symmetries,darkmatter,axion - mcgill physicsguymoore/talks/axion.pdf · symmetries,darkmatter,axion...
Post on 30-Apr-2020
11 Views
Preview:
TRANSCRIPT
Symmetries, Dark Matter, Axion
• The Fundamental Symmetries of Parity (mirror
reflection) and Charge conjugation (matter-antimatter)
• P and C in Electromagnetism: why are they conserved?
• P and CP in QCD: Why aren’t they violated?
• The Axion: a possible explanation
• The Axion, Cosmology, and the puzzle of Dark Matter
• Relating the Dark Matter abundance to the Axion
particle’s mass
Technische Universitat Darmstadt, 3 Juli 2015: Seite 1 von 35
A strange talk plan!
• I will speak in English (Englisch?)
• I will talk about work I have not finished!
• No conclusions at the end – more of a prospectus
• But some interesting issues (I hope!)
Technische Universitat Darmstadt, 3 Juli 2015: Seite 2 von 35
Parity
Physics as seen in a looking glass (mirror) (Spiegel)
Technische Universitat Darmstadt, 3 Juli 2015: Seite 3 von 35
Spontaneous Parity Violation
Circumstances choose to make it look different: laws same
Technische Universitat Darmstadt, 3 Juli 2015: Seite 4 von 35
Spontaneous Parity Violation
Could have occurred differently different places!
Technische Universitat Darmstadt, 3 Juli 2015: Seite 5 von 35
Explicit Parity Violation
Physical laws are different on the other side!
Technische Universitat Darmstadt, 3 Juli 2015: Seite 6 von 35
Parity–More Examples
Direction of motion reversed only orthogonal to mirror.
Sense of rotation and/or spin reversed (ǫijk → −ǫijk)
Technische Universitat Darmstadt, 3 Juli 2015: Seite 7 von 35
Parity and Fields
++
++
++
++
+
−−
−−
−−
−−
−
++
++
++
+++
−−
−−
−−
−−−
E fields: vector. Flips only along mirrored axis
B fields: axial-vector. Flips except along mirrored axis
Charges and currents act normally: B involves ∇×, or ǫijk
Technische Universitat Darmstadt, 3 Juli 2015: Seite 8 von 35
Another Possible Symmetry: C
Technische Universitat Darmstadt, 3 Juli 2015: Seite 9 von 35
C: Charge Conjugation Symmetry
Turn all matter into antimatter and vice versa.
Matter, antimatter have opposite sign charge–hence name.
Exact symmetry of gravity: e−, e+ have same mass.
Anti-atomic physics = Atomic physics
• e− → e+ flips sign: E,B flip signs (“odd under C”)
• But p+ → p− also flips sign.
• Attractive interaction between e−, p+ same as e+, p−.
Hydrogen and anti-hydrogen energy levels are the same.
Technische Universitat Darmstadt, 3 Juli 2015: Seite 10 von 35
Electromagnetism
E&M: a theory of fields. A (the first!) relativistic theory.
Nature is quantum mechanical ⇒
Need Relativistic Quantum Field Theory
Quantum: start with action,∫
dt of a Lagrangian. Field
Theory: Lagrangian is∫
d3x of a Lagrangian density.
S =∫
dt L =∫
dt∫
d3x L(E,B)
Relativity: L must be a (Lorentz) scalar.
Technische Universitat Darmstadt, 3 Juli 2015: Seite 11 von 35
Finding Lorentz scalars in E&M
Transformation rules: E,B fit in an antisymmetric tensor
Fµν =
0 Ex Ey Ez
−Ex 0 −Bz By
−Ey Bz 0 −Bx
−Ez −By Bx 0
= ∂µAν−∂νAµ , Aµ =
Φ
Ax
Ay
Az
Lorentz transform: multiply left-and-right by same matrix
used to transform (ct, x, y, z).
Long story short: two ways to form a scalar:
1
2F µνFµν = ~E2 − ~B2 ,
1
8ǫµναβF
µνF αβ = ~E · ~B
Technische Universitat Darmstadt, 3 Juli 2015: Seite 12 von 35
Most general version of Electromagnetism
The Action can be
S =∫
dt∫
d3x(
C1( ~E2 − ~B2) + C2
8π2~E · ~B
)
(Plus stuff for electrons, invariant under P and C)
Charge conjugation: E → −E and B → −B so each term
stays the same! E&M is C invariant!
