Lorentz Invariance, Strings and High -Energy Gamma Ray ...planckscale/lectures/3... · Lorentz...

Lorentz Invariance, Strings Lorentz Invariance, Strings

and and

HighHigh--Energy Gamma Ray Energy Gamma Ray

Astronomy Astronomy

Nick E. Nick E. MavromatosMavromatos

KingKing’’s College Londons College London

Physics DepartmentPhysics Department

MRT�MRT�--CTCT--

20062006--035863035863

XXV MAX BORN SYMPOSIUM, The Planck Scale,XXV MAX BORN SYMPOSIUM, The Planck Scale,

WROCLAW ITP (POLAND), 29 June WROCLAW ITP (POLAND), 29 June –– 3 July 20093 July 2009

22XXV Max Born Symposium XXV Max Born Symposium

Wroclaw ITP (Poland) 2009Wroclaw ITP (Poland) 2009 N.E. MavromatosN.E. Mavromatos

Effective Field Theory Approach to Quantum GravityEffective Field Theory Approach to Quantum Gravity

A.V. A.V. KosteleckyKostelecky and collaborators, other rich literature in the subject, Burgesand collaborators, other rich literature in the subject, Burgess,s,

MyersMyers--PospelovPospelov, , UrrutiaUrrutia, , :: SudarskySudarsky,,::

Represent effective Quantum Gravity (QG) effects as Lorentz and/Represent effective Quantum Gravity (QG) effects as Lorentz and/or CPTVor CPTV

higherhigher--dimension nondimension non--renormalizablerenormalizable operators in a flat spaceoperators in a flat space--time local time local

effective effective LagrangianLagrangian (Standard(Standard--Model Extension (SME) )Model Extension (SME) )

No idea what the order of their (No idea what the order of their (dimensionfuldimensionful) coefficients is) coefficients is::unless unless

Microscopic models become availableMicroscopic models become available::..

