Understanding Multi-Higgs Models for Higgs Boson Couplings
Explore the intriguing world of multi-Higgs models through the research collaboration led by Kei Yagyu of the University of Southampton. Delve into the significance of single-Higgs versus multi-Higgs scenarios, testing methodologies, and the necessity of additional Higgs multiplets. Discover the potential of these models in addressing beyond the Standard Model (BSM) phenomena.
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Higgs boson couplings in multi-Higgs models Kei Yagyu University of Southampton Collaboration with Shinya Kanemura (U. of Toyama) and Mariko Kikuchi (National Taiwan U. ) 7th Sep. 2016, Multi-Higgs Models, Lisbon
Single-Higgs or Multi-Higgs? Higgs discovery in h : Existence an SU(2)Ldoublet scalar. Question: single-Higgs or multi-Higgs? Kei Yagyu (U. of Southampton) Higgs boson couplings in multi-Higgs models 1/13
Single-Higgs or Multi-Higgs? Higgs discovery in h : Existence an SU(2)Ldoublet scalar. Question: single-Higgs or multi-Higgs? 1. Why not: no strong reason to restrict the Higgs sector to be minimal. c.f. Multi-gauges (SU(3) SU(2) U(1)) and Multi-fermions (3-gen.) 2. BSM for the Higgs mass problem: e.g., SUSY, pNGB Higgs scenarios. Non-minimal Higgs sectors are predicted. 3. BSM for the unsolved phenomena: masses, DM, baryon asymmetry, muon g-2. Additional Higgs multiplets are required. Studying multi-Higgs models Determination of BSM! Kei Yagyu (U. of Southampton) Higgs boson couplings in multi-Higgs models 1/13
How we can test multi-Higgs models h(125) Higgs sector hff hVV Gauge bosons Quarks & Leptons Kei Yagyu (U. of Southampton) Higgs boson couplings in multi-Higgs models 2/13
How we can test multi-Higgs models Additional Higgs fields: S, D, T, H, A, H , H , Direct search h(125) Higgs sector hff hVV Gauge bosons Quarks & Leptons Kei Yagyu (U. of Southampton) Higgs boson couplings in multi-Higgs models 2/13
How we can test multi-Higgs models Additional Higgs fields: S, D, T, H, A, H , H , Direct search Radiative correction Fields VEVs Mixing h(125) Higgs sector Indirect search hff hVV Deviations Gauge bosons Quarks & Leptons Kei Yagyu (U. of Southampton) Higgs boson couplings in multi-Higgs models 2/13
How we can test multi-Higgs models Additional Higgs fields: S, D, T, H, A, H , H , sector; i.e., # of multiplets, their reps., symmetry, Pattern of the deviation depends on the structure of the Higgs Direct search Radiative correction Fields VEVs Mixing Measurements of h couplings Determination of the Higgs sector h(125) Higgs sector Indirect search In this talk, we discuss the 2HDM and the HSM as the hff hVV Deviations simplest multi-Higgs models with tree=1. Gauge bosons Quarks & Leptons Kei Yagyu (U. of Southampton) Higgs boson couplings in multi-Higgs models 2/13
Two Higgs Doublet Model (2HDM) Davidson, Haber PRD71 (2005) The Higgs basis tan = v2/v1 NG boson Charged Higgs CP-even Higgs CP-odd Higgs SM-like Higgs with 125 GeV Kei Yagyu (U. of Southampton) Higgs boson couplings in multi-Higgs models 3/13
