Predictions for Higgs signal and background processes with - - PowerPoint PPT Presentation

Predictions for Higgs signal and background processes with many-particle final states at the LHC

Stefan Dittmaier MPI Munich

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 1

Contents 1 Introduction 2 The decays Higgs → WW/ZZ → 4 fermions 3 Higgs production via weak vector-boson fusion 4 Background processes with multi-particle final states 5 Technical issues in “NLO multi-leg calculations” 6 Conclusions

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 2

1 Introduction

Experiments at LEP/SLC/Tevatron

• confirmation of Standard Model as quantum field theory

(quantum corrections significant)

• top mass mt indirectly constrained by quantum corrections

↔ in agreement with mt measurement of Tevatron

• Higgs mass MH indirectly constrained by quantum corrections

֒ → impact on Higgs searches Great success of precision physics

1 2 3 4 5 6 100 30 300

mH [GeV] ∆χ2

Excluded

Preliminary

∆αhad = ∆α(5)

0.02758±0.00035 0.02749±0.00012

• incl. low Q2 data

Theory uncertainty

mLimit = 144 GeV

– MH > 114.4 GeV

(LEPHIGGS ’02)

e+e− / − → ZH at LEP2 – MH < 144 GeV

(LEPEWWG ’07)

fit to precision data i.e. via quantum corrections

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 3

Higgs search at present and future colliders Higgs bosons couple proportional to particle masses: ∝ MW H W, Z W, Z ∝ mf H ¯ f f ⇒ Higgs production mainly via coupling to W/Z bosons or top quarks

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 4

Higgs search at present and future colliders Higgs bosons couple proportional to particle masses: ∝ MW H W, Z W, Z ∝ mf H ¯ f f ⇒ Higgs production mainly via coupling to W/Z bosons or top quarks Processes at hadron colliders (p¯ p/pp):

H t t t H W, Z W, Z H q q W, Z W, Z H t ¯ t t t

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 4

Higgs search at present and future colliders Higgs bosons couple proportional to particle masses: ∝ MW H W, Z W, Z ∝ mf H ¯ f f ⇒ Higgs production mainly via coupling to W/Z bosons or top quarks Processes at hadron colliders (p¯ p/pp):

H t t t H W, Z W, Z H q q W, Z W, Z H t ¯ t t t

Processes at e+e− colliders:

H Z Z e+ e− H ¯ νe νe W W e+ e− t H γ, Z ¯ t e+ e−

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 4

Cross sections and significance of the Higgs signal at the LHC

Spira et al. ’98 ATLAS ’03

σ(pp→H+X) [pb] √s = 14 TeV Mt = 175 GeV CTEQ4M gg→H qq→Hqq qq

_’→HW

qq

_→HZ

gg,qq

_→Htt _

gg,qq

_→Hbb _

MH [GeV] 200 400 600 800 1000 10

• 4

10

• 3

10

• 2

10

• 1

1 10 10 2

favoured

1 10 10 2 100 120 140 160 180 200

mH (GeV/c2) Signal significance

H → γ γ ttH (H → bb) H → ZZ(*) → 4 l H → WW(*) → lνlν qqH → qq WW(*) qqH → qq ττ Total significance

∫ L dt = 30 fb-1 (no K-factors)

ATLAS

Typical size perturbative corrections at next-to-leading order (NLO): QCD: O(αs) ∼ 10−100% Electroweak: O(α) ∼ 10% ֒ → calculate / control higher orders to reduce theoretical uncertainty down to the level of PDF (q¯

q ∼ 5%, gg ∼ 10%) and experimental uncertainties

Complication: many channels involve multi-particle final states.

