Standard Model Yukawa corrections to b bH production at the LHC - PowerPoint PPT Presentation

Standard Model Yukawa corrections to b ¯ bH production at the LHC LE Duc Ninh leduc@lapp.in2p3.fr Laboratoire d’Annecy-le-Vieux de Physique THeorique (LAPTH) partly based on ref. arXiv:hep-ph/0711.2005; Phys. Rev. D in press (work in collaboration with F . Boudjema) LE Duc Ninh (LAPTH) Yukawa corrections to b ¯ bH – p.1/40 PSI, 22 Jan 2008

Outline Why pp → b ¯ bH ? Tree level (LO). QCD correction at NLO. EW correction at NLO. EW correction when λ bbH = 0 . Landau singularities. The problem Conditions for Landau singularities Nature of the singularities How to solve the problem? Examples Conclusions and outlooks. LE Duc Ninh (LAPTH) Yukawa corrections to b ¯ bH – p.2/40 PSI, 22 Jan 2008

At last, the LHC will start in a few months Primary goal: Discover the Higgs (+ surprises: SUSY?, Extra-dim, ??.??) LE Duc Ninh (LAPTH) Yukawa corrections to b ¯ bH – p.3/40 PSI, 22 Jan 2008

100 � ( pp ! H + X ) [pb℄ g g ! H p Higgs production at the LHC s = 14 T eV MRST/NLO m = 178 GeV t 10 q q ! H q q q q � ! W H q q � ! Z H q g W(Z) � pp ! t tH 1 H t H g W(Z) q W(Z) t 0.1 q 100 1000 g M [GeV℄ H H g t q H M. Spira, A. Djouadi The Higgs couples mainly to heavy particles, e.g. t , Z , W , b , τ . . . Higgs production associated with heavy quarks can provide a direct measurement of the quark-Higgs Yukawa coupling. LE Duc Ninh (LAPTH) Yukawa corrections to b ¯ bH – p.4/40 PSI, 22 Jan 2008

100 � ( pp ! H + X ) [pb℄ g g ! H p Why pp → b ¯ bH ? (I) s = 14 T eV MRST/NLO m = 178 GeV t 10 q q ! H q q q q � ! W H q q � ! Z H � pp ! t tH 1 0.1 100 1000 M [GeV℄ H M. Spira, A. Djouadi At the LHC, M H < 300 GeV : σ ( pp → b ¯ bH ) > σ ( pp → t ¯ tH ) because of large phase space and participation of small-x gluons. One-loop 2 → 3 process at the LHC: example of one-loop multileg processes incorporating a lot of techniques. Interplay between QCD and EW corrections. LE Duc Ninh (LAPTH) Yukawa corrections to b ¯ bH – p.4/40 PSI, 22 Jan 2008

Why pp → b ¯ bH ? (II) SM: λ qqH = − m q /υ with υ = 246 GeV. λ bbH =? MSSM: if tan β ≡ υ 1 /υ 2 is large, the bottom-Higgs Yukawa coupling is enhanced, leading to large cross section. Tagging b-jets with high p T to identify the process, QCD background is reduced. The final state observed in experiment depends on the value of the Higgs mass. If we want to look at photonic or leptonic production: For M H < 140 GeV : H → γγ ( BR ∼ 10 − 3 ) ⇒ pp → 2 b 2 γ , For 140 GeV < M H < 180 GeV: H → WW ∗ → lνlν ⇒ pp → 2 b 2 l 2 ν , For M H > 2 M Z : H → ZZ → 4 l ⇒ pp → 2 b 4 l . LE Duc Ninh (LAPTH) Yukawa corrections to b ¯ bH – p.5/40 PSI, 22 Jan 2008

q ) /σ ( gg ) : neglecting q ¯ q contribution σ ( q ¯ q q q b b H Z( γ ) g Z >> H H b Z q q q b b b qq−>ZH PDFs included; √ s = 14 TeV, M H = 120 GeV ; standard cut = ( | p b, ¯ T | > 20 GeV, | η b, ¯ b b | < 2 . 5 ) pp σ [ fb ] 79 . 110 × 10 − 3 u ¯ u d ¯ 56 . 716 × 10 − 3 d 10 . 363 × 10 − 3 s ¯ s gg 21 . 515 pp 21 . 6612 σ ( qq ) /σ ( gg ) = 0 . 7% → qq -contribution can be neglected. LE Duc Ninh (LAPTH) Yukawa corrections to b ¯ bH – p.6/40 PSI, 22 Jan 2008

