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

Herbstschule für Hochenergiephysik

Maria Laach04-14.09.2012

Walter Winter

Universität Würzburg

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Contents

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 13 affect our understanding of (lepton) flavor?

Summary and conclusions

Measuring neutrino mass

4

Tritium end point experiments

(Guido Drexlin, NOW 2008)

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

5

n

n

Two times simple beta decay:

Neutrinoless double beta decay:

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

p

e-

W-

p

n

e-

W-

p

e-

W-

2 x 2 x e

0 x 2 x e

n

p

e-

W-

=Caveat: discovering 0does not mean that one has actually

seen Majorana neutrinos!

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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 0!

The seesaw paradigm

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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 (0)

Other SM particles

Heavy partner

9

Leptonflavor

violation (LFV)

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

Effective field theories

: Scaleof new physics

Neutrinomass(LNV)

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

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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?

Seesaw mechanism

Type I Type II

Type III Seesaw

LL

?

Neutrino masses at the TeV scale?

… and physics at the LHC …

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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:

1) Radiative generation of neutrino mass (n loops)2) Neutrino mass from higher than d=5 effective operator3) Small lepton number violating contribution (e.g.

inverse see-saw, RPV SUSY models, …)

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Example (suppression 3):

Type-II, inverse seesaw

(Florian Bonnet@GGI Florence 2012)

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

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

Type I, II, IIseesaw

Depends on scale: > 4v ~ 3 TeV?

Discrete symmetryto forbid d=5?

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

Depends onmediators/int.

Zee, 1980;Ma, 1998; …

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Example: 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, 2009)

Can one avoid this?

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)

SUSY:only this one

(but: there canbe operators withthe scalar singletin the NMSSM)

Same for d=9

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

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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

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

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Generalizations of see-saws

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!

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

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A SUSY example

Neutral fermion mass matrix after EWSB in basis

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

Fermionic doublets#17 from list

Compare to “inverse see-saw“(suppression mechanism 3)

if heavy doublets integrated out

3 2 2 1 1Flavor struct. by Mass states: ni

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Test at the LHC? (example)

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

Test mediators

Test LFV Test LNV

compare

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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 Suppression mechanisms 1), 2), and 3)

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

Physics at TeV scale with O(1) couplings

Strategies for higher loops:Farzan, Pascoli, Schmidt,

arXiv:1208.2732

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)

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Evidence for sterile neutrinos?

LSND/MiniBooNE Reactor+gallium anomalies

Global fits(M

iniB

ooN

E @

Neu

trin

o 20

12)

(B. F

lemin

g, TA

UP

2011)

(Kopp, Maltoni, Schwetz, 1103.4570)

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Example: 3+1 framework(with addl. m2 ~ 1 eV2)

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

Need one or more new experiments which can test e disappearance (Gallium, reactor anomalies) disappearance (overconstrains 3+N frameworks) e- 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

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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 with N=(1+) U

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

also: “MUV“

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Non-standard interactions

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

May lead to matter NSI (for ==e)

May also lead to source/detector NSI

How plausible is a modelleading to such NSI(and showing up in

neutrino sector only)?

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Lepton flavor violation (d=6)

Charged leptonflavor violation

Strongbounds

e e

e

NSI

e e

e CLFV e

4-NSIEx.:

e e

Non-standard neutrino interact.

Effects in neutrino oscillations in matter

Non-standard int. with 4

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?

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Idea: d=8 operator?

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]

Davidson, Pena-Garay, Rius, Santamaria, 2003

Project outneutrino field

Project outneutrino field

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Systematic analysis for d=8

Decompose all d=8 leptonic operators systematicallyThe 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)

Basis (Berezhiani, Rossi, 2001)

Combinedifferent

basis elements

C1LEH, C3

LEH

Canceld=8

CLFV

But these mediators cause d=6 effects Additional cancellation condition

(Buchmüller/Wyler – basis)

Avoid CLFVat d=8:

C1LEH=C3

LEH

Feynman diagrams

Implications of large 13: flavor

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Short seesaw-I mixing primer

Charged leptonmass terms

Eff. neutrinomass terms

cf., charged current

Rotates left-handed fields

Block diag.

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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: 13=0 Obviously not!

Ways out for large 13?

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Impact on theory of flavor?

Structure:A4, S4, TBM, …

Anarchy:Random draw?

13 very small very large

Different flavor symmetry?

Corrections?CL sector?

RGR running?

Some structure + randomness:

Froggatt-Nielsen?

vs.

Quark-leptoncompementarity:

13 ~ C?

e.g. 12 = 35 + 13 cos (Antusch, King)

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Anarchy?

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

Challenge: define parameterization-independent measure

Result: large 13 “natural“, no magic needed

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

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“Structure+randomness“:Froggatt Nielsen mechanism?

L/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

(F. Plentinger)

Ml ~

Example:

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Hybrid alternatives?

Charged leptons:Strong hierarchy,masses through

SM Yukawas

Quarks:Strong hierarchies

Small mixings

Neutrinos:Mild (no?) hierarchy,

large mixings, Majorana masses?

Origin:physics BSM?LNV operator?

Flavor symmetry,structure?

Tri-bimaximal mixing“paradigm“?

Ansatz suitablefor hierarchies,

such as Froggatt-Nielsen?

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

13=0

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Consequences

Can control the size of 13 by suitable U(1) charges/mass texture for the charged lepton sector:

Challenge:Deviations from TBM 12 typically accompanied by large 13

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

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

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Summary and outlook Are neutrinos masses evidence for physics BSM?

Neutrinoless double beta decayTests at the LHC

0 signal + CPV in lepton sector + no evidence for mass at the LHCGUT 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 13 discovery