[PPT] - Baryogenesis through Leptogenesis Mu-Chun Chen, University of PowerPoint Presentation

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Baryogenesis through Leptogenesis

Mu-Chun Chen, University of California at Irvine

Workshop on Search of New physics with Leptons, UNAM, October 17, 2018

Giada Carminati for WPA

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Evidence of Matter-Antimatter Asymmetry

CMB anisotropy
Big Bang Nucleosynthesis
primordial deuterium abundance

⟺ agree with WMAP

4He & 7Li ⟺ discrepancies
WMAP + Deuterium Abundance

2

∆T T =

l,m

almYlm(θ, φ)

Cl =

|alm|2

nB nγ ≡ ηB = (6.1 ± 0.3) × 10−10

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Three Sakharov Conditions

Baryon number can be generated dynamically, if
violation of baryon number
violation of Charge (C) and Charge Parity (CP)
departure from thermal equilibrium

3

rs

[Picture credit: H. Murayama]

Early Universe Universe Now

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Baryon Number Asymmetry beyond SM

Within the SM:
CP violation in quark sector not sufficient to explain the observed matter-

antimatter asymmetry of the Universe

accidental symmetries Le, Lμ, Lτ, total L
massless neutrinos, no cLFV
neutrino oscillation ⇒ non-zero neutrino masses
physics beyond the Standard Model
new CP phases in the neutrino sector
neutrino masses open up a new possibility for baryogenesis

4

Leptogenesis

Fukugita, Yanagida, 1986

Mu-Chun Chen, UC Irvine Leptogenesis and Neutrino Masses

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Plans

Theoretical Foundation of Baryogenesis:
Sakharav’s Three Conditions
Mechanisms for Baryogenesis & Their Problems
Sources of CP violation
Standard Leptogenesis (“Majorana” Leptogenesis)
Dirac Leptogenesis
Gravitino Problem
Non-standard Scenarios
Resonant Leptogenesis
Soft Leptogenesis
Non-thermal Leptogenesis
Connection between leptogenesis & low energy CP violation

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

References

W. Büchmuller, hep-ph/0502169
A. Riotto, hep-ph/9901362
M. Trodden, hep-ph/0411301
“TASI 2006 Lectures on Leptogenesis,” M.-C. Chen, hep-

ph/0703087

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Three Sakharov Conditions

Baryon Number Violation

necessary for baryon symmetric Universe (B=0) →

Universe with B ≠ 0

GUT theories:
quarks and leptons in same representations → B-violation

naturally through interactions with gauge or scalar fields

SM:
B & L accidental symmetries
preserved at tree level
t’Hooft: non-perturbative instanton effects

(B+L) ≠ 0, (B-L) = 0

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Three Sakharov Conditions

Classically: B & L conserved
At quantum level, non-vanishing ABJ triangular anomaly

through interactions with EW gauge fields ⇒ (B+L) is violated

vacuum structure of non-abelian gauge theories:
changes in B & L ↔ changes in topological charges

∂µJµ

B = ∂µJµ L = Nf

32π2

g2W p

µν

W pµν − g2Bµν Bµν

s, ∆B = ∆L = Nf∆Ncs = ±3n,

OB+L =

i=1,2,3

(qLiqLiqLiLi) ,

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Three Sakharov Conditions

12 fermion Processes, e.g.
T=0: transition rate negligible
In thermal bath: transition by thermal fluctuations
at T > height of barrier: no Boltzmann suppression
T < Tew :
T > Tew :
Sphelaron process in thermal eq.

y, Γ ∼ e−Sint = e−4π/α = O(10−165)

ΓB+L V = k M 7

W

(αT)3 e−βEph(T) ∼ e

−MW αkT

≥ ΓB+L V ∼ α5 ln α−1T 4

Esp(T) 8π g H(T)

u + d + c → d + 2s + 2b + t + νe + νµ + ντ

⇒ B-violating process unsuppressed

Kuzmin, Rubakov, Shaposhnikov

TEW ∼ 100 GeV < T < Tsph ∼ 1012 GeV

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Three Sakharov Conditions

C and CP Violations

superheavy X boson decay
Baryon number produced
net Baryon number
if CP is conserved:
Toy Model: two heavy scalar fields: X, Y; 4 fermions fi
possible decays

process branching fraction ∆B X → qq α 2/3 X → q 1 − α

1/3

X → qq α

2/3

X → q 1 − α 1/3 BX = α 2 3

+ (1 − α)
−1

3

= α − 1

3 , BX = α

−2

3

+ (1 − α)

1 3

= −
α − 1

3

,

≡ BX + BX = (α − α)

d, α = α,r, = 0.

