quark universality is assumed ( u = d ). The results of the ρ (cid:48) NC , u + κ (cid:48) NC , u + PDF and ρ (cid:48) NC , d + κ (cid:48) NC , d + PDFfits are equivalent to the g uA + g uV + PDF and g dA + g dV + PDF fits, respectively, displayed in figure 4. compatible with the SM expectation. These results exhibit sizeable uncertainties, which aredue to the very strong correlations between the EW parameters. The exception is κ (cid:48) NC , u , whichexhibits less strong correlations with the other EW parameters.Assuming quark universality ( ρ (cid:48) NC , q = ρ (cid:48) NC , u = ρ (cid:48) NC , d and κ (cid:48) NC , q = κ (cid:48) NC , u = κ (cid:48) NC , d ), the results ofa ρ (cid:48) NC , q + κ (cid:48) NC , q + PDF fit is presented in table 4 and displayed in figure 5. These determinationsare dominated by the u -type quark couplings. The ρ (cid:48) NC , q and κ (cid:48) NC , q parameters can be deter-mined together with the electron parameters ρ (cid:48) NC , e and κ (cid:48) NC , e in a ρ (cid:48) NC , q + κ (cid:48) NC , q + ρ (cid:48) NC , e + κ (cid:48) NC , e + PDFfit. Results are given in the appendix B and no significant deviation from the SM expectation isobserved.Assuming the parameters ρ (cid:48) NC and κ (cid:48) NC to be identical for quarks and leptons, then denoted as17 it parameters Result Correlation ρ (cid:48) CC , eq + ρ (cid:48) CC , e ¯ q + PDF ρ (cid:48) CC , eq = . ± . ρ (cid:48) CC , e ¯ q = . ± . − . ρ (cid:48) NC , f + κ (cid:48) NC , f + ρ (cid:48) CC , f + PDF see appendix B
Table 5: Results for ρ (cid:48) CC parameters. The other parameters α , m W , m Z , m t , m H and m f are fixed to theirSM values. The uncertainties quoted correspond to the total uncertainties. ρ (cid:48) NC , f and κ (cid:48) NC , f , these parameters are determined in a ρ (cid:48) NC , f + κ (cid:48) NC , f + PDF fit and results are againlisted in table 4. The values exhibit the smallest uncertainties and no significant deviation fromunity is observed as expected in the SM.The values of the ρ (cid:48) CC , eq and ρ (cid:48) CC , e ¯ q parameters of the CC cross sections are determined in a ρ (cid:48) CC , eq + ρ (cid:48) CC , e ¯ q + PDF fit and results are listed in table 5. The 68% confidence level contours areshown in figure 6. The parameters are found to be consistent with the SM expectation.
CC,eq ' r q CC , e ' r )PDF+ qCC,e ' r + CC,eq ' r ( H1 SM
C.L. % H1 Figure 6: Results for the ρ (cid:48) CC , eq and ρ (cid:48) CC , e ¯ q parameters at the 68% confidence level (C.L.) obtained withthe ρ (cid:48) CC , eq + ρ (cid:48) CC , e ¯ q + PDF fit
Setting the two parameters equal, i.e. ρ (cid:48) CC , f = ρ (cid:48) CC , eq = ρ (cid:48) CC , e ¯ q , a higher precision is achieved. Theparameter ρ (cid:48) CC , f is determined together with the NC parameters in a ρ (cid:48) NC , f + κ (cid:48) NC , f + ρ (cid:48) CC , f + PDF fitto ρ (cid:48) CC , f = . ± . ρ (cid:48) NC , f + κ (cid:48) NC , f + PDF fit, as presented in table 4.The inclusive NC and CC cross sections have been measured over a wide range of Q values atHERA. This can be exploited to perform tests of models beyond the SM where scale-dependentmodifications of coupling parameters are predicted. Such tests could not be performed by theLEP and SLD experiments [40].In order to study the scale dependence of possible extensions of EW parameters in the NC sector18 [GeV] Q20 30 40 100 200 NC ,f ' r H1 SM NC,f ' r NC,q ' r NC,e ' r [GeV] Q20 30 40 100 200 NC ,f ' k H1 SM NC,f ' k NC,q ' k NC,e ' k Figure 7: Values of the ρ (cid:48) NC and κ (cid:48) NC parameters determined for four di ff erent values of Q . The errorbars, as well as the height of the shaded areas, indicate the total uncertainties of the measurement. Thewidth of the shaded areas indicates the Q range probed by the selected data. The values for the ρ (cid:48) NC , q , ρ (cid:48) NC , e , κ (cid:48) NC , q and κ (cid:48) NC , e parameters are horizontally displaced for better visibility. the values of κ (cid:48) NC and ρ (cid:48) NC are determined at di ff erent values of Q . The data at Q ≥
500 GeV are subdivided into four Q ranges and individual ρ (cid:48) NC and κ (cid:48) NC parameters are assigned to eachinterval. For Q ≤
500 GeV the SM expectation ρ (cid:48) NC = κ (cid:48) NC = ff ects at low energy scales. All parameters are determinedtogether with a common set of PDF parameters. Three separate fits are performed: first, for de-termining in each Q range two quark parameters ρ (cid:48) NC , q and κ (cid:48) NC , q assuming ρ (cid:48) NC , q = ρ (cid:48) NC , u = ρ (cid:48) NC , d and κ (cid:48) NC , q = κ (cid:48) NC , u = κ (cid:48) NC , d , while setting the lepton parameters to unity; second, for determiningthe lepton parameters κ (cid:48) NC , e and ρ (cid:48) NC , e while setting the quark parameters to unity; third, for de-termining fermion parameters κ (cid:48) NC , f and ρ (cid:48) NC , f common to both quarks and the lepton assuming ρ (cid:48) NC , f = ρ (cid:48) NC , u = ρ (cid:48) NC , d = ρ (cid:48) NC , e and κ (cid:48) NC , f = κ (cid:48) NC , u = κ (cid:48) NC , d = κ (cid:48) NC , e . Results for the ρ (cid:48) NC and κ (cid:48) NC parameters are presented in figure 7 and are given in appendix B. The values of ρ (cid:48) NC and κ (cid:48) NC in di ff erent Q intervals are largely uncorrelated, while the two parameters ρ (cid:48) NC and κ (cid:48) NC withinany given Q interval have strong correlations. The highest sensitivity to the κ (cid:48) NC f parameter ofabout 6% is found at about (cid:112) Q ∼
60 GeV. The results are found to be consistent with the SMexpectation and no significant scale dependence is observed.The possible scale dependence of the CC couplings is studied by determining the ρ (cid:48) CC parametersfor di ff erent values of Q . A total of three fits are performed, where either ρ (cid:48) CC , eq or ρ (cid:48) CC , e ¯ q (c.f.equation (20)) or ρ (cid:48) CC , f is scale dependent. The CC data are grouped into four Q intervals.Results of the ρ (cid:48) CC parameters are presented in figure 8 and are given in the appendix B. Theparameters ρ (cid:48) CC , e ¯ q have uncertainties of about 4% over a large range in Q , and the parameters ρ (cid:48) CC , eq are determined with a precision of 1.3% to 3% over the entire kinematically accessiblerange. The ρ (cid:48) CC , f parameters are determined with high precision of 1.0% to 1.8% over the entire Q range. The values are found to be consistent with the SM expectation of unity. These studiesrepresent the first determination of the ρ (cid:48) CC parameters for separate quark flavours and also its19 [GeV] Q20 30 100 200 CC ' r H1 SM CC,f ' r CC,eq ' r qCC,e ' r Figure 8: Values of the ρ (cid:48) CC parameters determined for four di ff erent values of Q . The error bars, aswell as the height of the shaded areas, indicate the total uncertainties of the measurement. The width ofthe shaded areas indicates the Q range probed by the selected data. The values for the ρ (cid:48) CC , eq and ρ (cid:48) CC , e ¯ q parameters are horizontally displaced for better visibility. first scale dependence test.The studies on the scale dependence of the ρ (cid:48) and κ (cid:48) parameters provide tests of the SM formal-ism. Investigations of specific models beyond the Standard Model such as contact interactionsor leptoquarks, also using the full H1 data sample, have been published previously [101, 102]. Parameters of the electroweak theory are determined from all neutral current and charged cur-rent deep-inelastic scattering cross section measurements published by H1, using NNLO QCDand one-loop electroweak predictions. The inclusion of the cross section data from HERA-IIwith polarised lepton beams leads to a substantial improvement in precision with respect to thepreviously published results based on the H1 HERA-I data only.In combined electroweak and PDF fits, boson and fermion mass parameters entering crosssection predictions in the on-shell scheme are determined simultaneously with the partondistribution functions. The mass of the W boson is determined from H1 data to m W = . ± .
