Alternatives to the GUT Seesaw

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1 Alternatives to the GUT Seesaw Motivations Higher-dimensional operators String instantons Other (higher dimensions, Higgs triplets)

2 Motivations Many mechanisms for small neutrino mass, both Majorana and Dirac Minimal Type I seesaw Bottom-up motivation: no gauge symmetries prevent large Majorana mass for ν R Connection with leptogenesis Argument that L must be violated is misleading (large 126 of SO(10) or HDO added by hand) New TeV or string scale physics/symmetries/constraints may invalidate assumptions

3 Standard alternatives: loops, R p violation Higgs triplets, extended (TeV) seesaws, Explore plausible possibilities of string landscape String-motivated alternatives: HDO (non-minimal seesaw, direct Majorana, Dirac); string instantons; geometric suppressions Alternatives often associated with new TeV physics, electroweak baryogenesis, etc.

4 Higher-dimensional operators The Weinberg operator (most Majorana models) l L = ( νl L φφ = C ( l L τ l ) ( R φ τ φ ) + h.c. 2M = C ( l φ) L (φ l ) R + h.c. M = C ( φ l 0 φ φ 0 φ 0 ) L l M φ φ φ φ 0 R + h.c., e L ), lr = ( e c R ν c R ), φ = ( φ + φ 0 ), φ = ( φ 0 φ ) Superpotential: W = C M LLH uh u Generate directly in string construction, or in effective 4d theory

5 Direct generation of Weinberg operator Simplest possibility: generate operator by underlying string dynamics ν L ν L φ 0 φ 0 W = C M LLH uh u, with C 1, M = M s M P = M P GeV 8π m ν 10 5 ev ( need M/C GeV M P ) Can compactify on internal volume V 6 M 6 s M 2 P M 8 s V 6 Can obtain m ν 0.1 ev for V M 6 s (Conlon,Cremades) M s GeV still large compared to LED scenarios Will discuss string instanton induced case

6 The ν L GUT seesaw ν L Realize Weinberg operator φ 0 via heavy φ 0 particle exchange in effective 4d theory Seesaw implementation Type I: heavy Majorana ν R Type II: heavy Higgs triplet ν L φ S ν R ν R h S φ 0 φ 0 ν L ν L h T ν L φ 0 T κ φ 0 φ 0 Type I in SO(10): φ S 126 H (Type II also possible) W h u H }{{} +h S }{{ H} ν L ν R φ 0 Alternative (Babu,Pati,Wilczek): replace 126 H operator: W λ M H 16 H Need h S φ 126 or λ H M φ 16 H GeV Typeset by FoilTEX 1 ν L ν c R φ S by higher-dimensional hu φ 10H 100 GeV 2

7 The string seesaw Heterotic: Majorana mass for N c from S q+1 W N c ij N c i N c S q+1 j (m N ) ij c ij, q 0 M q s M q s Simultaneous Dirac mass terms from W D ( S M s ) p LN c H u m D ( ) p S H u, p 0 M s SM singlet fields S may be different Typically, S M s = O(10 1 ) at minimum (e.g., if from FI term) Must be consistent with string constraints/symmetries; with F = D = 0 (supersymmetry); W = 0 (cosmological constant)

8 Difficult to satisfy all conditions Caveat: N1 cn 2 c Dirac; N 1 cn 2 c + N 1 cn 3 c Dirac + Weyl; need N1 cn 1 c or N 1 cn 2 c + N 1 cn 3 c + N 2 cn 3 c for Majorana No examples in Z 3 heterotic orbifold (Giedt,Kane,PL,Nelson) At least two examples in heterotic E 8 E 8 orbifold on Z 3 Z 2 (Buchmuller,Hamaguchi,Lebedev,Ramos-Sanchez,Ratz; Lebedev,Nilles,Raby,Ramos-Sanchez,Ratz,Vaudrevange,Wingerter) May be many (O(10 100)) N c ; p 0,..., 6, q 3,..., 8. Nonminimal. Simple SO(10) relations lost Will comment on intersecting brane, F-theory

