NEUTRINOLESS DOUBLE BETA DECAY
ANGULAR CORRELATION
AND NEW PHYSICS
Dmitry Zhuridov
Particles and Fields Journal club
Department of Physics
National Tsing Hua University
The talk is based mostly on the paper:
Probing new physics in the neutrinoless double beta decay
using electron angular correlation.
A. Ali (DESY) , A.V. Borisov, D.V. Zhuridov (Moscow State U.) .
DESY-07-097, Jun 2007. 36pp.
e-Print: arXiv:0706.4165 [hep-ph]
(to appear in Phyical Review D)
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Popularity of the theme
M. Doi, T. Kotani, E. Takasugi, Prog.Theor.Phys.Suppl.83 (1985)
329
 T. Tomoda, Rep.Prog.Phys.54 (1991)
133
 S.L. Adler et al., Phys.Rev.D11 (1975)
74
 H. Pas, M. Hirsch, H.V. Klapdor-Kleingrothaus, S.G. Kovalenko, Phys.Lett.B453
(1999)
26

SPIRES-HEP:
 FIND TITLE NEUTRINOLESS DOUBLE BETA DECAY
 FIND K NEUTRINOLESS DOUBLE BETA DECAY
470
476
E-print arXiv:
 1991-1995
 1996-2000
 2001-2005
 2006-p.t.
29
139
251
87
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Abstract: NEUTRINOLESS DOUBLE BETA DECAY
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Contents
Introduction
 Neutrinoless Double Beta Decay
 Angular Correlation in Long-Range Mechanism
 Analysis of the Angular Correlation
 Conclusion

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Introduction
SNO, Super-Kamiokande, KamLAND – ν oscillations
mij2  mi2  m2j  0
Neutrinos have non-zero masses and they mix with each other
Bounds on the neutrino masses:
2  m2  7.9105 эВ2
m21
sol
2  m2  2.3103 эВ2
m31
atm

 mi  0.75 эВ  mi  0.25 эВ (i  1, 3)
m   U ei
eff
e
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i
i
2
mi2

1/ 2
 2.05 эВ  m1  meff
e
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It is largely anticipated that the neutrinos are Majorana particles:
Correspondence between Dirac and Majoana fields
Dirac field can be constructed from two Majorana fields
Dirac field has additional freedom of phase trasformation
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How to induce small neutrino masses?
Other possible mechanisms





Model with scalar triplet:
Model with right-handed neutrino and scalar singlet:
In Zee model (with charged scalar singlet and additional scalar
doublets) Majorana neutrino masses arise at one loop level;
In models with doubly charged scalar singlet Majorana neutrino
masses arise at two loop level;
Models with effective nonrenormalizable term in Lagrangian:
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See-saw mechanism
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Neutrinoless Double Beta Decay
 0 2  decay
A(Z )  A(Z  2)  2e
e
A( Z )
{

p
p
n
n

}
A( Z  2)
e
Lepton number is changed by 2 units.
02 decay is forbidden in the SM.
Extended version of the SM could contain tiny nonrenormalizable terms that
violate LN and allow 02 decay.
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Probable mechanisms of LN violation may include exchanges by:
Majorana neutrinos
Scalar bilinears, e.g. doubly charged dileptons
SUSY particles
Leptoquarks
Right-handed W_R bosons etc.
Two possible classes of mechanisms for the 02 decay:
Long range
Short range
(with the light s in the intermediate state)
d
e
u
e
u
d
e
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d
u
u
d
e

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
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According to the Schechter-Valle theorem, any mechanism inducing
the 02 decay produces an effective Majorana mass for the neutrino,
which must therefore contribute to this decay.
e
e
u
u
d
d
Purpose: to examine the possibility to discriminate among the various
possible mechanisms contributing to the 02 decays using
the information on the angular correlation of the final electrons.
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Angular Distribution in Long-Range Mechanism
Most general Lorentz invariant effective Lagrangian for the long-range
mechanism of 0ν2β decay is:
j & J are leptonic & hadronic currents of definite tensor structure
and chirality;  , =V  A, S  P, TL,R ; U ei is PMNS mixing matrix;
i encode new physics.
Model
VM ARPV
MSSM
(Hirsch
M.,
Klapdor
H.V., Kovalenko
currents
(Doi
M.,M.,
Kotani
T., Takasugi
E. (1985))
with
LQ (Hirsch
Klapdor-Kleingrothaus
H.V.,S.G. (1996))
Kovalenko
(1996))
1 n1S.G.
gV S'  P V  1A n1 '
VVAA
n1 A
* gV
 i
 An1
V
VVAA,i,i  (0qe) RRUUnil2,V2 SS ,PP ,i VV2
U
,





4

U
 ni , Vei .

