Full Boltzmann equations for Leptogenesis (FHW, M. Plmacher, Y.Y.Y - - PowerPoint PPT Presentation

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Full Boltzmann equations for Leptogenesis (FHW, M. Plmacher, Y.Y.Y - - PowerPoint PPT Presentation

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Full Boltzmann equations for Leptogenesis (FHW, M. Plmacher, Y.Y.Y Wong: arXiv:0907.0205) Florian Hahn-Woernle Max-Planck-Institut fr Physik Mnchen Ringberg Young Scientist Workshop 2009 Florian Hahn-Woernle (MPI-Mnchen) Full

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SLIDE 1

Full Boltzmann equations for Leptogenesis

(FHW, M. Plümacher, Y.Y.Y Wong: arXiv:0907.0205)

Florian Hahn-Woernle

Max-Planck-Institut für Physik München

Ringberg Young Scientist Workshop 2009

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 1 / 18

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SLIDE 2

time evolution and energy budget of the universe

100 s 1 s 1 s 10−34 s

I n fl a t i

  • n

N e u t r i n

  • d

e c

  • u

p l i n g B B N M a t t e r

  • R

a d i a t i

  • n

d e c

  • u

p l i n g C M B

1014GeV 0.1 M eV 1 MeV 1 eV 10−4eV 105 yr 1013 Gyr

B a r y

  • g

e n e s i s

TRH ?

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 2 / 18

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SLIDE 3

Outline

1

Matter-Antimatter Asymmetry

2

Leptogenesis

3

Detailed look at Boltzmann equations

4

Conclusions

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 3 / 18

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SLIDE 4

Matter-Antimatter Asymmetry

from Nucleosynthesis and CMB: ηCMB

B

= nB − nB nγ = (6.2 ± 0.15) × 10−10

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 4 / 18

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SLIDE 5

Matter-Antimatter Asymmetry

from Nucleosynthesis and CMB: ηCMB

B

= nB − nB nγ = (6.2 ± 0.15) × 10−10 3 necessary ingredients (Sakharov, 1967):

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 4 / 18

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SLIDE 6

Matter-Antimatter Asymmetry

from Nucleosynthesis and CMB: ηCMB

B

= nB − nB nγ = (6.2 ± 0.15) × 10−10 3 necessary ingredients (Sakharov, 1967):

1

Baryon number violation

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 4 / 18

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SLIDE 7

Matter-Antimatter Asymmetry

from Nucleosynthesis and CMB: ηCMB

B

= nB − nB nγ = (6.2 ± 0.15) × 10−10 3 necessary ingredients (Sakharov, 1967):

1

Baryon number violation

2

C and CP violation

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 4 / 18

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SLIDE 8

Matter-Antimatter Asymmetry

from Nucleosynthesis and CMB: ηCMB

B

= nB − nB nγ = (6.2 ± 0.15) × 10−10 3 necessary ingredients (Sakharov, 1967):

1

Baryon number violation

2

C and CP violation

3

Departure from thermal equilibrium

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 4 / 18

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SLIDE 9

Matter-Antimatter Asymmetry

from Nucleosynthesis and CMB: ηCMB

B

= nB − nB nγ = (6.2 ± 0.15) × 10−10 3 necessary ingredients (Sakharov, 1967):

1

Baryon number violation

2

C and CP violation

3

Departure from thermal equilibrium

SM: relic density of baryons: nB

nγ = nB nγ ≃ 10−20

proton annihilation into pions

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 4 / 18

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SLIDE 10

Electroweak Baryogenesis

The SM contains all ingredients → Electroweak Baryogenesis

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 5 / 18

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SLIDE 11

Electroweak Baryogenesis

The SM contains all ingredients → Electroweak Baryogenesis

But: CP-violation too small and phase transition needs to be strongly first order: ∆vf (T)

TC

> 1 ⇒ mH < 45 GeV

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 5 / 18

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SLIDE 12

Electroweak Baryogenesis

The SM contains all ingredients → Electroweak Baryogenesis

But: CP-violation too small and phase transition needs to be strongly first order: ∆vf (T)

TC

> 1 ⇒ mH < 45 GeV Ruled out by LEP: mH > 114 GeV

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 5 / 18

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SLIDE 13

Electroweak Baryogenesis

The SM contains all ingredients → Electroweak Baryogenesis

But: CP-violation too small and phase transition needs to be strongly first order: ∆vf (T)

