Markus Wobisch Louisiana Tech University All D0 Meeting

1. Determination of alpha_sfrom the inclusive jet cross section Markus Wobisch Louisiana Tech University All D0 Meeting October 23, 2009

2. Overview Topic: Determination of alpha_s Basis: D0 Run IIapublished inclusive jet cross section (Mikko’s results) This analysis: - No new experimental work - QCD fit of existing data Status: - preliminary approval for Lepton Photon 2009 - Fermilab Today result of the week  now in review for publication in PRD-RC (no changes w.r.t. preliminary result)

3. Motivation From: 2008 Review of Particle Physics • Poor entry from “Hadronic Jets” (= CDF Run I result) •  Not competitive with other relevant results • Can (and should) be improved! • We have: • better data • better theory

4. Outline • alpha_s and the renormalization group equation • data set • basic fit principle • PDFs and alpha_s • PDFs and input data • fit method • results

5. alpha_s and the RGE • Alpha_s(mu_r) : coupling constant of strong interactiondepends on renormalization scale not predicted in QCD  to be determined in experiment • Renormalization Group Equation (RGE) predicts mu_r dependence if we know value at one scale (mu_0) we know the value at any scale knowledge of alpha_s(mu_1) is equivalent to knowledge of alpha_s(mu_2) • Agreement: for easy comparisons, quote alpha_s(Mz) • In jet production: mu_r = pT

6. Running of alphas S. Bethke, arXiv:0908.1135 • Running as predicted by • Renormalization Group Equation • has been confirmed for Q  200 GeV • (LEP e+e- data) • But not yet for larger scales

7. Run IIa Inclusive Jet Data Mikko’s results: 110 incl jet x-sect data points in six |y| regions • Every single data point is sensitive to alphas(pT) • Sensitive to running of alphas(pT) • Combined fit (of selected data points): alphas(Mz) result

8. Basic priciple (naïve version) • Cross section formula: • c_n: perturbative coefficients ( pQCD matrix elements) • f_1, f_2: PDFs • Determine alpha_s from data: • Vary alpha_s until sigma-theory agrees with sigma-experiment For a single bin 

9. two additional aspects: • Naïve version of basic principle can not be directly applied • There are two additional aspects to be considered • alpha_s dependence of PDFs • correlation of observable with observables used in PDF fits

10. (1): alphas dependence of PDFs • PDFs are always determined for a given value of alpha_s(Mz) PDF fit results depend on alpha_s Naïve x-section formula must be modified to take alphas dependence of PDFs into account:  Vary alphas in matrix elements AND in PDFsuntil sigma-theory(alpha_s) = sigma-experiment • need smooth alpha-s dependence of PDFs • Requires: interpolation between cross section for PDFs with different alpha-s(Mz) values

11. (1): alphas dependence of PDFs Interpolation must cover whole range of possible uncertainties  test interpolation over: 0.105 < alphas(Mz) < 0.130 • MSTW2008 has 21 PDFs sets for alpha_s 0.110-0.130 in 0.001 steps ( 21 “nodes”) use cubic interpolation based on 4 surrounding nodes • CTEQ6.6 has five PDFs sets for alpha_s(Mz)=0.112, 0.114, 0.118, 0.122, 0.125 ( 5 “nodes”) use Lagrangian interpolation based on either - nodes 1,2,3,4,5 (all five) (danger: 4th order – may fluctuate) - nodes 1, 3, 5 (2nd order - may not be accurate around center) - nodes 2, 3, 4 (2nd order – may not be accurate away from center) - nodes 1, 2, 4, 5 (3rd order – may be poor at center)

12. (1): alphas dependence of PDFs Compare cross section interpolations for MSTW2008 and CTEQ6.6 See: For MSTW2008: nice & smooth interpolation CTEQ6.6: Significant differences between different interpolations. No obvious preference (maybe points 1,3,5 because of monotonic behavior – but can’t be justified) • Can not justify to use CTEQ6.6 • But MSTW2008 is o.k.  provide NNLO

