Topics related to MSTW PDFs Robert Thorne September 26th, 2012 University College London IPPP Research Associate Together with Alan Martin, James Stirling, Graeme Watt and Arnold Mathijssen and Ben Watt PDF4LHC IPPP – September 2012
Variety of topics - related in various ways. ● Brief reminder of results from Monte Carlo approach using MSTW PDFs from JHEP 1208 (2012) 052 (G. Watt and RT). ● Some investigations using a 3-flavour FFNS fit - (RT to be in PRD). ● Comparison of MSTW PDFs with LHC data and implications. ● Investigation of parameterisation extension dependence. Related to deuterium corrections. Implication for LHC data. PDF4LHC IPPP – September 2012 1
Study supported correctness of “dynamic tolerance” approach. 2 4 2 2 2 Up valence distribution at Q = 10 GeV 4 Down valence distribution at Q = 10 GeV 1.1 1.1 1.2 1.2 Ratio to MSTW 2008 NLO Ratio to MSTW 2008 NLO Ratio to MSTW 2008 NLO Ratio to MSTW 2008 NLO MSTW 2008 NLO (68% C.L.) MSTW 2008 NLO (68% C.L.) 1.08 1.08 1.15 1.15 Random params. (40) Random params. (40) Easiest in Hessian study with Random params. (40) Random params. (40) 1.06 1.06 Random PDFs (1000) Random PDFs (1000) 1.1 1.1 1.04 1.04 1.05 1.05 eigenvectors. 1.02 1.02 1 1 1 1 0.98 0.98 0.95 0.95 0.96 0.96 0.9 0.9 0.94 0.94 However, can generate “random” 0.85 0.85 0.92 0.92 0.9 0.9 0.8 0.8 -5 -5 -4 -4 -3 -3 -2 -2 -1 -1 -5 -5 -4 -4 -3 -3 -2 -2 -1 -1 PDF sets directly from parameters 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 x x x x and variation from eigenvectors. i + � n ± t ± a i ( S k )= a 0 � � j =1 e ij | R jk | j 2 4 2 2 4 2 Up antiquark distribution at Q = 10 GeV Down antiquark distribution at Q = 10 GeV 1.1 1.1 1.1 1.1 Ratio to MSTW 2008 NLO Ratio to MSTW 2008 NLO Ratio to MSTW 2008 NLO Ratio to MSTW 2008 NLO ( k = 1 , . . . , N pdf ) . Or from MSTW 2008 NLO (68% C.L.) MSTW 2008 NLO (68% C.L.) 1.08 1.08 1.08 1.08 Random params. (40) Random params. (40) Random params. (40) Random params. (40) 1.06 1.06 1.06 1.06 Random PDFs (1000) Random PDFs (1000) 1.04 1.04 1.04 1.04 eigenvectors directly (see LHCb 1.02 1.02 1.02 1.02 1 1 1 1 study and De Lorenzi thesis). Far 0.98 0.98 0.98 0.98 0.96 0.96 0.96 0.96 0.94 0.94 0.94 0.94 quicker. 0.92 0.92 0.92 0.92 0.9 0.9 0.9 0.9 -5 -5 -4 -4 -3 -3 -2 -2 -1 -1 -5 -5 -4 -4 -3 -3 -2 -2 -1 -1 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 x x x x F ( S ± � � � F ( S k )= F ( S 0 ) + j ) − F ( S 0 ) | R jk | j 2 4 2 2 4 2 Strange quark distribution at Q = 10 GeV Gluon distribution at Q = 10 GeV 1.1 1.1 1.05 1.05 Ratio to MSTW 2008 NLO Ratio to MSTW 2008 NLO Ratio to MSTW 2008 NLO Ratio to MSTW 2008 NLO Use in reweighting studies as MSTW 2008 NLO (68% C.L.) MSTW 2008 NLO (68% C.L.) 1.08 1.08 1.04 1.04 Random params. (40) Random params. (40) Random params. (40) Random params. (40) 1.06 1.06 1.03 1.03 Random PDFs (1000) Random PDFs (1000) 1.04 1.04 1.02 1.02 NNPDF. 1.02 1.02 1.01 1.01 1 1 1 1 0.98 0.98 0.99 0.99 0.96 0.96 0.98 0.98 0.94 0.94 0.97 0.97 0.92 0.92 0.96 0.96 0.9 0.9 0.95 0.95 -5 -5 -4 -4 -3 -3 -2 -2 -1 -1 -5 -5 -4 -4 -3 -3 -2 -2 -1 -1 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 x x x x PDF4LHC IPPP – September 2012 2
Speed of convergence of prediction for Z cross section. 0 0 NLO Z cross section at the LHC ( s = 7 TeV) NLO Z cross section at the LHC ( s = 7 TeV) 1.06 1.06 Ratio to best-fit prediction Ratio to best-fit prediction MSTW 2008 NLO PDFs (68% C.L.) MSTW 2008 NLO PDFs (68% C.L.) 1.04 1.04 Average and s.d. over N predictions Average and s.d. over N predictions pdf pdf 1.02 1.02 1 1 0.98 0.98 0.96 0.96 Same random numbers for each value of N Different random numbers for each value of N pdf pdf 0.94 0.94 3 3 2 2 10 10 10 10 10 10 Number of random predictions, N Number of random predictions, N pdf pdf Left, add a new random set to existing ones sequentially. Right, increasing numbers of independent random sets. Very good with 40 sets. Excellent with 100 sets. PDF4LHC IPPP – September 2012 3
