1 / 53

MAGIC & The Speed of Light

MAGIC & The Speed of Light. Nick E. Mavromatos King’s College London HSSHEP 2008 Workshop, Ancient Olympia, Greece, April 16-19 2008. OUTLINE I. High-Energy Gamma Ray Astrophysics as a probe for New Physics

jacie
Télécharger la présentation

MAGIC & The Speed of Light

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. MAGIC & The Speed of Light Nick E. Mavromatos King’s College London HSSHEP 2008 Workshop, Ancient Olympia, Greece, April 16-19 2008

  2. OUTLINEI • High-Energy Gamma Ray Astrophysics as a probe for New Physics • The MAGIC results:non-simultaneous arrival of TeV photons from AGN Mk 501, more energetic photons arrive later… • Possible Interpretations: (i) Astro-Physics at source: synchrotron radiation, Compton scattering produce delays at emission: Non conclusive (ii) Exotic Interpretation: Quantum Gravity (QG) propagation effects (?): QG as a medium with refractive index, Modified Dispersion Relations for matter probes with Linear QG scale suppression (LMDR) • Check on other tests on (LMDR) modified dispersion relations:Electrons: Synchrotron Radiation from Crab Nebula Photons: Birefringence constraints for LMDR MAGIC & The Speed of Light N.E. Mavromatos

  3. OUTLINEII • Stringy Models of space time foam (SMSTF) : Non-universal action of ``gravity foam’’ on matter probes: Electrons (and in general charged particles) transparent, Photons (and neutral particles) feel the foam medium effects • String Uncertainties, Non-commutative geometry atstring scales& the MAGIC result :a uniquely stringy effect ? …. Compatible with other tests constraining LMDR • Other consequences of the SMSTF:CPT Violation (ill-definition) due to decoherenceand unique effects (?) in entangled states of meson factories • Outlook:NEED TO CONFIRM MAGIC effect by H.E.S.S. and other experiments, further tests using High-Energy Neutrino astrophysics MAGIC & The Speed of Light N.E. Mavromatos

  4. OUTLINEII • Stringy Models of space time foam (SMSTF) : Non-universal action of ``gravity foam’’ on matter probes: Electrons (and in general charged particles) transparent, Photons (and neutral particles) feel the foam medium effects Sub-luminal Refractive index in vacuo, No Birefringence • String Uncertainties, Non-commutative geometry atstring scales& the MAGIC result :a uniquely stringy effect ? …. Compatible with other tests constraining LMDR • Other consequences of the SMSTF:CPT Violation (ill-definition) due to decoherenceand unique effects (?) in entangled states of meson factories • Outlook:NEED TO CONFIRM MAGIC effect by H.E.S.S. and other experiments, further tests using High-Energy Neutrino astrophysics MAGIC & The Speed of Light N.E. Mavromatos

  5. OUTLINEII • Stringy Models of space time foam (SMSTF) : Non-universal action of ``gravity foam’’ on matter probes: Electrons (and in general charged particles) transparent, Photons (and neutral particles) feel the foam medium effects Sub-luminal Refractive index in vacuo, No Birefringence • String Uncertainties, Non-commutative geometry atstring scales& the MAGIC result :a uniquely stringy effect ? …. Compatible with other tests constraining LMDR • Other consequences of the SMSTF:CPT Violation (ill-definition) due to decoherenceand unique effects (?) in entangled states of meson factories • Outlook:NEED TO CONFIRM MAGIC effect by H.E.S.S. and other experiments, further tests using High-Energy Neutrino astrophysics MAGIC & The Speed of Light N.E. Mavromatos

  6. A flow of high energy particles reaches Earth: Cosmic Rays 90% protons, < 10% He nuclei, < 1% heavier ionised elements , < 1% electrons 0,1 – 1 % PHOTONS > MeV energies (Gamma Rays) High Energy Gamma Ray Astrophysics MAGIC & The Speed of Light N.E. Mavromatos

  7. A flow of high energy particles reaches Earth: Cosmic Rays 90% protons, < 10% He nuclei, < 1% heavier ionised elements , < 1% electrons 0,1 – 1 % PHOTONS > MeV energies (Gamma Rays) High Energy Gamma Ray Astrophysics MAGIC & The Speed of Light N.E. Mavromatos