115 GeV, fixing m Z to the world average. Alternatively the Z -boson mass or thetop-quark mass are determined with uncertainties of 110 MeV and 26 GeV, respectively, taking m W to the world average. Despite their moderate precision, these results are complementary todirect measurements where particles are produced on-shell in the final state, since here the massparameters are determined from purely virtual particle exchange only.The axial-vector and vector weak neutral-current couplings of u - and d -type quarks to the Z boson are determined and consistency with the Standard Model expectation is observed. The20xial-vector and vector couplings of the u -type quark are determined with a precision of about6% and 14%, respectively.Potential modifications of the weak coupling parameters due to physics beyond the SM arestudied in terms of modifications of the form factors ρ NC , κ NC and ρ CC . For this purpose, multi-plicative factors to those parameters are introduced, denoted as ρ (cid:48) NC , κ (cid:48) NC and ρ (cid:48) CC , respectively.A precision as good as 7% or 5% of the ρ (cid:48) NC , f and κ (cid:48) NC , f parameters is achieved, respectively.The ρ (cid:48) CC parameters are determined with a precision of up to 8 per mille, and consistency withthe Standard Model expectation is found. The Q dependence of the H1 data allows for a studyof the scale dependence of the ρ (cid:48) NC , κ (cid:48) NC and ρ (cid:48) CC parameters in the range 12 < (cid:112) Q <
100 GeV,and no significant deviation from the SM expectation is observed .
Acknowledgements
We are grateful to the HERA machine group whose outstanding e ff orts have made this ex-periment possible. We thank the engineers and technicians for their work in constructing andmaintaining the H1 detector, our funding agencies for financial support, the DESY technicalsta ff for continual assistance and the DESY directorate for support and for the hospitality whichthey extend to the non–DESY members of the collaboration.We would like to give credit to all partners contributing to the EGI computing infrastructure fortheir support for the H1 Collaboration.We express our thanks to all those involved in securing not only the H1 data but also the softwareand working environment for long term use, allowing the unique H1 data set to continue tobe explored in the coming years. The transfer from experiment specific to central resourceswith long term support, including both storage and batch systems, has also been crucial to thisenterprise. We therefore also acknowledge the role played by DESY-IT and all people involvedduring this transition and their future role in the years to come.21 ppendixA Cross section tables The reduced cross section measurements for NC DIS, as used in this analysis together withtheir systematic uncertainties [58], for di ff erent lepton beam longitudinal polarisations and forelectron and positron scattering from the HERA-II running period are given in tables 6 to 9,and the di ff erential cross section for CC DIS are given in tables 10 and 11. The reduced crosssection is related to the di ff erential cross section, equation (1), by σ red = d σ NC dxdQ xQ πα Y + . (23)The changes compared to the previously published cross sections [58] comprise the luminosityerratum [59] and the changes discussed in section 3.22 x σ red δ stat [GeV ] [%]120 0.0020 1.337 0.87120 0.0032 1.205 1.24150 0.0032 1.218 0.73150 0.0050 1.091 0.88150 0.0080 0.9375 1.20150 0.0130 0.8139 1.68200 0.0032 1.247 1.35200 0.0050 1.100 0.96200 0.0080 0.9576 0.99200 0.0130 0.7821 1.14200 0.0200 0.6935 1.23200 0.0320 0.5849 1.38200 0.0500 0.5208 1.63200 0.0800 0.4427 1.73200 0.1300 0.3591 2.09200 0.1800 0.3046 2.71250 0.0050 1.118 1.12250 0.0080 0.9705 1.10250 0.0130 0.8206 1.20250 0.0200 0.6944 1.23250 0.0320 0.5931 1.30250 0.0500 0.5069 1.48250 0.0800 0.4251 1.52250 0.1300 0.3632 1.54250 0.1800 0.3097 2.11300 0.0050 1.133 1.89300 0.0080 0.9826 1.28300 0.0130 0.8196 1.28300 0.0200 0.7027 1.42300 0.0320 0.5867 1.50300 0.0500 0.4994 1.62300 0.0800 0.4250 1.72300 0.1300 0.3621 1.71300 0.1800 0.3023 2.26300 0.4000 0.1468 2.75400 0.0080 1.048 1.54400 0.0130 0.8622 1.50400 0.0200 0.7260 1.54400 0.0320 0.6114 1.63400 0.0500 0.4951 1.84400 0.0800 0.4279 1.91400 0.1300 0.3676 1.93400 0.1800 0.3055 2.43400 0.4000 0.1469 3.09 Q x σ red δ stat [GeV ] [%]500 0.0080 1.010 2.57500 0.0130 0.9106 1.85500 0.0200 0.7435 1.83500 0.0320 0.6373 1.87500 0.0500 0.5533 1.99500 0.0800 0.4263 2.27500 0.1300 0.3740 2.54500 0.1800 0.3373 2.86500 0.2500 0.2585 3.32650 0.0130 0.9046 2.08650 0.0200 0.7765 2.14650 0.0320 0.6486 2.23650 0.0500 0.5354 2.35650 0.0800 0.4403 2.66650 0.1300 0.3684 2.94650 0.1800 0.3215 3.18650 0.2500 0.2529 4.13650 0.4000 0.1251 6.14800 0.0130 0.9258 3.50800 0.0200 0.7391 2.51800 0.0320 0.6353 2.67800 0.0500 0.5523 2.74800 0.0800 0.4430 3.04800 0.1300 0.3476 3.58800 0.1800 0.3205 3.75800 0.2500 0.2468 4.63800 0.4000 0.1373 5.931000 0.0130 0.8664 3.451000 0.0200 0.7899 2.871000 0.0320 0.6760 2.821000 0.0500 0.5166 3.151000 0.0800 0.4428 3.431000 0.1300 0.3396 4.211000 