Total cross section P 1 b x 1 H PP @ LHC x 2 P 2 ¯ b R 1 R 1 σ ( pp → b ¯ σ ( g 1 g 2 → b ¯ bH ) ≈ 0 dx 1 g ( x 1 , Q ) 0 dx 2 g ( x 2 , Q )ˆ bH ) Q : arbitrary renormalisation/factorisation scale. LE Duc Ninh (LAPTH) Yukawa corrections to b ¯ bH – p.7/40 PSI, 22 Jan 2008

NLO QCD correction 5000 _ h + X) [ fb ] _ H + X) [ fb ] σ (pp → bb σ (pp → bb 2000 √ s = 14 TeV √ s = 14 TeV µ = (2m b + M h )/4 M H = 120 GeV 1000 _ tot b/b µ 0 = m b + M H /2 p T > 20 GeV 10 500 | η b/b _ | < 2.5 NLO LO 200 LO NLO 100 1 p Tb and p Tb _ > 20 GeV 50 NLO 20 LO 10 -1 10 100 150 200 250 300 350 400 450 500 0.1 0.2 0.5 1 2 5 10 µ / µ 0 M h [ GeV ] 2 groups: S. Dittmaier, M. Kr¨ amer, M. Spira, Phys. Rev. D70 (2004); S. Dawson et al. Phys. Rev. D69 (2004). σ QCD ∼ λ 2 σ top − loop ∼ λ ttH λ bbH bbH At NLO, the scale dependence is reduced by requiring p b/ ¯ b > 20 GeV. T If M H = 120 GeV, µ = M Z : δ NLO QCD ≈ − 22% . If λ bbH = 0 : σ NLO QCD = σ 0 = 0 . LE Duc Ninh (LAPTH) Yukawa corrections to b ¯ bH – p.8/40 PSI, 22 Jan 2008

Why EW correction? * EW radiative correction: There are two dominant mechanisms to produce the Higgs via: H √ λ ttH ≡ − m t υ , λ t = − 2 λ ttH ≈ g s b t χ W b λ χ + χ − H ≡ M 2 υ , λ tbχ = iλ t ( P L − λ b H H λ t P R ) t χ W * The questions: δ NLO EW /δ NLO QCD =? If λ bbH = m b = 0 then δ EW � = 0 ? LE Duc Ninh (LAPTH) Yukawa corrections to b ¯ bH – p.9/40 PSI, 22 Jan 2008

Helicity structures: Tree level Process: g ( p 1 , λ 1 ) + g ( p 2 , λ 2 ) → b ( p 3 , λ 3 ) + ¯ b ( p 4 , λ 4 ) + H ( p 5 ) . T U S m b = 0 BUT λ bbH � = 0 : A 0 (ˆ u ( λ 3 )Γ even λ 1 ,λ 2 v ( λ 4 ) = δ λ 3 , − λ 4 A even λ ) = ¯ (Chiral symmetry) 0 A 0 ( − λ 1 , − λ 2 ; − λ 3 , − λ 4 ) = −A 0 ( λ 1 , λ 2 ; λ 3 , λ 4 ) ∗ (QCD Parity conservation) ⇒ {A 0 (+ + − +) , A 0 (+ − − +) , A 0 ( − + − +) , A 0 ( − − − +) } : even structure LE Duc Ninh (LAPTH) Yukawa corrections to b ¯ bH – p.10/40 PSI, 22 Jan 2008

Helicity structures: Tree level Process: g ( p 1 , λ 1 ) + g ( p 2 , λ 2 ) → b ( p 3 , λ 3 ) + ¯ b ( p 4 , λ 4 ) + H ( p 5 ) . T U S m b = 0 BUT λ bbH � = 0 : A 0 (ˆ u ( λ 3 )Γ even λ 1 ,λ 2 v ( λ 4 ) = δ λ 3 , − λ 4 A even λ ) = ¯ (Chiral symmetry) 0 A 0 ( − λ 1 , − λ 2 ; − λ 3 , − λ 4 ) = −A 0 ( λ 1 , λ 2 ; λ 3 , λ 4 ) ∗ (QCD Parity conservation) ⇒ {A 0 (+ + − +) , A 0 (+ − − +) , A 0 ( − + − +) , A 0 ( − − − +) } : even structure m b � = 0 : mass insertion “ ” A 0 (ˆ Γ even λ 1 ,λ 2 + Γ odd λ ) = ¯ u ( λ 3 ) v ( λ 4 ) λ 1 ,λ 2 odd ” even “ + m b ˜ + δ λ 3 ,λ 4 m b ˜ A even = δ λ 3 , − λ 4 A 0 A 0 0 A 0 ( − λ 1 , − λ 2 ; − λ 3 , − λ 4 ) = λ 3 λ 4 A 0 ( λ 1 , λ 2 ; λ 3 , λ 4 ) ∗ (QCD Parity conservation) ⇒ #4 A 0 ( λ 1 , λ 2 ; λ, − λ ) (even) AND #4 A 0 ( λ 1 , λ 2 ; λ, λ ) (odd) LE Duc Ninh (LAPTH) Yukawa corrections to b ¯ bH – p.10/40 PSI, 22 Jan 2008

