Probing Majorana Neutrinos in Rare Meson Decays

Claudio DibUTFSM

I.S. & B.K. Fest, UTFSM, May 2010

G. Cvetic, C.D., S.K. Kang, C.S. Kim, PRD 82, 053010, 2010

Outline

1. Recent history

2. Issues on neutrino masses

3. Probing Majorana neutrinos via (a) 0nbb (b) K, D, Ds, B, Bc Rare Meson decays

4. Concluding remarks

Before: Neutrinos are massless in the SM

1. History

• No right-handed ’s Dirac mass term is not allowed.

• SU(2)_L symmetry, and Higgs doublet only: (B - L) con-servation

Majorana mass term is forbidden.

The Neutrino Era

• Atmospheric nm’s disappearance (SK) (1998)

• …converted most likely to n t (2000)

• Solar ne is converted to either nm or nt (SNO) (2002)

• Only LMA solution for solar neutrinos (Homestake+Gallium+SK+SNO) (2002)• Reactor anti-ne oscillate (KamLAND) (2004)

4

What we have learned• Lepton Flavor is not conserved• Neutrinos have tiny mass (a hierarchy issue)• Neutrinos have large mixing• Very different from quark sectors

the first evidence for incompleteness of Minimal Standard Model

1. History

What we don’t know absolute mass scale of neutrinos remains an open ques-

tion. m1, 2 < or > m3 ? normal or inverted hierarchy?

What is the value of q13? Is it zero or not? how small?

Reactor & accelerator -oscillation experiments can an-swer, but possibly estimated from a global fit Why q23 and q12 are large and close to special values?

Very strong hints at a certain (underlying) flavor sym-metry. Is CP violated in leptonic sector?

Neutrinos are Dirac or Majorana?

1. History

6

Window to high energy physics beyond the SM

Why is the neutrino mass interesting?

The problem of mass in the SM The problem of Baryon Asymmetry in Cosmology Candidate for Dark Matter

2. Issues on Neutrino masses

Experimental ways to learn about neutrinos:

Neutrino oscillation exp. (solar, atm, reactors, accel.) Nuclear decays (beta and double-beta) Nu-Nuclei scattering (accel.) Rare decays (high intensity accel.) etc.

2. Issues on Neutrino masses

The issue of Dirac vs Majorana character:

-> Majorana particle: nu(right) = anti-nu(left)

-> Possible mass terms:

Dirac mass terms are invariant under global symmetry Majorana mass terms are not invariant.

Dirac mass conserved quantum number ( L ) but Majorana mass L not conserved

, : Majorana

,: Diracc

c

c

c

ie

etc ,)( : Majorana

,: Diracc

LL

LRRL

2. Issues on Neutrino masses

Majorana Masses must have a different origin than masses of charged leptons and quarks.

A natural theoretical way to understand why 3 -masses are very small :

Seesaw mechanism

• Type-I : Right-handed Majorana neu-

trinos.

• Type-II : Higgs triplet.

• Type-III : Triplet fermions.

ν

:

2. Issues on Neutrino masses

If Neutrinos are Majorana

Majorana character is observable in processes with ΔL=2 :

Mass term connects neutrinos with antineutrinos:

AZ A(Z+2) + 2e-, μ- + AZ e+ + A(Z-2), etc.

(0-n 2Beta) (m-e conversion in nuclei)

some rare decays

2. Issues on Neutrino masses

Lepton number violation by 2 units, , plays a crucial role to probe the Majorana nature of ’s,

Provides a promising lab. method for determining the absolute neutrino mass scale complementary to other measurement techniques

2L

3.a. Neutrinoless double-beta nuclear decay: 0

3. Probing Majorana Neutrinos

The half-life time of the 0nbb decay, , can be factorized as:

2/10T

phase space factor Nuclear matrix element(large uncertainties)

(depends on neutrino mass hierarchy)

2200

012/10 ||||),(][

eemMZEGT

3121 233

222

211

ie

ieeee eUmeUmUmm

3.a …in neutrinoless double-Beta decay in the limit of small neutrino masses :

Effective neutrino mass (model independent)

3. Probing Majorana Neutrinos

21 : Processes 2 llMML

…taking mesons in the initial and final state to be pseudoscalars (M : K+, D+, Ds , B+, Bc M’ = p-, K-, D-,…)

(G.Cvetic, C.D., S.Kang, C.S.Kim)

(S. Kovalenko, I. Schmidt, A. Gribanov, C.D.)

