Jet production at the LHC in NNLO QCD Jo ao Pires The Latsis - PowerPoint PPT Presentation

M OTIVATION NNLO CALCULATIONS A NTENNA SUBTRACTION N UMERICAL RESULTS Jet production at the LHC in NNLO QCD Jo˜ ao Pires The Latsis Symposium 2013 June 5, 2013 - in collaboration with A. Gehrmann-De Ridder, T. Gehrmann, N.Glover

M OTIVATION NNLO CALCULATIONS A NTENNA SUBTRACTION N UMERICAL RESULTS I NCLUSIVE JET AND DIJET CROSS SECTIONS ◮ look at the production of jets of hadrons with large transverse energy in ◮ inclusive jet events pp → j + X ◮ exclusive dijet events pp → 2 j ◮ cross sections measured as a function of the jet p T , rapidity y and dijet invariant mass m jj in double differential form 13 10 d|y| (pb/GeV) × |y| < 0.5 ( 10 4 ) CMS × 3 11 0.5 < |y| < 1.0 ( 10 ) 10 s = 7 TeV × 1.0 < |y| < 1.5 ( 10 2 ) -1 L = 5.0 fb × 1 1.5 < |y| < 2.0 ( 10 ) × 0 anti-k R = 0.7 2.0 < |y| < 2.5 ( 10 ) T 7 10 T /dp 3 10 σ 2 d -1 10 µ µ = = p -5 10 T R F ⊗ NNPDF2.1 NP Corr. 200 300 1000 2000 Jet p (GeV) T

M OTIVATION NNLO CALCULATIONS A NTENNA SUBTRACTION N UMERICAL RESULTS I NCLUSIVE JET AND DIJET CROSS SECTIONS state of the art: ◮ dijet production is completely known in NLO QCD [Ellis, Kunszt, Soper ’92], [Giele, Glover, Kosower ’94], [Nagy ’02] ◮ NLO+Parton shower [Alioli, Hamilton, Nason, Oleari, Re ’11] ◮ threshold corrections [Kidonakis, Owens ’00] Goal: ◮ obtain the jet cross sections at NNLO accuracy in double differential form d 2 σ d 2 σ d m jj d y ∗ d p T d | y | this talk: ◮ NNLO inclusive jet and dijet cross section (gluons only, leading colour)

M OTIVATION NNLO CALCULATIONS A NTENNA SUBTRACTION N UMERICAL RESULTS T HEORETICAL VS EXPERIMENTAL UNCERTAINTIES 0.3 Cross section uncertainty |y| < 0.5 NNPDF2.1 0.4 Cross section uncertainty Total CMS s = 7 TeV |y| < 0.5 0.2 PDF s = 7 TeV Total anti-k R = 0.7 0.3 T Nonpert. L = 5.0 fb -1 JES anti-k R = 0.7 0.1 Scale Unfolding T 0.2 Luminosity 0 0.1 0 -0.1 -0.1 -0.2 -0.2 -0.3 200 300 400 1000 2000 Jet p (GeV) -0.3 200 300 400 1000 2000 T Jet p (GeV) T relative theoretical uncertainties relative experimental uncertainties for the inclusive jet production for the inclusive jet production (NLO theory input) [CMS, arXiv:1212.6660] [CMS, arXiv:1212.6660] ◮ residual uncertainty due to scale choice at NNLO expected at ≈ few percent level ◮ jet energy scale uncertainty has been determined to less than 5 % for central jets → expect steady improvement with higher statistics ◮ theoretical prediction with the same precision as the experimental data → need pQCD predictions at NNLO accuracy

M OTIVATION NNLO CALCULATIONS A NTENNA SUBTRACTION N UMERICAL RESULTS I NCLUSIVE JET AND DIJET CROSS SECTIONS Ratio to NNPDF2.1 Ratio to NNPDF2.1 CMS |y| < 0.5 CMS |y| < 0.5 Exp. Uncertainty Exp. Uncertainty 1.6 max Data s = 7 TeV Data s = 7 TeV CT10 Theo. Uncertainty -1 CT10 Theo. Uncertainty -1 L = 5.0 fb 1.5 L = 5.0 fb anti-k R = 0.7 anti-k R = 0.7 HERA1.5 HERA1.5 T T 1.4 MSTW2008 MSTW2008 ABKM09 ABKM09 1.2 1 1 0.8 0.5 0.6 200 300 400 1000 2000 200 300 400 1000 2000 3000 Jet p (GeV) M (GeV) jj T (NLO theory input) (NLO theory input) [CMS, arXiv:1212.6660] [CMS, arXiv:1212.6660] Phenomenological applications with NNLO: ◮ data can be used to constrain parton distribution functions ◮ size of NNLO correction important for precise determination of PDF’s ◮ inclusion of jet data in NNLO parton distribution fits requires NNLO corrections to jet cross sections ◮ α s determination from hadronic jet observables limited by the unknown higher order corrections

