Analytical calculation of massive Feynman diagrs and the NLO - PowerPoint PPT Presentation

Analytical calculation of massive Feynman diagrs and the NLO corrections to gg → H and H → γγ Roberto BONCIANI Departament de F´ ısica Te` orica, IFIC CSIC-Universitat de Val` encia E-46071 Val` encia, Spain In collaboration with: U. Aglietti, G. Degrassi and A. Vicini RADCOR 2007, Florence, October 2, 2007 – p.1/31

Plan of the Talk Introduction NLO QCD corrections: analytical expressions for the virtual and real contributions U. Aglietti, R. B., G. Degrassi and A. Vicini R. B., G. Degrassi and A. Vicini Applications: Manohar-Wise model MSSM: squark contribution Summary RADCOR 2007, Florence, October 2, 2007 – p.2/31

SM Higgs production at the LHC Large gluon luminosity = ⇒ dominant production mech. g t, b σ (pp → H+X) [ pb ] H 10 2 √ s = 14 TeV g M t = 175 GeV gg → H VBF: 10 CTEQ4M q q W, Z 1 H W, Z qq → Hqq _ ’ → HW q q -1 qq 10 Associated prod. with Q ¯ Q : -2 10 g Q _ → Htt _ gg,qq -3 H 10 _ → Hbb _ gg,qq _ → HZ qq ¯ g Q -4 10 0 200 400 600 800 1000 Associated prod. with W, Z : M H [ GeV ] q W, Z (Djouadi-Spira-Zerwas) q ¯ H RADCOR 2007, Florence, October 2, 2007 – p.3/31

SM Higgs decays (BR) m H < 140 GeV H → b ¯ b dominant process, but at LHC 1 _ huge QCD background! bb WW H → γγ is a rare process BR(H) ( BR ∼ 10 − 3 ), but ZZ experimentally clean -1 10 τ + τ − γ t, b _ cc H - tt gg γ -2 10 m H > 140 GeV dominant decay channels are γγ Z γ H → WW, ZZ f -3 ¯ 10 f V 50 100 200 500 1000 H M H [ GeV ] ¯ V f f (Djouadi-Spira-Zerwas) RADCOR 2007, Florence, October 2, 2007 – p.4/31

SM predictions for Higgs production RADCOR 2007, Florence, October 2, 2007 – p.5/31

SM predictions for Higgs production LO Georgi-Glashow-Machacek-Nanopoulos ’78 RADCOR 2007, Florence, October 2, 2007 – p.5/31

SM predictions for Higgs production LO Georgi-Glashow-Machacek-Nanopoulos ’78 NLO QCD corrections at large p T Ellis-Hinchliffe-Soldate-van der Bij ’88, Bauer-Glover ’90 RADCOR 2007, Florence, October 2, 2007 – p.5/31

SM predictions for Higgs production LO Georgi-Glashow-Machacek-Nanopoulos ’78 NLO QCD corrections at large p T Ellis-Hinchliffe-Soldate-van der Bij ’88, Bauer-Glover ’90 NLO QCD corrections (they enhance the lowest order cross-section by 60-70%) Dawson ’91, Djouadi-Spira-Zerwas ’91, Spira-Djouadi-Graudenz-Zerwas ’95 RADCOR 2007, Florence, October 2, 2007 – p.5/31

SM predictions for Higgs production LO Georgi-Glashow-Machacek-Nanopoulos ’78 NLO QCD corrections at large p T Ellis-Hinchliffe-Soldate-van der Bij ’88, Bauer-Glover ’90 NLO QCD corrections (they enhance the lowest order cross-section by 60-70%) Dawson ’91, Djouadi-Spira-Zerwas ’91, Spira-Djouadi-Graudenz-Zerwas ’95 NNLO QCD corrections: they enhance the NLO by 15-25% ( m t → ∞ ) Harlander ’00, Catani-De Florian-Grazzini ’01, Harlander-Kilgore ’01 ’02, Anastasiou-Melnikov ’02, Ravindran-Smith-Van Neerven ’03 RADCOR 2007, Florence, October 2, 2007 – p.5/31

