Alternatives to the GUT Seesaw - sns.ias.edupgl/talks/LBV09_pgl.pdf · Alternatives to the GUT...

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Alternatives to the GUT Seesaw Motivations Higher-dimensional operators String instantons Other (higher dimensions, Higgs triplets) Madison (September 21, 2009) Paul Langacker (IAS)

Transcript of Alternatives to the GUT Seesaw - sns.ias.edupgl/talks/LBV09_pgl.pdf · Alternatives to the GUT...

Page 1: Alternatives to the GUT Seesaw - sns.ias.edupgl/talks/LBV09_pgl.pdf · Alternatives to the GUT Seesaw Motivations Higher-dimensional operators String instantons ... Invoke extra symmetries

Alternatives to the GUT Seesaw

• Motivations

• Higher-dimensionaloperators

• String instantons

• Other (higher dimensions,Higgs triplets)

Madison (September 21, 2009) Paul Langacker (IAS)

Page 2: Alternatives to the GUT Seesaw - sns.ias.edupgl/talks/LBV09_pgl.pdf · Alternatives to the GUT Seesaw Motivations Higher-dimensional operators String instantons ... Invoke extra symmetries

Motivations

• Many mechanisms for small neutrino mass, both Majorana andDirac

• Minimal Type I seesaw

– Bottom-up motivation: no gauge symmetries prevent largeMajorana mass for νR

– 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 mayinvalidate assumptions

Madison (September 21, 2009) Paul Langacker (IAS)

Page 3: Alternatives to the GUT Seesaw - sns.ias.edupgl/talks/LBV09_pgl.pdf · Alternatives to the GUT Seesaw Motivations Higher-dimensional operators String instantons ... Invoke extra symmetries

• Standard alternatives: Higgs triplets, extended (TeV) seesaws,loops, Rp violation

• String-motivated alternatives: HDO (non-minimal seesaw, direct

Majorana, Dirac); string instantons; geometric suppressions

• Alternatives often associated with new TeV physics, electroweakbaryogenesis, etc.

Madison (September 21, 2009) Paul Langacker (IAS)

Page 4: Alternatives to the GUT Seesaw - sns.ias.edupgl/talks/LBV09_pgl.pdf · Alternatives to the GUT Seesaw Motivations Higher-dimensional operators String instantons ... Invoke extra symmetries

Higher-dimensional operators

• The Weinberg operator (most Majorana models)

−Lφφ =C

2M

“¯L~τ ˜

R

”·“φ†~τφ”

+ h.c.

=C

M

“¯L φ” “φ† ˜R

”+ h.c.

=C

M¯L

„φ0†φ− φ0†φ0†

−φ−φ− −φ−φ0†

«˜R + h.c.,

`L =(νLeL

), ˜

R =(

ecR−νcR

), φ =

(φ+

φ0

), φ =

(φ0†

−φ−)

• Superpotential: W = CMLLHuHu

• Generate directly in string construction, or in effective 4d theory

Madison (September 21, 2009) Paul Langacker (IAS)

Page 5: Alternatives to the GUT Seesaw - sns.ias.edupgl/talks/LBV09_pgl.pdf · Alternatives to the GUT Seesaw Motivations Higher-dimensional operators String instantons ... Invoke extra symmetries

Direct generation of Weinberg operator

• Simplest possibility:generate operatorby underlying stringdynamics

!L !L

!"0" !"0"

!R !R

!"S"

!"0" !"0"

!L !L !LhT !L

!"0T "

– Typeset by FoilTEX – 1

W =C

MLLHuHu, with C . 1,M = Ms ∼MP =

MP√8π∼ 2.4×1018 GeV

⇒ mν . 10−5 eV (⇒ need M ∼ 1014 GeV�MP )

• Can compactify on internal volume

V6 �M−6s ⇒M

2P ∼M

8sV6

• Can obtain mν ∼ 0.1 eV for V6 ∼ 1015M−6s (Conlon,Cremades)

• Ms ∼ 1014 GeV still large compared to LED scenarios

Madison (September 21, 2009) Paul Langacker (IAS)

Page 6: Alternatives to the GUT Seesaw - sns.ias.edupgl/talks/LBV09_pgl.pdf · Alternatives to the GUT Seesaw Motivations Higher-dimensional operators String instantons ... Invoke extra symmetries