L = g1Xf †

2f1 + g2Xf † 4f3 + g3Y f † 1f3 + g4Y f † 2f4 + h.c.

X → f 1 + f2, f 3 + f4 , Y → f 3 + f1, f 4 + f2 ,

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Three Sakharov Conditions

at tree level:
at one-loop

→ Γ(X → f1 + f2) = |g1|2IX Γ(X → f1 + f 2) = |g∗

1|2IX

phase space factor equal ⇒ no asymmetry

→ s IX and IX

→ → Γ(X → f 1 + f2) = g1g∗

2g3g∗ 4IXY + c.c.

Γ(X → f1 + f 2) = g∗

1g2g∗ 3g4IXY + c.c.

IXY: phase space + kinematics

Γ(X → f 1 + f2) − Γ(X → f1 + f 2) = 4Im(IXY )Im(g∗

1g2g∗ 3g4)

→ Γ(X → f3 + f4) − Γ(X → f3 + f4) = −4Im(IXY )Im(g∗

1g2g∗ 3g4)

X f1 f2 g2 f3 f4 g3

∗

g4 Y X f3 f4 g1 f1 f2 g3 g4

∗

Y Y f3 f1 g4 f4 f2 g2 g1

∗

X Y f4 f2 g3 f3 f1 g2

∗

g1 X X f1 f2 g1

X f3 f4 g2 Y f3 f1 g3 Y f4 f2 g4

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Three Sakharov Conditions

total asymmetry
non-zero total asymmetry ε = εX + εY
two B-violating bosons with masses > sum of loop

fermion masses

complex coupling constants: CP violation from

interference between tree and 1-loop diagrams

non-degenerate X and Y masses

X = (B1 − B2)∆Γ(X → f 1 + f2) + (B4 − B3)∆Γ(X → f3 + f4) ΓX (

X = 4 ΓX Im(IXY )Im(g∗

1g2g∗ 3g4)[(B4 − B3) − (B2 − B1)]

Y = 4 ΓY Im(I

XY )Im(g∗ 1g2g∗ 3g4)[(B2 − B4) − (B1 − B3)]

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Three Sakharov Conditions

Departure from Thermal Equilibrium

B: odd under C and CP
in equilibrium:

⇒ average <B>T = 0

Possible ways to achieve departure from thermal

equilibrium

out-of-equilibrium decay of heavy particles:
GUT baryogenesis, leptogenesis
EW phase transition: EW baryogenesis

< B >T = Tr[e−βHB] = Tr[(CPT)(CPT)−1e−βHB)] = Tr[e−βH(CPT)−1B(CPT)] = −Tr[e−βHB]

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Three Sakharov Conditions

Leptogenesis: Out-of-equilibrium decay of heavy particles
superheavy particle X: decay rate ΓX , Mass MX
at T ~ MX : become non-relativistic
if ΓX < H:
X cannot decay on the time scale of the expansion
remains thermal abundance
at T > MX : interact so weakly, cannot catch up expansion
decouple from thermal bath while relativistic
populate at T ~ MX with abundance >> than in equilibrium
recall: in equilibrium

nX = nX nγ for T MX , nX = nX (MXT )3/2e−MX/T nγ for T MX

xpansion. The X particles will then rem

e, nX = nX ∼ nγ ∼ T 3, for T MX.

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Three Sakharov Conditions

Over abundance at T < MX

⇒ departure from thermal equilibrium ⇒ final non-vanishing B-asymmetry Γ H ∝ 1 MX To have Γ < H ⇒ heavy particle

decay thru renormalizable operators ⇒ Gauge boson: Mx ≥ 10(15-16) GeV Scalar fields: Mx ≥ 10(10-16) GeV

Precise computation ⇒ Boltzmann equations

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Relating ∆B to ∆L

weakly couple plasma: chemical potential
SM: Nf generations of fermions + 1 Higgs
(5Nf + 1) chemical potential μi
number density of non-interacting, massless fermions
thermal equilibrium → relations among μi
sphaleron process OB+L :
QCD instanton processes, :
hypercharge charge:

ni − ni = 1 6gT 3 βµi + O((βµi)3), fermions 2βµi + O((βµi)3), bosons .

⇤

i

(3µqi + µ⇧i) = 0

⇥ ⇤

i

(2µqi − µui − µdi) = 0 ⇤

i

(µqi + 2µui − µdi − µ⇧i − µei + 2 Nf µH) = 0

and RH quarks.

i(qLiqLiuc

Ridc Ri).

