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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

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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 2

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In the classically conformal SM, due to the large top mass the effective potential is rendered unstable, and CW mechanism does not work. However, top quark is heavy, so the stability condition does not satisfy. The effective potential is not stabilized. We need to extend SM. We propose classically conformal minimal B-L extended model. 3

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Contents Introduction Classically conformal B-L extended Standard Model Phenomenological bound Collider physics Thermal leptogenesis Neutrino oscillation data and resonant leptogenesis Conclusion 4

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Classically conformal B-L extended Model Gauge symmetry New particles right-handed neutrino SM singlet scalar gauge field 6

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Lagrangian We assume classically conformal invariance Yukawa sector Dirac YukawaMajorana Yukawa See-Saw mechanism associates with B-L symmetry breaking. 7

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Potential at planck scale Renormalization group equations for masses Classically conformal invariance

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Potential at planck scale Renormalization group equations for masses Classically conformal invariance

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Potential at planck scale Assumption Renormalization group equations for quartic couplings is very small and negative

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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. 11

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Electroweak symmetry breaking Effective tree-level mass squared is induced. EW symmetry breaking occurs as usual in the SM. 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. 12

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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.

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LEP bound LEP experiments provided a severe constraint. LEP bound 15

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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. SM background Z’ exchange A clear peak of Z’ resonance 17

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Z’ boson at ILC (International Linear Collider) We calculate the cross section of the process → at the ILC with a collider energy =1 TeV. 18

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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.

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Leptogenesis ε=0.01 Initial condition 21 Wash out for inverse decay suppressed by Z’ exchange process

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CP Asymmetry Vertex contribution Self-energy contribution Right-handed Majorana neutrino can decay into lepton and anti-lepton. 22

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Majorana mass bound The Majorana mass is heavier than. 23 If right-handed neutrinos have a hierarchical mass spectrum,we can write a CP asymmetry as Baryon asymmetry is

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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 24

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resonant-leptogenesis If two right-handed neutrinos have mass differences comparable to their decay widths, self-energy correction dominate. can be even. 25

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More realistic case Neutrino oscillation data(2σ) Any model of leptogenesis should reproduce these masses and mixing angles. 27

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Assumptions Assumption Ⅱ Neutrino mixing matrix is tri-bimaximal matrix, when CP phase is zero. Assumption Ⅰ Only two right-handed neutrino are relevant to neutrino oscillation. Dirac Yukawa matrix is 2×3 matrix. Assumption Ⅲ Hierarchal neutrino mass spectrum. 28

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Baryon asymmetry in our universe 29

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Mass difference 30

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Mixing angle 31

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Conclusions We propose the classically conformal minimal B- L 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. 33

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Theoretical bound The bound of B-L gauge coupling 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 αB-L scale Planck scale 34

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35 We consider minimal flavor violation Flavor symmetry violates the effect of Dirac Yukawa coupling Resonant leptogenesis At high energy scale, the Majorana masses have same value Quantum correction for the Majorana masses

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