Right-Handed Neutrinos as the Origin of the Electroweak Scale

Transcription

1 Right-Handed Neutrinos as the Origin of the Electroweak Scale Hooman Davoudiasl HET Group, Brookhaven National Laboratory Based on: H. D., I. Lewis, arxiv: [hep-ph] Origin of Mass 2014, CP 3 Origins, SDU, Odense, Denmark, May 19-22, 2014

2 Introduction Higgs boson discovery: the minimal SM seemingly complete Higgs boson, the simplest SM sate: no spin, no charge This unique state however challenges our QFT intuitions Apparent puzzle: its sole quantum number m H 126 GeV Why is m H small compared to some potentially large scales? One-loop contributions δm 2 H g2 Λ 2 /(16π 2 ) Λ the cutoff scale of the effective theory; g Higgs coupling The hierarchy problem: Λ m H (no significant deviations from SM) Unnatural fine-tuning

3 Is Λ physically significant? Appears in cutoff regularization. Not explicit in dimensional regularization (dim-reg). A cutoff not generally related to a physical mass scale. How about massive states with M m H? They contribute, even in dim-reg as g 2 M 2 /(16π 2 ) Present on physical grounds, no good reason to ignore them. Unavoidable fine-tuning for g 1 and M m H.

4 Let us focus on masses of physical states. Maintain naturalness for g 1 or M < m H SM automatically natural, in this sense. Bardeen, 1995 Naturalness: only weakly coupled heavy states in SM extensions. Finite Naturalness ; Farina, Pappadopulo, and Strumia, 2013; see also de Gouvea, Hernandez, Tait, 2014 May explain the insular nature of SM - Discard quadratic divergences; no partner states needed This talk: assume EW Lagrangian classically scale free Motivated by apparent smallness of m H Masses only via quantum effects. Coleman and Weinberg, 1973 Here referred to as Physical Naturalness Principle (PNP). Heikinheimo, Racioppi, Raidal, Spethmann, Tuominen, 2013

5 There are many related works: R. Hempfling, Phys. Lett. B 379, 153 (1996) [hep-ph/ ]; K. A. Meissner and H. Nicolai, Phys. Lett. B 648, 312 (2007) [hep-th/ ]; W. -F. Chang, J. N. Ng and J. M. S. Wu, Phys. Rev. D 75, (2007) [hep-ph/ ]; R. Foot, A. Kobakhidze, K..L. McDonald and R..R. Volkas, Phys. Rev. D 76, (2007) [arxiv: [hep-ph]]; T. Hambye and M. H. G. Tytgat, Phys. Lett. B 659, 651 (2008) [arxiv: [hep-ph]]; R. Foot, A. Kobakhidze, K. L. McDonald and R. R. Volkas, Phys. Rev. D 77, (2008) [arxiv: [hep-ph]]; S. Iso, N. Okada and Y. Orikasa, Phys. Lett. B 676, 81 (2009) [arxiv: [hep-ph]]; M. Holthausen, M. Lindner and M. A. Schmidt, Phys. Rev. D 82, (2010) [arxiv: [hep-ph]]; R. Foot, A. Kobakhidze and R. R. Volkas, Phys. Rev. D 82, (2010) [arxiv: [hep-ph]]; L. Alexander-Nunneley and A. Pilaftsis, JHEP 1009, 021 (2010) [arxiv: [hep-ph]]; T. Hur and P. Ko, Phys. Rev. Lett. 106, (2011) [arxiv: [hep-ph]]; S. Iso and Y. Orikasa, PTEP 2013, 023B08 (2013) [arxiv: [hep-ph]]; C. Englert, J. Jaeckel, V. V. Khoze and M. Spannowsky, JHEP 1304, 060 (2013) [arxiv: [hep-ph]]; T. Hambye and A. Strumia, Phys. Rev. D 88, (2013) [arxiv: [hep-ph]]; G. Marques Tavares, M. Schmaltz and W. Skiba, Phys. Rev. D 89, (2014) [arxiv: [hep-ph]]; C. D. Carone and R. Ramos, Phys. Rev. D 88, (2013) [arxiv: [hep-ph]]; A. Farzinnia, H. -J. He and J. Ren, Phys. Lett. B 727, 141 (2013) [arxiv: [hep-ph]]; O. Antipin, M. Mojaza and F. Sannino, arxiv: [hep-ph]; C. T. Hill, Phys. Rev. D 89, (2014) [arxiv: [hep-ph]]...

