Higgs Pair Production at the LHC - Desy

Introduction 

Calculations 

Numerical results 

Conclusion 

Higgs Pair Production at the LHC 

Marina Billoni 1,2 

in collaboration with S. Dittmaier 1,2 and A. Mück 3 

1 Albert-Ludwigs-Universität, Freiburg 

2 Max-Planck-Institut für Physik, München 

3 RWTH Aachen 

DESY Theory Workshop 

October 1, 2009 

Marina Billoni Higgs Pair Production at the LHC

Outline 

Introduction 

Introduction 



Conclusion 


at Leading Order 

at Next-to-Leading Order QCD 


within the Standard Model 

within the Minimal Supersymmetric Standard Model 

Conclusion 


Introduction 

Why Higgs Pairs? 

Introduction 



Conclusion 

Discovery of a neutral scalar particle at the CERN Large Hadron Collider: 

SM Higgs Boson H ? 


Introduction 


Introduction 



Conclusion 



→ Determination of the properties and experimental reconstruction of the 

Higgs potential: 

V(H) = 1 

2 M2 H H 2 + λHHH H 3 + 1 

λHHHH H4 

4 


Introduction 


Introduction 



Conclusion 





V(H) = 1 

2 M2 H H 2 + λHHH H 3 + 1 

λHHHH H4 

4 

λHHH = M2 H 

2 v , 

„ 

v = 2 MW À « 

sin θW 

e 

Marina Billoni Higgs Pair Production at the LHC 

À À

Introduction 


Introduction 



Conclusion 





V(H) = 1 

2 M2 H H 2 + λHHH H 3 + 1 

λHHHH H4 

4 

λHHH = M2 H 

2 v , 

„ 

v = 2 MW À « 

sin θW 

e 

Production mechanisms at the LHC 

◮ Gluon–Gluon Fusion g g → H H (NLO QCD known 

approx.) Dawson, Dittmaier, Spira ’98 

◮ Vector-Boson Fusion V V → H H (NLO QCD known) 

Figy ’08 

◮ Higgs-strahlung q ¯q ′ → H H V 


À À

This Work 

Introduction 



Conclusion 

Aim: Calculation of NLO QCD corrections to the following processes 

SM 

p p → H H Z 

p p → H H W + 

p p → H H W − 

MH =? 

„ 

Φ = 

φ + 

1 

√ 2 (v + H + iφ 0 ) 


« 

,

This Work 

Introduction 



Conclusion 


SM 

p p → H H Z 

p p → H H W + 

p p → H H W − 

MSSM 

H1 = 

MH =? 

„ 

Φ = 

„ 1√2 (v1 + φ1 − iχ1) 

−φ − 

1 

„ « 

H 

= R(α) 

h 

„ « 0 

G 

= R(β) 

A 

„ φ1 

φ2 

„ 

χ1 

φ + 

1 

√ 2 (v + H + iφ 0 ) 

« 

, H2 = 

« 

, R(α) = 

χ2 

« „ ± 

G 

, 

H ± 

« 

„ 

« 

, 

φ + 

2 

√ 

1 

(v2 + φ2 + iχ2) 

2 

“ ” 

cos α sin α 

− sin α cos α , 

„ ± 

φ 

= R(β) 1 

φ ± 

« 

2 

tan β = v2 

= ?, MA = ?, α = F(tanβ, MA, MW,MZ, . . . ) 

v1 


«

This Work 

Introduction 



Conclusion 


SM 

p p → H H Z 

p p → H H W + 

p p → H H W − 

MSSM 

p p → h h V 

p p → h H V 

p p → H H V 

p p → A A V 

(+etc.) 

H1 = 

MH =? 

