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Determination of the Strange-Quark Density of the Proton from ATLAS Measurements of the W ! ‘ and Z ! ‘‘ Cross Sections

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Determination of the Strange-Quark Density of the Proton from ATLAS Measurements of the W ! ‘� and Z ! ‘‘ Cross Sections week ending PRL 109, 012001 (2012) PHYSICAL REVIEW LETTERS 6 JULY 2012 Determination of the Strange-Quark Density of the Proton from ATLAS Measurements of the W ! ‘ and Z ! ‘‘ Cross Sections G. Aad et al.* (ATLAS Collaboration) (Received 19 March 2012; published 5 July 2012) A QCD analysis is reported of ATLAS data on inclusive WÆ and Z boson production in pp collisions at the LHC, jointly with ep deep-inelastic scattering data from HERA. The ATLAS data exhibit sensitivity to the light quark sea composition and magnitude at Bjorken x 0:01. Specifically, the data support the hypothesis of a symmetric composition of the light quark sea at low x. The ratio of the strange-to-down 1 00þ0:25 2 ¼ sea quark distributions is determined to be : À0:28 at absolute four-momentum transfer squared Q 1:9 GeV2 and x ¼ 0:023. DOI: 10.1103/PhysRevLett.109.012001 PACS numbers: 12.38.Qk, 13.38.Be, 13.38.Dg, 14.20.Dh Little is known about the strange-quark distribution in with s= d ’ 1 (unsuppressed strangeness). Recent the proton. Flavor SUð3Þ symmetry suggests that the three HERMES kaon multiplicity data [13] point to a strong light sea quark distributions are equal. However, the x dependence of the strange-quark density and a rather strange quarks may be suppressed due to their larger large value of xðs þ sÞ at x ’ 0:04 and Q2 ’ 1:3 GeV2. mass. The nucleon strange density plays an important However, the interpretation of these data depends on the role for a number of physics processes, ranging from knowledge of the fragmentation of strange quarks to K measurements at proton-proton colliders of W boson pro- mesons at low Q2. duction associated with charm jets [1] and of the W boson In the present Letter it is shown that the differential mass [2], to the formation of strange matter [3] and neu- measurements of the inclusive WÆ and Z boson cross trino interactions at ultrahigh energies [4]. sections at the LHC, recently performed by the ATLAS Knowledge of the parton distribution functions (PDFs) collaboration using 35 pbÀ1 of pp collision data recorded of the proton comes mainly from deep-inelastic lepton in 2010 [14], provide new constraints on the strange-quark 2 2 proton scattering experiments covering a broad range of distribution at high scale, Q MW;Z, which imply con- 2 Q , the absolute four-momentum transfer squared, and of straints at low Q2 through pQCD evolution. Because of the Bjorken x. The PDFs are determined from data using weak couplings of the quarks involved, complementary perturbative quantum chromodynamics (pQCD). The re- information to F2 is provided which also constrains xÆ. gion x & 0:01 is primarily constrained by the precise mea- A quantity of special interest is the ratio of the (Wþ þ WÀ) 2 surement of the proton structure function F2ðx; Q Þ at and Z cross sections which is sensitive to the flavor com- HERA [5], which determines a specific combination of position of the quark sea [12,15,16] and is rather insensi- light quark and antiquark distributions. However, the flavor tive to the influence of higher order pQCD corrections [17]. composition of the total light sea, xÆ ¼ 2xðu þ d þ sÞ, The inclusive electromagnetic and weak Drell-Yan scatter- has not been determined at these x values. ing process is theoretically well understood [18,19]. The The strange-quark distribution has been accessed in parton distribution analysis is performed here in next-to- charged current neutrino scattering through the subpro- next-to leading order (NNLO) QCD using the ATLAS data þ À cesses W s ! c and W s ! c. This measurement has jointly with inclusive deep-inelastic scattering data from been made by the NuTeV [6] and CCFR [7] experiments, HERA. providing information on the strange and antistrange den- The combined eÆp cross-section measurements of H1 2 2 sity at x 0:1 and Q 10 GeV . However, the interpre- and ZEUS [5] cover a kinematic range of Q2 from near tation of these data is sensitive to uncertainties from charm 1 GeV2 to above 104 GeV2 and of x from 0:6 down to fragmentation and nuclear corrections. The analyses 10À4. The ATLAS data access a kinematic range pre- of Refs. [8–11] suggest strangeness suppression, with scribed by the boson masses, MW;Z, and the proton beam s= d & 0:5, whereas the analysis of Ref. [12] is consistent ¼ 3 5 TeV 2 ’ 2 