Oscillations and propagation of Neutrinos through Magnetized GRB - - PowerPoint PPT Presentation

SLIDE 1

Oscillations and propagation of Neutrinos through Magnetized GRB Fireball

Yong-Yeon Keum

IEU, Ewha Womans University GRB2010, Kyoto in Japan April 18, 2010

Collaboration with S. Sahu and N. Fraija: PRD 80, 033009 (2009), arXiv: 0909.3003(JCAP,2009)

April 18, 2010 seminar Oscillations and propagation of Neutrinos through Magnetized GRB Fireball

(page 1)

Yong-Yeon Keum IEU, Ewha Womans University

SLIDE 2

Magentic Filed in the GRBs Questions of Magnetic Field in the GRBs:

• There is no way to get the magnetic field information directly from the fireball.
• It is strongly believed in the GRB community that the non-thermal γ-rays which we

detect are mostly due to the sychrotron radiation of charged particles in the magnetic field although the strength of it is still unkonwn.

• Large magnetic field is expected if the progenitor is highly magnetized. Also

amplification of small field due to turbulent dynamo mechanism, compression or

• shearing. Decreasing of magnetic field due to the expansion at large radii

(B(r) = B0/r2)

• Here we take the weak field approximation and study the oscillation of neutrinos in

the fireball environment.

• The fireball model explains the temporal strucutre of the bursts and nonthermal

spctral behavior.

• Expanding fireball runs into the surrounding ISM to give afterglow.

April 18, 2010 seminar Oscillations and propagation of Neutrinos through Magnetized GRB Fireball

(page 2)

Yong-Yeon Keum IEU, Ewha Womans University

SLIDE 3

Neutrino Oscillations in the Fireball:

Sources for the Neutrinos:

• Neutrinos of about 5-20 MeV are generated due to the stellar collapse or merger of

compact binaries that trigger the burst.

• From nucleonic bremsstrahlung:

N + N − → N + N + ν + ¯ ν From e+e− annihilation : e+ + e− − → ν + ¯ ν

• In the fireball:

p + e− − → n + νe

• All these neutrinos have the energy in the MeV range and will propagate though the

fireball. Effect of Heat Bath on Particle Properties:

• Massive Photons (Plasmon)
• Plasmon decay: γL → ν¯

ν

• Massless neutrino acquires an effective mass
• MSW effect of neutrinos–flavor conversion
• Modification of dispersion relation in the medium with and without magnetic field:

p2 − m2 = 0

April 18, 2010 seminar Oscillations and propagation of Neutrinos through Magnetized GRB Fireball

(page 3)

Yong-Yeon Keum IEU, Ewha Womans University

SLIDE 4

Neutrino Oscillations in the Fireball:

Effective Potential for the Neutrinos: (a) νe(k) e(p) νe(k) W(k − p) (b) νe(k) νe(p) νe(k) Z(k − p) (c) νe(k) νe(k) Z f(q) Figure 1: One-loop diagrams for the neutrino self-energy in a medium.

April 18, 2010 seminar Oscillations and propagation of Neutrinos through Magnetized GRB Fireball

(page 4)

Yong-Yeon Keum IEU, Ewha Womans University

SLIDE 5

Neutrino Self-Energy-I: The total self-energy of neutrino in a magnetized medium:

Σ(k) = ΣW(k) + ΣZ(k) + Σt(k) . (1) with −iΣW(k) =

• d4p

(2π)4

−ig

√ 2

• γµ L iSℓ(p)

−ig

√ 2

• γν L iW µν(q) ,

(2) −iΣZ(k) =

• d4p

(2π)4

• −ig

√ 2 cos θW

• γµ L iSνℓ(p)
• −ig

√ 2 cos θW

• γν L iZµν(q) ,

(3) and −iΣt(k) = −

• g

2 cos θW

2

R γµ iZµν(0)

• d4p

(2π)4Tr [γν (CV + CAγ5) iSℓ(p)] . (4) W-boson diagram contributions: Re ΣW(k) = R

• aW⊥/

k⊥ + bW/ u + cW/ b

• L,

(5) aW⊥ = − √ 2GF M 2

W

• Eνe(Ne − ¯

Ne) + k3(N 0

e − ¯

N 0

e )

• + eB

2π2

∞

dp3

∞

• n=0

(2 − δn,0)

m2

e

En − H En

• (fe,n + ¯

fe,n)

• ,

(6)

April 18, 2010 seminar Oscillations and propagation of Neutrinos through Magnetized GRB Fireball

(page 5)

