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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
1
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|)
2
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
4
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
5
Spontaneous Symmetry Breaking
V = 1/2µ2|ϕ|2 + λ/4|ϕ4|
symmetry is now broken
Vacuum Expectation Value(VEV) is now nonzero
6
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!
8
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!
11
U(1)PQ and Axion
U(1)PQ and Axion
12
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
13
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
14
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
15
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
16
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
18
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
19
U(1)PQ and Axion
the bottom line indicates TM010 mode
20
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