Parity: E → −E and B → B.
The (E2 − B2) term stays the same.
But the E ·B term reverses sign.
If C2 6= 0, it appears E&M violates P and CP .
Technische Universitat Darmstadt, 3 Juli 2015: Seite 13 von 35
CP violation is Illusory!
The C2~E · ~B term has no consequences because it turns out
that ~E · ~B is a total derivative
1
4ǫµναβF
µνF αβ = ∂µKµ , Kµ ≡1
2ǫµναβA
νF αβ
I can integrate C2~E · ~B to a boundary term. For any local
charge/current configuration, F αβ and therefore Kµ
vanishes at the boundary.
So the term has no physical consequences.
But it would in QCD(the theory of the strong [nuclear] interactions) !!!
Technische Universitat Darmstadt, 3 Juli 2015: Seite 14 von 35
QCD and its Lagrangian
QCD is like 8 copies of E&M, but with non-linearities:
Field strength : Fµνa = ∂µAν
a − ∂νAµa + gfabcA
µbA
νc ,
g: coupling. Fa, Aa: E&M-like fields (a = 1, 2, . . . 8)
fabc the constants which describe nonlinearity
S =
∫
dt
∫
d3x
(
C1( ~E2
a − ~B2
a) +C2
8π2~Ea · ~Ba
)
where ~Ea · ~Ba still a total derivative:
~Ea · ~Ba = ∂µKµ , 2Kµ = ǫµναβ
(
AνaF
αβa +
gfabc
3Aν
aAαb A
βc
)
Last term need not vanish on boundary even if ~Ea = 0 = ~Ba there!
It’s always 8π2N with N integer. So C2 mod 2π has physical consequences
Technische Universitat Darmstadt, 3 Juli 2015: Seite 15 von 35
Neutron Electric Dipole Moment
A Test of whether QCD obeys P , CP symmetries:
BB N
Put neutron in ~B field – spin lines up with ~B.
Does it have an electric dipole moment aligned with spin?
If so: physics of mirror-image apparatus 6= physics seen in mirror: P violating
Technische Universitat Darmstadt, 3 Juli 2015: Seite 16 von 35
Neutron Electric Dipole Moment
Theory: Neutron electric dipole moment should exist,
dn = −3.8× 10−16 e cm× C2
so long as C2 is not zero! Guo et al, arXiv:1502.02295, assumes C2 , modulo 2π, is small
Experiment: Consistent with zero! Baker et al (Grenoble), arXiv:hep-ex/0602020
|dn| < 2.9× 10−26 e cm
Either∣
∣
∣
C2
8π2
∣
∣
∣ < 10−10 by (coincidence? accident?) or there is
something deep going on here.
Technische Universitat Darmstadt, 3 Juli 2015: Seite 17 von 35
Why an accident seems unlikely
• CP is not a fundamental symmetry. We have observed
its violation (Kaon, B-meson, possibly D-meson physics)
• More CP violation almost surely out there – otherwise,
tough to explain why Universe is filled with matter!
• Renormalization: CP viol. one place finds its way into
other places, including C2. C2 does not get smaller as
you go from high to low scales R.G. marginal – feels CP viol
from all scales.
Technische Universitat Darmstadt, 3 Juli 2015: Seite 18 von 35
Axion: an explanation for C2 = 0
Hypothesize an extra complex scalar field ϕ = φeiθA:
• Field: takes a value at each point in space Think ~E
• Scalar: value is a number, without direction but with units ...
• Complex scalar: value is a real and imaginary part
Energy can depend on |ϕ|2 + |~∇ϕ|2, and on the value of ϕ.
Assume a symmetry: φ → eiθφ:
Energy/volume = λ(ϕ∗ϕ)2 − µ2ϕ∗ϕ+ constant
Technische Universitat Darmstadt, 3 Juli 2015: Seite 19 von 35
Axion: spontaneous symmetry breaking
If µ2 > 0, potential looks like this:
Min of V
at ϕ 6= 0!
