Parton distribution function dependence of benchmark Standard Model total cross sections at the 7 TeV LHC (pdf)

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

https://link.springer.com/content/pdf/10.1007%2FJHEP09%282011%29069.pdf

Parton distribution function dependence of benchmark Standard Model total cross sections at the 7 TeV LHC

G. Watt 0 E-mail: 0 0 Theory Group, Physics Department , CERN, CH-1211 Geneva 23, Switzerland We compare predictions for the W , Z, gg H and tt total cross sections at the Large Hadron Collider (LHC), for a centre-of-mass energy of 7 TeV, using the most recent publicly available next-to-leading order and next-to-next-to-leading order parton distribution functions (PDFs) from all PDF fitting groups. In particular, we focus on the dependence on the different values of the strong coupling, S(MZ2 ), used by each group. We also perform a comparison of the relevant quark-antiquark and gluon-gluon luminosity functions. We make some comments on the recent PDF4LHC recommendations. Finally, we discuss the comparison of data and theory for W and Z cross sections at the LHC. Contents 1 Introduction 2 3 4 PDF sets considered 2.1 Definition of PDF uncertainties 2.2 Definition of PDF correlations 2.3 Values and uncertainties of strong coupling S Comparison of partonic luminosities Total cross sections as a function of S(MZ2 ) 4.1 W and Z0 production 4.2 gg H production 4.3 tt production Discussion of PDF4LHC interim recommendations Discussion of W and Z production at the LHC Conclusions Introduction Higgs Cross Sections [17]. 2 PDF sets considered Definition of PDF uncertainties hF i = 1 NXrep F (Sk), F (Sk+) F (Sk) 2, hF Gi hF ihGi , F G F = F (S0) + F cos , G = G(S0) + G cos ( + FG) , total cross sections by 12%, with a smaller change in the Higgs cross section [52]. The combined HERA I and II inclusive data, together with the combined charm structure function F charm, will be included in a future update to MSTW08, after it is finally published. 2 Definition of PDF correlations 1 Xn F (Sk+) F (Sk) G(Sk+) G(Sk) , where [0, 2] and F (S0) should be replaced by hF i in the Monte Carlo approach. We give explicit examples in section 6 for the W and Z total cross sections at the LHC. Finally, we note that the uncertainty in a general function of the two quantities, H(F, G), is given by (see also section 4 of ref. [13]): + 2 F G cos FG HF HG . As a specific example, the fractional uncertainty in the ratio of the two quantities R F/G is therefore given by 2 NLO aS(M2Z) values used by different PDF groups NNLO aS(M2Z) values used by different PDF groups Z0 + W/Z0 ratio W+/W ratio