Neutrinos from Neutrinos from Gamma-Ray Bursts Gamma-Ray Bursts

Sarira SahuICN, UNAM

APCTP Focus Program on Recent Developments in Neutrino Physics and APCTP Focus Program on Recent Developments in Neutrino Physics and Astroparticle PhysicsAstroparticle Physics

June 15­25, Pohang, South Korea  June 15­25, Pohang, South Korea  

  (In memory of Prof. Benjamin W. Lee)(In memory of Prof. Benjamin W. Lee)

Neutrino Energy in the Neutrino Energy in the rangerange

        MeV < E < Few GeVMeV < E < Few GeV

                                                                           

➔Introduction to Physics of Gamma­Ray Burst Introduction to Physics of Gamma­Ray Burst (GRB)(GRB)➔Why to look for neutrinos ?Why to look for neutrinos ?➔High temperature and/or Density matter (Plasma)High temperature and/or Density matter (Plasma)➔Particle Propagation in a Heat Bath  (Low energy)Particle Propagation in a Heat Bath  (Low energy)➔        Neutrino Propagation in a medium  with B=0Neutrino Propagation in a medium  with B=0➔        Application to GRB FireballApplication to GRB Fireball➔        Neutrino Propagation in a medium with Neutrino Propagation in a medium with ➔        Application to GRB FireballApplication to GRB Fireball

B≠0

➔High Energy Neutrinos propagation in a mediumHigh Energy Neutrinos propagation in a medium➔      With no Magnetic field in the background (B=0)With no Magnetic field in the background (B=0)➔        With Magnetic Field in the backgroundWith Magnetic Field in the background➔        Application to Physics of magnetar and GRB   Application to Physics of magnetar and GRB   PhysicsPhysics➔    Multi­GeV Neutrinos From GRBsMulti­GeV Neutrinos From GRBs➔    SummarySummary

Physics of Gamma-Ray Bursts & fireball Model                         

                                                                                              

Physics of Gamma­Ray Physics of Gamma­Ray Bursts & Fireball ModelBursts & Fireball Model

What are GRBs ?What are GRBs ?

These are flashes of non­thermal bursts of low energy (~100 KeV­1 MeV) photons.Release about                         erg in few seconds, making them the most luminous object in the Universe.They occur at cosmological distance,     homogeneous distribution in the sky.

1051 −1055

T. Piran, 1999, 2000, Zhang, Meszaros, 2003

The burst duration ranges from several micro seconds toseveral hundred seconds with complicated and irregular structure.

No two grbs are the same. Some are short, some are long, some are weak, some are strong, some have many spikes, some have none, each unlike the other one.

Spectrum

Non­thermalPower­LawN(E) dE ∝ E−

≃ 2

Fluence: F=      ∫ flux. dt

Type of GRBsType of GRBs

Short - Hard (Short - Hard (≤ 2 sec) about 25%≤ 2 sec) about 25%Long - Soft (> 2 sec) 75%Long - Soft (> 2 sec) 75%Long GRBs are produced due to core col-lapse of massive stars (Hypernovae)Probably coalescence of compact bia-naries are responsible for the short-hard bursts (observation of afterglow from GRBs 050709, 050709b, 050724)/MagnetarsMeszaroes 2006, Zhang & meszaroes 2003

What are Fireballs ?What are Fireballs ?Sudden release of copious amount of Gamma-Rays into a compact region with a size ~100-1000 Km creates an opaque fireball due to pair creation.

The optical depth is very high ( ) so photons can not escape freely.

The fireball expands relativistically with a Lorentz Factor ~100 – 1000 under its own pressure and cools adiabatically. The radiation emerges freely to ISM when optical depth is ≈ 1.

e e−

≃1013

Irrespective of the nature of the Irrespective of the nature of the progenitorprogenitor

Gamma-Ray emission due to collision of Gamma-Ray emission due to collision of internal shocks (shells); relativistic outinternal shocks (shells); relativistic out--flow from the source ?flow from the source ?TheThe Fireball Model Fireball Model explains the explains the

temporal structure of the bursts and non-temporal structure of the bursts and non-thermal spectral behavior.thermal spectral behavior.Expanding fireball runs into the surroundExpanding fireball runs into the surround­­ing ISM  to give afterglow.ing ISM  to give afterglow.

EeV neutrinos from external shocks

(Waxman & Bahcall 2000)(Dermer 2002)

(KM 2007)

PeV neutrinos from internal shocks

HL GRBs (Waxman & Bahcall 1997)

LL GRBs(KM et al. 2006)

(Gupta & Zhang 2006)

MeV neutrinosat collapse

TeV neutrinosfrom inside the star

(Meszaros & Waxman 2001)(Schneider et al. 02)

( Razzaque et al. 2003)(Fabio, KM, et al. 07)

Meszaros (2001)

PeV­EeV neutrinos from flares

(KM &Nagataki 2006)

High Density/Temperature PlasmaHigh Density/Temperature PlasmaEarly UniverseEarly UniverseNeutron StarNeutron StarGRB FireballGRB FireballAccretion Disk................Accretion Disk................Modified Particle PropertiesModified Particle Propertiesin the medium; new phenomenain the medium; new phenomena

