TeV scale seesaws from higher than d5 effective operators

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TeV scale see-saws from higher than d5 effective
operators

• CTP International Conference on Neutrino Physics
  in the LHC Era
• Luxor, Egypt
• November 15, 2009Walter Winter
• Universität Würzburg

TexPoint fonts used in EMF AAAAAAAA
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Contents

• Introduction
• Neutrino mass from eff. operators higher than d5
• TeV completions for effective operators
• Summary and outlook

Based on F. Bonnet, D. Hernandez, T. Ota, W.
Winter, arXiv0907.3143, JHEP 10 (2009)
076. Special thanks to Belen Gavela.
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Effective theory
BSM physics described by effective operators in
the low-E limit (gauge invariant)
L Scaleof new physics
Neutrinomass(LNV)0nbb decay!
Leptonflavorviolation (LFV)
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 d5 (Weinberg) - Operator
• Fundamental theories at tree level
• Neutrino mass Y2 v2/L (type I, III see-saw)
• For Y O(1), v 100 GeV L GUT scale
• For L TeV scale Y ltlt 10-5
• Interactions difficult to observe at LHC
• Couplings unnaturally small?

H
H
?
f H, L l
Type II
Type III
Seesaw
Type I
L
L
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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 d5 effective
  operator (d5 forbidden)

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Neutrino mass from higher dimensional operators

• Approach Use higher dimensional operators,
  e.g.
• Leads to
• Estimate for L 1 10 TeV and mn 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
H
H
H
H
H
H
Close loop
L
L
L
L
H
d5 operator
d7 operator

• Loop d5 contribution dominates for
  or L gt 3 TeV
• Conclusion If assumed that d7 leading, one
  effectively has to put L ltlt 3 TeV by hand(see
  e.g. Babu, Nandi, Tavartkiladze, arXiv0905.2710)
• But this is only a subclass of LHC-testable
  models!?

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Forbid lower dim. operators

• Define genuine dD operator as leading
  contribution to neutrino mass with all operators
  dltD forbidden
• Use new U(1) or discrete symmetry (matter
  parity)
• Problem HH 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, arXiv0809.0703)(e.g.
  Babu, Nandi, hep-ph/9907213 Giudice, Lebedec,
  arXiv0804.1753)

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Higher dim. operators in THDM
d7 operatorwhich is allowed inSUSY and for
whichd5 can beindependentlyforbidden
Same for d9

• Simplest possibility (d7) Z5 with e.g.(SUSY
  Z3)

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TeV completions for d7 op.

• Example two extra fermions, one scalarZ5
  chargesLeads to neutrino mass via effective
  d7 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
  fieldswith? LNV term suppressed by new
  physics scale!
• That also works for the e-term

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Systematic study of d7

• Systematically decompose d7 operator in all
  possible ways
• Notation for mediators

Lorentz
SU(2)
YQ-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)CharacteristicsSim
  ilar phenomenology!

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Even higher suppression?
Loop suppression, controlled by 1/(16 p2)
Tree
1-loop
2-loop
d5
Switched off bydiscrete symmetry
Switched off by discrete symmetry
To beavoided
d7
Suppression by d, controlled by 1/L2
d8
for L lt 3 TeV
d11
Example 1 d9 at tree level
Example 2 d7 at two loop
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Example 1 d9 tree level

• Inverse see-saw-like,with even higher
  suppression of LNV term
• Requires Z7 symmetry

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Example 2 two-loop d7
Without scalar potential Respects U(1)Y, U(1)L,
and a new U(1) no n mass
Violates all cont. symmetries except from U(1)Y,
while respecting Z5If S is integrated out Term
f5 (respects Z5, violates U(1) )

• Neutrino masses emerge from breaking of the new
  symmetry
• Charges (Z5)

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Neutrino mass in example 2

• Neutral fermion fields (integrate out
  scalars)Contributions to neutrino mass

Leading contribution for L gt 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 d5 effective
  operator (d5 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
• L 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 d5 effective
  operators often lead to inverse see-saw-like
  structures with the LNV term suppressed by
  L-(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, arXiv0907.3143, JHEP 10 (2009) 076.

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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 d7 tree level)
• Enhanced scalar sector with eff. term
• Soft-breaking term (a la MSSM)Contribution
  (ltlt tree level d7)