Associated Higgs Production with Bottom Quarks at Hadron Colliders

Transcription

1 Associated Higgs Production with Bottom Quarks at Hadron Colliders Michael Krämer (RWTH Aachen) Kickoff Meeting of the working group on Higgs and heavy quarks Wuppertal /25

2 Higgs production at hadron colliders through heavy quarks inclusive heavy-quark associated Heavy quarks are special because they couple strongly to Higgs they are perturbative: m Q Λ QCD 2 /25

3 Associate QQH production: two calculational schemes At leading order À 3 /25

4 Associate QQH production: two calculational schemes At leading order À }{{}}{{}}{{} M Q M H : α 2 s ln 2 (M H /M Q ) α 2 s ln(m H /M Q ) α 2 s 3 /25

5 Associate QQH production: two calculational schemes At leading order À }{{}}{{}}{{} M Q M H : α 2 s ln 2 (M H /M Q ) α 2 s ln(m H /M Q ) α 2 s Summation of ln(m H /M Q ) terms by using heavy quark PDFs [Collins, Olness, Tung; Barnett, Haber, Soper; Dicus, Willenbrock,...] M Q M H À À 3 /25

6 Associate QQH production: two calculational schemes 4-flavour scheme 5-flavour scheme À À + exact g b b splitting & mass effects no summation of ln(m H /M b ) terms + summation of ln(m H /M b ) terms LL approximation to g b b splitting 4 /25

7 Associate QQH production: two calculational schemes 4-flavour scheme 5-flavour scheme À À + exact g b b splitting & mass effects no summation of ln(m H /M b ) terms + summation of ln(m H /M b ) terms LL approximation to g b b splitting The 4- and 5-flavour schemes are both theoretically consistent & well-defined represent different ways of ordering perturbation theory should agree at sufficiently high order do not match exactly at finite order 4 /25

8 Associate bbh production: two calculational schemes Comparison at leading order 10 σ LO (pp _ (bb _ ) H) [fb] S = 1.96 TeV M H = 120 GeV bb _ H 1 µ Y = M H µ R = µ F = µ gg bb _ H µ/m H 5 /25

9 Associate bbh production: two calculational schemes Comparison at leading order σ LO (pp _ (bb _ ) H) [fb] σ LO (pp (bb _ ) H) [fb] 10 S = 1.96 TeV M H = 120 GeV bb _ H 10 3 S = 14 TeV M H = 120 GeV bb _ H 1 µ Y = M H µ R = µ F = µ gg bb _ H µ/m H 10 2 µ Y = M H µ R = µ F = µ gg bb _ H µ/m H 5 /25

10 Associate bbh production: two calculational schemes Comparison at leading order σ LO (pp _ (bb _ ) H) [fb] σ LO (pp (bb _ ) H) [fb] 10 S = 1.96 TeV M H = 120 GeV bb _ H 10 3 S = 14 TeV M H = 120 GeV bb _ H 1 µ Y = M H µ R = µ F = µ gg bb _ H µ/m H strong scale dependence 10 2 µ Y = M H µ R = µ F = µ gg bb _ H µ/m H σ(b b H) σ(gg b bh) at µ = M H discrepancy reduced at µ F = M H /4 [Harlander, Kilgore; see also Spira; Maltoni, Sullivan, Willenbrock; Boos, Plehn] 5 /25

11 NNLO 5FS calculation σ(pp (bb )H+X) [pb] LHC M H =120 GeV Harlander, Kilgore LO NLO 0.2 NNLO µ R =M H µ F /M H 6 /25

12 Two calculational schemes Compare Å Å where corresponds to α 1 s contribution to the distribution of heavy quarks in an on-mass shell gluon: ( ) b(x, µ) = α s(µ) 2π ln µ 2 1 ( ) dξ x x ξ P(1) qg g(ξ, µ). ξ m 2 Q 7 /25

13 Two calculational schemes σ LO (pp _ (bb _ ) H) [fb] s = 2 TeV σ(b b H) / σ(gg bb _ H) Tevatron M H [GeV] 10-2 µ R = µ F = M H / bb _ H b b H gg bb _ H M H [GeV] σ( b b H)/σ(gg b bh) 1.5 σ(bb H)/σ( b b H) /25