●Effect of Heat bath on particle properties Effect of Heat bath on particle properties 

●Massive Photon (Plasmon)Massive Photon (Plasmon)●Cherenkov radiation (Refractive Index > 1)Cherenkov radiation (Refractive Index > 1)●Plasmon decay (                    )Plasmon decay (                    )●Massless neutrino acquires an effective massMassless neutrino acquires an effective mass●MSW effect of neutrinos ­­­ flavor conversionMSW effect of neutrinos ­­­ flavor conversionModification of dispersion relation in the Modification of dispersion relation in the medium with and without magnetic field.medium with and without magnetic field.

p2−m2≠0

L

Neutrino Propagation in Neutrino Propagation in a Medium without a Medium without 

Magnetic fieldMagnetic field

Effective Potential of a Neutrino in the medium      

 

     Constituent of the medium Forward Scattering Amplitude Same as considering the Real Part of the Neutrino Self-Energy Imaginary part corresponds to the Damping

DependsDepends

To calculate the self­energyTo calculate the self­energy

Thermal Field Theory has to be usedThermal Field Theory has to be usedReal Time Finite Temperature Field TheoryReal Time Finite Temperature Field Theory    Imaginary Time Formalism  Imaginary Time Formalism      Thermo Field DynamicsThermo Field DynamicsAll the calculations are done using All the calculations are done using the medium at restthe medium at restThe Feynman diagrams which will contribute to the neutrino self­energy are (Real Part Only) (Real Part Only)Kapusta 93, Niemi 84, Weldon 83, Nieves 93

To drder 1/M^4 (M-Vector Boson Mass) correction to the neutrino self energy in a medium.

−i W k =g2

2R∫ d 4 p

24[ S e p D

q]L

−i Z=−ig2cosW

C V

−C A

5 i Dq=0

× ∫ d 4 p

24−1Tr [

−ig2cosW

CV

f−C A

f5 i SF p]

Wolfenstein 79, Pal 89, Bravo 07, Notzold 88  

− =akbu , ℜ=R L u=1,0

det 1akbu=0

−∣k∣=−b

V eff=−b

V e≃2GF N [

122sin2W Le

12−2sin2W L p−

12

Ln2 LeL

L−1

12cos2W

74T3M W

2

]

La=N a−N a

N

V=V e−V

=2GF N [ LeL e−L

−7 4 3

2

T 2

M W2 ]

In the Early Universe, For electron neutrino goes to muon neutrino the potential is 

V=V e−V

=2GF N [Le−743

2 T 2

M W2 ]

In the charge neutral GRB fireball

If the asymmetry                 in the Early Universe then it is exactly same as the GRB fireball

Le=L

For anti­neutrinos            will be replaced by ­   LaLa

Bravo 07,  Sahu 05

Mimic Early Universe

Neutrino Oscillation in GRB FireballNeutrino Oscillation in GRB Fireball

Sources for the MeV neutrinos:Neutrinos of about 5­20 MeV are generated due to the stellar   collapse or merger event that trigger the burst. Nucleon bremsstrahlung,    

                    In the Fireball,                         

All have energy in the  MeV range.Some of  these neutrinos will propagate through the fireball.

And

NN NN

e e−

pe− ne

Kumar 99, Janka 99

MeV MeV neutrinoneutrinoss

at collapseat collapse

NN NN

e e

−

pe− n e

EeV neutrinos from external shocks

(Waxman & Bahcall 2000)(Dermer 2002)

(KM 2007)

MeV neutrinosat collapse

Meszaros (2001)

PeV­EeV neutrinos from flares

(KM &Nagataki 2006)

Multi­GeV

Neutrino oscillations:Neutrino oscillations:In a relativistic and non degenerate  plasma, the effective potential experience by a electron neutrino is 

e e−

By a muon neutrino

V e≃ 2 GF N Le−7

[4 ] [3 ]

2 T 2

MW2 . V

,≃ 2 GF N L

, .

Oscillation processesOscillation processes

e , , e s , , s

Baryon Load in the fireball:

Computer simulation suggests baryon loadhas to be very small (outstanding problem)

~ 10−8 M ⊙ − 10−5 M ⊙

Otherwise the expansion is Newtonian & NO  GRBFireball has to expand relativistically !!!Consistent with the OBSERVATION.

Piran 99

V ≃ 1.02×10−12 T MeV3 [± Le− 6.14 ×10−9 T MeV

2 ] MeV. ± ,

P t =

2 sin2 2

2 sin2 t

2 . =m2

2 E

= V−cos 2 2

2 sin2 2           is the neutrino energy ( 5­20 MeV), ө is the mixing angleE

Neutrino potential:

Probability of conversion after a time t

Resonance condition

V = cos2

Le 6.14×10−9 T MeV2

Lres ≃ 2 48EMeV

m2 sin 2cm

T MeV5

0.2×108 m2 cos 2 EMeV

M baryon ~ 2.23×10−4 R73 T MeV

3 Le M⊙

At resonance:

We assume:

Assumptions 

The fireball is spherical with radius  R~100­1000 KM

It is charge neutral   &  having equal number of protons and neutrons.

