g-2 with Variant Axion Models
Michihisa Takeuchi (Kavli IPMU, Univ. of Tokyo)
based on arxiv:1807.00593 (and JHEP11(2015)057 [arXiv:1507.04354],PhysRevD.97.035015 [arXiv:1711.02993])

at Ikaho on 2nd Oct 2018

No signature of BSM yet
No evidence of SUSY anywhere yet: Higgs measurements, DM Direct-Detection, …
SUSY dead?

I personally think still attractive as a solution of the big hierarchy problem(don’t confuse with ‘little hierarchy’)attractive points:
natural WIMP DM, solve big hierarchy problem ~ O(10 -26 ) to O(10 -4 ), coupling unification, …

Another fine tuning problem in the SM : strong CP problem — Why ✓e↵ < 10Attractive solution : PQ mechanism

11?

L✓ =

✓Gaµ⌫ G̃a,µ⌫232⇡

Axion : good DM candidate

similarly attractive and don’t require new particles : naturally explain the current situation1

Strong CP problem
QCD Lagrangian contains the total derivative term: ✓-term✓aa,µ⌫L✓ =GG̃µ⌫232⇡|✓ >=1X

n= 1ein✓ |n >|n >! |m > but✓-vacuum|✓ >! |✓ >Note that θ is physical 0  ✓ < 2⇡
Furthermore,chiral tr. q ! ei↵ 5 q induces ✓ ! ✓2↵

massive fermion mass term is also changed.

✓e↵ = ✓ + arg det[M u M d ] is invariant under the chiral tr.
/ arg det[v 6 Y u Y d ]θeff can be measured from Neutron EDM |dn | = 4.5 ⇥ 10 15 ✓e↵ ecm
26|dobs|
<2.9⇥
10ecm
nWhy ✓e↵ < 10 11 ?

while the origin of θ and arg M is completely different
Fine tuning problem

2Peccei-Quinn mechanism and domain wall problem[R. D. Peccei, H. R. Quinn, PhysRevLett.38.1440]

If the theory has U (1)P Q , which spontaneously breakdowns to provide axion, at ⌘.
and at least one fermion mass from yukawa coupling,
Due to the anomaly, U(1)P Q current is not conserved,⌘ei✓P Q ⇠ ⌘ + iaaa! +✏⌘⌘, induce the potential in the effective Lagrangianinduces

Fa = ⌘/AA depends on the model (⇠ N )at low temperature, QCD instanton e↵ects give an axion a potential and minimizing it gives < a >=1cos(a¯+ ✓)Fa¯ a.
✓F✓¯ = ✓strong + ✓EM

in theta space2⇡Fa4⇡Fa¯ aa0 ⌘ a + ✓F

<a0 >✓e↵ = ✓¯ + <a>=Fa
Fa = 2n⇡(n = 1, . . . , N )NDW = NPQ [C.Q. Geng, J. N. Ng, PhysRevD.41.3848]
Variant Axion modelin <a> space
U (1)P Q ! ZN , N = |X(2qi + ui + di )|PQ

NPQ = 1 is free from the domain wall problem[R.D. Peccei, T.T. Wu and T. Yanagida, Phys. Lett. B172, 435 (1986)][C-R Chen, P. Frampton, F. Takahashi, T. T. Yanagida JHEP1006(2010)059]

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Strong CP problem
PQ solution with axion

very attractive, provide good DM candidate
timely: rapid progress of axion DM searches

invisible axion models
KSVZ

NDM = 1heavy Q introduced
no problem but no low energy phenomenology (not interesting)(Kim 1979,Shifman, Vainshtein, Zakharov 1980)

ZDFS

NDM = 6

†
12m

†
1

(Zhitnitsky1980,Dine, Fischler, Srednicki 1981)

NDM = 3

NDM = 122

two Higgs doublet model,no new fermion necessary introduced
can discuss low energy phenomenology!

but suffer from Domain wall problem

only 1 quark coupled to PQ-Higgs
domain wall problem absent

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up-type speciﬁc Variant Axion model
σ field integrated out, the effective theory is just a 2HDM
two Higgs easily results in FCNC.
Usually people impose Z2 sym. to avoid FCNC.

1

top-specific VA Model
charm-specific VA Model
up-specific VA Model+++2tR++cR++uR++dR+++`R+++QL+++mix within higgs basis

YuSM , Yu0100A⇤when we take up-type VAM,
top/charm/up FCNC is the prediction
2 only couple with uR3For example, top-specific case,
Lu =1 uRa [Yu1 ]ai Qi
2 uR3 [Yu2 ]i Qi + h.c.
010⇤ ⇤ ⇤0 0
Yu1 = @⇤ ⇤ ⇤A , Yu2 = @0 00 0 0⇤ ⇤to avoid domain wall problem,
we have to assign PQ charge only onequark.

