Decay of polarized muon at rest as a source of polarized neutrino beam

Abstract

In this paper, we indicate the theoretical possibility of using the decay of polarized muons at rest as a source of the transversely polarized electron antineutrino beam. Such a beam can be used to probe new effects beyond standard model. We mean here new tests concerning CP violation, Lorentz structure and chirality structure of the charged current weak interactions. The main goal is to show how the energy and angular distribution of the electron antineutrinos in the muon rest frame depends on the transverse components of the antineutrino beam polarization. Our analysis is model-independent and consistent with the current upper limits on the non-standard couplings. The results are presented in a limit of infinitesimally small mass for all particles produced in the decay.

Full text

Page 1

arXiv:0705.4258v1 [hep-ph] 29 May 2007
Decay of polarized muon at rest as a source of
polarized neutrino beam
S. Ciechanowicza, W. Sobk´ owa,∗, M. Misiaszekb
aInstitute of Theoretical Physics, University of Wroc? law, Pl. M. Born 9,
PL-50-204 Wroc? law, Poland
bM. Smoluchowski Institute of Physics, Jagiellonian University, ul. Reymonta 4,
PL-30-059 Krak´ ow, Poland
Abstract
In this paper, we indicate the theoretical possibility of using the decay of polarized
muons at rest as a source of the transversely polarized electron antineutrino beam.
Such a beam can be used to probe new effects beyond standard model. We mean
here new tests concerning CP violation, Lorentz structure and chirality structure of
the charged current weak interactions. The main goal is to show how the energy and
angular distribution of the electron antineutrinos in the muon rest frame depends
on the transverse components of the antineutrino beam polarization. We admit the
participation of the complex exotic scalar and tensor couplings of the right-chirality
electron antineutrinos in addition to the standard vector coupling of the left-chirality
ones, while the muon neutrinos are always left-chirality. It means that the outgoing
electron antineutrino beam is a mixture of the left- and right-chirality antineutrinos
and has the fixed direction of the transverse spin polarization with respect to the
production plane. Our analysis is model-independent and consistent with the current
upper limits on the non-standard couplings. The results are presented in a limit of
infinitesimally small mass for all particles produced in the decay.
Key words: polarized muon decay, exotic couplings, transverse antineutrino spin
polarization
PACS: 13.15.+g, 13.35.Bv, 13.88.+e
∗Corresponding author
Email addresses: ciechano@sunflower.ift.uni.wroc.pl (S. Ciechanowicz),
sobkow@sunflower.ift.uni.wroc.pl (W. Sobk´ ow),
misiaszek@zefir.if.uj.edu.pl (M. Misiaszek).
Preprint submitted to Physic Letters B1 February 2008

