Non-Standard Neutrino Interactions

Enrique Fernández-Martínez MPI für Physik Munich

Non-unitarity and NSI

Generic new physics affecting n oscillations can beparameterized as 4-fermion Non-Standard Interactions:

fPflPG RLLF ,22

Production or detection of a nb associated to a la

So that

The general matrix N can be parameterized as:

UN 1 where †

Also gives but with *

p → m +nt

n +nm → p + t

Non-unitarity and NSI matter effects

Non-Standard n scattering off matter can also be parameterized as 4-fermion Non-Standard Interactions:

fPfPG RLLm

F ,22

Integrating out the W and Z, 4-fermion operators are obtained also for the non-unitary mixing matrix

They are related to the production and detection NSI

so that

Non-unitarity and NSI matter effects

Integrating out the W and Z, 4-fermion operators for matter NSI are obtained from non-unitary mixing matrix

They are related to the production and detection NSI

fPfPG RLLm

F ,22

enenene

enenene

eneeneeneem

nnnnnn

nnnnnn

nnnnnn

1

1

112

Direct bounds on prod/det NSI

C. Biggio, M. Blennow and EFM 0907.0097

dPuPlG RLLud

F ,22

13.0013.0087.0

013.01.0106.2

042.0025.0042.05ud

ePPG LLe

F

22

03.003.0025.0

03.003.0025.0

03.003.0025.0e

From , , m b p decays and zero distance oscillations

Bounds order ~10-2

5.01.044.0

1.003.01.0

44.01.014.0em

Direct bounds on matter NSI

If matter NSI are uncorrelated to production and detectiondirect bounds are mainly from n scattering off e and nuclei

S. Davidson, C. Peña garay, N. Rius and A. Santamaria hep-ph/0302093J. Barranco, O. G. Miranda, C. A. Moura and J. W. F. Valle hep-ph/0512195

J. Barranco, O. G. Miranda, C. A. Moura and J. W. F. Valle 0711.0698C. Biggio, M. Blennow and EFM 0902.0607

fPfPG RLLm

F ,22

Rather weak bounds… …can they be saturated avoiding additional constraints?

305.05.0

05.0008.005.0

5.005.01um

605.05.0

05.0015.005.0

5.005.06.0dm

Gauge invariance

However fPfPG RLLm

F ,22

is related to fPflPlG RLLm

F ,22

by gauge invariance and very strong bounds exist

m → e g m → e in nuclei t decays

S. Bergmann et al. hep-ph/0004049Z. Berezhiani and A. Rossi hep-ph/0111147

See Toshi’s talk

Large NSI?

We searched for gauge invariant SM extensions satisfying:

Matter NSI are generated at tree level

4-charged fermion ops not generated at the same level

No cancellations between diagrams with different messenger particles to avoid constraints

The Higgs Mechanism is responsible for EWSBS. Antusch, J. Baumann and EFM 0807.1003

Large NSI?

At d=6 only one possibility: charged scalar singlet

M. Bilenky and A. Santamaria hep-ph/9310302

cc LiLLiL 22

Present in Zee model orR-parity violating SUSY

Large NSI?

Very constrained:

F. Cuypers and S. Davidson hep-ph/9310302S. Antusch, J. Baumann and EFM 0807.1003

m → e g m decays

t decaysCKM unitarity

Since lab = -lba only e mm , e mt and e tt ≠0

Large NSI?

At d=8 more freedom

Can add 2 H to break the symmetry between n and l with the

vev

There are 3 topologies to induce effective d=8 ops with

HHLLff legs:

-v2/2 ff

ffLiHHiL t

2

*2

Z. Berezhiani and A. Rossi hep-ph/0111147; S. Davidson et al hep-ph/0302093

Large NSI?

We found three classes satisfying the requirements:

Large NSI?

We found three classes satisfying the requirements:

Just contributes to the scalar propagator after EWSB

Same as the d=6 realization with the scalar singlet

v2/2 cc LiLLiL 22

1

Large NSI?

We found three classes satisfying the requirements:

The Higgs coupled to the NR selects n after EWSB

-v2/2 ff

ffLiHHiL t

2

*2

2

Large NSI?

But can be related to non-unitarity and constrained

122

†

22

NNM

Yv

M

Yv

i i i

i

i

i 122

†

22

NNM

Yv

M

Yv

j j j

j

j

j

Fij G10

2

Large NSI?

For the matter NSI

Where is the largest eigenvalue of

And additional source, detector and matter NSI aregenerated through non-unitarity by the d=6 op

Large NSI?