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 5

2 The decays Higgs → WW/ZZ → 4 fermions

Hdecay

• t
• t

• s
• s
• b
• b

Hdecay

Importance of decays H → WW(∗)/ZZ(∗) at the LHC: – most important Higgs decay channels for MH > ∼ 125 GeV – most precise determination of MH via H→ZZ→4l for MH > ∼ 130 GeV

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 6

Theoretical description of H → WW(∗)/ZZ(∗):

• previous work on partial decay widths not sufficient:

⋄ O(α) corrections to H → WW/ZZ with stable W’s/Z’s Fleischer, Jegerlehner ’81; Kniehl ’91; Bardin, Vilenskii, Khristova ’91 ⋄ lowest-order predictions for H → WW(∗)/ZZ(∗)

e.g. by Hdecay (Djouadi, Kalinowski, Spira ’98)

• however: proper description of distributions required

⋄ for the kinematical reconstruction of Z’s, W’s, and H

֒ → invariant-mass distributions

⋄ for the verification of spin 0 and CP parity of the Higgs boson Nelson ’88; Soni, Xu ’93; Chang et al.’93; Skjold, Osland ’93; Barger et al.’93; Arens, Sehgal ’94; Buszello et al.’02; Choi et al.’03

֒ → angular and invariant-mass distributions Recent progress:

• PROPHECY4F: Monte Carlo generator for H → WW/ZZ → 4f

with EW and QCD corrections

Bredenstein, Denner, S.D., Weber ’06

• combination of production and decay:

(gg → H in NNLO QCD) ⊗ (H → WW/ZZ → 4l in LO)

Anastasiou et al. ’07,’08; Frederix, Grazzini ’08; Grazzini ’08

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 7

Survey of Feynman diagrams for NLO EW and QCD corrections to H → 4f Lowest order:

H V V f f f f

❵ ❵

Typical one-loop diagrams:

# diagrams = O(200−400)

pentagons

H f f f f V V V f f

boxes

H f f f f V V V f f

H f f f f V V S f V

vertices

H f f f f V V f V V H f f f f V V V V

self-energies

H f f f f V S V S V H f f f f V V V f f

+ photon / gluon bremsstrahlung

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 8

Features of PROPHECY4F:

Bredenstein, Denner, S.D., Weber ’06

• O(α) and O(αs) corrections to all channels H → WW/ZZ → 4f
• final-state radiation off leptons beyond O(α) via structure functions
• leading 2-loop heavy-Higgs effects ∝ G2

µM 4 H

Ghinculov ’95; Frink, Kniehl, Kreimer, Riesselmann ’96

• multi-channel Monte Carlo integration

(checked by VEGAS)

Berends, Kleiss, Pittau ’94; Kleiss, Pittau ’94

• improved Born approximation for simplified evaluation

Main complications in the loop calculation:

• numerical instabilities in Passarino–Veltman reduction of tensor integrals

֒ → new reduction methods developed

Denner, S.D. ’02,’05

• gauge-invariant treatment of W and Z resonances

֒ → “complex-mass scheme”

Denner, S.D., Roth, Wieders ’05

New concepts already used in O(α) correction to e+e− → 4f

Denner, S.D., Roth, Wieders ’05

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 9

The complex-mass scheme for unstable particles

Problem of unstable particles: description of resonances requires resummation of propagator corrections ֒ → mixing of perturbative orders potentially violates gauge invariance Dyson series and propagator poles

(scalar example)

= + + + . . . Gφφ(p) = i p2 − m2 + i p2 − m2 iΣ(p2) i p2 − m2 + . . . = i p2 − m2 + Σ(p2)

Σ(p2) = renormalized self-energy, m = ren. mass

stable particle: Im{Σ(p2)} = 0 at p2 ∼ m2 ֒ → propagator pole for real value of p2, renormalization condition for physical mass m: Σ(m2) = 0 unstable particle: Im{Σ(p2)} = 0 at p2 ∼ m2 ֒ → location µ2 of propagator pole is complex, possible definition of mass M and width Γ: µ2 = M 2 − iMΓ

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 10

The complex-mass scheme at NLO Basic idea: mass2 = location of propagator pole in complex p2 plane ֒ → consistent use of complex masses everywhere ! Application to gauge-boson resonances:

• replace

M 2

W → µ2 W = M 2 W − iMWΓW,

M 2

Z → µ2 Z = M 2 Z − iMZΓZ

and define (complex) weak mixing angle via c2

W = 1 − s2 W =

µ2

W

µ2

Z

• virtues:

⋄ gauge-invariant result

(Slavnov–Taylor identities, gauge-parameter independence)

֒ → unitarity cancellations respected !

⋄ perturbative calculations as usual (loops and counterterms) ⋄ no double counting of contributions (bare Lagrangian unchanged !)