0.1800 0.3682 3.981000 0.2500 0.2659 4.611000 0.4000 0.1299 6.561200 0.0130 0.9440 5.431200 0.0200 0.7891 3.601200 0.0320 0.6964 3.271200 0.0500 0.5465 3.481200 0.0800 0.4591 3.731200 0.1300 0.3602 5.381200 0.1800 0.3308 4.651200 0.2500 0.2207 5.581200 0.4000 0.1264 7.08 Q x σ red δ stat [GeV ] [%]1500 0.0200 0.8335 4.261500 0.0320 0.6943 4.061500 0.0500 0.5646 4.021500 0.0800 0.5143 4.051500 0.1300 0.3622 5.251500 0.1800 0.3159 5.421500 0.2500 0.2365 6.051500 0.4000 0.1393 8.821500 0.6500 0.01511 14.782000 0.0219 0.9308 6.582000 0.0320 0.6562 4.892000 0.0500 0.5678 4.872000 0.0800 0.4520 5.022000 0.1300 0.3780 5.982000 0.1800 0.3071 6.522000 0.2500 0.2566 6.682000 0.4000 0.1289 8.562000 0.6500 0.01095 19.673000 0.0320 0.8036 4.413000 0.0500 0.6145 4.013000 0.0800 0.5119 4.373000 0.1300 0.4313 5.173000 0.1800 0.3004 6.143000 0.2500 0.2216 6.553000 0.4000 0.1292 7.493000 0.6500 0.01350 14.625000 0.0547 0.6974 5.985000 0.0800 0.5881 4.655000 0.1300 0.5103 5.235000 0.1800 0.3976 6.135000 0.2500 0.2348 8.025000 0.4000 0.1101 9.885000 0.6500 0.01502 16.488000 0.0875 0.6943 8.898000 0.1300 0.5661 7.108000 0.1800 0.4017 8.018000 0.2500 0.2807 9.078000 0.4000 0.1232 12.628000 0.6500 0.01091 21.8912000 0.1300 0.7921 15.4512000 0.1800 0.5805 9.5912000 0.2500 0.3347 11.1512000 0.4000 0.2244 12.4212000 0.6500 0.01526 27.8020000 0.2500 0.6549 13.3420000 0.4000 0.2329 16.5520000 0.6500 0.01985 40.8930000 0.4000 0.1845 36.0130000 0.6500 0.04510 37.8350000 0.6500 0.1250 57.78 Table 6: The NC e − p reduced cross section σ red with lepton beam polarisation P e = − .
8% with theirstatistical ( δ stat ) uncertainties. The full uncertainties are available in ref. [58], while the respective crosssection values are updated according to section 3 and ref. [59]. x σ red δ stat [GeV ] [%]120 0.0020 1.340 1.29120 0.0032 1.213 1.78150 0.0032 1.208 1.09150 0.0050 1.104 1.29150 0.0080 0.9534 1.78150 0.0130 0.7840 2.42200 0.0032 1.189 2.06200 0.0050 1.092 1.46200 0.0080 0.9487 1.44200 0.0130 0.7938 1.67200 0.0200 0.6910 1.81200 0.0320 0.5630 2.12200 0.0500 0.5323 2.48200 0.0800 0.4308 2.51200 0.1300 0.3616 2.84200 0.1800 0.3113 4.12250 0.0050 1.100 1.69250 0.0080 0.9277 1.64250 0.0130 0.7978 1.80250 0.0200 0.6690 1.86250 0.0320 0.5657 1.95250 0.0500 0.4677 2.20250 0.0800 0.4305 2.24250 0.1300 0.3710 2.29250 0.1800 0.3035 3.24300 0.0050 1.163 2.77300 0.0080 0.9754 1.89300 0.0130 0.8091 1.92300 0.0200 0.6930 2.10300 0.0320 0.5937 2.18300 0.0500 0.5014 2.46300 0.0800 0.4269 2.56300 0.1300 0.3530 2.61300 0.1800 0.2847 3.47300 0.4000 0.1523 3.91400 0.0080 0.9979 2.41400 0.0130 0.8314 2.24400 0.0200 0.6742 2.36400 0.0320 0.5909 2.46400 0.0500 0.4953 2.70400 0.0800 0.3995 3.05400 0.1300 0.3666 2.96400 0.1800 0.3074 3.45400 0.4000 0.1482 4.99 Q x σ red δ stat [GeV ] [%]500 0.0080 0.9586 3.93500 0.0130 0.8227 2.80500 0.0200 0.6873 2.80500 0.0320 0.5849 2.89500 0.0500 0.5161 3.01500 0.0800 0.4334 3.28500 0.1300 0.3687 4.14500 0.1800 0.3218 4.06500 0.2500 0.2447 5.05650 0.0130 0.8753 3.13650 0.0200 0.7334 3.26650 0.0320 0.6383 3.33650 0.0500 0.5511 3.46650 0.0800 0.4102 4.01650 0.1300 0.3354 4.99650 0.1800 0.3324 4.67650 0.2500 0.2521 5.55650 0.4000 0.1130 8.49800 0.0130 0.8344 5.20800 0.0200 0.7130 3.76800 0.0320 0.6115 3.87800 0.0500 0.5470 4.04800 0.0800 0.3842 4.83800 0.1300 0.3592 5.90800 0.1800 0.3187 6.28800 0.2500 0.2272 6.66800 0.4000 0.1210 9.461000 0.0130 0.8399 5.191000 0.0200 0.7135 4.481000 0.0320 0.6349 4.661000 0.0500 0.5027 4.741000 0.0800 0.4182 5.211000 0.1300 0.3902 5.821000 0.1800 0.3002 6.431000 0.2500 0.2774 6.711000 0.4000 0.1267 9.921200 0.0130 0.7777 9.001200 0.0200 0.7689 5.371200 0.0320 0.6439 5.031200 0.0500 0.5285 5.221200 0.0800 0.4649 5.531200 0.1300 0.3395 7.001200 0.1800 0.2714 7.601200 0.2500 0.2206 8.261200 0.4000 0.1337 10.01 Q x σ red δ stat [GeV ] [%]1500 0.0200 0.7317 6.681500 0.0320 0.6439 6.221500 0.0500 0.5514 6.001500 0.0800 0.4600 6.351500 0.1300 0.3344 10.171500 0.1800 0.2695 8.791500 0.2500 0.2555 8.681500 0.4000 0.09316 13.161500 0.6500 0.01262 23.632000 0.0219 0.7628 10.622000 0.0320 0.6464 7.292000 0.0500 0.5190 7.572000 0.0800 0.4552 7.372000 0.1300 0.3166 9.692000 0.1800 0.2939 9.832000 0.2500 0.2322 10.392000 0.4000 0.1216 12.932000 0.6500 0.008022 33.443000 0.0320 0.6126 7.463000 0.0500 0.6022 5.963000 0.0800 0.4925 6.633000 0.1300 0.3542 8.443000 0.1800 0.3105 9.003000 0.2500 0.2919 8.593000 0.4000 0.09196 12.933000 0.6500 0.005166 35.575000 0.0547 0.5881 9.545000 0.0800 0.4575 7.685000 0.1300 0.4144 8.495000 0.1800 0.3602 9.475000 0.2500 0.2529 16.815000 0.4000 0.1434 12.825000 0.6500 0.01324 25.888000 0.0875 0.6279 13.948000 0.1300 0.4992 11.138000 0.1800 0.3997 11.748000 0.2500 0.2553 14.048000 0.4000 0.1182 18.938000 0.6500 0.01682 26.7712000 0.1300 0.7385 23.4212000 0.1800 0.4153 16.7312000 0.2500 0.3198 16.7212000 0.4000 0.1575 21.8612000 0.6500 0.01281 44.8320000 0.2500 0.2146 34.1120000 0.4000 0.2378 24.3020000 0.6500 0.01372 70.8930000 0.4000 0.2765 43.4030000 0.6500 0.04110 57.81 Table 7: The NC e − p reduced cross section σ red with lepton beam polarisation P e = .