  8. A flow of high energy particles reaches Earth: Cosmic Rays 90% protons, < 10% He nuclei, < 1% heavier ionised elements , < 1% electrons 0,1 – 1 % PHOTONS > MeV energies (Gamma Rays) High Energy Gamma Ray Astrophysics Gamma Rays: most interesting part of spectrum from Astrophysical Sources: e.g. from Active Galactic Nuclei (AGN) : > 20 MeV MAGIC & The Speed of Light N.E. Mavromatos

  9. A flow of high energy particles reaches Earth: Cosmic Rays 90% protons, < 10% He nuclei, < 1% heavier ionised elements , < 1% electrons 0,1 – 1 % PHOTONS > MeV energies (Gamma Rays) High Energy Gamma Ray Astrophysics • Classification of High-Energy Gamma Rays : High Energy: 20 MeV -100 GeV Very High Energy: 100 GeV-30 TeV Ultra High Energy: 30 TeV – 30 PeV Extremely High Energy : 30 PeV - ? Gamma Rays: most interesting part of spectrum from Astrophysical Sources: e.g. from Active Galactic Nuclei (AGN) : > 20 MeV MAGIC & The Speed of Light N.E. Mavromatos

  10. PRODUCTION OF HIGH ENERGY GAMMA RAYS • Photons from conversion of gravitational Energy (AGN) • From self-annihilation of Dark Matter • Decays of exotic massive particle in very Early Universe MAGIC & The Speed of Light N.E. Mavromatos

  11. PRODUCTION OF HIGH ENERGY GAMMA RAYS • Photons from conversion of gravitational Energy (AGN) • From self-annihilation of Dark Matter • Decays of exotic massive particle in very Early Universe MAGIC & The Speed of Light N.E. Mavromatos

  12. AGN High Energy Gamma Rays High-Energy Photons from Gravitational Energy Conversion, released by collapses towards a central massive object (black hole); angular momentum implies accretion disk, and jets outflowing the accretion plane… Most popular Interpretation is Self-Synchrotron-Compton (SSC): Time-varying populations of Ultrarelativistic electrons accelerated in strong magnetic fields Synchrotron Radiation generating Inverse Compton Emission (100 MeV-100 GeV) from soft photons scattered off energetic electrons. Compton components peak at TeV energies. MAGIC & The Speed of Light N.E. Mavromatos

  13. Sy IC log(energy density) leptonic acceleration Synchrotron  (eV-keV) e- (TeV) B  (TeV) Inverse Compton log(E) eVkeVMeVGeVTeV  (eV) AGN High Energy Gamma Rays - electron accelerators: synchrotron: e B -> e gamma + inverse Compton: e gamma -> gamma e MAGIC & The Speed of Light N.E. Mavromatos

  14. Gamma Ray Detection Detection by Cherenkov Telescopes • Do not detect the Gamma Ray directly but the Cherenkov radiation it produces entering the atmosphere…. MAGIC & The Speed of Light N.E. Mavromatos

  15. Electromagnetic Shower Hadronic Shower Cherenkov Effect MAGIC & The Speed of Light N.E. Mavromatos

  16. Detection of TeV gamma rays using Cherenkovtelescopes Gamma- ray Particle shower ~ 10 km ~ 1o Cherenkov light ~ 120 m Observation Technique MAGIC & The Speed of Light N.E. Mavromatos

  17. VHE Experimental World Today TIBET MILAGRO MAGIC STACEE TACTIC CANGAROO HESS TIBET ARRAY ARGO-YBJ MILAGRO STACEE CACTUS TACTIC PACT GRAPES MAGIC & The Speed of Light N.E. Mavromatos M. MARTINEZ

  18. VHE Experimental World Today TIBET MILAGRO MAGIC STACEE TACTIC CANGAROO HESS TIBET ARRAY ARGO-YBJ MILAGRO STACEE CACTUS TACTIC PACT Canary Islands GRAPES MAGIC & The Speed of Light N.E. Mavromatos M. MARTINEZ

  19. The MAGIC Collaboration (Major Atmospheric Gamma-ray ImagingCherenkov Telescope ) Observation of Flares from AGN Mk 501 Red-shift: z=0.034 MAGIC & The Speed of Light N.E. Mavromatos