The GUT seesaw

• Realize Weinberg operator via heavy particle exchange in effective4d theory

• Seesaw implementationType I: heavy Majorana νR;

Type II: heavy Higgs triplet

!L !L

!"0" !"0"

!R !R

!"S"

!"0" !"0"

!L !L

hS

"0T

!L hT !L

!"0" !"0"

#

– Typeset by FoilTEX – 1

• Type I in SO(10): φS ∈ 126∗H (Type II also possible)

W ∼ hu 16× 16× 10H| {z }νLνRφ

0

+hS 16× 16× 126∗H| {z }νLν

cRφS

• Alternative (Babu,Pati,Wilczek): replace 126∗H by higher-dimensionaloperator: W ∼ λ

M16× 16× 16∗H × 16∗H

– Need hS|〈φ126∗H〉| or λ

M |〈φ16∗H〉|2 ∼ 1014 GeV

˛hu〈φ10H

〉100 GeV

˛2

Madison (September 21, 2009) Paul Langacker (IAS)

Page 7: Alternatives to the GUT Seesaw - sns.ias.edupgl/talks/LBV09_pgl.pdf · Alternatives to the GUT Seesaw Motivations Higher-dimensional operators String instantons ... Invoke extra symmetries

The string seesaw

• Majorana mass for Nc from

WN ∼ cijSq+1

Mq

P

NciN

cj ⇒ (mN)ij ∼ cij

〈S〉q+1

Mq

P

, q ≥ 0

– Simultaneous Dirac mass terms from

WD ∼(S

MP

)pLNcHu ⇒ mD ∼

( 〈S〉MP

)p〈Hu〉, p ≥ 0

– SM singlet fields S may be different

– Typically, 〈S〉MP

= O(10−1) at minimum (e.g., if from FI term)

– Must be consistent with string constraints/symmetries; withF = D = 0 (supersymmetry); W = 0 (cosmological constant)

Madison (September 21, 2009) Paul Langacker (IAS)

Page 8: Alternatives to the GUT Seesaw - sns.ias.edupgl/talks/LBV09_pgl.pdf · Alternatives to the GUT Seesaw Motivations Higher-dimensional operators String instantons ... Invoke extra symmetries

• Difficult to satisfy all conditions

– Caveat: Nc1N

c2 ⇒ Dirac; Nc

1Nc2 + Nc

1Nc3 ⇒ Dirac + Weyl;

need Nc1N

c1 or Nc

1Nc2 +Nc

1Nc3 +Nc

2Nc3 for Majorana

– No examples in Z3 heterotic orbifold (Giedt,Kane,PL,Nelson)

• At least two examples in heterotic E8 × E8 orbifoldon Z3 × Z2 (Buchmuller,Hamaguchi,Lebedev,Ramos-Sanchez,Ratz;

Lebedev,Nilles,Raby,Ramos-Sanchez,Ratz,Vaudrevange,Wingerter)

– May be many (O(10− 100)) Nc; p ∼ 0, . . . , 6, q ∼ 3, . . . , 8.

• Nonminimal. Simple SO(10) relations lost

Madison (September 21, 2009) Paul Langacker (IAS)

Page 9: Alternatives to the GUT Seesaw - sns.ias.edupgl/talks/LBV09_pgl.pdf · Alternatives to the GUT Seesaw Motivations Higher-dimensional operators String instantons ... Invoke extra symmetries

Other higher-dimensional operators

• HDO probably necessary for string seesaw, but other HDO alsopossible from string or effective theory

• Example: W = µHuHd

– µ problem: why is µ = O(MSUSY )?

– Many solutions promote µ to dynamical variable(i.e., d > 2 in W or in K)

– NMSSM, nMSSM, UMSSM: W = λSSHuHd

⇒ µeff = λS〈S〉 (S= SM singlet; usually 〈S〉 = O(ν) ∼ 246 GeV)

– Giudice-Masiero: K = X†MHuHd + h.c., where X = θθF

(SM singlet); for MSUSY = F/M ⇒ µeff = O(MSUSY )(e.g., M = MP )

– Both cases: assume new symmetry of effective theory or stringconstraints forbids elementary µ

Madison (September 21, 2009) Paul Langacker (IAS)

Page 10: Alternatives to the GUT Seesaw - sns.ias.edupgl/talks/LBV09_pgl.pdf · Alternatives to the GUT Seesaw Motivations Higher-dimensional operators String instantons ... Invoke extra symmetries

• Many other possibilities for small neutrino masses utilizing W orK (both Majorana and Dirac)(Cleaver,Cvetic,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 or string constraints to forbid, e.g.,elementary Dirac Yukawa W = LNcHu

• Example: small Dirac from HDO in W (CCEEL): W ∼ SMLNcHu

mν ∼〈S〉νuM

⇒ 〈S〉 = 1000 TeV for M = MP

– e.g. (approximately) flat breaking of U(1)′(CCEEL);Z′ mediation (PL,Paz,Wang,Yavin), . . .

