Journal ArticleDOI

# Tests of the Standard Model and α(mZ2)

01 Dec 2006-Vol. 162, pp 18-21

Abstract: Tests of the Standard Model and influence of α ( m Z 2 ) on these tests are discussed
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Tests of the Standard Model and α(m
2
_Z)
B. Pietrzyk
To cite this version:
B. Pietrzyk. Tests of the Standard Model and α(m
2
_Z). II International Workshop on e+e- Collisions
from phi to psi, Feb 2006, Novosibirsk, Russia. pp.18-21, �10.1016/j.nuclphysbps.2006.09.059�. �in2p3-
00117377�

1
Tests of the Standard Model and α(m
2
Z
)
B. Pietrzyk
a
a
Laboratoire de Physique des Particules (LAPP), IN2P3-CNRS,
F-74019 Annecy-le-Vieux, France
Tests of the Standard Model and inﬂuence of α(m
2
Z
) on these tests are discussed.
The ﬁnal results on precision measurements
at the Z pole are recently published 10 years
after the end of measurements at LEP1. The
LEP/SLD measurements had to take into account
huge ISR corrections which were calculated with
the precision 10
4
. The precision of measure-
ments to 10
3
exceeded suﬃciently the natural
size of genuine ElectroWeak (EW) corrections
α(m
2
Z
)
πsin
2
θ
1% (1)
-
e
e
f
f
+
Figure 1. The eﬀective coupling.
The notion of eﬀective couplings has been in-
troduced in which radiative corrections, both to
the vertex and to the propagator, have been in-
cluded. The precise EW measurements included
the Z line-shape measurement, the asymmetries,
τ polarisation from LEP1, the left-right asym-
metries from SLD, m
W
and Γ
W
from LEP2 and
Tevatron and m
t
from Tevatron. The asymme-
tries and τ polarisation results have been con-
verted into the sin
2
Θ
lept
eﬀ
measurements. An in-
teresting feature of sin
2
Θ
lept
eﬀ
measurements is
that there is a 3σ diﬀerence between measure-
ments made with leptons and quarks.
pietrzyk@lapp.in2p3.fr
The radiative corrections have been divided in
two parts: the running of α(QED) and genuine
1996, is shown in Fig. 2 [1].
0.229
0.23
0.231
0.232
0.233
0.234
0.235
83 83.5 84 84.5 85
LEP/SLD/CDF/D0 March 1996
Preliminary
α(m
z
2
)=1/128.89±0.09
m
t
=175 ± 9 GeV
Γ
lepton
(MeV)
sin
2
θ
eff
lept
STANDARD MODEL
m
t
120
220
m
H
1000
300
60
68% C.L.
99% C.L.
Figure 2. sin
2
Θ
lept
eﬀ
versus leptonic Z width
Γ
lepton
.
The star shows the prediction of the SM if
among radiative corrections only running of α
is included. The value of alpha at the Z pole,
α(m
2
Z
), is not any more 1/137.(), α(0), but
1/128.940±0.048, α(s), [2].
α(s) =
α(0)
1 Δα
l
(s) Δα
(5)
(s) Δα
t
(s)
(2)
LAPP-EXP-2006-13