T.Piran, Phys. Rep. 314,575 (1999)

Derishev et al., A&A 345, L51 (1999); APJ 521, 640 (1999) 

Solar neutrinos:

SNO  +  KamLAND (reactor)     SNO Collaboration, PRL 92, 181301 (2004)     KamLAND Collaboration, hep­ex/0406035

6×10−5 eV 2 m2

10−4 eV2 0.8 sin2 0.98, 

Best fit is at

m2~ 7.1 × 10−5 eV 2, sin2 ~ 0.83

Le ≃0.5 × 10−5 T MeV−3 EMeV

−1 ,

M baryon ~ 0.23×10−9 R73 M⊙ M baryon ~ 0.58×10−10 R7

3 M ⊙

Lres ~ 211Km L res ~ 845 Km

EMeV = 5 EMeV = 20

T MeV 2.8

Probably  very few or NO resonant oscillations take place within the fireball and most of the neutrinos will come out.

Atmospheric Neutrinos:

Super­Kamiokande:     SK Collaboration, PRL 93, 101801 (2004)

1.9 ×10−3 eV 2 m2

3.0 ×10−3 eV20.9 sin2 2 1.0, 

We take Average Value

m2~ 2.5 × 10−3 eV 2 , sin2 2 ~ 0.9

Le ≃0.98 × 10−4 T MeV−3 E MeV

−1

M baryon ~ 0.44×10−8 R73 M⊙ M baryon ~ 0.11×10−8 R7

3 M⊙Lres ~ 5 Km Lres ~ 21 Km

EMeV = 5EMeV = 20

T MeV 5gives

Neutrinos can have many resonant oscillations within the fireball.

Reactor Neutrinos:Liquid Scintillator Neutrino Detector (LSND) & KARMEN 2, combined Analysis:     Phys. Rev D66, 013001 (2002)

0.45 eV 2 m2

1 eV 2 , 2×10−3 sin2 2 7×10−3

 

We consider

m2~ 0.5 eV 2 , sin 2 ~ 0.07

M baryon ~ 0.3×10−5 R73 M⊙

M baryon ~ 0.7×10−6 R73 M⊙Lres 1 Km

Lres 1.4 Km

EMeV = 5 EMeV = 20

T MeV 18

Neutrinos will oscillate several times before coming out of the fireball.                 Sahu 05

Gives

Neutrino oscillation is possible

If.....Neutrino mass square difference & mixing angle are in the

Atmospheric  and/or Reactor expt. ranges

for  SOLARMay be just............

Is it possible to detect these               neutrinos....

Unfortunately not with the present generation detectors.........Similar to SN1987A burst but  very very far, flux is very small

GRB NeutrinosGRB NeutrinosPart­IIPart­II

Neutrino Propagation in Neutrino Propagation in a Medium with Magnetic a Medium with Magnetic 

fieldfield

Magnetic Field in the Jet Outflow

It is believed that non-thermal emission is due to synchrotron emission/inverse Compton scattering. For synchrotron emission strong magnetic field is required. There is no way to estimate the magnetic field from the first principle.

Large magnetic field is expected if the progenitor is highly magnetized. Also amplification of small field due to turbulent dynamo mechanism, compression or shearing.

Decrease of Magnetic field due to expansion at larger radii.

Magnetic Field in .......Recently it has been suggested that,

emission in GRBs cab be explained through Compton-drag process and no magnetic field is needed (APJ 529, 2000; APJ 511, 1999, APJ 491, L15, 1997)

Despite all these, there is no satisfactory explanation for the existence of strong field.

We use Magnetic field as a parameter here.

Neutrino in the presence of a Magnetic fieldNeutrino in the presence of a Magnetic field

Calculation of neutrino-self energy in the presence of a magnetic field to order 1/M^4_W

−i W k =∫ d 4 p

24−ig

2 L i S l p

−ig

2 L i W q

¿

−i T k =−g

2cosW

2

R i Z 0∫ d 4 p

24Tr [ cVc A5 i S l p ]

−i Z k =∫ d 4 p

24

−ig

2cosW

2

L i S l p L i Z q

Elizalde 02, Erdas 98, Bravo 08

k =R a ∥ k ∥a ⊥ k ⊥

bu

c b L

u=1,0 b

=0, b

S l p=S l0 pS l

p

iS l0 p=∫0

∞

e p , sG p , sds

S l p=i p.u∫

−∞

∞

e p , s G p , sds

p , s=i s p ∥2 −ml

2−tan z

zp ⊥2

p ∥2= p0

2− p3

2 p ⊥2= p1

2 p2

2 z=eBsSchwinger 51

G p , s=sec2 z [ Ai B5m l cos2 z−i 3sin z cos z ]

A= p−sin2 z p.u u− p.b b

3=5

bu

B=sin z cos z p.u b− p.bu

W q=−1

q2−M W2 [ g−

1

M W2 qq

ie2

F ]2ieF

q2−M W22

−1

q2−M W2 /

1

M W2 qq

ie2

F

               W q=

g

M W2 1

q2

M W2 −

qq

M W4

3 ie F

2M W4 q2≪M W

2 ,=0

In the unitary gauge and low momentum limit

V eff=b−c cosa ∥ −a ⊥ ∣k∣sin2

The       is the angle between the magnetic field and the momentum of the neutrino

b=g 2 N l− N l

2 M W2 2cV

2 ml2

2 M W2

g 2 eB

2 M W2 N l

2− N l

2

g 2

2 M W2 [N l

− N l−

22

k 2

M Z2 ⟨El

B⟩N l

⟨E l

B⟩ N l

]