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Relating ∆B to ∆L

Yukawa coupling and gauge interactions:
T=100 - 1012 GeV: gauge interactions in equilibrium
Yukawa interactions: more restricted range of temperatures →

flavor effects

B and L in terms of chemical potentials:
equilibrium among generations:

µqi − µH − µdj = 0 , µqi + µH − µuj = 0 , µ⇧i − µH − µej = 0 . y nB = 1

6gBT 2

individual lepto

(1.44), the bary y nL = 1

6gLiT 2

(e, µ, τ), can be

B =

i

(2µqi + µui + µdi)

L =
i

Li, Li = 2µi + µei µe = 2Nf + 3 6Nf + 3µ, µd = −6Nf + 1 6Nf + 3µ, µu = 2Nf − 1 6Nf + 3µ

µq = −1 3µ, µH = 4Nf 6Nf + 3µ

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Relating ∆B to ∆L

Corresponding B & L asymmetries:
Relation between B and L:
where
For model with NH Higgses

B = −4 3Nfµ

− L = 14N 2

f + 9Nf

6Nf + 3 µ

− B = cs(B − L),

L = (cs − 1)(B − L) cs = 8Nf + 4 22Nf + 13 cs = 8Nf + 4NH 22Nf + 13NH

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Mechanisms for Baryongenesis

GUT Baryogenesis
single particle physics interaction at high T
B-violation natural
quarks & leptons in same representation
superheavy gauge boson mediating B-changing

processes

C & CP violation: naturally built in
Out-of-equilibrium
GUT effects at very early times
cosmic expansion much faster (than gauge interactions)
decay inherently out-of-equilibrium Γ < H

G → H → ..... → SU(3)c × SU(2)L × U(1)Y → U(1)EM

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Mechanisms for Baryogenesis

GUT Baryogenesis
problems:
require high reheating temperature after inflation →

dangerous production of relics -- gravitino problem

extremely hard to test GUT models experimentally at

colliders

EW theory violates baryon number and can erase

pre-existing asymmetry, unless GUT mechanism generates excess in (B-L) → SO(10) attractive

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Mechanisms for Baryogenesis

EW Baryogenesis
departure from thermal equilibrium provided by strong

1st order phase transition

can be tested at collider experiments
problems:
require more CP violation than provided in SM (may

be found in SUSY)

need strong enough 1st order phase transition
MSSM: strong bound on Higgs mass < 120 GeV
stringent constraints on SUSY parameter space

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Sources of CP Violation: SM

SM: CP is not exact symmetry in weak interactions (Kaon &

B-meson systems)

charged current interactions in weak basis
rotate to mass basis

LW = g √ 2 U LγµDLWµ + h.c. where UL = (u, c, t)L and DL = (d, s, b)L. diagonalized by bi-unitary transformations,

diag(mu, mc, mt) = V u

L M uV u R ,

diag(md, ms, md) = V d

LM dV d R .

re U

L ≡ V u L UL and D L ≡ V d L DL d †

d UCKM ≡

L

V u

L (V d L)†

LW = g √ 2U

LUCKMγµD

LWµ + h.c. ,

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Sources of CP Violation: SM

CKM: 3 families, unitary matrix
3 angles
(6-5) = 1 phase
CP phase in CKM matrix:
effects of CP violation suppressed by small quark mixing
too small to account for the observed value

B α4

wT 3

s δCP 10−8δCP pression factor due to CP vio δCP ACP T 12

C

10−20 ACP = (m2

t − m2 c)(m2 c − m2 u)(m2 u − m2 t)

− − − ·(m2

b − m2 s)(m2 s − m2 d)(m2 d − m2 b) · J

f B ∼ 10−28,

B ∼ 10−10.

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Sources of CP Violation: MSSM

soft SUSY breaking terms → new sources of CPV
superpotential of MSSM
parameters in soft SUSY breaking sector
tri-linear couplings:
bi-linear coupling in Higgs sector:
gaugino masses:
soft scalar masses:
cMSSM w/ mSUGRA → 2 physical phases → soft

leptogenesis

W = µ ˆ H1 ˆ H2 + hu ˆ H2 ˆ Qˆ uc + hd ˆ H1 ˆ Q ˆ dc + he ˆ H1 ˆ Lˆ ec : ΓuH2 Q cc + ΓdH1 Q dc + ΓeH1 L ec + h.c.,

(u,d,e)

r: µBH1H2;

s: Mi for i = 1, 2, 3

i

s: mf.