6 With PNP, SM cannot lead to v H 246 GeV One needs source of mass scale from beyond SM Possibility: loop-induced Higgs mass parameter from physical states Quadratic sensitivity A well-motivated choice: right-handed neutrinos N Yukawa coupling y N H LN M N H : seesaw for m ν 0 and B 0 via leptogenesis However, m ν 0.1 ev and leptogenesis inconsistent with PNP

7 Leptogenesis: L from CP violation: ε y 2 N /(8π) L B via EW sphalerons: n Bs ε g y2 N 8πg y N > (leptogenesis) g 100 (at T 100 GeV) Seesaw mechanism: m ν y2 N H 2 M N 0.1 ev For y N M N 10 8 GeV δm 2 H y2 N 4π 2M2 N (8 TeV)2 requires fine-tuning Conflict with PNP

8 Violation of PNP: same interactions for leptogenesis and seesaw. Simple resolution: SM Higgs field, H 1, not directly coupled to N. - Assume N odd under a Z 2. A second doublet, H 2, also odd under the Z 2. - New Yukawa couplings: N LH 2. Leptogenesis through CP violation in N LH 2. H 2 =0 ( inert doublet ): H 2 not responsible for m ν 0. However, m ν 0 at 1-loop; no other fields needed. Also, H 2 =0 unbroken Z 2 ; can stabilize a scalar DM candidate.

9 The Model Massive Majorana neutrinos N a, a=1,2: L N = y ai H 2 L in a M N a N c an a +H.C. i=1,2,3 the lepton generation index No hierarchy from M N (origin beyond this effective theory). May come from classically scale free UV sector (non-perturbative,...) H 1 and H 2 SM Higgs-like doublets. H 2 and N a are Z 2 odd. Scalar potential at high scales above M Ni : V 0 = λ 1 2 H λ 2 2 H λ 3 H 1 2 H λ 4 H 1 H λ 5 2 [(H ] 1 H 2) 2 +H.C. For simplicity, the iso-spin breaking coupling λ 4 = 0 later. V 0 has no mass scales, at tree-level, and cannot yield EWSB. However, quantum corrections change this picture.

10 Using 1-loop Coleman-Weinberg potential Dimensional regularization to focus on physical mass dependence. We need the mass eigenvalues as a function of scalar fields. Start from high scale M N and proceed. The neutrino sector masses: with α = 1,2. m 2 α(h 2 )= M2 Nα 2 M 2 α(h 2 )= M2 Nα 2 ( ) 1+2y 2 α H 2 2 M 2 1+4y 2 α H 2 2 M Nα 2 Nα ( 1+2y 2 α H 2 2 M 2 Nα + ) 1+4y 2 α H 2 2 M 2 Nα

11 Effective potential for H 2 V 1 (H 2, µ) = 1 2 { [ ( ) ] 32π 2 Mα(H 4 M 2 2 ) log α(h 2 ) α=1 µ 2 κ N 1 2 [ ( ) ] } + mα(h 4 m 2 2 ) log α(h 2 ) µ 2 κ N 1 2 µ is renormalization scale. Constant κ N parameterizes scheme dependence: κ N = 1 for MS. One finds V 1 (H 2, µ)= α y 2 αm 2 N α 8π 2 [ κ N log( M 2 Nα µ 2 )] H For κ N 1, induced H 2 mass parameter µ 2 M N.

12 Consider EFT at scale µ 2 M N : V 0 V 0 + µ 2 2 H 2 2 One-loop Coleman-Weinberg from the EFT: ( ) ( V 1 (H 2,H 1, µ)= µ2 2 16π 2 κ 2 log µ2 2 µ 2 3λ 2 H λ 3 H 1 2) +... κ 2 accounts for scheme dependence Mass parameter λ 3 for H 1 at scale µ 2 Simplifying assumption: M N1 = M N2 = M N and y 1 = y 2 = y N. Match the high and low scale potentials at µ = M N : µ 2 2 = M2 N y2 N κ N 4π 2 [ 1+ 3λ 2 16π 2 ( κ 2 log y2 N κ N 4π 2 )] Unbroken Z 2 for DM requires µ 2 2 > 0 κ N > 0. PNP implies κ O(1)

13 Match 1-loop SM and high scale (µ 2 ) potentials at µ = µ 2 The SM potential: µ 2 1 H λ 1 2 H 1 4 µ 2 1 = λ 3κ 2 8π 2 µ2 2 [ 1+ 3λ ( 1 16π 2 κ 1 log λ )] 3κ 2 8π 2 κ 1 1 EWSB: µ 2 1 > 0 κ 2λ 3 > 0 Simplicity λ 4 = 0, no dependence on λ 5 (does not yield H 1 H 1). log( 1): expansion around H 1 = 0 instead of H 1 =v/ 2. In MS scheme, finite part gives κ > 0 µ 1 2, µ2 2 > 0. For κ 2 = κ N κ µ 2 1 κ2 λ 3 y 2 N M2 N /(32π4 ) µ 2 1 (89 GeV)2 (m H 126 GeV) M N TeV λ3 κ(y N /10 3 ) y N > (leptogenesis)