0% with theirstatistical ( δ stat ) uncertainties. The full uncertainties are available in ref. [58], while the respective crosssection values are updated according to section 3 and ref. [59]. x σ red δ stat [GeV ] [%]120 0.0020 1.367 0.97120 0.0032 1.249 1.38150 0.0032 1.248 0.82150 0.0050 1.096 1.00150 0.0080 0.9470 1.36150 0.0130 0.8224 1.92200 0.0032 1.263 1.55200 0.0050 1.122 1.08200 0.0080 0.9667 1.09200 0.0130 0.8071 1.24200 0.0200 0.7003 1.38200 0.0320 0.5918 1.61200 0.0500 0.5312 1.79200 0.0800 0.4385 1.99200 0.1300 0.3722 2.25200 0.1800 0.3266 2.97250 0.0050 1.128 1.25250 0.0080 0.9659 1.24250 0.0130 0.8085 1.38250 0.0200 0.6896 1.40250 0.0320 0.5789 1.46250 0.0500 0.5079 1.57250 0.0800 0.4438 1.71250 0.1300 0.3836 1.81250 0.1800 0.3011 2.39300 0.0050 1.135 2.13300 0.0080 0.9749 1.45300 0.0130 0.8181 1.45300 0.0200 0.7086 1.60300 0.0320 0.5926 1.69300 0.0500 0.5053 1.82300 0.0800 0.4462 1.85300 0.1300 0.3717 1.93300 0.1800 0.3081 2.52300 0.4000 0.1551 3.06400 0.0080 1.025 1.77400 0.0130 0.8345 1.71400 0.0200 0.7131 1.77400 0.0320 0.6080 1.91400 0.0500 0.5019 2.05400 0.0800 0.4265 2.15400 0.1300 0.3662 2.11400 0.1800 0.3066 2.76400 0.4000 0.1572 3.56 Q x σ red δ stat [GeV ] [%]500 0.0080 0.9862 2.93500 0.0130 0.8805 2.10500 0.0200 0.7446 2.09500 0.0320 0.6097 2.28500 0.0500 0.5252 2.29500 0.0800 0.4306 2.48500 0.1300 0.4018 2.93500 0.1800 0.3160 3.13500 0.2500 0.2502 3.83650 0.0130 0.8789 2.35650 0.0200 0.7456 2.47650 0.0320 0.6240 2.56650 0.0500 0.5102 2.74650 0.0800 0.4037 3.04650 0.1300 0.3624 3.30650 0.1800 0.3269 3.57650 0.2500 0.2449 4.65650 0.4000 0.1366 6.70800 0.0130 0.7990 3.94800 0.0200 0.7034 2.84800 0.0320 0.5953 3.09800 0.0500 0.5276 3.14800 0.0800 0.4697 3.35800 0.1300 0.3511 4.04800 0.1800 0.3237 4.18800 0.2500 0.2226 5.17800 0.4000 0.1247 7.211000 0.0130 0.8326 3.891000 0.0200 0.7443 3.281000 0.0320 0.5882 3.381000 0.0500 0.5003 3.581000 0.0800 0.4275 3.881000 0.1300 0.3378 4.751000 0.1800 0.3008 4.921000 0.2500 0.2354 5.561000 0.4000 0.1210 7.751200 0.0130 0.7975 6.751200 0.0200 0.6749 4.321200 0.0320 0.6406 3.761200 0.0500 0.5253 3.951200 0.0800 0.4256 4.331200 0.1300 0.3242 5.381200 0.1800 0.2971 5.471200 0.2500 0.2680 5.621200 0.4000 0.1086 8.59 Q x σ red δ stat [GeV ] [%]1500 0.0200 0.6695 5.311500 0.0320 0.5980 5.221500 0.0500 0.5295 4.551500 0.0800 0.4702 5.121500 0.1300 0.3057 6.351500 0.1800 0.2927 6.321500 0.2500 0.2585 6.391500 0.4000 0.1211 8.891500 0.6500 0.01573 16.042000 0.0219 0.6690 8.552000 0.0320 0.5502 5.992000 0.0500 0.5168 5.632000 0.0800 0.4365 5.552000 0.1300 0.3138 7.222000 0.1800 0.2954 7.372000 0.2500 0.2150 7.852000 0.4000 0.1188 9.922000 0.6500 0.01324 19.283000 0.0320 0.5883 5.613000 0.0500 0.4774 5.023000 0.0800 0.4114 5.363000 0.1300 0.3340 6.383000 0.1800 0.2711 7.113000 0.2500 0.2219 7.073000 0.4000 0.1272 8.293000 0.6500 0.01302 16.945000 0.0547 0.4324 7.865000 0.0800 0.3520 6.385000 0.1300 0.3150 7.325000 0.1800 0.2647 8.195000 0.2500 0.2278 8.925000 0.4000 0.09719 11.655000 0.6500 0.007011 27.878000 0.0875 0.2552 15.588000 0.1300 0.2586 11.148000 0.1800 0.2346 11.318000 0.2500 0.2234 11.018000 0.4000 0.1034 15.108000 0.6500 0.01192 25.0712000 0.1300 0.2033 28.5212000 0.1800 0.2078 17.5312000 0.2500 0.1426 18.7012000 0.4000 0.07284 24.3512000 0.6500 0.008088 44.9320000 0.2500 0.1039 32.8620000 0.4000 0.07670 31.8220000 0.6500 0.01353 57.87 Table 8: The NC e + p reduced cross section σ red with lepton beam polarisation P e = − .