13. (2): PDFs and input data • Conceptual problem: • Tevatron jet data have already been used in PDF fits •  only source of high-x gluon information • alpha_s extraction would be circular argument • PDFs uncertainties are correlated to experimental uncertainties(but correlation is not documented) • Restrict the data set used in the fit to x-values whereTevatron jets are not the dominant source of information • Somewhere up to x = 0.2-0.3 (see next slide)

14. (2): PDFs and input data MSTW2008 paper (see also Figs. 51, 53)  Tevatron jet data don’t affect gluon for x < 0.2 – 0.3

15. x-sensitivity? Jet cross section has access to x-values of: (in LO kinematics) • What is the x-value for a given incl. jet data point @(pT, |y|) ? • Not completely constrained (unknown kinematics since we integrate over other jet) • Construct “test-variable” (treat as if other jet was at y=0): • Apply cut on this test-variable to restrict accessible x-range • Find: requirement x-test < 0.15 removes most of the contributions with x > 0.2 - 0.3

16. x-min / x-max distributions • Fig. 3 in analysis note • Every analysis bin  one plot • Each plot: x-min/x-max distributions • Cut on test-variable x-test < 0.15 22 data points remain • These have small contributions from • x>0.2-0.3 • Only data points above green line are used • central result: stable • very minor increase in uncertainties

17. Theory Use two alternative theory predictions: • pQCD: • NLO + 2-loop threshold corrections (“NLO + 2-loop”) (threshold corrections from Kidonakis/Owens) • NLO • Uncertainties: scale dependence mu=pT (x0.5 , x2.0) • PDFs: • MSTW2008NNLO (for “NLO+2-loop”) • MSTW2008NLO (for NLO) • Uncertainties: from 20 PDF eigenvectors (68%CL) • Non perturbative corrections: (hadronization / UE) • from PYTHIA (as published with data) • Uncertainties: half the size of the correction(separately for hadronization and UE)

18. Fit Method • Minimize chi2 (as used in dijet angular distributions) •  23 experimental correlated sources of uncertainty non-perturbative corrections uncertainties PDF uncertainties • Separate treatment for renormalization and factorization scales (convention from LEP, HERA): • perform fits for fixed scale • repeat for scale factors 2.0, 0.5 • quote differences as “scale uncertainty” •  does not assume Gaussian distributed scale uncertainties

19. Single alpha_s results • Every pT data point gives one alpha_s(pT) and/or alpha_s(Mz) theory: NLO + 2-loop threshold corrections

20. x-cut dependence • Now combine all data points up to some maximum x-test (=x-cut)and extract combined alpha_s(Mz) value •  Study x-cut dependence of result •  result are stable within 1% in 0.1 < x-cut < 0.17 • Decide: use x-cut=0.15 • Consistent with assumption • that for x-test<0.15 the • Tevatron jet data are not the • dominant source of PDF information theory: NLO + 2-loop threshold corrections

21. Running of alpha_s(pT) • combine points in different |y| regions at same pT •  Produce 9 alphas(pT) points from selected 22 data points • Compare to HERA results • from H1 and ZEUS • consistency •  our results extend pT reach of HERA results theory: NLO + 2-loop threshold corrections

22. Combined alpha_s(Mz) Based on 22 inclusive jet data points with x-test<0.15 Combined alpha_s(MZ):

23. Summary New alpha_s result from Tevatron jets Run I CDF result (still quoted in alpha_s summaries): Our new result (strong improvement / same precision as HERA jets)alpha_s(Mz) = 0.1173 +0.0041 -0.0049

24. Backup

25. CDF Run I result CDF Collaboration, T. Affolder et al., Phys. Rev. Lett. 88, 042001 (2002) • Claim:“Test running over 40 < ET < 440 GeV” • Not really!!because analysis uses PDFsfor which DGLAP evolutionis already done under assumption of running according to RGE • RGE was already assumed • No independent test •  Avoid this mistake in the present D0 analysis