• drawbacks:

⋄ unitarity-violating spurious terms of O(α2)

→ but beyond NLO accuracy !

(from t-channel/off-shell propagators and complex mixing angle)

⋄ complex gauge-boson masses also in loop integrals

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 11

Comparison to other proposals:

• naive fixed-width schemes:

1 p2 − M 2 → 1 p2 − M 2 + iMΓ in all or at least in resonant propagators ֒ → breaks gauge invariance only mildly (?), but partial inclusion of widths in loops screws up singularity structure

• pole expansions

Stuart ’91; Aeppli et al. ’93, ’94; etc.

֒ → consistent, gauge invariant, but not reliable at threshold or in off-shell tails of resonances

• effective field theory approach

Beneke et al. ’04; Hoang, Reisser ’04

֒ → gauge invariant, involves pole expansions, but can be combined with threshold expansions

• complex-mass scheme Denner, S.D., Roth, Wackeroth ’99; Denner, S.D., Roth, Wieders ’05

֒ → gauge invariant, valid everywhere in phase space

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 12

Some results for H → ZZ → 4l

Partial decay width for H → ZZ → e−e+µ−µ+

Gµ-scheme

Bredenstein, Denner, S.D., Weber ’06

• rre ted

• e

• +

• [MeV

• 10

IBA NWA corrected H → e−e+µ−µ+ MH [GeV] δ [%]

200 190 180 170 160 150 140 130 120 14 12 10 8 6 4 2

δ =

Γ ΓBorn − 1

↑

threshold effect in loops for MH ∼ 2MW

↑

kinematic threshold at MH ∼ 2MZ

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 13

Comparison with HDECAY

• rre ted

• e

• +

• [MeV

• 10

HDecay

• ne loop

H → e−e+µ−µ+ MH [GeV] δ [%]

200 190 180 170 160 150 140 12 10 8 6 4 2

δ =

Γ ΓBorn − 1

↑

threshold effect in loops for MH ∼ 2MW

↑

kinematic threshold at MH ∼ 2MZ

Note: peak structure in HDECAY is an artefact of the

• n-shell approximation above threshold.

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 14

Sensitivity of distributions to non-standard effects in H → ZZ → f1 ¯ f1f2 ¯ f2 invariant Z mass: angle between Z decay planes:

Choi, Miller, Mühlleitner, Zerwas ’02

M* (GeV)

• No. of Events

SM H → Z*Z → (f1f

– 1)(f2f – 2)

MH = 150 GeV Spin 1 Spin 2 5 10 15 20 25 30 30 35 40 45 50 55 ϕ 1/Γ dΓ/dϕ H → ZZ → (f1f

– 1)(f2f – 2)

MH = 280 GeV SM pseudoscalar 0.1 0.12 0.14 0.16 0.18 0.2 0.22 π/2 π 3π/2 2π

M∗ = Mf1 ¯

f1

histograms = SM simulation for L = 300 fb−1

֒ → distributions sensitive to spin and parity

H Z Z f1 ¯ f1 f2 ¯ f2 φ

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 15

Electroweak corrections to the invariant Z mass

Gµ-scheme

Bredenstein, Denner, S.D., Weber ’06 corrected

MH = 170 GeV H → e−e+µ−µ+ Mµµ [GeV]

dΓ dMµµ

10−3 100 95 90 85 80 75 70 65 60 0.0025 0.002 0.0015 0.001 0.0005 µ−µ+ (no recomb.) e−e+ (no recomb.) µ−µ+ (γ recomb.) e−e+ (γ recomb.)