Madison (September 21, 2009) Paul Langacker (IAS)

Page 11: Alternatives to the GUT Seesaw - sns.ias.edupgl/talks/LBV09_pgl.pdf · Alternatives to the GUT Seesaw Motivations Higher-dimensional operators String instantons ... Invoke extra symmetries

• Example: small Majorana from non-holomorphic K (CEN)

K ∼1

M2LHuLHd + h.c., Hd ≡

(H+d

−H0†d

)

– But FH∗d

= −µHu (or −µeffHu) ⇒ mν ∼ µν2u

M2

– µ ∼ 100 GeV⇒M ∼ 108 GeV, e.g., SUSY mediation scale

Madison (September 21, 2009) Paul Langacker (IAS)

Page 12: Alternatives to the GUT Seesaw - sns.ias.edupgl/talks/LBV09_pgl.pdf · Alternatives to the GUT Seesaw Motivations Higher-dimensional operators String instantons ... Invoke extra symmetries

• Example: small Dirac from non-holomorphic K (DEL)

K1 ∼1

M2X†LNcHd + h.c., with X = θθF

– M = SUSY mediation scale (e.g., 1014 GeV), MSUSY = F/M

– “W ′′ = MSUSYM

LNcHd⇒ mν ∼ MSUSY νdM

(breaks SUSY, but safe)

– Alternative, non-holomorphic A terms (suppressed by MSUSY /M)

K2 ∼1

M3XX†LNcHd + h.c.⇒ A ∼

M2SUSY

M

– Small Dirac mass from loop (need U(1)′; also forbids normal Yukawa)

!L !R

!R~

!L~

Hd0

W 3~ Z’~ Z’~~B, ,

Madison (September 21, 2009) Paul Langacker (IAS)

Page 13: Alternatives to the GUT Seesaw - sns.ias.edupgl/talks/LBV09_pgl.pdf · Alternatives to the GUT Seesaw Motivations Higher-dimensional operators String instantons ... Invoke extra symmetries

Intersecting Branes

• Heterotic E8 × E8 (closed strings)

• Intersecting D-brane (Type IIA)

– 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

Madison (September 21, 2009) Paul Langacker (IAS)

Page 14: Alternatives to the GUT Seesaw - sns.ias.edupgl/talks/LBV09_pgl.pdf · Alternatives to the GUT Seesaw Motivations Higher-dimensional operators String instantons ... Invoke extra symmetries

• Gauge interactions from strings beginning/ending on stack ofparallel branes (one for each group factor) →moduli-dependent gaugecouplings and no simple unification unless U(5) stack

• Chiral matter: strings at intersection of branes, e.g., U(N) ×U(M)→ bifundamental (N, M)

U(1)U(1)

W+

W−

Intersecting Brane Worlds – A Path to the Standard Model? 5

a

b

Gauge bosons in adj.

Chiral matter in (N, M)

The open string spectrum on these intersecting branes contains the following fields [52]:

(i) N = 4 gauge bosons in adjoint representation of U(N) × U(M).

(ii) Massless fermions in the chiral (N, M) representation.

(iii) In general massive scalar fields, again in the (N, M) representation.

The latter two fields originate from open strings stretching from one stack of Dp-

branes to the other one. Since the scalar fields are in general massive, such a

intersecting D-brane configurations generically breaks all space-time supersymmetries.This supersymmetry breaking manifests itself as the a massive/tachyonic scalar ground

state with mass:

M2ab =

1

2

∑I

∆ΦIab − max{∆ΦI

ab} . (4)

(ΦIab is the angle between stacks a and b in some spatial plane I.) Only if the

intersection angles take very special values, some of the scalars become massless, and

some part of space-time supersymmetry gets restored. Specifically consider two special

flat supersymmetric D6-brane configurations, as shown in the following figure:

x x

4

5

6

7

8

9

Φ1

Φ2Φ3

Supersymmetry now gets restored for the following choice of angles:

• 2 D6-branes, with common world volume in the 123-directions, being parallel in

the 4-5, 6-7 and 8-9 planes:

1/2 BPS (N = 4 SUSY): Φ1 = Φ2 = Φ3 = 0 .

