Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC

吳世哲

(Sechul Oh)

國立臺灣大學

With Xiao-Gang He, Jusak Tandean, Chung-Cheng Wen Phys. Rev. D80, 073012 (2009) 2 nd Workshop on LHC Physics, NCKU, October 24, 2009

Outline

Introduction Type-I seesaw

Large mixing between light & heavy neutral particles Some implications for testing Type-I seesaw at LHC

Type-III seesaw case Summary

S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 2

Introduction

S. Oh To accommodate the observation on neutrino masses and mixing with each other, the Standard Model must be extended.

Among many possibilities, the most popular are the seesaw scenarios :  New particles are introduced that have masses sufficiently large to make the light-neutrino masses small. It is very important to see if models for neutrino masses can be directly tested experimentally.  The best way to verify the seesaw mechanism directly would be by observing the new heavy particles responsible for generating the tiny neutrino masses at colliders like the LHC.

Explore this possibility in Type-I and Type-III seesaw models.

Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 3

S. Oh Important fact: Whether the new heavy particles can be produced and detected at colliders crucially depends on the strength of their interactions with SM particles.  proportional to mixing between the “light” and “heavy” neutrinos.  Large mixing is favored!

Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 4

Type-I seesaw

By introducing right-handed neutrinos N R that are singlets under the SM gauge group and can have large Majorana masses M N : In the weak-eigenstate basis, mass terms are S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 5

Type-I seesaw: Mass terms

Diagonalization of M seesaw unitary matrix To leading order, : Pontecorvo-Maki-Nakagawa-Sakata matrix  unitary light-heavy mixing matrix S. Oh

Tiny !

Huge !

Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 6

Type-I seesaw: Interactions

(1/2)

In terms of the weak eigenstates, the neutrinos couple to the gauge and Higgs bosons in the SM: In the mass-eigenstate basis, S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 7

Type-I seesaw: Interactions

(2/2)

N R do not directly have SM gauge interactions.

But, through mixing, N R can interact with the SM gauge bosons.

N couples to W, Z, h at tree level.  N can be singly produced via the quark level processes  In principle, the LHC can test the seesaw mechanism for N mass values up to a TeV or so. Since all these N productions depend on the elements of U n N , their size plays a crucial role as far as the testability of the seesaw mechanism is concerned. S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 8

Small m

n

vs. Large light-heavy mixing

With only one generation of neutrinos and the requirement for the N mass, the light-neutrino mass is given by For one generation, the mixing between the light and heavy neutrinos has a magnitude of

~

  for The mixing is extremely small.

Naively, it would not be possible to test Type-I seesaw at LHC. However, with more than one generation , it is possible to have large enough U n N can be achieved. such that testing the seesaw mechanism at LHC S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 9

A systematic way to find “large mixing U

n

N

”

First, find U 0 that satisfies Then, add a small perturbation: To find a nontrivial solution for U 0 , it is convenient to work in the basis where U 0 is already diagonalized. In that case, M N generally is not diagonal. The three heavy neutrinos have nonzero masses.  M N must be of rank 3  U 0 must not be more than rank 2 (due to ) turns out to be rank 1 S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 10

The rank of a matrix

The rank of a square matrix is the maximum number of independent rows (or columns).

 If a matrix A has a N x N submatrix that is its largest submatrix whose determinant is nonzero, then (The rank of the matrix A) = N .

: rank 3 : rank 2 : rank 1 S. Oh : rank 1 : rank 1 Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 11

The form of

U 0

Proof that the rank of U 0 is 1 : Begin with rank 2 Since M N is of rank 3, M 11, 12, 22 cannot all be simultaneously 0 .

If keep at least one of a & b nonzero, two types of nontrivial solutions:  U 0 must be a rank 1 matrix.

In the basis where M N is diagonal, : biunitary transf.

rank 1 S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 12

Specific examples of

U 0

In the basis where M N is diagonal, S. Oh  The parameters a, b, c are to be fixed from experimental data.

Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 13

Explicit solutions for

U

n

N

One can find solutions for U n N which satisfy all experimental data on light neutrinos by adding a perturbation matrix S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 14

Neutrino data

S. Oh U PMNS in the tri-bimaximal form Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 15

Solutions with one of the light-neutrino masses being zero (1/3)

Define Take S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 16

Solutions with one of the light-neutrino masses being zero (2/3)

In both cases (i) and (ii), This leads to S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 17

Solutions with one of the light-neutrino masses being zero (3/3)

Numerical examples:

Indeed, large elements in U

n

N are possible!

S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 18

Some implications for probing Type-I at LHC

(1/3)

The elements of U n N can be large & simultaneously satisfy the constraints from the tiny neutrino masses. Two other constraints from (a) Electroweak precision data : measured mainly at LEP (b) FCNC transitions in the charged lepton sector  In Type I seesaw: loop-induced processes Due to these constraints, the elements of U n N can be as large as 0.01 .

S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 19

Some implications for probing Type-I at LHC

(2/3)

The production channel  it involves a light charged lepton, which makes the signal more detectable.

The cross section s for arising from at center-of-mass energy of With U n N ~ 0.01, s > 1 fb for m N up to 115 GeV With U n N ~ 0.04, s > 1 fb for m N up to 250 GeV With 100 fb -1 of integrated luminosity, the production of more than 3000 N’s having a 100 GeV mass is possible.

The number of events drops to a few for m N = 600 GeV S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 20

Some implications for probing Type-I at LHC

(3/3)

S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 21

Type-III seesaw

( Foot, Lew, He, Joshi (1989) )

In addition to the SM particles, Type III seesaw model consists of SU(2) triplets of fermions with zero hypercharge. The fermion triplet SU(3) C x SU(2) L S x U(1) transforms under the SM gauge group Y as (1, 3, 0).

right-handed left-handed S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 22

Type-III seesaw: Interactions

The interaction Lagrangian in the mass basis : 3 x 3 matrix Non-zero off diagonal elements in e are the new sources of tree level FCNC in the charged lepton sector.

S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 23

Type-III seesaw: FCNC constraints

The most stringent constraints on FCNC effects: Example: S. Oh  Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 24

Some implications for probing Type-III at LHC

The elements of U n N can be large & simultaneously satisfy the constraints from the tiny neutrino masses & FCNC transitions in the charged lepton sector.

Also, constraints from Electroweak precision data  Constraints on the diagonal elements of Due to these constraints, the elements of U n N can be as large as 0.01 .

S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 25

Some implications for probing Type-III at LHC

The production channel  same as the Type-I case The heavy charged lepton: The cross section s for arising from at center-of-mass energy of With U n N ~ 0.01, s > 1 fb for m N up to 115 GeV With 100 fb -1 of integrated luminosity, the production of more than 200 E’s having a 100 GeV mass is possible.

The number of events drops to a few for m N = 300 GeV S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 26

Some implications for probing Type-III at LHC

S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 27

Summary

With only one generation of the neutrinos, it is not possible to have large light-heavy mixing to allow Type-I seesaw to be directly tested at LHC. However, with more than one generation of the neutrinos, the mixing can be much larger in certain special circumstances, providing more hope for probing the models at LHC. In Type-I seesaw, the main channel for the production of the heavy neutrinos at LHC is , corresponding to In Type-III seesaw, the main channels for single production are and , corresponding to and S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 28

BACK UP SLIDES

S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 29

Type-III seesaw: Lagrangian

The renormalizable Lagrangian involving S Define In terms of the component fields, the Lagrangian becomes S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 30

Type-III seesaw: Mass terms

One can easily identify the mass terms: S. Oh After diagonalizing the mass matrices, one can obtain the light neutrino mass matrix: “Seesaw mechanism” Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 31

Type-III seesaw: Mass terms

Diagonalization of the mass matrices: U L,R,0 : (3+3)-by-(3+3) matrices if 3 triplets are present.

S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 32

(A) Large U

n

N

: solutions with suppress

e

12

& large

e

23

S. Oh Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 33

(A) Large U

n

N

: solutions with suppress

e

12

& large

e

23

Numerical examples: S. Oh  Large Mixing of Light and Heavy Neutrinos in Seesaw Models and the LHC 34