  20. The MAGIC ``Effect’’ MAGIC & The Speed of Light N.E. Mavromatos

  21. Possible Interpetations • Delays of more energetic photons are a result of AGN source Physics (SSC mechanism) MAGIC Coll. ApJ 669, 862 (2007) : SSC I Bednarek & Wagner arXive:0804.0619 : SSCII • Delays of more energetic photons occur in propagation due to new fundamental Physics (e.g. refractive index in vacuo due to Quantum Gravity space-time Foam Effects…) MAGIC Coll & Ellis, NM, Nanopoulos, Sakharov, Sarkisyan [arXive:0708.2889] (individual photon analysis) MAGIC & The Speed of Light N.E. Mavromatos

  22. SSC as explanation of the MAGIC Effect • Classical SSC model: emission region moves along the jet with constant Lorentz factors . In other AGN (e.g.; Crab Nebula), such factors are of order 10 – 20 . However, to account for the 4 ± 1 minute delay observed in MAGIC requires Lorentz factors four orders of magnitude higher. • Modify SSC model :(i) assume gradual acceleration of relativistic electrons inside blob (SSC I) (ii) assume the blob captured in inner part of the jet during its acceleration phase (SSC II): lower-energy part of flare close to base of the jet, lower Lorentz factor, higher-energy at larger distances from jet base, higher Lorentz factor. Time-delay in SSC II inversely proportional to γ-ray Energies • SITUATION NON CONCLUSIVE: DOES FLARE PHYSICS DEPEND ON INDIVIDUAL FLARES (SSC I) ? MATTER OF LUCK TO HAVE OBSERVED BLOB IN ITS ACCELERATION PHASE IN Mk501 (SSC II) ? MAGIC & The Speed of Light N.E. Mavromatos

  23. SSC as explanation of the MAGIC Effect • Classical SSC model: emission region moves along the jet with constant Lorentz factors . In other AGN (e.g.; Crab Nebula), such factors are of order 10 – 20 . However, to account for the 4 ± 1 minute delay observed in MAGIC requires Lorentz factors four orders of magnitude higher. • Modify SSC model :(i) assume gradual acceleration of relativistic electrons inside blob (SSC I) (ii) assume the blob captured in inner part of the jet during its acceleration phase (SSC II): lower-energy part of flare close to base of the jet, lower Lorentz factor, higher-energy at larger distances from jet base, higher Lorentz factor. Time-delay in SSC II inversely proportional to γ-ray Energies • SITUATION NON CONCLUSIVE: DOES FLARE PHYSICS DEPEND ON INDIVIDUAL FLARES (SSC I) ? MATTER OF LUCK TO HAVE OBSERVED BLOB IN ITS ACCELERATION PHASE IN Mk501 (SSC II) ? MAGIC & The Speed of Light N.E. Mavromatos

  24. SSC as explanation of the MAGIC Effect • Classical SSC model: emission region moves along the jet with constant Lorentz factors . In other AGN (e.g.; Crab Nebula), such factors are of order 10 – 20 . However, to account for the 4 ± 1 minute delay observed in MAGIC requires Lorentz factors four orders of magnitude higher. • Modify SSC model :(i) assume gradual acceleration of relativistic electrons inside blob (SSC I) (ii) assume the blob captured in inner part of the jet during its acceleration phase (SSC II): lower-energy part of flare close to base of the jet, lower Lorentz factor, higher-energy at larger distances from jet base, higher Lorentz factor. Time-delay in SSC II inversely proportional to γ-ray Energies • SITUATION NON CONCLUSIVE: DOES FLARE PHYSICS DEPEND ON INDIVIDUAL FLARES (SSC I) ? MATTER OF LUCK TO HAVE OBSERVED BLOB IN ITS ACCELERATION PHASE IN Mk501 (SSC II) ? MAGIC & The Speed of Light N.E. Mavromatos

