Photon splitting in magnetic fields as a probe of ultralight spin-0 fields

1
Photon splitting in magnetic fields as a probe of
ultralightspin-0 fields

• Emidio Gabrielli
• Helsinki Institute of Physics

in collaboration with K. Huitu and S. Roy
2
Photon splitting

• g external magnetic field ? g g
• it is due to non-linear photon interactions
  induced by vacuum polarization effects
• in QED the absorption coefficient K is very small
  for magnetic fields of the order of Tesla K
  (B/B(crit))6
• B(crit) m2/e 4.41 x 109 T
• new physics could contribute with sizeable effects

3

• At tree-level there are no photon
  self-interactions
• Quantum effects, induced by interactions of
  photons
• with charged particles (i.e. electrons,
  positrons, etc.),
• generate ? photon self-interactions
• described by the Heisenberg-Euler effective
  lagrangian,
• obtained in the constant EM field strength
  limit
• observable (but rare) effects
• - photon propagating in constant magnetic
  fields
• birefringence of vacuum ?
• ellipticity, rotation of the light
  polarization-plane
• - the light-light scattering g g ? g g

4
(No Transcript)
5
Heisenberg-Euler lagrangian
gauge-invariant Lagrangian
non-linear interactions
L(int) ? is a function of two gauge invariant
quantities
6
Heisenberg-Euler lagrangian
( in relativistic unities c1, h1)
as derived by J.Schwinger PR 82, 664 (51)
m electron mass
7
Expanding the H-E lagrangian at order a2
m electron mass
provides the leading correction to the
non-linear interactions
8
Dispersions effects photon propagating in
static and homogeneous magnetic field B
? refraction index
q
B
k
polarizations of photons magnetic vectors
parallel ? perpendicular ? to (k,B) plane
vacuum polarized by B becomes birefringent
9

• a method to measure vacuum birefringence

E.Iacopini and E.Zavattini PLB 8, 151 (79)
from PVLAS webpage

• different polarization vectors will propagate
• with different phase velocities
• linear polarization ? elliptical polarization
• out of B . Ellipticity y induced by
  birefringence

10
Photon splitting (no dispersion)
g(k) external magnetic field ? g (k1) g(k2)

• not possible in vacuum, but in presence of
  external B
• according to the Heisenberg-Euler theory,
  photon
• dispersion relations are modified,
• refraction index ? n gt 1
• let consider first the case of no-dispersion
  (n1)

S.Adler, Ann. Phys. 67, 599 ( 71)
matrix element can be obtained from the H-E
lagrangian or equivalently from
11
resumming the full series of diagrams

permutations

S
only an even number of total vertices
can contribute due to the Furrys theorem
? Trodd-number of Dirac-gammas0
12
no dispersion case
kinematic allowed solution
only one light-like four-momentum
all three-momenta parallel
13

• in the case of no dispersions the photon
  splitting with only one interaction of the
  external field is forbidden
• the leading effect is given by three external
  insertions, the hexagon diagram
• this is due to gauge invariance and the fact
  that there is only one light-like four momentum
  in the reaction.

leading order for the matrix element M(g?g g)
14
P(d) survival probability traveling a
distance d
k absorption coefficient
d k ltlt 1
Mmatrix element
g g phase-space
15
Adler, Ann. Phys. 67, 599 ( 71)
no-dispersion
m electron mass
parallel and perp. polarization vectors with
respect to the plane (k,B)
w/m ltlt1
16
phase space integral
energy distribution
17
Effects of dispersions on photon splitting

• momenta of final photons are not anymore
• parallel to initial ones ? small opening angle.

• in the Golden Rule formula for the absorption
• coefficient one has to change

18
Effects of dispersion on photon splitting
Kinematical condition
selection rules for polarized transitions
19
Adler, Bahacall, Callan, Rosenbluth, PRL 25, 1061
(70) Adler ( 71)
CP
Kinematic
reaction
allowed
forbidden
forbidden
allowed
allowed
allowed
forbidden
forbidden
forbidden
allowed
forbidden
forbidden
20
conclusions (QED)

• splitting of perpendicular-polarized photons is
  absolutely FORBIDDEN by dispersive effects
• splitting of parallel-polarized photons is
  ALLOWED
• photon splitting provides a mechanism for
• the production of polarized photons
• effects of dispersion on matrix element are small

21

• difficult to detect photon splitting in typical
• laboratory experiment , too rare event

• one needs very large B Bcrit and/or w gt MeV
• for w gtgt 2m MeV, the pair production
  mechanism
• g ? ee- dominates over g? gg

• Adler ( 71) provided the exact calculation of
• k valid beyond the approximation w/m ltlt 1.

22
neutral ultra-light spin-0 bosons

• Neutral scalar/pseudoscalar particles can have
  gauge invariant couplings with photons

• L ? effective scale of dimension mass
• F(m,n)? EM field strentgh
• F(m,n) e(m,n,a,b) F(a,b)

23
known examples are

• light axion boson
• pseudo-scalar particle
• pseudo-goldstone boson of Peccei-Quinn
• symmetry (solve the strong-CP problem in QCD)
• mass expected in the range of m O(meV)

• heavy Higgs boson
• scalar particle
• necessary to provide all masses in the SM
• mass expected in the range m 100-800 GeV
• coupling H-g-g generated at 1-loop

24

• The axion has a very weak coupling
• If astrophysical constraints are taken into
• account L 106-1011 GeV
• G.Raffelt, Phys. Rept. 198, 1 (90)
• Recently, it has been shown that it is possible
• to relax astrophysical constraints
• E.Masso and J.Redondo, JCAP, 0505, 015 (05)
• decay-width (G) of the axion is VERY small,
• G m3/L2 ? almost stable particle on
• cosmic time scale