0% with theirstatistical ( δ stat ) uncertainties. The full uncertainties are available in ref. [58], while the respective crosssection values are updated according to section 3 and ref. [59]. x σ red δ stat [GeV ] [%]120 0.0020 1.353 0.87120 0.0032 1.192 1.27150 0.0032 1.224 0.74150 0.0050 1.096 0.88150 0.0080 0.9530 1.22150 0.0130 0.7836 1.71200 0.0032 1.225 1.40200 0.0050 1.094 0.97200 0.0080 0.9510 0.98200 0.0130 0.7985 1.11200 0.0200 0.6889 1.22200 0.0320 0.5832 1.40200 0.0500 0.5022 1.62200 0.0800 0.4385 1.77200 0.1300 0.3558 1.96200 0.1800 0.3053 2.68250 0.0050 1.124 1.13250 0.0080 0.9603 1.10250 0.0130 0.8134 1.22250 0.0200 0.7022 1.25250 0.0320 0.5830 1.31250 0.0500 0.5018 1.45250 0.0800 0.4335 1.46250 0.1300 0.3587 1.60250 0.1800 0.2972 2.20300 0.0050 1.140 1.94300 0.0080 0.9790 1.29300 0.0130 0.8001 1.31300 0.0200 0.7169 1.44300 0.0320 0.5788 1.51300 0.0500 0.4936 1.66300 0.0800 0.4384 1.71300 0.1300 0.3724 1.75300 0.1800 0.3087 2.26300 0.4000 0.1476 2.95400 0.0080 0.9859 1.60400 0.0130 0.8665 1.49400 0.0200 0.7125 1.57400 0.0320 0.5910 1.68400 0.0500 0.4989 1.85400 0.0800 0.4340 2.00400 0.1300 0.3538 1.94400 0.1800 0.3076 2.51400 0.4000 0.1435 3.13 Q x σ red δ stat [GeV ] [%]500 0.0080 0.9862 2.69500 0.0130 0.8622 1.85500 0.0200 0.7448 1.89500 0.0320 0.6130 1.95500 0.0500 0.5351 2.06500 0.0800 0.4512 2.21500 0.1300 0.3739 2.49500 0.1800 0.3124 2.91500 0.2500 0.2508 3.60650 0.0130 0.8444 2.14650 0.0200 0.7301 2.21650 0.0320 0.6681 2.28650 0.0500 0.5319 2.38650 0.0800 0.4372 2.68650 0.1300 0.3882 3.20650 0.1800 0.3478 3.07650 0.2500 0.2389 3.85650 0.4000 0.1352 5.35800 0.0130 0.8458 3.47800 0.0200 0.7083 2.52800 0.0320 0.6392 2.60800 0.0500 0.5330 2.90800 0.0800 0.4504 3.06800 0.1300 0.3663 3.54800 0.1800 0.3316 3.68800 0.2500 0.2574 4.23800 0.4000 0.1215 6.451000 0.0130 0.7831 3.641000 0.0200 0.7302 2.971000 0.0320 0.6470 2.861000 0.0500 0.5420 3.091000 0.0800 0.4554 3.401000 0.1300 0.3484 4.491000 0.1800 0.3044 4.351000 0.2500 0.2559 4.741000 0.4000 0.1382 8.521200 0.0130 0.8759 5.781200 0.0200 0.7496 3.641200 0.0320 0.5929 3.511200 0.0500 0.5162 3.521200 0.0800 0.4456 3.761200 0.1300 0.3656 4.551200 0.1800 0.3449 5.251200 0.2500 0.2404 5.971200 0.4000 0.1103 7.57 Q x σ red δ stat [GeV ] [%]1500 0.0200 0.7066 4.631500 0.0320 0.6057 4.291500 0.0500 0.5409 4.001500 0.0800 0.4435 4.311500 0.1300 0.3634 5.161500 0.1800 0.3161 5.381500 0.2500 0.2148 6.221500 0.4000 0.1278 7.551500 0.6500 0.01479 14.782000 0.0219 0.7342 7.482000 0.0320 0.5603 5.242000 0.0500 0.5596 4.832000 0.0800 0.4293 5.032000 0.1300 0.3821 6.712000 0.1800 0.3152 6.342000 0.2500 0.2608 6.452000 0.4000 0.1368 8.152000 0.6500 0.01480 17.193000 0.0320 0.6145 5.013000 0.0500 0.5424 4.223000 0.0800 0.4717 4.453000 0.1300 0.3559 5.533000 0.1800 0.3364 7.173000 0.2500 0.2359 6.203000 0.4000 0.1200 7.643000 0.6500 0.01293 15.665000 0.0547 0.5109 6.665000 0.0800 0.4688 4.985000 0.1300 0.3724 5.995000 0.1800 0.3302 6.595000 0.2500 0.2143 8.445000 0.4000 0.1151 9.785000 0.6500 0.01243 18.628000 0.0875 0.4324 10.538000 0.1300 0.3196 9.018000 0.1800 0.2936 9.018000 0.2500 0.2262 13.158000 0.4000 0.1021 13.638000 0.6500 0.01562 19.2812000 0.1300 0.2127 27.7312000 0.1800 0.2220 15.0312000 0.2500 0.1707 15.3312000 0.4000 0.1257 16.9412000 0.6500 0.02261 24.2920000 0.2500 0.1423 25.0620000 0.4000 0.1118 23.6720000 0.6500 0.006952 71.0030000 0.4000 0.07828 51.2830000 0.6500 0.01392 70.94 Table 9: The NC e + p reduced cross section σ red with lepton beam polarisation P e = .
5% with theirstatistical ( δ stat ) uncertainties. The full uncertainties are available in ref. [58], while the respective crosssection values are updated according to section 3 and ref. [59]. x σ δ stat [GeV ] [pb / GeV ] [%]300 0.008 2 .
03 40.6300 0.013 0 .
934 14.4300 0.032 0 .
309 14.0300 0.080 0 . · − .
799 9.8500 0.032 0 .
252 8.1500 0.080 0 . · − . · − .
482 10.21000 0.032 0 .
232 6.21000 0.080 0 . · − . · − .
150 5.82000 0.080 0 . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − Q x σ δ stat [GeV ] [pb / GeV ] [%]300 0.008 1 .
18 47.2300 0.013 0 .
428 35.0300 0.032 0 .
129 24.9300 0.080 0 . · − .
412 20.5500 0.032 0 .
143 16.3500 0.080 0 . · − . · − .
286 19.91000 0.032 0 .
116 12.81000 0.080 0 . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − Table 10: The CC e − p cross section σ = d σ CC / dxdQ for lepton polarisation P e = − .
8% (left)and P e = .
0% (right) with their statistical ( δ stat ) uncertainties. The full uncertainties are available inref. [58], while the respective cross section values are updated according to section 3 and ref. [59]. x σ δ stat [GeV ] [pb / GeV ] [%]300 0.008 1 .
