Muon g-2 and other observables in models
with extended Higgs and matter sectors
with N. McGinnis and K. Hermanek
arXiv:2011.11812 [hep-ph]
arXiv:2103.05645 [hep-ph]
Radovan Dermisek
Indiana University, Bloomington

20th Lomonosov Conference, Moscow, Russia, August 21, 2021

to appearSimple Extensions of the Standard Model
Standard Model±¯3 × {q, ū, d, l, ē}, g, γ, Z, W , hmore Higgses? 2HDM?

H, A, H±

more matter?

Q, Ū, D̄, L, Ē
+Q̄, U, D, L̄, E

Appear in many models: SUSY, composite Higgs, phenomenologically motivated extensions…
My personal motivation: exactly this particle content + SUSY provide an understandingof the values of all large couplings in the SM from the IR fixed point behavior fromrandom large boundary conditions
R.D. and N. McGinnis, arXiv:1812.05240 [hep-ph]
Radovan Dermisek

20th Lomonosov Conference, Moscow, August 21, 2021

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7 largest SM couplings from random b.c.
Q = 3.5× 10 16 GeV

Q = 3.5× 10 16 GeV

MSSM+1VF

3.00.252.5λh , y τ , y b , y t ( Q )∼ 3 × 1016 GeV

α1 , α2 , α3 ( Q )GUT scale

0.30

0.20
0.15
0.10
0.05

2.0
1.5
1.00.5

Random unrelated boundary conditions:α1(MG), α2(MG), α3(MG) ∈ [0.1,0.3]yt(MG), yb(MG), yτ(MG), YV (MG) ∈ [1,3](larger values of couplings do not affect results significantly)
Higgs quartic given by gauge couplings at any scale:g22(Q) + (3/5)g12(Q)λh(Q) ≡cos2 2β4
the plots assume:

Radovan Dermisek

20th Lomonosov Conference, Moscow, August 21, 2021

tan β = 40

37 largest SM couplings from random b.c.
Q = 3.5× 10 16 GeV

Q = 3.5× 10 16 GeV
3.00.252.5

λh , y τ , y b , y t ( Q )∼ 3 × 1016 GeV

α1 , α2 , α3 ( Q )GUT scale

0.30

0.20
0.15
0.10
0.05

MSSM+1VF

2.0
1.5
1.0
0.5

0.30

3.0

0.25

2.5

0.20
0.15
0.10

solid line are SM
0.05
measured values
evolved to a given scale,they include SUSY
threshold corrections
assuming tan β = 40
Radovan Dermisek

Q = 7.0× 10 3 GeV

λh , y τ , y b , y t ( Q )M = few TeV

α1 , α2 , α3 ( Q )Q = 7.0× 10 3 GeV

2.0
1.5
1.00.5Distinctive pattern of couplings emerges

20th Lomonosov Conference, Moscow, August 21, 2021

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7 largest SM couplings from random b.c.
Q = 3.5× 10 16 GeV

Q = 3.5× 10 16 GeV
3.00.25

2.5

0.20
0.15
0.10
0.05

MSSM+1VF

λh , y τ , y b , y t ( Q )∼ 3 × 1016 GeV

α1 , α2 , α3 ( Q )GUT scale

0.30

2.01.51.00.5

GUT: Random boundary conditions

SMEW scale
Radovan Dermisek

α1 , α2 , α3 ( MZ )

0.30
0.25
0.20
0.15
0.10
0.05mτ , mb , mh , mt [GeV( MZ ) ]EW: familiar pattern of couplings and masses

M = few TeV

100
50
105
1
0.5

20th Lomonosov Conference, Moscow, August 21, 2021

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Optimizing parameters related to scales
R.D. and N. McGinnis, arXiv:1812.05240 [hep-ph]

For random unrelated (or unified) parameters:α1(MG), α2(MG), α3(MG) ∈ [0.1,0.3]yt(MG), yb(MG), yτ(MG), YV (MG) ∈ [1,3]three parameters,MG, M, tan β,
can be optimized so that none of the seven observables ismore than 25% (or 15%) from the measured values.
Further optimizing YV to obtain the required overall scale of Yukawa couplings,
all 7 observables are within 11% (or 7.5%) from their measured values.
Radovan Dermisek

