THEORETICAL ASPECTS

Marco Roncadelli, INFN – Pavia (Italy)

OUTLINE

1. QED VACUUM EFFECTS2. AXION-LIKE PARTICLES3. ASTROPHYSICAL CONSTRAINTS4. IMPLICATIONS OF PVLAS5. DOUBLE PULSAR J0737-3039

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.

At one-loop, proceeds via a box diagram and at low-energy is described by

Presently a photon can be replaced by B ….

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 .

• …. 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.

Net effect: ELLIPTICITY with ellipse’s 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 .

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

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.

WAY OUT: …. INVISIBLE axion models.

Yukawa couplings of axion to quarks produce an effective 2 photon coupling at one-loop of the form

with

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

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.

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.

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.

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).

• 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 actualPRESENCE of axions in the laboratory.

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.

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.

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

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.

Remarkably CAST yields for .

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.

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.

“Sic stantibus rebus”…. INDEPENDENT CHECKS of PVLAS claim look COMPELLING.

• Experiments similar to PVLAS.• Photon regeneration experiments.• Astrophysical effects with

UNSUPPRESSED 2 photon coupling.

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.

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.

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.

• 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)).

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

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.

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.

GB 4106.1 km3min 104

• 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

This effect turns out to be OBSERVABLE with GLAST.

For example, ABSENCE of attenuation A at 10 % level yields the exclusion plot

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.

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