−g2 eB

M W2 ∫2

∞ dp 2

2 2∑n=2

∞

∑=±2

[k 2

E l , n

p22

ml2

2 ,2

n , 2k 2 E l , n] f l , nf l ,n

Garcia 08

c=g 2N l

0− N l

0

4M W2

1−c Aml2

2M W2

g 2eB

4M W4N l− N l

−g2 eB

M W4 ∫0

∞ dp322

∑n=0

∞

∑=±1

[k 0 E l ,n−ml2

E l , n

,1n ,0

k 3 p32

E l ,n

] f l , nf l , n

a ⊥ =−g 2eB

M W4 ∫0

∞ dp32

2∑n=0

∞

∑=±1

H2E l , n

m l2

E l ,n

f l , n f l , n

g 2

4M W2 [ k 3N l

0− N l0k 0 N l− N lN l

− N l23 ⟨E l

B ⟩ N l⟨E l

B ⟩ N l ]

H=eB 2n1−

a ∥ =−g 2 eB

M W4 ∫0

∞ dp32

2∑n=0

∞

∑=±1

m l2

E l ,n

f l ,nf l ,n

g 2

4M W2 [ k 3N l

0− N l

0k 0 N l− N lN l

− N l23 ⟨E l

B⟩ N l

⟨E l

B⟩ N l

]

●If neutrino is moving along the magnetic field ●If  the magnetic field is very strong, only lowest Landau levels are filled n=0●If the magnetic field is very weak 

a ∥ −a ⊥ sin2=0

V eff ≃b−c

Self­Energy of the neutrino in a medium in the presence of a classical uniform Magnetic field calculated.

The calculation is carried out in the unitary gauge, where unphysical Higgs Contributions does not appear.

Magnetic field is Weak compared to the W­Boson mass only,  but not for electron mass. 

For B­­>0 limit our results matches with the result in a matter background.

Neutrino oscillation in the magnetized GRB fireball Neutrino oscillation in the magnetized GRB fireball arXiv:0904.0138 With Nissim Fraija and Y. Y. Keum

In the presence of a magnetic field (weak)In the presence of a magnetic field (weak)

V =b−c cos Is the angle between K and B and for 

phi=0 we have

V = 2GFm3

2 [ 1− 2−

4

2

mM W

2 E

m 3− 4 ]

N e0− N e

0=

m3

2

BBc∑ l=0

∞

−1l sinh K 1 =m3

2 1

N e− N e=m3

2

BBc∑ l=0

∞

−1l sinh [ 2 K 2 −BBc

K 1 ]= m3

2 1

Nissim 09

3=∑ l=0

∞

−1l cosh [ 3 2−14

BBc

K 0 16 2 K 1

]

4=∑ l=0

∞

−1l cosh1 2 [ K 0

2

K 1

]

= l1 ;= m l1

The Resonance condition is The Resonance condition is 

1− 2−3.196×10−11 E MeV 3− 4=2.26

m2

E MeV

cos 2

m2≃7.1×10−5eV 2 ; sin22≃0.69B/Bc = 0.1

5 MeV

10

20

30

L_e ~5 x10^{­8}­­2x 10^{­7}L_{res} ~ 210­842kmM_b ~10^{­10} M_sun­­­10^{­8} Msun

SNOSNO

Le≃7×10−7−−2×10−7

5­20 MeV5­20 MeV

Lres≃5.2km−−21 km

M b≃4.24×10−9−−4.54×10−8

5 MeV5 MeV

10 MeV10 MeV

m2~2.5×10−3 eV 2 ; sin22~0.9

Super­KamioKande Super­KamioKande 

  

5 MeV5 MeV

10 MeV10 MeV

Le≃3.28×10−6−−4.77×10−4

Lres≃0.4 km−1.4 km

M b≃ .3210−7M sun−−2.87×10−6 M sun

m2~0.5 eV 2 ; sin22~0.0049LSNDLSND

W

With Super­K and LSND Neutrino parametersResonant Oscillation is PossibleWith SNO (Solar)  ­­­­May be just so 

The Magnetic field effect changes the Lepton Asymmetry and the Baryon Load of the fireball

Effective Potential for Highly relativistic Effective Potential for Highly relativistic neutrinos in a weakly magnetized neutrinos in a weakly magnetized

medium and their oscillationmedium and their oscillation

EPJ­C 58, 608 (2008) with W­Y. P. Hwang

We  have  calculated  the  effective  potential  experienced  by  highly  relativistic neutrinos  in  a weakly magnetized  electron­positron plasma, where momentum dependence finite width correction to the W­propagator is considered to account for  the  threshold  effect.  Magnetars  are  believed  to  be  sources  of  TeV­PeV neutrinos which are produced due to photomeson and proton proton interaction in their atmosphere.We have studied the resonant oscillation process 

of the highly relativisticneutrinos in SGR 1806­20 atmosphere which is a magnetar. It is shown that, for high  energy  neutrinos  propagating  within  the  magnetar  atmosphere,  the resonance condition can never be satisfied. On the other hand if GeV neutrinos are  produced  deep  inside  the  magnetar  atmosphere,  where  the  temperature  is about 50 keV or more, then these neutrinos can undergo resonant oscillation.

