Neutrino Mass, Dark Matter, and Leptogenesis

Transcription

1 UCRHEP-T44 November 006 arxv:hep-ph/ v1 13 Nov 006 Neutrno Mass, Dark Matter, and Leptogeness Ernest Ma Physcs and Astronomy Department, Unversty of Calforna, Rversde, Calforna 951 Abstract It s proposed that dark matter s the orgn of neutrno mass, thereby lnkng nexorably two undsputed (and seemngly unrelated) peces of evdence for physcs beyond the Standard Model. Leptogeness at the TeV scale may also be possble, as well as a measurable contrbuton to the muon anomalous magnetc moment. Talk at NOW006, Conca Specchulla, Otranto, Italy.

2 1 INTRODUCTION Any theory beyond the Standard Model (SM) should ncorporate neutrno mass and dark matter. Are they related? In ths talk, I propose that neutrno mass s due to the exstence of dark matter. I wll dscuss some recent models and ther phenomenologcal consequences. A canddate for dark matter should be neutral and stable, the latter mplyng at least an exactly conserved odd-even (Z ) symmetry. In the Mnmal Supersymmetrc Standard Model (MSSM), the lghtest neutral partcle havng odd R party s a canddate. It s usually assumed to be a fermon,.e. the lghtest neutralno. [The lghtest neutral boson, presumably a scalar neutrno, s ruled out phenomenologcally.] If all one wants s dark matter, the smplest way s to add a second Hggs double (η +, η 0 ) [1] whch s odd under Z wth all SM partcles even. Ths dffers from the scalar MSSM ( ν, l) doublet, because ηr 0 and ηi 0 are splt n mass by the Z conservng term (λ 5 /)(Φ η) + H.c. whch s absent n the MSSM. NEUTRINO MASS AND DARK MATTER To obtan a small Majorana neutrno mass n the SM, consder the unque dmenson-fve operator [] f αβ Λ (ν αφ 0 l α φ + )(ν β φ 0 l β φ + ). (1) It has exactly 3 tree-level realzatons [3] by nsertng the approprate ntermedate state: (I) N, (II) (ξ ++, ξ +, ξ 0 ), (III) (Σ +, Σ 0, Σ ); and 3 generc one-loop realzatons [3]: (IV) one external scalar lne coupled to the nternal fermon lne and the other to the nternal scalar lne, (V) both coupled to the scalar lne, (VI) both coupled to the fermon lne. Radatve mechansm (IV) domnates the lterature, the prme example beng the Zee

3 model [4]. I propose nstead [5] mechansm (V) wth the addton of N, = 1,, 3 and (η +, η 0 ), all beng odd under Z. As a result, ether η 0 R or η0 I s dark matter wth mass 60 to 80 GeV [1], or the lghtest N s dark matter, wth all masses of order 350 GeV or less [6] for the new partcles. 3 NEUTRINO MASS AND LEPTOGENESIS Because of the assumed Z symmetry, ν α does not couple to N through φ 0. Hence N s not the Drac mass partner of ν α as n the canoncal seesaw model. Instead ν α couples to N through η 0 (whch has no vacuum expectaton value) and obtans a radatve Majorana mass n one loop,.e. (M ν ) αβ = h α h β M 16π [ f ( M m R ) f ( M m I )], () where f(x) = ln x/(1 x). Let m R m I = λ 5 << m 0 = (m R + m I )/, then where For x >> 1,.e. N very heavy, (M ν ) αβ = I(x) = λ 5v 8π (M ν ) αβ = λ 5v 8π ( ) h α h β M I, (3) M m 0 ( ) [ x 1 + x lnx ]. (4) 1 x 1 x h α h β M [ln x 1] (5) nstead of the canoncal seesaw expresson of v h α h β /M. In leptogeness, the lghtest M may then be much below the Davdson-Ibarra bound [7] of about 10 9 GeV, thus avodng a potental conflct of gravtno overproducton and thermal leptogeness. In ths scenaro, η 0 s dark matter. 3

