1. Koji TSUMURA (ICTPNTU) LC10 Frascati, 2/12/2010
Higgs boson pair production in new physics models
at hadron, lepton, and photon colliders
Koji TSUMURA (ICTPNTU) LC10 Frascati, 2/12/2010
Higgs boson pair production in new physics models at hadron, lepton, and photon colliders
E. Asakawa, D. Harada, S. Kanemura, Y. Okada and K.T., Phys.Rev. D82, (2010)

2. Higgs self-coupling (hhh) constant Non-decoupling effect
Outline
Introduction
Higgs self-coupling (hhh) constant
Non-decoupling effect
Double Higgs production
Complementarity of hadron, lepton, photon colliders
Summary 2

3. The last unknown particle of the SM
The Higgs boson
The last unknown particle of the SM
LEP & Tevatron direct search
Below 114GeV, and around 160GeV were excluded.
EW precision data
Light Higgs boson is favored in the SM.

4. The last unknown part of the SM
Higgs sector
The last unknown part of the SM
Higgs potential:
2 parameters in Higgs sector:
hhh(hhhh) coupling is a prediction of the SM
Can new physics effect appear in hhh coupling ?
Measurement of hhh self-coupling is not only a test of the SM,
but also a probe of new physics !!

5. Triple Higgs coupling @ 1-loop
Triple Higgs boson vertex function
~10% deviation from tree-level coupling by top-loop
Correction is propotional to 4th power of mt
“Non-decoupling” effect in the large mt limit !
How can large corrections come from new particles ?

6. Triple Higgs coupling @ 1-loop in New physics models
Chiral 4th generation
Including momentum dependence: Light Higgs mh=120GeV
Ch4
-70% corr. for mf’=256GeV
-150% corr. for mf’=300GeV
-590% corr. for mf’=400GeV
It can easily be more than 100% effect.

7. Triple Higgs coupling @ 1-loop in New physics models
Chiral 4th generation
Including momentum dependence: Heavy Higgs mh=210GeV
Ch4
For heavy Higgs, it can still be 100% effect.
However, the vacuum may be unstable.
Heavy Higgs ? Extensions of Higgs sector ?
The vacuum instability can be evaded in 2HDM with Ch4.
Hashimoto PRD81,075023(2010)

8. Higgs mass bound in Ch4
Low energy theorem (non-decoupling effect of heavy fermions)
GG  h in SM with Ch4: F = t, t’, b’
amplitude = 3 x (SM amp.)  s = 9 x sSM
mh= GeV is excluded
arXiv:

9. Triple Higgs coupling from bosonic loop
Model with extra scalar (ex. 2HDM,LQ)
Scalar pot.
Decoupling or Non-decoupling
Mass formula:
hhh coupling corr.
SM Higgs doublet
an extra complex scalar singlet (for simplicity)
Decoupling limit
Non-Decoupling limit
Non-decoupling effect can
enhance hhh coupling significantly!!
For M=0, corr. maximal.
For M=mf, corr. Vanishes.

10. Triple Higgs coupling from bosonic loop
Adding extra doublet (2HDM), singlet (Leptoquark)
Difference comes from # of extra degree, color factor.
Threshold enhancements (real production of extra scalar pair) can be seen.
2HDM
mh=120GeV LQ
mh=120GeV
Non-decoupling case !!
More than 100% effects.

11. Triple Higgs coupling from bosonic loop
Adding extra doublet (2HDM), singlet (LQ)
+(positive) corr. to SM hhh coupling  EWPT can be strongly 1st order (EWBG possible). Bonus!
Below the threshold, corr. to hhh can be well approximated by a constant shift.
2HDM
mh=160GeV LQ
mh=185GeV
Non-decoupling case !!

12. Triple Higgs coupling @ 1-loop (Decoupling theory)
Vector-like top: left- and right-handed SU(2) singlets
Mass matrix: [t-T mixing]
hhh coupling corr.
EW precision constraints:
Almost decoupling !!

13. Triple Higgs coupling @ 1-loop (Decoupling theory)
Vector-like top: left- and right-handed SU(2) singlets
hhh coupling corr.
Vec
Vec
mh=120GeV
mh=160GeV
Decoupling !!
Less than 10% effect on hhh-coupling constant.

14. Triple Higgs coupling (Summary)
Corrections to the SM tree-level hhh coupling
Non-decoupling theories
SM top: -10% effect
Chiral 4th gen.: can easily be -100% effect for large mf’
Vacuum may be unstable. (heavy Higgs or extensions of Higgs sector)
2HDM & LQ with : can be +100% effect for large mF
Well approximated by dim6 op., EWBG possible
Decoupling theories
2HDM and LQ with
Vector-like top: less than +10% effect

15. hhh coupling at Collider experiment
let us first consider model independently

16. hhh coupling @ colliders
Double Higgs production with hhh coupling
LHC:
ILC:
PLC (Photon linear collider):
Hard photon can be produced by compton backward scattering Ginzburg et.al. (83)
Purpose of this talk: show complimentality among these processes

17. Double Higgs production (tree-level) with dK
hhh coupling at e+e- collider
e+e-  hhnn becomes important for
hhh coupling measurement at high energy
(ACFA WG)
mh=120GeV
mh=120GeV
low and high energy complementarity !

18. Double Higgs production (tree-level) with dK
hhh coupling at e+e- collider
Different correlations with the deviation of hhh coupling
mh=160GeV
mh=160GeV
Different interference effect.
+ and – variation complementarity !