M OTIVATION NNLO CALCULATIONS A NTENNA SUBTRACTION N UMERICAL RESULTS pp → 2 j AT NNLO: GLUONIC CONTRIBUTIONS A ( 0 ) A ( 1 ) A ( 2 ) 6 ( gg → gggg ) 5 ( gg → ggg ) 4 ( gg → gg ) [Berends, Giele ’87], [Mangano, Parke, Xu ’87], [Britto, Cachazo, Feng ’06] [Bern, Dixon, Kosower ’93] [Anastasiou, Glover, Oleari, Tejeda-Yeomans ’01],[Bern, De Freitas, Dixon ’02] � � � σ RR σ RV σ VV d ˆ σ NNLO = d ˆ NNLO + d ˆ NNLO + d ˆ NNLO d Φ 4 d Φ 3 d Φ 2 ◮ explicit infrared poles from loop integrations ◮ implicit poles in phase space regions for single and double unresolved gluon emission ◮ procedure to extract the infrared singularities and assemble all the parts in a parton-level generator

M OTIVATION NNLO CALCULATIONS A NTENNA SUBTRACTION N UMERICAL RESULTS NNLO IR SUBTRACTION SCHEMES ◮ sector decomposition: expansions in distributions, numerical integration [Binoth, Heinrich ’02], [Anastasiou, Melnikov, Petriello ’03] ◮ pp → H [Anastasiou, Melnikov, Petriello ’04] ◮ pp → V [Melnikov, Petriello ’06] ◮ q T -subtraction for colorless high-mass systems [Catani, Grazzini ’07] ◮ pp → H [Catani, Grazzini ’07] ◮ pp → V [Catani, Cieri, Ferrera, de Florian, Grazzini ’09] ◮ pp → VH [Ferrera, Grazzini, Tramontano ’11] ◮ pp → γγ [Catani, Cieri, de Florian, Grazzini ’11] ◮ sector decomposition combined with subtraction [Czakon’ 11], [Boughezal, Melnikov, Petriello ’11] ◮ pp → t ¯ t [Baernreuther, Czakon, Fiedler, Mitov ’13] ◮ pp → Hj (gluons only) [Boughezal, Caola, Melnikov, Petriello, Schulze ’13] ◮ antenna subtraction [Gehrmann-De Ridder, Gehrmann, Glover ’05] ◮ e ¯ e → 3 j [Gehrmann-De Ridder, Gehrmann, Glover, Heinrich ’07], [Weinzierl 08] ◮ pp → 2 j (gluons only) [Gehrmann-De Ridder, Gehrmann, Glover, JP ’13]

M OTIVATION NNLO CALCULATIONS A NTENNA SUBTRACTION N UMERICAL RESULTS NNLO ANTENNA SUBTRACTION � � � σ RR σ S d ˆ σ NNLO = d ˆ NNLO − d ˆ NNLO d Φ 4 � � � σ RV σ T + d ˆ NNLO − d ˆ NNLO d Φ 3 � � � σ VV σ U + d ˆ NNLO − d ˆ NNLO d Φ 2 σ S σ RR ◮ d ˆ NNLO : real radiation subtraction term for d ˆ NNLO ◮ d ˆ σ T σ RV NNLO : one-loop virtual subtraction term for d ˆ NNLO ◮ d ˆ σ U σ VV NNLO : two-loop virtual subtraction term for d ˆ NNLO ◮ subtraction terms constructed using the antenna subtraction method at NNLO for hadron colliders → presence of initial state partons to take into account ◮ contribution in each of the round brackets is finite, well behaved in the infrared singular regions and can be evaluated numerically