( ,i)
LL  ni
S ,P ,i V  A,2i(
q )V
LRei , (V 
) LR
 U ei

A
A
,
i
2
2
1
   2G2 M  M , ei   4G M  MgV ,    44G M ,    4G M . gV
V A
V -A
F

( L)
S
2
S
( L)
V
2
V

V A
V A
F

( R)
S
2
S
( R)
V
2
V

S P
S P
F
V
2
V
S P
S P
F
S
2
S
1
  (nq1) LRU ni* .
TR
TR ,i
8
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Approximations:
• leading order in the Fermi constant
• leading contribution of the parameters \epsilon
• relativistic electrons and non-relativistic nucleons
• S_{1/2} and P_{1/2} waves for the outgoing electrons
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Expressions for A for one ∈, considered at a time
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Expressions for B for one ∈ at a time
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In these tables:

m
m

,    , with effective Majorana masses:
me
me
m   U ei2 mi ,
i
mSS PP   U ei SS  PP ,i mi , mVV AA   U ei VV  AA,i mi , mTTLL,R  U ei TTLL ,R ,i mi ;
i
i
i
ci  cos i , with the relative phases:  01  arg   VV AA*  ,  1  arg   VV  AA*  ...
A0  C1  , B0  D1  .
2
2
The quantities Ci , Ci( SP , T ) , Di and Di( SP , T ) are expressed through
the intergated phase space factors A0 k , A0( kSP , T ) , B0 k , B0( kSP , T ) and
the combinations of nuclear parameters.
The expressions associated with the coefficients VV  AA confirm the results
of Doi et al. (1985), while the expressions associated with the other
coefficients  transcend the earlier work.
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The integrated kinematic A- and B-factors [in 10-15 yr -1 ]
for the 0+  0 transition of the 0 2 decay of 76Ge.
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Analysis of the Electron Angular
Correlation
If the ``nonstandard" effects, are zero then K = B01/A01. Its values are
given in the Table for various decaying nuclei of current experimental
interest:
The presence of the ``nonstandard" parameters VV - AA , SS  PP , TTLR or TTLR
does not change significantly the form of the angular correlation.
The presence of the ``nonstandard" parameters VV  AA , SS  PP , TTLL or TTRR
does change this correlation.
The angular correlation coefficient K for various SM extensions for decays
of 76 Ge.:
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Particular cases for the parameter space:
Constraints on the couplings of the effective LQ-quark-lepton interactions:
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1a
1b
2a
2b
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Angular correlation in left-right symmetric models
For the model SU (2) L  SU (2) R  U (1) using the condition m WL  mWR :
mWR  mWL

V A
,



arctan

with  = U eiVei .
V A /  ,
V A
V  A


Using mWL  mW1  80.4 GeV for the values  106 , 5 10-7
we have got the correlation shown in Figs 3, 4.
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Figs 3a, 3b.
 =10-6
10^3*ς
Figs 4a, 4b.
10^3*ς
 =5  10-7
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Experiments in the 0 2 decay would measure mWL / mWR and U eiVei .
Experiments at the Tevatron and the LHC can measure mWL / mWR .
Differential width vs. cos for  =10-6 :
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Conclusion

We have presented a detailed study of the electron angular
correlation for the long range mechanism of 02 decays in a
general theoretical context. This information, together with
the ability of observing these decays in several nuclei, would
help greatly in identifying the dominant mechanism
underlying these decays.

The running experimental facility that in principle can
measure the electron angular correlation in the 02 decay
NEMO3 possibly has no the sufficient sensitivity. The
proposed facilities are SuperNEMO, MOON and EXO. We have
argued that there is a strong case in building at least one of
them.
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