21 38.5300 0.013 0 .
414 28.4300 0.032 0 .
102 23.6300 0.080 0 . · − .
286 20.4500 0.032 0 .
105 15.2500 0.080 0 . · − . · − .
241 18.41000 0.032 0 .
124 9.91000 0.080 0 . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − Q x σ δ stat [GeV ] [pb / GeV ] [%]300 0.008 0 .
778 49.3300 0.013 0 .
593 20.4300 0.032 0 .
273 11.9300 0.080 0 . · − .
57 23.2500 0.013 0 .
670 11.4500 0.032 0 .
252 8.5500 0.080 0 . · − . · − .
392 12.51000 0.032 0 .
176 7.41000 0.080 0 . · − . · − .
104 7.32000 0.080 0 . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − . · − Table 11: The CC e + p cross section σ = d σ CC / dxdQ for lepton polarisation P e = − .
0% (left)and P e = .
5% (right) with their statistical ( δ stat ) uncertainties. The full uncertainties are available inref. [58], while the respective cross section values are updated according to section 3 and ref. [59]. Results of fits with many parameters
Table 12 quotes the fit of ρ (cid:48) NC , κ (cid:48) NC and ρ (cid:48) CC parameters and their correlation coe ffi cients. Ta-bles 13 to 18 quote fits of scale-dependent ρ (cid:48) NC , κ (cid:48) NC and ρ (cid:48) CC parameters and their correlationcoe ffi cients. Fit parameters Result Correlation ρ (cid:48) NC , u + κ (cid:48) NC , u + ρ (cid:48) NC , d + κ (cid:48) NC , d + PDF ρ (cid:48) NC , u = ± κ (cid:48) NC , u = ± ρ (cid:48) NC , d = ± − . − .
26 1.00 κ (cid:48) NC , d = − . ± − . − .
34 0.993 1.00 ρ (cid:48) NC , q + κ (cid:48) NC , q + ρ (cid:48) NC , e + κ (cid:48) NC , e + PDF ρ (cid:48) NC , q = ± κ (cid:48) NC , q = ± − .
02 1.00 ρ (cid:48) NC , e = ± − .
99 0.09 1.00 κ (cid:48) NC , e = ± − . − .
10 0.33 1.00 ρ (cid:48) NC , f + κ (cid:48) NC , f + ρ (cid:48) CC , f + PDF ρ (cid:48) NC f = ± κ (cid:48) NC f = ± ρ (cid:48) CC , f = ± − .
12 1.00
Table 12: Results for ρ (cid:48) NC , κ (cid:48) NC and ρ (cid:48) CC parameters, and their correlation coe ffi cients, from fits withmore than two EW parameters. For the ρ (cid:48) NC , d + κ (cid:48) NC , d + ρ (cid:48) NC , u + κ (cid:48) NC , u + PDF fit the uncertainties are onlyapproximate since χ is not described by a quadratic dependence on the fit parameters. The uncertaintiesquoted correspond to the total uncertainties. Q range [GeV ] Parameter Result Correlation[561 , ρ (cid:48) NC , q ± , ρ (cid:48) NC , q ± , ρ (cid:48) NC , q ± , ρ (cid:48) NC , q ± , κ (cid:48) NC , q ± , κ (cid:48) NC , q ± , κ (cid:48) NC , q ± , κ (cid:48) NC , q ± Table 13: Results for the ρ (cid:48) NC , q and κ (cid:48) NC , q parameters determined at di ff erent values of Q . The Q rangeof the data selection, and the correlation coe ffi cients of the fit parameters are indicated. range [GeV ] Parameter Result Correlation[561 , ρ (cid:48) NC , e ± , ρ (cid:48) NC , e ± , ρ (cid:48) NC , e ± , ρ (cid:48) NC , e ± , κ (cid:48) NC , e ± , κ (cid:48) NC , e ± , κ (cid:48) NC , e ± , κ (cid:48) NC , e ± Table 14: Results for the ρ (cid:48) NC , e and κ (cid:48) NC , e parameters determined at di ff erent values of Q . The Q rangeof the data selection, and the correlation coe ffi cients of the fit parameters are indicated. Q range [GeV ] Parameter Result Correlation[561 , ρ (cid:48) NC , f ± , ρ (cid:48) NC , f ± , ρ (cid:48) NC , f ± , ρ (cid:48) NC , f ± , κ (cid:48) NC , f ± , κ (cid:48) NC , f ± , κ (cid:48) NC , f ± , κ (cid:48) NC , f ± Table 15: Results for the ρ (cid:48) NC , f and κ (cid:48) NC , f parameters determined at di ff erent values of Q . The Q rangeof the data selection, and the correlation coe ffi cients of the fit parameters are indicated. Q range [GeV ] Parameter Result Correlation[224 , ρ (cid:48) CC , eq ± , ρ (cid:48) CC , eq ± , ρ (cid:48) CC , eq ± , ρ (cid:48) CC , eq ± − .
03 0.01 0.12 1.00
Table 16: Results for the ρ (cid:48) CC , eq parameters determined at di ff erent values of Q . The Q range of thedata selection, and the correlation coe ffi cients of the fit parameters are indicated. Q range [GeV ] Parameter Result Correlation[224 , ρ (cid:48) CC , e ¯ q ± , ρ (cid:48) CC , e ¯ q ± , ρ (cid:48) CC , e ¯ q ± , ρ (cid:48) CC , e ¯ q ± Table 17: Results for the ρ (cid:48) CC , e ¯ q parameters determined at di ff erent values of Q . The Q range of thedata selection, and the correlation coe ffi cients of the fit parameters are indicated. range [GeV ] Parameter Result Correlation[224 , ρ (cid:48) CC , f ± , ρ (cid:48) CC , f ± , ρ (cid:48) CC , f ± , ρ (cid:48) CC , f ± − . − .
01 0.12 1.00
Table 18: Results for the ρ (cid:48) CC , f parameters determined at di ff erent values of Q . The Q range of the dataselection, and the correlation coe ffi cients of the fit parameters are indicated. eferences [1] Gargamelle Neutrino Collaboration, F. J. Hasert et al. , Phys. Lett.
46B (1973) 138.[2] D. Haidt,
Adv. Ser. Direct. High Energy Phys.
23 (2015) 165.[3] S. L. Glashow,
Nucl. Phys.
22 (1961) 579.[4] S. Weinberg,
Phys. Rev. Lett.
19 (1967) 1264.[5] S. Weinberg,
Phys. Rev. Lett.
27 (1971) 1688.[6] S. Weinberg,
Phys. Rev.
D5 (1972) 1412.[7] A. Salam and J. C. Ward,
Phys. Lett.
13 (1964) 168.[8] P. W. Higgs,
Phys. Lett.
12 (1964) 132.[9] P. W. Higgs,
Phys. Rev. Lett.
13 (1964) 508.[10] F. Englert and R. Brout,
Phys. Rev. Lett.
13 (1964) 321.[11] C. Y. Prescott et al. , Phys. Lett.