types of Yukawa interactions In order to avoid tree level FCNC, (softly-broken) Z2is imposed. Under the Z2, we can define 4 independent types of Yukawa interactions. Barger, Hewett, Phillips, PRD41 (1990) Grossman, NPB426 (1994) Type-Y (Flipped) Type-II Type-I Type-X (Leptophilic) u d u u d u d e d e e e Kei Yagyu (U. of Southampton) Higgs boson couplings in multi-Higgs models 4/13
Gauge/Yukawa Interaction Kinetic term u cot d cot e cot Yukawa couplings Type I Type II cot -tan -tan Type X cot cot -tan Type Y cot -tan cot V f = (SM) [sin( - ) + fcos( - )] h = (SM) sin( - ) h f V Kei Yagyu (U. of Southampton) Higgs boson couplings in multi-Higgs models 5/13
Higgs Singlet Model (HSM) We consider a model with an SU(2) singlet real scalar field S. Singlet VEV (vS) does not contribute to EWSB and fermion mass gen. We can simply take vS = 0 without loss of generality. The double-singlet mixing is induced from the S term. The h couplings deviate only by the mixing at the tree level. V f = (SM) cos = (SM) cos h h f V Kei Yagyu (U. of Southampton) Higgs boson couplings in multi-Higgs models 6/13
H-COUP Fortran code to calculate the h couplings at 1-loop level in MHMs based on the (modified) on-shell renormalization scheme. The gauge dependence in the h couplings from C.T. of mixing angles is removed. 2HDMs (Type-I, II, X and Y) Kanemura, Kikuchi, KY, PLB731 (2014) Kanemura, Kikuchi, KY, NPB896 (2015) Inert 2HDM Kanemura, Kikuchi, Sakurai, 1605.08520 HSM Kanemura, Kikuchi, KY, NPB907 (2016) Kanemura, Kikuchi, KY, 1608.01582 Higgs Triplet Model (HTM) Aoki, Kanemura, Kikuchi, KY, PLB714 (2012) Aoki, Kanemura, Kikuchi, KY, PRD87 (2013) The first version of H-COUP (ver. 1.0) will be public in early 2017. Kei Yagyu (U. of Southampton) Higgs boson couplings in multi-Higgs models 7/13
Important diagrams X= ghXX(MHM)/ghXX(SM), X= X- 1 = = - h~ +30% for m = 300 GeV, V( F) ~ - 0.6% for m = 300 GeV, h = 1.5v ( =H,A,H ) h = 1.5v ( =H,A,H ) Kei Yagyu (U. of Southampton) Higgs boson couplings in multi-Higgs models 8/13
VS b in 2HDMs (Tree) V= (-1 0.4)%, t< 0 Parameter scan: - tan > 1 Kei Yagyu (U. of Southampton) Higgs boson couplings in multi-Higgs models 9/13
VS b in 2HDMs (1-loop) V= (-1 0.4)%, t< 0 Parameter scan: - tan > 1 - m > 300 GeV - sin( - ) < 1 - | h | > 0 - cutoff> 3 TeV Kei Yagyu (U. of Southampton) Higgs boson couplings in multi-Higgs models 9/13
VVS F in 2HDM-I and HSM (Tree) Parameter scan (2HDM-I): - sin( - ) < 1 Parameter scan (HSM): - cos( ) < 1 Kei Yagyu (U. of Southampton) Higgs boson couplings in multi-Higgs models 10/13
VVS F in 2HDM-I and HSM (1-loop) Parameter scan (2HDM-I): - sin( - ) < 1 - m > 300 GeV - | h | > 0 - cutoff> 3 TeV Parameter scan (HSM): - cos( ) < 1 - mH> 300 GeV - | S| > 0 - cutoff> 3 TeV Kei Yagyu (U. of Southampton) Higgs boson couplings in multi-Higgs models 10/13
Fingerprint the Higgs sector ( e, d)= (+,+) Type-II 2HDM Non-univ. F Type- 2HDM ( e, d)= (+, ) ( u< 0 ) V Type- 2HDM ( e, d)= ( ,+) Type-I 2HDM w/o large tan V F Universal F HSM or Type-I w/ large tan V F Kei Yagyu (U. of Southampton) Higgs boson couplings in multi-Higgs models 11/13