Yong-Yeon Keum IEU, Ewha Womans University

SLIDE 6

Neutrino Self-Energy-II:

bW = bW0 + ˜ bW = √ 2GF

• 1 + 3

2 m2

e

M 2

W

+ E2

νe

M 2

W

• (Ne − ¯

Ne) +

eB

M 2

W

+ Eνek3 M 2

W

• (N 0

e − ¯

N 0

e )

− eB 2π2M 2

W

∞

dp3

∞

• n=0

(2 − δn,0)

• 2k3Enδn,0 + 2Eνe
• En + m2

e

2En

• (fe,n + ¯

fe,n)

• cW

= cW0 + ˜ cW = √ 2GF

• 1 + 1

2 m2

e

M 2

W

− k2

3

M 2

W

• (N 0

e − ¯

N 0

e ) +

eB

M 2

W

− Eνek3 M 2

W

• (Ne − ¯

Ne) − eB 2π2M 2

W

∞

dp3

∞

• n=0

(2 − δn,0)

• 2Eνe
• En − m2

e

2En

• δn,0

+2k3

• En − 3

2 m2

e

En − H En

• (fe,n + ¯

fe,n)

• .

April 18, 2010 seminar Oscillations and propagation of Neutrinos through Magnetized GRB Fireball

(page 6)

Yong-Yeon Keum IEU, Ewha Womans University

SLIDE 7

Neutrino Self-Energy-III:

Z-boson diagram contributions: ReΣZ(k) = R(aZ/ k + bZ/ u)L, (8) where aZ = √ 2GF

Eνe

M 2

Z

(Nνe − ¯ Nνe) + 2 3 1 M 2

Z

• EνeNνe + ¯

Eνe ¯ Nνe

• ,

(9) and bZ = √ 2GF

• (Nνe − ¯

Nνe) − 8Eν 3M 2

Z

• EνeNνe + ¯

Eνe ¯ Nνe

• .

(10) Tadpole diagram contributions: ReΣt(k) = √ 2GFR

• CVe(Ne − ¯

Ne) + CVp(Np − ¯ Np) + CVn(Nn − ¯ Nn) + (Nνe − ¯ Nνe) +(Nνµ − ¯ Nνµ) + (Nντ − ¯ Nντ)

• /

u − CAe(N 0

e − ¯

N 0

e )/

b

• L.

(11)

April 18, 2010 seminar Oscillations and propagation of Neutrinos through Magnetized GRB Fireball

(page 7)

Yong-Yeon Keum IEU, Ewha Womans University

SLIDE 8

Neutrino Oscillations in the Fireball: Effective Potential for the Neutrinos:

In a relativistic and non-degenerate e+ − e− plasma,

• the effective potential for the (anti-)electron neutrino is: (if the fireball is charge

neutral: Le = Lp): Vνe,¯

νe =

√ 2GFNγ

 ±Le ∓ 1

2Ln −

7ξ(4)

ξ(3)

2 T 2

M 2

W

  .

(12)

• For the muon (tau)-neutrinos:

Vνµ,τ ≃ √ 2GFNγLµ,τ. (13) where the particle asymmetry is defined as Li ≡ Ni − ¯ Ni Nγ

April 18, 2010 seminar Oscillations and propagation of Neutrinos through Magnetized GRB Fireball

(page 8)

Yong-Yeon Keum IEU, Ewha Womans University

SLIDE 9

Neutrino Oscillations in the Fireball: Effective Potential for the Neutrinos:

Including the (weak) magnetic field contributions (B << m2/e = Bc≃ 1013 G), The effective potentials is given: V = Vνe − Vνµ ≃ √ 2GF m3 π2

• Φ1 − Φ2 − 4

π2

m

MW

2 Eνe

m (Φ3 − Φ4)

• .

(14) N 0

e − ¯

N 0

e = m3

π2 B Bc

∞

• l=0

(−1)l sinh α K1(σ) = m3 π2 Φ1, (15) Ne − ¯ Ne = m3 π2

∞

• l=0

(−1)l sinh α

2

σK2(σ) − B Bc K1(σ)

• = m3

π2 Φ2, (16) Φ3 =

∞

• l=0

(−1)l cosh α

3

σ2 − 1 4 B Bc

• K0(σ) +
• 1 + 6

σ2

K1(σ)

σ

• ,

(17) Φ4 =

∞

• l=0

(−1)l cosh α 1 σ2

• K0(σ) + 2

σK1(σ)

• ,

(18)

April 18, 2010 seminar Oscillations and propagation of Neutrinos through Magnetized GRB Fireball

(page 9)