Γ(u,d,e) ≡ A(u,d,e) · h(u,d,e)

φA = Arg(AM), φµ = −Arg(B)

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CP Violation in Neutrino Oscillation

With leptonic Dirac CP phase δ ≠ 0 ➜

leptonic CP violation

Predict different transition probabilities for

neutrinos and antineutrinos

One of the major scientific goals at

current and planned neutrino experiments

25

P (να→νβ) ≠ P ( να→νβ)

DUNE

Mu-Chun Chen, UC Irvine Leptogenesis and Neutrino Masses

SLIDE 26

Connection to Low Energy Observables

Lagrangian at high energy (in the presence of RH neutrinos)

in fij and Mij diagonal basis → hij general complex matrix:

Low energy effective Lagrangian (after integrating out RH neutrinos)

in fij diagonal basis → hij symmetric complex matrix:

high energy → low energy:

numbers of mixing angles and CP phases reduced by half L = Liiγµ∂µLi + eRiiγµ∂µeRi + N Riiγµ∂µNRi 1

+fijeRiLjH† + hijN RiLjH − 1 2MijNRiNRj + h.c. Leff = Liiγµ∂µLi + eRiiγµ∂µeRi + fiieRiLiH†

+1

2

k

hT

ikhkjLiLj

H2 Mk + h.c.

9-3 = 6 mixing angles 9-3 = 6 physical phases 6-3 = 3 mixing angles 6-3 = 3 physical phases

{ {

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Observation of Neutrino Oscillations ⇒ CP violation in lepton sector ⇒ Leptogenesis

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Standard Leptogenesis

GUT Baryogenesis:
B-violation mediated by gauge boson (V) or

leptoquarks (S)

SU(5): B-violating decays
(B-L) conserved: V and S carry (B-L) charge of 2/3
no (B-L) can be generated dynamically
sphaleron processes: <B> = <B-L> = 0

V → Luc

R,

B = −1/3, B − L = 2/3 V → qLdc

R,

B = 2/3, B − L = 2/3 S → LqL, B = −1/3, B − L = 2/3 S → qLqL, B = 2/3, B − L = 2/3 .

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Standard Leptogenesis

SO(10):
(B-L) is a gauged subgroup: spontaneously broken
decay of heavy particle X with Mx < MB-L → (B-L)
heavy X ~ MGUT: highly suppressed asymmetry

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Standard Leptogenesis

observation of neutrino oscillation
SO(10) GUT:
hierarchical fermion masses:
N: Majorana fermion
RH neutrino decays → lepton number asymmetry

ψ(16) = (qL, uc

R, ec R, dc R, L, νc R)

MN MB−L ∼ MGUT

N → H, N → H ,

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Standard Leptogenesis

most general Lagrangian in lepton sector
mass generation
see-saw mechanism in neutrino sector
resulting effective masses
basic idea:
T < MR: out-of-equilibrium decays of N → ∆L
sphaleron processes: ∆L → ∆B

LY = fijeRiLjH† + hijνRiLjH − 1 2(MR)ijνc

RiνRj + h.c.

m = fv, mD = hv MR

mD mT

D MR

ν V T

ν νL + V ∗ ν νc L,

N νR + νc

R

mν −V T

ν mT D

1 MR mDVν, mN MR

Luty, 1992; Covi, Roulet, Vissani, 1996; Flanz et al, 1996; Plumacher, 1997; Pilaftsis, 1997; Buchmuller, Plumacher, 1998; Buchmuller, Di Bari, Plumacher, 2004

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Standard Leptogenesis- Asymmetry

Tree-level:
total decay width
∆L from N2,3 decays at T >> M1: wash out by L-violating

interactions of N1 ⇒ N1 decay dominate

out-of-equilibrium condition
heavy neutrinos not able to follow equilibrium particle

distribution @ T < M1

N1 decay → ∆L

r, Ni → H + α, where α = (e, µ, τ)

ΓDi =

α
Γ(Ni → H + α) + Γ(Ni → H + α)
= 1

8π(hh†)iiMi

ΓD1 < H

T =M1

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Standard Leptogenesis- Asymmetry

CP Asymmetry from interference of tree and 1-loop

diagrams

Total Asymmetry

Nk li H∗ Nk ll H Nj H∗ li Nk ll H Nj H∗ li

1 =

α
Γ(N1 → αH) − Γ(N1 → α H)
α
Γ(N1 → αH) + Γ(N1 → α H)
1

8π 1 (hνhν)11

i=2,3

Im

(hνh†

ν)2 1i

·
f

M 2

i

M 2

1

+ g

M 2

i

M 2

1

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Standard Leptogenesis- Asymmetry

vertex corrections
wave function renormalization

Nk ll H Nj H∗ li

f(x) = √x

1 − (1 + x) ln

1 + x x

Nk

ll H Nj H∗ li

r |Mi − M1| |Γi − Γ1|,

for :

g(x) = √x 1 − x

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Standard Leptogenesis- Asymmetry