Helicity structures: Tree level Process: g ( p 1 , λ 1 ) + g ( p 2 , λ 2 ) → b ( p 3 , λ 3 ) + ¯ b ( p 4 , λ 4 ) + H ( p 5 ) . T U S m b = 0 BUT λ bbH � = 0 : A 0 (ˆ u ( λ 3 )Γ even λ 1 ,λ 2 v ( λ 4 ) = δ λ 3 , − λ 4 A even λ ) = ¯ (Chiral symmetry) 0 A 0 ( − λ 1 , − λ 2 ; − λ 3 , − λ 4 ) = −A 0 ( λ 1 , λ 2 ; λ 3 , λ 4 ) ∗ (QCD Parity conservation) ⇒ {A 0 (+ + − +) , A 0 (+ − − +) , A 0 ( − + − +) , A 0 ( − − − +) } : even structure m b � = 0 : mass insertion “ ” A 0 (ˆ Γ even λ 1 ,λ 2 + Γ odd λ ) = ¯ u ( λ 3 ) v ( λ 4 ) λ 1 ,λ 2 odd ” even “ + m b ˜ + δ λ 3 ,λ 4 m b ˜ A even = δ λ 3 , − λ 4 A 0 A 0 0 A 0 ( − λ 1 , − λ 2 ; − λ 3 , − λ 4 ) = λ 3 λ 4 A 0 ( λ 1 , λ 2 ; λ 3 , λ 4 ) ∗ (QCD Parity conservation) ⇒ #4 A 0 ( λ 1 , λ 2 ; λ, − λ ) (even) AND #4 A 0 ( λ 1 , λ 2 ; λ, λ ) (odd) [ σ (0) − σ ( m b )] /σ ( m b ) = 3 . 7% (1.1%) if p b, ¯ b > 20 GeV ( 50 GeV) T LE Duc Ninh (LAPTH) Yukawa corrections to b ¯ bH – p.10/40 PSI, 22 Jan 2008

Helicity structures: One-loop m b = 0 BUT λ bbH � = 0 : m t insertion “ ” v ( λ 4 ) = δ λ 3 , − λ 4 A even + δ λ 3 ,λ 4 A odd Γ even λ 1 ,λ 2 + Γ odd A ( λ 1 , λ 2 ; λ 3 , λ 4 ) = ¯ u ( λ 3 ) λ 1 ,λ 2 m b � = 0 : mass insertion “ A even + m b ˜ A odd ” “ A odd + m b ˜ A even ” A ( λ 1 , λ 2 ; λ 3 , λ 4 ) = δ λ 3 , − λ 4 + δ λ 3 ,λ 4 one -loop correction → A odd LE Duc Ninh (LAPTH) Yukawa corrections to b ¯ bH – p.11/40 PSI, 22 Jan 2008

One-loop EW correction: diagrams ◭ t H (a) b b χ W H t (b) b b χ W H χ W (c) b b t # diagrams: 115 ( 19 boxes, 8 pentagons) Each group is QCD gauge invariant λ bbH = 0 → ( a ) = 0 , ( b, c ) � = 0 LE Duc Ninh (LAPTH) Yukawa corrections to b ¯ bH – p.12/40 PSI, 22 Jan 2008

λ bbH expansion The total cross section as a function of λ bbH can always be written in the form σ ( λ bbH = 0) + λ 2 bbH σ ′ ( λ bbH = 0) + · · · σ ( λ bbH ) = λ 2 bbH σ ′ ( λ bbH = 0) = σ 0 [1 + δ EW ( m t , M H )] , σ ( λ bbH = 0) = σ EW ( λ bbH = 0) . Approximation: the leading EW contribution comes from the Feynman diagrams with the top quark and charged Goldstones ( W ± L ) running in the loops (Yukawa correction). Γ odd Γ even tree -level λ bbH 0 λ 2 ( a ) t λ bbH λ b λ t λ bbH ≈ 0 λ 2 ( b ) λ b λ t λ ttH t λ ttH , ( P R ) λ 2 ( c ) λ b λ t λ χχH t λ χχH , ( P R ) For m b = 0 : Γ even → λ 2 bbH σ ′ ( λ bbH = 0) and Γ odd → σ ( λ bbH = 0) . LE Duc Ninh (LAPTH) Yukawa corrections to b ¯ bH – p.13/40 PSI, 22 Jan 2008