Nevertheless obtain interesting limits experimentally on such efNevertheless obtain interesting limits experimentally on such effectsfects::

````reaching or exceeding Planck Scale sensitivityreaching or exceeding Planck Scale sensitivity’’’’ (whatever that means (whatever that means

in EFT context)in EFT context)::

SME Tests:SME Tests: Mainly from atomic Physics experiments, but also particle/nucleMainly from atomic Physics experiments, but also particle/nuclear ar

physics systems, such as neutral physics systems, such as neutral kaonskaons ((KTeVKTeV, , φφ--factories), factories),

hydorgenhydorgen/anti/anti--hydrogen hydrogen spectroscopiesspectroscopies ::



STANDARD MODEL EXTENSIONSTANDARD MODEL EXTENSION




KTeV: aX, aY < 10-21 GeV

Φ-factories: a0 < 10-18 GeVSidereal variations

H-Masers: bZ < 10-31 GeV



OUTLINEOUTLINE –– PARTPART II

HighHigh--Energy Gamma Ray Astrophysics as a probe for New PhysicsEnergy Gamma Ray Astrophysics as a probe for New Physics

The MAGIC and Fermi resultsThe MAGIC and Fermi results:: nonnon--simultaneous arrival of highsimultaneous arrival of high--energy photons from celestial objects: more energetic photons arenergy photons from celestial objects: more energetic photons arrive rive laterlater;; (Non(?)) Observation by H.E.S.S. ;;

Possible Interpretations: Possible Interpretations:

(i)(i) AstroAstro--Physics at source:Physics at source: hadronic mechanisms orsynchrotron radiation + inverse Compton scattering producedelays at emission: Non conclusive :

(ii) Exotic Interpretation(ii) Exotic Interpretation: : Quantum Gravity (QG) propagation Quantum Gravity (QG) propagation effects (?): effects (?): QG as a medium with refractive index, Modified QG as a medium with refractive index, Modified Dispersion Relations for matter probes with Linear QG scale Dispersion Relations for matter probes with Linear QG scale suppression (LMDRsuppression (LMDR)

Check on other tests on (LMDR) modified dispersion relations:Electrons: Synchrotron Radiation from Crab Nebula Electrons: Synchrotron Radiation from Crab Nebula

Photons: Birefringence constraints for LMDR Photons: Birefringence constraints for LMDR

N.E.M 0903.0318



OUTLINEOUTLINE –– PARTPART IIII

Stringy Models of Space Time Foam (SMSTF) : NonNon--universal universal action of ``gravity foamaction of ``gravity foam’’’’ on matter probes: on matter probes:

Electrons (and in general charged particles): foam transparent,

Photons (and neutral particles) feel the foam medium effects

String Uncertainties, (Induced, String Uncertainties, (Induced, FinslerFinsler--type) Nontype) Non--commutative commutative geometry atgeometry at string scales:string scales: a uniquely stringy effect ?a uniquely stringy effect ?

Beyond EFT?Beyond EFT?

::. Compatible with other tests constraining LMDR . Compatible with other tests constraining LMDR

Other consequences of the SMSTF:Other consequences of the SMSTF: CPT Violation (ill(ill--definition) definition) due to due to decoherence and unique effects (?) in and unique effects (?) in entangled states of of meson factories meson factories

Outlook:Outlook: NEED TO CONFIRM MAGIC effect by H.E.S.S. and other experiments, much more statistics needed (, much more statistics needed (GRBGRB’’ss;;))

further tests using High-Energy Neutrino astrophysics

N.E.M 0906.2712







Sub-luminal Refractive index in vacuo, No Birefringence


Beyond EFT? Beyond EFT? Time Delays of Astrophysical photonsTime Delays of Astrophysical photons::





N.E.M 0906.2712







Sub-luminal Refractive index in vacuo, No Birefringence


Beyond EFT?Beyond EFT?





N.E.M 0906.2712



MultiMulti--messenger observations of the Cosmosmessenger observations of the Cosmos

cosmic

accelerator

photons: Absorbed by dust & radiation field (CMB)

gammas ( z < 1 )

Us

neutrinos

neutrinos: Difficult to detect

⇒⇒⇒⇒ Three “astronomies” possible...

protons E>1019 eV ( 10 Mpc )

protons E<1019 eV

protons/nuclei: Deviated by magnetic fields,

Absorbed by radiation field (GZK)

DeNaurois 2008



