NLO electroweak corrections to SM Higgs production gg H and decay H - PowerPoint PPT Presentation

Corrections to gg → H Method for NLO EW Threshold behaviour Results Conclusions NLO electroweak corrections to SM Higgs production gg → H and decay H → γγ Stefano Actis Institut für Theoretische Physik E, RWTH Aachen University in collaboration with G. Passarino, C. Sturm and S. Uccirati 4 Dec 2008, PSI Villigen

Corrections to gg → H Method for NLO EW Threshold behaviour Results Conclusions Outline Corrections to gg → H 1 Method for NLO EW 2 Threshold behaviour 3 4 Results 5 Conclusions

Corrections to gg → H Method for NLO EW Threshold behaviour Results Conclusions Hadronic SM Higgs production Main production channel for the Standard Model Higgs in hadron collisions g q q g q t V t t H V V H H t V t t g q q g q t H SM Higgs production SM Higgs production 10 5 LHC 10 3 TeV II σ [ fb ] gg → h σ [ fb ] gg → h 10 4 qq → Wh qq → qqh 10 2 qq → qqh 10 3 bb → h qq → Wh bb → h 10 qq → Zh gg,qq → tth 10 2 gg,qq → tth qb → qth qq → Zh TeV4LHC Higgs working group TeV4LHC Higgs working group 1 100 120 140 160 180 200 100 200 300 400 500 m h [ GeV ] m h [ GeV ] Hahn,Heinemeyer,Maltoni,Weiglein,Willenbrock [hep-ph/0607308] Gluon-fusion production channel does not lead to the cleanest signal, but it has by far the largest cross section both at the T EVATRON and the LHC

Corrections to gg → H Method for NLO EW Threshold behaviour Results Conclusions LO production cross section through gluon fusion • LO cross section for gg → H by interfering quark 1-loop diagrams ˛ –˛ 2 σ LO = G F α S 2 ( µ 2 ˛ » „ « ˛ R ) 3 1 1 − 1 X ˛ ˛ f ( τ q ) τ q = M 2 H / ( 4 M 2 √ 1 + q ) ˛ ˛ ˛ 2 τ q τ q ˛ 288 2 π q ˛ ˛ f = arcsin , ln Georgi,Glashow,Machacek,Nanopoulos’78

Corrections to gg → H Method for NLO EW Threshold behaviour Results Conclusions LO production cross section through gluon fusion • LO cross section for gg → H by interfering quark 1-loop diagrams ˛ –˛ 2 σ LO = G F α S 2 ( µ 2 ˛ » „ « ˛ R ) 3 1 1 − 1 X ˛ ˛ f ( τ q ) τ q = M 2 H / ( 4 M 2 √ 1 + q ) ˛ ˛ ˛ 2 τ q τ q ˛ 288 2 π q ˛ ˛ f = arcsin , ln Georgi,Glashow,Machacek,Nanopoulos’78 • Partonic σ LO ⇒ σ LO ⊗ PDFs ⇒ LO total cross section for h 1 h 2 → H ★ ★ ⇐ Djouadi [hep-ph/0503172] ✧ ✔ ✘ ✙ ✛ ✜ ✗ ✓ ✕ ✕ ✖ ✚ ✠ ☛ ☞ ✡ ✌ ✄ ☎ ✆ ✝ ✟ � ✁ ✂ ✞ ★ ✧ ✍ ✄ ✒ ✡ ✟ ✎ ✂ ✞ ✧ ✍ ✄ ✑ ✌ ✡ ✟ ✎ ✞ ✂ ✏ ★ ✩ ✧ ★ ★ ✩ ✧ ★ ★ ★ ★ ★ ✧ ✙ ✤ ✜ ✧ ✢ ✦ ✥ ✣