MH = 170 GeV H → e−e+µ−µ+ Mf ¯

f [GeV]

δ [%]

100 95 90 85 80 75 70 65 60 40 20 −20 −40

γ recombination if Meγ/µγ < 5 GeV

Large corrections from photon radiation in Z reconstruction

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 16

Electroweak corrections to the angle between Z decay planes

Gµ-scheme

Bredenstein, Denner, S.D., Weber ’06

• , orre ted

• e

• +

• [deg

• M

• e

• +

• [deg

H Z Z e− e+ µ− µ+ φ

cos φ =

• pe−e+ ×pe−
• −pµ−µ+ ×pµ−
• pe−e+ )×pe−
• −pµ−µ+ )×pµ−
• cos φ′ = (pe−e+ ×pe−)
• pe−e+ ×pµ−
• |pe−e+ ×pe−|
• pe−e+ ×pµ−
• PSI Villigen, March 3, 2008

Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 17

Combination of gg → H production with H → WW/ZZ → 4l decay

QCD corrections to gg → H:

• complete NLO correction known

Graudenz, Spira, Zerwas ’93 Djouadi, Graudenz, Spira, Zerwas ’95

• NNLO correction known for mt → ∞

K = σNNLO σLO ∼ 2.0

Harlander, Kilgore ’01,’02 Catani, de Florian, Grazzini ’01 Anastasiou, Melnikov ’02 Ravindran, Smith, van Neerven ’03,’04 Anastasiou, Melnikov, Petriello ’05

• soft-gluon resummation

up to NNNLO for mt → ∞

Catani et al. ’03 Moch, Vogt ’05

• residual scale uncertainty ∼ 5−10%

Moch, Vogt ’05

20 40 60 80 1

µr / MH 0.2 0.5 2 3

σ(pp → H+X) [pb]

MH = 120 GeV

LO NLO N2LO N3LOapprox

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 18

NNLO QCD corrections to gg → H → WW → llνν

Anastasiou, Dissertori, Stöckli ’07

φll = angle between charged decay leptons in the transverse plane K factors in general depend on decay phase space.

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 19

3 Higgs production via weak vector-boson fusion (VBF) H q q W, Z W, Z

colour exchange between quark lines suppressed ⇒ small QCD corrections

Han, Valencia, Willenbrock ’92; Spira ’98; Djouadi, Spira ’00; Figy, Oleari, Zeppenfeld ’03 ֒ → t-channel approximation (vertex corrections)

VBF cuts and background suppression:

• 2 hard “tagging” jets demanded:

pTj > 20 GeV, |yj| < 4.5

• tagging jets forward–backward directed:

∆yjj > 4, yj1 · yj2 < 0. signature = Higgs + 2jets ֒ → Suppression of background

• from other (non-Higgs) processes,

such as t¯ t or WW production Zeppenfeld et al. ’94-’99

• induced by Higgs production via gluon fusion,

such as gg → ggH Del Duca et al. ’06; Campbell et al. ’06

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 20

Recent progress: complete NLO QCD and EW corrections

Ciccolini, Denner, S.D. ’07 NLO, cuts LO, cuts NLO, no cuts LO, no cuts pp → Hjj + X MH [GeV] σ [fb]

700 600 500 400 300 200 100 10000 1000 100

EW, cuts EW, no cuts QCD, cuts QCD, no cuts pp → Hjj + X MH [GeV] δ [%]

700 600 500 400 300 200 100 10 5 −5 −10

QCD and EW corrections are of same size ! (µren = µfact = MW)

Features of the calculation:

• NLO corrections to all LO diagrams

and interferences included:

q q q q H V V q q q q H V V q q q q H V V

• leading 2-loop heavy-Higgs effects ∝ G2

µM 4 H

Ghinculov ’95; Frink, Kniehl, Kreimer, Riesselmann ’96

• fully flexible Monte Carlo generator

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 21

Classification of QCD corrections Possible Born diagrams:

(1) H V V fa ¯ fb fc ¯ fd (2) H V ′ V ′ fa ¯ fb fc ¯ fd

diagrams (2) only for q¯ qq¯ q and q¯ qq′¯ q′ channels

(q′ = weak-isospin partner of q)

Classification of QCD corrections into four categories:

(typical diagrams shown)

(a)

(a) contains previously known “t-channel approximation”

(b) (c) (d)

(b,c,d) = corrections to interferences (only for q¯

qq¯ q and q¯ qq′ ¯ q′ channels)

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 22

Size of specific corrections and subcontributions to cross sections: no cuts VBF cuts MH[ GeV] 120−200 700 120−200 700 various corrections: δQCD(a)[%] 4−0.5 +1 ≈ −5 −7

O(5−10%)