Hierarchical RH neutrino masses:
total asymmetry
near degenerate Ni and Nj: enhancement from self-

energy diagram resonant leptogenesis

allowing low M1
solving gravitino over-production problem

s, M1 M2, M3

1 − 3 8π 1 (hνh†

ν)11

i=2,3

Im

(hνh†

ν)2 1i

M1 Mi

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Standard Leptogenesis - Washout

asymmetry can be washed out by inverse decays and

scattering processes

out-of-equilibrium condition
expansion rate of the Universe
constraint on effective mass
g∗ : # of relativistic dof (SM: 106.75 ; MSSM:

228.75) r ≡ Γ1 H|T =M1 = Mpl (1.7)(32π)√g∗ (hνh†

ν)11

M1 < 1

m1 ≡ (hνh†

ν)11

v2 M1 4√g∗ v2 Mpl ΓD1 H

T =M1

< 10−3 eV

as the annihilati H 1.66 g1/2

∗ T 2 mp 2

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Standard Leptogenesis - washout

final amount of asymmetry
k: parametrizing washout effects
EW Sphaleron effects ∆L → ∆B
final B asymmetry

YL ≡ nL − nL s = κ 1 g∗

YB ≡ nB − nB s = cYB−L = c c − 1YL

cs = 8Nf + 4NH 22Nf + 13NH

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Standard Leptogenesis - Washout

For 1< r < 10:
can still have sizable asymmetry
k can be obtained by solving Boltzmann eq
in general
EW Sphaleron effects ∆L → ∆B
final B asymmetry

106 r : κ = (0.1r)1/2e− 4

3 (0.1)1/4

(< 10−7) 10 r 106 : κ =

0.3 r(ln r)0.8

(10−2 ∼ 10−7) 0 r 10 : κ =

1 2 √ r2+9

(10−1 ∼ 10−2) .

YB ≡ nB − nB s = cYB−L = c c − 1YL

YL ≡ nL − nL s = κ 1 g∗

SLIDE 39

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Standard Leptogenesis - Washout

Precise value for k: Boltzmann equations
Main relevant processes in thermal bath
decay of N:
inverse decay of N:

N → + H, N → + H

N l H∗

+ H → N, + H → N

SLIDE 40

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Standard Leptogenesis - Washout

2-2 scattering
∆L = 1

[s-channel] : N1 ↔ t q , N1 ↔ t q

N l H t q

↔ ↔ [t-channel] : N1t ↔ q , N1 t ↔ q

N t H l q

SLIDE 41

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Standard Leptogenesis - Washout

2-2 scattering
∆L = 2
T > M1: strong enough to keep N1 in equilibrium
T < M1: weak enough to allow asymmetry

generation

H ↔ H , ↔ H H, ↔ H H

l H Ni l H l H Ni H l

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Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Standard Leptogenesis - Washout

Boltzmann equations → evolution of N1 density and (B-

L) number density

D: decay and inverse decays
S: ∆L = 1 scatterings
W: inverse decays + ∆L = 1, 2 scatterings

− dNN1 dz = −(D + S)(NN1 − N eq

N1)

dNB−L dz = −1D(NN1 − N eq

N1) − WNB−L

(D, S, W) ≡ (ΓD, ΓS, ΓW ) Hz , z = M1 T

SLIDE 43

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Standard Leptogenesis - Washout

strongly hierarchical RH neutrino masses, M1 << M2:
Davidson-Ibarra bound
exp constraint
lower bound on M1:

⇒ lower bound on reheating temperature (gravitino problem)

equivalently,

|1| ≤ 3 16π M1(m3 − m2) v2 ≡ DI

1

|m3 − m2| ≤

∆m2

32 ∼ 0.05 eV

M1 ≥ 2 × 109 GeV

ly m1 0.1 − 0.2

m1

eV

SLIDE 44

Is Leptogenesis Possible without LNV?

SLIDE 45

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Dirac Leptogenesis

Leptogenesis possible when neutrinos are Dirac particles
small Dirac mass through suppressed Yukawa coupling
Characteristics of Sphaleron effects:
only left-handed fields couple to sphalerons
sphalerons change (B+L) but not (B-L)
sphaleron effects in equilibrium for T > Tew
If L stored in RH fermions can survive below EW phase

transition, net lepton number can be generated even with L=0 initially

for SM quarks and leptons: rapid left-right equilibration through

large Yukawa

LH: (B+L) ← RH: (B+L)

Dick, Lindner, Ratz, Wright, 2000; Murayama, Pierce, 2002; ...

no net asymmetry if B = L = 0 initially

SLIDE 46

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Dirac Leptogenesis

LR equilibration for neutrinos:
neutrino Y

ukawa coupling

rate for conversion
for LR conversion not to be in equilibrium
Thus LR equilibration can occur at much later time

he left-right s, λLHνR, conversion

ΓLR ∼ λ2T

ΓLR H , for T > Teq

H ∼ T 2 MPl

, T

Hence the Teq TEW

λ2 Teq MPl TEW MPl .

