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

Photon splitting in magnetic fields as a probe of ultralight spin-0 fields. Emidio Gabrielli Helsinki Institute of Physics. in collaboration with K. Huitu and S. Roy. Photon splitting. g + external magnetic field  g g

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

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  1. Photon splitting in magnetic fields as a probe of ultralightspin-0 fields Emidio Gabrielli Helsinki Institute of Physics in collaboration withK. Huitu and S. Roy

  2. Photon splitting g+ external magnetic field  g g • it is due to non-linear photon interactions induced byvacuum polarization effects • in QED the absorption coefficient K is very small for magnetic fields of the order of TeslaK ~ (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 theHeisenberg-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 scatteringg g  g g

  4. Heisenberg-Euler lagrangian gauge-invariant Lagrangian non-linear interactions L(int)  is a function of two gauge invariant quantities

  5. Heisenberg-Euler lagrangian ( in relativistic unities c=1, h=1) as derived by J.Schwinger PR 82, 664 (’51) m = electron mass

  6. Expanding the H-E lagrangian at order a2 m =electron mass provides the leading correction to the non-linear interactions

  7. 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 byBbecomes birefringent

  8. 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

  9. 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 > 1 • let consider first the case of no-dispersion (n=1) S.Adler, Ann. Phys. 67, 599 ( ’71) matrix element can be obtained from the H-E lagrangian or equivalently from …

  10. resumming the full series of diagrams + + permutations + S only an even number of total vertices can contribute due to the Furry’s theorem  Tr[odd-number of Dirac-gammas]=0

  11. no dispersion case kinematic allowed solution : only one light-like four-momentum all three-momenta parallel

  12. 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)

  13. P(d)= survival probability traveling a distance d k= absorption coefficient d k << 1 M=matrix element g gphase-space

  14. no-dispersion Adler, Ann. Phys. 67, 599 ( ’71) m =electron mass parallel and perp. polarization vectors with respect to the plane (k,B) w/m <<1

  15. phase space integral energy distribution

  16. 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 :

  17. Effects of dispersion on photon splitting Kinematical condition selection rules for polarized transitions

  18. 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

  19. 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

  20. difficult to detect photon splitting in typical • laboratory experiment , too rare event • one needs very large B ~ Bcrit and/or w > MeV • for w >> 2m ~ MeV, the pair production mechanism • g  e+e- dominates over g gg • Adler (’ 71) provided the exact calculation of • k valid beyond the approximation w/m << 1.

  21. 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)

  22. 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 ofm ~ 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-ggenerated at 1-loop

  23. The axion has a very weak coupling • If astrophysical constraints are taken into • accountL ~ 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

  24. Effects of spin0-g-gcouplings on photon propagationin external magnetic/electric fields • replacing g g f  <B> g fgives 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-0oscillations 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

  25. 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

  26. 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

  27. Photon splitting in magnetic fieldinduced by gg-spin-0coupling 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

  28. no physical effect. absorbed by field renormalization A radiation field F(ext) external field tadpoles mixing term

  29. effective photon propagator summed up at all orders full propagator of spin-0 field including self-energy diagrams

  30. temporal gauge A0=0 effective photon propagator (case scalar field + B) 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

  31. effective photon propagator (case pseudoscalar field + B) T selects polarizations with electric component parallel to (B,k) plane R selects polarizations with electric component perpendicular to (B,k) plane

  32. 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

  33. master equation for photon dispersion m = renormalized mass of spin-0 particle gauge invariant solutions external electric field external magnetic field

  34. hierarchy of scales of the same order of D characteristic small parameters solutions easily found by expanding in D/m4

  35. solutions massless mode massive mode in order to have real solutions critical field

  36. the massive mode can be excited from the vacuum if analogous results for external electric fields and/or pseudoscalar interactions

  37. 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(-) < 0 • there are only 2 physical solutions, one massless • and one massive

  38. photon dispersions refraxion index of massless mode n(w=0) dispersion relation of massive mode

  39. photon absorption coefficient k massive mode from optical theorem G= width of spin-0 particle

  40. when B approaches the critical value • (x1) there is a resonant effect • however, unitarity requires Z(+) < 1 • validity of perturbation theory up to

  41. same results can be re-obtained by using the Golden Formula for absorption coefficient,where the matrix element M is: k2=M+2 for the massless mode Z+ Z0 ~ 1 and k2=M02

  42. photon absorption coefficient massless mode (w/m)2 (B/m2)2 <<1 • scalar case + B: allowed by kinematic incidentally, PVLAS data have central value m ~ 2me k > kQED if m < 5 me • pseudoscalar + B: forbidden by kinematic

  43. Numerical results • for Laser frequency 1eV <w < 102eV , • 10-2eV < m < 102eV and 103 GeV <L < 1010 GeV • B=1T, 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

  44. E.G., K.Huitu, S.Roy, PRD 74, 073002 (06) • colored areas excluded at 95 % C.L. • B= 5 Tesla of L=10m length, dN/dt=1018 /s • (left) 1 day (right) 1 year running time

  45. E.G., K.Huitu, S.Roy, PRD 74, 073002 (06) • colored areas excluded at 95 % C.L. • (1 year running)

  46. 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 m~10-3 eV, L~106 GeV, and B~O(T) • large areas of the parameter space could be tested • by optical Laser experiments, with B=1-10 T • Lasers with w >> 1eV would allow in principle • to explore regions of smaller couplings. • Not clear how to detect photon splitting in this case

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