BESIII Detector
3.7 Tau Physics
3.7.1 Current Status and Prospects of the  Lepton Physics
The  lepton physics has achieved a great progress since its discovery in 1975.
Particularly in the last ten years, it starts to become a precision physics, thanks to high
statistics data samples and high quality detectors, mainly at high energy ee colliders
running in the  energy range (DORIS and CESR) and at the Z0 peak (SLC and
LEP)[1]. In addition, the BES experiment at BEPC running at the threshold of the 
pair production, measured the mass of the  lepton precisely[2]. The  physics study
will be continued in the high energy region at the asymmetric ee colliders of B
factories (KEK-B and PEP-II) over the next decade.
While the efforts in  lepton physics at high energy ee colliders have been quite
successful, there still exist both unique and complementary possibilities at lower
energy facilities running close to the threshold of the  pair production. There are
some distinct advantages with respect to high energy machines: the cross section
turns on rapidly at the threshold of the  pair production, reaching a maximum of
3.6nb at s =4.25GeV; the background is small and experimentally measurable,
completely free of c quark background when running below the charm threshold; the
nearly monochromatic momentum spectra for two body decays are of benefit for the
event selection; the maximum energy of a decay particle is significantly less than the
beam energy, easy to reject backgrounds from Bhabha and  pair, etc. These
advantages are of ultimate importance for more precise branching fraction
measurements and the Lorentz structure analysis of charged current. BEPCII/BESIII
with its high luminosity and a good detector will provide fruitful results for the 
physics.
3.7.2 Data Sample at BEPCII
Data taking for  pairs could be at s =3.557GeV, just near the threshold of the
 pair production, and s =3.67GeV, just below (2S). The expected  pair yields
are shown in Table 3.7-1.
Table 3.7-1 Data taking dedicated for the  lepton physics
L(fb-1)
N
^
 (0 ) (nb)
33
-2 -1
s (GeV)
L (10 cm s )
3.557
0.9
0.25/3weeks
0.42
1105/3weeks
3.67
1.0
3/1year
2.4
12106/1year
The data sample at
s =3.557GeV, just near the threshold of the  pair
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BESIII Detector
production, could be used for the  mass measurement while the data sample at
s =3.67GeV, just below (2S), could be used for precise measurements of
branching fractions of  decays and for the Lorentz structure analysis of charged
current. BESIII will take data at energy points such as J/, (2S) and (3770) or
s =4.14GeV. For energies above the  pair production threshold, such as
3.686GeV(), 3.77GeV() and 4.14GeV( Ds Ds ), the expected  pair yields are
shown in Table 3.7-2. These data samples are not as pure as those dedicated for the 
lepton physics and may have some complications due to the background from the c
quark, but they are still more clean than those taken in the B energy region. Therefore,
good physics results can still be obtained with a high statistics at the expense of
efficiencies.
Table 3.7-2 Data samples of  lepton as by-products of charm data taking
s (GeV)
^
33
-2 -1
L (10 cm s )
3.686 ()
3.77()
4.14( Ds Ds )
1.0
1.0
0.6
L(fb-1)
/year
5
5
3
 (0 ) (nb)
N/year
4.2(E=1.2MeV)
2.95
3.56
21106
15106
11106
3.7.3 Physics of  Leptons at BEPCII
From an experimental point of view, the  lepton holds a special place among the
quarks and leptons. It is the only lepton massive enough to decay to hadronic final
states, probably the most sensitive lepton to new physics at higher mass scales. The 
lepton constitutes an ideal laboratory to test the Standard Model and search for new
physics. The expected subjects of the  lepton physics at BEPCII are listed as follows:
1. Precise Measurement of the  Lepton Mass
The
currently
most
precise
measurement
of
the