  25. Quantum Gravity as a dispersive medium (space-time foam) , modified dispersion relations (MDR) for matter, radiation Phenomenological Models of MDR Gonzalez-Mestres, Amelino-Camelia, Ellis, NM, Nanopoulos, Sarkar Stochastically fluctuating space time backgrounds Ford, Yu , Sarben Sarkar, NM… String & Brane-inspired Models Ellis, NM, Nanopoulos, Szabo, Sakharov, Farakos, Mitsou, … Loop Quantum Gravity (?) Gambini, Pullin, Urrutia, … Deformed Special Relativity Models (unclear if there is a consistent quantum version) Amelino-Camelia, Magueijo, Smolin, Kowalski- Glikman … New fundamental Physics Interpretation MAGIC & The Speed of Light N.E. Mavromatos

  26. Quantum Gravity as a dispersive medium (space-time foam) , modified dispersion relations (MDR) for matter, radiation Phenomenological Models of MDR Gonzalez-Mestres, Amelino-Camelia, Ellis, NM, Nanopoulos, Sarkar Stochastically fluctuating space time backgrounds Ford, Yu , Sarben Sarkar, NM… String & Brane-inspired Models Ellis, NM, Nanopoulos, Szabo, Sakharov, Farakos, Mitsou, … Loop Quantum Gravity (?) Gambini, Pullin, Urrutia, … Deformed Special Relativity Models (unclear if there is a consistent quantum version) Amelino-Camelia, Magueijo, Smolin, Kowalski- Glikman … New fundamental Physics Interpretation Complex refractive index MAGIC & The Speed of Light N.E. Mavromatos

  27. Quantum Gravity as a dispersive medium (space-time foam) , modified dispersion relations (MDR) for matter, radiation Phenomenological Models of MDR Gonzalez-Mestres, Amelino-Camelia, Ellis, NM, Nanopoulos, Sarkar Stochastically fluctuating space time backgrounds Ford, Yu , Sarben Sarkar, NM… String & Brane-inspired Models Ellis, NM, Nanopoulos, Szabo, Sakharov, Farakos, Mitsou, … Loop Quantum Gravity (?) Gambini, Pullin, Urrutia, … Deformed Special Relativity Models (unclear if there is a consistent quantum version) Amelino-Camelia, Magueijo, Smolin, Kowalski- Glikman … New fundamental Physics Interpretation Complex refractive index MAGIC & The Speed of Light N.E. Mavromatos

  28. Quantum-Gravity Induced Modified Dispersion for Photons Modified dispersion due to QG induced space-time (metric) distortions (c=1 units): MAGIC & The Speed of Light N.E. Mavromatos

  29. Quantum-Gravity Induced Modified Dispersion for Photons Modified dispersion due to QG induced space-time (metric) distortions (c=1 units): MAGIC & The Speed of Light N.E. Mavromatos

  30. Quantum-Gravity Induced Modified Dispersion for Photons Modified dispersion due to QG induced space-time (metric) distortions (c=1 units): MAGIC & The Speed of Light N.E. Mavromatos

  31. Try to use the FULL gamma-ray information to study the Eg v.s. tg correlation. Low statistics (as compared with typical GRBs) need for development of new analysis approaches: 1) Maximize Energy Cost Function (ECF) – Exploit individual photon study possibility : reproduce peak of flare by using modified dispersion relations for individual photons (both linear and quadratic in MQG) MAGIC Coll. & Ellis, N.M. Sakharov, Sarkisyan, arXive: 07082889 2) Fit likelihood function – using different shapes of flare and energy spectra M.Martinez, M.Errando, arXive: 08032120 Fitting the MAGIC Effect MAGIC & The Speed of Light N.E. Mavromatos

  32. Fitting the MAGIC Effect • The 4 ± 1 minute delay of most energetic photons observed in the MAGIC Telescope can be reproduced by a subluminal refractive index (propagation effect), either scaling linearly or quadratic with the quantum-gravity scale… MAGIC & The Speed of Light N.E. Mavromatos

  33. ENERGY COST FUNCTIONAL (ECF) METHEOD arXive: 07082889 MAGIC & The Speed of Light N.E. Mavromatos

  34. LIKELIHOOD METHOD arXive: 07082889 MAGIC & The Speed of Light N.E. Mavromatos

  35. MAGIC Results (ECF Method): Quadratic Linear 95% CL MAGIC & The Speed of Light N.E. Mavromatos

  36. MDR for other matter probes Massive Probes (e.g. electrons): Constraints from Crab Nebula via Synchrotron Radiation Jacobson, Liberatti, Mattingly, Ellis, NM, Sakharov Electron moving in magnetic field H emits discrete frequency spectrum with a maximum at critical frequency: R=orbit radius, c(ωc)=photon group velocity, v(E)=electron group velocity δ(E) = angle for forward radiation pattern Experimental measurement of ωc (Crab Nebula) yields For MQG = MQG1 (MAGIC)~ 1018GeV that α > 1.74 MAGIC & The Speed of Light N.E. Mavromatos