Yong-Yeon Keum IEU, Ewha Womans University

SLIDE 10

Neutrino Oscillations νe ↔ νµ,τ: Neutrino Oscillation νe ↔ νµ,τ (I):

The evolution equation for the propagation of neutrinos is: i

˙

νe ˙ νµ

• =
• V − ∆ cos 2θ

∆ 2 sin 2θ ∆ 2 sin 2θ

νe

νµ

• ,

∆ = δm2/2Eν, V = Vνe − Vνµ, Eν is the neutrino energy (5-20 MeV)and θ is the neutrino mixing angle. The conversion probability at a given time t is given by Pνe→νµ(ντ)(t) = ∆2 sin2 2θ ω2 sin2

ωt

2

• ,

(19) with ω =

• (V − ∆ cos 2θ)2 + ∆2 sin2 2θ.

(20) the effective potential for the (anti-)electron neutrino is: The oscillation length for the neutrino is given by Losc = Lv

• cos2 2θ(1 −

V ∆ cos 2θ)2 + sin2 2θ

, (21) where Lv = 2π/∆ is the vacuum oscillation length.

April 18, 2010 seminar Oscillations and propagation of Neutrinos through Magnetized GRB Fireball

(page 10)

Yong-Yeon Keum IEU, Ewha Womans University

SLIDE 11

Neutrino Oscillations νe ↔ νµ,τ: Neutrino Oscillation νe ↔ νµ,τ (II):

At Resonance, V = ∆ cos 2θ. (22) The resonance condition is Φ1 − Φ2 − 3.196 × 10−11EMeV (Φ3 − Φ4) = 2.26 ˜ δm2 EMeV cos 2θ, (23) The left had side depends on the chemical potential µ of the background electrons and positrons, temperature T of the plasma and the neutrino energy. On the other hand the right hand side depends only on the neutrino energy (for a given set of neutrino mass square difference and the mixing angle). The resonance condition can be written as Le T 3

MeV = 0.124

˜ δm2 cos2θ EMeV (24) Baryon Load: Mb ∼ 2.23 × 10−4 R3

7 T 3 MeV Le M⊙.

(25)

April 18, 2010 seminar Oscillations and propagation of Neutrinos through Magnetized GRB Fireball

(page 11)

Yong-Yeon Keum IEU, Ewha Womans University

SLIDE 12

Our Analysis: Our Analysis of Neutrino Oscillations :

• We take into account the neutrino oscillation parameters from solar, atmospheric

(SNO and SuperKamiokande), and the Liquid Scintillator Neutrino Detector (LSND) reactor neutrinos to study the resonance conditions in the fireball.

• The resonance oscillation of neutrinos can constraint the fireball parameters.
• For the best fit neutrino oscillation parameter sets δm2 and sin2 2θ of the above

three different state of the art experiments (SNO, Super Kamiokande and LSND), we have shown what should be the values of µ and T to satisfy the resonance condition for different neutrino energies in the fireball plasma.

• Afterward these values of µ and T are used to calculate the lepton asymmetry Le,

baryon load Mb and the resonance length Lres of the propagating neutrinos.

April 18, 2010 seminar Oscillations and propagation of Neutrinos through Magnetized GRB Fireball

(page 12)

Yong-Yeon Keum IEU, Ewha Womans University

SLIDE 13

Solar Neutrinos: Solar Neutrinos: SNO + KamLAND

6 × 10−5 eV 2 < δm2 < 10−4 eV 2 and 0.64 < sin2 2θ < 0.96. Probably very few or No resonant oscillations take place within the fireball and most of the neutrinos will come out. Table 1: SNO: The best fit values

• f

the neutrino

• scillation

parameters δm2 ∼ 7.1 × 10−5 eV 2 and sin2 2θ ∼ 0.69 from the combined analysis of the salt phase data of SNO and KamLAND are used in the resonance condition for different neutrino energies in this table. The magnetic field used here is B/Bc = 0.1. EMeV T(MeV) Le Lres(cm) Mb(R3

7 M⊙)

3 4.93 × 10−8 2.97 × 10−10 5 5 3.28 × 10−8 2.10 × 107 9.14 × 10−10 10 5.07 × 10−8 1.13 × 10−8 3 4.71 × 10−8 2.83 × 10−10 10 5 5.34 × 10−8 4.21 × 107 1.49 × 10−9 10 9.99 × 10−8 2.23 × 10−8 3 6.83 × 10−8 4.11 × 10−10 20 5 1.02 × 10−7 8.42 × 107 2.85 × 10−9 10 1.99 × 10−7 4.44 × 10−8

April 18, 2010 seminar Oscillations and propagation of Neutrinos through Magnetized GRB Fireball