δQCD(b+c+d)[%] < ∼ 0.2 −0.1 < 0.1 < 0.1

negligible

δEW,qq[%] ≈ −6 +6 ≈ −7 +5

O(5−10%)

δEW,qγ[%] ≈ +1 +2 ≈ +1 +2 δG2

µM4 H[%]

< 0.1 +4 < 0.1 +4

negligible for MH < 400 GeV

specific contributions: ∆s−channel[%] 30−10 1 < 0.6 < 0.1

negligible with VBF cuts

∆t/u−interference[%] < 0.5 < 0.1 < 0.1 < 0.1

negligible

∆b−quarks[%] ≈ 4 1 ≈ 2 1

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 23

Distribution in the azimuthal angle difference ∆φjj of the tagging jets Sensitivity to non-standard effects:

Hankele, Klämke, Zeppenfeld, Figy ’06

0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009

• 160 -120 -80
• 40

40 80 120 160 1/ σ dσ / d ∆φjj ∆φjj CP-even, CP-odd CP-even CP-odd SM

(Individual contributions without SM)

CP-even: L ∝ HW +

µνW −,µν,

ΓHW +W −

µν

∝ gµν(k+k−) − k+,νk−,µ CP-odd: L ∝ H ˜ W +

µνW −,µν,

ΓHW +W −

µν

∝ ǫµνρσkρ

+kσ −

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 24

Corrections to the ∆φjj distribution:

Ciccolini, Denner, S.D. ’07

LO EW+QCD

MH = 120 GeV pp → Hjj + X ∆φjj

dσ d∆φjj [fb]

180 135 90 45 13 12 11 10 9 8 7 QCD EW EW+QCD

MH = 120 GeV pp → Hjj + X ∆φjj

dσ dσLO − 1 [%]

180 135 90 45 −2 −4 −6 −8 −10 −12 −14

Corrections induce small distortions (which are larger for pT and y distributions).

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 25

4 Background processes with multi-particle final states

At the LHC the background to some signals cannot be measured ! ֒ → precise predictions for many background processes required Examples for important missing NLO predictions for background:

“Les Houches wishlist ’05”

background for pp → WW + jet t¯ tH, new physics

S.D., Kallweit, Uwer ’07; Campbell, R.K.Ellis, Zanderighi ’07

pp → t¯ tb¯ b t¯ tH pp → t¯ t + 2jets t¯ tH pp → VVb¯ b VBF → H → VV, t¯ tH, new physics pp → VV + 2jets VBF → H → VV

VBF: Jäger et al. ’06; Bozzi et al. ’07

pp → V + 3jets t¯ t, new physics pp → VVV SUSY tri-lepton

ZZZ: Lazopoulos et al. ’07

֒ → Many long-termed NLO calculations for theorists !

(several 104 diagrams, many “(wo)men-decades”)

Note: calculations only possible with technical progress of recent years

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 26

An example: simulation of H → WW via VBF at ATLAS

0.1 0.2 0.3 0.4 0.5 50 100 150 200 250

mT (GeV) σacc (fb)

0.1 0.2 0.3 0.4 0.5 50 100 150 200 250

mT (GeV) σacc (fb)

Higgs signal appears as “Jacobian peak” in transverse mass of the W-boson pair.

(t¯ tj is major background component.)

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 27

NLO QCD corrections to pp → t¯ t+jet + X and pp → W+W−+jet + X

S.D., Uwer, Weinzierl ’07 S.D., Kallweit, Uwer ’07

g g t ¯ t g g g t g ¯ t

etc.

u ¯ u u u u d g W+ W− g g ¯ u g u u d u W+ W− g

etc.

• t¯

t+jet:

⋄ understand top-quark dynamics ⋄ background to t¯

tH and Higgs via VBF

• WW+jet:

⋄ background to H → WW ⋄ background to SUSY searches

Cross sections at the LHC: NLO corrections significantly stabilize predictions

LO (CTEQ6L1) NLO (CTEQ6M)

pT,jet > 20GeV √s = 14 TeV pp → t¯ t+jet+X µ/mt σ[pb]

10 1 0.1 1500 1000 500

• <

• +jet+X

• [pb

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 28

ttH, H → b¯ b

(30 fb−1)

Backgrounds: t¯

tjj, t¯ tb¯ b (irreducible).