Speed of convergence of prediction for W + /W − cross section ratio. - - + + NLO W /W cross-section ratio at the LHC ( s = 7 TeV) NLO W /W cross-section ratio at the LHC ( s = 7 TeV) 1.03 1.03 Ratio to best-fit prediction Ratio to best-fit prediction MSTW 2008 NLO PDFs (68% C.L.) MSTW 2008 NLO PDFs (68% C.L.) 1.02 1.02 Average and s.d. over N predictions Average and s.d. over N predictions pdf pdf 1.01 1.01 1 1 0.99 0.99 0.98 0.98 Same random numbers for each value of N Different random numbers for each value of N pdf pdf 0.97 0.97 2 3 2 3 10 10 10 10 10 10 Number of random predictions, N Number of random predictions, N pdf pdf Left, add a new random set to existing ones sequentially. Right, increasing numbers of independent random sets. Very good with 40 sets. Excellent with 100 sets. PDF4LHC IPPP – September 2012 4
Speed of convergence of prediction for t ¯ t cross section. NLO t t cross section at the LHC ( s = 7 TeV) NLO t t cross section at the LHC ( s = 7 TeV) 1.1 1.1 Ratio to best-fit prediction Ratio to best-fit prediction 1.08 1.08 MSTW 2008 NLO PDFs (68% C.L.) MSTW 2008 NLO PDFs (68% C.L.) 1.06 1.06 Average and s.d. over N predictions Average and s.d. over N predictions pdf pdf 1.04 1.04 1.02 1.02 1 1 0.98 0.98 0.96 0.96 0.94 0.94 Same random numbers for each value of N 0.92 0.92 Different random numbers for each value of N pdf pdf 0.9 0.9 2 3 2 3 10 10 10 10 10 10 Number of random predictions, N Number of random predictions, N pdf pdf Left, add a new random set to existing ones sequentially. Right, increasing numbers of independent random sets. Very good with 40 sets. Excellent with 100 sets. PDF4LHC IPPP – September 2012 5
Speed of convergence of prediction for H cross section. → → NLO gg H at the LHC ( s = 7 TeV) for M = 120 GeV NLO gg H at the LHC ( s = 7 TeV) for M = 120 GeV H H 1.05 1.05 Ratio to best-fit prediction Ratio to best-fit prediction 1.04 1.04 MSTW 2008 NLO PDFs (68% C.L.) MSTW 2008 NLO PDFs (68% C.L.) 1.03 1.03 Average and s.d. over N predictions Average and s.d. over N predictions pdf pdf 1.02 1.02 1.01 1.01 1 1 0.99 0.99 0.98 0.98 0.97 0.97 Same random numbers for each value of N 0.96 0.96 Different random numbers for each value of N pdf pdf 0.95 0.95 3 3 2 2 10 10 10 10 10 10 Number of random predictions, N Number of random predictions, N pdf pdf Left, add a new random set to existing ones sequentially. Right, increasing numbers of independent random sets. Very good with 40 sets. Excellent with 100 sets. PDF4LHC IPPP – September 2012 6
Can combine different PDF sets, e.g. comparison to PDF4LHC prescription. Smaller uncertainty and shifted central value if disagreement between individual predictions. (Plots by G. Watt at http://mstwpdf.hepforge.org/random/). PDF4LHC IPPP – September 2012 7
Results using a FFNS MSTW08 GMVFNS1 GMVFNS2 0.3 Performed a fit to DIS only data GMVFNS3 GMVFNS4 GMVFNS5 using the FFNS scheme. (At NLO GMVFNS6 2 (x,Q 2 ) 0.2 GMVFNSopt since NNLO still requires potentially ZMVFNS F c FFNS significant approximations). 0.1 Do not include Drell-Yan or Tevatron jet x=0.0001 data as FFNS calculations do not exist. 0 Q 2 1 2 3 4 5 6 7 8 9 As seen at higher Q 2 charm structure 0.2 MSTW08 function for FFNS always lower than any GMVFNS1 GMVFNS2 GM-VFNS. GMVFNS3 GMVFNS4 0.15 2 (x,Q 2 ) GMVFNS5 GMVFNS6 GMVFNSopt Fit a few tens of units worse than F c ZMVFNS FFNS 0.1 MSTW08 to same data (even without refitting). Slightly better for F c 2 ( x, Q 2 ) , but flatter in Q 2 for x ∼ 0 . 01 for 0.05 x=0.001 inclusive structure function. 0 Q 2 1 2 3 4 5 6 7 8 9 PDF4LHC IPPP – September 2012 8
1.1 MSTW08 PDFs evolved up to Q 2 = 10 , 000GeV 2 GMVFNSa/2008 at NLO for g(x,Q 2 ) GMVFNS1 (using variable flavour evolution for 1.05 GMVFNS2 GMVFNS3 consistent comparison) different in form to MSTW08 and GM-VFNS variants. 1 α S ( M 2 Z ) = 0 . 1187 , a bit lower than GMVFNSopt 0.95 GMVFNS4 GMVFNS5 MSTW NLO value of 0 . 1202 . GMVFNS6 ZMVFNS FFNS 0.9 PDFs do not automatically fit Tevatron -5 -4 -3 -2 -1 10 10 10 10 10 jet data well at all, and are not good for 1.1 MSTW08 GMVFNSa/2008 at NLO for u(x,Q 2 ) GMVFNS1 CDF Z rapidity data. GMVFNS2 GMVFNS3 1.05 1 GMVFNSopt 0.95 GMVFNS4 GMVFNS5 GMVFNS6 ZMVFNS FFNS 0.9 -5 -4 -3 -2 -1 10 10 10 10 10 PDF4LHC IPPP – September 2012 9
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