19. Double Higgs production (1-loop-level) with dK
hhh coupling in GGhh at LHC
Invariant mass distribution
Destructive interference (only for very large hhh, dK=+1)
Total s is larger than
those at ILC by 1-2
orders of magnitude.
However,
BG is more serious.
( Next slide)
mh=120GeV
mh=160GeV

20. Sensitivity study of hhh coupling at the LHC
A sensitivity plot PRD67, (2003) Baur, Plehn, Rainwater
200% error in the hhh coupling
measurement for L=300 fb-1
L=3000 fb-1 is required for determining
the hhh coupling with 20% accuracy.
LHC needs ILC help !!

21. Double Higgs production (1-loop-level) with dK
hhh coupling in gghh at PLC
Hard photon: energy distribution is narrow band.
(gluon distribution at LHC is broad band and mainly low energy)
Additional W-boson loop contribuion
(only top-loop contributes to GGhh)
Structure of interference can change from GGhh !!

22. Double Higgs production (1-loop-level) with dK
hhh coupling in gghh at PLC
e-e-(gg)hh cross section as a function of
Despite one loop process,
s (~ fb) are
comparable to e+e-hhZ
mh=120GeV
mh=160GeV
Photon luminosity spectra
Controlled by laser frequency:

23. Double Higgs production (1-loop-level) with dK
hhh coupling in gghh at PLC
Interference structure is different (not simple correlations)!
mh=120GeV
mh=160GeV
from left to right, mh=120GeV
GGhh
e-e+hhZ
e-e+hhnn
complementarity with hhh variations !

24. Case study:
model dependent considerations

25. eehhZ in New physics models
eehhZ with mh=120GeV
NP effects appear only in hhh coupling
Dk is good approximation (cannot distinguish 2HDM & LQ)
SM+Dk
2HDM LQ
Decoupling/Non-decoupling nature of 2HDM/LQ will be determined !

26. eehhZ in New physics models
eehhZ with mh=120GeV
In Ch4 (Non-decoupling)
hhh coupling depend on momentum
Non-decoupling effect is significant
In Vec (Decoupling)
Negligibly small effect
SM+Dk
Ch4
Vec
Ch4

27. eehhnn in New physics models
eehhnn with mh=120GeV
NP effects appear only in hhh coupling
Dk is good approximation (cannot distinguish 2HDM & LQ)
SM+Dk
2HDM LQ
Decoupling/Non-decoupling nature of 2HDM/LQ will be determined !

28. eehhnn in New physics models
eehhnn with mh=120GeV
In Ch4 (Non-decoupling)
hhh coupling depend on momentum
Non-decoupling effect is significant
In Vec (Decoupling)
Negligibly small effect
SM+Dk
Ch4
Vec
Ch4

29. GG  hh in New physics models
Additional colored particles can contribute to GGhh
Ch4: t’, b’ (analogous to SM quarks)
LQ: f (scalar QCD, Scalar pot.)
Vec: T (QCD, t-T FCNC-Yukawa int.)

30. GG  hh in New physics models
GGhh with mh=120GeV
Non-decoupling effects can be seen.
Threshold enhancement in LQ models.
But, impact on total s is small, because G-dist. is mainly low energy regime.
Cross section can be reduced by non-decoupling effect.
2HDM
SM+Dk LQ
hhh measurement can distinguish Decoupling/Non-decoupling nature.

31. GG  hh in New physics models
GGhh with mh=120GeV
Cross section becomes huge (more than 1000%) in Ch4.
Although Ch4 is non-decoupling theory, However, enhancement of s mainly comes from extra-quark loop.
ILC plays the complementary role to test the non-decoupling nature of theory.
Effect of t-T FCNC-Yukawa is small (less than 10%).
SM+Dk
Ch4
Vec
logarithmic scale

32. gg  hh in New physics models
Additional electrically charged particles can contribute to gghh
Ch4: t’, b’
THDM: H+, H-
LQ: f with Q=1/3 or 4/3
Vec: T

33. gg  hh in New physics models
gghh with mh=120GeV
Non-decoupling effects and
threshold effects can be seen.
These effects can be accessible by tuning the collision energy !!
2HDM
SM+Dk LQ
Q=1/3 LQ
Q=4/3

34. gg  hh in New physics models
gghh with mh=120GeV
In Ch4, cross section enhances by factor of O(10).
loop corr. to hhh and gghh vertices are significant.
In Vec, effects are tiny.
loop effects are generically small.
Ch4
SM+Dk
logarithmic scale
Vec

35. Summary
Determination of hhh coupling constant is not only a test of SM but also a probe of New Physics.
Non-decoupling effect on hhh coupling can be significant in New Physics models
Variation of hhh coupling affects double Higgs production processes, eehhZ, hhnn, GGhh, and gghh quite differently.
Different interferences  Complementarity of different colliders
LHC will search for entire range of non-decoupling theory (m ~ v), and ILC/PLC can test the its nature precisely.

36. Back Up

37. Non-decoupling effect
Decoupling theorem Appelquist, Carazzone PRD (1975)

38. A simple example
Gluon fusion: GG  h

39. 2HDM
Softly Z2 broken 2HDM potential
Higgs mixing
Higgs mass

40. 2HDM (Constraints)
EW precision
Unitarity
Stability

41. SU(2) singlet Leptoquark
Scalar self-interaction: Q=1/3 or 4/3
Leptoquark mass:
Indirect LFV constraints
 LQs are assumed to be coupled with 1 fermion family
Direct search constraints
 mLQ > 256GeV (1st), 316GeV (2nd), 229GeV (3rd)
GGh cross section: sSM x 16/9