VVS h in 2HDM and HSM ( cutoff> 3 TeV) HSM 2HDM (tan = 1) 1-loop tree 1-loop tree h can be non-zero when V is non-zero. Maximally possible allowed region depends on the model. Kei Yagyu (U. of Southampton) Higgs boson couplings in multi-Higgs models 12/13
Summary The Higgs sector can be fingerprinted from Vand F . 1-loop EW corrections do not qualitatively change this strategy. The hhh coupling can deviate from the SM prediction by -40 ~ +20% in the 2HDM and 0 ~ +100% in the HSM at V~ -2% under cutoff> 3TeV. The Fortran code H-COUP (ver. 1.0) will be public in early 2017 Kei Yagyu (U. of Southampton) Higgs boson couplings in multi-Higgs models 13/13
Buck up Kei Yagyu (U. of Southampton) Higgs boson couplings in multi-Higgs models
h (tree) HSM 2HDM-I
h (tree and 1-loop) HSM 2HDM-I Tree Tree 1-loop 1-loop
Higgs potential of 2HDM (CPC + Z2) Higgs potential with softly-broken Z2symmetry and CP-conservation 8 parameters v (=246 GeV), mh(=125 GeV), mH, mA, mH+, sin( - ), tan , and M2 Mass parameters [sin( - ) ~1] mh2~ v2, m 2 ~ M2+ v2 = H , A, H
Higgs potential of HSM The most general potential 7 parameters v (=246 GeV), mh(=125 GeV), mH, sin( ), S, S, and S Scalar Masses
Renormalization 1. Count the # of parameters in the Lagrangian. 2. Prepare the same # of counter terms by shifting the parameters. 3. Set the same # of ren. conditions to determine the CT s. 4. Calculate the renormalized quantities.
Renormalized Higgs Couplings 4. Calculate the renormalized quantities. Counter term Tree PI hWW hZZ hff hhh
Renormalization in the Higgs sector 1. Count the # of parameters in the Lagrangian. Parameters in the potential (8) : mh, mH, mA, mH+, , , v, M2 Tadpoles (2) : Th, TH Wave functions (12) : Zeven(2 ), Zodd(2 ), Z (2 ) Total (22) 2. Prepare the same # of counter terms by shifting the parameters. Parameter shift : m m + m , + , Tadpole shift : Th 0 + Th, TH 0 + Th Field shift :
Renormalization in the Higgs sector v : Ren. in EW sector Hollik M2: Minimal subtraction Kanemura, Okada, Senaha, Yuan 3. Set the same # of ren. conditions. = 0 Th, TH(2) Tadpole condition H, h = 0 On-shell condition I m (4) @ p2= m 2 Z (6) On-shell condition II = 0 @ p2= m 2 , CHh, ChH , CAG, CGA CG+H-, CH+G-(8) On-shell condition III = 0 @ p2= m 2= m 2
Uncertainty for QCD corrections Lepage, Mackenzie and Peskin, 1404.0319 [hep-ph]
Measurements of Higgs couplings LHC Run-I Future arXiv: 1606.02266 [hep-ex] arXiv: 1310.8361 [hep-ex] ~10% ~10% ~15% ~15% ~20% ~120% Kei Yagyu (U. of Southampton) 9/25
Measurements of h couplings (future) Snowmass Higgs Working Group Report, arXiv: 1310.8361 [hep-ex] h couplings will be measured with a few % @HL-LHC and O(1)% or better than 1% @ ILC500.
Upper limit on hfrom triviality 2HDMs HSM V = S| |2S2+ S S4 + Kei Yagyu (U. of Southampton) Non-Minimal Higgs Sectors & Linear Colliders 17/13
mHVS h in 2HDM and HSM 2HDM (tan = 1) HSM tree tree + 1-loop x= cos( - ) x= sin( ) Kei Yagyu (U. of Southampton) Non-Minimal Higgs Sectors & Linear Colliders 20/13
VVS h in 2HDM and HSM HSM 2HDM (tan = 1) tree tree + 1-loop Kei Yagyu (U. of Southampton) Non-Minimal Higgs Sectors & Linear Colliders 21/13