  37. MDR for other matter probes Massive Probes (e.g. electrons): Constraints from Crab Nebula via Synchrotron Radiation Jacobson, Liberati, Mattingly, Ellis, NM, Sakharov Electron moving in magnetic field H emits discrete frequency spectrum with a maximum at critical frequency: R=orbit radius, c(ωc)=photon group velocity, v(E)=electron group velocity δ(E) = angle for forward radiation pattern WHAT ABOUT PHOTONS & THE MAGIC RESULT? Experimental measurement of ωc (Crab Nebula) yields For MQG = MQG1 (MAGIC)~ 1018GeV that α > 1.74 MAGIC & The Speed of Light N.E. Mavromatos

  38. Birefringence Constraints on photons MDR • If MDR for probes stem from Local Effective Lagrangians (LEL): Maccione et al., arXive0707.2673 Photons :Electrons: Myers- Pospelov QED Difference in polarization angle over cosmological distance d: ± signs indicate left/right movers and for Circularly polarized photons imply rotation of linear polarization angle (BIREFRINGENCE). UV radiation from Galaxies: For FromGRB polarization MAGIC & The Speed of Light N.E. Mavromatos

  39. Birefringence Constraints on photons MDR • If MDR for probes stem from Local Effective Lagrangians (LEL): Maccione et al., arXive0707.2673 Photons :Electrons: Myers- Pospelov QED Difference in polarization angle over cosmological distance d: ± signs indicate left/right movers and for Circularly polarized photons imply rotation of linear polarization angle (BIREFRINGENCE). UV radiation from Galaxies: For FromGRB polarization MAGIC EFFECT due to QG ruled out ? MAGIC & The Speed of Light N.E. Mavromatos

  40. A Stringy Model of Space -Time Foam Ellis, NM, Nanopoulos Open strings on D3-brane world represent electrically neutral matter or radiation, interacting via splitting/capture with D-particles (electric charge conservation) . D-particle foam medium transparent to (charged) Electrons no modified dispersion for them Photons or electrically neutral probes feel the effects of D-particle foam Modified Dispersion for them…. MAGIC & The Speed of Light N.E. Mavromatos

  41. A Stringy Model of Space -Time Foam Ellis, NM, Nanopoulos Open strings on D3-brane world represent electrically neutral matter or radiation, interacting via splitting/capture with D-particles (electric charge conservation) . D-particle foam medium transparent to (charged) Electrons no modified dispersion for them Photons or electrically neutral probes feel the effects of D-particle foam Modified Dispersion for them…. NON-UNIVERSAL ACTION OF D-PARTICLE FOAM ON MATTER & RADIATION MAGIC & The Speed of Light N.E. Mavromatos

  42. A Stringy Model of Space -Time Foam Ellis, NM, Nanopoulos Open strings on D3-brane world represent electrically neutral matter or radiation, interacting via splitting/capture with D-particles (electric charge conservation) . D-particle foam medium transparent to (charged) Electrons no modified dispersion for them Photons or electrically neutral probes feel the effects of D-particle foam Modified Dispersion for them…. NON-UNIVERSAL ACTION OF D-PARTICLE FOAM ON MATTER & RADIATION MAGIC & The Speed of Light N.E. Mavromatos

  43. Stringy Uncertainties & the Capture Process During Capture: intermediate String stretching between D-particle and D3-brane is Created. It acquires N internal Oscillator excitations & Grows in size & oscillates from Zero to a maximum length by absorbing incident photon Energy p0 : Minimise right-hand-size w.r.t. L. End of intermediate string on D3-brane Moves with speed of light in vacuo c=1 Hence TIME DELAY(causality) during Capture: DELAY IS INDEPENDENT OF PHOTON POLARIZATION, HENCE NO BIREFRINGENCE…. MAGIC & The Speed of Light N.E. Mavromatos

