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The classically conformal B-L extended standard model Yuta Orikasa Satoshi Iso(KEK,SOKENDAI) Nobuchika Okada(University of Alabama) Phys.Lett.B676(2009)81 Phys.Rev.D80(2009)115007 Phys.Rev.D83(2011)093011 2 Classically conformal SM We assume the classically conformal invariance. This invariance forbids the Higgs mass term. 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) Calculate quantum correction 3 However, top quark is heavy, so the stability condition does not satisfy. The effective potential is not stabilized. In the classically conformal SM, due to the large top mass the effective potential is rendered unstable, and CW mechanism does not work. We need to extend SM. We propose classically conformal minimal B-L extended model. 4 Contents • Introduction • Classically conformal B-L extended Standard Model • Phenomenological bound • Collider physics • Thermal leptogenesis • Neutrino oscillation data and resonant leptogenesis • Conclusion 5 6 Classically conformal B-L extended Model Gauge symmetry New particles right-handed neutrino SM singlet scalar gauge field 7 Lagrangian We assume classically conformal invariance Yukawa sector Dirac Yukawa Majorana Yukawa See-Saw mechanism associates with B-L symmetry breaking. Potential Renormalization group equations for masses Classically conformal invariance at planck scale Potential Renormalization group equations for masses Classically conformal invariance at planck scale Potential Renormalization group equations for quartic couplings Assumption is very small and negative at planck scale 11 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. 12 Electroweak symmetry breaking Once the B-L symmetry is broken, the SM Higgs doublet mass is generated through the mixing term between H and Φ in the scalar potential. Φ has VEV M. Effective tree-level mass squared is induced. EW symmetry breaking occurs as usual in the SM. TeV scale B-L model If the B-L gauge coupling and the SM gauge couplings are same order, B-L breaking scale is around a few TeV. 14 15 LEP bound LEP experiments provided a severe constraint. LEP bound 16 17 Z’ boson at LHC We calculate the dilepton production cross section through the Z’ boson exchange together with the SM processes mediated by Z boson and photon. Z’ exchange A clear peak of Z’ resonance SM background 18 Z’ boson at ILC (International Linear Collider) We calculate the cross section of the process at the ILC with a collider energy =1 TeV. → 19 Excluded by LEP LHC reach ILC reach The figure indicates that if the B-L gauge coupling is not much smaller than the SM gauge couplings, Z’ boson mass is around a few TeV. 20 21 Leptogenesis suppressed by Z’ exchange process Wash out for inverse decay Initial condition ε=0.01 22 CP Asymmetry Right-handed Majorana neutrino can decay into lepton and anti-lepton. Vertex contribution Self-energy contribution 23 Majorana mass bound If right-handed neutrinos have a hierarchical mass spectrum ,we can write a CP asymmetry as Baryon asymmetry is The Majorana mass is heavier than . 24 Resonant Leptogenesis • The Majorana mass 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. Resonant-Leptogenesis 25 resonant-leptogenesis If two right-handed neutrinos have mass differences comparable to their decay widths , self-energy correction dominate. can be even . 26 27 More realistic case Neutrino oscillation data(2σ) Any model of leptogenesis should reproduce these masses and mixing angles. 28 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. Assumption Ⅲ Hierarchal neutrino mass spectrum. 29 Baryon asymmetry in our universe 30 Mass difference 31 Mixing angle 32 33 Conclusions • We propose the classically conformal minimal BL model. • B-L symmetry and EW symmetry are broken by CW mechanism. • Our model naturally predicts B-L breaking scale at TeV. Z’ boson can be discovered in the near future. • Based on assumptions, we analyze neutrino oscillation data and B 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. 34 Theoretical bound Planck scale The bound of B-L gauge coupling αB-L We impose the condition that B-L gauge coupling does not blow up to Planck scale. For TeV scale B-L symmetry breaking, we find scale 35 Resonant leptogenesis We consider minimal flavor violation At high energy scale, the Majorana masses have same value Flavor symmetry violates the effect of Dirac Yukawa coupling Quantum correction for the Majorana masses