⇒ h MPl ∼ 1019 GeV d TEW ∼ 102 GeV

λ < 10−(8∼9)

es mD < 10 keV

SLIDE 47

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Dirac Leptogenesis

Dick, Lindner, Ratz, Wright, 2000

SLIDE 48

Gravitino Overproduction Problem

SLIDE 49

Bound on Light Neutrino Mass

sufficient leptogenesis

requires

upper bound on light

neutrino mass

incompatible with

quasi-degenerate spectrum

constraints slightly

alleviated with flavored case

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10

16

10

8

10

9

10

11

10

12

10

13

10

14

10

15

10

16

M1 (GeV) m1 (eV)

m1 < 0.12 eV

M1 t 3x10

9 GeV

⇒ ⇒ ⇒ ⇒ Treh t 10

9 GeV

M1 t 3x10

9 GeV

m1 < 0.12 eV

P . Di Bari, 2012

Mu-Chun Chen, UC Irvine Leptogenesis and Neutrino Masses

SLIDE 50

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Gravitino Problem

Thermally produced N:
high reheating temperature needed:
TRH > MR > 2 x 109 GeV
over production of light states: gravitinos
For gravitinos LSP:
DM constraint from WMAP
stringent bound on gluinio mass for any given gravitino

mass & TRH

For unstable gravitinos:
long life time
decay during and after BBN

SLIDE 51

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Gravitino Problem

Effects on BBN:
speed up cosmic expansion ⇒ increase n/p ⇒ 4He
radiative decay of gravitinos

⇒ increase ⇒ reduce

photo dissociated reactions: destroy light elements (D, T, 3He,

4He)

s, ψ → γ + ˜ γ,

/nγ

e nB/nγ

reaction threshold (MeV) D + γ → n + p 2.225 T + γ → n + D 6.257 T + γ → p + n + n 8.482

3He + γ → p + D

5.494

4He + γ → p + T

19.815

4He + γ → n +3 He

20.578

4He + γ → p + n + D

26.072

SLIDE 52

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Gravitino Problem

observed abundance of light elements
constraint on gravitino number density
more stringent constraint from hadronic mode

0.22 < Yp = (ρ4He/ρB)p < 0.24 , (nD/nH) > 1.8 × 10−5 , nD + n3He nH

p

< 10−4 . n3/2 s 10−2 TRH MPl 10−12

t TRH < 108−9 GeV

⇒ s, ψ → g + ˜ g,

t, TR < 106−7 GeV, s m3/2 ∼ 100 GeV

for ⇒

SLIDE 53

Gravitino Problem: Bound on TRH

For light gravitino mass, BBN constraints ⇒ TRH < 10(5-6) GeV

53

Kawasaki, Kohri, Moroi, Yotsuyanagi, 2008

Sufficient leptogenesis ⇒ TRH > MR > 2 x 109 GeV

tension! (if SUSY)

Mu-Chun Chen, UC Irvine Leptogenesis and Neutrino Masses

SLIDE 54

Non-standard Scenarios

SLIDE 55

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Non-standard Scenarios

To avoid this tension
resonant enhancement in self-energy diagram
resonant leptogenesis (near degenerate RH neutrinos)
relaxing relations between lepton number asymmetry and RH

neutrino mass

soft leptogenesis (SUSY CP phases)
relaxing relation between TRH and RH neutrino mass
non-thermal leptogenesis

Leptogenesis ↔ Gravitino Overproduction

SLIDE 56

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Resonant Leptogenesis

Recall: Standard Leptogenesis
self-energy diagram dominates for
enhanced asymmetry if
O(1) asymmetry if
Leptogenesis possible with M1,2 ~ TeV

Nk li H∗ Nk ll H Nj H∗ li Nk ll H Nj H∗ li

it MNi − MNj

diagr MNi

Self

Ni =

Im[(hνh†

ν)ij]2

(hνh†

ν)ii(hνh† ν)jj

(M 2

i − M 2 j )MiΓNj

(M 2

i − M 2 j )2 + M 2 i Γ2 Nj

s, M 2

1 −

When the l M 2

2 ∼ Γ2 N2,

asymmetry

O M1 − M2 ∼ 1 2ΓN1,2 , assuming Im(hνh†

ν)2 12

(hνh†

ν)11(hνh† ν)22

∼ 1 Nk ll H Nj H∗ li

Pilaftsis, 1997 Pilaftsis, Underwood, 2003

SLIDE 57

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Soft Leptogenesis

leptogenesis:
CP violation in decays → standard leptogenesis
CP violation in mixing → soft leptogenesis
Recall: Kaon system
mismatch between CP eigenstates & mass eigenstates ⇒ CP

violation

CP eigenstates
time evolution

1 √ 2

K0

±

K

by the following

d dt

K0

K

= H
K0

K

y H = M − i

2A.