Corrections to gg → H Method for NLO EW Threshold behaviour Results Conclusions LO production cross section through gluon fusion • LO cross section for gg → H by interfering quark 1-loop diagrams ˛ –˛ 2 σ LO = G F α S 2 ( µ 2 ˛ » „ « ˛ R ) 3 1 1 − 1 X ˛ ˛ f ( τ q ) τ q = M 2 H / ( 4 M 2 √ 1 + q ) ˛ ˛ ˛ 2 τ q τ q ˛ 288 2 π q ˛ ˛ f = arcsin , ln Georgi,Glashow,Machacek,Nanopoulos’78 • Partonic σ LO ⇒ σ LO ⊗ PDFs ⇒ LO total cross section for h 1 h 2 → H ❍ ❍ ⇐ Djouadi [hep-ph/0503172] ● ✾ ❂ ❃ ❅ ❆ ❁ ✽ ✿ ✿ ❀ ❄ ✳ ✵ ✶ ✴ ✷ ✭ ✮ ✯ ✰ ✲ ✪ ✫ ✬ ✱ ❍ • both setting µ R = µ F = M H ● ✸ ✭ ✼ ✴ ✲ ✹ ✬ ✱ ● • LO → strong dependence on µ R , F ✸ ✭ ✻ ✷ ✴ ✲ ✹ ✱ ✬ ✺ ❍ ■ ● • QCD corrections for reliability ❍ ❍ ■ ● ❍ ❍ ❍ ❍ ❍ ● ❃ ❉ ❆ ● ❇ ❋ ❊ ❈

Corrections to gg → H Method for NLO EW Threshold behaviour Results Conclusions QCD corrections (I) QCD corrections to the total cross section very well under control • NLO at the LHC + 80 % LO, uncertainty µ R , F variation ± 20 % Dawson’91,Djouadi,Spira,Zerwas’91 տ large M t limit Spira,Djouadi,Graudenz,Zerwas’95,Harlander,Kant’05,Anastasiou, Beerli,Bucherer,Daleo,Kunszt’06,Aglietti,Bonciani,Degrassi,Vicini’06 տ full M H , M q dependence

Corrections to gg → H Method for NLO EW Threshold behaviour Results Conclusions QCD corrections (I) QCD corrections to the total cross section very well under control • NLO at the LHC + 80 % LO, uncertainty µ R , F variation ± 20 % Dawson’91,Djouadi,Spira,Zerwas’91 տ large M t limit Spira,Djouadi,Graudenz,Zerwas’95,Harlander,Kant’05,Anastasiou, Beerli,Bucherer,Daleo,Kunszt’06,Aglietti,Bonciani,Degrassi,Vicini’06 տ full M H , M q dependence • NNLO at the LHC + 20 % NLO, uncertainty µ R , F variation ± 10 % Harlander’00,Catani,de Florian,Grazzini’01,Harlander,Kilgore’01, Anastasiou,Melnikov’02,Ravindran,Smith,van Neerven’03 տ large M t limit: integrate out top quark ⇒ point-like Hgg interaction

Corrections to gg → H Method for NLO EW Threshold behaviour Results Conclusions QCD corrections (I) QCD corrections to the total cross section very well under control • NLO at the LHC + 80 % LO, uncertainty µ R , F variation ± 20 % Dawson’91,Djouadi,Spira,Zerwas’91 տ large M t limit Spira,Djouadi,Graudenz,Zerwas’95,Harlander,Kant’05,Anastasiou, Beerli,Bucherer,Daleo,Kunszt’06,Aglietti,Bonciani,Degrassi,Vicini’06 տ full M H , M q dependence • NNLO at the LHC + 20 % NLO, uncertainty µ R , F variation ± 10 % Harlander’00,Catani,de Florian,Grazzini’01,Harlander,Kilgore’01, Anastasiou,Melnikov’02,Ravindran,Smith,van Neerven’03 տ large M t limit: integrate out top quark ⇒ point-like Hgg interaction • Total cross section dominated by long-wavelength gluon effects, insensitive to the reduction to an effective vertex ⇒ σ NNLO ≃ σ LO × K EFT NLO 90 % result up to M H ≃ 1 TeV Krämer,Laenen,Spira’96