14 Light Neutrino Masses No direct H 1 (source of EWSB) coupling to N α. However, seesaw (Weinberg) operator at 1-loop Ma, 2006 L eff = α y 2 αλ 5 16π 2 M N α Neutrino mass ( ) 1+log µ2 2 M 2 H 1 L c H 1 L+H.C. Nα [ ( ) ] m ν λ 5 y 2 N v2 8π 2 log 4π 2 M N y 2 N κ 1 H 1 H 1 H 2 H 2 N L L Leptogenesis (y N ), PNP (M N ), and m ν = 0.1 ev λ λ3 κ µ 2 κ 2.7 TeV Conditions satisfied for reasonable values of λ 3 and λ 5.

15 Scalar DM Good Z 2 Lightest parity odd state stable A mass eigenstate from H 2 =[H +,(S+iA)/ 2] T. Scalar spectrum after EWSB H 1 =v/ 2 m 2 h = λ 1 v 2 m 2 S = µ λ S v 2 m 2 A = µ2 2 + λ A v 2 m 2 H ± = µ λ 3 2 v2 λ S (λ 3 + λ 4 + λ 5 )/2 and λ A (λ 3 + λ 4 λ 5 )/2 λ 4 = 0 A the lightest parity odd state and a DM candidate.

16 We have m S > m H ± > m A, with splitting: λ 5 v 2 /(4µ 2 ) Decay rate, assuming M w : Γ G2 F 64π 3 5 G F Fermi s constant Scalar decays before BBN (t 1 s) 5 MeV ( TeV λ 5 ) λ 5 0 to split S and A, avoid Z-mediated direct detection constraints TeV-scale DM, virial velocity 200 km/s kinetic energy few 100 kev µ 2 H-mediated: σ n f 2 n λ 2 A π f N 0.3 and m n 1 GeV µ 2 1 TeV and λ : σ n cm 2 Consistent with LUX bounds m 4 n µ 2 2 m4 H Could be within near future reach LUX Collaboration, 2013

17 With λ 4 = 0, DM relic density depends on λ 3, λ 5, µ 2 and gauge couplings. SM values of Higgs parameters relate λ 3 and µ 2. We require 2σ consistency with Planck 2013 results Ω DM h 2 = ± y N 3 x y N 3 x 10-4 y N 5 x 10-4 y N 7 x 10-4 λ y N 5 x 10-4 y N 7 x 10-4 λ κ = 2 Ω DM = ± µ 2 (TeV) κ = 0.5 Ω DM = ± µ 2 (TeV) For µ 2 > 550 GeV annihilation only from gauge couplings insufficient Hambye, Ling, Lopez Honorez, Rocher, 2009 Need co-annihilation from scalar quartic couplings For λ 5 λ 3 relic density gives µ 2 0.8(1.3) TeV for κ = 0.5(2) For µ 2 1 TeV, λ 3 can be neglected and λ 5 µ 2 2 TeV max 7 GeV (unconstrained by precision EW data)

18 Running Couplings 5 1 µ 2 = 1.1 TeV κ = 1 λ λ 5 λ λ 1 λ 2 λ µ (GeV) λ 5 λ 3 (µ 2 ) = 0.55 λ 5 (µ 2 ) = 0.06 One-loop running 10-1 λ 3 λ 1 λ 2 µ 2 = 4 TeV κ = 1 λ 3 (µ 2 ) = 0.04 λ 5 (µ 2 ) = 1.9 One-loop running µ (GeV) λ 1 = 0.26 (SM value) at µ = m H and λ 2 (µ 2 )=0.01 RGE: Hill, Leung, Rao, 1985 λ 3 and λ 5 fixed by PNP and Ω DM for given (µ 2,κ) Avoid large scalar masses from Landau poles Meissner and Nicolai, 2007 Perturbative quartic couplings to M P DM mass near 1 TeV

19 Conclusions Insular nature of SM may argue against relevance of Higgs quadratic divergence No partner states required Classically scale free EW sector, scales from quantum effects of physical states Physical Naturalness Principle (PNP): physical consequences Example: Heavy right-handed neutrinos weakly coupled to Higgs Seesaw and leptogenesis (sufficient CP violation) in conflict Z 2 odd sector: second inert doublet and right-handed neutrinos Disentangle leptogenesis and tree-level seesaw Natural scalar DM candidate (lightest Z 2 scalar state) The framework can accommodate PNP, realistic leptogenesis, m ν 0, and DM! TeV-scale scalars, degenerate spectrum Perturbative scalar couplings to M P : DM mass near 1 TeV May be accessible to near future direct detection experiments