1. TeV-Scale Leptogenesis and the LHC
Chang-Hun Lee
National Center for Theoretical Sciences, Hsinchu
P.S. Bhupal Dev, CHL, R.N. Mohapatra, Phys. Rev. D 90 (2014) no.9,
P.S. Bhupal Dev, CHL, R.N. Mohapatra, J. Phys. Conf. Ser. 631 (2015) no.1,
CHL, arXiv:17xx.xxxxx.

2. Can the LHC falsify leptogenesis?
J.-M. Frere, T. Hambye, and G. Vertongen, 2009

3. Outline Basic Leptogenesis
Leptogenesis in the Left-Right Symmetric Model
Boltzmann Equations and Numerical Results

4. Basic Leptogenesis

5. Observed Baryon Asymmetry
The value of baryon asymmetry of the Universe is inferred from observations in two different ways:
Big bang nucleosynthesis
Abundances of the light elements, D, He, Li.
Measurement of the cosmic microwave background anisotropies
Leptogenesis is one scenario of baryogenesis.
Baryogenesis
M. Fukugita and T. Yanagida, 1986

6. Basic Leptogenesis Lepton asymmetry Generation of lepton asymmetry
Majorana
Lepton asymmetry
Generation of lepton asymmetry
Washout of lepton asymmetry
Temperature of the Universe drops below due to the expansion
→ Suppression of the inverse decay by a factor
→ Lepton asymmetry is generated!
Complex couplings

7. Basic Leptogenesis Sphaleron Baryon and lepton numbers
B and L are anomalous at the quantum level (Adler-Bell-Jackiw triangular anomaly)
B and L are violated at the quantum level. However, B – L is preserved.
The violation of B + L is due to the non-trivial structure of non-abelian gauge theories. The change in B and L are related to the change in the topological charge (Chern-Simons number)
Transitions from one vacuum to another vacuum are possible with a change of B and L by 3 units.
Effective operator which gives interactions involving 12 fermions

8. Basic Leptogenesis Boltzmann equation (non-equilibrium below ) →
1+2 ↔ 3+4
Assumptions
Kinetic equilibrium
Maxwell-Boltzmann distribution
Thermally averaged reaction rates
Strong/weak washout
LHS of BE
RHS of BE
→ Strong washout of →
→ Weak washout of

9. Leptogenesis in the Left-Right Symmetric Model

10. Left-Right Symmetric Model
J.C. Pati and A. Salam, 1974
R.N. Mohapatra and J.C. Pati, 1975
G. Senjanovic and R.N. Mohapatra, 1975
Gauge group
PMNS matrix
Mixing between WL and WR
Lepton
Charged gauge boson
Majorana Neutrinos (ν= νc)
Scalar
Complex!
CP asymmetry
VEV
Charged lepton
Neutrino
Hermitian matrices in the symmetry basis
Seesaw
Parity symmetry (gL = gR)
Type-II
Type-I

11. Left-Right Symmetric Model
Basic steps
Parity breaking at a high scale
All the particles are massless.
→ All the interactions are in equilibrium.
→ No baryon or lepton asymmetry is generated, and any initial asymmetry is washed out.
Spontaneous symmetry breaking at
The RH neutrinos obtain masses.
The inverse decay and scattering processes get suppressed by
→ The lepton asymmetry is generated by the CP-violating decay processes. The lepton asymmetry at the moment right before the EW SSB is transformed into the baryon asymmetry through the sphaleron process.
Spontaneous symmetry breaking at the electroweak scale

12. Left-Right Symmetric Model
TeV-scale leptogenesis
Resonant leptogenesis
In order to enhance CP asymmetry
Strong washout of RH neutrinos and lepton asymmetry

13. Boltzmann Equations and Numerical Results

14. Dominant Decay and Scattering Processes
2-body decay
3-body decay
-mediated scattering

15. Boltzmann Equations and Lepton Asymmetry
A. Pilaftsis and T.E.J. Underwood, 2005
Washout
Dilution

16. Dominant Decay and Scattering Processes
2-body decay
Generation and washout of lepton asymmetry
3-body decay
Dilution of the lepton asymmetry
-mediated scattering
→ Which values of Yukawa couplings and are compatible with leptogenesis? = 18 TeV?
J.-M. Frere, T. Hambye, and G. Vertongen, 2009

17. Boltzmann Equations and Lepton Asymmetry
Lepton asymmetry (analytic expression)
Strong washout of RH neutrino density
Strong washout of lepton asymmetry
A. Pilaftsis and T.E.J. Underwood, 2005
F.F. Deppish and A. Pilaftsis, 2011

18. Resonant Leptogenesis
Dirac and Majorana mass matrices
Resummed effective Yukawa couplings
RH neutrino mixing effect
CP asymmetry regulation
Decay rate
CP asymmetry
J.A. Casas and A. Ibarra, 2001
A. Pilaftsis and T.E.J. Underwood, 2005
A. Pilaftsis, 2008

19. Numerical Result

20. Numerical Result

21. Plots

22. Plots
Lepton asymmetry within 3 σ

23. Dominant Decay and Scattering Processes
2-body decay
Generation of lepton asymmetry
3-body decay
Dilution of the lepton asymmetry
-mediated scattering
Dilution and washout of the generated lepton asymmetry
→ Which values of Yukawa couplings and are compatible with leptogenesis? = 18 TeV?
What about Yukawa couplings?
J.-M. Frere, T. Hambye, and G. Vertongen, 2009

24. CLFV (μ → e γ)

25. 0νββ

26. EDM’s of Charged Leptons

27. Large EDM’s of charged leptons and CLFV
No large EDM’s of charged leptons are allowed without fine-tuning of model parameters in the MLRSM.
Degeneracy in heavy neutrino masses allows large EDM’s.
EDM and CLFV
CHL, arXiv:
Large
Large components in MD require large Yukawa couplings

28. Plots
Lepton asymmetry within 3 σ

29. Experimental Constraints

30. Conclusion

31. Conclusion The lower bound of WR compatible with leptogenesis is
= 6.6 TeV, which is beyond the reach of LHC.
If with a smaller mass is discovered at the LHC, leptogenesis will be falsified.
For > 600 GeV, the lower bounds increases.
Any non-trivial correlation between the leptogenesis constraint and EDM’s of charged leptons or CLFV effects are under investigation.

32. Backup Slides

33. Sakharov Conditions
The baryon asymmetry can be dynamically generated in the decay of heavy particles if the following three conditions are satisfied.
B number violation
If baryon number is conserved, no baryon number can be generated.
C and CP violation
If C and CP are conserved, then → No net effect.
Departure from thermal equilibrium
In thermal equilibrium, the production rate of baryons is equal to the destruction rate: → No net effect.

34. Basic Leptogenesis (Revised) Sakharov conditions
B – L number violation
If heavy particles are Majorana neutrinos.
C and CP violation
If Yukawa couplings are complex.
Departure from thermal equilibrium
Due to the expansion of the Universe.
Non-equilibrium physics → Boltzmann equation

35. Left-Right Symmetric Model
Sakharov conditions revisited
B – L number violation
The B – L symmetry is broken due to the Majorana nature of the neutrinos at the scale when the scalar field acquires VEV by spontaneous symmetry breaking .
C and CP violation
The Yukawa couplings and are complex.
Departure from thermal equilibrium
The inverse decay and scattering rates get suppressed by when the temperature of the Universe drops below the mass of the lightest RH neutrinos.