2
The contribution of leptonic loops to the running
of alpha, Δα
l
(s), is calculated with a practically
negligible uncertainty. The top quark contribu-
tion, Δα
t
(s), is calculated separately since the
value of the top quark mass is a result of the
SM ﬁt. The contribution of the other 5 quark
loops, ”hadronic contribution to the running of
α”, Δα
(5)
(m
2
Z
)=0.02758 ± 0.00035 [2] at the Z
pole, is calculated by integrating the experimen-
tally measured R
=
σ
σ
µµ
in e
+
e
annihilation
(Fig. 3).
ρ,ω,φ Ψ’s Υ’s
0
1
2
3
4
5
6
7
s in GeV
Bacci et al.
Cosme et al.
PLUTO
CESR, DORIS
MARK I
CRYSTAL BALL
MD-1 VEPP-4
VEPP-2M ND
DM2
BES 1999
BES 2001BES 2001
CMD-2 2004
KLOE 2005
Burkhardt, Pietrzyk 2005
15% 5.9% 6% 1.4% 0.9%
rel. err. cont.
01234567891
0
R
Figure 3. R
.
The genuine EW radiative corrections depend
strongly ( m
2
t
) on the top mass and weaker
( ln
m
2
H
m
2
W
) on the Higgs mass, as shown in Fig. 2.
Therefore the prediction of the value of the top
mass was the main result of the SM ﬁts, before
its value was measured at Tevatron in 1994, as
shown in Fig. 4. In fact, the prediction of the SM
ﬁts for the top mass, just before it was measured,
was 177
+11+18
1119
GeV [3].
Year
M
t
[GeV]
SM constraint
Tevatron
Direct search lower limit (95% CL)
68% CL
50
100
150
200
1990 1995 2000 2005
Figure 4. Direct and indirect determination of
the top quark mass as a function of time.
The region of the SM predictions is strongly
reduced when the top mass value is known as in-
dicated by the shadowed region on Fig. 2. The
prediction of the value of the Higgs mass becomes
then the main result of the SM ﬁts. The winter
2006 ﬁt result is shown on Fig. 5.
The preferred value of the Higgs mass, cor-
responding to the minimum of the ”blue band
curve”, is 89
+42
30
[1], the one-sided 95% conﬁdence
level upper limit is 175 GeV. The resent variation
of the ﬁtted value of the Higgs mass are caused
by the progress in the top mass measurements as
seen in Table 1.
Table 1
The recent variation of the ﬁtted value of the
Higgs mass with the value of the measured top
mass
year m
t
m
H
upper limit
(GeV) (GeV) (GeV)
2003 174.3 ± 5.196
+60
38
219
2004 178.0 ± 4.3 114
+69
45
260
2005 172.7 ± 2.991
+45
32
186
2006 172.5 ± 2.389
+42
30
175
The role of α(m
2
Z
) in the SM ﬁts can be under-
stood from Fig. 2. If the value of α(m
2
Z
) (star) is
changed, the SM prediction is shifted with respect
to the experimental results causing the change in

3
0
1
2
3
4
5
6
10030 300
m
H
[GeV]
Δχ
2
Excluded
Δα
=Δα
(5)
0.02758±0.00035
0.02749±0.00012
incl. low Q
2
data
Theory uncertainty
Figure 5. Δχ
2
as a function of Higgs mass m
H
.
the prediction for the Higgs mass.
The prediction of the SM ﬁts in the plane
α(m
2
Z
)-m
H
, when α(m
2
Z
) is removed from the ﬁt
input, is shown on Fig. 6. A strong correlation
is observed. It is interesting to observe that the
SM prediction for the hadronic contribution to
the running of α coincides well with the value ob-
tained from the integration of R
in the region
of m
H
still compatible with the direct searches.
There were mainly two major changes in the
history of determination of Δα
(5)
, as shown on
Fig. 7. The Crystal Ball measurements [4] in
e
+
e
c.m.s. energy region between 5 and 7.4
GeV, used in 1995 evaluation of Δα
(5)
, signiﬁ-
cantly lowered the R values reported previously
by the MARK I Collaboration [5], as seen on Fig.
3. The BES measurements in the energy region
between 2 and 5 GeV, ﬁrst reported in ICHEP
2000 Conference in Osaka [6,7], caused the shift
of the Higgs mass prediction by about 30 GeV [8].
The recent measurements of the CMD2 [9] and
KLOE [10] Collaboration in the ρ region shown in
Fig. 8 had only a very minor impact since the pre-
vious measurement were already relatively precise
in this e
+
e
c.m.s. energy region. In our analy-
sis [2] we have integrated separately CMD2 and
KLOE points and then combined the results of
0.026
0.028
0.03
0.032
10 10
2
10
3
m
H
[GeV]
Δα
(5)
Excluded
High Q
2
except Δα
High Q
2
except Δα
(5)
68% CL
Δα
(5)
Figure 6. Contour curve of 95% probability in
the α
(5)
(m
2
Z
), m
H
) plane, when Δα
(5)
(m
2
Z
)is
removed from the ﬁt input.
0.026 0.027 0.028 0.029 0.03
Burkhardt, Jegerlehner, Verzegnassi,Penso 1989
Jegerlehner 1992
Nevzorov 1994
Geshkenbein, Morgunov 1994
Martin, Zeppenfeld 1994
Swartz 1994
Geshkenbein, Morgunov 1995
Eidelman, Jegerlehner 1995
Burkhardt, Pietrzyk 1995
Swartz 1995
Alemany, Davier, H cker 1997
Davier, H cker 1997
K hn, Steinhauser 1998
Groote, K rner 1998
Davier, H cker 1998
Jegerlehner 1999
Erler 1999
Osaka 2000 update of Burkhardt, Pietrzyk 1995
Martin,Outhwaite,Ryskin 2000
Burkhardt, Pietrzyk 2001
Jegerlehner 3/01
Jegerlehner 3/01
Troconiz, Yndurain 11/01
Jegerlehner 03/03 Zeuthen 2003 presentation
HMNT 2003
Burkhardt, Pietrzyk 2005
Figure 7. History of evaluation of Δα
(5)
.
SND [11] results changes Δα
(5)
by less than
1
10
σ.
The revised SND results [12] would change the
Δα
(5)
even less.
Fig. 9 shows the relative contribution of dif-
ferent e
+
e
c.m.s. energy regions to Δα
(5)
both
in magnitude and uncertainty. The region be-
tween 1.05-2 GeV has important contribution to
the uncertainty despite its small contribution to
the magnitude. Improving the precision of mea-
surements from 15% (Fig. 3) to 5% would change
the total uncertainty on Δα
(5)
from 0.00035 to

