TeV scale see-saws from higher than d=5 effective operators

CTP International Conference on Neutrino Physics in the LHC EraLuxor, EgyptNovember 15, 2009

Walter WinterUniversität Würzburg

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Contents

Introduction Neutrino mass from eff. operators

higher than d=5 TeV completions for effective

operators Summary and outlook

Based on F. Bonnet, D. Hernandez, T. Ota, W. Winter,

arXiv:0907.3143, JHEP 10 (2009) 076.

Special thanks to Belen Gavela.

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Leptonflavor

violation (LFV)

BSM physics described by effective operators in the low-E limit (gauge invariant):

Effective theory

: Scaleof new physics

Neutrinomass(LNV)

0 decay!

But these are no fundamental theories (non-renormalizable operators). Idea: Investigate fundamental theories (TeV completions) systematically!

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See-saw mechanism Neutrino mass from d=5 (Weinberg) - Operator Fundamental theories at tree level:

Neutrino mass ~ Y2 v2/ (type I, III see-saw) For Y = O(1), v ~ 100 GeV: ~ GUT scale For ~ TeV scale: Y << 10-5

Interactions difficult to observe at LHCCouplings „unnaturally“ small?

~ H, L ~ l

Type I Type II

Type III Seesaw

LL

?

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Typical ways out

Goals: New physics scale „naturally“ at TeV scale

(i.e., TeV scale not put in by hand) Yukawa couplings of order one

Requires additional suppression mechanisms. The typical ones: Radiative generation of neutrino mass Small lepton number violating contribution (e.g.

inverse see-saw, RPV SUSY models, …) Neutrino mass from higher than d=5 effective

operator (d=5 forbidden)

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Neutrino mass from higher dimensional operators

Approach: Use higher dimensional operators, e.g.

Leads to

Estimate: for ~ 1 – 10 TeV and m linear in Yukawas (worst case): d = 9 sufficient if no other suppression mechanism d = 7 sufficient if Yukawas ~ me/v ~ 10-6 allowed

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The loop issue

Loop d=5 contribution dominates for or >~ 3 TeV

Conclusion: If assumed that d=7 leading, one effectively has to put << 3 TeV by hand(see e.g. Babu, Nandi, Tavartkiladze, arXiv:0905.2710)

But this is only a subclass of LHC-testable models!?

LL

LL

Close loop

d=7 operator d=5 operator

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Forbid lower dim. operators

Define genuine d=D operator as leading contribution to neutrino mass with all operators d<D forbidden

Use new U(1) or discrete symmetry („matter parity“) Problem: H+H can never be charged under the new

symmetry! Need new fields! The simplest possibilities are probably

(e.g. Chen, de Gouvea, Dobrescu, hep-ph/0612017; Godoladze, Okada, Shafi, arXiv:0809.0703)

(e.g. Babu, Nandi, hep-ph/9907213; Giudice, Lebedec, arXiv:0804.1753)

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Higher dim. operators in THDM

Simplest possibility (d=7): Z5 with e.g.

(SUSY: Z3)

d=7 operatorwhich is allowed in

SUSY and for which

d=5 can beindependently

forbidden

Same for d=9

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TeV completions for d=7 op.

Example: two extra fermions, one scalar

Z5 charges

Leads to neutrino mass via effective d=7 operator:

Issue: also new U(1) Need enhanced scalar sector (explicit breaking) or a soft breaking term (a la MSSM)

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… and the inverse see-saw

Similar to inverse see-saw

Mass matrix for neutral fermion fields:

with

LNV term suppressed by new physics scale!

That also works for the -term

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Systematic study of d=7

Systematically decompose d=7 operator in all possible ways

Notation for mediators:

SU(2)

Lorentz

Y=Q-I3

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Generalizations of see-saws

Generalizations of orginial see-saws: Duplication of the original see-saws plus scalars

Type I (fermionic singlet)

Type II(scalar triplet)

Type III(fermionic triplet)

Characteristics:Similar phenomenology!

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Even higher suppression?

Tree 1-loop 2-loop

d=5

d=7

d=8

d=11

Loop suppression, controlled by 1/(16 2)

Suppression by d, controlled by 1/

2

Switched off bydiscrete symmetry

Switched off by discrete symmetry

To beavoided

for

< 3

TeV

Example 1: d=9 at tree levelExample 2: d=7 at two loop

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Example 1: d=9 tree level

Inverse see-saw-like,with even higher suppression of LNV term

Requires Z7 symmetry

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Example 2: two-loop d=7

Neutrino masses emerge from breaking of the new symmetry

Charges (Z5)

Without scalar potential: Respects U(1)Y, U(1)L, and a new U(1); no mass

Violates all cont. symmetries except from U(1)Y, while respecting Z5

If S is integrated out: Term ~ 5 (respects Z5, violates U(1) )

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Neutrino mass in example 2

Neutral fermion fields (integrate out scalars):

Contributions to neutrino mass:

Leading contribution for > 3 TeV

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Features of example 2

Incorporates all three suppression mechanisms: Radiative generation of neutrino mass Small lepton number violating contribution

(optional: LNV couplings can be chosen small) Neutrino mass from higher than d=5 effective

operator (d=5 forbidden)

Neutrino mass related to breaking of new U(1) to discrete symmetry

TeV scale naturally coming out, with large Yukawa couplings possible

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Summary and outlook „Natural“ TeV see-saw requires additional suppression

mechanisms beyond three standard see-saws Framework of additional Higgs doublet (THDM) used ~ 3 TeV is the splitting point between tree level and loop

contributions dominating neutrino mass Generic models should be „stable“ with whole LHC-testable

range requires symmetries to control leading contribution to neutrino mass

TeV completions of higher than d=5 effective operators often lead to inverse see-saw-like structures with the LNV term suppressed by d-6)

LHC phenomenology of such models still needs to be worked out (partly work in progress)

Some of the generic results can be translated to other extensions of the SM (such as different Higgs sector)

Reference: F. Bonnet, D. Hernandez, T. Ota, W. Winter, arXiv:0907.3143, JHEP 10 (2009) 076.

BACKUP

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On the U(1) problem

Lagrangian invariant under new U(1) symmetry (aka Peccei-Quinn symmetry wrt Higgs potential)Unwanted Goldstone bosons?

Typical ways out (example d=7 tree level): Enhanced scalar sector with eff. term

Soft-breaking term (a la MSSM)

Contribution ~

(<< tree level d=7)