e ,

The coherent forward scattering of low energy neutrinos in The coherent forward scattering of low energy neutrinos in a medium give the matter potentiala medium give the matter potential

V e=2GF N e−N e

This is derived by considering the contact interaction and assuming the momentum transfer smaller than the vector boson mass. For q² ~M²this is no more valid. In this case the energy limit is 

E≃M W2/2me≃10

7GeV

W q=−g

q2−M [W ]2

iW MW

W q=−g

q2−M [W ]2 iq2W /MW

Using finite temperature temperature field theory as a tool to calculate the neutrino self energy in a background medium in the presence of a magnetic field, we get  

¿

24

¿

d 4 p¿

k =−g2∫ ¿

k=g2

2 ∫d 4 p

24 R S l p LW

q

i S p =∫0

∞

ds e p , sG p , s

=R L=akbu

cb

¿

The dispersion relation of the neutrino in the The dispersion relation of the neutrino in the background is given bybackground is given by

k0−k≃b−c cos

V e=V = 1− 12 e B

me Tcos 2GF N e f sW −N e f −sW

f ±sW =1± sW

1± sW2 sW

2W2 sW=2E me /MW

2

W=W / M W≃0.0266

Reduction due to B field, B~0.01me^2/e, T=0.05 me, 10% reduction Konstandin 06, Sahu 08

The discontinuity in function function f(­sw) st sW=1 corresponds to The discontinuity in function function f(­sw) st sW=1 corresponds to W­boson production.W­boson production.The calculation of the effective potential of the neutrino in the e+e­ The calculation of the effective potential of the neutrino in the e+e­ background.background.Threshold behavior forThreshold behavior for

ee W ee− W−

Application in MagnetarsApplication in Magnetars

SGR 1806­20SGR 1806­20

2727thth of October 2004 in our galaxy  of October 2004 in our galaxy with ~ 15 Kpc distancewith ~ 15 Kpc distance

E≃3×1046 erg 0.1 sec

Presence of baryons in the fireball are responsiblePresence of baryons in the fireball are responsible for the production of high energy neutrinos throughfor the production of high energy neutrinos through

p , pp

Neutrino oscillation in magnetar atmosphere

P t =2 sin2

2 sin2

t2

=V − cos2 2sin2 2

= m2

2E

V= cos2

Resonance conditionResonance condition

At resonance, the length isAt resonance, the length is

l res=2.5×1010 E ,14 cm

m2 sin 2

On the surface of the magnetar, the photon number On the surface of the magnetar, the photon number density is  density is  

n≃9.73×1029L47.5 r0, 6

−2 cm−3

T~313keV

By equating the e+e­annihilation rate  to the local By equating the e+e­annihilation rate  to the local expansion rate, the remaining pair is given byexpansion rate, the remaining pair is given by

T≃18KeV

N≃6.1×1044 E 46.53 / 4 r 0, 6

−1 / 2 t−11 / 4

Pair temperature is Pair temperature is 

at a distance r_{+­}at a distance r_{+­}

r± ~2.1×109 cm

Piran 05

Number density of photon at this point is

n≃1.8×1026 cm−3

Number density of pair isNumber density of pair is

N e≃2.2×1030 T

me 3 /2

e−me /T cm−3≃6.8×1015cm−3¿

r± ¿

≃2.1×109 cm

The radius is 

2 r±

m2cos2 ≃1.7×10−7

Analysis is done by considering the large and small mixingAnalysis is done by considering the large and small mixing

Large Mixing range 

We get

Samall Mixing range 

We get

The l_res obtained are much larger than r_(+­) and the Temp also will be very small at l_res. So High Energy Neutrinos will never satisfy the resonance condition and no supression of their flux due to matter and magnetic field effect.

0.64≤sin22≤0.96

2.8×10−7 eV 2≤ m

2 ≤8.5×10−7 eV 2 , E=1014eV

3.16×1016 cm≤ l res ≤1.1×1017 cm

2×10−3≤sin22≤7×10−3

m

2~10−7 eV 2

l res ~1018cm

2.8×10−7 eV 2≤ m

2 ≤8.5×10−7 eV 2 , E=1014eV

3.16×1016 cm≤ l res ≤1.1×1017 cm

But if the Neutrinos are of GeV energy or less, Temp ~ 50 keV or moreFor large mixing we get:

Resonant oscillation is possible if GeV neutrinos are produced deep inside the Magnetar atmosphere where Temperature is of Order 50 keV or so.

10−3eV 2≤ m

2 3.1×10−3eV 2

6.7×107 cm≤ l res ≤3×108cm r±

300keV18 keV

E =1014eV 1GeV

X= log [ m

2] , Y=log [ sin22 ]

Electromagnetic Effects of neutrinosElectromagnetic Effects of neutrinos

About the electromagnetic properties of a medium that consists of a matter background (electron gas) and a neutrino gas that moves as a whole relative to the electron gas.