77B (1978) 347.[12] C. Y. Prescott et al. , Phys. Lett.
84B (1979) 524.[13] MuLan Collaboration, V. Tishchenko et al. , Phys. Rev.
D87 (2013) 052003, arXiv:1211.0960 .[14] G. L. Fogli and D. Haidt,
Z. Phys.
C40 (1988) 379.[15] A. Blondel et al. , Z. Phys.
C45 (1990) 361.[16] CHARM Collaboration, J. V. Allaby et al. , Z. Phys.
C36 (1987) 611.[17] E770, E744, CCFR Collaboration, K. S. McFarland et al. , Eur. Phys. J.
C1 (1998) 509, arXiv:hep-ex/9701010 .[18] NuTeV Collaboration, G. P. Zeller et al. , Phys. Rev. Lett.
88 (2002) 091802, arXiv:hep-ex/0110059 . [Erratum: Phys. Rev. Lett. 90 (2003) 239902].[19] SLD Electroweak Group, DELPHI, ALEPH, SLD, SLD Heavy Flavour Group, OPAL,LEP Electroweak Working Group, L3 Collaboration, S. Schael et al. , Phys. Rept. arXiv:hep-ex/0509008 .[20] CMS Collaboration, S. Chatrchyan et al. , Phys. Rev.
D84 (2011) 112002, arXiv:1110.2682 .[21] DELPHI, OPAL, LEP Electroweak, ALEPH, L3 Collaboration, S. Schael et al. , Phys.Rept.
532 (2013) 119, arXiv:1302.3415 .[22] LHCb Collaboration, R. Aaij et al. , JHEP
11 (2015) 190, arXiv:1509.07645 .[23] ATLAS Collaboration, G. Aad et al. , JHEP
09 (2015) 049, arXiv:1503.03709 .[24] CDF, D0 Collaboration, T. A. Aaltonen et al. , Phys. Rev.
D97 (2018) 112007, arXiv:1801.06283 . 3225] H1 Collaboration, T. Ahmed et al. , Phys. Lett.
B324 (1994) 241.[26] H1 Calorimeter Group Collaboration, B. Andrieu et al. , Nucl. Instrum. Meth.
A336(1993) 460.[27] H1 Collaboration, I. Abt et al. , Nucl. Instrum. Meth.
A386 (1997) 310.[28] H1 Collaboration, I. Abt et al. , Nucl. Instrum. Meth.
A386 (1997) 348.[29] H1 SPACAL Group Collaboration, R. D. Appuhn et al. , Nucl. Instrum. Meth.
A386(1997) 397.[30] H1 Collaboration, S. Aid et al. , Phys. Lett.
B379 (1996) 319, arXiv:hep-ex/9603009 .[31] ZEUS Collaboration, J. Breitweg et al. , Eur. Phys. J.
C12 (2000) 411, arXiv:hep-ex/9907010 . [Erratum: Eur. Phys. J. C2 (2003) 305].[32] H1 Collaboration, C. Adlo ff et al. , Eur. Phys. J.
C13 (2000) 609, arXiv:hep-ex/9908059 .[33] H1 Collaboration, C. Adlo ff et al. , Eur. Phys. J.
C19 (2001) 269, arXiv:hep-ex/0012052 .[34] ZEUS Collaboration, S. Chekanov et al. , Phys. Lett.
B539 (2002) 197, arXiv:hep-ex/0205091 . [Erratum: Phys. Lett. B552 (2003) 308].[35] H1 Collaboration, A. Aktas et al. , Phys. Lett.
B632 (2006) 35, arXiv:hep-ex/0507080 .[36] ZEUS Collaboration, H. Abramowicz et al. , Phys. Rev.
D93 (2016) 092002, arXiv:1603.09628 .[37] I. Abt et al. , Phys. Rev.
D94 (2016) 052007, arXiv:1604.05083 .[38] A. M. Cooper-Sarkar, A. Bodek, K. Long, E. Rizvi and H. Spiesberger,
J. Phys.
G25(1999) 1387, arXiv:hep-ph/9902277 .[39] M. Klein and T. Riemann,
Z. Phys.
C24 (1984) 151.[40] Particle Data Group Collaboration, C. Patrignani et al. , Chin. Phys.
C40 (2016) 100001.[41] A. Sirlin,
Phys. Rev.
D22 (1980) 971.[42] A. Sirlin,
Phys. Rev.
D29 (1984) 89.[43] M. B¨ohm, H. Spiesberger and W. Hollik,
Fortsch. Phys.
34 (1986) 687.[44] W. Hollik,
Fortsch. Phys.
38 (1990) 165.[45] M. B¨ohm and H. Spiesberger,
Nucl. Phys.
B294 (1987) 1081.[46] D. Yu. Bardin, C. Burdik, P. C. Khristova and T. Riemann,
Z. Phys.
C42 (1989) 679.[47] W. Hollik, D. Yu. Bardin, J. Bl¨umlein, B. A. Kniehl, T. Riemann and H. Spiesberger,“Electroweak parameters at HERA: Theoretical aspects,” in
Workshop on physics atHERA Hamburg, Germany, October 29-30, 1991 , p. 923. 1992, MPI-PH-92-30.3348] M. B¨ohm and H. Spiesberger,
Nucl. Phys.
B304 (1988) 749.[49] D. Yu. Bardin, K. C. Burdik, P. K. Khristova and T. Riemann,
Z. Phys.
C44 (1989) 149.[50] B. Heinemann, S. Riess and H. Spiesberger, “Radiative corrections for charged currentscattering: A comparison of computer codes,” in
Monte Carlo generators for HERAphysics. Proceedings, Workshop, Hamburg, Germany, 1998-1999 , p. 530. 1998.[51] H. Spiesberger, “EPRC: A program package for electroweak physics at HERA,” in
Future physics at HERA. Proceedings, Workshop, Hamburg, Germany, September 25,1995-May 31, 1996. Vol. 1, 2 . 1995.[52] A. Kwiatkowski, H. Spiesberger and H. J. M¨ohring,
Comput. Phys. Commun.
69 (1992)155.[53] K. Charchula, G. A. Schuler and H. Spiesberger,
Comput. Phys. Commun.
81 (1994)381.[54] H. Spiesberger,
Adv. Ser. Direct. High Energy Phys.
14 (1995) 626.[55] W. J. Marciano and A. Sirlin,
Phys. Rev.
D22 (1980) 2695. [Erratum: Phys. Rev. D31(1985) 213].[56] H1 Collaboration, F. D. Aaron et al. , Eur. Phys. J.
C71 (2011) 1579, arXiv:1012.4355 .[57] H1 Collaboration, C. Adlo ff et al. , Eur. Phys. J.
C30 (2003) 1, arXiv:hep-ex/0304003 .[58] H1 Collaboration, F. D. Aaron et al. , JHEP
09 (2012) 061, arXiv:1206.7007 .[59] H1 Collaboration, F. D. Aaron et al. , Eur. Phys. J.
