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Neutrino physics Lecture 2: Theory of neutrino mass, and physics BSM?. Herbstschule für Hochenergiephysik Maria Laach 04-14.09.2012 Walter Winter Universität Würzburg. TexPoint fonts used in EMF: A A A A A A A A. Contents. Measuring neutrino mass The seesaw paradigm

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Neutrino physics lecture 2 theory of neutrino mass and physics bsm

Neutrino physicsLecture 2: Theory of neutrino mass, and physics BSM?

Herbstschule für Hochenergiephysik

Maria Laach


Walter Winter

Universität Würzburg

TexPoint fonts used in EMF: AAAAAAAA


  • Measuring neutrino mass

  • The seesaw paradigm

  • Neutrino mass models at the TeV scale:What ingredients do “natural” models need?

  • Is it possible that new physics shows up in the neutrino sector only?

  • How does the large q13 affect our understanding of (lepton) flavor?

  • Summary and conclusions

Tritium end point experiments
Tritium end point experiments

  • Direct test of neutrino mass by decay kinematics

  • Current bound: 1/250.000 x me (2 eV) TINY!

  • Future experiment: KATRIN (Karlsruhe Tritium Neutrino Experiment)1/2.500.000 x me (0.2 eV)

~8800 km

(Guido Drexlin, NOW 2008)

Neutrinoless double beta decay if the neutrino is ist own antiparticle a majorana neutrino





Neutrinoless double beta decay… if the neutrino is ist own antiparticle, a Majorana neutrino!

  • Two times simple beta decay:

  • Neutrinoless double beta decay:



2 x n2 x e









Caveat: discovering 0nbb does not mean that one has actually seen Majorana neutrinos!

0 x n2 x e




Cosmological tests
Cosmological tests

  • Example:Relativistic neutrinos damp the formation of structure

  • Essentially sensitive to sum of neutrino masses

  • Information from different cosmological datasets used in literature

  • Limit ~ eV

(S. Hannestad)

… might finally be used rule to out that neutrino physics in charge of 0nbb!

Why is the neutrino mass so small
Why is the neutrino mass so small?

  • Why are the neutrinos morethan 250.000 times lighter than the electron?

    • Cannot be described in simple extensions of the Standard Model

    • Is the neutrino mass the lowest order perturbation of physics BSM?

  • Seesaw mechanism: Neutrino mass suppressed by heavy partner, which only exists in the early universe (GUT seesaw)?

    • Decay of MR origin of matter-antimatter-asymmetry?

    • CP violation? Test in neutrino oscillations!

    • Requires Majorana nature of neutrino!Test in neutrinoless double beta decay (0nbb)

Other SM particles

Heavy partner

Effective field theories
Effective field theories

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

L: Scaleof new physics


Leptonflavorviolation (LFV)

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

Seesaw mechanism
Seesaw mechanism

  • Neutrino mass from d=5 (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 << 10-5

    • Interactions difficult to observe at LHC

    • Couplings “unnaturally“ small?




Type II

Type III


Type I



Neutrino masses at the tev scale

Neutrino masses at the TeV scale?

… and physics at the LHC …

Neutrino masses at the tev scale1
Neutrino masses at the TeV scale

  • Goals:

    • New physics scale “naturally“ at TeV scale(i.e., TeV scale not put in by hand) Testable at the LHC?!

    • Yukawa couplings of order one

  • Requires additional suppression mechanisms. The typical ones:

    • Radiative generation of neutrino mass (n loops)

    • Neutrino mass from higher than d=5 effective operator

    • Small lepton number violating contribution e (e.g. inverse see-saw, RPV SUSY models, …)

Example suppression 3 type ii inverse seesaw
Example (suppression 3): Type-II, inverse seesaw

(Florian [email protected] Florence 2012)

Additional suppression mechanisms 1 2 loops versus dimension
Additional suppression (mechanisms 1+2):Loops versus dimension

Loop suppression, controlled by 1/(16 p2)

Type I, II, IIseesaw

Depends onmediators/int.

Zee, 1980;Ma, 1998; …





Discrete symmetryto forbid d=5?

Depends on scale:L > 4pv ~ 3 TeV?


Suppression by d, controlled by 1/L2



How can I make sure that no lower order operators are generated?

