Introduction on the search for Axion

Hojin Yoon2018/11/19

Department of Physics, KAIST

Table of contents

1. Gauge invariance (Higgs mechanism)

2. Spontaneous Symmetry Breaking(SSB)

3. U(1)A problem & Strong CP problem

4. U(1)PQ and Axion

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Gauge invariance (Higgsmechanism)

Gauge invariance(Higgs mechanism)

consider such a ”winebottle” potential

V = 1/2µ2|ϕ|2 + λ/4|ϕ4|

Lagrangian is given as

L = 1/2(∂νϕ∗)(∂νϕ)− (1/2µ2|ϕ|2 + λ/4|ϕ4|)

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Gauge invariance(Higgs mechanism)

loacal gauge transformation

ψ → eiθ(x)ψ

local gauge invariant Lagrangian

L = 1/2(∂νϕ∗)(∂νϕ)− (1/2µ2|ϕ|2 + λ/4|ϕ4|)

with ∂ν → Dν = ∂ν + iq/ℏcAν and dynamic terms

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Gauge invariance(Higgs mechanism)

but m has to be zero : how to give mass? → Higgs mechanism!

L = 1/2(∂νϕ∗)(∂νϕ)− (1/2µ2|ϕ|2 + λ/4|ϕ4|)

we deal with fluctuation

ϕ(x) = (v+ σ(x))iπ(x)/fπ

→ nonzero σ mass, zero π mass

σ : massive Higgs boson

π : massless Goldstone boson

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Spontaneous SymmetryBreaking(SSB)

Spontaneous Symmetry Breaking

V = 1/2µ2|ϕ|2 + λ/4|ϕ4|

evolution of the Higgs potential of the universe

as Time flows... universe cools, µ2 decreases

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Spontaneous Symmetry Breaking

V = 1/2µ2|ϕ|2 + λ/4|ϕ4|

symmetry is now broken

Vacuum Expectation Value(VEV) is now nonzero

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U(1)A problem & Strong CPproblem

U(1)A problem & Strong CP problem

in high E the symmetry SU(3)C × SU(2)W × U(1)Y is conserved

in our scale E, SU(2)W × U(1)Y is broken(EWSB & QCD confinement)

Higgs gauge boson mass is given

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U(1)A problem & Strong CP problem

QCD LagrangianmddLdR +muuLuR + h.c.

invariance under SU(2)V × SU(2)A × U(1)V × U(1)Ano particle corresponding to U(1)A? → anomalous symmetry!

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U(1)A problem & Strong CP problem

for the classical case∂µJµ = 0

for the quantum case

∂µJµA = g2/32π2Fµνa Fµνa

due to topoligical aspects of gauge transformation

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U(1)A problem & Strong CP problem

n vacuuas |n⟩|θ⟩ =

∑ne−inθ|n⟩

additional Lagrangian term

Lθ = g2/32π2θFµνa Fµνa

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U(1)A problem & Strong CP problem

Lθ violates CP symmetry(ϵµναβ in Fµνa term)→ neutron ElectroDipole Moment(nEDM)

nEDM∼ θemumd/(mu +md)m2n ∼ 10−16θ e-cm

observation limit : 10−26 e-cm : 10−10 scale...

fine tuning? unnatural→ StrongCP problem!

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U(1)PQ and Axion

U(1)PQ and Axion

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U(1)PQ and Axion

mechanism that θ should be zero :

introduction of a new global chiral symmetry U(1)PQ similar to U(1)Aadditional dynamic term added to make θ zero

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U(1)PQ and Axion

SSB for a new symmetry→ new boson : Axion!

g2/32π2(θ + a/fa)Fµνa Fµνa

vacuum energy minimized when

θ + a/fa = 0

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U(1)PQ and Axion

field→ decomposition into radial, axial parts

U(1)PQ SSB : the ”tipping” of the potential with tipping angle Λ4QCD/fa

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Models

PQWW, KSVZ, DFSZ models were suggested

PQWW, DFSZ : coupling to the SM quark

KSVZ : coupling to a new quark

KSVZ, DFSZ are currently valid models

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U(1)PQ and Axion

to actually detect an axion, inverse Primakoff effect is used

photon in B field is absorbed to axion and transformed into a newphoton

axion-photon-photon coupling gaγγ in Lagrangian

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U(1)PQ and Axion

various coupling values

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U(1)PQ and Axion

Cavity in low T and high B

tuning rod is used to vary resonance frequency of the cavity

scanning rate : df/dt ∼ B4/T2

in order to increase scanning rate, high B and low T is required

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U(1)PQ and Axion

the bottom line indicates TM010 mode

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