LL+++

other quarks only couples with0tan

Yu0,diag = @0

Hu ⌘ V @tancot001AV †100@01A Yudiag + (tan100A ! 1 @02101+ cot )Hu Yudiag ,01 cos ⇢sin ⇢10sin ⇢ Acos ⇢ 16g-2 in Lepton-speciﬁc 2HDM
muon g-2, long standing 3σ level anomaly
order 10 -9 positive deviation
lepton-specific (type-X) 2HDM with light A is known as a solution

2loop can dominates by large yukawa compared with yμ
In lepton-specific 2HDM model, tanβ enhanced tau contribution is crucial.
mA ~ 30GeV and tanβ ~ 40 will give a enough contribution -> require large tanβ
It is known that LHC constraints are weak as all quark couplings to heavier bosons are suppressed.
W -> H+ A, Z -> A H etc, and Z -> tau tau A, would be the dominant production we can constrain

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g-2 in Lepton-speciﬁc 2HDM with VAM
VAM is essentially just a 2HDM with various PQ charge assignments (only one q R PQ charged)
lepton sector is irrelevant to the strong CP problem nor domain wall problem
lepton yukawa has to be enhanced to accommodate muon g-2

corresponding VEV is small (tanβ>>1)

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g-2 in Lepton-speciﬁc 2HDM with VAMVAM is essentially just a 2HDM with various PQ charge assignments (only one q R PQ charged)
lepton sector is irrelevant to the strong CP problem nor domain wall problem
lepton yukawa has to be enhanced to accommodate muon g-2

corresponding VEV is small (tanβ>>1)

to enhance lepton yukawa

v2 ⌧ v18

g-2 in Lepton-speciﬁc 2HDM with VAM
VAM is essentially just a 2HDM with various PQ charge assignments (only one q R PQ charged)
lepton sector is irrelevant to the strong CP problem nor domain wall problem
lepton yukawa has to be enhanced to accommodate muon g-2

corresponding VEV is small (tanβ>>1)

to enhance lepton yukawav2 ⌧ v1
to avoid non-perturbativity

8g-2 in Lepton-speciﬁc 2HDM with VAM
VAM is essentially just a 2HDM with various PQ charge assignments (only one q R PQ charged)
lepton sector is irrelevant to the strong CP problem nor domain wall problem
lepton yukawa has to be enhanced to accommodate muon g-2

corresponding VEV is small (tanβ>>1)

to enhance lepton yukawav2 ⌧ v1
to avoid non-perturbativity
to avoid domain wallthe 3rd gen. part becomes identical to the type II 2HDM -> very constrained by LHC via bbA production
also by Bs→μμ
not viable possibility8g-2 in Lepton-speciﬁc 2HDM with VAM
VAM is essentially just a 2HDM with various PQ charge assignments (only one q R PQ charged)
lepton sector is irrelevant to the strong CP problem nor domain wall problem
lepton yukawa has to be enhanced to accommodate muon g-2

corresponding VEV is small (tanβ>>1)

to enhance lepton yukawa

v1 ⌧ v2

8

g-2 in Lepton-speciﬁc 2HDM with VAM
VAM is essentially just a 2HDM with various PQ charge assignments (only one q R PQ charged)
lepton sector is irrelevant to the strong CP problem nor domain wall problem
lepton yukawa has to be enhanced to accommodate muon g-2

corresponding VEV is small (tanβ>>1)

to enhance lepton yukawa

v1 ⌧ v2

Bs -> mumu
constraints
to avoid non-perturbativity

8g-2 in Lepton-speciﬁc 2HDM with VAMVAM is essentially just a 2HDM with various PQ charge assignments (only one q R PQ charged)
lepton sector is irrelevant to the strong CP problem nor domain wall problem
lepton yukawa has to be enhanced to accommodate muon g-2

corresponding VEV is small (tanβ>>1)

to enhance lepton yukawa

v1 ⌧ v2

Bs -> mumu
constraints
to avoid non-perturbativity

8g-2 in Lepton-speciﬁc 2HDM with VAM
VAM is essentially just a 2HDM with various PQ charge assignments (only one q R PQ charged)
lepton sector is irrelevant to the strong CP problem nor domain wall problem
lepton yukawa has to be enhanced to accommodate muon g-2

corresponding VEV is small (tanβ>>1)

to enhance lepton yukawa

v1 ⌧ v2

Bs -> mumu
constraints
to avoid non-perturbativity
several choices, but up-specific is most interesting possibility8g-2 in Lepton-speciﬁc 2HDM with VAM
order 10 -9 positive deviation
without pre-factor, O(1) positive contribution required

each numerical contribution without the pre-factor (m=1 TeV)