Nieves 05

The quantity of interest is the photon self­energy and from this other macroscopic quantities of physical interest can be determined

In an isotropic medium the most general parametrization of the photon polarization tensor is 

=T RL QP P

Consistent with gauge invariance

R= g−Q , Q=u u

u2,=q.u

u= gu , g=g−q q

q2Q=2

−q2

P=iQq u u

=1,0 .

T , L , P               scalar functions of Q and      .               related to dielectric        and magnetic permeability           functions of the medium  

T , L

                Activity Constant related to the natural optical activity p

Arises as a result of  Parity (P), CP as well as CPT asymmetric effects.

ExampleWeak Interactions violate P and CP at some levelNormal matter is CPT­asymmetricActivity Constant is present in all normal matter

  In a background if                                  n−n≠0, p≠0

Standard Bing Bang predicts relic neutrino background comparable to CMB radiation. Light from all astrophysical sources travel through this background before reaching to us and if it induces some optical activity , interesting physical effects on Light can be observed.

We compute the photon self­energy in the 

Electron background at rest                           

and  Neutrino background moving                  

u=1,0

v=v0, V

Both electron and neutrino/anti­neutrino backgrounds  are contributing to the photon polarization tensor

Photon self energy can be expressed as 

=T RL QP PP' P

'

Due to neutrino background

Static background Moving background anisotropic

P =i

Q q u P ' =

iQ q v' , v'

=v−uu.v

Mimic Mag. Field

                          are finite for                         limit  , participate in Macroscopic effects in long wavelength and staticlimit.          

P , ' P q0

A class of diagrams which contribute to the photon A class of diagrams which contribute to the photon self­energy in the presence of a neutrino background areself­energy in the presence of a neutrino background are

=

e

e

Purely neutrino Purely neutrino backgroundbackground neutrinoneutrino

+electron+electron

One loop diagrams for theelectron self­energy in a neutrino gas

e = v vA5

V=2 GF [ aeZ=e , , n

−nne

−ne ]

A=2 GF [ beZ=e , , n

−n−ne

−ne ]

Proportional to the difference of neutrino number density

n−n≠0

Pe

= −4 e2A Q [ I1u.v I 2 ]

P' e

= −4 e2A Q I 2

I1=u.vQ2∫

d3 p23 2 E

∂ f e fe

∂E [ q2 p.u−q.u p.q

q22 p.q ]q−q

I2=2 me2∫

d3 p23 2 E

∂∂E [ 1

2 E f e fe

q22p.q ]q−q

T≃Te ,L≃L

e P≃0, q0

i=− ie 2∫ d 4 p

24Tr [ i S e pq i S e p ]

The expressions for and allows us to evaluate and for situations of interest for physical applications

Pe

P' e

I 1 I 2

We consider the regime                                        ≫v Q

Degenerate electron gas

Pe=− e2

32 A pF3

EF3 Q u.v

P' e=− e2

22 A pF

EF

QA=232 GF T 3

=

−

n

−

n

−e

−e

n

MACROSCOPIC ELECTRODYNAMICS

The presence of neutrino gas influence the electromagnetic properties of the system in the static and long wavelength limit q------>0.

We assume the neutrino gas is at rest with respect to the electron gas

v=u , P

'=0

For simplicity

2−Q2

−T±P =0

2−Q2− T±P∓

QV ' P =0 Q∥V

With Finite velocity

F=−i q A−A q

The equation of motion can be written as

−iq F= jext j

ind

We obtain the Maxwell equation

i Q×Bi E=jextj ind

jind=− A

Induced current 

The induced current is 

j ind=i [1− l E1−

1 Q×Bi

2

Q p

B ]where  1−t=

T

2 , 1−l=

L

q2 , p= p

2

1=1

2

Q2 l− tDielectric constant

Magnetic permeability

Evaluation of Magnetic Field:

i Q×Bi E=j ind

Consider the initial evaluation of magnetic perturbationin the medium 

In the long wavelength limit 

No external source

1i

≫V QAverage velocity of the background particles

Also

Conductivityof the mediumAll these finally give

=−

2

Q p=−

p

Q

Where 

∂ B∂ t

=2∇

2 B ∇×BInduction Equation of Magnetohydrodynamics

An equation of same form was obtained in PRL 92, 131301 (2004) by different method and suggesting a new mechanism for generation of large­scale magnetic field in the early Universe as a consequence of neutrino­plasma  interaction. The mechanism can result in the self­excitation of an almost constant magnetic perturbation.

Consider a plane wave magnetic field

B=B ei Q .x− t e

=i Q−

Q2

, = ±

The sign of    depends on the sign of the neutrino­antineutrino asymmetry. But one will be damped and another will grow.

B~e∓Q/ ∣∣±Q/ t

Qmax=∣∣

2will grow provided  Q∣∣

The mode with max. growth implies 

Growth (decay) of Magnetic field

=

2

4,

−1≃

e2

42 T

=2×10−20

2 TGeV

5

GeV

This is the growth rate of the field

Applications:Growth of Magnetic field in Astrophysical objects                   Where there are JETSAGN, QUASAR, MICROQUASAR,NASCANT NEUTRON STARS,PULSAR, GRB

Internal & External Shocks implies promt & afterglow

Optical activity of the neutrino gas

Photon that propagate through a  gas of neutrinos with non zero chemical potential, the left ­handed and right­handed polarization modes acquire different dispersions.