TC

> 1 ⇒ mH < 45 GeV Ruled out by LEP: mH > 114 GeV Still possible in SUSY models but constrained → non-minimal models

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 5 / 18

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SLIDE 14

Neutrino Masses

Neutrino masses: m1 < m2 < m3 (neutrino mixing data)

∆m2

atm = m2 3 − m2 2, with matm =

  • ∆m2

atm ≃ 0.05 eV

∆m2

sol = m2 2 − m2 1, with msol =

  • ∆m2

sol ≃ 0.009 eV

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 6 / 18

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SLIDE 15

Seesaw Mechanism

introduce right-handed neutrinos with mass M into the SM LN =

  • LHλνN
  • − 1

2

  • NcMN
  • + h.c.

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 7 / 18

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SLIDE 16

Seesaw Mechanism

introduce right-handed neutrinos with mass M into the SM LN =

  • LHλνN
  • − 1

2

  • NcMN
  • + h.c.

Yukawa couplings lead to Dirac mass: mD = λνv Lν = −1 2

  • νc

L, N

  • mT

D

mD M νL N

  • + h.c.

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 7 / 18

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SLIDE 17

Seesaw Mechanism

M 100 GeV 1 eV 1014 GeV

seesaw mechanism: assuming M ≫ mD: N with mN ≃ M ν with mν ≃ −mD 1

MmT D = O

  • v2

M

  • Florian Hahn-Woernle (MPI-München)

Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 7 / 18

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SLIDE 18

CP violation

N are Majorana particles → L violation N’s decay into lepton-Higgs pairs: ΓN ∝ ˜ m1 = v2 M1 (λ†

νλν)11

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 8 / 18

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SLIDE 19

CP violation

CP violation by interference of tree level and one loop amplitude

N i l
  • N
i N j;k l
  • l
  • N
i
  • l
  • l
  • N
j;k

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 8 / 18

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SLIDE 20

CP violation

N are Majorana particles → L violation N’s decay into lepton-Higgs pairs: ΓN ∝ ˜ m1 = v2 M1 (λ†

νλν)11

Assumptions:

◮ hierarchical neutrino masses M1 ≪ M2,3,

m1 < m2 < m3

◮ one-flavor approximation

CP violation by interference of tree level and one loop amplitude:

[Asaka et al. ’01; Davidson, Ibarra ’02; Buchmüller, Di Bari, Plümacher ’02]

εmax

1

(M1, ˜ m1, m1, m3) = εmax

1

(M1)β (˜ m1, m1, m3) , β ≤ 1. εmax

1

(M1) = 3 16π M1matm v2 ≈ 10−6

  • M1

1010GeV matm 0.05eV

  • ,

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 8 / 18

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SLIDE 21

From L to B Asymmetry

L asymmetry is partially transformed into a B asymmetry by sphalerons:

(Klinkhammer & Manton ’84; Kuzmin et al. ’85)

sphalerons in thermal equilibrium at temperatures: TEW ∼ 100 GeV ≤ T ≤ 1012 GeV ηB = αsphηB−L = αsph αsph − 1ηL, with αsph ≈ 1 3

Sphaleron

b L b L t L s L s L c L d L d L u L νe νµ ντ

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 9 / 18

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SLIDE 22

Boltzmann Equations

distribution functions in the expanding universe

∂fN(z, y) ∂z = z H(M) C[fN(z, y)] ∂fl−l(z, y) ∂z = z H(M) C[fl−l(z, y)] z = M/T y = p/T C[f(N,l−l(z, y)] : change of fi due to interactions