Grossman,Kashti,Nir,Roulet, 03 D’Ambrosio,Giudice,Raidal, 03

SLIDE 58

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Soft Leptogenesis

Mass eigenstates
mismatch between mass eigenstates & CP eigenstates
KL
= p
K0

+ q

K
KS
= p
K0

− q

K
q

p

= 1 ,

where q p 2 = 2M∗

12 − iA∗ 12

2M12 − iA12

SLIDE 59

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Soft Leptogenesis

For soft leptogenesis
diagonalization of mass matrix in basis
− Lsoft =

1 2BM1 νR1 νR1 + AY1i Li νR1Hu + h.c.

+

m2 ν†

R1

νR1 W = M1N1N1 + Y1iLiN1Hu

⇒

− LA = νR1(M1Y ∗

1i

∗

i H∗ u + Y1i

Hui

L + AY1i

iHu) + h.c.

− LM = (M 2

1

ν†

R1

νR1 + 1 2BM1 νR1 νR1) + h.c.

interactions: mass terms: es νR1 and ν†

R1

⇒

− M± M1

1 ± |B|

2M1

eutrino mass t

es N+ and N−

mass eigenstates: mass splitting due to SUSY breaking

SLIDE 60

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Soft Leptogenesis

time evolution of system
total decay width of

e νR1- ν†

R1

d

dt νR1

ν†

R1

= H

νR1

ν†

R1

is H = M − i

2A

M =
1

B∗ 2M1 B 2M1

1

M1
A =
1

A∗ M1 A M1

1

Γ1
,

νR1

Γ1 = 1 4π (YνY†

ν)11M1

SLIDE 61

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Soft Leptogenesis

eigenstates of H:
for A12 << M12 :
mismatch between and

⇒ CP violation in lepton asymmetry non-zero CPV ⇒ ⇒ i.e. SUSY breaking

e N

± = p

N ± q N †,

re |p|2 +

The eige |q|2 = 1.

M

q p 2 = 2M∗

12 − iA∗ 12

2M12 − iA12 1 + Im 2Γ1A BM1

iolation in t

es ( N+, N−)

al mass s, ( N

+,

uantity

eigen

N

−).

− |q/p| = 1,

Im AΓ1 M1B

= 0

SLIDE 62

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Soft Leptogenesis

total lepton number asymmetry
final states: (L=+1)
after time integration
=
f

∞

0 [Γ(

νR1, ν†

R1 → f) − Γ(

νR1, ν†

R1 → f)]

f

∞

0 [Γ(

νR1, ν†

R1 → f) + Γ(

νR1, ν†

R1 → f)]

=
4Γ1B

Γ2

1 + 4B2

Im(A) M1 δB−F

s f = (

L H), (L H)

r δB−F : take into account thermal effects

SLIDE 63

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Non-thermal Leptogenesis

conflict between leptogenesis ↔ gravitino problem:
thermal leptogenesis: dependence of TRH on MR
Inflation:
horizon and flatness problem
density fluctuation
dominant inflaton decay
assume decay modes into N2,3 energetically forbidden
subsequent N1 decay

s, Φ → N1 +N1

htest R ss mΦ n 2M1.

>

d N1 → H +L or H† +†

L r Fuji, Hamaguchi, Yanagida, 2002

SLIDE 64

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Non-thermal Leptogenesis

out-of-equilibrium condition satisfied automatically if
N1 decays also entropy of thermal bath
sufficient asymmetry with

TR < M1.

nL s −3 2 TR mΦ 3 × 10−10

TR

106 GeV M1 mΦ

m3

0.05 eV

M1 mΦ, and TR 106 GeV

Fuji, Hamaguchi, Yanagida, 2002

SLIDE 65

65

Testing Leptogenesis?

Mu-Chun Chen, UC Irvine Leptogenesis and Neutrino Masses

SLIDE 66

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Testing Leptogenesis?