Due to CP and CPT­odd terms induced by neutrino.

Differential time delay

V g± =

∂±

∂Q, t= l

V g−

lV g

− Group velocity

To study the Effect of Velocity dependent term 

Wavelength independent Optical rotation

l ∝Q− −Q lIndependent of the wavelength of the propagating wave.

It is like Faraday rotation due to magnetic field 

l ∝2

Polarization dependent bending of light

=2 G M

b 1V

2 −1

V−

2

Growth of magnetic perturbation

Growth + anisotropic effect P'

 

We showed

n−n≠0In a medium with  Optically active one 

Multi GeV neutrinos from the fireballMulti GeV neutrinos from the fireball

Bahcall & Meszaros Mechanism, 2000

Neutrons can also contribute to the baryonic Neutrons can also contribute to the baryonic component as protons.component as protons.Initial stage of the relativistic flow e, p, n all are Initial stage of the relativistic flow e, p, n all are coupled. p,n through nuclear elastic scattering.coupled. p,n through nuclear elastic scattering.Expansion of the fireball­­­dynamical Expansion of the fireball­­­dynamical decoupling, neutrons and protons have decoupling, neutrons and protons have different velocities, inelastic scattering—pion different velocities, inelastic scattering—pion production­­­neutrinos production­­­neutrinos 

MeV MeV neutrinoneutrinoss

at collapseat collapse

NN NN

e e

−

pe− n e

Bac, Mes 2000Mes, Rees 20005­25 GeV

Neutrons and protons are coupled untilComoving n­p scatting timelonger than the  comoving  expansion time 

tnp´~

1

np´ c

texp´ ~r / c t np

´ texp´

np´=

L1 4 r2m p c3

nn´/ np

´=

Neutron, proton decoupling during the coasting/ accelerating regime depends on the critical value of the dimensionless entropy

= [ L

4 mp c3 ro 1 ]1 / 4

=3.9×102L521 / 4 ro7

−1 / 4[1] /2−1 /4

i ≤

ii ≥

Two conditions:Two conditions:

i ≤

t np´≥ texp

´ at a radius

rnp / ro= / 3

This radius is beyond the saturation radius

r s / ro~

Here both n & p coast with                 even after decoupling they coast together due to inertia and the relative velocity is small to have inelastic scattering.

~=const.

ii ≥

Decoupling condition is satisfied

tnp´≥ t exp

´ at a radius

rnp / ro= / −1 /3

Beyond this radius proton can still continue to accelerate with  p≃r / ro

Neutrons coast with 

nf≃3×102L52

1 /4 ro7−1 / 4 [1 ] / 2−1 / 4 /

−1 / 3

Drift velocity is sufficient to have inelastic scattering and production of pions.

v rel cpion production threthold

´140MeV

At  this point  tnp´~ texp

´ , rnp≃rpionosphere radius

pn p p−

− e− e

pn nn

e e

pn pno

PRL 85, 1362 (2000)

N n=

1 E

mp c2

~0.83×1053E53 21 400

Total number of neutrons in the fireball Total number of neutrons in the fireball 

Pion formation takes place below the ү

-photosphere because, ≪T

=3×10−26 cm2

T =6.65×10−25 cm2

Photons from pion decay has energy

~70 nf

1 z MeV≃10 GeV

Fluence of this photon which is emitted from the skin depth of the photosphere on Earth:

N ~N n P / 4 D p2~10−5 cm2

NeutrinosNeutrinos e e~5 GeV

~10 GeV

Event rate on Earth (km^3 detector)Event rate on Earth (km^3 detector)R =

N t

4 Dp2 Rb Nn

R ~7E53N t39 Rb3 21

4 /3

h652 2−21 z−1 z / year

Burst rate within a Hubble distance/year

Target proton

Distance to the GRB

Coincident with the electromagnetic flashes within 10 sec diff. Followed by120 MeV electron anti­neutrinos from neutron decay.

The neutrino production The neutrino production 

depends ondepends on

Neutron fraction         in the Neutron fraction         in the fireballfireballdimensionless entropy of the dimensionless entropy of the fireballfireball

Multi-GeV neutrinos from Internal Multi-GeV neutrinos from Internal Dissipation in FireballDissipation in Fireball

Meszaros & Rees mechanism 2000

Below the radiation photosphere internal shocks can lead to the rapid diffusion of neutrons both parallel and perpendicular to the radial direction .

In this case inelastic collision of neutrons with protons can give rise to about 3 GeV neutrinos. Both below and above the critical value of the entropy

, sh ~ 120 , sh ~ 120

In realistic flow there should be inhomogeneities intemporal or angular component. Both types of inhomogeneities implies presence of density gradients and thus the possibility of neutrons to diffuse from one region to another.During this period when the neutron encounter proton with a relative velocity of order v=0.6 c or more this corresponds to the CM energy more than 140 MeV, leading to pion formation and then neutrinos.