3. Probing Majorana Neutrinos

3.b. …via Rare Meson Decays

Effective Hamiltonian:

Decay Amplitude:

2 2

2

[ ]2

Feff t t s

N N

N Ns

N N

GH C O C O L

p m

p m im

*5[ (1 ) ]i i NL U U u v

2 1 2 1

2 1 2 1

*

*

t q q q Q q q q Q

s q q qQ q q qQ

O V V J J

O V V J J

5(1 )qQJ Q q

' '1 2 1 2( ) | |effA M M M H M

3.a. Probing Majorana Neutrinos ..via Rare Meson De-cays

The leptonic tensor:

5 5(1 ) (1 )( )

2 2( )i i i iL U U v v

2 2* 5 5(1 ) (1 )

( )2 2

i i

i ii

i i

p m

pU U v

mu

2 2* 5(1 )

2i

i

ii

iiU U u

m

p mv

W WiU iU

i i

3.a. Probing Majorana Neutrinos ..via Rare Meson De-cays

transition rates are proportional to

production resonant for )()(

heavy for

light for

23

4

23

1

2

21

2121

NN

n

i i

ilil

iiililll

m

fNiN

m

UU

mUUm

2 2i j

Nl N l N

N N N

p mU U

p m im

,t sC C

3.a. Probing Majorana Neutrinos …via Rare Meson De-cays

Mm m (i) Light neutrino case:

Dominant contribution comes from the “t-type” diagram when the light neutrino and intermediate hadron state goes on its mass shell.

- Analogous to nuclear 0n2b decay

3.a. Probing Majorana Neutrinos ..via Rare Meson De-cays

1 2B D (i) Light neutrino case: e.g. in

3.a. Probing Majorana Neutrinos ..via Rare Meson De-cays

M Mm m m

Dominant contribution comes from the “s-type” diagram

because the neutrino alone can be on its mass shell.

(ii) Intermediate neutrino mass case:

3.a. Probing Majorana Neutrinos ..via Rare Meson De-cays

Effective amplitude at meson level:

(neglecting charged lepton masses)

M Mm m m

(ii) Intermediate neutrino mass case:

3.a. Probing Majorana Neutrinos ..via Rare Meson De-cays

Branching ratio for as function of m, with mixing factor divided out

( , )K e

M Mm m m

(ii) Intermediate neutrino mass case:

3.a. Probing Majorana Neutrinos ..via Rare Meson De-cays

M Mm m m

(ii) Intermediate neutrino mass case:

3.a. Probing Majorana Neutrinos ..via Rare Meson De-cays

(E. Nardi, E. Roulet, D. Tommasini (2005) )

M Mm m m

(ii) Intermediate neutrino mass case:

3.a. Probing Majorana Neutrinos ..via Rare Meson Decays

Mm m

Now both amplitudes, “s-type” and “t-type”, are comparable

neutrino propagators reduce to -1/(mN)2

(iii) Heavy neutrino case:

3.a. Probing Majorana Neutrinos ..via Rare Meson De-cays

The effective amplitude and rate:

Mm m (iii) Heavy neutrino case:

3.a. Probing Majorana Neutrinos ..via Rare Meson De-cays

Mm m (iii) Heavy neutrino case:

3.a. Probing Majorana Neutrinos ..via Rare Meson De-cays

4. Concluding Remarks

• Much to be discovered about neutrinos:

• For light (standard) neutrinos: • Mass hierarchy, absolute masses, mixings (especially 1-3)• Dirac vs Majorana?

• Are there more neutrinos? Majorana? (Seesaw says yes…)

• Look for Majorana neutrinos in DL=2 processes:• Neutrinoless double beta decays• Rare meson Decays

• Intermediate masses may lead to signals…

• Let us build the next meson factory…