VHE Experimental World TodayVHE Experimental World Today

STACEE

CACTUS

MILAGRO

TIBET ARRAY

ARGO-YBJ

PACT

GRAPES

TACTIC

MAGIC

HESS

CANGAROO

TIBETMILAGRO

STACEE

TACTIC

Canary Islands

M. MARTINEZ



The MAGIC Collaboration The MAGIC Collaboration

((MMajor ajor AAtmospheric tmospheric GGammaamma--ray ray IImagingmaging

CCherenkov Telescope )herenkov Telescope )

Observation of

Flares from AGN

Mk 501

Red-shift: z=0.034



The MAGIC ``EffectThe MAGIC ``Effect’’’’



SSC as explanation of the MAGIC EffectSSC as explanation of the MAGIC Effect

Classical SSC modelClassical SSC model: emission region moves along the jet with : emission region moves along the jet with

constant constant Lorentz factorsLorentz factors . In other AGN (e.g.; Crab Nebula), such . In other AGN (e.g.; Crab Nebula), such

factors are of order factors are of order 10 10 –– 2020 . However, to account for the . However, to account for the 4 4 ±± 1 1

minute delay minute delay observed observed in in MAGICMAGIC requires requires Lorentz factors four Lorentz factors four

orders of magnitude higher.orders of magnitude higher.

Modify SSC model :Modify SSC model : (i)(i) assume gradual acceleration of assume gradual acceleration of

relativistic electrons inside blob relativistic electrons inside blob (SSC I) (SSC I)

(ii)(ii) assume the assume the blob capturedblob captured in in inner inner part of the jet during its part of the jet during its

acceleration phase acceleration phase (SSC II)(SSC II) : : lowerlower--energy energy part of flare close to part of flare close to

basebase of the jet, lower Lorentz factor, of the jet, lower Lorentz factor, higherhigher--energenergy at y at larger larger

distancesdistances from jet base, higher Lorentz factor.from jet base, higher Lorentz factor.

TimeTime--delay in SSC II inversely proportional to delay in SSC II inversely proportional to γγ--ray ray EnergiesEnergies

SITUATION NON CONCLUSIVE:SITUATION NON CONCLUSIVE: DOES FLARE PHYSICS DEPEND ON DOES FLARE PHYSICS DEPEND ON

INDIVIDUAL FLARES INDIVIDUAL FLARES (SSC I)(SSC I) ? MATTER OF LUCK TO HAVE OBSERVED BLOB ? MATTER OF LUCK TO HAVE OBSERVED BLOB

IN ITS ACCELERATION PHASE IN Mk501 IN ITS ACCELERATION PHASE IN Mk501 (SSC II)(SSC II) ? ?



- electron accelerators:

synchrotron: e B -> e gamma

+ inverse Compton: e gamma -> gamma e

e- (TeV) Synchrotronγ (eV-keV)

γ (TeV) Inverse Comptonγ (eV)

B

leptonic acceleration

AGN High Energy Gamma Rays AGN High Energy Gamma Rays

log(E)lo

g(e

nerg

ydensity)

eV keV MeV GeV TeV

Sy IC



AGN HE AGN HE γγ: : HadronicHadronic accelerationacceleration

Alternative models for explaining high energy Gamma Rays from Alternative models for explaining high energy Gamma Rays from

AGN involve AGN involve hadronichadronic acceleration: acceleration: ππ00 →→ γγγγ



E2

dN

/dE

ln(E)

Stars

radio infrared visible light X-rays VHE γ-rays

CMB

Dust

CosmicElectron

AcceleratorsB↑Ee↓

Synchrotron Radiation Inverse Compton

rad

e

e UdE

d�×

2BdE

d�

e

e× B↑Ee↓

Cosmic Proton

Accelerators

density

Matter×

p

p

dE

d�

π0→γγSynchrotron Radiation of

Secondary Electrons

Electron or Electron or HadronHadron Accelerator?Accelerator?

DeNaurois 2008



VHE Experimental World TodayVHE Experimental World Today

STACEE

CACTUS

MILAGRO

TIBET ARRAY

ARGO-YBJ

PACT

GRAPES

TACTIC

MAGIC

HESS

CANGAROO

TIBETMILAGRO

STACEE

TACTIC

Canary Islands

M. MARTINEZ



H.E.S.S. (non) Observations of timeH.E.S.S. (non) Observations of time--lagslags

H.E.S.S. Telescopes array (Namibia) H.E.S.S. Telescopes array (Namibia)

1ST TELESCOPE (2002)

No appreciableNo appreciable

TimeTime--Lag claimed forLag claimed for

Photons fromPhotons from

AGN PKS 2155AGN PKS 2155--304304

At redAt red--shifts z=0.116shifts z=0.116

PRL 101,170402 (2008)



FERMI/GLAST ObservationsFERMI/GLAST Observations

Highest energy EmissionHighest energy Emission:

4.5 s time-lag between E > 100 MeV

and E < 100 KeV

Time-Lag (Delay) Measured for

high-energy Photons of 13 GeV:

∆t = 16.5 s

(Image courtesy NASA/Swift/Stefan (Image courtesy NASA/Swift/Stefan