M OTIVATION NNLO CALCULATIONS A NTENNA SUBTRACTION N UMERICAL RESULTS pp → 2 j AT NNLO [A. Gehrmann-De Ridder, T. Gehrmann, N. Glover, JP] Implementation checks (gluons only channel at leading colour): ◮ subtraction terms correctly approximate the matrix elements in all unresolved configurations of partons j , k ∀{ j , k } , { j }→ 0 σ RR , RV σ S , T d ˆ − − − − − − − − → d ˆ NNLO NNLO ◮ local (pointwise) analytic cancellation of all infrared explicit ǫ -poles when integrated subtraction terms are combined with one, two-loop matrix elements � � σ RV σ T P oles d ˆ NNLO − d ˆ = 0 NNLO � � σ VV σ U P oles d ˆ NNLO − d ˆ = 0 NNLO ◮ process independent NNLO subtraction scheme ◮ singularities in intermediate steps cancel analytically ◮ allows the computation of multiple differential distributions in a single program run

M OTIVATION NNLO CALCULATIONS A NTENNA SUBTRACTION N UMERICAL RESULTS N UMERICAL SETUP [A. Gehrmann-De Ridder, T. Gehrmann, N. Glover, JP] ◮ jets identified with the anti- k T jet algorithm ◮ jets accepted at rapidities | y | < 4 . 4 ◮ leading jet with transverse momentum p t > 80 GeV ◮ subsequent jets required to have at least p t > 60 GeV ◮ MSTW2008nnlo PDF ◮ dynamical factorization and renormalization central scale equal to the leading jet p T ( µ R = µ F = µ = p T 1 )

M OTIVATION NNLO CALCULATIONS A NTENNA SUBTRACTION N UMERICAL RESULTS N UMERICAL SETUP [A. Gehrmann-De Ridder, T. Gehrmann, N. Glover, JP] ◮ jets identified with the anti- k T jet algorithm ◮ jets accepted at rapidities | y | < 4 . 4 ◮ leading jet with transverse momentum p t > 80 GeV ◮ subsequent jets required to have at least p t > 60 GeV ◮ MSTW2008nnlo PDF ◮ dynamical factorization and renormalization central scale equal to the leading jet p T ( µ R = µ F = µ = p T 1 ) Integrated cross section results (gluons only channel) with scale variations σ 8 TeV − LO σ 8 TeV − NLO σ 8 TeV − NNLO ( pb ) ( pb ) ( pb ) incl . jet incl . jet incl . jet ( 12 . 586 ± 0 . 001 ) × 10 5 ( 11 . 299 ± 0 . 001 ) × 10 5 ( 15 . 33 ± 0 . 03 ) × 10 5 µ = 0 . 5 p T 1 ( 9 . 6495 ± 0 . 001 ) × 10 5 ( 12 . 152 ± 0 . 001 ) × 10 5 ( 15 . 20 ± 0 . 02 ) × 10 5 µ = p T 1 ( 7 . 5316 ± 0 . 001 ) × 10 5 ( 11 . 824 ± 0 . 001 ) × 10 5 ( 15 . 21 ± 0 . 01 ) × 10 5 µ = 2 . 0 p T 1 ◮ NNLO result increased by about 25% with respect to the NLO cross section

M OTIVATION NNLO CALCULATIONS A NTENNA SUBTRACTION N UMERICAL RESULTS INCLUSIVE JET p T DISTRIBUTION [A. Gehrmann-De Ridder, T. Gehrmann, N. Glover, JP] 5 10 (pb/GeV) LO 4 10 NLO NNLO 3 10 T 10 2 /dp σ 10 d 1 s =8 TeV -1 10 anti-k R=0.7 -2 10 T MSTW2008nnlo -3 10 µ µ = = p -4 10 R F T1 -5 10 -6 10 3 2 10 10 p (GeV) T 1.8 NLO/LO NNLO/NLO NNLO/LO 1.6 1.4 1.2 1 3 2 10 10 p (GeV) T ◮ NNLO effect stabilizes the NLO k-factor growth with p T

M OTIVATION NNLO CALCULATIONS A NTENNA SUBTRACTION N UMERICAL RESULTS INCLUSIVE JET p T DISTRIBUTION [A. Gehrmann-De Ridder, T. Gehrmann, N. Glover, JP] × 3 10 90 (pb) LO s =8 TeV T NLO /dp anti-k R=0.7 80 NNLO σ T d MSTW2008nnlo µ µ µ = = 70 R F 80 GeV < p < 97 GeV T 60 50 40 30 20 1 µ /p T1 ◮ flat scale dependence at NNLO