SM predictions for Higgs production g g t = ⇒ H H g g single real virtual double real Gluon-fusion production cross section for a Standard Model Higgs boson at the LHC (14 TeV) and at the Tevatron (2 TeV) at leading, next-to-leading, and next-to-next-to-leading order. Increase of 15-20% of the cross section. (R. Harlander) RADCOR 2007, Florence, October 2, 2007 – p.5/31

SM predictions for Higgs production LO Georgi-Glashow-Machacek-Nanopoulos ’78 NLO QCD corrections at large p T Ellis-Hinchliffe-Soldate-van der Bij ’88, Bauer-Glover ’90 NLO QCD corrections (they enhance the lowest order cross-section by 60-70%) Dawson ’91, Djouadi-Spira-Zerwas ’91, Spira-Djouadi-Graudenz-Zerwas ’95 NNLO QCD corrections: they enhance the NLO by 15-25% ( m t → ∞ ) Harlander ’00, Catani-De Florian-Grazzini ’01, Harlander-Kilgore ’01 ’02, Anastasiou-Melnikov ’02, Ravindran-Smith-Van Neerven ’03 NNLO QCD corrections with soft-gluon NNLL resummation (enhancement of 6-15% and stabilization with respect to the µ ) Catani-De Florian-Grazzini-Nason ’03 RADCOR 2007, Florence, October 2, 2007 – p.5/31

SM predictions for Higgs production NNLL and NNLO cross-sections at the LHC (left) and Tevatron (right) using MRST2002 parton densities. Additional increase of the cross section ∼ 6 %. Decrease in the scale dependence = ⇒ Theoretical uncertainty < 10 % (confirmed by Moch-Vogt ’05). (Catani, de Florian, Grazzini and Nason) RADCOR 2007, Florence, October 2, 2007 – p.5/31

SM predictions for Higgs production LO Georgi-Glashow-Machacek-Nanopoulos ’78 NLO QCD corrections at large p T Ellis-Hinchliffe-Soldate-van der Bij ’88, Bauer-Glover ’90 NLO QCD corrections (they enhance the lowest order cross-section by 60-70%) Dawson ’91, Djouadi-Spira-Zerwas ’91, Spira-Djouadi-Graudenz-Zerwas ’95 NNLO QCD corrections: they enhance the NLO by 15-25% ( m t → ∞ ) Harlander ’00, Catani-De Florian-Grazzini ’01, Harlander-Kilgore ’01 ’02, Anastasiou-Melnikov ’02, Ravindran-Smith-Van Neerven ’03 NNLO QCD corrections with soft-gluon NNLL resummation (enhancement of 6-15% and stabilization with respect to the µ ) Catani-De Florian-Grazzini-Nason ’03 Higher order p T distribution ( m t → ∞ ); Rapidity distribution De Florian-Grazzini-Kunst ’99, Del Duca-Kilgore-Oleari-Schmidt-Zeppenfeld ’01, Bozzi-Catani-De Florian-Grazzini ’03, ’06, ’07, Anastasiou-Dixon-Melnikov ’03 RADCOR 2007, Florence, October 2, 2007 – p.5/31

SM predictions for Higgs production For small transverse momentum ( q T ≪ m H ) the q T -spectrum is affected by large logarithms of the form S ln 2 n ( m 2 α n H /q 2 T ) . They spoil the reliability of the perturba- tive series and they must be resummed. LO+NLL and NLO+NNLL q T -spectra for m H = 125 GeV Note that the NLO+NNLL band lies in the one of LO+NLL Enhancement of central value and re- (Bozzi, Catani, de Florian, Grazzini) duction of the scale dependence RADCOR 2007, Florence, October 2, 2007 – p.5/31