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 10 / 18

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SLIDE 23

Boltzmann Equations

distribution functions in the expanding universe

∂fN(z, y) ∂z = z H(M) C[fN(z, y)] ∂fl−l(z, y) ∂z = z H(M) C[fl−l(z, y)] z = M/T y = p/T C[f(N,l−l(z, y)] : change of fi due to interactions

assumptions needed for BE of number densities

I kinetic equilibrium

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 10 / 18

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SLIDE 24

Boltzmann Equations

distribution functions in the expanding universe

∂fN(z, y) ∂z = z H(M) C[fN(z, y)] ∂fl−l(z, y) ∂z = z H(M) C[fl−l(z, y)] z = M/T y = p/T C[f(N,l−l(z, y)] : change of fi due to interactions

assumptions needed for BE of number densities

I kinetic equilibrium II neglecting Pauli-Blocking and Bose-emission factors

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 10 / 18

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SLIDE 25

Boltzmann Equations

distribution functions in the expanding universe

∂fN(z, y) ∂z = z H(M) C[fN(z, y)] ∂fl−l(z, y) ∂z = z H(M) C[fl−l(z, y)] z = M/T y = p/T C[f(N,l−l(z, y)] : change of fi due to interactions

assumptions needed for BE of number densities

I kinetic equilibrium II neglecting Pauli-Blocking and Bose-emission factors III analytical solution for number density: dnN

dz =

  • d3pN

(2π)3 dfN dz

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 10 / 18

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SLIDE 26

Decays and inverse-decays

Collision integral

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 11 / 18

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SLIDE 27

Decays and inverse-decays

Collision integral

full CI: CD [fN] = MΓrf

ENpN

(EN+pN)/2

(EN−pN)/2 dpΦ [fΦfl(1 − fN) − fN(1 − fl)(1 + fΦ)]

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 11 / 18

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SLIDE 28

Decays and inverse-decays

Collision integral

full CI: CD [fN] = MΓrf

ENpN

(EN+pN)/2

(EN−pN)/2 dpΦ [fΦfl(1 − fN) − fN(1 − fl)(1 + fΦ)]

neglecting blocking factors: CD [fN] = MΓrf

ENpN

(EN+pN)/2

(EN−pN)/2 dpΦ [fΦfl − fN]

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 11 / 18

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SLIDE 29

Decays and inverse-decays

Collision integral

full CI: CD [fN] = MΓrf

ENpN

(EN+pN)/2

(EN−pN)/2 dpΦ [fΦfl(1 − fN) − fN(1 − fl)(1 + fΦ)]

neglecting blocking factors: CD [fN] = MΓrf

ENpN

(EN+pN)/2

(EN−pN)/2 dpΦ [fΦfl − fN]

using energy conservation: fΦfl = e−(EΦ+El)/T = e−EN/T = f eq

N

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 11 / 18

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SLIDE 30

Decays and inverse-decays

Collision integral

full CI: CD [fN] = MΓrf

ENpN

(EN+pN)/2

(EN−pN)/2 dpΦ [fΦfl(1 − fN) − fN(1 − fl)(1 + fΦ)]

neglecting blocking factors: CD [fN] = MΓrf

ENpN

(EN+pN)/2

(EN−pN)/2 dpΦ [fΦfl − fN]

using energy conservation: fΦfl = e−(EΦ+El)/T = e−EN/T = f eq

N

yields: CD[fN] = MΓrf

EN pN

(EN+pN)/2

(EN−pN)/2 dpΦ

  • f eq

N − fN

  • .

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 11 / 18

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SLIDE 31

Decays and inverse-decays

Collision integral

full CI: CD [fN] = MΓrf

ENpN

(EN+pN)/2

(EN−pN)/2 dpΦ [fΦfl(1 − fN) − fN(1 − fl)(1 + fΦ)]

neglecting blocking factors: CD [fN] = MΓrf

ENpN

(EN+pN)/2

(EN−pN)/2 dpΦ [fΦfl − fN]

using energy conservation: fΦfl = e−(EΦ+El)/T = e−EN/T = f eq

N

yields: CD[fN] = MΓrf

EN pN

(EN+pN)/2

(EN−pN)/2 dpΦ

  • f eq

N − fN

  • .

using kinetic equilibrium: fN ≈ f eq

N nN/neq N

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 11 / 18

slide-32
SLIDE 32

Decays and inverse-decays

Collision integral

full CI: CD [fN] = MΓrf

ENpN

(EN+pN)/2

(EN−pN)/2 dpΦ [fΦfl(1 − fN) − fN(1 − fl)(1 + fΦ)]

neglecting blocking factors: CD [fN] = MΓrf

ENpN

(EN+pN)/2

(EN−pN)/2 dpΦ [fΦfl − fN]

using energy conservation: fΦfl = e−(EΦ+El)/T = e−EN/T = f eq

N

yields: CD[fN] = MΓrf

EN pN

(EN+pN)/2

(EN−pN)/2 dpΦ

  • f eq

N − fN

  • .

