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, 115002 (2010)

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

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.

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 !!

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 ?

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.

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)

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=130-200GeV is excluded arXiv:1005.3216

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.

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.

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 !!

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 !!

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.

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

hhh coupling at Collider experiment let us first consider model independently

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

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 !

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 !

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

Sensitivity study of hhh coupling at the LHC A sensitivity plot PRD67, 033003 (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 !!

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 !!

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 (~0.1-0.2fb) are comparable to e+e-hhZ mh=120GeV mh=160GeV Photon luminosity spectra Controlled by laser frequency:

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 !

Case study: model dependent considerations

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 !

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

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 !

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

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.)

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.

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

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

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

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

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.

Back Up

Non-decoupling effect Decoupling theorem Appelquist, Carazzone PRD11.2856(1975)

A simple example Gluon fusion: GG  h

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

2HDM (Constraints) EW precision Unitarity Stability

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