ImmlerImmler) )



FERMI/GLAST ObservationsFERMI/GLAST Observations

Highest energy EmissionHighest energy Emission:

4.5 s time-lag between E > 100 MeV

and E < 100 KeV

Time-Lag (Delay) Measured for

high-energy Photons of 13 GeV:

∆t = 16.5 s Z = 4.2 Z = 4.2 ±± 0.30.3



New fundamental Physics InterpretationNew fundamental Physics Interpretation

Quantum Gravity as a Quantum Gravity as a

dispersive medium (spacedispersive medium (space--

time foam) , modified time foam) , modified

dispersion relations dispersion relations (MDR)(MDR) for for

matter, radiationmatter, radiation

Phenomenological Models of MDRPhenomenological Models of MDR

GonzalezGonzalez--MestresMestres, , AmelinoAmelino--CameliaCamelia, Ellis, NM, , Ellis, NM, NanopoulosNanopoulos, , SarkarSarkar

Stochastically fluctuating space time Stochastically fluctuating space time backgroundsbackgrounds

Ford, Yu , Ford, Yu , SarbenSarben SarkarSarkar, NM, NM::

String & String & BraneBrane--inspired Modelsinspired Models

Ellis, NM, Ellis, NM, NanopoulosNanopoulos, , SzaboSzabo, ,

Sakharov, Sakharov, FarakosFarakos, , MitsouMitsou, , ::

Loop Quantum Gravity (?)Loop Quantum Gravity (?)

GambiniGambini, , PullinPullin, , UrrutiaUrrutia, , ::

Deformed Special Relativity Models Deformed Special Relativity Models (unclear if there is a consistent quantum (unclear if there is a consistent quantum version)version)

AmelinoAmelino--CameliaCamelia, , MagueijoMagueijo, ,

SmolinSmolin, Kowalski, Kowalski-- GlikmanGlikman ::

Complex refractive indexComplex refractive index



QuantumQuantum--Gravity Induced Modified Dispersion for PhotonsGravity Induced Modified Dispersion for Photons

Modified dispersion due to QG induced spaceModified dispersion due to QG induced space--time (metric) time (metric)

distortions (c=1 units):distortions (c=1 units):



MAGIC QG scale Bounds (individual photon study, reproduction of MAGIC QG scale Bounds (individual photon study, reproduction of flare peak) flare peak)

LinearLinear QuadraticQuadratic

95% CL95% CL



n=1n=1

Ellis, NM, Nanopoulos



1

2

+0.19

-0.19

0.43

Ellis, NEM, Ellis, NEM, NanopoulosNanopoulos, PLBB674:83, PLBB674:83--86,200986,2009.



MDR for other matter probes MDR for other matter probes Massive Probes (e.g. electrons):

Constraints from Crab Nebula via Synchrotron RadiationJacobson, Jacobson, LiberattiLiberatti, Mattingly, , Mattingly,

Ellis, NM, SakharovEllis, NM, SakharovElectron 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)~ 1018 GeV that α > 1.74




Constraints from Crab Nebula via Synchrotron RadiationJacobson, Jacobson, LiberatiLiberati, Mattingly, , Mattingly,








WHAT ABOUT

PHOTONS & THE

MAGIC RESULT?



Birefringence Constraints on photons MDRBirefringence Constraints on photons MDR

If MDR for probes stem from Local Effective If MDR for probes stem from Local Effective LagrangiansLagrangians (LEL):(LEL):

MaccioneMaccione et al., arXive0707.2673et al., arXive0707.2673

Photons Photons :: Electrons:Electrons:

± signs indicate left/right movers and for

Circularly polarized photons imply rotation

of linear polarization angle (BIREFRINGENCE).

Difference in polarization angle

over cosmological distance d:

UV radiation from Galaxies: For

From GRB polarization

MyersMyers--

PospelovPospelov

QEDQED













From GRB polarization MAGIC EFFECT

due to QG ruled out ?

MyersMyers--

PospelovPospelov

QEDQED















MyersMyers--

PospelovPospelov

QEDQED



UltraUltra--highhigh--energy photonsenergy photonsGalaverniGalaverni & & SiglSigl

Severe constraints on LIVSevere constraints on LIV

Parameters from Parameters from absenceabsence of:of:

(i) Observations on UHE photons,(i) Observations on UHE photons,

which would evade pair productionwhich would evade pair production

due to threshold modifications if due to threshold modifications if

MDR hold:MDR hold:

X

(ii) Photon Decay(ii) Photon Decay

Allowed,Allowed,

above above

threshold threshold

if MDRif MDR



Avoid MDR but still have Time Delays?Avoid MDR but still have Time Delays?