(page 13)

Yong-Yeon Keum IEU, Ewha Womans University

SLIDE 14

Atmospheric Neutrinos: Atmospheric Neutrinos: Super-Kamiokande

1.9 × 10−3 eV 2 < δm2 < 3.0 × 10−3 eV 2 and 0.9 ≤ sin2 2θ ≤ 1.0 Neutrinos can have many resonant oscillations within the fireball. Table 2: SK: The best fit values of the atmospheric neutrino oscillation parameters δm2 ∼ 2.5 × 10−3 eV 2 and sin2 2θ ∼ 0.9 from Super-Kaminkande Collaboration are used in the resonance condition for different neutrino energies in this table. EMeV T(MeV) Le Lres(cm) Mb(R3

7M⊙)

3 7.04 × 10−7 4.24 × 10−9 5 5 1.73 × 10−7 522763 4.83 × 10−9 10 6.92 × 10−8 1.54 × 10−8 3 3.81 × 10−7 2.30 × 10−9 10 5 1.30 × 10−7 1.05 × 106 3.62 × 10−9 10 1.09 × 10−7 2.44 × 10−8 3 2.38 × 10−7 1.44 × 10−9 20 5 1.37 × 10−7 2.09 × 106 3.81 × 10−9 10 2.04 × 10−7 4.54 × 10−8

April 18, 2010 seminar Oscillations and propagation of Neutrinos through Magnetized GRB Fireball

(page 14)

Yong-Yeon Keum IEU, Ewha Womans University

SLIDE 15

Three Neutrino Mixing (I)

The effective Hamiltonian is H = U · Hd

0 · U † + diag(Ve, 0, 0),

(26) with Hd

0 =

1 2Eν diag(−∆m2

21, 0, ∆m2 32).

(27) Here Ve is the charge current (CC) matter potential and U is the three neutrino mixing matrix. The different neutrino probabilities are given as Pee = 1 − 4s2

13,mc2 13,mS31,

Pµµ = 1 − 4s2

13,mc2 13,ms4 23S31 − 4s2 13,ms2 23c2 23S21 − 4c2 13,ms2 23c2 23S32,

Pττ = 1 − 4s2

13,mc2 13,mc4 23S31 − 4s2 13,ms2 23c2 23S21 − 4c2 13,ms2 23c2 23S32,

Peµ = 4s2

13,mc2 13,ms2 23S31,

Peτ = 4s2

13,mc2 13,mc2 23S31

Pµτ = −4s2

13,mc2 13,ms2 23c2 23S31 + 4s2 13,ms2 23c2 23S21 + 4c2 13,ms2 23c2 23S32,

(28)

April 18, 2010 seminar Oscillations and propagation of Neutrinos through Magnetized GRB Fireball

(page 15)

Yong-Yeon Keum IEU, Ewha Womans University

SLIDE 16

Three Neutrino Mixing (II)

where sin 2θ13,m = sin 2θ13

• (cos 2θ13 − 2EνVe/∆m2

32)2 + (sin 2θ13)2,

(29) and Sij = sin2

∆µ2

ij

4Eν L

• .

(30) ∆µ2

21

= ∆m2

32

2

sin 2θ13

sin 2θ13,m − 1

• − EνVe

∆µ2

32

= ∆m2

32

2

sin 2θ13

sin 2θ13,m + 1

• + EνVe

∆µ2

31

= ∆m2

32

sin 2θ13 sin 2θ13,m (31) where sin2 θ13,m = 1 2

• 1 −
• 1 − sin2 2θ13,m
• cos2 θ13,m

= 1 2

• 1 +
• 1 − sin2 2θ13,m
• (32)

April 18, 2010 seminar Oscillations and propagation of Neutrinos through Magnetized GRB Fireball

(page 16)

Yong-Yeon Keum IEU, Ewha Womans University

SLIDE 17

Three Neutrino Mixing (III)

The oscillation length for the neutrino is given by Losc = Lv

• cos2 2θ13(1 −

2EνVe ∆m2

32 cos 2θ13)2 + sin2 2θ13

, (33) where Lv = 4πEν/∆m2

32 is the vacuum oscillation length. For resonance to occur, we

should have Veff,B = Ve > 0 and cos 2θ13 = 2EνVe ∆m2

32

. (34) Comparision between B = 0.1Bc and B=0 ΦA − 1.58027 × 10−10Eν,MeV ΦB ≃ 2.24208 ˜ ∆m2

32

Eν,MeV cos 2θ13, (35)

April 18, 2010 seminar Oscillations and propagation of Neutrinos through Magnetized GRB Fireball