using kinetic equilibrium: fN ≈ f eq

N nN/neq N

⇒ ∂NN

∂z = − D

  • NN − Neq

N

  • Florian Hahn-Woernle (MPI-München)

Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 11 / 18

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SLIDE 33

Thermal Leptogenesis

for a review Buchmüller, di Bari, Plümacher, Annals Phys.315:305-351,2005

Thermal Production of RHN

Boltzmann equations to compute Baryon asymmetry: dNN1 dz = −(D + S)

  • NN1 − Neq

N1

  • dNB−L

dz = −ε1 D

  • NN1 − Neq

N1

  • − W NB−L

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 12 / 18

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SLIDE 34

Thermal Leptogenesis

for a review Buchmüller, di Bari, Plümacher, Annals Phys.315:305-351,2005

Thermal Production of RHN

Boltzmann equations to compute Baryon asymmetry: dNN1 dz = −(D + S)

  • NN1 − Neq

N1

  • dNB−L

dz = −ε1 D

  • NN1 − Neq

N1

  • − W NB−L

with the solution NB−L(z) = − 3

4ε1κ(z; ˜

m1, m2) κf ≤ 1 measures efficiency of asymmetry production

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 12 / 18

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SLIDE 35

Thermal Leptogenesis

for a review Buchmüller, di Bari, Plümacher, Annals Phys.315:305-351,2005

e

m1

(eV )

M1

(GeV )

m

= 0 :05 eV :15 eV :21 eV

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 12 / 18

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SLIDE 36

Thermal Leptogenesis

for a review Buchmüller, di Bari, Plümacher, Annals Phys.315:305-351,2005

Thermal Production of RHN

Boltzmann equations to compute Baryon asymmetry: dNN1 dz = −(D + S)

  • NN1 − Neq

N1

  • dNB−L

dz = −ε1 D

  • NN1 − Neq

N1

  • − W NB−L

with the solution NB−L(z) = − 3

4ε1κ(z; ˜

m1, m2) κf ≤ 1 measures efficiency of asymmetry production For succesfull LG: lower bound on TRH 109 GeV upper bound on absolute neutrino mass scale m1 < 0.12 eV

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 12 / 18

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SLIDE 37

Effect on κf

Assumption of kinetic equilibrium Including quantum statistics

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 13 / 18

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SLIDE 38

Effect on κf

Assumption of kinetic equilibrium Including quantum statistics D1 Yes No κf as function of decay parameter K: K > 1 : strong wash-out K < 1 : weak wash-out

D1 K
  • f
100 10 1 0:1 0:01 1 0:1 0:01 0:001 10 4

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 13 / 18

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SLIDE 39

Effect on κf

Assumption of kinetic equilibrium Including quantum statistics D1 Yes No D2 No No kinetic equilibrium has virtually no effect on κf

D2 D1 K
  • f
100 10 1 0:1 0:01 1 0:1 0:01 0:001 10 4

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 13 / 18

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SLIDE 40

Effect on κf

Assumption of kinetic equilibrium Including quantum statistics D1 Yes No D2 No No D3 Yes Yes K > 1 : reduction: < 20% due to additional wash-

  • ut

K < 1 : enhancement: ∼ 50% due to Pauli emission

D3 D2 D1 K
  • f
100 10 1 0:1 0:01 1 0:1 0:01 0:001 10 4

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 13 / 18

slide-41
SLIDE 41

Effect on κf

Assumption of kinetic equilibrium Including quantum statistics D1 Yes No D2 No No D3 Yes Yes D4 No Yes again negligible effect of kin.eq