MyersMyers--

PospelovPospelov

QEDQED



(1) Time Delays (1) Time Delays

proportional to Eproportional to E

(2) Stable Photons(2) Stable Photons

(3) No birefringence(3) No birefringence

(4) Beyond EFT(4) Beyond EFT



STRING/DSTRING/D--BRANE BASICSBRANE BASICS

String theory

type p-brane types allowed

HeteroticHeterotic Strings admit no Strings admit no pp--branesbranes




String theory






String theory



CompactifyCompactify toto

3 + 1 Large Dim3 + 1 Large Dim




String theory





Wrap up alongWrap up along

Three cyclesThree cycles

(``D(``D--particlesparticles’’’’))



A Stringy (type IA) Model of Space A Stringy (type IA) Model of Space --Time FoamTime Foam

Open strings on D3-brane world represent

electrically neutralelectrically neutral matter or radiation,

interacting via splitting/capture with D-particles

(electric charge conservation) (electric charge conservation) ..

DD--particle foam medium particle foam medium transparent transparent to (charged)to (charged)

Electrons no modified dispersion for themElectrons no modified dispersion for them

Ellis, NM, Ellis, NM, WestmuckettWestmuckett

Photons or electrically neutral probes

feel the effects of D-particle foam

Modified Dispersion for themModified Dispersion for them::..

Orientifold planes, stacks of D8 branes














NONNON--UNIVERSAL ACTION OF UNIVERSAL ACTION OF

DD--PARTICLE FOAM ON MATTER PARTICLE FOAM ON MATTER

& RADIATION& RADIATION




Stringy Uncertainties & the Capture ProcessStringy Uncertainties & the Capture Process

During Capture:During Capture: intermediate

String stretchingstretching between

D-particle and D3-brane is

Created. It acquires N internalN internal

OscillatorOscillator excitations &

Grows in size & oscillatesGrows in size & oscillates from

Zero to a maximum length by

absorbing incident photonincident photon

Energy pp0 0 ::

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 DELAYTIME DELAY (causality)(causality) during

Capture: DELAY IS INDEPENDENT OF

PHOTON POLARIZATION, HENCE

NO BIREFRINGENCENO BIREFRINGENCE:.

Ellis, NM, Ellis, NM, NanopoulosNanopoulos arXiv:0804.3566arXiv:0804.3566



Stringy Uncertainties & the MAGIC EffectStringy Uncertainties & the MAGIC Effect

DD--foam: transparent to electronsfoam: transparent to electrons

DD--foam captures photons & refoam captures photons & re--emits thememits them

Time Delay (Causal) in Time Delay (Causal) in each each Capture: Capture:

Independent of photon polarization Independent of photon polarization (no Birefringence(no Birefringence))

Total DelayTotal Delay from emission of photonsfrom emission of photons

till observation over till observation over a distance Da distance D (assume n(assume n* * defectsdefects

per string length): per string length):

REPRODUCE 4REPRODUCE 4±±1 MINUTE DELAY OF MAGIC from Mk501 (1 MINUTE DELAY OF MAGIC from Mk501 (redshiftredshift z=0.034)z=0.034)

For For n* n* =O(1) & M=O(1) & Mss ~ 10~ 101818 GeVGeV, consistently with Crab Nebula & other , consistently with Crab Nebula & other

Astrophysical constraints on modified dispersion relationsAstrophysical constraints on modified dispersion relations::::

Effectively modifiedEffectively modified

Dispersion relationDispersion relation

for photons due to for photons due to

induced metricinduced metric

distortion Gdistortion G0i 0i ~ p~ p00



















COMPATIBLE WITH STRI�G U�CERTAI�TY COMPATIBLE WITH STRI�G U�CERTAI�TY

PRI�CIPLES:PRI�CIPLES:

∆∆t t ∆∆x x ≥≥ αα’’ , , ∆∆p p ∆∆x x ≥≥ 1 + 1 + αα’’ ((∆∆p )p )22 + + ……

((αα’’ = = ReggeRegge slope = Square of minimum string length scale)slope = Square of minimum string length scale)



Induced (Induced (FinslerFinsler--type) Nontype) Non--CommutativityCommutativity

DD--particle recoilparticle recoil σσ--model deformationmodel deformation

Written as worldWritten as world--sheet sheet

Bulk operatorBulk operator

(Stokes theorem)(Stokes theorem)

Open strings in `èlectricOpen strings in `èlectric’’’’ field background , provided here by recoil velocity field background , provided here by recoil velocity uuii