„ 

Φ = 

„ 1√2 (v1 + φ1 − iχ1) 

−φ − 

1 

„ « 

H 

= R(α) 

h 

„ « 0 

G 

= R(β) 

A 

„ φ1 

φ2 

„ 

χ1 

φ + 

1 

√ 2 (v + H + iφ 0 ) 

« 

, H2 = 

« 

, R(α) = 

χ2 

« „ ± 

G 

, 

H ± 

« 

„ 

« 

, 

φ + 

2 

√ 

1 

(v2 + φ2 + iχ2) 

2 

“ ” 

cos α sin α 

− sin α cos α , 

„ ± 

φ 

= R(β) 1 

φ ± 

« 

2 

tan β = v2 

= ?, MA = ?, α = F(tanβ, MA, MW,MZ, . . . ) 

v1 


«

Ô 

Ô 

Ü 

Ü 

Hadronic Cross Section 

QCD-improved Parton model 

Introduction 



Conclusion 

Î 



Ë Ë 

Î 

{S1 S2} = 

{H H, h h, h H, H H, A A}, 

V = {Z, W + , W − } 

◮ QCD factorization → Redefinition of parton densities to absorb collinear 

initial-state singularities 

σ(P1, P2) = X 

Z1 

dx1dx2 fi(x1, µF) fj(x2, µF) ˆσij(p1, p2, αs(µR), µF). 

i,j 

0 


Feynman Diagrams at LO 

SM: q ¯q ′ ÕÕ ÎÎ À → H 

ÎÀ 

Õ H V 

Õ ÎÎ À 

ÎÀ 

ÕÕ Î¨ 

À 

ÎÀ 

ÕÕ Î¨ 

À 

ÎÀ 

ÕÕ Î À 

ÎÀ 

ÕÕ Î Î 

Introduction 



Conclusion 

À À 

À 



MSSM: q ¯q ′ → h h V 




ÎÀ 

Õ H V 

Õ ÎÎ À 

ÎÀ 

ÕÕ Î¨ 

À 

ÎÀ 

ÕÕ Î¨ 

À 

ÎÀ 

ÕÕ Î À 

ÎÀ 

ÕÕ Î Î 

Introduction 



Conclusion 

À À 

À 



MSSM: q ¯q ′ ÕÕ ÎÎ 

→ Î 

Õ h h V 

Õ ÎÎ 

Î 

ÕÕ Î 

Î 

ÕÕ Î 

Î 

ÕÕ Î 

Î 

ÕÕ Î Î 




ÎÀ 

Õ H V 

Õ ÎÎ À 

ÎÀ 

ÕÕ Î¨ 

À 

ÎÀ 

ÕÕ Î¨ 

À 

ÎÀ 

ÕÕ Î À 

ÎÀ 

ÕÕ Î Î 

Introduction 



Conclusion 

À À 

À 

Possible resonances in the MSSM: 

◮ A → h Z, H ± → h W ± 

◮ H → h h 



MSSM: q ¯q ′ ÕÕ ÎÎ 

→ Î 

Õ h h V 

Õ ÎÎ 

Î 

ÕÕ Î 

Î 

ÕÕ Î 

Î 

ÕÕ Î 

Î 

ÕÕ Î 

Õ Î 

Õ ÎÀ¦ 

Î 

ÕÕ ÎÀ¦ 

Î 

ÕÕ Î Î 


 

À

Introduction 



Conclusion 

Next-to-leading order QCD corrections 

Virtual corrections 

Real corrections Õ 



σNLO = σLO + σvirt + σreal 


Õ Õ 

Õ 

Õ 

Õ 

 

Ë ÎË Ë 

Î 

Ë 

Ë Ë 

Î

Æ 

Introduction 



Conclusion 




σNLO = σLO + σvirt + σreal 


Calculation of the renormalized vertex function 

σvirt = δvirt · σBorn, δvirt = 2 Re(F + δF) UV finite ! 

