Determination of the Polarization of the Decay
Positrons in Polarized Muon Decay
K.-U. Köhler , K. Bodek† , A. Budzanowski , N. Danneberg ,
W. Fetscher , C. Hilbes , L. Jarczyk† , K. Kirch‡ , S. Kistryn† , J. Klement ,
A. Kozela , J. Lang , G. Llosá Llácer , T. Schweizer , J. Smyrski† ,
J. Sromicki , E. Stephan§ , A. Strzałkowski† and J. Zejma†
Institute for Particle Physics, ETH Zürich, Switzerland
Institute of Physics, Jagellonian University, Kraków, Poland
H. Niewodniczanski Institute of Nuclear Physics, Kraków, Poland
‡
Paul Scherrer Institut, Villigen, Switzerland
§
Institute of Physics, University of Silesia, Katowice, Poland
†
Abstract. The standard model of electroweak interactions predicts that the positrons from the decay of polarized positive muons are mainly longitudinally polarized. The measurement of the two
transverse polarization components of the positron PT and PT is a sensitive tool to look for contri1
2
butions from additional, exotic interactions and for the violation of time reversal invariance in this
purely leptonic decay.
The µP - experiment at the Paul Scherrer Institute determines the three positron polarization compoT
nents simultaneously with the same apparatus by making use of three different effects. By examining
the temporal dependence of annihilation-in-flight of the decay positrons with polarized electrons a
possible non-zero value of the transverse polarization is determined. The phase of this transverse
polarization can be measured by making use of the decay asymmetry. Using the dependence of
annihilation-in-flight on the angle between electron polarization and positron momentum leads to
the determination of the longitudinal polarization which not only completes the measurement of the
entire polarization vector but also serves as a sensitivity check.
In order to deduce the polarization at the time and location of the muon decay a method based on
Monte-Carlo simulations with full spin-dependence implemented is being developed.
INTRODUCTION
Precision measurements of muon decay provide low energy tests of the standard model.
Only a few years ago it has been shown that V A, as one of the basic assumptions of
the standard model, follows from the results of a selected set of muon decay experiments
(including inverse muon decay) [1].
However, the experimental limits obtained up to now still allow for substantial contributions from non-standard couplings in addition to the V A interaction. The limits on
these couplings can be efficiently improved by performing experiments with polarized
muons and their decay positrons.
The measurement of the positrons’ transverse polarization component PT (as defined
1
below) as a function of the positron energy, in particular, offers the possibility to obtain
the low energy Michel parameter η without the suppression factor m e mµ , which makes
CP675, Spin 2002: 15th Int'l. Spin Physics Symposium and Workshop on Polarized Electron
Sources and Polarimeters, edited by Y. I. Makdisi, A. U. Luccio, and W. W. MacKay
© 2003 American Institute of Physics 0-7354-0136-5/03/$20.00
241
the determination of η from the electron energy spectrum extremely difficult. The simultaneous determination of the polarization component PT allows one to test time reversal
2
invariance in a purely leptonic decay.
OBSERVABLES IN THE DECAY OF POLARIZED MUONS
The kinematic variables for the decay of polarized positive muons are illustrated in
figure 1.
While the e from µ decay is mainly longitudinally polarized (polarization PL ),
there also is a transverse polarization component PT lying in the plane of muon polar1
ization Pµ and positron momentum k e .
Within the standard model, PT is negligibly small at large positron energies, but
1
substantial at lower energies and reaches the value 13 in the limiting case of a positron
at rest (see figure 1, η 0). Due to the low rate at small positron energies the energy
averaged transverse polarization predicted by the standard model is PT 0003
1
which at present cannot be detected.
The second transverse polarization component PT , which is perpendicular to the
2
plane spanned by muon polarization and positron momentum (see figure 1), is exactly
equal to zero according to the standard model.
In contrast to the determination of η from the energy spectrum of the decay positrons,
the energy dependence of PT yields η without the suppression factor m e mµ . With the
1
experimental knowledge that V A is dominant [1], and neglecting exotic contributions
in second order, one obtains
1
η RegSRR (1)
2
PT1
x
η = −0.08
0.1
Pµ
PT
θ
ke
z
y
0.2
0.15
0.05
1
η = −0.008
0
η = 0.008
-0.05
PL
-0.1
η = 0.08
-0.15
PT
2
-0.2
0.2
0.4
0.6
0.8
1
reduced energy x
FIGURE 1. On the left: Polarization components of the decay positrons. On the right: Transverse
positron polarization PT as a function of the reduced positron energy x. The standard model predicts
1
η 0 (solid curve). The present experimental limit is η 242
Here, gSRR represents a scalar, charge-changing interaction with right-handed charged
leptons [1]. In the general case there will be a phase between V A and an additional
interaction which leads to a transverse component PT . Correspondingly one derives
a value for ImgSRR from the energy dependence of PT . A non-zero value for this
2
polarization component violates time reversal invariance.
The transverse polarization has been measured previously with a precision of ∆PT 2
∆PT 23 10 3 [2]. A more precise value of PT and thus of η is needed for a model2
1
independent determination of the Fermi coupling constant G F : The influence of the
uncertainty in the experimental value of η on the value of G F is at present 20 times
larger than the one of the more precisely known muon life time [3].