Page 2

1 Introduction
Decay of polarized muon at rest (DPMaR) is the very appropriate process to
test both the time reversal violation (TRV) and the space-time, and chirality
structure of the purely leptonic charged weak interactions (PLCWI). More-
over, we investigate here if the DPMaR can also be used as a strong source of
the transversely polarized antineutrino (neutrino) beam which would be scat-
tered on the polarized electron target (PET). A detailed analysis of new effects
beyond the Standard Model (SM) of electroweak interactions [1,2,3] is carried
out in [4]. Ciechanowicz et al. show that the scattering of the left-chirality and
longitudinally polarized neutrino beam on the PET would allow to test the
possibility of CP-breaking in the (νµe−) scattering. The measurement of the
azimuthal asymmetry of recoil electrons could detect the CP-violating phase
between the standard complex vector and axial-vector couplings. The other
problem considered in [4] concerns the scattering of the transversely polarized
mixture of left-chirality and right-chirality neutrinos on the PET. If such a
neutrino beam would be scattered, the dependence on the angle between the
transverse neutrino spin polarization of incoming beam and the transverse
electron polarization of target in the recoil electron energy spectrum could be
tested. That would be a direct signature of the right-chirality neutrinos.
As is well-known, the SM of electro-weak interactions has a vector-axial (V-A)
structure [5] which has been put by hand in order to obtain agreement with ex-
periments. This means that only left-chirality Dirac neutrinos may take part
in the charged and neutral current weak interaction. This structure follows
among other from the low energy measurements of the muon decay such as;
the spectral shape, angular distribution, and polarization of the outgoing elec-
trons (positrons). At present, there is no evidence for the deviations from the
SM for the Michel parameters. The neutrino oscillation experiments indicate
the non-zero neutrino mass and provide first evidence for physics beyond the
minimal SM. On the other hand, the experimental precision of present tests
still allows the participation of the exotic scalar S, tensor T and pseudoscalar
P couplings of the right-chirality Dirac neutrinos beyond the SM [6]. The
KARMEN experiment [7] has measured the energy distribution of electron
neutrinos emitted in positive muon decay at rest (µ+→ e++ νe+ νµ). The
obtained result is in agreement with the SM prediction on the neutrino Michel
parameter ωL= 0. They get for the first time a 90% confidence upper limit of
ωL≤ 0.113, which leads to a limit of |gS
between the scalar and tensor couplings. The current upper limits on the all
non-standard couplings, obtained from the normal and inverse muon decay,
are presented in the Table 1 [8]. The coupling constants are denoted as gγ
where γ = S,V,T indicates the type of weak interaction, i.e. scalar S, vector
V, tensor T; ǫ,µ = L,R indicate the chirality of the electron or muon and the
neutrino chiralities are uniquely determined for given γ,ǫ,µ. It means that
the neutrino chirality is the same as the associated charged lepton for the V
RL+ 2gT
RL| ≤ 0.78 for the interference
ǫµ,
2

Page 3

Coupling constantsSM Current limits
|gV
|gV
|gV
|gV
|gS
|gS
|gS
|gS
|gT
|gT
|gT
|gT
LL|
LR|
RL|
RR|
LL|
LR|
RL|
RR|
LL|
LR|
RL|
RR|
1> 0.960
0< 0.036
0< 0.104
0< 0.034
0< 0.550
0< 0.088
0< 0.417
0< 0.067
00
0< 0.025
0< 0.104
00
Table 1
Current limits on the non-standard couplings.
interaction, and opposite for the S, T interactions [8]. In the SM, only gV
non-zero value.
LLis
It is necessary to point out that the existence of the exotic right-chirality
neutrinos in the few keV region, that are sterile in SM, can have numerous
consequences in astrophysics and cosmology. We mean here the mechanism
of neutrino “spin flip” in the Sun’s convection zone in order to explain the
observed deficit of the solar neutrinos [9]. In addition, the sterile neutrinos
could also account for pulsar kicks (high pulsar velocities), could explain all
or some fraction of the dark matter in the Universe and would affect emission
of supernova neutrinos [10].
Recent analysis carried out by Erwin et al. for the muon decay [11] shows
that there exist four-fermion operators that do not contribute to the neutrino
mass matrix through radiative corrections. These operators generate the exotic
couplings gS,T
contribute to the neutrino mass matrix.
So far the CP violation is observed only in the decays of neutral K- and
B-mesons [12], and is described by a single phase of the Cabibbo-Kobayashi-
Maskawa quark-mixing matrix (CKM)[13]. There is no experimental evidence
on the TRV in the PLCWI, e.g. the muon decay and neutrino-electron elas-
tic scattering. However, the baryon asymmetry of the Universe can not be
explained by the CKM phase only, and new sources of the CP violation are
required [14]. According to the prediction of non-standard models, the effects
of new CP-breaking phases could be measured in observables where the SM
LR,RL, while all operators generating the vector couplings gV
LR,RL
3