Singularities: 

◮ UV → D-dim. ǫ = 4−D 

2 

◮ soft → infinitesimal gluon mass mg 

◮ collinear → small quark masses m 

→ δvirt = UV finite (after renormalization) 


Õ 

 

Õ 

1 

, ln mg, ln m 

ǫ 

Ë Ë 

Î

Æ 

Introduction 



Conclusion 




σNLO = σLO + σvirt + σsoft + σcoll + σhard 


Calculation of the renormalized vertex function 

σvirt = δvirt · σBorn, δvirt = 2 Re(F + δF) UV finite ! 

Real corrections 

→ Phase Space Slicing: ∆E, ∆Θ 

Soft region: 0 < mg < Eg < ∆E ≪ √ ˆs 

Collinear region: Eg > ∆E, θqg < ∆Θ ≪ 1 

Hard non-collinear region: Eg > ∆E, θqg > ∆Θ 

σvirt + σsoft + σcoll ∝ 

Z1 

0 

dz ln m Pqq(z) σBorn(zˆs) + finite 

| {z } 

absorbed into PDFs ! 


Õ 

 

Õ 

1 

Õ 

, ln mg, ln m 

ǫ 

Ë Õ ÎË Õ ËË Õ Î 

Ë Ë 

Î

Drell-Yan like process 

σ S1S2 V 

(s) = 

NLO 

1 

Z 

1 

Z 

1 

Z 

Introduction 



Conclusion 

Ô 

Ô 

Ü 

Ü 

Î 



Ë Ë 

Î 

dx1 dx2 dx ˆσ 

0 0 0 

S1S2 V 

(q 

Born 

2 ) 

( 

X 

× 

q,q ′ 

(f¯q (x1 , µ 2 F )f q ′ (x2 , µ2F ) + f¯q (x2 , µ2F )f q ′ (x1 , µ2F )) 

2 

4∆ (0) 

¯qq (x) + ∆1 0 

αs 

¯qq (x) − ln @ 

π 

µ2 F 

q2 1 

3 

A [Pqq(x)] + 

5 

+ X 

[fg(x1 , µ 

q 

2 F )(fq(x2 , µ2F ) + f¯q (x2 , µ2F )) + x1 ↔ x2 ] 

2 

4∆qg(x) − αs 

0 

ln @ 

2 π 

µ2 F 

q2 1 3) 

A Pgq(x) 5 

Hamberg, van Neerven, Matsuura ’91 


internal check

Introduction 



Conclusion 


 


ÆÄÇÀÀÏ ÀÀÏ ÄÇÀÀÏ 

SM Results: Cross section as a function of the SM-Higgs mass 

ÆÄÇÀÀÏ ÀÀÏ ÄÇÀÀÏ ÆÄÇÀÀ ÀÀ ÄÇÀÀ 

q = kS1S2V 

℄ 

σ ∼ O(0.1 fb) 

 

Ã 

ÅÀÎ℄ 

ÅÀÎ℄ 

K = σNLO 

∼ 1.25 

σLO 

ÔÔÀÀÎ Õ Ô×ÌÎ 


Introduction 



ÆÄÇÀÀÏ 

Conclusion 

ÀÀÏ ÄÇÀÀÏ 

ÆÄÇÀÀÏ ÀÀÏ ÄÇÀÀÏ ÆÄÇÀÀ ÀÀ ÄÇÀÀ 

Õ 

ËÅ 



SM Results: Impact of non-standard triple H coupling λ 

℄ 

ÅÀ Ô×ÌÎ ÔÔÀÀÎ Î 


High sensitivity: 

∆λ 

= ±100% 

λSM 

→ ∆σ 

σ 

∼ ±40%

Introduction 



Conclusion 

MSSM Results Example: p p → h h W + + X 



◮ SPS1a, tan β = 3, 30; MA = 100 − 300 GeV 

À ÀÏ ÆÄÇÛÓÀ ÛÓÀ 

℄ ÔÔÏ Ô×ÌÎ ØÒ¬ ◮ only tree-level masses and 

ÅÎ℄ 

 

couplings 


Introduction 



Conclusion 





◮ Calculation 

À 

of improved Born cross sections via 

FeynHiggs 

ÀÏ 

(FH) Heinemeyer et al. 