Many discriminating variables:

jj (W): mass, momentum, ∆ R(j, j)

(∆R =

p ∆η2 + ∆φ2)

bjj (top-quark): mass, ∆ R(b, jj) bℓν (top-quark): mass,∆ R(b, ℓν) bjj, bℓν (tt-pair): mass, ∆ R(bjj, bℓν)

H t t b b b b

+

W

• W

+

l ν q ’ q

50 100 150 200 250 300

3

10 × 20 40 60 50 100 150 200 250 300

3

10 × 20 40 60 =3.0 291 S=51/ ttH ttbb EW ttbb QCD tt+jets

hypothesis, NN4 ″ Sig+Bgd ″

Hmass

Entries 9140 Mean 1.347e+05 RMS 6.472e+04 / ndf

2

χ 605 / 26 p0 29.3 ±

• 27.3

p1 0.0016458 ± 0.0004013 p2 2.210e-08 ± 4.688e-08 p3 1.559e-06 ± 2.121e-05

[MeV]

bb

m

50 100 150 200 250 300

3

10 ×

Events/9 GeV

20 40 60

Hmass

Entries 9140 Mean 1.347e+05 RMS 6.472e+04 / ndf

2

χ 605 / 26 p0 29.3 ±

• 27.3

p1 0.0016458 ± 0.0004013 p2 2.210e-08 ± 4.688e-08 p3 1.559e-06 ± 2.121e-05

hypothesis, NN4 ″ Bgd only ″

Important issues: NLO cross-sections for the signal, ttbb, ttjj. Signal and background shape are very similar.

⇒ Essential to reduce the theoretical uncertainties on x-sections.

5/7

Slide borrowed from S.Horvat (MPI/ATLAS) ’07

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 29

5 Technical issues in “NLO multi-leg calculations”

Complications in NLO corrections to many-particle processes:

• huge amount of algebra, long final expressions

֒ → computer algebra / automation

• multi-dimensional phase-space integration

֒ → Monte Carlo techniques

• complicated structure of singularities and matching of virtual and real corrections

֒ → subtraction

R.K.Ellis et al. ’81; S.D.Ellis et al. ’89; Mangano et al. ’92; Kunszt/Soper ’92; Frixione et al. ’96; Nagy/Z. Trócsányi ’96; Campbell et al. ’98; Catani/Seymour ’96; S.D. ’99; Phaf/Weinzierl ’01; Catani et al. ’02

and slicing techniques

Giele/Glover ’92; Giele et al. ’93; Keller/Laenen ’98; Harris/Owens ’01, etc.

• numerically stable evaluation of one-loop integrals with up to 5,6,. . . external legs

֒ → techniques to solve problems with inverse kinematical (e.g. Gram) det’s

Stuart et al. ’88/’90/’97; v.Oldenborgh/Vermaseren ’90; Campbell et al. 96; Ferroglia et al. ’02; del Aguila/Pittau ’04; Binoth et al. ’02/’05; Denner/S.D. ’02/’05; v.Hameren et al. ’05; R.K.Ellis et al. ’05; Anastasiou/Daleo ’05; Ossola et al. ’06/’07; Lazopoulos et al. ’07; Forde ’07; R.K.Ellis et al. ’07; Kilgore ’07; Giele et al. ’08

[But: many proposed methods not (yet?) used in complicated applications]

• treatment of unstable particles, issue of complex masses

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 30

Dipole subtraction formalism → process-independent treatment of singularities in real NLO corrections worked out for

• QCD with massless partons (Catani, Seymour ’96)
• γ radiation off massive fermions (S.D. ’99)

   QCD with massive partons

Phaf, Weinzierl ’01 Catani, S.D., Seymour, Trócsányi ’02

basic idea: NLO correction to process with m partons

σNLO =

• m+1
• dσreal−dσsub
• finite

+

• m
• dσvirtual+d¯

σsub

1

• finite

+

• 1

dx

• m
• dσfact(x)+
• d¯

σsub(x)

• +
• finite

conditions on dσsub:

• sum rule:

−

• m+1

dσsub +

• m

d¯ σsub

1

+ 1 dx

• m
• d¯

σsub(x)

