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, 095012. P.S. Bhupal Dev, CHL, R.N. Mohapatra, J. Phys. Conf. Ser. 631 (2015) no.1, 012007. CHL, arXiv:17xx.xxxxx.

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

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

Basic Leptogenesis

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

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

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

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

Leptogenesis in the Left-Right Symmetric Model

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

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

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

Boltzmann Equations and Numerical Results

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

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

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

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

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

Numerical Result

Numerical Result

Plots

Plots Lepton asymmetry within 3 σ

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

CLFV (μ → e γ)

0νββ

EDM’s of Charged Leptons

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:1705.05358 Large Large components in MD require large Yukawa couplings

Plots Lepton asymmetry within 3 σ

Experimental Constraints

Conclusion

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.

Backup Slides

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.

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

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.