Corrections to gg → H Method for NLO EW Threshold behaviour Results Conclusions QCD corrections (II) QCD corrections improved beyond FO and for exclusive quantities 80 σ (pp → H+X) [pb] σ (pp → H+X) [pb] 20 M H = 120 GeV M H = 240 GeV 60 15 40 10 NLO NLO 20 N 3 LO approx 5 N 3 LO approx LO LO N 2 LO N 2 LO √ 0 0 0.2 0.5 1 2 3 0.2 0.5 1 2 3 µ r / M H µ r / M H Catani,de Florian,Grazzini,Nason Moch,Vogt [hep-ph/0508265] N 3 LO soft limit ⇒ stabilized µ R [hep-ph/0306211] NNLL = + 6 % NNLO • effect of a jet veto on total CS Catani,de Florian,Grazzini’01 • differential cross section evaluated at NNLO in QCD Anastasiou,Melnikov,Petriello’04,Catani,Grazzini’07 • . . .

Corrections to gg → H Method for NLO EW Threshold behaviour Results Conclusions EW corrections (I) NLO EW corrections for matching the precision of QCD predictions • ”Dominant” contributions enhanced by M 2 t Djouadi,Gambino’94 √ σ LO × [ 1 + G F 2 / ( 16 π 2 ) M 2 t ] 0 . 4 % accidental 1) < 0 corrections to ∂ Π gg /∂ M 2 t ⇔ V Hgg through a low-energy theorem 2) > 0 ” renormalization constants for the top and the Higgs

Corrections to gg → H Method for NLO EW Threshold behaviour Results Conclusions EW corrections (I) NLO EW corrections for matching the precision of QCD predictions • ”Dominant” contributions enhanced by M 2 t Djouadi,Gambino’94 √ σ LO × [ 1 + G F 2 / ( 16 π 2 ) M 2 t ] 0 . 4 % accidental 1) < 0 corrections to ∂ Π gg /∂ M 2 t ⇔ V Hgg through a low-energy theorem 2) > 0 ” renormalization constants for the top and the Higgs • Light-quark analytically Aglietti,Bonciani,Degrassi,Vicini’04 0.1 2-loop EW q g 0.08 V 0.06 q q H 0.04 V δ g 0.02 q 0 -0.02 -0.04 100 150 200 250 300 350 400 m H (GeV) Aglietti,Bonciani,Degrassi,Vicini [hep-ph/0404071]

Corrections to gg → H Method for NLO EW Threshold behaviour Results Conclusions EW corrections (II) Top diagrams by a Taylor expansion in q H Degrassi,Maltoni’04 • for M H < 2 M W ⇒ check the cuts of each Feynman diagram • Im: M H = 2 M W ⇒ Taylor expansion in q 2 H / ( 4 M 2 W ) allowed g g g g d t b b b t Z W W H H H L R H d d t Z b t b t L L Z t W W g g g g d t b b b Im: q 2 H = M Z Im: q 2 H = 2 M t Im: q 2 H = 0 ⇒ no Taylor exp?

Corrections to gg → H Method for NLO EW Threshold behaviour Results Conclusions EW corrections (II) Top diagrams by a Taylor expansion in q H Degrassi,Maltoni’04 • for M H < 2 M W ⇒ check the cuts of each Feynman diagram • Im: M H = 2 M W ⇒ Taylor expansion in q 2 H / ( 4 M 2 W ) allowed g g g g d t b b b t Z W W H H H L R H d d t Z b t b t L L Z t W W g g g g d t b b b Im: q 2 H = M Z Im: q 2 H = 2 M t Im: q 2 H = 0 ⇒ no Taylor exp? ∗ Cut vanishes because helicites on two sides cannot match ⇒ ”naive” Taylor expansion allowed for top-quark diagrams