THEORETICAL ASPECTS

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THEORETICAL ASPECTS

• Marco Roncadelli, INFN Pavia (Italy)

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OUTLINE

• QED VACUUM EFFECTS
• AXION-LIKE PARTICLES
• ASTROPHYSICAL CONSTRAINTS
• IMPLICATIONS OF PVLAS
• DOUBLE PULSAR J0737-3039

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QED VACUUM EFFECTS

• Consider a photon beam in vacuo with k along the
  z-axis. External B field present (only x, y
  components of B relevant).
• CLASSICALLY beam propagation UNAFFECTED by B.
• QUANTUM corrections change the situation, since
  virtual fermion exchange produces a photon-photon
  interaction.

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• At one-loop, proceeds via a box
  diagram and at low-energy is described by
• Presently a photon can be replaced by B .

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• From above lagrangian propagation eigenstates are
  polarization states ,
• (with respect to the B-k plane). Because
  amplitude for depends on initial
  photon polarization, two conclusions follow.
• . , propagate
  with different velocities .
  .
• BIREFRINGENCE .

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• . do not split but
  split into
• two . selective photon absorption .
  DICHROISM .
• Suppose now the photon beam is at the beginning
  LINEARLY polarized.
• Owing to birefringence alone an ELLIPTICAL
  polarization shows up
• Due to dichroism alone polarization ROTATEs,
  since decreases and increases.

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• Net effect ELLIPTICITY with ellipses major axis
  ROTATED.
• In 1979 E. Iacopini and E. Zavattini proposed to
  measure the B-induced vacuum birefringence with a
  PVLAS-like apparatus.
• N.B. Dichroism down by .

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AXION-LIKE PARTICLES

• In 1977 R. Peccei and H. Quinn proposed a
  solution of the strong CP problem based on an
  additional global U(1) symmetry. Soon after S.
  Weinberg and F. Wilczek realized that the PQ
  symmetry is spontaneously broken, thereby giving
  rise to a Goldstone boson the Axion. Actually
  QCD instanton effects break the PQ symmetry also
  explicitly, so that the axion gets a mass

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• where is the scale at which the PQ
  symmetry is spontaneously broken.
• Originally it was supposed that
• but it was soon realized that resulting axion
  is experimentally RULED OUT.

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• WAY OUT . INVISIBLE axion models.
• Yukawa couplings of axion to quarks produce an
  effective 2 photon coupling at one-loop of the
  form

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• with
• where k O(1) is model-dependent. So
• the axion obeys the mass-coupling relation

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• N.B. Invisible axions excellent candidates for
  cold nonbaryonic DARK MATTER candidates for
  .
• In 1983 Sikivie pointed out that invisible axions
  can be DETECTED owing to their 2 photon coupling.
  Axion-photon conversion analogous to neutrino
  OSCILLATIONS but here a nonvanishing transverse B
  is necessary to account for spin mismatch.

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• Transition probability energy-independent for
  oscillation wavenumber dominated by photon-axion
  mixing term. As long as photon energy is much
  larger than m WKB approximation the
  SECOND-order propagation equation for a
  monochromatic beam reduces to a FIRST-order one.

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• Sikivie considered 3 observational strategies (2
  based on a tunable resonant cavity).
• Axion ELIOSCOPE . detection of SOLAR axions.
• Axion HALOSCOPE . detection of DARK MATTER
  axions.
• Regeneration experiment . shining light through
  a wall.

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• In 1986 L. Maiani, R. Petronzio and E. Zavattini
  realized that axions can be searched for by a
  PVLAS-like experiment.
• Consider again a photon beam LINEARLY polarized
  initially which propagates in a magnetized
  vacuum. MIX with the axion while do NOT
  (pseudoscalar coupling).

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• Virtual axion exchange affects propagation of
  but not of .... BIREFRINGENCE.
• Real axion photo-production depletes the
• polarization mode only .DICHROISM.
• M and m UNIQUELY determined in terms of the beam
  ellipticity and rotation angle.
• N.B. MPZ strategy INDEPENDENT of actual
• PRESENCE of axions in the laboratory.

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• AXION-LIKE PARTICLES (ALPs) are present in many
  extensions of the SM and are described by either
• or
• with m and M ARBITRARY parameters (a priori).
• N.B. All above considerations apply to ALPs as
  well.