Statistically averaged << ui >> over

D-particle populations, might lead to

Uniform èlectric field’ backgrounds

NEM, arXive:0906.2712



Induced (Induced (FinslerFinsler--type) Nontype) Non--CommutativityCommutativity (N.C.) (N.C.)

NEM, arXive:0906.2712Mixed Mixed BoundaryBoundary ConditionsConditions

Neumann Dirichlet

WorldWorld--sheet 1sheet 1stst quantization leads to N.C. (induced by recoil here)quantization leads to N.C. (induced by recoil here)

Seiberg-Witten

Seiberg, Susskind, Toumbas

But of But of FinslerFinsler typetype

(i.e. momentum dependent)(i.e. momentum dependent)



NonNon--commutative effective field theories & CPTcommutative effective field theories & CPT

CPT invariant SME type field theory (Q.E.D. ) CPT invariant SME type field theory (Q.E.D. ) -- only only even number of indices appear in effective noneven number of indices appear in effective non--renormalisablerenormalisable terms.terms. (Carroll et al. hep(Carroll et al. hep--th/0105082)th/0105082)



Induced (Induced (FinslerFinsler) Space) Space--Time MetricTime Metric

WorldWorld--Sheet Propagator in the presence of recoil backgroundSheet Propagator in the presence of recoil background

Implies Implies FinslerFinsler--type targettype target--space metricspace metric

and effective string couplingand effective string coupling



















COMPATIBLE WITH STRI�G U�CERTAI�TY COMPATIBLE WITH STRI�G U�CERTAI�TY

PRI�CIPLES:PRI�CIPLES:

∆∆t t ∆∆x x ≥≥ αα’’ , , ∆∆p p ∆∆x x ≥≥ 1 + 1 + αα’’ ((∆∆p )p )22 + + ……

((αα’’ = = ReggeRegge slope = Square of minimum string length scale)slope = Square of minimum string length scale)



CPT may be Violated in DCPT may be Violated in D--particle particle

Foam models but only through Foam models but only through

TargetTarget--space effective space effective

(low(low--energy) energy) DecoherenceDecoherence, ,

induced by quantum fluctuations induced by quantum fluctuations

of recoil velocity, and hence of recoil velocity, and hence

of induced metric and N.C.of induced metric and N.C.

DecoherenceDecoherence--inducedinduced

IllIll--defined (Effective)defined (Effective)

CPT Operator (Wald 1979) CPT Operator (Wald 1979)

10-35 m



String theory




Wrap up alongWrap up along

Three cyclesThree cycles

(``D(``D--particlesparticles’’’’))

Type IIB String Model of DType IIB String Model of D--particle Foamparticle FoamT.LiT.Li, NM, , NM, NanopoulosNanopoulos, D. , D. XieXie



Type IIB String Model of DType IIB String Model of D--particle Foamparticle FoamT.LiT.Li, NM, , NM, NanopoulosNanopoulos, D. , D. XieXie

D7 Brane compactified

D3−branes wrapped up along 3 cycles(‘‘D−particles’’)

BULK

Consider FourConsider Four--point point VenezianoVeneziano

Amplitude for scattering of two open Amplitude for scattering of two open

string states to two open string string states to two open string

states in the Dstates in the D--particle/D3particle/D3--branes branes

backgroundsbackgrounds

Antoniadis, Benakli, Laugier



Type IIB String Model of DType IIB String Model of D--particle Foamparticle Foam

T.LiT.Li, NM, , NM, NanopoulosNanopoulos, D. , D. XieXie

Couplings of ND Couplings of ND stringsStretchedstringsStretched

between D3 and D7 between D3 and D7 branesbranes

(Capture process)(Capture process)

DD--Foam:Foam: Uniform Distribution Uniform Distribution

of Dof D--particles in space with particles in space with

VVA3A3 = their average 3D= their average 3D--volumevolume,,

RR’’ = radius of forth space dim= radius of forth space dim

transverse to D3 transverse to D3 branesbranes..

Avoid tachyon condensationAvoid tachyon condensation::

D3 D3 branesbranes have widths 1.55 have widths 1.55 sl



CAUSAL TIME DELAYS CAUSAL TIME DELAYS

First approx: ignoreFirst approx: ignore

DD--particle recoilparticle recoil



Mandelstam variables



Time delays arise by consideringTime delays arise by considering

Backward scattering u=0.Backward scattering u=0.

Seiberg,Susskind

Toumbas





For For masslessmassless particles particles