4
0
1
2
3
4
5
6
7
8
9
10
0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
Burkhardt, Pietrzyk 2005
W in GeV
R
CMD-2 2004
KLOE 2005
SND 2005
Figure 8. CMD2, KLOE and SND measurements.
0.00027. The change in the ﬁtted value of the
Higgs mass would be small. However, the change
R
by ±1σ in this c.m.s. energy region would
shift the central value of the ﬁtted Higgs mass by
+16
9
GeV. Therefore more precise measurements
in this e
+
e
c.m.s. energy region are important.
LHC will start at 2007. Will the prediction
from the SM for m
H
be as successful as it was for
m
t
?
I would like to thank the organizers for inviting
me to come to this very interesting and important
workshop and also my collaborator H. Burkhardt
for helping me in the preparation of this talk.
REFERENCES
1. LEP Electroweak Working Group,
http://lepewwg.web.cern.ch/LEPEWWG/.
2. H. Burkhardt and B. Pietrzyk, Phys. Rev.
D72:057501,2005, Phys. Lett. B513 (2001)46.
3. B. Pietrzyk, Proc. of the XXIX Rencontres
de Moriond, EW Interactions, March 12-19,
> 12 GeV
7 - 12 GeV
5 - 7 GeV
2.0 - 5 GeV
1.05 - 2.0 Ge
V
narrow resonance
s
ρ
> 12 GeV
7 - 12 GeV
5 - 7 GeV
2.0 - 5 GeV 1.05 - 2.0 GeV
narrow resonances
ρ
c
ontributions at m
Z
in magnitude
in uncertainty
Burkhardt, Pietrzyk 200
5
Figure 9. Relative contribution to Δα
(5)
in mag-
nitude and uncertainty.
1994, Ed. J. Tan Thanh an, page 137.
4. C. Edwards et al., Crystal Ball Collaboration,
SLAC-PUB-5160, Jan. 1990.
5. J.L. Siegrist et al., MARKI Collaboration,
Phys. Rev. D 26 (1982) 969.
6. Z.G. Zhao, Proc. of ICHEP 2000, Osaka,
Japan, 27 July-2 August 2000, Ed. C.S. Lim
and T. Yamanaka, page 644.
7. J.Z. Bai, BES Collaboration, Phys.Rev.Lett.
88:101802,2002.
8. B. Pietrzyk, Proc. of ICHEP 2000, Osaka,
Japan, 27 July-2 August 2000, Ed. C.S. Lim
and T. Yamanaka, page 710.
9. R.R. Akhmetshin et al., CMD-2 Collabora-
tion, Phys. Lett. B578 (2004)285.
10. A. Aloisio et al., KLOE Collaboration, Phys.
Lett. B606 (2005)12.
11. M.N. Achasov, SND Collaboration, J. Exp.
Theor. Phys. 101:1053-1070, 2005.
12. M.N. Achasov, I. Logashenko, these proceed-
ings.
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