Lowest energy state has ϕ 6= 0.
Minimum not unique; all values of θA equally good.
Or are they??
Technische Universitat Darmstadt, 3 Juli 2015: Seite 20 von 35
Indirect Interactions with QCD
Suppose Axions ⇔ New Heavy quarks ⇔ QCD
Introduces axion-QCD interactions at low energy:
LQCD+ = k1 ln(φ)( ~E2a − ~B2
a) +n
8π2θA ~Ea · ~Ba
k1: (heavy) radial φ excitations interact with QCD not important.
Last term looks like the mysterious C2~E · ~B interaction!
n is integer and can be 1. I will assume n = 1
CP violation determined by C2 + θA (modulo 2π)
No CP violation if θA happens to take value −C2.
Technische Universitat Darmstadt, 3 Juli 2015: Seite 21 von 35
Now the fun part
θA is a field and can change value.
QCD cares about value of C2 + θA. Detailed QCD
calculation Topological Susceptibility of QCD: Potential tilted
Energy lowest
where
C2 + θA = 0,
where CP
conserved.
Size of tilt: nonperturbative QCD. Solved.
Technische Universitat Darmstadt, 3 Juli 2015: Seite 22 von 35
What is predicted:
• Neutron EDM: 10−5 smaller than current limit
• New particle, Axion, exists, with specific interactions
• Strength of axion interactions scale with its mass
(Pseudo-Nambu-Goldstone Boson)
What is not predicted: Axion Mass!
The larger φ, the
flatter the potential,
and lighter the
axion. φ not
predicted by model.
Technische Universitat Darmstadt, 3 Juli 2015: Seite 23 von 35
One more prediction: Dark Matter!!
Recall: Cold Dark Matter makes up 25% of the density of the
Universe. Mystery. We know only 3 things about it:
• It is matter: feels gravitational attraction, which makes it
clump (makes up 80% of galactic haloes, galaxy clusters)
• It is dark: electric charge ≃ 0, interactions too feeble for us
to have detected it except gravitationally
• It is cold: almost pressureless. When Universe was 50,000yr
old and 3000× hotter, it was non-relativistic enough to
gravitationally clump (|v| < 10−5
c)
Could the CDM be axions?
Technische Universitat Darmstadt, 3 Juli 2015: Seite 24 von 35
Axion in the Early Universe
If the Universe started out hot enough, or Inflation had a
high enough scale, ϕ initially took random values at
different places. Currently seems likely.
Around time tmA = 1, field would start to oscillate;
amplitude damped by expansion of the Universe.
Leaves coherent field oscillations in modern Universe –
which behave like ideal Cold Dark Matter
Larger φ → Smaller mA → later onset of oscillations → less
damping → more Dark Matter today.
Modern CDM density ⇐⇒ mA!
Technische Universitat Darmstadt, 3 Juli 2015: Seite 25 von 35
Axion mass is key input for experiments meant to find them.
Theorists need to do their job, predict mA from CDM
density.
Complications:
• Axion mass arises from QCD effects. Different for hot
QCD (early Universe) than vacuum QCD (Universe today).
• Axion field would start out inhomogeneous. Dynamics
complicated by topological structures.
I am studying both problems.
Technische Universitat Darmstadt, 3 Juli 2015: Seite 26 von 35
QCD effects: Instantons
QCD cares about ~Ea · ~Ba because of topological structures
Instantons which ensure the boundary term will not vanish.
People study these using Lattice QCD.
Vacuum: now well under control.
Hi-Temp: Instantons get rarer. Algorithms become
inefficient.
My goal: use reweighting techniques to overcome these
problems. Early stages.
Technische Universitat Darmstadt, 3 Juli 2015: Seite 27 von 35
Axions and Topology
The allowed (low-energy) values of the axion field lie on a
circle. This has consequences for the space-time dynamics:
B
Real (coord) space Field space
AC
x
y
z
A
BC
Im ϕ
Reϕ
Each point in space maps to a point in field-space.
Points around a circle can map around the field-space circle.