u + t + s =0u + t + s =0





For For masslessmassless particles particles

u + t + s =0u + t + s =0

IndependentIndependent

of photon polarizationof photon polarization

NO BIREFRINGENCENO BIREFRINGENCE



OTHER PARTICLES OTHER PARTICLES

Backward scattering u=0 impliesBackward scattering u=0 implies

JUST POLE TERMSJUST POLE TERMS::

NO TIME DELAY AT LEADING ORDER in NO TIME DELAY AT LEADING ORDER in ηη



At order At order ηη, there are time delays, there are time delays::



INCLUDE DINCLUDE D--PARTICLE RECOILPARTICLE RECOIL

Inclusion of DInclusion of D--particle recoil, leads to an particle recoil, leads to an

effective ``electriceffective ``electric’’’’ field background,field background,

Affects Time delays as follows:Affects Time delays as follows:

But also replaces string couplingBut also replaces string coupling

And thus string scattering amplitudes And thus string scattering amplitudes



INCLUDE DINCLUDE D--PARTICLE RECOILPARTICLE RECOIL

Inclusion of DInclusion of D--particle recoil, leads to an particle recoil, leads to an

effective ``electriceffective ``electric’’’’ field background,field background,

Affects Time delays as follows:Affects Time delays as follows:

But also replaces string couplingBut also replaces string coupling

And thus string scattering amplitudes And thus string scattering amplitudes

Thus DThus D--particle/string scattering particle/string scattering

suppressed suppressed for relativistic situations for relativistic situations

where Dwhere D--particle recoil velocity approaches 1, particle recoil velocity approaches 1,

i.e. momentum transfer approaches Mi.e. momentum transfer approaches Mss//ggss

Important for discriminatingImportant for discriminating

Low (Low (TeVTeV) from High) from High--string string

scale Phenomenology via scale Phenomenology via

such Dsuch D--foam models, foam models,

using UHE cosmic photonsusing UHE cosmic photons



Conclusions so farConclusions so far;;

MAGIC, FERMI MAGIC, FERMI ;; (?) observations indicate that high energy (?) observations indicate that high energy photons arrive later than lowerphotons arrive later than lower--energy onesenergy ones;; H.E.S.S . compatibleH.E.S.S . compatible

Source Effect or Propagation in Quantum Gravity Medium? Source Effect or Propagation in Quantum Gravity Medium?

There is a (unique?) string model of DThere is a (unique?) string model of D--particle spaceparticle space--time foam time foam reproducing the effect, using reproducing the effect, using time delays proportional to photon time delays proportional to photon energyenergy (or MDR with linear QG scale suppression), consistent with (or MDR with linear QG scale suppression), consistent with all other tests of Lorentz invariance.all other tests of Lorentz invariance. No birefringence, No birefringence,

ΕΕffectffect Beyond Local EFT! (stringy uncertainties, intermediate string)Beyond Local EFT! (stringy uncertainties, intermediate string)

Very important:Very important: Improve on statistics Improve on statistics ;; Find other flares, Find other flares, GRBsGRBsand check the energy dependence of photon arrival times: and check the energy dependence of photon arrival times: Very Very High Energy High Energy γγ--ray Astronomy very exciting prospects for the ray Astronomy very exciting prospects for the near futurenear future::

Also Also high energy Neutrino Astrophysicshigh energy Neutrino Astrophysics may provide may provide complementary test of such fundamentally new physicscomplementary test of such fundamentally new physics;;



Other Consequences of DOther Consequences of D--particle Foamparticle Foam

LowLow--energy CPT Violation & energy CPT Violation & DecoherenceDecoherencefrom stochastic fluctuations of Dfrom stochastic fluctuations of D--particle defects: particle defects: Capture/reCapture/re--emission process for neutral probes implies emission process for neutral probes implies recoil of Drecoil of D--particle defect, particle defect, momentummomentum--directiondirection--dependent induced metricsdependent induced metrics GG0i 0i ~ ~ ∆∆kkii ~ ~ kkii ~ p~ p00