20th Lomonosov Conference, Moscow, August 21, 2021

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Muon g-2

Muon g-2, arXiv:2104.03281 [hep-ex]
T. Aoyama, et al., Phys. Rept. 887, 1-166 (2020)

New physics contributions to muon g-2
Typical NP contributionXγ
2mμ2gNPΔaμ ≃216π 2 mNP

Radovan Dermisek

20th Lomonosov Conference, Moscow, August 21, 2021

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New physics contributions to muon g-2
Typical NP contribution

Mass enhanced NP contribution

XX
Zx

Y
⟨H⟩

γ
2mμ2gNPΔaμ ≃216π 2 mNP

Radovan Dermisek

γ3mμv
λNP
Δaμ ≃
216π 2 mNP

20th Lomonosov Conference, Moscow, August 21, 2021

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New physics contributions to muon g-2
Typical NP contribution

Mass enhanced NP contribution

XXZx

Y
⟨H⟩

γ
2mμ2gNPΔaμ ≃216π 2 mNPEnhancement:

λNPvmμγ3mμv
λNPΔaμ ≃216π 2 mNP

possible to explain Δaμ with NP at 10s TeV
Radovan Dermisek

20th Lomonosov Conference, Moscow, August 21, 2021

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Mass enhanced NP contributions to ΔaμX
ZxY⟨H⟩γX, Y, Z can have any quantum numbers (allowing for the loop):• X = h, Z, W and Y, Z = vectorlike leptons

minimal, just SM with new leptons, constrained the mostK. Kannike, M. Raidal, D. M. Straub and A. Strumia, arXiv:1111.2551 [hep-ph]R. D. and A. Raval, arXiv:1305.3522 [hep-ph]

Radovan Dermisek

20th Lomonosov Conference, Moscow, August 21, 2021

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Mass enhanced NP contributions to ΔaμXZxY⟨H⟩γX, Y, Z can have any quantum numbers (allowing for the loop):• X = h, Z, W and Y, Z = vectorlike leptons

minimal, just SM with new leptons, constrained the mostK. Kannike, M. Raidal, D. M. Straub and A. Strumia, arXiv:1111.2551 [hep-ph]R. D. and A. Raval, arXiv:1305.3522 [hep-ph]• X = S (not participating in EWSB)

the most popular, many options, the least constrained(similar options with new gauge fields, X = V, or superpartners)
Radovan Dermisek

20th Lomonosov Conference, Moscow, August 21, 2021

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Mass enhanced NP contributions to ΔaμX
ZxY
⟨H⟩

γ

X, Y, Z can have any quantum numbers (allowing for the loop):• X = h, Z, W and Y, Z = vectorlike leptons

minimal, just SM with new leptons, constrained the mostK. Kannike, M. Raidal, D. M. Straub and A. Strumia, arXiv:1111.2551 [hep-ph]R. D. and A. Raval, arXiv:1305.3522 [hep-ph]• X = H, A, H and Y, Z = vectorlike leptons• X = S (not participating in EWSB)±e.g. 2HDM with new leptons, interpolates between the the other two options

the most popular, many options, the least constrained(similar options with new gauge fields, X = V, or superpartners)
Radovan Dermisek

20th Lomonosov Conference, Moscow, August 21, 2021

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Type-II 2HDM with L + E (+ N)
General lagrangian describing mixing of the 2nd generation
with new leptons:

Charged lepton mass matrix (after EWSB):
diagonalizing this matrix leads to:two new mass eigenstates, e4, e5,
modification of muon couplings,
and couplings between the muon and e4, e5Radovan Dermisek

20th Lomonosov Conference, Moscow, August 21, 2021

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Type-II 2HDM with L + E (+ N)
General lagrangian describing mixing of the 2nd generation
with new leptons:

At energies much below ML, ME:

dim. 6 operator is a new source of muon mass:

and is directly linked to contributions to Δaμ
Radovan Dermisek

20th Lomonosov Conference, Moscow, August 21, 202111

Δaμ in type-II 2HDM with L + E (+ N)
R.D., N. McGinnis, and K. Hermanek, arXiv:2011.11812 [hep-ph]
arXiv:2103.05645 [hep-ph]

kW = 1k Z = − 1/2hk = − 3/2}

kW + kZ + kh = − 1k H = − (11/12) tan2 βA

2k = − (5/12) tan βkH±2= (1/3) tan β}

HAk +k +kH±= − tan2 β±2contributions of H, A, H to Δaμ enhanced by tan βRadovan Dermisek

20th Lomonosov Conference, Moscow, August 21, 2021

12Δaμ in type-II 2HDM with L + E
depending on the size of couplings

all experimental constraints from direct searches and precision EW data satisfied

multi TeV (10s TeV) new leptons and Higgses can explain ΔaμRadovan Dermisek

20th Lomonosov Conference, Moscow, August 21, 202113

Δaμ in type-II 2HDM and muon Yukawa c.
depending on the size of couplings

hhNOTE, both −δλμμ/(λμμ)SM = 0 and 2 correspond to SM expectation for h → μ + μ −−3muon Yukawa coupling modified at ≳ 10
Radovan Dermisek

20th Lomonosov Conference, Moscow, August 21, 2021

−4or 5 × 10levels
14Δaμ in type-II 2HDM and muon gauge c.
depending on the size of couplings

muon Z couplings modified at > 3 × 10−5 or 5 × 10−6 levels
Radovan Dermisek

20th Lomonosov Conference, Moscow, August 21, 2021

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Standard Model with L + E
R.D., N. McGinnis, and K. Hermanek, arXiv:2103.05645 [hep-ph]Δaμ and h → μ + μ − highly correlated,
no free parameter for ML,E ≫ MEW

excluded by+1.40
1σ range of Δaμ predicts Rh→μ+μ− = 1.32−0.90
Radovan Dermisek

20th Lomonosov Conference, Moscow, August 21, 202116

Δaμ in SM with L+E and muon couplings

muon Z couplings modified at > 3 × 10−4 levels
Radovan Dermisek

20th Lomonosov Conference, Moscow, August 21, 2021

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Related observables in SM with L + E
Effective lagrangian:is completely fixed by muon mass and g-2:

Interactions of the muon with SM Higgs boson:are predicted without a free parameter!
Radovan Dermisek

20th Lomonosov Conference, Moscow, August 21, 2021

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Di-Higgs and tri-Higgs signals of ΔaμR.D., N. McGinnis, and K. Hermanek, to appear

1σ range of Δaμ1 TeV muon collider with 0.2 ab−1could see ~50 di-Higgs events

3 TeV muon collider with 1 ab−1could see ~30 tri-Higgs events

Radovan Dermisek

20th Lomonosov Conference, Moscow, August 21, 2021

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Di-Higgs and tri-Higgs in 2HDM with L+E
In 2HDM one free parameter, tan β, remains:

1σ range of Δaμdi-Higgs and tri-Higgs cross sections large at small tan βat large tan β: HH, hHH, hH +H −, . . . expected for sufficient
Radovan Dermisek

20th Lomonosov Conference, Moscow, August 21, 2021

s20Conclusions
Models with more Higgses and vectorlike matter areamong the simplest extensions of the standard model,
and can provide understanding of values of 7 largest couplings in the SM.

Muon g-2 can be explained with multi TeV (10s TeV) leptons:• SM with L + E (+ N):• the most economical• the most constrained by precision EW data
• the most unique predictions
possible effects at the LHC, can be tested at Giga-Z or 1 TeV muon collider• 2HDM with L + E (+ N)

di-Higgs and tri-Higgs signals especially striking

2tan• β enhanced contributions of heavy Higgses• would require FCC-ee (precision) and FCC-hh (energy) to be tested• interpolates between the SM and models with scalars not participating in EWSBRadovan Dermisek

20th Lomonosov Conference, Moscow, August 21, 2021

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