D4 D3 D2 D1 K
  • f
100 10 1 0:1 0:01 1 0:1 0:01 0:001 10 4

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 13 / 18

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SLIDE 42

Inlcude Scattering with the top Quark

p 1 p 3 p 2 p 4 q N 1 t l
  • p
1 p 3 p 2 p 4 l t N 1 q

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 14 / 18

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SLIDE 43

Inlcude Scattering with the top Quark

p 1 p 3 p 2 p 4 q N 1 t l
  • p
1 p 3 p 2 p 4 l t N 1 q

Boltzmann equation

H(M) z ∂fN ∂z = CD [fN] + 2 CS,s [fN] + 4 CS,t [fN] , with CS,(s,t) [fN] = 1 2EN

  • i=l,q,t

dp3

i

(2π)32Ei (2π)4δ4(pN + pl − pt − pq) |M(s,t)|2 ×

  • (1 − fN)(1 − f(l,q))ftf(q,l) − fNf(q,l)(1 − ft)(1 − f(q,l))
  • Florian Hahn-Woernle (MPI-München)

Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 14 / 18

slide-44
SLIDE 44

Reduction to two dimensional integral

Remaining to be integrated numerically

C(1)

S,(s,t) =

  • µ

3 T 26π3 ˜ EN yN h2

t M ˜

m1 v2 u(˜

El,q,t) g(˜ El,q,t)

d˜ El z(˜

El,t,q) w(˜ El,q,t)

d˜ Et Λ(N)

(s,t) I(µ) (s,t)

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 15 / 18

slide-45
SLIDE 45

Reduction to two dimensional integral

Remaining to be integrated numerically

C(1)

S,(s,t) =

  • µ

3 T 26π3 ˜ EN yN h2

t M ˜

m1 v2 u(˜

El,q,t) g(˜ El,q,t)

d˜ El z(˜

El,t,q) w(˜ El,q,t)

d˜ Et Λ(N)

(s,t) I(µ) (s,t)

with Λ(N)

s

(fN, fl, ft, fq) = − e˜

El+˜ Et

  • −1 + fN + e˜

EN fN

  • 1 + e˜

El

1 + e˜

Et

e˜

El+˜ EN + e˜ Et

  • Λ(N)

t

(fN, fq, fl, ft) = − e˜

El+˜ Eq

  • −1 + fN + e˜

EN fN

  • 1 + e˜

El

1 + e˜

Eq

e˜

El + e˜ El+˜ Eq

  • Florian Hahn-Woernle (MPI-München)

Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 15 / 18

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SLIDE 46

Distribution function for K = 0.1

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 16 / 18

slide-47
SLIDE 47

Effect on the efficiency factor

Assumption of kinetic equilibrium Including quantum statistics

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 17 / 18

slide-48
SLIDE 48

Effect on the efficiency factor

Assumption of kinetic equilibrium Including quantum statistics D1 Yes No D4 No Yes decays and inverse- decays alone

D4 D1 K
  • f
100 10 1 0:1 0:01 1 0:1 0:01 0:001 10 4

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 17 / 18

slide-49
SLIDE 49

Effect on the efficiency factor

Assumption of kinetic equilibrium Including quantum statistics D1 Yes No D4 No Yes S1 Yes No including scatterings: K > 1 : large enhancement due to N production K < 1 : reduction due to addi- tional wash-out

S1 D4 D1 K
  • f
100 10 1 0:1 0:01 1 0:1 0:01 0:001 10 4

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 17 / 18

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SLIDE 50

Effect on the efficiency factor

Assumption of kinetic equilibrium Including quantum statistics D1 Yes No D4 No Yes S1 Yes No S2 No Yes K > 1 : small effects: < 10% K < 1 : reduction compared to S1 due to quantum statistics

S2 S1 D4 D1 K
  • f
100 10 1 0:1 0:01 1 0:1 0:01 0:001 10 4

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 17 / 18

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SLIDE 51

Conclusions

First calculation of mode equations including scattering with the top quark

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 18 / 18

slide-52
SLIDE 52

Conclusions

First calculation of mode equations including scattering with the top quark All effects below 20% in the strong wash-out regime

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 18 / 18

slide-53
SLIDE 53

Conclusions

First calculation of mode equations including scattering with the top quark All effects below 20% in the strong wash-out regime Reduction of the final asymmetry in the weak wash-out

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 18 / 18

slide-54
SLIDE 54

Conclusions

First calculation of mode equations including scattering with the top quark All effects below 20% in the strong wash-out regime Reduction of the final asymmetry in the weak wash-out Influence of scatterings reduced using complete mode equations

Florian Hahn-Woernle (MPI-München) Full Bolztmann Equations for Leptogenesis Ringberg Young Scientist 2009 18 / 18