14 Two calculational schemes 10 3 σ LO (pp (bb _ ) H) [fb] S = 14 TeV σ(b b H) / σ(gg bb _ H) LHC M H [GeV] 10 µ R = µ F = M H /4 bb _ H b b H gg bb _ H M H [GeV] σ( b b H)/σ(gg b bh) 1.1 σ(bb H)/σ( b b H) /25

15 Two calculational schemes determine factorization scale from collinear region where dσ/dt 1/t [Maltoni, McElmurry, Willenbrock] µ F m H m H 100 GeV µ F m H m H 500 GeV (Tevatron) 10/25

16 Available calculations for pp bbh 4FS 5FS NLO-QCD: Dittmaier, MK, Spira, PRD 70 (2004); Dawson, Jackson, Reina, Wackeroth, PRD 69 (2004), PRL 94 (2005) bb h: NLO QCD: Dicus, Stelzer, Sullivan, Willenbrock, PRD 59 (1999); Balazs, He, Yuan, PRD 60 (1999); NNLO-QCD: Harlander, Kilgore, PRD 68 (2003); NLO SUSY QCD/EW: Dittmaier, MK, Mück, Schlüter, JHEP03 (2007); Hollik, Rauch (2007) bg bh: NLO-QCD: Campbell, Ellis, Maltoni, Willenbrock, PRD67 (2003); NLO SUSY-QCD: Dawson, Jackson, PRD 77 (2007); NLO EW: Dawson, Jaiswal (2010) 11/25

17 NLO 4FS calculation tot Dittmaier, MK, Spira σ(pp bb _ H + X) [fb] s = 14 TeV M H = 120 GeV µ 0 = m b + M H /2 NLO p Tb and p Tb _ > 20 GeV LO NLO LO µ/µ 0 12/25

18 Inclusive Higgs plus bottom-quark production Comparison of 4- and 5-flavour schemes at (N)NLO (SM Higgs, LHC) 13/25

19 Inclusive Higgs plus bottom-quark production Comparison of 4- and 5-flavour schemes at (N)NLO (SM Higgs, LHC) Harlander, Kilgore; Dittmaier, MK, Spira 10 3 σ(pp bb _ h + X) [fb] s = 14 TeV µ = (2m b + M h )/ bb _ h (NNLO) 10 gg bb _ h (NLO) M h [GeV] 13/25

20 Higgs plus 1 bottom-jet production Comparison of 4- and 5-flavour schemes at NLO (SM Higgs, LHC) 14/25

21 Higgs plus 1 bottom-jet production Comparison of 4- and 5-flavour schemes at NLO (SM Higgs, LHC) Campbell, Ellis, Maltoni, Willenbrock; Dittmaier, MK, Spira; Dawson, Jackson, Reina, Wackeroth 10 2 σ(pp b/b _ +h + X) [fb] s = 14 TeV µ = (2m b + M h )/4 b/b _ p T > 20 GeV _ η b/b < 2.5 gb/b _ b/b _ +h gg bb _ +h M h [GeV] 14/25

22 Comments & questions 4FS calculation includes Higgs radiation off top loops 10% no consistent treatment of pdfs in previous comparisons (need pdf with four active flavours gluon flux larger by 5-10%) should repeat comparison with consistent inputs (e.g. m b ) and up-to-date pdfs (MSTW FS pdf) 15/25

23 Comments & questions 4FS calculation includes Higgs radiation off top loops 10% no consistent treatment of pdfs in previous comparisons (need pdf with four active flavours gluon flux larger by 5-10%) should repeat comparison with consistent inputs (e.g. m b ) and up-to-date pdfs (MSTW FS pdf) no proper analytic understanding of differences between 4FS and 5FS calculations... what is the best estimate for the inclusive cross section? 15/25

24 Comments & questions 4FS calculation includes Higgs radiation off top loops 10% no consistent treatment of pdfs in previous comparisons (need pdf with four active flavours gluon flux larger by 5-10%) should repeat comparison with consistent inputs (e.g. m b ) and up-to-date pdfs (MSTW FS pdf) no proper analytic understanding of differences between 4FS and 5FS calculations... what is the best estimate for the inclusive cross section? Maybe the Santander matching [Harlander, MK, Schumacher]: σ(best of all worlds) = weight 5FS + (1 weight) 4FS with weight = ln(m H /37)/(1 + ln(m H /37)) We should be able to do better really, but for the time being... 15/25

