Title: TeV scale seesaws from higher than d5 effective operators
1TeV 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
2Contents
- 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.
3Effective 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!
4See-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
5Typical 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)
6Neutrino 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
7The 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!?
8Forbid 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)
9Higher 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)
10TeV 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)
11 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
12Systematic study of d7
- Systematically decompose d7 operator in all
possible ways - Notation for mediators
Lorentz
SU(2)
YQ-I3
13Generalizations 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!
14Even 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
15Example 1 d9 tree level
- Inverse see-saw-like,with even higher
suppression of LNV term - Requires Z7 symmetry
16Example 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)
17Neutrino mass in example 2
- Neutral fermion fields (integrate out
scalars)Contributions to neutrino mass
Leading contribution for L gt 3 TeV
18Features 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
19Summary 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.
20BACKUP
21On 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)