Continuity → somewhere in middle, field “goes over top”
Technische Universitat Darmstadt, 3 Juli 2015: Seite 28 von 35
Axionic Strings
Consider a loop, where ϕ wraps around the circle as you
traverse the loop, and a surface bounded by the loop:
Im ϕ
Reϕ
B
A
BC A
C
Real (coord) space Field space
x
y
z
Somewhere on surface, ϕ “leaves the circle.” True of any
surface. Locus of such points must form a (wiggly) line,
called a “string defect.” Universe will start with a network
of these.
Technische Universitat Darmstadt, 3 Juli 2015: Seite 29 von 35
String evolution
Angle θA uncorrelated between causally disconnected points
Network of strings is inevitable
Quickly evolves to a scaling solution Statistically insensitive to starting conditions
Typical string-string distance ∼ Hubble scale at that epoch
Net work evolves, strings move under 2 effects:
• Tension – |∇ϕ|2 energy of string. Tries to shorten string.
• Long-range interaction – ϕ is massless field, causes
long-range string-string interactions
Each “unwinds” the network – long-range interaction more
efficient.
Technische Universitat Darmstadt, 3 Juli 2015: Seite 30 von 35
Technische Universitat Darmstadt, 3 Juli 2015: Seite 31 von 35
What makes it fun
Early times – string network.
Time passes, t grows, mA grows.
Around tmA ∼ 1, field “discovers” that potential is tilted.
Angle starts oscillating around θA + C2 = 0.
Domain walls where θA + C2 = π. Bounded by strings.
Domain walls “pull in” strings, destroy network. Fun string -
domain wall dynamics. No true symmetry breaking – no defects in the end.
This physics produces axions – need to get it right to find
the final axion density, amount of Dark Matter
Technische Universitat Darmstadt, 3 Juli 2015: Seite 32 von 35
What makes it complicated
Network dynamics controlled by ratio: string tensionstring-interactions
String – cylindrical coordinates – tension
T =energy
length=
∫
|∇ϕ|2rdr ∼∫
φ2
r2rdr ∼ φ2 ln
lstring−to−string
rcore
while string interactions controlled by φ2.
Tension/interactions = log(Hubble-length/core-size)
or ln(mplφ/T2) ∼ 1030. Strongly 2-scale problem.
Technische Universitat Darmstadt, 3 Juli 2015: Seite 33 von 35
Two-scale problem
To get axion density right → get string dynamics right.
→ get string tension right.
Naively, need to resolve large scale hierarchy.
Dynamic mesh refinement? A challenge with strings!
Hybrid model with explicit string cores?
What I am working on currently...
Technische Universitat Darmstadt, 3 Juli 2015: Seite 34 von 35
Conclusions
• C, P potential symmetries of nature
• E&M naturally respects both symmetries
• QCD need not respec P , CP . Experiment: it does!
• Axion could explain CP invariance of QCD
• Axion role in Dark Matter requires new inputs:
∗ thermal QCD inputs
∗ Field-string-network dynamics
• I hope a tight prediction of the axion mass can be made!
Technische Universitat Darmstadt, 3 Juli 2015: Seite 35 von 35
How do experimentalists look for Axions?
Most sensitive method: resonant cavity in magnetic field
Microwave cavity inside
superconducting solenoid. ~E field of
cavity mode aligned with ~B of
solenoid. Cavity oscillation: oscillating~E · ~B. If cavity resonance matches
mA/h: cavity resonance driven.
Squid readout – tuneable cavity . . .
Technische Universitat Darmstadt, 3 Juli 2015: Seite 36 von 35
What about Anthropic Principle?
Trendy Explanation for “coincidences” or “tunings”
Why is Cosmological Constant so small?
If the value were 100 times bigger, matter would fly apart or
collapse before sufficient time for life to evolve. Nature plays
dice, only universes with life get observed.
Why does QCD respect CP symmetry?
If QCDviolated CP , something would go wrong with
nuclear physics, which would make life impossible. Nature
plays dice, only universes where life is possible get observed.
Except that life is fine in a world where C2 = 10−2!
Technische Universitat Darmstadt, 3 Juli 2015: Seite 37 von 35
top related