25
Effects of spin0-g-g couplings on photon
propagationin external magnetic/electric fields

• replacing g g f ? ltBgt g f gives a mixing
  mass-term in the photon-spin-0 system
• the gamma? spin-0 conversion is possible in
  external EM field (Primakof effect)
• it could generate photon ?? spin-0 oscillations
  for photons propagating in magnetic fields
• G.Raffelt, L.Stodoslky, PRD 37, 1237 (88)
• angular momentum and 3-momentum not conserved ?
  3-momentum absorbed by external field

26

• mass, coupling and parity of ultra-light spin0
• particle can be determined from measurement
• of vacuum birefringence and dichroism
• L.Maiani, R. Petronzio, E. Zavattini, PLB 175,
  359 (86)
• the birefringence can induce ellipticity on a
  linearly polarized Laser beam in external
  magnetic field
• R. Cameron et. al. BFRT collab. PRD 47,
  3707 (93)
• recently PVLAS collaboration (05) has measured a
  large value for the ellipticity
• E.Zavattini et. al. PVLAS collab., PRL 96,
  110406 (06)
• too large for QED ! New physics effect ?
• if interpreted in terms of light axion implies
• an axion mass m 10-3 eV and L 106 GeV

27

• Ultralight axions can also be tested in
  laboratory by
• different kind of experiments.
• P.Sikivie, PRL 51, 1415 (83)
• After a Laser beam passes through a magnetic
  field
• an axion component can be generated.
• Light shining from a wall by using a second
  magnet
• It is possible to check the parameter region
• explored by PVLAS data, by using Xray laser
  facility
• R.Rabadan, A.Ringwald, K.Sigurdson, PRL 96,
  110407, (06)

very small effect P(g?g) P(g?a)2
28
Photon splitting in magnetic fieldinduced by
gg-spin-0 coupling
E.G., K.Huitu, S.Roy PRD 74, 073002 (06)

• We used the technique of effective photon
  propagator
• optical theorem to calculate absorption
  coefficient
• Imaginary part of (pseudo)scalar propagator
  (width)
• gives the leading effect in the
  photon-splitting
• absorption coefficient
• the full series of diagrams has been exactly
  summed
• up in the effective photon propagator

29
no physical effect. absorbed by
field renormalization
A? radiation field F(ext)? external field
tadpoles
mixing term
30
effective photon propagator
summed up at all orders
full propagator of spin-0 field including
self-energy diagrams
31
effective photon propagator (case scalar field
B)
temporal gauge A00
T selects polarizations with magnetic component
parallel to Plane (B,k)
R selects polarizations with magnetic
component perpendicular to (B,k) plane
R, T are projectors
32
effective photon propagator (case pseudoscalar
field B)
R selects polarizations with electric
component perpendicular to (B,k) plane
T selects polarizations with electric component
parallel to (B,k) plane
33
photon self-energy (scalar magnetic field)
? self-energy of scalar field
modifies the photon dispersions for the
polarizations with magnetic component parallel
to (B, k) plane
solutions of photon dispersions are obtained by
looking at the poles of the propagator
34
master equation for photon dispersion
gauge invariant solutions
m renormalized mass of spin-0 particle
external electric field
external magnetic field
35
hierarchy of scales
of the same order of D
characteristic small parameters
solutions easily found by expanding in D/m4
36
solutions
massless mode
massive mode
in order to have real solutions
critical field
37
the massive mode can be excited from the vacuum
if
analogous results for external electric
fields and/or pseudoscalar interactions
38
residue (Z) at the poles

• it is connected to the norm of the quantum state
• physical solutions must have positive value
• for the residue at the pole of the propagator
• M(-) massive solution is unphysical since Z(-) lt
  0
• there are only 2 physical solutions, one
  massless
• and one massive

39
photon dispersions
refraxion index of massless mode n(w0)
dispersion relation of massive mode
40
photon absorption coefficient k massive mode
from optical theorem
G width of spin-0 particle
41

• when B approaches the critical value
• (x?1) there is a resonant effect

• however, unitarity requires Z() lt 1

• validity of perturbation theory up to

42
same results can be re-obtained by using
the Golden Formula for absorption
coefficient,where the matrix element M is
k2M2
for the massless mode Z ? Z0 1 and k2M02
43
photon absorption coefficient massless mode
(w/m)2 (B/m2)2 ltlt1

• scalar case B allowed by kinematic

incidentally, PVLAS data have central value m
2me k gt kQED if m lt 5 me

• pseudoscalar B forbidden by kinematic

44
Numerical results

• for Laser frequency 1eV lt w lt 102eV ,
• 10-2eV lt m lt 102eV and 103 GeV lt L lt 1010 GeV
• B1T, the massive mode gives largest contribut.

• photon splitting could be tested in lab
• experiments by using high brilliance Lasers

dN/dt 1018 s-1

• we assume that in the range of mass explored
• the dominant decay channel is in two photons

45
E.G., K.Huitu, S.Roy, PRD 74, 073002 (06)

• colored areas excluded at 95 C.L.
• B 5 Tesla of L10m length, dN/dt1018 /s
• (left) 1 day (right) 1 year running time

46
E.G., K.Huitu, S.Roy, PRD 74, 073002 (06)

• colored areas excluded at 95 C.L.
• (1 year running)

47
Conclusions

• two-photon-spin0 coupling can induce photon
  splitting
• on static and homogeneous magnetic fields

• the absorption coefficient is much larger than
  in QED
• for typical masses m10-3 eV, L106 GeV, and
  BO(T)

• large areas of the parameter space could be
  tested
• by optical Laser experiments, with B1-10 T

• Lasers with w gtgt 1eV would allow in principle
• to explore regions of smaller couplings.
• Not clear how to detect photon splitting in
  this case