C72 (2012) 2163, arXiv:1205.2448 . [Erratum: Eur. Phys. J. C74 (2012) 2733].[60] H1 Collaboration, C. Adlo ff et al. , Nucl. Phys.
B497 (1997) 3, arXiv:hep-ex/9703012 .[61] H1 Collaboration, C. Adlo ff et al. , Eur. Phys. J.
C21 (2001) 33, arXiv:hep-ex/0012053 .[62] H1 Collaboration, F. D. Aaron et al. , Eur. Phys. J.
C63 (2009) 625, arXiv:0904.0929 .[63] H1 Collaboration, F. D. Aaron et al. , Eur. Phys. J.
C64 (2009) 561, arXiv:0904.3513 .[64] A. Vogt, S. Moch and J. A. M. Vermaseren,
Nucl. Phys.
B691 (2004) 129, arXiv:hep-ph/0404111 .[65] S. Moch, J. A. M. Vermaseren and A. Vogt,
Nucl. Phys.
B688 (2004) 101, arXiv:hep-ph/0403192 .[66] H1 and ZEUS Collaborations, H. Abramowicz et al. , Eur. Phys. J.
C75 (2015) 580, arXiv:1506.06042 .[67] H1 Collaboration, V. Andreev et al. , Eur. Phys. J.
C77 (2017) 791, arXiv:1709.07251 .[68] S. Alekhin et al. , Eur. Phys. J.
C75 (2015) 304, arXiv:1410.4412 .3469] M. Botje,
Comput. Phys. Commun.
182 (2011) 490, arXiv:1005.1481 .[70] M. Botje, arXiv:1602.08383 .[71] H1 Collaboration, V. Andreev et al. , Eur. Phys. J.
C75 (2015) 65, arXiv:1406.4709 .[72] B. Sobloher, R. Fabbri, T. Behnke, J. Olsson, D. Pitzl, S. Schmitt and J. Tomaszewska, arXiv:1201.2894 .[73] J. Bl¨umlein, M. Klein and T. Riemann, “Testing the electroweak Standard Model atHERA,” in
Physics at future accelerators, Proceedings, 10th Warsaw symposium onelementary particle physics, Kazimierz, Poland, May 24-30, 1987 , p. 39. 1987,PHE-87-03.[74] G. Cowan, K. Cranmer, E. Gross and O. Vitells,
Eur. Phys. J.
C71 (2011) 1554, arXiv:1007.1727 . [Erratum: Eur. Phys. J. C73 (2013) 2501].[75] F. James and M. Roos,
Comput. Phys. Commun.
10 (1975) 343.[76] ALEPH Collaboration, R. Barate et al. , Phys. Lett.
B415 (1997) 435.[77] L3 Collaboration, M. Acciarri et al. , Phys. Lett.
B407 (1997) 419.[78] OPAL Collaboration, K. Ackersta ff et al. , Phys. Lett.
B389 (1996) 416.[79] DELPHI Collaboration, J. Abdallah et al. , Eur. Phys. J.
C55 (2008) 1, arXiv:0803.2534 .[80] D0 Collaboration, V. M. Abazov et al. , Phys. Rev. Lett.
108 (2012) 151804, arXiv:1203.0293 .[81] CDF Collaboration, T. Aaltonen et al. , Phys. Rev. Lett.
108 (2012) 151803, arXiv:1203.0275 .[82] CDF Collaboration, T. A. Aaltonen et al. , Phys. Rev.
D89 (2014) 072003, arXiv:1311.0894 .[83] ATLAS Collaboration, M. Aaboud et al. , Eur. Phys. J.
C78 (2018) 110, arXiv:1701.07240 .[84] CDF, D0 Collaboration, T. A. Aaltonen et al. , Phys. Rev.
D88 (2013) 052018, arXiv:1307.7627 .[85] R. Beyer, E. Elsen, S. Riess, F. Zetsche and H. Spiesberger, “Electroweak precision testswith deep inelastic scattering at HERA,” in
Future physics at HERA. Proceedings,Workshop, Hamburg, Germany, September 25, 1995-May 31, 1996. Vol. 1, 2 . 1995.[86] V. Brisson, F. W. B¨usser, F. Niebergall, E. Elsen, D. Haidt, M. Hapke and M. Kuhlen,“The Measurement of electroweak parameters at HERA,” in
Workshop on Physics atHERA Hamburg, Germany, October 29-30, 1991 , p. 947. 1991.[87] ATLAS Collaboration, G. Aad et al. , Eur. Phys. J.
C75 (2015) 330, arXiv:1503.05427 . 3588] CMS Collaboration, V. Khachatryan et al. , Phys. Rev.
D93 (2016) 072004, arXiv:1509.04044 .[89] CMS Collaboration, A. M. Sirunyan et al. , Phys. Rev.
D96 (2017) 032002, arXiv:1704.06142 .[90] ATLAS Collaboration, M. Aaboud et al. , JHEP
09 (2017) 118, arXiv:1702.07546 .[91] CMS Collaboration, “Measurement of the top quark mass with lepton + jets final statesin pp collisions at √ s =
13 TeV,” CMS-PAS-TOP-17-007, CERN, Geneva, 2017. https://cds.cern.ch/record/2284594 .[92] CDF and D0 Collaboration, T. E. W. Group and T. Aaltonen, arXiv:1608.01881 .[93] ATLAS, CMS Collaboration, G. Aad et al. , Phys. Rev. Lett.
114 (2015) 191803, arXiv:1503.07589 .[94] J. de Blas, M. Ciuchini, E. Franco, S. Mishima, M. Pierini, L. Reina and L. Silvestrini,
JHEP
12 (2016) 135, arXiv:1608.01509 .[95] J. Haller, A. Hoecker, R. Kogler, K. M¨onig, T. Pei ff er and J. Stelzer, Eur. Phys. J.
C78(2018) 675, arXiv:1803.01853 .[96] D0 Collaboration, V. M. Abazov et al. , Phys. Rev.
D84 (2011) 012007, arXiv:1104.4590 .[97] S. Alekhin, J. Bl¨umlein, S. Moch and R. Placakyte,
Phys. Rev.
D96 (2017) 014011, arXiv:1701.05838 .[98] S. Dulat, T.-J. Hou, J. Gao, M. Guzzi, J. Huston, P. Nadolsky, J. Pumplin, C. Schmidt,D. Stump and C. P. Yuan,
Phys. Rev.
D93 (2016) 033006, arXiv:1506.07443 .[99] L. A. Harland-Lang, A. D. Martin, P. Motylinski and R. S. Thorne,
Eur. Phys. J.
C75(2015) 204, arXiv:1412.3989 .[100] NNPDF Collaboration, R. D. Ball et al. , JHEP
04 (2015) 040, arXiv:1410.8849 .[101] H1 Collaboration, F. D. Aaron et al. , Phys. Lett.
B704 (2011) 388–396, arXiv:1107.3716 .[102] H1 Collaboration, F. D. Aaron et al. , Phys. Lett.
B705 (2011) 52–58, arXiv:1107.2478arXiv:1107.2478