Neutrino physics lecture 2 theory of neutrino mass and physics bsm
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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?

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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

Measuring neutrino mass

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!

  • 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

  • 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!

The seesaw paradigm

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

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

  • 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?

… and physics at the LHC …

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

(Florian [email protected] Florence 2012)

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

  • 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



  • 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

  • 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

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

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

  • Systematically decompose d=7 operator in all possible ways

  • Notation for mediators:




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

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)

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

  • Test mediators

  • Test LFV

  • Test LNV


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?

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?

  • 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. 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

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

  • 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)

  • 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?

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

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)

Implications of large q13: flavor

Short seesaw-I mixing primer

Block diag.

Charged leptonmass terms

Eff. neutrinomass terms

cf., charged current

Rotates left-handed fields

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?



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?

(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?

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

  • 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

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