25 Backup 16/25

26 Inclusive Higgs plus bottom-quark production Comparison of 4- and 5-flavour schemes at (N)NLO (SM Higgs, LHC) Harlander, Kilgore; Dittmaier, MK, Spira σ(pp _ bb _ h + X) [fb] 10 s = 1.96 TeV µ = (2m b + M h )/4 1 bb _ h (NNLO) gg bb _ h (NLO) M h [GeV] 17/25

27 Higgs plus 1 bottom-jet production Comparison of 4- and 5-flavour schemes at NLO (SM Higgs, LHC) Campbell, Ellis, Maltoni, Willenbrock; Dittmaier, MK, Spira; Dawson, Jackson, Reina, Wackeroth 10 2 σ(pp b/b _ +h + X) [fb] s = 14 TeV µ = (2m b + M h )/4 b/b _ p T > 20 GeV _ η b/b < 2.5 gb/b _ b/b _ +h gg bb _ +h M h [GeV] 18/25

28 Higgs plus 1 bottom-jet production Comparison of 4- and 5-flavour schemes at NLO (SM Higgs, TeV) Campbell, Ellis, Maltoni, Willenbrock; Dittmaier, MK, Spira; Dawson, Jackson, Reina, Wackeroth 1 σ(pp _ b/b _ +h + X) [fb] s = 1.96 TeV µ = (2m b + M h )/4 b/b _ p T > 20 GeV _ η b/b < 2 gb/b _ b/b _ +h gg bb _ +h M h [GeV] 19/25

29 Higgs plus 1 bottom-jet production Comparison of 4- and 5-flavour schemes at NLO (SM Higgs, LHC) Campbell, Ellis, Maltoni, Willenbrock; Dittmaier, MK, Spira; Dawson, Jackson, Reina, Wackeroth σ(pp b/b _ +h + X) [fb] 500 s = 14 TeV µ = (2m b + M h )/4 400 _ η b/b < 2.5 gb/b _ b/b _ +h 300 gg bb _ + h p Tcut [GeV] 20/25

30 Higgs plus 1 bottom-jet production Comparison of 4- and 5-flavour schemes at NLO (SM Higgs, TeV) Campbell, Ellis, Maltoni, Willenbrock; Dittmaier, MK, Spira; Dawson, Jackson, Reina, Wackeroth 5 σ(pp _ b/b _ +h + X) [fb] 4 s = 1.96 TeV µ = (2m b + M h )/4 _ 3 η b/b < 2 gb/b _ b/b _ +h gg bb _ + h p Tcut [GeV] 21/25

31 Higgs plus 2 bottom-jet production Calculation only in 4FS (SM Higgs, LHC) Dittmaier, MK, Spira; Dawson, Jackson, Reina, Wackeroth 10 σ(pp bb _ h + X) [fb] s = 14 TeV µ = (2m b + M h )/4 b/b _ p T > 20 GeV _ η b/b < 2.5 LO NLO M h [GeV] 22/25

32 Higgs plus 2 bottom-jet production Calculation only in 4FS (SM Higgs, TeV) Dittmaier, MK, Spira; Dawson, Jackson, Reina, Wackeroth 10-1 σ(pp _ bb _ h + X) [fb] s = 1.96 TeV µ = (2m b + M h )/4 b/b _ p T > 20 GeV _ η b/b < 2 LO NLO M h [GeV] 23/25

33 Higgs plus 2 bottom-jet production Calculation only in 4FS (SM Higgs, LHC) Dittmaier, MK, Spira; Dawson, Jackson, Reina, Wackeroth σ(pp bb _ h + X) [fb] s = 14 TeV µ = (2m b + M h )/4 _ η b/b < 2.5 LO NLO p Tcut [GeV] 24/25

34 Higgs plus 2 bottom-jet production Calculation only in 4FS ((SM Higgs, TeV) Dittmaier, MK, Spira; Dawson, Jackson, Reina, Wackeroth σ(pp _ bb _ h + X) [fb] s = 1.96 TeV µ = (2m b + M h )/4 _ η b/b < 2 LO NLO p Tcut [GeV] 25/25