Neutrino masses respecting string constraints

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1 Neutrino masses respecting string constraints Introduction Neutrino preliminaries The GUT seesaw Neutrinos in string constructions The triplet model (Work in progress, in collaboration with J. Giedt, G. Kane, B. Nelson.)

2 Neutrino mass Nonzero mass may be first break with standard model Enormous theoretical effort: GUT, family symmetries, bottom up Majorana masses may be favored because not forbidden by SM gauge symmetries GUT seesaw (heavy Majorana singlet). Usually ordinary hierarchy. Higgs triplets ( type II seesaw ), often assuming GUT, Left- Right relations

3 Very little work from string constructions, even though probably Planck scale Key ingredients of most bottom up models forbidden in known constructions (heterotic or intersecting brane) Large representations difficult to achieve (bifundamentals, singlets, or adjoints) String symmetries/constraints restrict couplings, e.g., diagonal Majorana masses Very nonstandard triplet or singlet seesaws, favoring inverted hierarchy, extended seesaw, or small Dirac masses from HDO. (Work in progress, in collaboration with J. Giedt, G. Kane, B. Nelson.)

4 Models and spectra Weyl fermion Minimal (two-component) fermionic degree of freedom ψ L ψr c by CPT Active Neutrino (a.k.a. ordinary, doublet) in SU(2) doublet with charged lepton normal weak interactions ν L νr c by CPT Sterile Neutrino (a.k.a. singlet, right-handed) SU(2) singlet; no interactions except by mixing, Higgs, or BSM N R NL c by CPT Almost always present: Are they light? Do they mix?

5 Dirac Mass Connects distinct Weyl spinors (usually active to sterile): (m D ν L N R + h.c.) 4 components, L = 0 I = 1 2 Higgs doublet Why small? LED? HDO? Variant: couple active to antiactive, e.g., m D ν el ν c µr L e L µ conserved; I = 1 ν L h N R v = φ m D = hv

6 Majorana Mass Connects Weyl spinor with itself: 1 2 (m T ν L νr c + h.c.) (active); 1 2 (m S N L cn R + h.c.) (sterile) 2 components, L = ±2 Active: I = 1 triplet or seesaw Sterile: I = 0 singlet or bare mass Mixed Masses Majorana and Dirac mass terms ν L ν c R ν L ν L Seesaw for m S m D Ordinary-sterile mixing for m S and m D both small and comparable (or m S m d (pseudo-dirac))

3 ν Patterns Solar: LMA (SNO, Kamland) m 2 8 10 5 ev 2, nonmaximal

7 3 ν Patterns Solar: LMA (SNO, Kamland) m ev 2, nonmaximal Atmospheric: m 2 Atm ev 2, near-maximal mixing Reactor: U e3 small

8 Mixings: let ν ± 1 2 (ν µ ± ν τ ): ν 3 ν + ν 2 cos θ ν sin θ ν e ν 1 sin θ ν + cos θ ν e Hierarchical pattern Analogous to quarks, charged leptons ββ 0ν rate very small Inverted quasi-degenerate pattern ββ 0ν if Majorana SN1987A energetics (if U e3 0)? May be radiative unstable

9 The GUT Seesaw Elegant mechanism for small Majorana masses Leptogenesis Expect small mixings in simplest versions (can evade by lopsided e/d, Majorana textures, etc.) Large Majorana often forbidden, e.g., by extra U(1) s Direct Majorana masses and large scales forbidden in some string constructions GUTs, adjoint Higgs, large Higgs hard to accomodate in simplest heterotic constructions

10 LSND: active-sterile difficult in simple versions Therefore, explore alternatives, e.g., with small Dirac and/or Majorana masses Small Majorana from loops, R p violation, TeV seesaw, or triplet Small Dirac from large extra dimension or by higher dimensional operators in intermediate scale models (e.g. U(1) ) Variant ordinary and triplet seesaws motivated by string constructions

11 Neutrinos in string constructions Key ingredients of most GUT/bottom up models forbidden or different in known constructions (heterotic or intersecting brane) Bifundamentals, singlets, or adjoints; not large representations String symmetries/constraints may forbid couplings allowed by 4d symmetries Diagonal superpotential terms (e.g., diagonal Majorana masses) usually absent GUT Yukawa relations broken Non-zero superpotential terms may be equal (gauge couplings) Hierarchies from HDO (heterotic), intersection triangles (intersecting brane)

12 Dirac masses Can achieve small Dirac masses (neutrino or other) by higher dimensional operators or by large intersection areas L ν ( S M P l ) p LN c L H 2, S M P l m D ( S M P l ) p H 2 Large p S close to M P l (e.g., anomalous U(1) ) Small p intermediate scale M P l

13 Intermediate scale in (non-anomalous) U(1) from D and (almost) F flat direction: Two SM singlets charged under U(1). If no F terms, V (S 1, S 2 ) = m 2 1 S2 1 + m2 2 S2 2 + g 2 Q 2 ( S S2 2 )2 Break at EW scale for m m2 2 > 0, at intermediate scale for m m2 2 < 0 (stabilized by loops or HDO)

14 The ordinary seesaw Active neutrinos ν L, N R (3 flavors each) L = 1 2 ( νl N L) ( c m T m D m T D m S ) ( ) ν c R N R + hc m T = m T T = triplet Majorana mass matrix (Higgs triplet) m D = Dirac mass matrix (Higgs doublet) m S = m T S = singlet Majorana mass matrix (Higgs singlet); eg, 126 of SO(10)