Page 4

CP-violation is suppressed, while alternative sources can generate a sizable
effect, e.g. the electric dipole moment of the neutron, the transverse lepton
polarization in three-body decays of charged kaons K+[15,16], transverse po-
larization of the electrons emitted in the decay of polarized8Li nuclei [17].
The other possibility of measuring the exotic CP-breaking phases is to use the
neutrino observables which consist only of the interference terms between the
standard coupling of the left-chirality neutrinos and exotic couplings of the
right-chirality neutrinos and do not depend on the neutrino mass. We mean
here both T-even and T-odd transverse components of the neutrino spin polar-
ization. At present, the direct tests are still impossible. The possible solution
can be the scattering of the transversely polarized (anti)neutrino beam, com-
ing from the polarized muon decay at rest, on the PET and the measurement
of the maximal asymmetry of the cross section, [4].
Left-right symmetric models (LRSM) and composite models (CM) can be
proposed as an example of the non-standard models of purely leptonic weak
interactions, in which the exotic couplings of the right-chirality neutrinos (an-
tineutrinos) can appear. Recently TWIST Collaboration [18] has measured the
Michel parameter ρ in the normal µ+decay and has set new limit on the WL−
WRmixing angle in the LRSM. Their result ρ = 0.75080 ± 0.00044(stat.) ±
0.00093(syst.)±0.00023 is in good agreement with the SM prediction ρ = 3/4,
and sets new upper limit on mixing angle |χ| < 0.030 (90% CL). The CM have
been proposed to probe the scale for compositeness of quarks and leptons. La-
grangian of the new effective contact interactions (CI) for the muon decay
includes among other the contributions from the standard vector coupling of
the left-chirality neutrinos and exotic scalar coupling of the right-chirality ones
[19].
Our analysis is model-independent and the calculations are made in the limit
of infinitesimally small mass for all particles produced in the muon decay. The
density operators [20] for the polarized initial muon and for the polarized out-
going electron antineutrino are used, see Appendix A. We use the system of
natural units with ? = c = 1, Dirac-Pauli representation of the γ-matrices
and the (+,−,−,−) metric [21].
2Transversely Polarized Electron-Antineutrino Beam
To show how the energy and angular distribution of the electron antineutrinos
may depend on the angle between the transverse antineutrino spin polarization
and the muon polarization vectors, we assume that the DPMaR (µ−→ e−+
νe+ νµ) is a source of the electron antineutrino beam. It is worth to notice
that if one takes into account the positive muon decay (µ+→ e++ νµ+ νe),
the electron neutrino beam is produced. The production plane is spanned by
the direction of the initial muon polarization ˆ ηµand of the outgoing electron
4

Page 5

µ
-
target
source
^
^
^
^
??
q ?
?
?
?
?e
q
?
?
?
?
Fig. 1. Figure shows the production plane of the νe-antineutrinos for the process of
(µ−→ e−+νe+νµ), η⊥
The production plane is spanned by the direction of the initial muon polarization
ˆ ηµand of the outgoing antineutrino momentum ˆ q.
ν- the transverse polarization of the outgoing antineutrino.
SMNonstandard Interference ofInterference of
couplings (NC) SM with NC SM with NC
ab
gV
LL
gS
LL
gV
LLgS∗
LL= 0gV
LLgS∗
LL= 0
gS
LR
gV
LLgS∗
LR?= 0gV
LLgS∗
LR= 0
gS
RL
gV
LLgS∗
RL= 0gV
LLgS∗
RL= 0
gS
RR
gV
LLgS∗
RR= 0gV
LLgS∗
RR= 0
gT
LL
gV
LLgT∗
LL= 0gV
LLgT∗
LL= 0
gT
LR
gV
LLgT∗
LR?= 0gV
LLgT∗
LR= 0
gT
RL
gV
LLgT∗
RL= 0
gV
LLgT∗
RL= 0
gT
RR
gV
LLgT∗
RR= 0gV
LLgT∗
RR= 0
Table 2
Table shows non-vanishing interferences between the gV
LL,LR,RL,RR) couplings after a computation of traces for two cases: a. Polarized
muon and polarized electron antineutrino. b. Polarized muon and polarized muon
neutrino.
LLand gS,T
ǫµ
(ǫµ=
antineutrino momentum ˆ q, Fig. 1. We admit a presence of the exotic scalar
gS
It means that the outgoing electron antineutrino flux is a mixture of the left-
chirality antineutrinos produced in the gV
chirality ones produced in the gS
our analysis is carried out in the limit of vanishing antineutrino mass, the
left-chirality antineutrino has positive helicity, while the right-chirality one
LRand tensor gT
LRcouplings in addition to the standard vector gV
LLcoupling.
LLweak interaction and the right-
LRand the gT
LRweak interactions. Because
5