4 4 MUON g AND NEUTRINO MASS Another model of ths class has recently been proposed [8] agan wth an exactly conserved Z where N, N c, (η+, η 0 ), χ are odd. Lepton number,.e. U(1) L, s also assgned to these felds: 1, 1, 0, 0 respectvely. γ η + χ µ N c µ c N Fgure 1: Domnant contrbutons to muon anomalous magnetc moment. The muon gets an anomalous magnetc moment from the Drac mass terms lnkng N wth N c and the mxng of η ± wth χ ± (formng the egenstates X and Y wth mxng angle θ), resultng n a µ = sn θ cosθ 16π h µ h m µ µ [F(x ) F(y )], (6) M where x = m X /M, y = m Y /M, and F(x) = [1 x +x ln x]/(1 x) 3. Let y << x 1, M 1 TeV, ( h µ h µ sn θ cosθ/4π ) 10 5, then a µ 10 9, whereas ( a µ ) exp t = (.4 ± 10) to (6.1 ± 9.4) φ 0 φ 0 η 0 η 0 ν α N c N c j ν β Fgure : Radatve Majorana neutrno mass. To obtan a nonzero neutrno mass, U(1) L s broken softly by the terms 1 m jn c N c j + 1 m jn N j + H.c., (7) 4

5 resultng n the resdual symmetry ( 1) L. The one-loop radatve Majorana neutrno mass matrx s then gven by (M ν ) αβ =,j h α h βj λ 5 v [ m j M 8π (M Mj ) m 0 M + M4 ln(m /m ] 0) ( j). (8) (m 0 M ) Let M,j 1 TeV, m j 0.1 GeV, h α 10, λ 5 0.1, m 0 v 10 GeV, then the entres of M ν are of order 0.1 ev. Suppose the h α1 couplngs are very small,.e. N c 1 decouples from M ν, t s stll possble to obtan a realstc neutrno mass matrx. For example, let then usng the [ν e, (ν µ + ν τ )/, ( ν µ + ν τ )/ ] bass,.e. θ 3 = π/4, θ 13 = 0, m 3 = 0 (nverted orderng) h α h 0 0 1/ 0 0 1/, (9) m m 3 0 M ν h m 3 m 33 0, (10) NOVEL TEV LEPTOGENESIS Let (N 1, N1 c) be the lghtest par wth h α1, h α to satsfy the out-of-equlbrum condton for leptogeness at the TeV scale. Rotate ( ) ( ) m 11 M 1 M1 + A B, (11) M 1 m 11 B M 1 + A where A = (m 11 + m 11)/, B = (m 11 m 11)/. Choose phases so that M 1 > 0, A > 0 are real and B = B exp(α). Dagonalze above matrx wth ( exp(β) cosθ sn θ sn θ exp( β) cos θ 5 ), (1)

6 then sn β = M 1 tanα/c, cosβ = A/C, tan θ = cosα B C/AM 1, where C = (A + M 1 tan α) 1/. Let A << M 1 tan α, then exp(β) = (A/M 1 tan α), and the lepton asymmetry s gven by ( ) 1 B [ sn α cos α 4( α h α1 ) ( α h α1 ) ] 64π A + B sn α α h α1 +. (13) α h α1 The novel feature of ths mechansm s that CP volaton orgnates n the mass matrx, not the Yukawa couplngs. However, because h α1, h α1 10 7, ths effect s too small. Ths means that (N, N c ) must also be consdered, and the complete expresson of the asymmetry becomes rather complcated. Now because h α are mostly unconstraned, ths asymmetry may well be of order 10 6 for M 1, of order 1 TeV for a realstc scenaro of leptogeness, whch s also verfable at the forthcomng Large Hadron Collder (LHC). 6 CONCLUSION The evdence of dark matter sgnals a new class of partcles at the TeV scale, whch may manfest themselves ndrectly through loop effects. They may be responsble for neutrno mass, muon anomalous magnetc moment, as well as leptogeness. Two smple examples predct observable bosonc dark matter at the electroweak scale, and perhaps also neutral snglet fermons at the TeV scale. Afterword Ths talk was gven on September 11, 006. Exactly 5 years ago, I was also n Italy gvng a talk durng that most fateful event of recent tmes. 6

7 Acknowledgement I thank Ganlug Fogl, Carlo Gunt, and the other organzers of NOW006 for ther great hosptalty at Conca Specchulla, Otranto. Ths work was supported n part by the U. S. Department of Energy under Grant No. DE-FG03-94ER References [1] R. Barber, L. J. Hall, and V. S. Rychkov, Phys. Rev. D74, (006). [] S. Wenberg, Phys. Rev. Lett. 43, 1566 (1979). [3] E. Ma, Phys. Rev. Lett. 81, 1171 (1998). [4] A. Zee, Phys. Lett. B93, 389 (1980). [5] E. Ma, Phys. Rev. D73, (006); Mod. Phys. Lett. A1, 1777 (006); hep-ph/ [6] J. Kubo, E. Ma, and D. Suematsu, Phys. Lett. B64, 18 (006). [7] S. Davdson and A. Ibarra, Phys. Lett. B535, 5 (00). [8] T. Hambye, K. Kannke, E. Ma, and M. Radal, hep-ph/