We found three classes satisfying the requirements:

Mixed case, Higgs selects one n and scalar singlet S the other

3

Large NSI?

Can be related to non-unitarity and the d=6 antisymmetric op

3

122

†

22

NNM

Yv

M

Yv

i i i

i

i

i j j Sj

j

Sj

j

Mv

Mv

2

2

Fij G10

Large NSI?

At d=8 we found no new ways of selecting n

The d=6 constraints on non-unitarity and the scalar singlet

apply also to the d=8 realizations

What if we allow for cancellations among diagrams?

B. Gavela, D. Hernández, T. Ota and W. Winter 0809.3451

Large NSI?

B. Gavela, D. Hernández, T. Ota and W. Winter 0809.3451

Large NSI?

B. Gavela, D. Hernández, T. Ota and W. Winter 0809.3451

tick means selects n at d=8 without 4-charged fermion

bold means induces 4-charged fermionat d=6, have to cancel it!!

Large NSI?

There is always a 4 charged fermion op that needs canceling

Toy model

B. Gavela, D. Hernández, T. Ota and W. Winter 0809.3451

EELiHHiL t2

*2

Cancelling the 4-charged fermion ops.

NSI in loops

Even if we arrange to have

We can close the Higgs loop, the triplet terms vanishes and

NSIs and 4 charged fermion ops induced with equal strength

Extra fine-tuning required at loop level to have k=0 or loop contribution dominates when 1/16p2 > v2/M2

EELiHHiLM

O t2

*24

EEHHLLHHLLM

O ††42

EELLk

M

O2

2

4 162

C. Biggio, M. Blennow and EFM 0902.0607

Conclusions

Models leading “naturally” to NSI imply:

O(10-3) bounds on the NSI

Relations between matter and production/detection NSI

Probing O(10-3) NSI at future facilities very challenging but not impossible, near detectors like MINSIS excellent probes

Saturating the mild model-independent bounds on matter NSI and decoupling them from production/detection requires strong fine tuning

Other models for n masses

Type I seesawMinkowski, Gell-Mann, Ramond, Slansky, Yanagida, Glashow, Mohapatra, Senjanovic, …

NR fermionic singlet

Type II seesawMagg, Wetterich, Lazarides, Shafi, Mohapatra, Senjanovic, Schecter, Valle, …

D scalar triplet

Type III seesawFoot, Lew, He, Joshi, Ma, Roy, Hambye et al., Bajc et al., Dorsner, Fileviez-Perez

SR fermionic triplet

Different d=6 ops

Type II:• LFV 4-fermions interactions

Type I:• non-unitary mixing in CC• FCNC for n

Type III:• non-unitary mixing in CC• FCNC for n• FCNC for charged leptons

A. Abada, C. Biggio, F. Bonnet, B. Gavela and T. Hambye 0707.4058

Types II and III induce flavour violation in the charged lepton sectorStronger constraints than in Type I

Low scale seesaws

But

DNtD mMmmd 1

5

NDND M

mmMmd 2†

6

so

!!!

Low scale seesaws

The d=5 and d=6 operators are independent

Approximate U(1)L symmetry can keep d=5 (neutrino mass) small and allow for observable d=6 effects

See e.g. A. Abada, C. Biggio, F. Bonnet, B. Gavela and T. Hambye 0707.4058

Inverse (Type I) seesaw Type II seesaw L= 1 -1 1

DNNtD mMMmd 11

5

DND mMmd 2†6

25 4

M

Yd

2

†

6

M

YYd

Magg, Wetterich, Lazarides, Shafi, Mohapatra, Senjanovic, Schecter, Valle,…

Wyler, Wolfenstein, Mohapatra, Valle, Bernabeu, Santamaría, Vidal, Mendez, González-García, Branco, Grimus, Lavoura, Kersten, Smirnov,….

m << M

Low scale seesaws

The d=5 and d=6 operators are independent

Approximate U(1)L symmetry can keep d=5 (neutrino mass) small and allow for observable d=6 effects

See e.g. A. Abada, C. Biggio, F. Bonnet, B. Gavela and T. Hambye 0707.4058

Inverse (Type I) seesaw Type II seesaw L= 1 -1 1

DNNtD mMMmd 11

5

DND mMmd 2†6

25 4

M

Yd

2

†

6

M

YYd

Magg, Wetterich, Lazarides, Shafi, Mohapatra, Senjanovic, Schecter, Valle,…

Wyler, Wolfenstein, Mohapatra, Valle, Bernabeu, Santamaría, Vidal, Mendez, González-García, Branco, Grimus, Lavoura, Kersten, Smirnov,….

m << M