9 Other higher-dimensional operators HDO for ν R mass possible for string seesaw, but other HDO also possible from string or effective theory Example: W = µh u H d µ problem: why is µ = O(M SUSY )? Can promote µ to dynamical variable (e.g., d > 2 in W or in K, or string instanton) NMSSM, nmssm, UMSSM: W = λ S SH u H d µ eff = λ S S (S= SM singlet; usually S = O(ν) 246 GeV) Giudice-Masiero: K = X M H uh d + h.c., where X = θθf (SM singlet); for M SUSY = F/M µ eff = O(M SUSY ) (e.g., M = M P in supergravity) Both cases: assume new symmetry of effective theory or string constraints forbids elementary µ

10 Many other possibilities for small neutrino masses utilizing W or K (both Majorana and Dirac) (Cleaver,Cvetič,Espinosa,Everett,PL; PL; Arkani-Hamed,Hall,Murayama,Smith,Weiner; Borzumati,Nomura; March-Russel,West; Dvali,Nir; Frere,Libanov,Troitsky; Casas,Espinosa,Navarro; Demir,Everett,PL) Invoke extra symmetries (e.g., U(1) ) or string constraints to forbid, e.g., elementary Dirac Yukawa W = LN c H u Example: small Dirac from HDO in W (CCEEL): W S M LN c H u m ν S ν u M S = 1000 TeV for M = M P e.g. (approximately) flat breaking of U(1) (CCEEL); Z mediation (PL,Paz,Wang,Yavin),...

11 Example: small Majorana from non-holomorphic K (CEN) K 1 M 2LH ul H d + h.c., H d ( H + d H 0 d ) But F H d = µh u (or µ eff H u ) m ν µν2 u M 2 µ 100 GeV M 10 8 GeV, e.g., SUSY mediation scale Example: small Dirac from non-holomorphic K (DEL) K 1 M 2X LN c H d + h.c., with X = θθf M = SUSY mediation scale (e.g., GeV), M SUSY = F/M W = M SUSY M LN c H d m ν M SUSY ν d M

12 Alternative K 1 M LN c H d + h.c., with F H d = µh u Non-holomorphic A terms (suppressed by M SUSY /M)(DEL) K 1 M 3XX LN c H d + h.c. A M 2 SUSY M Small Dirac mass from loop (need U(1) ; also forbids normal Yukawa) ~! L H d 0 ~! R ~ W ~ 3 ~ B,, Z ~ Z! L! R

13 String Instantons Intersecting brane: hard to achieve Majorana or small Dirac masses perturbatively Anomalous U(1) : M Z M s, but acts like perturbative global symmetry (may forbid µ, R P violation, N c N c, LN c H u, QU c H u,... ) String instantons: nonperturbative violation of global symmetries ( exp( S inst ) exp 2π ) V E2 α GUT V D6 V E2 = f(winding numbers) V D6

14 Majorana masses from string instantons (seesaw) (also, µ, Yukawas) (Blumenhagen,Cvetič,Weigand;Ibanez,Uranga) m νr M s e S inst Small Dirac, e S instln c H u (natural scale, ev) (Cvetič,PL) Stringy Weinberg operator with low M s (Cvetič,Halverson,PL,Richter) W 5 = e S inst M s LLH u H u, M s ( ) GeV Systematic analysis of semi-realistic 4 and 5 stack D-brane quivers yielding W 5 Examples include M s ( ) GeV (µ eff ) and M s ( ) GeV (Yukawa)

15 Other possibilities Large extra dimensions, with ν R propagating in bulk small Dirac masses from wave function overlap, cf., gravity (Dienes,Dudas,Gherghetta; Arkani-Hamed,Dimopoulos,Dvali,March-Russell) m ν νm ( 2 ) δ+2 1 F M P, M F = = fundamental scale M P V δ Small Dirac from wave function overlap in warped dimensions, L and ν R in bulk (Chang,Ng,Wu) Majorana ν R as Kaluza-Klein modes, moduli, etc (F-theory) (Tatar,Tsuchiya,Watari; Bouchard,Heckman,Seo,Vafa) Heavy Higgs triplets with Y = ±1 (Type II seesaw). Difficult to embed in strings (singlets, bifundamentals, adjoints) (PL,Nelson; Cvetič,PL)

16 Conclusions Can implement version of seesaw in strings, using complicated higher-dimensional operators, string instantons, Kaluza-Klein states, Other HDO in W or K, string instantons, or volume effects also possible, yielding small Majorana (stringy Weinberg operator) or Dirac

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