2-loop ∝ 1/m2

mA ~ 15GeV gives 4x103 enhancement, with (tanβ~40)2 gives another 2x10 3 enhancementc: opposite sign, b: disfavored by Bs→μμ, so τ would be the only possibility

u is only possibility PQ charged

9g-2 in Lepton-speciﬁc 2HDM with VAM
order 10 -9 positive deviationeach numerical contribution without the pre-factor (m=1 TeV)

⇢u = 0⇢u = ⇡/100

without pre-factor, O(1) positive contribution required
2-loop ∝ 1/m2
mA ~ 15GeV gives 4x103 enhancement, with (tanβ~40)2 gives another 2x10 3 enhancementc: opposite sign, b: disfavored by Bs→μμ, so τ would be the only possibility
u is only possibility PQ charged
for muon g-2 introducing mixing doesn’t help to accommodate the lepton universality constraints
including Bs→μμ, small mixing ⇢u = ⇡/100 slightly improves the fit, large mixing is disfavored9t -> u A , A -> tautau
even for slight mixing provides large BR(t→uA) ~ O(10%)
A decays dominantly to ττ about 100%
LHC searches for bbA, A→ττ, in the context of MSSM.
CMS searches at 8TeV is the most constraining: using μτ, eτ, eμ modes
the kinematics is different between tuA and bbAtuAbbA

tuAbbAmA lightermA lighter

efficiency is in general higher due to pT,⌧ cut
efficiency quickly goes down due toefficiency up"# stronger boundR cutwhen mA ! 0BR(t→uA) < 0.2% (mA>25GeV), 10% (mA=15GeV)

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boosted A -> tautau
The reason for rapid drop of the efficiency is due to the overlapping τ’s due to the boost

τ-taggingR = 0.5
R = 0.1 (core)f=E(R = 0.1)> 0.95
E(R = 0.5)

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boosted A -> tautau
The reason for rapid drop of the efficiency is due to the overlapping τ’s due to the boost

τ-taggingR = 0.5
R = 0.1 (core)di-τ-tagging

R = 0.5

f=E(R = 0.1)
> 0.95E(R = 0.5)

usual isolation fails

R = 0.1 (core) mutual isolation[A. Katz, M. Son, B. Tweedie, PRD 83, 114033(2011).]

R = 0.1 (core 2)

if core 1 is removed, the rest is τ-tagged
if core 2 is removed, the rest is also τ-tagged

11boosted A -> tautau
The reason for rapid drop of the efficiency is due to the overlapping τ’s due to the boost

BR(t→uA) < 0.08% at mA=15GeV(BR(t→uA) < 10% at mA=15GeV by CMS study)

BR(t→uA) < 0.003-0.01% in futuredi-τ-tagging

R = 0.5

usual isolation fails

R = 0.1 (core) mutual isolation[A. Katz, M. Son, B. Tweedie, PRD 83, 114033(2011).]

R = 0.1 (core 2)

if core 1 is removed, the rest is τ-tagged
if core 2 is removed, the rest is also τ-tagged11

Flavor violating Heavy higgs decays⇣f f 0 =very striking signature of the model12

u-speciﬁc VAM with muon-speciﬁc lepton sector
An extreme model: muon-specific 2HDM to accommodate muon g-2[T. Abe, R. Sato, K. Yagyu JHEP 1707, 012 (2017)]

only muon yukawa is tanβ enhanced ~ 3000
better fit against the lepton universality constraints
constrained by multi-muon searches at LHC (A/H→μμ 100%)
VAM is essentially just a 2HDM with various PQ charge assignments (only one q R PQ charged)
lepton sector is irrelevant to the strong CP problem nor domain wall problem
muon yukawa has to be enhanced to accommodate muon g-2

corresponding VEV is small (tanβ>>1)

to enhance lepton yukawa

v1 ⌧ v2

Bs -> mumu
constraints
to avoid non-perturbativity
in this setup, suppressed muon BR to accommodate LHC constraints

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conclusions
strong CP problem

domain wall problem
variant axion models (only 1 right-handed quark PQ charged)

Lepton sector has freedom for PQ charge assignments and muon g-2 anomaly can be accommodated!

by assign PQ charge to all leptons

mA~ 15GeV, tanβ ~ 40

by assign PQ charge only to muon

mA~ 1 TeV, tanβ ~ 3000

For light A case, t →uA, A→ττ current constraints marginal!

using boosted di-tau-tagging improves sensitivity significantly

For both cases, flavor violating heavy higgs decays would be the signatures of this model.

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