To occur with significant probability 

l ´~np

´

−1≃ l inhomo

They produce 2­25 GeV neutrinos

These mechanisms operateEven for low neutron density in the outflowInelastic collision with optical depth > 1 can convert proton to neutron and vice versa.

In ICECUBE, BAIKAL...the predicated event rates are of order 3­15/ year with sufficiently packed photo tubes. (30­50 times)

APJ 541, L5 (2000)

Role of Neutron in GRBs

Changes the dynamics of the fireball (Derishev et. al.)

Dynamical decoupling of the neutron from the rest of the shell will give rise to inelastic n-p scattering and lead to the emission of observable multi-GeV (5-10 GeV) neutrinos (Bahcall, Mészáros, PRL 2000; Mészáros, Rees, APJ 2000).

Role of Neutron in GRBs

Changes the dynamics of the fireball (Derishev et. al.)

Dynamical decoupling of the neutron from the rest of the shell will give rise to inelastic n-p scattering and lead to the emission of observable multi-GeV (5-10 GeV) neutrinos (Bahcall, Mészáros, PRL 2000; Mészáros, Rees, APJ 2000).

Is baryon number a good symmetry of Nature ?

It is believed that Baryon number is not a good symmetry of Nature (Universe is matter dominated) and it require baryon number violating interactions: proton decay,& oscillation (no success so far), oscillation occurs due to ΔB=2 transition

The existence of baryon number violating processes generic prediction of GUT to unify the fundamental forces.

n n

oscillation mechanismn n

N n=12

N n mE

2

=0.6×10−25 N n BG −2

m=n n−1 n n ≃109 sec.

In the presence of a magnetic field, neutrons energy levels are splitted by an amount ΔE=gμB and this is responsible for the oscillation. Due to oscillation, the number of anti-neutron is with

Number of anti-neutron at a distance r from the source is

neutron to proton ration and due to neutron decay.

protons, neutrons and electrons are coupled with the radiation in the expanding jet outflow until the Compton scattering time scale and the elastic n-p scattering time scale are shorter than the co-moving plasma expansion time scale

N n≃12 1 E

m p

e−r / r mE

2

=2×1027 BG

−2

21 E53

100e−r /r

≃1 e−r /r

tTh'≃n p

'Th

−1

tnp'≃n p

'np

−1

t exp'≃r /

np~3×10−26 cm2

np1

rnpLnp

14m p2

~6×1010L52

11002 100

cm

rr npr gives r6×1010 cm 1016 cm

r

The neutrons and protons are coupled until the opacity , which corresponds to neutron, proton decoupling radius The np coupling radius lies So we can neglect the effect of neutron beta decay. Decay of with in the fireball

n pe e

Produced anti-neutron will annihilate with the protons in the background through (also ppbar annihilation) Pion decay

nn

−

0

nn

−

nn0

0

±

±

± e± e e

0

The neutral pion decay will give photons of energies 45 and 71 GeVs.

The optical depth , so GeVs photons will degrade by pair production and can not escape.

The total amount of energy released in annihilation is

A major fraction of it will be in the form of neutrinos.

≫1

n n

n n=2m p N n≃6×1024 E53

100 BG −2

21 erg

Proton anti-proton annihilation, each pion carry energy

Average energy carried by muons is 80% and rest is by neutrinos. in the pion decay.

In muon decay ~1/3 energy is carried by each particle. Average energy of neutrino in muon decay the co-moving frame. In observer frame normalizing at z=1

Energy of muon neutrinos due to pion decay

1.88 GeV /k

, '≃0.5 GeV /k

,≃75 GeV

k

30021z

, k=3,2, 25−37.5 GeV

, ≃56 GeV

k

30021z

, 19−28 GeV

Neutrino Event RateShort and Long GRBs rate within a Hubble

radius of per year, number of events per year in a detector with protons is By considering Earth as the detector with protons and a magnetic field of in the jet outflow the event rate is

Rb~105 Rb5

N t

R~ N t

4D2 Rb Nn

1051 10−6G

R~4h702 Rb5

E53

100N t51300 B

10−6G −2

21 3−222z−21z year−1

Production of neutrinos and anti-neutrinos due to nnbar/ppbar annihilation is inversely proportional to the square of the mag. filed. So if nnbar oscillation exist in the GRBs outflow, mag. field can't be arbitrarily strong or weak.

Very Weak filed enhance neutrino production and take away huge energy.

Is it possible to observe these neutrinos?

May be in future, the Extreme Universe Space Observatory (EUSO) will be able to see it !

OutlookNo other process can give rise to neutrinos

inbetween source and the n-p decoupling radius.

19-38 GeV neutrinos will be produced much before the 5-10 GeV neutrinos due to dynamical decoupling of neutrons

It will tell about the nature of the progenitor of GRBs.

Observation of these multi-GeV neutrinos will be unique signature of Physics Beyond the Standard Model.

t~rnp /2~4.10−6 s

Summary:

We have studied the neutrino propagation in a medium, where we found :

The interaction of neutrino background with an electron background can give rise to the growth of magnetic field. 

Resonant Oscillation of MeV neutrinos  in the GRB medium with/without Magnetic field  and calculation of Baryon Load and Lepton asymmetry.

Possibility of Resonant Oscillation of neutrinos in the Magnetar Atmosphere.