Classically conformal B-L extended Standard Model Yuta Orikasa (IEAP CTU) Collaborators Satoshi Iso (KEK) Nobuchika Okada (Alabama U) Phys.Lett.B, 676, 81 (2009), Phys.Rev.D, 80, 115007 (2009) Phys.Rev.D, 83, 093011 (2011), Phys.Rev.D, 85, 115006 (2012)

Contents Hierarchy problem Classically conformal symmetry Coleman-Weinberg mechanism Classically conformal B-L model Dark matter Leptogenesis

Hierarchy problem Standard Model(SM) has hierarchy problem The Standard Model is the best theory of describing the nature of particle physics, which is in excellent agreement with almost of all current experiments. However SM has hierarchy problem. It is the problem that the quadratic divergence in quantum corrections to the Higgs self energy, which should be canceled by the Higgs mass parameter with extremely high precision when the cutoff scale is much higher than the electroweak scale. We need fine-tuning between bare mass and quantum corrections　　　　　　　　　　　

Quadratic divergence Hierarchy problem Classically conformal symmetry W.A. Bardeen,　FERMILAB-CONF-95-391-T Hierarchy problem subtracted at UV scale Once subtracted, no longer appears We need about 30 digits fine-tuning. There are many solutions for hierarchy problem. GHU, SUSY, and so on. We consider another solution for hierarchy problem. SM has CC invariance expected for Higgs mass term. If there is classically conformal invariance, natural boundary condition is no mass terms at Planck scale. As discussed earlier, Classically means this invariance is violated by quantum effect. But once quadratic divergence is subtracted at Planck scale, there are only logarithmic divergences. Classically conformal symmetry Natural boundary condition is no mass terms at Planck scale

Classically conformal symmetry Logarithmic divergence SM + Classically conformal symmetry Logarithmic divergences are represented by RG equations.

Classically conformal symmetry Logarithmic divergence SM + Classically conformal symmetry The Ward Identity associated with the vanishing of the trace of the renormalized stress-tensor will forbid radiative mass generation The SM has a built-in scale, the (negative) Higgs mass-squared parameter The SM generates other scales at loop order via dimensional transmutation This is just the trace anomaly. It modifies the Ward Identity to allow multiplicative mass corrections, but not additive ones

Classically conformal symmetry Logarithmic divergence SM + Classically conformal symmetry Logarithmic divergence SM + Classically conformal symmetry + New physics Large logarithmic divergence by mixing with a large mass scale Classically conformal theory with no intermediate scale can be an alternative solution to the naturalness problem

Classically conformal SM 　 If theory has the classical conformal invariance, the Higgs mass term is forbidden. 　Therefore there is no electroweak symmetry breaking at the classical level. We need to consider origin of the symmetry breaking. Coleman-Weinberg Mechanism (radiative symmetry breaking)

Coleman-Weinberg Mechanism CW Mechanism S.R.Coleman, E.Weinberg PRD7 (1973) 1888 Potential First derivative Second derivative

CW mechanism in SM For heavy top quark, potential is unstable CW mechanism does’t work in SM

Classically conformal B-L extended Model We propose classically conformal minimal B-L extended model. The B-L (baryon minus lepton) number is a unique anomaly free global symmetry that the SM possesses and can be easily gauged. The classically conformal minimal B-L model as a phenomenologically viable model that realizes the CW type breaking of the electroweak symmetry.

Classically conformal B-L extended Model Gauge symmetry Lagrangian We assume classically conformal symmetry Yukawa sector Potential The mass terms are forbidden by classically conformal symmetry. Dirac Yukawa Majorana Yukawa Three generations of right-handed neutrinos are necessarily introduced to make the model free from all the gauge and gravitational anomalies. 　SM singlet scalar The SM singlet scalar works to break the U(1)B-L gauge symmetry by its VEV.

CW mechanism in our model In our model, if majorana Yukawa coupling is small, the stability condition satisfies. The potential has non-trivial minimum. B-L symmetry is broken by CW mechanism.

Right-handed neutrinos Dark matter Parity Resonant leptogenesis Degenerate masses

Dark matter We introduce the Z2 parity into the model and impose one of three right-handed neutrinos to be odd, while the others even.

Resonant Leptogenesis The Majorana masses is heavier than ,if the spectrum of Majorana masses has hierarchy. If the Majorana mass of right-handed neutrino is smaller than a few TeV, general leptogenesis can not work. We want to consider TeV scale leptogenesis. We need resonant-Leptogenesis. Resonant Leptogenesis

Resonant Leptogenesis If two right-handed neutrinos have mass differences comparable to their decay widths , CP asymmetry parameter becomes large. This is self-energy contribution. If mass difference is given this value, CP asymmetry parameter become this form. due to the low seesaw scale, which implies that the Yukawa couplings of the RH neutrinos be very small, the adequate lepton asymmetry can arise only via the so-called resonant leptogenesis, which requires at least two of the RH neutrinos be very degenerate in mass. can be even .

Assumptions Assumption Ⅰ Only two right-handed neutrino are relevant to neutrino oscillation. Dirac Yukawa matrix is 2×3 matrix. Assumption Ⅱ Neutrino mixing matrix is tri-bimaximal matrix, when CP phase is zero. Under these assumption, we consider whether that we can generate sufficiently baryon asymmetry. TB maximal matrix is almost best fit of neutrino oscillation. When CP phase switch on One see-saw mass is 0 because we assume dirac yukawa matrix is 2×3 matrix. Assumption Ⅲ Hierarchal neutrino mass spectrum.

Baryon asymmetry in our universe These values depend only phase.

Mass difference

Mixing angle

Conclusions The classically conformal theory may be free from the hierarchy problem. We propose the classically conformal minimal B-L model. B-L symmetry and EW symmetry are broken by CW mechanism. Based on assumptions, we analyze neutrino oscillation data and baryon number as a function of a single CP phase. We have found a fixed CP phase can reproduce both all neutrino oscillation data and observed baryon asymmetry.