1
EXPERIMENTAL SETUP AND METHODS
The setup [4] of the µP - experiment at the Paul Scherrer Institute in Villigen, SwitzerT
land is shown in figure 2.
A beam of highly polarized muons (Pµ 91% enters the beryllium stop target in
bunches every 20 ns. The polarization of the stopped muons precesses in a homogeneous magnetic field with the same frequency as the accelerator high frequency. Thus
the polarization of new muons entering the beryllium target is added coherently to the
polarization of the muons that are already in the target.
50 cm
12
3
4
5
6 7 8
9
10
11
FIGURE 2. Experimental setup: 1 - Be target; 2 - C moderator; 3 - spin precession magnet; 4 and
6 - trigger scintillation counters; 5, 8 and 9 - drift chambers; 7 - magnetized foil within iron return yoke;
10 - veto scintillation counters; 11 - BGO calorimeter. A telescope of scintillation counters above the
target region and cosmic trigger scintillation counters on top and below the BGO wall are not shown.
243
Decay positrons emitted approximately parallel to the B-field are tracked by means of
a set of drift chambers and can annihilate with polarized electrons in a magnetized foil.
The direction of the magnetic field applied to that foil is reversed approximately every
hour.
The two annihilation quanta are then detected by a hexagonal calorimeter consisting of
127 BGO crystals.
A valid annihilation event requires a coincidence of two plastic scintillator counters
before the magnetized foil with two separated clusters of BGO detectors and anticoincidences with the last drift chamber and the scintillation counter array in front of the BGO
calorimeter (9 and 11 in figure 2).
DATA ANALYSIS AND PRELIMINARY RESULTS
The orientation of the plane in which the two annihilation quanta are emitted depends
on the relative orientation of the transverse positron polarization and the polarization
of the electrons in the magnetized foil. As the muon polarization precesses due to the
magnetic field in the beryllium target, the axis of the transverse positron polarization also
0 would be
precesses with the same frequency. Therefore, a transverse polarization P
T
detected as a harmonic time dependence of the annihilation rate for a given pair of BGO
detectors.
Since the accepted decay positrons are emitted into a cone whose axis coincides with
the symmetry axis of the apparatus and is perpendicular to the precession plane of
the muon polarization, there is a small remnant µ SR effect (i.e., a time-dependent rate
variation due to the decay asymmetry with respect to the precessing muon polarization).
This effect depends on the azimuthal emission angle of the positron and yields time
µ at a given time.
zero, i.e. the position of the precessing muon polarization vector P
This information allows one to distinguish the two perpendicular components of the
transverse polarization of the positrons.
In addition one can make use of the fact that the positrons usually hit the magnetized
foil off the symmetry axis and therefore “see” a component of the electron polarization
which is either parallel or anti-parallel to the positrons’ longitudinal polarization. For
positrons hitting a given spatial area of the foil, a difference in annihilation rates for the
two different directions of the magnetic field in the magnetized foil can be observed.
From this asymmetry the longitudinal polarization of the positrons can directly be
deduced.
In fall of 1999 the first data taking run yielded a data sample containing approximately
11 106 annihilation events that could be analyzed.
The preliminary result for the longitudinal polarization is PL 109 015. This is in
good agreement with the standard model expectation and with the current experimental
limit PL 100 004 [5] and proves the sensitivity of this experiment to polarization.
From the analysis of the measured data the absolute value of the transverse polarization at the time of annihilation in the magnetized foil is determined. The energy dependence of two orthogonal transverse polarization components P1 and P2 is given in
figure 3. The preliminary results for the energy averaged values are P1 0006 0016
244
P1
P2
0.5
0.5
0
0
-0.5
-0.5
0
20
40
Energy [MeV]
0
20
40
Energy [MeV]
FIGURE 3. Energy dependence of two orthogonal transverse polarization components of the positrons
from polarized muon decay at the time of annihilation (preliminary result). The grey bars indicate the one
sigma standard deviations of the average values given in the text.
and P2 0004 0016.
To obtain the transverse polarization components PT and PT at the time of muon de1
2
cay a method based on Monte-Carlo simulations is being used. Our simulation package
is based on GEANT 3.21 and features full spin transport for positrons with different
initial polarization distributions. After tracking from the beryllium target to the magnetized foil, the resulting polarization distributions at the time of annihilation can then be
compared to the experimental distribution.
REFERENCES
1. W. Fetscher, H.-J. Gerber and K.F. Johnson, Phys. Lett. 173B (1986) 102.
2. H. Burkard et al., Phys. Lett. 160 B (1985) 343.
3. W. Fetscher and H.-J. Gerber, in Precision Tests of the Standard Electroweak Model, ed. P. Langacker
(World Scientific, Singapore, 1995).
4. I. Barnett et al., Nucl. Instr. Meth. A 455 (2000) 329.
5. J. Bartels, D. Haidt and A. Zichichi (editors), The European Physical Journal C - Review of Particle
Physics 15 (Springer, Hamburg, 2000).
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