(Logarithmic Conformal Field Theory of (Logarithmic Conformal Field Theory of recoil/capture on worldrecoil/capture on world--sheet of string model) sheet of string model)

Kogan,NM,Wheater,SzaboKogan,NM,Wheater,Szabo, Ellis, , Ellis, NanopoulosNanopoulos

CPT Operator CPT Operator illill--defineddefined, , unique unique consequences in consequences in modifications of EPRmodifications of EPR correlations of entangled correlations of entangled states of neutral mesons in meson factories (states of neutral mesons in meson factories (ΦΦ--, B, B--factories) factories) BernabeuBernabeu, NM, , NM, Papavassiliou,NebotPapavassiliou,Nebot, Alvarez, , Alvarez, SarbenSarben SarkarSarkar

Estimates of such DEstimates of such D--particle foam effects in neutral mesons complicated particle foam effects in neutral mesons complicated

due to strong QCD effects present in such composite neutral partdue to strong QCD effects present in such composite neutral particles icles




If CPT Operator If CPT Operator wellwell--defined as operatordefined as operator, even if CPT , even if CPT

is broken in the Hamiltonianis broken in the Hamiltonian:: (e.g. Lorentz violating (e.g. Lorentz violating

models)models)

ΦΦKSKL KSKL



EPR Modifications & DEPR Modifications & D--particle Foamparticle Foam

If CPT Operator If CPT Operator illill--defineddefined, , unique unique consequences in consequences in

modifications of EPRmodifications of EPR correlations of entangled correlations of entangled

states of neutral mesons in meson factories (states of neutral mesons in meson factories (ΦΦ--, B, B--

factories) factories) BernabeuBernabeu, NM, , NM, Papavassiliou,NebotPapavassiliou,Nebot, Alvarez, , Alvarez, SarbenSarben SarkarSarkar

Induced metric due to capture/recoil, stochastic fluctuations, Induced metric due to capture/recoil, stochastic fluctuations, DecoherenceDecoherence

ΦΦKSKL KSKL

IF CPT ILLIF CPT ILL--DEFINED DEFINED

(e.g. D(e.g. D--particle Foam)particle Foam)

KSKL



EPR Modifications & DEPR Modifications & D--particle Foamparticle Foam

CPT Operator CPT Operator illill--defineddefined, , unique unique consequences in consequences in

modifications of EPRmodifications of EPR correlations of entangled correlations of entangled

states of neutral mesons in meson factories (states of neutral mesons in meson factories (ΦΦ--, B, B--

factories) factories) BernabeuBernabeu, NM, , NM, Papavassiliou,NebotPapavassiliou,Nebot, Alvarez, , Alvarez, SarbenSarben SarkarSarkar

Induced metric due to capture/recoil, stochastic fluctuations, Induced metric due to capture/recoil, stochastic fluctuations, DecoherenceDecoherence



ΦΦKSKL KSKL

KKSSKKSS , ,

KKLLKKLL

KKSSKKSS , ,

KKLLKKLL

KSKL

IF CPT ILLIF CPT ILL--DEFINED (e.g. flavour DEFINED (e.g. flavour

violating (FV) Dviolating (FV) D--particle Foam)particle Foam)



If QCD effects, subIf QCD effects, sub--structure in neutral mesons ignored, and Dstructure in neutral mesons ignored, and D--foam actsfoam acts

as if they were as if they were structurelessstructureless particles, then for particles, then for MMQG QG ~ 10~ 101818 GeVGeV (MAGIC) (MAGIC)

the estimate for the estimate for ωω: : | | ωω | | ~ 10~ 10--4 4 ||ζζ|, for 1 > |, for 1 > ||ζζ| > 10| > 10--22 (natural)(natural)

Not far from sensitivity of upgraded meson factories ( e.g. DAFNNot far from sensitivity of upgraded meson factories ( e.g. DAFNE2)E2)

ΦΦ KSKL

KKSSKKSS , ,

KKLLKKLL

KKSSKKSS , ,

KKLLKKLL

IF CPT ILLIF CPT ILL--DEFINED (e.g. flavour DEFINED (e.g. flavour

violating (FV) Dviolating (FV) D--particle Foam)particle Foam)

KSKL

Neutral mesons Neutral mesons nono longer longer indistinguishableindistinguishable particles, particles,

initial entangled stateinitial entangled state: :







ΦΦ KSKL

KKSSKKSS , ,

KKLLKKLL

KKSSKKSS , ,

KKLLKKLL


(e.g. FV D(e.g. FV D--particle Foam)particle Foam)

KSKL









ΦΦ KSKL

KKSSKKSS , ,

KKLLKKLL

KKSSKKSS , ,

KKLLKKLL



KSKL



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