Sakharov Conditions:
out-of-equilibrium
expanding Universe
smallness of neutrino masses
Baryon/Lepton Number Violation
abound in many extensions of the SM
neutrinoless double beta decay
Leptogenesis with Majorana (if observed) or Dirac (if not observed)

neutrinos

Cosmology
if Dirac: Neff enhanced
CP violation
Long baseline neutrino oscillation experiments

66

Leptogenesis with Majorana neutrino:

ut-of-equilibrium heavy field decay

Dirac Leptogenesis: late equilibration temperature

SLIDE 67

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Connection to Low Energy Observables

Standard Leptogenesis: seesaw mechanism, Majorana neutrinos
Seesaw Lagrangian at high energy (in the presence of RH neutrinos)
Low energy effective Lagrangian (after integrating out RH neutrinos)
No model independent connection
BUT, in certain predictive models, connection can be established
Flavor effects important

67

presence of low energy leptonic CPV (neutrino oscillation, neutrinoless double beta decay)

↔

leptogenesis ≠ 0 6 mixing angles + 6 physical phases 3 mixing angles + 3 physical phases high energy → low energy: numbers of mixing angles and CP phases reduced by half

SLIDE 68

Flavor Effects

At M1 ~ T ~ 1012 GeV:
At M1 ~ T ~ 109 GeV:
two flavor regime:
three flavor regime
asymmetry associated with each flavor

α = − 3M1 16πv2 Im

βρ m1/2

β

m3/2

ρ

U ∗

αβUαρR1βR1ρ

β mβ|R1β|2

leptogenesis ≠ 0 low energy CPV ≠ 0

Pascoli, Petcov, Riotto, 2006

: Yτ - in equilibrium, Ye,µ - not;

ε1τ and (ε1e + ε1µ) ≡ ε2 evolve independently.

: Yτ, Yµ - in equilibrium, Ye - not.

ε1τ, ε1e and ε1µ evolve independently.

M1 ⇤ 109 1012 GeV M1 < 109 GeV

SLIDE 69

Connection in Specific Models

models for neutrino masses:
additional symmetries
reduce the number of parameters ⇒ connection can be established
rank-2 mass matrix (may be realized by symmetry)
models with 2 RH neutrinos (2 x 3 seesaw)
sign of baryon asymmetry ↔ sign of CPV in ν oscillation
all CP come from a single source
models with spontaneous CP violation:
SM + vectorial quarks + singlet scalar
minimal LR model: only 1 physical leptonic CP phase
SCPV in SO(10): <126>B-L complex
SUSY SU(5) x T′ Model: 9 parameters accommodate 22 observables
group theoretical origin of mixing parameters ⇒ only low energy phases

≠ 0

Frampton, Glashow, Yanagida, 2002 M.-.C.C, Mahanthappa, 2005 Branco, Parada, Rebelo, 2003 Achiman, 2004, 2008 Kuchimanchi & Mohapatra, 2002 M.-.C.C, Mahanthappa, 2009

69

Mu-Chun Chen, UC Irvine Leptogenesis and Neutrino Masses

SLIDE 70

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Connection to Other B/L Violating Processes

e.g. n-nbar oscillation searches →

complementarity test of leptogenesis (baryogenesis) mechanisms

constrain the scale of leptogenesis
observation of neutron antineutron oscillation
new physics with ∆B = 2 at 10(5-6) GeV
erasure of matter-antimatter generated at

high scale, e.g. standard leptogenesis

Low scale leptogenesis scenarios preferred:
Dirac Leptogenesis
Resonance Leptogenesis
Soft leptogenesis; ...

70

Babu, Mohapatra, 2012

SLIDE 71

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Conclusions

origin of matter: one of the great mysteries in particle physics and

cosmology

leptogenesis: appealing mechanism connected to neutrino physics
various leptogenesis realizations:
standard leptogenesis: gravitino problem, tension with SUSY
Low scale alternatives:
resonance leptogenesis
Dirac leptogenesis
ARS leptogenesis
Soft leptogenesis
non-thermal leptogenesis

71

SLIDE 72

Mu-Chun Chen, UC Irvine Baryogenesis through Leptogenesis

Conclusions

tested by “archeological” evidences
model-independent ways:
Kinematic test, Cosmology (absolute neutrino mass bound, Neff)
Neutrino-less double beta decay (Majorana vs Dirac leptogenesis)
Leptonic CP violation:
important fundamental property of neutrinos, independent of

leptogenesis

model-dependent connections to CPV in other sectors possible
correlations: single source of CPV (Jcp, <mββ>, EDM, etc)
searches at neutrino experiments, cLFV (leptonic CPV, mixing

parameters)

complementarity test from other B or L violating processes
e.g. N-Nbar oscillation ⇒ constraint scale of leptogenesis

72