  44. Stringy Uncertainties & the MAGIC Effect • D-foam: transparent to electrons • D-foam captures photons & re-emits them • Time Delay (Causal) in each Capture: • Independent of photon polarization (no Birefringence) • Total Delay from emission of photons till observation over a distance D (assume n* defects per string length): Effectively modified Dispersion relation for photons due to induced metric distortion G0i ~ p0 REPRODUCE 4±1 MINUTE DELAY OF MAGIC from Mk501 (redshift z=0.034) For n* =O(1) & Ms ~ 1018 GeV, consistently with Crab Nebula & other Astrophysical constraints on modified dispersion relations…… MAGIC & The Speed of Light N.E. Mavromatos

  45. Other Consequences of D-particle Foam • Low-energy CPT Violation & Decoherence from stochastic fluctuations of D-particle defects: Capture/re-emission process for neutral probes implies recoil of D-particle defect, momentum-direction-dependent induced metricsG0i ~ Δki ~ ki ~ p0 (Logarithmic Conformal Field Theory of recoil/capture on world-sheet of string model) Kogan,NM,Wheater,Szabo, Ellis, Nanopoulos • CPT Operator ill-defined, unique consequences in modifications of EPR correlations of entangled states of neutral mesons in meson factories (Φ-, B-factories) Bernabeu, NM, Papavassiliou,Nebot, Alvarez, Sarben Sarkar Estimates of such D-particle foam effects in neutral mesons complicated due to strong QCD effects present in such composite neutral particles MAGIC & The Speed of Light N.E. Mavromatos

  46. Other Consequences of D-particle Foam • If CPT Operator well-defined as operator, even if CPT is broken in the Hamiltonian… (e.g. Lorentz violating models) Φ KSKL KSKL MAGIC & The Speed of Light N.E. Mavromatos

  47. EPR Modifications & D-particle Foam • If CPT Operator ill-defined, unique consequences in modifications of EPR correlations of entangled states of neutral mesons in meson factories (Φ-, B-factories) Bernabeu, NM, Papavassiliou,Nebot, Alvarez, Sarben Sarkar Φ KSKL KSKL KSKL IF CPT ILL-DEFINED (e.g. D-particle Foam) Induced metric due to capture/recoil, stochastic fluctuations, Decoherence MAGIC & The Speed of Light N.E. Mavromatos

  48. EPR Modifications & D-particle Foam • CPT Operator ill-defined, unique consequences in modifications of EPR correlations of entangled states of neutral mesons in meson factories (Φ-, B-factories) Bernabeu, NM, Papavassiliou,Nebot, Alvarez, Sarben Sarkar Φ KSKL KSKL KSKL KSKS , KLKL KSKS , KLKL IF CPT ILL-DEFINED (e.g. D-particle Foam) Induced metric due to capture/recoil, stochastic fluctuations, Decoherence Estimates of such D-particle foam effects in neutral mesons complicated due to strong QCD effects present in such composite neutral particles MAGIC & The Speed of Light N.E. Mavromatos

  49. Neutral mesons no longer indistinguishable particles, initial entangled state: Φ KSKL KSKL KSKS , KLKL KSKS , KLKL IF CPT ILL-DEFINED (e.g. D-particle Foam) If QCD effects, sub-structure in neutral mesons ignored, and D-foam acts as if they were structureless particles, then for MQG ~ 1018 GeV (MAGIC) the estimate for ω: | ω | ~ 10-4 |ζ|, for 1 > |ζ| > 10-2 (natural) Not far from sensitivity of upgraded meson factories ( e.g. DAFNE2) MAGIC & The Speed of Light N.E. Mavromatos

  50. Neutral mesons no longer indistinguishable particles, initial entangled state: Φ KSKL KSKL KSKS , KLKL KSKS , KLKL IF CPT ILL-DEFINED (e.g. D-particle Foam) If QCD effects, sub-structure in neutral mesons ignored, and D-foam acts as if they were structureless particles, then for MQG ~ 1018 GeV (MAGIC) the estimate for ω: | ω | ~ 10-4 |ζ|, for 1 > |ζ| > 10-2 (natural) Not far from sensitivity of upgraded meson factories ( e.g. DAFNE2) MAGIC & The Speed of Light N.E. Mavromatos

More Related