ÆÄÇÀÐÓÓÔ ÆÄÇÛÓÀ ÀÐÓÓÔ ÛÓÀ 

℄ ÔÔÏ Ô×ÌÎ ØÒ¬ ◮ only tree-level masses and 

couplings 

ÅÎ℄ 

 

◮ FH loop=0: loop-improved 

triple Higgs couplings 


Introduction 



Conclusion 






À 



ÀÏ 


ÆÄÇÀÐÓÓÔ ÆÄÇÀÐÓÓÔ ÆÄÇÛÓÀ ÀÐÓÓÔ ÀÐÓÓÔ ÛÓÀ 

℄ Ô×ÌÎ ÔÔÏ ØÒ¬ 

◮ only tree-level masses and 

couplings 


ÅÎ℄ 

 


◮ FH loop=1: 1-loop improved 

masses and couplings 


Introduction 



Conclusion 






À 



ÀÏ 


ÆÄÇÀÐÓÓÔ ÆÄÇÀÐÓÓÔ ÆÄÇÛÓÀ ÀÐÓÓÔ 

ÆÄÇÀÐÓÓÔ ÀÐÓÓÔ ÛÓÀ 

℄ ÀÐÓÓÔ ◮ only tree-level masses and 

Ô×ÌÎ ØÒ¬ ÔÔÏ 

couplings 



ÅÎ℄ 

 






Introduction 



Conclusion 






À 



ÀÏ 


ÆÄÇÀÐÓÓÔ ÆÄÇÀÐÓÓÔ ÆÄÇÛÓÀ ÀÐÓÓÔ 

ÆÄÇÀÐÓÓÔ ÀÐÓÓÔ ÛÓÀ Ô×ÌÎ 

℄ ÀÐÓÓÔ ØÒ¬ ÔÔÏ ÆÄÇÀÐÓÓÔ ÆÄÇÀÐÓÓÔ ÆÄÇÛÓÀ ÀÐÓÓÔ 

Ô×ÌÎ ØÒ¬ ÔÔÏ ÆÄÇÀÐÓÓÔ ÀÐÓÓÔ ÛÓÀ 

℄ ÀÐÓÓÔ 

ÅÎ℄ 

ÅÎ℄ 

 


Introduction 



Conclusion 

MSSM Results 

Example: p p → A A W + + X 

ÆÄÇÀÐÓÓÔ ÆÄÇÀÐÓÓÔ ÆÄÇÀÐÓÓÔ ÆÄÇÛÓÀ 

ÀÐÓÓÔ ÀÐÓÓÔ ÀÐÓÓÔ ÛÓÀ 

℄ 

ÔÔÏ ØÒ¬ Ô×ÌÎ 

ÅÎ℄ 

 



℄ 

ÔÔÏ ØÒ¬ Ô×ÌÎ 

ÅÎ℄ 


ÆÄÇÀÐÓÓÔ ÆÄÇÀÐÓÓÔ ÆÄÇÀÐÓÓÔ ÆÄÇÛÓÀ 

ÀÐÓÓÔ ÀÐÓÓÔ ÀÐÓÓÔ ÛÓÀ

Conclusion 

Results 

Introduction 



Conclusion 

◮ 25% QCD corrections to Born cross sections in the SM and MSSM 

◮ SM processes 

small cross sections < 1 fb 

but: high sensitivity to the 3-Higgs coupling λ 

◮ MSSM processes 

- with resonances: p p → ˘ h h, h H ¯ V 

cross sections > 1 fb 

strong dependence on loop-improved couplings and masses 

→ smaller cross sections 

strong dependence on tanβ 

- without resonances: p p → ˘ H H, A A ¯ V 

small cross sections < 1 fb 

Outlook 

Measurability at the LHC → compare signals to backgrounds

Higgs Pair Production at the LHC - Desy

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