Example neutrino mass from higher dimensional operators
Example: 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

The loop issue
The loop issue



  • Loop d=5 contribution dominates for or L > 3 TeV

  • Conclusion: If assumed that d=7 leading, one effectively has to put L << 3 TeV by hand(see e.g. Babu, Nandi, Tavartkiladze, 2009)

  • Can one avoid this?





Close loop






d=5 operator

d=7 operator

Forbid lower dim operators
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)

Higher dim operators in thdm
Higher dim. operators in THDM

Bonnet, Hernandez, Ota, Winter, JHEP 10 (2009) 076

  • Simplest possibility (d=7): Z5 with e.g.(SUSY: Z3)

SUSY:only this one(but: there canbe operators withthe scalar singletin the NMSSM)

Same for d=9

Systematic study of d 7
Systematic study of d=7

Bonnet, Hernandez, Ota, Winter, JHEP 10 (2009) 076

  • Systematically decompose d=7 operator in all possible ways

  • Notation for mediators:




Generalizations of see saws
Generalizations of see-saws

Bonnet, Hernandez, Ota, Winter, JHEP 10 (2009) 076

  • Generalizations of originial 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!

A susy example
A SUSY example

Krauss, Ota, Porod, Winter, Phys. Rev. D84 (2011) 115023

  • Neutral fermion mass matrix after EWSB in basis


Flavor struct. by





Mass states: ni

Fermionic doublets#17 from list

Compare to “inverse see-saw“(suppression mechanism 3)if heavy doublets integrated out

Test at the lhc example
Test at the LHC? (example)

Krauss, Ota, Porod, Winter, Phys. Rev. D84 (2011) 115023

  • Test mediators

  • Test LFV

  • Test LNV


Even higher suppression
Even higher suppression?

Bonnet, Hernandez, Ota, Winter, JHEP 10 (2009) 076

Loop suppression, controlled by 1/(16 p2)




Switched off by discrete symmetry

Switched off bydiscrete symmetry


Strategies for higher loops:Farzan, Pascoli, Schmidt, arXiv:1208.2732

To beavoided


Suppression by d, controlled by 1/L2


for L < 3 TeV


Example 1: d=9 at tree level

Physics at TeV scale with O(1) couplings

Example 2: d=7 at two loop  Suppression mechanisms 1), 2), and 3)

New physics in neutrino sector only

New physics in neutrino sector only?

Most discussed options in literature:

Light sterile neutrinos (aka: light SM singlets)

Heavy SM singlets ( non-unitary mixings)

Non-standard interactions (aka: flavor changing neutral currents)

Evidence for sterile neutrinos
Evidence for sterile neutrinos?

  • LSND/MiniBooNE

  • Reactor+gallium anomalies

    • Global fits

(MiniBooNE @ Neutrino 2012)

(B. Fleming, TAUP 2011)

(Kopp, Maltoni, Schwetz, 1103.4570)

Example 3 1 framework with addl d m 2 1 ev 2
Example: 3+1 framework(with addl. Dm2 ~ 1 eV2)

  • Well known tension between appearance and disapp. data (appearance  disappearance in both channels)

  • Need one or more new experiments which can test

    • ne disappearance (Gallium, reactor anomalies)

    • nm disappearance (overconstrains 3+N frameworks)

    • ne-nm oscillations (LSND, MiniBooNE)

    • Neutrinos and antineutrinos separately (CP violation? Gallium vs reactor?)

  • Example: nuSTORM - Neutrinos from STORed Muons(LOI: arXiv:1206.0294) Summary of options: Appendix of white paper arXiv:1204.5379

Non unitarity of mixing matrix

also: “MUV“

Non-unitarity of mixing matrix?

  • Integrating out heavy fermion fields (such as in a type-I TeV see-saw), one obtains neutrino mass and the d=6 operator (here: fermion singlets)

  • Re-diagonalizing and re-normalizing the kinetic terms of the neutrinos, one has

  • This can be described by an effective (non-unitary) mixing matrix e with N=(1+e) U

  • Relatively stroung bounds already, perhaps not so good candidate for future measurements(see e. g. Antusch, Baumann, Fernandez-Martinez, arXiv:0807.1003)

Non standard interactions
Non-standard interactions

  • Typically described by effective four fermion interactions (here with leptons)

  • May lead to matter NSI (for g=d=e)

  • May also lead to source/detector NSI

How plausible is a modelleading to such NSI(and showing up inneutrino sector only)?