energy, Ep : , corresponding to Q MW;Z and an x range 0:001 & x & 0:1, with a mean x ¼ MZ=2Ep ¼ 0:013 for the Z boson. The WÆ and Z boson differential *Full author list given at the end of the article. cross sections have been measured [14] as functions of the W decay lepton (e, ) pseudorapidity, , and of the Z Published by the American Physical Society under the terms of l the Creative Commons Attribution 3.0 License. Further distri- boson rapidity, yZ, respectively, with an experimental pre- bution of this work must maintain attribution to the author(s) and cision of typically ð1–2Þ% in each bin. The absolute nor- the published article’s title, journal citation, and DOI. malization of the three cross sections is known to within 0031-9007=12=109(1)=012001(17) 012001-1 Ó 2012 CERN, for the ATLAS Collaboration week ending PRL 109, 012001 (2012) PHYSICAL REVIEW LETTERS 6 JULY 2012 2 3.4%. Many systematic uncertainties on the measurements Both fits result in good overall =NDF values of of the WÆ and Z boson cross sections are fully correlated. 546:1=567 with 13 free parameters, for fixed s,andof These correlations are taken into account in the analysis. 538:4=565 with 15 free parameters, for free s. For the fixed 2 The present QCD analysis uses the HERAFITTER frame- s fit, the partial of the ATLAS data is 44.5 for 30 work [5,20,21]. The light quark coefficient functions are data points. This improves significantly to 33.9 for the fit calculated to NNLO as implemented in QCDNUM [22]. The with free s. This fit determines the value of rs ¼0:5ðsþsÞ=d contributions of heavy quarks are calculated in the general- to be mass variable-flavor-number scheme of Refs. [23,24]. The ¼ 1 00 Æ 0 20 expÆ0 07modþ0:10parþ0:06 Æ 0 08th electroweak parameters and corrections relevant for the W rs : : : À0:15 À0:07 S : ; and Z boson production processes are determined follow- (2) ing the procedure described in Ref. [14], and the results are 2 cross-checked between the FEWZ [19] and the DYNNLO [18] at Q0 and x ¼ 0:023,thex value, which corresponds to ¼ 0 013 2 ¼ 2 programs. The HERAFITTER package uses the APPLGRID x : at Q MZ as a result of QCD evolution. The ¼ 1 00þ0:25 code [25] interfaced to the MCFM program [26] for fast combined result is rs : À0:28. calculation of the differential W and Z boson cross sections The uncertainty of rs, Eq. (2), is dominated by the at NLO and a K-factor technique to correct from NLO to experimental (exp) uncertainty, which is mostly driven NNLO predictions. The data are compared to the theory by the statistical and systematic uncertainties of the W using the 2 function defined in Refs. [27–29]. and Z cross-section measurements. The model (mod) un- The evolution equations yield the PDFs at any value of certainty includes effects due to variations (1:25 <mc < 2 Q given that they are parametrized as functions of x at an 1:55 GeV and 4:5 <mb < 5:0 GeV) of the charm and 2 initial scale Q0. In the present analysis, this scale is chosen beauty quark masses following Ref. [30], of the minimum 2 2 2 5 2 10 GeV2 to be Q0 ¼ 1:9 GeV such that it is below the charm mass Q cut value ( <Qmin < ), and the value of the 2 2 1 5 GeV2 threshold mc. The heavy quark masses are chosen to be starting scale (Q0 lowered to : ). The largest con- Æ0 05 mc ¼ 1:4 GeV and mb ¼ 4:75 GeV. The strong coupling tribution to the model uncertainty of : comes from the constant is fixed to SðMZÞ¼0:1176, as in Ref. [5]. A variation of the charm quark mass. The parametrization 2 2 2 minimum Q cut of Qmin 7:5 GeV is imposed on the (par) uncertainty corresponds to the envelope of the results HERA data. obtained with the polynomials Pi, in Eq. (1), extended by The quark distributions at the initial scale are repre- one or two terms, resulting in somewhat different parton 2 sented by the generic form distributions with similar as for the nominal fit. The parametrization uncertainty also includes a fit with Bs free. Bi Ci The uncertainty corresponds to a variation of ðM Þ xqiðxÞ¼Aix ð1 À xÞ PiðxÞ; (1) s s Z from 0.114 to 0.121. Finally, a theoretical (th) uncertainty is assessed by comparing the DYNNLO and FEWZ predic- where PiðxÞ denotes polynomials in powers of x. The þ À parametrized quark distributions, xq , are chosen to be tions on the Z, W , and W fiducial cross sections, which i agree at the level of 0.2, 0.5, and 1.0%, respectively. In the valence quark distributions (xuv, xdv) and the light antiquark distributions (xu, xd, xs). The gluon distribution addition, remaining missing pure electroweak corrections may alter the QCD predictions at the per-thousand level.
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