H (120 GeV) H (180 GeV) H (240 GeV) Pert. Central PDF Exact Quad. Exact Quad. +2.1% +2.4% NLO 0.931 nb 1.5% 1.8% +1.7% +2.5% NNLO 0.959 nb 1.6% 1.8% +2.2% +2.4% NLO 10.15 nb 1.6% 1.8% +1.7% +2.6% NNLO 10.47 nb 1.6% 1.9% +2.2% +2.4% NLO 5.96 nb 1.6% 2.0% +1.8% +2.6% NNLO 6.16 nb 1.6% 1.9% +2.2% +2.5% NLO 4.19 nb 1.7% 1.9% +1.7% +2.5% NNLO 4.31 nb 1.7% 1.9% +0.2% +0.2% 10.91 0.2% 0.2% +0.2% +0.3% 10.92 0.1% 0.2% +1.0% +1.0% 1.422 0.8% 0.8% +1.0% +1.1% 1.429 0.7% 0.7% +1.4% +3.3% NLO 12.41 pb 1.7% 2.7% +1.1% +3.7% NNLO 15.71 pb 1.6% 2.8% +1.7% +3.4% NLO 5.20 pb 2.1% 2.7% +1.5% +3.8% NNLO 6.53 pb 1.8% 3.1% +2.1% +3.6% NLO 2.81 pb 2.5% 3.0% +1.9% +3.9% NNLO 3.52 pb 2.1% 3.4% +2.7% +4.3% NLO 167.9 pb 3.3% 3.9% NNLO 173.0 pb +22..77%% 4.2% +4.4% +2.3% +3.5% +4.6% 1.8% 3.2% 3.8% +2.0% +3.4% +4.4% 1.9% 3.1% 3.9% +2.3% +3.5% +4.6% 1.9% 3.3% 3.9% +2.0% +3.4% +4.6% 1.9% 3.1% 3.9% +2.3% +3.6% +4.7% 1.9% 3.3% 4.0% +2.1% +3.6% +4.9% 1.9% 3.2% 4.0% +2.4% +3.6% +4.7% 1.9% 3.5% 4.1% +2.0% +3.5% +4.4% 2.0% 3.3% 4.2% +0.2% +0.3% +0.4% 0.2% 0.3% 0.3% +0.2% +0.4% +0.5% 0.1% 0.3% 0.4% +1.0% +2.2% +2.3% 0.8% 1.6% 1.6% +1.0% +2.2% +2.3% 0.7% 1.5% 1.5% +2.3% +2.8% +7.6% 2.8% 3.1% 6.6% +2.9% +2.6% +7.3% 3.0% 3.2% 7.0% +2.5% +3.3% +7.6% 3.0% 3.5% 6.4% +3.1% +3.2% +7.5% 3.1% 3.6% 7.3% +2.8% +4.0% +7.7% 3.3% 4.1% 6.6% +3.4% +4.0% +7.9% 3.4% 4.3% 7.7% +3.5% +5.3% +8.8% 4.3% 5.4% 8.3% +4.2% +5.2% +9.5% 4.1% 5.4% 9.0% 3 Comparison of partonic luminosities Lq(qq) = 1 Z 1 dx X s s x q=d,u,s,c,b Lsgg = 1s Z 1 dxx fg(x, s)fg( /x, s), LGsG = 1s Z 1 dxx fG(x, s)fG( /x, s), (fq + fq) , Sq(qq) luminosity at LHC ( s = 7 TeV) Sq(qq) luminosity at LHC ( s = 7 TeV) gg luminosity at LHC ( s = 7 TeV) gg luminosity at LHC ( s = 7 TeV) Sq(qq) luminosity at LHC ( s = 7 TeV) gg luminosity at LHC ( s = 7 TeV) Sq(qq) luminosity at LHC ( s = 7 TeV) Sq(qq) luminosity at LHC ( s = 7 TeV) gg luminosity at LHC ( s = 7 TeV) gg luminosity at LHC ( s = 7 TeV) 4 Total cross sections as a function of S(MZ2 ) Sq(qq) luminosity at LHC ( s = 7 TeV) Sq(qq) luminosity at LHC ( s = 7 TeV) gg luminosity at LHC ( s = 7 TeV) gg luminosity at LHC ( s = 7 TeV) Sq(qq) luminosity at LHC ( s = 7 TeV) Sq(qq) luminosity at LHC ( s = 7 TeV) gg luminosity at LHC ( s = 7 TeV) gg luminosity at LHC ( s = 7 TeV) B /10.95 W s10.9 n l B10.85 0.116 0.118 0.116 0.118 NLO Z0 fi l+l- at the LHC ( s = 7 TeV) NLO Z0 fi l+l- at the LHC ( s = 7 TeV) NLO W fi ln at the LHC ( s = 7 TeV) NLO W fi ln at the LHC ( s = 7 TeV) 0.116 0.118 0.116 0.118 NLO W/Z ratio at the LHC ( s = 7 TeV) NLO W/Z ratio at the LHC ( s = 7 TeV) 0.116 0.118 0.116 0.118 Figure 7. W and Z0 total cross section (...truncated)