(page 17)

Yong-Yeon Keum IEU, Ewha Womans University

SLIDE 18

Comparision between B = 0.1Bc and B=0 (I)

5 MeV 10 MeV 20 MeV 30 MeV (a) 6.0 5.8 5.6 5.4 5.2 5.0 4.8 4.6 5 10 15 20 25 p Tm_e 5 MeV 10 MeV 20 MeV 30 MeV (b) 6.0 5.8 5.6 5.4 5.2 5.0 4.8 4.6 5 10 15 20 25 p Tm_e

The contour plot of the resonance condition as functions of T/me and µ = 10pme is shown for different neutrino energies and B = 0.1 Bc where (a) is for ∆m2

32 = 10−2.9 eV 2 and ∆m2 32 = 10−2.2 eV 2. April 18, 2010 seminar Oscillations and propagation of Neutrinos through Magnetized GRB Fireball

(page 18)

Yong-Yeon Keum IEU, Ewha Womans University

SLIDE 19

Comparision between B = 0.1Bc and B=0 (II)

Comparision between B = 0.1Bc and B=0 in Pµµ:

(a) L=100 Km E=5 MeV, B=0 E=30 MeV, B=0.1 Bc E=30 MeV, B=0 E=5 MeV, B=0.1 Bc 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 0.0 0.2 0.4 0.6 0.8 1.0 X P_ΜΜ L=1000 Km (b) E=5 MeV, B 0.1 Bc E=30 MeV, B 0 E=30 MeV, B 0.1 Bc E=5 MeV, B 0 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 0.0 0.2 0.4 0.6 0.8 1.0 X P_ΜΜ

The survival probability of muon neutrinos Pµµ is plotted as a function of ∆m2

32 eV 2 = 10X eV 2, for the fireball radius

L = 100 km (a) and L = 1000 km (b) . The neutrino energy and magnetic field are shown in it.

April 18, 2010 seminar Oscillations and propagation of Neutrinos through Magnetized GRB Fireball

(page 19)

Yong-Yeon Keum IEU, Ewha Womans University

SLIDE 20

Comparision between B = 0.1Bc and B=0 (III)

Comparision between B = 0.1Bc and B=0 in Peµ:

L=100 Km E=5 MeV, B=0 E=5 MeV, B=0.1Bc . (a) 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.109 4.109 6.109 8.109 1.108 X P_eΜ L=100 Km (a) E=30 MeV, B=0 E=30 MeV, B=0.1 Bc 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 5.1011 1.1010 1.51010 2.1010 2.51010 3.1010 3.51010 X P_eΜ

The probability Peµ is plotted as a function of ∆m2

32, for the fireball radius L = 100 km with Eν = 5.0 MeV (a) and

Eν = 30 MeV (b).

Comparision between B = 0.1Bc and B=0 in Pµτ:

L=100 Km (a) E=30 MeV, B=0.1 Bc E=30 MeV, B=0 E=5 MeV, B=0 E=5 MeV, B=0.1 Bc 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 0.0 0.2 0.4 0.6 0.8 1.0 X P_ΜΤ L=1000 Km (b) E=5 MeV, B=0.1 Bc E=30 MeV, B=0 E=30 MeV, B=0.1 Bc E=5 MeV, B=0 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 0.0 0.2 0.4 0.6 0.8 1.0 X P_ΜΤ

The probability Pµτ is plotted as a function of ∆m2

32, for the fireball radius L = 100 km (a) and L = 1000 km (b) . The

neutrino energy and magnetic field are shown in it.

April 18, 2010 seminar Oscillations and propagation of Neutrinos through Magnetized GRB Fireball

(page 20)

Yong-Yeon Keum IEU, Ewha Womans University

SLIDE 21

Summary and Discussions:

• From the Collapsar/Hypernova model of GRBs, lots of neutrinos will be produced

and fractions of these neutrinos will propagate through the fireball. We studied the resonant oscillation of these neutrinos in the fireball.

• We assume

– Spherical Fireball R 100 - 1000 Km – Charge Neutral – No. of Protons = No. of Neutrons – Le > 6.14 × 10−9 T 2

MeV

Neutrino Oscillation can be occurred for the Neutrino mass square difference mixing angle are in the Atmospheric and Reactor expt. ranges, so that the average conversion probability of neutrinos will be 0.5. however for the solar neutrino range, a few or no resonant oscillation will take place.

April 18, 2010 seminar Oscillations and propagation of Neutrinos through Magnetized GRB Fireball

(page 21)

Yong-Yeon Keum IEU, Ewha Womans University