Neutrino Mass in Strings

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

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 Neutrino Preliminaries 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?

4 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? HDO? LED? 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

5 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))

6 The minimal seesaw Active (sterile) 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)

7 Ordinary (type I) seesaw: m T = 0 and (eigenvalues) m S m D : m eff ν = m Dm 1 S mt D diagonalized by U ν, with U P MNS = U e U ν To achieve large mixings, most models assume either U e I in basis with manifest symmetries for m D,S need large mixings in U ν (requires clever m D, m S collaboration) 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, combined with family symmetries, often large Higgs representations (e.g., 126-plet); typically, m S GeV

8 Extended (TeV) Seesaw m ν m p+1 /m p S, p > 1 (e.g., m 100 MeV, m S 1 TeV for p = 2) ν L, N R, N R (3 flavors each) L = 1 ( νl N c L 2 N 0 m D m D L) c m T D 0 m SS m T D m T SS 0 νc R N R N R + hc or L = 1 2 ( νl N c N L L) c 0 m D 0 m T D 0 m SS 0 m T SS m S νc R N R N R + hc

9 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.

10 Dirac Masses Can achieve small Dirac masses (neutrino or other) by higher dimensional operators 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) A ) Small p intermediate scale M P l Similar HDO may give light steriles and ordinary/sterile mixing

11 Other Models Large extra dimensions (suppressed Dirac Yukawa couplings) R-parity violation in supersymmetry TeV scale loops with new ad hoc scalars Ad hoc flavor symmetries, textures, anarchic models Anthropic considerations (string landscape)

12 Neutrino Mass in Strings Very little work from string constructions, even though may be Planck scale effect Key ingredients of most bottom up models forbidden in known constructions (heterotic or intersecting brane) (Due to string symmetries or constraints, not simplicity or elegance) Right-handed neutrinos may not be gauge singlets Large representations difficult to achieve (bifundamentals, singlets, or adjoints) GUT Yukawa relations broken String symmetries/constraints severely restrict couplings, e.g., Majorana masses, or simultaneous Dirac and Majorana masses

13 Quasi-realistic string constructions Two classes of quasi-realistic: intersecting D-brane, heterotic Intersecting D-brane (review: R. Blumenhagen, M. Cvetic, P.L., G. Shiu, hep-th/ ) Closed strings (gravitons) and open strings ending on D-branes D6-branes: fill ordinary space and 3 of the 6 extra dimensions Stringy implementation of brane world ideas

14 Gauge interactions from strings beginning/ending on stack of parallel branes (one for each group factor) Chiral matter: strings at intersection of branes, e.g., SU(N) SU(M) bifundamental (N, M) a Gauge bosons in adj. U(1) W U(1) b W + Chiral matter in (N, M)

15 Family replication from multiple intersections on compactified geometry Yukawa interactions exp( A ijk ) hierarchies Existing models: conserved L; no diagonal (Majorana) triangles However, no realistic model with large enough A for small Dirac neutrino masses (more generic geometries?) (1, 1) (1,3) (1, 1) (1,2) (1,0) (1,1) T 2 T 2 T 2 H Q 3 L U 3 SU(3) Q 2 L U2 Q 1 L SU(3) SU(2) U U(1) 1 SU(3)

16 The E 8 E 8 Heterotic String Dirac masses Can achieve small Dirac masses (neutrino or other) by higher dimensional operators 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 Recent variant: N c L is a modulus (Bouchard, Cvetič, Donagi, hepth/ )

17 Majorana masses Can one 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 consistent with D and F flatness? M q P l Can one have such terms simultaneously with Dirac couplings, consistent with flatness and other constraints? Are bottom-up model assumptions for relations to quark, charged lepton masses maintained?

18 The Z 3 Heterotic Orbifold (J. Giedt, G. Kane, P.L., B. Nelson, hepth/ ) Systematically studied large class of vacua Is minimal seesaw common? If rare, possibly guidance to model building Clues to textures, etc. Several models from each of 20 patterns; W through degree 9; huge number of D flat directions reduced greatly by F -flatness Only two patterns had Majorana mass operators S 1 S n 2 NN/M n 3 PL None had simultaneous Dirac operators S 1 S d 3 NLH u/m d 3 PL leading to m 2 > ev 2 (one apparent model ruined by offdiagonal Majorana) Feature of Z 3 orbifold? Or more general?

19 Systematic searches in other constructions important (Is seesaw generic? Rare? Alternatives?) Consider alternatives seriously Small Dirac masses from high degree terms (very common in constructions) (could also give light sterile ν s and mixing) Extended seesaws, m ν m 2+k D /M 1+k, with k 1 and low (e.g., TeV) scale M Higgs triplet models: non-trivial to embed in strings (higher level), but very predictive (e.g., inverted hierarchy with nearly bi-maximal mixing) (B. Nelson, PL, hep-ph/ )

20 Triplet models Introduce Higgs triplet T = (T ++ T + T 0 ) T with weak Y = 1 Majorana masses m T generated from L ν = λ T ij L it L j if T 0 0 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 needed to avoid Majoron +M T T T + µh 1 H 2 T, T are triplets with Y = ±1, M T GeV. Typically, T 0 λ 2 H /M T m ν ij = λt ij λ 2 v 2 2 M T Most previous models: GUT/LR symmetry, ordinary hierarchy

21 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, B. Nelson, PL, hep-ph/ ) 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

22 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

23 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)

24 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)

25 m ν 0 a b a 0 0 b 0 0 New aspects Strong string motivation Motivation for special case a = b Can perturb by HOT No reason for U e = I in this basis Yields inverted hierarchy, with eigenvalues 0, ± a 2 + b 2 Diagonalization: tan θ Atm = b/a need b = a for maximal

26 If U e = I: θ = π 4 (maximal) (experiment: π 4 θ = , 2σ) Comparable to Cabibbo angle, θ C 0.23 Perturbations on m ν cannot give both m 2 and π 4 θ 0.19 (cf θ C 0.23) without fine-tuning between terms, e.g., m 2 2 m 2 Atm π (m ν 23 + mν 11 ) θ 1 4 (mν 23 mν 11 ) 0.19

27 However, U e I with small angles (comparable to CKM) can give agreement with experiment (Frampton, Petcov, Rodejohann; Romanino; Altarelli, Feruglio, Masina) U e 1 se 12 0 s e yields π 4 θ se 12 s e U e3 2 (se 12 )2 2 ( ), 2σ (exp : < 0.032) m ββ m 2 (cos 2 θ sin 2 θ ) ev

28 Outlook 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 No examples of minimal seesaw in large class of heterotic Z 3 orbifold vacua Small Dirac, extended seesaw, Higgs triplet (inverted hierarchy in string context) should be seriously considered