• + = 0
• asymptotics:

σsub

• σreal

in all collinear/IR regions

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 31

Strategy for extracting or translating IR (soft / collinear) singularities in loops: Idea: convert integrals I(D) in D=4−2ǫ dim. → 4-dim. integrals I(λ) with mass regulator λ Procedure: consider finite and regularization-scheme-independent difference

• I(D) − I(D)

sing

• D→4 =
• I(λ) − I(λ)

sing

• λ→0

⇒ I(D) = I(D)

sing +

• I(λ) − I(λ)

sing

• λ→0 + O(ǫ)

Note: mass-singular part can be universally constructed from 3-point integrals

Beenakker et al. ’01

֒ → general result known explicitly

S.D. ’03

An example from gg → t¯ tg:

• sing

       1 ǫ2 , 1 ǫ ln2 λ, ln λ        1 ǫ ln λ n = 1 2 3 4 = A04 × + A43 × + A02 × + A42 × + A03 ×

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 32

Numerical evaluation of one-loop integrals Passarino–Veltman reduction of tensor to scalar integrals ֒ → inverse Gram determinants of external momenta ֒ → serious numerical instabilities where det(Gram) → 0

(at phase-space boundary but not only !)

Our solutions:

Denner, S.D., Nucl.Phys. B734 (2006) 62 [hep-ph/0509141]

• 1- and 2-point integrals

→ stable direct calculation

• 3- and 4-point integrals

→ two hybrid methods (i) Passarino–Veltman ⊕ seminumerical method ⊕ analytical special cases (ii) Passarino–Veltman ⊕ expansions in small Gram and other kin. determinants

• 5- and 6-point integrals

֒ → stable reduction to lower-point integrals without Gram determinants ⇒ Techniques ready for further applications

(dim. regularization for IR singularities possible; complex masses supported)

Practical experience ֒ → Power + reliability of techniques can only be assessed via non-trivial applications !

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 33

A typical example with small Gram determinant: Box integral appears, e.g., in subgraph of diagram

MZ te¯

d

s¯

νu

t¯

eµ

sµ¯

νu

e+ e− e µ− ¯ νµ u ¯ d Z Z W µ d

Gram det.: det(Gram) → 0 if te¯

d → tcrit ≡ sµ¯ νu(sµ¯ νu − s¯ νu + t¯ eµ)

sµ¯

νu − s¯ νu

Numerical comparison: maximal tensor rank = 6 (similar to ee → 4f application)

Relative deviations from ”best” x 10−7 10−5 10−3 10−1 10−14 10−12 10−10 10−8 10−6 10−4 10−2 1 Relative deviations from ”best” x 10−7 10−5 10−3 10−1 10−14 10−12 10−10 10−8 10−6 10−4 10−2 1

improved by Gram expansion

(etc.)

Passarino–Veltman reduction

D111 D11 D1 D0 Absolute predictions x 10−7 10−5 10−3 10−1

Passarino-Veltman region

x ≡ te¯

d

tcrit − 1

sµ¯

νu = +2×104 GeV2

s¯

νu

= +1×104 GeV2 t¯

eµ

= −4×104 GeV2 tcrit = −6×104 GeV2 PV reduction breaks down, but Gram exp. stable for det(Gram) → 0 !

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 34

A typical example with small Gram determinant: Box integral appears, e.g., in subgraph of diagram

MZ te¯

d

s¯

νu

t¯

eµ

sµ¯

νu

e+ e− e µ− ¯ νµ u ¯ d Z Z W µ d

Gram det.: det(Gram) → 0 if te¯

d → tcrit ≡ sµ¯ νu(sµ¯ νu − s¯ νu + t¯ eµ)

sµ¯

νu − s¯ νu

Numerical comparison: maximal tensor rank = 12

Relative deviations from ”best” x 10−7 10−5 10−3 10−1 10−14 10−12 10−10 10−8 10−6 10−4 10−2 1 Relative deviations from ”best” x 10−7 10−5 10−3 10−1 10−14 10−12 10−10 10−8 10−6 10−4 10−2 1

improved by Gram expansion

(etc.)