15 Ordinary (type I) seesaw: m T = 0 and (eigenvalues) m S m D : m eff ν = m Dm 1 S mt D with U P MNS = U e U ν Most models assume either U e I in basis with manifest symmetries for m D,S large mixings in U ν Large U e mixings from lopsided m e in basis with m D,S diagonal (harder to achieve in SO(10) than SU(5)) SO(10) models usually yield ordinary hierarchy

16 String constructions: may be able to generate large effective m S from S q+1 S q+1 W ν c ij N i N j (m S ) ij c ij M q P l M q P l Can one have such terms simultaneously with Dirac couplings, consistent with flatness and other constraints? (Under investigation for Z 3 orbifold.) c ii = 0 in all known examples m S = 0 m 12 m 13 m 12 0 m 23 m 13 m 23 0

17 Very different from standard seesaw textures Case with three large eigenvalues requires complicated m D and/or m e 2 2 case could resemble special pseudo-dirac inverse hierarchy model found for triplets Extended seesaw with greater than 3 N fields? (Coriano, Faraggi; F., Thormeier)

18 Triplet models Introduce Higgs triplet T = (T ++ T + T 0 ) T with weak hypercharge Y = 1 Majorana masses m T generated from L ν = λ T ij L it L j if T 0 0 Old Gelmini-Roncadelli model: T 0 EW scale with spontaneous L violation Excluded by Z Majoron + scalar (equivalent to N ν = 2) Modern triplet models (type II seesaw) break L explicity by T HH couplings, giving large Majoron mass (Lazarides, Shafi, Wetterich, Mohapatra, Senjanovic, Schechter, Valle, Ma, Hambye, Sarkar, Rossi,...) Often considered in SO(10) or LR context, with both ordinary and triplet mechanisms competing and with related parameters, but can consider independently.

19 General SUSY case W ν = λ T ij L it L j + λ 1 H 1 T H 1 + λ 2 H 2 T H 2 +M T T T + µh 1 H 2 T, T are triplets with Y = ±1, M T GeV. Typically, T 0 λ H /m T m ν ij = λt ij λ 2 v 2 2 M T

20 String constructions Expect λ T ij = 0 for i = j (off-diagonal) mν ii = 0 Also, need multiple Higgs doublets H 1,2 with λ 1,2 off diagonal Partial explanation: SU(2) triplet with Y 0 requires higher level embedding, e.g., of SU(2) SU(2) SU(2) (Have Z 3 constructions with some but not all of the features.) W λ T 1j L 1(2, 1)T (2, 2)L j (1, 2), j = 2, 3 yields m ν = 0 a b a 0 0 b 0 0 Typical string case: a = b

21 HDO (or SU(2) SU(2) SU(2) SU(2)) can give m ν 23 0 For m ν = 0 a b a 0 c b c 0 can take a, b, c real w.l.o.g. by redefinition of fields (not true for general m ν ) Tr m ν = 0 and m ν = m ν m 1 + m 2 + m 3 = 0

22 m 2 Atm ev 2, m ev 2 two solutions For m 2 =0 (a) m i 1, 1 2, 1 (ordinary, with shifted masses) 2 (b) m i 1, 1, 0 (inverted) With m 2 0 (a) m i = 0.054, 0.026, ev ( m i = ev (cosmology)) (b) m i = 0.046, 0.045, ev ( m i = ev (cosmology)) m ν a m ν b 0 a b a 0 0 b 0 0 (a) leads to unrealistic mixing matrix consider (b)

23 A special texture The L e L µ L τ conserving texture m ν 0 a b a 0 0 b 0 0 has been considered phenomenologically by many authors (Zee; Barbieri, Hall, Smith, Strumia, Weiner; King, Singh; Ohlsson; Barbieri, Hambye, Romanino; Lebed, Martin; Babu, Mohapatra; Lavignac, Masina, Savoy; Feruglio, Strumia, Vissani; Altarelli, Feruglio, Masina)

24 m ν 0 a b a 0 0 b 0 0 New aspects Strong string motivation Motivation for special case a = b Most likely perturbation in 23 element from HOT Diagonalization: tan θ Atm = b/a need b = a for maximal tan 2 θ = 1 (maximal) (experiment tan 2 θ = )

25 Majorana mass matrix m ν Inverted hierarchy Bimaximal mixing for U e = I: U ν

26 Perturbations on m ν cannot give both m 2 and π 4 θ θ C 0.23 without fine-tuning between terms, e.g., 1 m m 2 Atm = ɛ π 4 θ 0.23

27 However, U e I with small angles (comparable to CKM) can can give agreement with experiment (Frampton, Petcov, Rodejohann; Romanino; Altarelli, Feruglio, Masina) U e 1 se 12 0 s e yields θ π 4 se 12 2 = U e3 2 (se 12 )2 2 ( ), 90% (exp : < 0.03) m ββ m 2 (cos 2 θ sin 2 θ ) ev

28 In progress Detailed Z 3 constructions for higher level embeddings (triplets) and for heavy Majorana neutrinos Implications for m e, m q Implications of additional Higgs RGE effects Leptogenesis

29 Conclusions Neutrino mass likely due to large or Planck scale effects, but little work in string context Specific orbifold string constructions (heterotic, intersecting brane) not consistent with common GUT and bottom up assumptions for m ν Preliminary conclusion: inverted hierarchy (pseudo Dirac), extended seesaw, or small Dirac favored Inverted hierarchy (e.g., from triplet) very predictive

Neutrino Mass in Strings

Neutrino Mass in Strings Introduction Neutrino preliminaries Models String embeddings Intersecting brane The Z 3 heterotic orbifold Embedding the Higgs triplet Outlook Neutrino mass Nonzero mass may be