Lepton flavor violation d 6
Lepton flavor violation (d=6)

  • Charged leptonflavor violation

  • Strongbounds

















  • Non-standard neutrino interact.

  • Effects in neutrino oscillations in matter

  • Non-standard int. with 4n

  • Effects in environments with high neutrino densities (supernovae)

BUT: These phenomena are not independent (SU(2) gauge invariance!)Is it possible that new physics is present in the neutrino sector only?

Idea d 8 operator
Idea: d=8 operator?

Davidson, Pena-Garay, Rius, Santamaria, 2003

  • Decouple CLFV and NSI by SU(2) symmetry breaking with operator

  • Works at effective operator level, but are there theories allowing that? [at tree level]

Project outneutrino field

Project outneutrino field

Systematic analysis for d 8
Systematic analysis for d=8

Feynman diagrams

Basis (Berezhiani, Rossi, 2001)

  • Decompose all d=8 leptonic operators systematically

    • The bounds on individual operators from non-unitarity, EWPT, … are very strong! (Antusch, Baumann, Fernandez-Martinez, arXiv:0807.1003)

  • Need at least two mediator fields plus a number of cancellation conditions(Gavela, Hernandez, Ota, Winter, Phys. Rev. D79 (2009) 013007)

Avoid CLFVat d=8:C1LEH=C3LEH

Combinedifferentbasis elements C1LEH, C3LEH


But these mediators cause d=6 effects Additional cancellation condition(Buchmüller/Wyler – basis)

Short seesaw i mixing primer
Short seesaw-I mixing primer

Block diag.

Charged leptonmass terms

Eff. neutrinomass terms

cf., charged current

Rotates left-handed fields

The tbm prejudice
The TBM “prejudice“

  • Tri-bimaximal mixings probably most discussed approach for neutrinos (Ul often diagonal)

  • Can be obtained in flavor symmetry models (e.g., A4, S4)

  • Consequence: q13=0  Obviously not!

  • Ways out for large q13?

Impact on theory of flavor
Impact on theory of flavor?



very small

very large

Structure:A4, S4, TBM, …

Anarchy:Random draw?


Some structure + randomness:Froggatt-Nielsen?

Corrections?CL sector?RGR running?

e.g. q12 = 35 + q13cosd(Antusch, King)

Quark-leptoncompementarity:q13 ~ qC?

Different flavor symmetry?


  • Idea: perhaps the mixing parameters are a “random draw“?

  • Challenge: define parameterization-independent measure

  • Result: large q13 “natural“, no magic needed

(Hall, Murayama, Weiner, 2000; de Gouvea, Murayama, 2003, 2012)

Structure randomness froggatt nielsen mechanism
“Structure+randomness“:Froggatt Nielsen mechanism?

(F. Plentinger)

  • YL/R are SM fermions

  • After integrating out the heavy fermions:

  • Integer power n is controlled by the (generation/flavor-dependent) quantum numbers of the fermions under the flavor symmetry

  • K: (complex) generation dependent (random) order one coefficients

  • Well-suited to describe hierarchies



Hybrid alternatives
Hybrid alternatives?

Meloni, Plentinger, Winter, PLB 699 (2011) 244

Charged leptons:Strong hierarchy,masses throughSM Yukawas Quarks:Strong hierarchiesSmall mixings

Neutrinos:Mild (no?) hierarchy,large mixings, Majorana masses? Origin:physics BSM?LNV operator?

 q13=0

Ansatz suitablefor hierarchies,such as Froggatt-Nielsen?

Flavor symmetry,structure?Tri-bimaximal mixing“paradigm“?


  • Can control the size of q13 by suitable U(1) charges/mass texture for the charged lepton sector:

  • Challenge:

    • Deviations from TBM q12 typically accompanied by large q13

    • Re-think zeroth order paradigm (TBM)???

Meloni, Plentinger, Winter, PLB 699 (2011) 244

Summary and outlook
Summary and outlook

  • Are neutrinos masses evidence for physics BSM?

    • Neutrinoless double beta decay

    • Tests at the LHC

  • 0nbb signal + CPV in lepton sector + no evidence for n mass at the LHC

    • GUT seesaw, leptogenesis?

  • Natural TeV neutrino mass model requires additional suppression mechanism; then, however, plausible to discover it at the LHC

  • Most likely case for new physics in neutrino sector: fourth generation (light sterile neutrino)?

  • Theory of flavor has to be re-thought after q13 discovery