• 2 intersecting D6-branes, with common world volume in the 123-directions, and

which intersect in 4-5 and 6-7 planes, being parallel in 8-9 plane:

Madison (September 21, 2009) Paul Langacker (IAS)

Page 15: Alternatives to the GUT Seesaw - sns.ias.edupgl/talks/LBV09_pgl.pdf · Alternatives to the GUT Seesaw Motivations Higher-dimensional operators String instantons ... Invoke extra symmetries

• Family replication from multiple intersections on compactifiedgeometry

• Yukawa interactions ∼ exp(−Aijk)→ hierarchies

• Existing models: additional gauge factors, Higgs, chiral matter

• Perturbative models: conserved L; no diagonal (Majorana)triangles

• ALNcHu not large enough, at least for toroidal compactifications

(1,0)

T TT2 2 2

(1,1)

(1,2)(1,−1)(1,3)(1,−1)

HLQ 3

LQ 2LQ 1

U3 U21USU(3)

SU(3)SU(3)

SU(2)

U(1)

Madison (September 21, 2009) Paul Langacker (IAS)

Page 16: Alternatives to the GUT Seesaw - sns.ias.edupgl/talks/LBV09_pgl.pdf · Alternatives to the GUT Seesaw Motivations Higher-dimensional operators String instantons ... Invoke extra symmetries

String Instantons

• Field theory instantons: nonperturbative e−1/g2effects from

topologically non-trivial classical field configurations(e.g., B + L violation in SM)

• String theory: anomalous U(1)′: MZ′ ∼ Ms, but acts likeperturbative global symmetry(may forbid µ, RP violation, NcNc, LNcHu, QUcHu, . . . )

Madison (September 21, 2009) Paul Langacker (IAS)

Page 17: Alternatives to the GUT Seesaw - sns.ias.edupgl/talks/LBV09_pgl.pdf · Alternatives to the GUT Seesaw Motivations Higher-dimensional operators String instantons ... Invoke extra symmetries

• String instantons: nonperturbative violation of the globalsymmetries

exp(−Sinst) ∼ exp(−

αGUT

VE2

VD6

)VE2

VD6= f(winding numbers)

• Majorana masses in intersecting brane (seesaw)(Blumenhagen,Cvetic,Weigand;Ibanez,Uranga)

mνR ∼Mse−Sinst

• Small Dirac (natural scale, 10−3 − 10−1 eV) (Cvetic,PL)

Madison (September 21, 2009) Paul Langacker (IAS)

Page 18: Alternatives to the GUT Seesaw - sns.ias.edupgl/talks/LBV09_pgl.pdf · Alternatives to the GUT Seesaw Motivations Higher-dimensional operators String instantons ... Invoke extra symmetries

Other possibilities

• Large extra dimensions, with νR propagating in bulk ⇒small Dirac masses from wave function overlap, cf., gravity(Dienes,Dudas,Gherghetta; Arkani-Hamed,Dimopoulos,Dvali,March-Russell)

mν ∼νMF

MP

, MF =

(M

2P

) 1δ+2

= fundamental scale

• Small Dirac from wave function overlap in warped dimensions, Land νR in bulk (Chang,Ng,Wu)

• Heavy Higgs triplets with Y = ±1 (Type II seesaw). Difficult toembed in strings (singlets, bifundamentals, adjoints)

– Heterotic embedding: higher Kac-Moody ⇒ approximateLe − Lµ − Lτ (PL,Nelson)

– Type IIA embedding via symmetric 5× 5 in U(5) (Cvetic,PL)

Madison (September 21, 2009) Paul Langacker (IAS)

Page 19: Alternatives to the GUT Seesaw - sns.ias.edupgl/talks/LBV09_pgl.pdf · Alternatives to the GUT Seesaw Motivations Higher-dimensional operators String instantons ... Invoke extra symmetries

Conclusions

• Can implement version of seesaw in strings, using complicatedhigher-dimensional operators or string instantons

• Other HDO in W or K, string instantons, or volume effects alsopossible, yielding small Majorana or Dirac

Madison (September 21, 2009) Paul Langacker (IAS)