mass[2],
0.25
-1
m =1776.96 00..18
data sample from a
21  0.17 MeV, is from BES, based on a 5pb
scanning near the  production threshold. The statistical error could be reduced
greatly and the systematic error due to uncertainties in the acceptance and
reconstruction efficiencies could be improved with 50 times more statistics near the
threshold as shown in Table 3.7-1. For the relative beam energy spread of
2.73Eb10-4[3] at BEPCII, a precision of 0.1MeV for the  mass measurement is
possible.
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BESIII Detector
2. Measurement of the Upper Limit of the  Neutrino Mass
The most stringent limit of the  neutrino mass is 18.2MeV(95%CL)[4]. A total of
12106  pairs could be produced with BEPCII running at s =3.67GeV for one year
as shown in Table 3.7-1. The semileptonic decay of   l l  (l  e,  ) can be
chosen as tagging channels for the two hadronic channels of KK and 5.
Both decay channels and the 2-dimensional fit of normalized energy vs invariant
mass distribution of the hadronic final states can be used to get a better mass
sensitivity. From a Monte Carlo study, the upper limit of the  neutrino mass at the
level of 1 digit (in MeV) is possible[5].
3. Measurement of the Strong Coupling Constant  s
The  hadronic decay is related to the strong coupling constant  s (m ) at m
scale, through the ratio of the hadronic decay width of the  lepton to its leptonic
decay width R=
(  hadrons    )
. So,  s (m ) can be obtained from the
(  e )
measurement of R, which can be obtained experimentally from the following two
approaches:
R=
  (  e )  (    )
,
(  e )
or
R=
1  Br (  e )  Br (    )
.
Br (  e )
That means, through the precise measurement of partial widths or branching fractions
of the leptonic decays, we can get R, and finally the precise measurement of
 s (m ) .
Using the renormalization group equation, one can evolve  s (m ) at the scale
m to  s (mz ) at the scale of mz and compare it with the direct measurement at the
Z0 peak. The error of  s (m ) must also be evolved using the renormalization group
equation, so a modest precision of  s (m ) results in a very high precision of
 s (mz ) . The current experimental value of  s (m ) is 0.3450.020, corresponding to
 s (mz ) of 0.12080.0025, in excellent agreement with the direct measurement from
the hadronic Z0 decays  s (mz ) =0.1190.003, but with a better accuracy [6].
4. Investigation of CP/T Violation
It is interesting to search for CP/T violation in the  sector, proposed by many
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BESIII Detector
theoretical physicists. An attempt of precision measurement of the electric dipole
moment dE of the  lepton is one of the many efforts. The BES experiment has tried
to give some information on the CP/T violation through the measurement of the



momentum triplet product pe  ( k1 k 2 ) in the production-decay sequence e(p1) +
e(p2)    (k1)   + e(k2) e , suggested by T.D. Lee. Using the existing



data sample collected at s =4.03GeV, BES has given a result A pe  ( k1 k 2 ) =
-0.0270.031 0.006 [5]. The precision of this measurements can be improved using a
larger data sample of  leptons.
5. Lorentz Structure Analysis of Charged Current
The current structure of the --W vertex can be studied by measuring the
lepton energy spectrum in the decay      l  l . The shape of the lepton energy
spectrum, sensitive to non-Standard Model contributions, can be characterized in
terms of 4 Michel parameters , ,  and , written in the  rest frame as:
1
d
x2
4
m 1 x
4

 {12(1  x) 
(8 x  6)  24 l
 P  cos [4(1  x)   (8 x  6)]}
 dxd cos
2
3
m x
3
where P is the average  polarization,  is the angle between the  spin and the lepton
momentum in the  rest frame, and x=El/Emax is the lepton energy scaled to the
maximum energy Emax=( m2  ml2 )/2m in the  rest frame.
The current world average values of 4 Michel parameters , ,  and  are:
=0.7520.0085, =0.0310.031, =0.9840.031 and =0.7450.022[7]. The
precision of the measurements of the 4 Michel parameters , ,  and  could be
improved, with a larger data sample of  lepton, especially collected at the threshold
of the  pair production.
6. Search for Rare and Forbidden Decays
Search for rare and forbidden decays, such as that with lepton number violation:
e+, e+ l  l , …, that with a (pseudo-) goldstone particle:  l X ( l =e,;
X=Majoron, familon, flavon, …), and so-called second class current:  are
possible.
CLEOII has achieved a limit on the decay of  of 1.410-4 (95% CL),
using a data sample of 3.2106  pairs[1,7,8]. The present upper limits on lepton-flavor
and lepton-number violating decays of the  are in the range of 10-5 to 10-6. With a 
samples of 107 events per year, an improvement of one to two orders of magnitude is
possible[6,9].
7. Precise Measurements of Branching Fractions of  Decays
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BESIII Detector
Accurate global analysis of all  lepton decay channels, particularly those
involving K’s and multiple ’s, are possible, using a large data sample of  lepton as
shown in Table 3.7-1 and 3.7-2. These precise measurements will allow the test of
universality of charged current of leptons to a new level. It will also provide a precise
determination of the vector and axial vector current spectral functions and some
useful information to test QCD.
Reference
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(eds.), Proceedings of the First Workshop on Tau Lepton Physics (Orsay, France,
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British
Columbia,
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2000),
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[3] Yuan Changzheng et al., “-charm physics and restriction to the accelerator and
detector design”, to be published in High Energy Physics and Nuclear Physics (in
Chinese)
[4] ALEPH Collaboration, R.Barate et al., Eur.Phys.J.C2(1998)395
[5] Feasibility Study Report on BEIJING TAU-CHARM FACTORY, IHEP-BTCF
Report-03, Oct. 1996, IHEP, CAS, CHINA
[6] A.Pich, Nucl.Phys.B(Proc.Suppl)98(2001)385-396
[7] K.K.Gan, Nucl.Phys.B(Proc.Suppl)98(2001)397-416
[8] CLEO collab., J.Bartelt et al., Phys.Rev.Lett. 76(1996)4119
[9] CLEO collab., Phys.Rev.D61(2000)071101, D57(1998)5903, D55(1997)R3919;
Phys.Rev.Lett. 79(1997)1221
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