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• Everything goes like for the axion case .... in a
  PVLAS-like experiment both m and M of an ALP can
  be DETERMINED by measuring both ellipticity and
  rotation angle of a laser beam with initial
  linear polarization.
• N.B. I assume ALP to be pseudoscalar.

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ASTROPHYSICAL CONSTRAINTS

• THEORETICAL BOUND Thermal photons produced in
  central regions of stars can become ALPs in the
  fluctuating EM field of stellar plasma. In
  main-sequence stars this occurs via Primakoff
  scattering off ions. The ALPs escape . star
  looses energy . central temperature increases .
  observed properties change. Agreement between
  standard stellar models and observations

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• demands that unwanted ALP effects have to be
  sufficiently suppressed.
• Sun . .
• Red giants .
• CAST EXPERIMENT Blind magnetic telescope is
  pointed toward the Sun detection of KeV-energy
  photons would the signal for axions coming from
  the Sun.

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• Remarkably CAST yields
  
• for .

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IMPLICATIONS OF PVLAS

• ASSUME that PVLAS has detected an ALP with
  and .
• N.B. Alternatives are possible!
• A look back at m-M relation . this ALP is NOT
  the axion.
• Theoretical astrophysical bound as well as CAST
  bound VIOLATED by 5 orders of magnitudes.

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• MORAL
• A NEW PARTICLE has been discovered.
• NEW PHYSICS at low-energy MUST exist to make
  the 2 photon coupling MUCH WEAKER in stellar
  environment than in laboratory.
• Some possibilities have been explored based on
  plasma effects in paraphoton models and a sub-KeV
  phase transition.

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• Sic stantibus rebus. INDEPENDENT CHECKS of
  PVLAS claim look COMPELLING.
• Experiments similar to PVLAS.
• Photon regeneration experiments.
• Astrophysical effects with UNSUPPRESSED 2 photon
  coupling.

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DOUBLE PULSAR J0737-3039

• Discovered in 2003.
• Orbital period T 2.45 h.
• Rotation periods P(A) 23 ms, P(B)
• 2.8 s.
• Inclination of orbital plane i 90.29 deg . it
  is seen almost EDGE-ON.
• Focus on emission from A.

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• Pulsar B has DIPOLAR magnetic field
• on the surface.
• LARGE impact parameter . NOTHING interesting
  happens.
• SMALL impact parameter . beam from A traverses
  magnetosphere of B .
• photon-ALP conversion IMPORTANT depending on
  m, M.

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• TWO effects are expected.
• Production of real ALPs . periodic attenuation
  of photon beam which depends on T, P(B).
• N.B. Analog of DICHROISM in PVLAS experiment.

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• Exchange of virtual ALPs . periodic LENSING
  which depends on T, P(B).
• N.B. Analog of BIREFRINGENCE in PVLAS
  experiment.
• Here I consider only attenuation effect (A.
  Dupays, C. Rizzo, M. R., G. F. Bignami, Phys.
  Rev.Lett. 95 211302 (2005)).

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• We work within WKB approximation and solve
  numerically the first-order propagation equation
  for an UNPOLARIZED, monochromatic beam travelling
  in the dipolar B produced by pulsar B. Resulting
  transition probability as a function of beam
  frequency is

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• N.B. Effect relevant ABOVE 10 MeV . remarkable
  result.
• J0737-3039 is expected to be a gamma-ray SOURCE.
• Interaction of photon beam with plasma in
  magnetosphere of B is NEGLIGIBLE.
• WKB approximation JUSTIFIED.

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• INTUITIVE explanation assuming B constant i.e.
  for .
• Mixing effects important for mixing angle in
  photon-ALP system of order 1 . OK with THRESHOLD
  behaviour.

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• Transition probability becomes energy-independent
  for oscillation wavenumber dominated by
  photon-ALP mixing term . OK with FLAT behaviour.
• TEMPORAL behaviour best described by TRANSMISSION
  1 P. We find beam attenuation up to 50 as

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• This effect turns out to be OBSERVABLE with
  GLAST.
• For example, ABSENCE of attenuation A at 10
  level yields the exclusion plot

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• This attenuation requires 100 counts during
  observation time. For 2 weeks
• in agreement with expectations and about 1000
  times LARGER than GLAST sensitivity threshold for
  point sources.