Passarino–Veltman reduction

D111 D11 D1 D0 Absolute predictions x 10−7 10−5 10−3 10−1

Passarino-Veltman region

x ≡ te¯

d

tcrit − 1

sµ¯

νu = +2×104 GeV2

s¯

νu

= +1×104 GeV2 t¯

eµ

= −4×104 GeV2 tcrit = −6×104 GeV2 PV reduction breaks down, but Gram exp. stable for det(Gram) → 0 !

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 34

A typical example with small Gram determinant: Box integral appears, e.g., in subgraph of diagram

MZ te¯

d

s¯

νu

t¯

eµ

sµ¯

νu

e+ e− e µ− ¯ νµ u ¯ d Z Z W µ d

Gram det.: det(Gram) → 0 if te¯

d → tcrit ≡ sµ¯ νu(sµ¯ νu − s¯ νu + t¯ eµ)

sµ¯

νu − s¯ νu

Numerical comparison: maximal tensor rank = 25

Relative deviations from ”best” x 10−7 10−5 10−3 10−1 10−14 10−12 10−10 10−8 10−6 10−4 10−2 1 Relative deviations from ”best” x 10−7 10−5 10−3 10−1 10−14 10−12 10−10 10−8 10−6 10−4 10−2 1

improved by Gram expansion

(etc.)

Passarino–Veltman reduction

D111 D11 D1 D0 Absolute predictions x 10−7 10−5 10−3 10−1

x ≡ te¯

d

tcrit − 1

sµ¯

νu = +2×104 GeV2

s¯

νu

= +1×104 GeV2 t¯

eµ

= −4×104 GeV2 tcrit = −6×104 GeV2 PV reduction breaks down, but Gram exp. stable for det(Gram) → 0 !

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 34

6 Conclusions

Radiative corrections and the search for the Higgs boson

• Bounds on the Higgs mass from LEP2 search and precision physics:

114 GeV < MH < ∼ 200 GeV

• LHC has sensitivity to SM-like Higgs up to MH <

∼ 1 TeV QCD corrections = substantial part of predictions

⋄ signal processes up to O(5−20%) known in SM

֒ → continuous refinements (e.g. QCD resummations, EW corrections)

⋄ extended Higgs sectors (THDM, MSSM, etc.)

֒ → many improvements necessary (e.g. pp → b¯ bh/H/A)

⋄ background processes

֒ → hard work at theoretical frontier (e.g. pp → t¯ tb¯ b)

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 35

6 Conclusions

Radiative corrections and the search for the Higgs boson

• Bounds on the Higgs mass from LEP2 search and precision physics:

114 GeV < MH < ∼ 200 GeV

• LHC has sensitivity to SM-like Higgs up to MH <

∼ 1 TeV QCD corrections = substantial part of predictions

⋄ signal processes up to O(5−20%) known in SM

֒ → continuous refinements (e.g. QCD resummations, EW corrections)

⋄ extended Higgs sectors (THDM, MSSM, etc.)

֒ → many improvements necessary (e.g. pp → b¯ bh/H/A)

⋄ background processes

֒ → hard work at theoretical frontier (e.g. pp → t¯ tb¯ b) ⇒ Theory is on track, but there is still a long way ! Please support young people who take the challenge !

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 35

6 Conclusions

Radiative corrections and the search for the Higgs boson

• Bounds on the Higgs mass from LEP2 search and precision physics:

114 GeV < MH < ∼ 200 GeV

• LHC has sensitivity to SM-like Higgs up to MH <

∼ 1 TeV QCD corrections = substantial part of predictions

⋄ signal processes up to O(5−20%) known in SM

֒ → continuous refinements (e.g. QCD resummations, EW corrections)

⋄ extended Higgs sectors (THDM, MSSM, etc.)

֒ → many improvements necessary (e.g. pp → b¯ bh/H/A)

⋄ background processes

֒ → hard work at theoretical frontier (e.g. pp → t¯ tb¯ b) ⇒ Theory is on track, but there is still a long way ! Please support young people who take the challenge ! Otherwise . . .

PSI Villigen, March 3, 2008 Stefan Dittmaier (MPI Munich), Predictions for Higgs signal and background processes with many-particle final states at the LHC – 35