SM predictions for Higgs production LO Georgi-Glashow-Machacek-Nanopoulos ’78 NLO QCD corrections at large p T Ellis-Hinchliffe-Soldate-van der Bij ’88, Bauer-Glover ’90 NLO QCD corrections (they enhance the lowest order cross-section by 60-70%) Dawson ’91, Djouadi-Spira-Zerwas ’91, Spira-Djouadi-Graudenz-Zerwas ’95 NNLO QCD corrections: they enhance the NLO by 15-25% ( m t → ∞ ) Harlander ’00, Catani-De Florian-Grazzini ’01, Harlander-Kilgore ’01 ’02, Anastasiou-Melnikov ’02, Ravindran-Smith-Van Neerven ’03 NNLO QCD corrections with soft-gluon NNLL resummation (enhancement of 6-15% and stabilization with respect to the µ ) Catani-De Florian-Grazzini-Nason ’03 Higher order p T distribution ( m t → ∞ ); Rapidity distribution De Florian-Grazzini-Kunst ’99, Del Duca-Kilgore-Oleari-Schmidt-Zeppenfeld ’01, Bozzi-Catani-De Florian-Grazzini ’03, ’06, ’07, Anastasiou-Dixon-Melnikov ’03 Differential distributions Anastasiou-Melnikov-Petriello ’04-’05, Catani-Grazzini ’07 RADCOR 2007, Florence, October 2, 2007 – p.5/31

MSSM predictions for Higgs production RADCOR 2007, Florence, October 2, 2007 – p.6/31

MSSM predictions for Higgs production NLO QCD corrections fermionic corrections to A (Spira-Djouadi-Graudenz-Zerwas ’93) squark corrections to h, H , m 0 → ∞ (Dawson-Djouadi-Spira ’96) full set of corr h, H and A , m 0 → ∞ (Harlander-Steinhauser ’03/’04, Harlander-Hofmann ’06) squark contrib to h, H retaining the full dependence on m 0 (Muhlleitner-Spira ’06) RADCOR 2007, Florence, October 2, 2007 – p.6/31

MSSM predictions for Higgs production NLO QCD corrections fermionic corrections to A (Spira-Djouadi-Graudenz-Zerwas ’93) squark corrections to h, H , m 0 → ∞ (Dawson-Djouadi-Spira ’96) full set of corr h, H and A , m 0 → ∞ (Harlander-Steinhauser ’03/’04, Harlander-Hofmann ’06) squark contrib to h, H retaining the full dependence on m 0 (Muhlleitner-Spira ’06) H+jet complete one-loop MSSM calculation for the production of the lighter neutral Higgs boson in association with a high- p T hadronic jet, in hadronic collisions (Brein-Hollik ’03) fermionic one-loop contributions h, H plus one jet (Field-Dawson-Smith ’04) The NLO QCD corrections to A plus one jet ( m 0 → ∞ ) (Field-Smith-Tejeda-Yeomans-van Neerven ’03) RADCOR 2007, Florence, October 2, 2007 – p.6/31

SM predictions for H → γγ LO Ellis-Gaillard-Nanopoulos ’76, Shifman-Vainshtein-Voloshin-Zakharov ’79, NLO QCD corrections Zheng-Wu ’90, Djouadi-Spira-van der Bij-Zerwas ’91, Dawson-Kauffman ’93, Djouadi-Spira-Zerwas ’93, Melnikov-Yakovlev ’93, Inoue-Najima-Oka-Saito ’94, Steinhauser ’96 Fleischer-Tarasov-Tarasov ’04, Harlander-Kant ’05, Anastasiou-Beerli-Bucherer-Daleo-Kunst ’06, Aglietti-B.-Degrassi-Vicini ’06, Passarino-Sturm-Uccirati ’07 NLO EW corrections corrections at O ( G µ m 2 t ) (Liao-Li ’97) corrections at O ( G µ m 2 H ) (Korner-Melnikov-Yakovlev ’96) exact light-fermion contribution (Aglietti-B.-Degrassi-Vicini ’04) contributions involving top and weak bosons below W thr. (Degrassi-Maltoni ’05) full EW contributions (Passarino-Sturm-Uccirati ’07) RADCOR 2007, Florence, October 2, 2007 – p.7/31

Decay Width RADCOR 2007, Florence, October 2, 2007 – p.8/31