Table Of Content– 1–
THE MASS OF THE W BOSON
Revised March 2006 by C. Caso (University of Genova) and
A. Gurtu (Tata Institute).
Till 1995 the production and study of the W boson was
the exclusive domain of the pp colliders at CERN and FNAL.
W production in these hadron colliders is tagged by a high
pT lepton from W decay. Owing to unknown parton–parton
effective energy andmissing energy inthelongitudinaldirection,
the experiments reconstruct only the transverse mass of the W
and derive the W mass from comparing the transverse mass
distribution with Monte Carlo predictions as a function of MW.
Beginning 1996 the energy of LEP increased to above 161
GeV,the threshold forW–pair production. Aprecise knowledge
of the e+e− center-of-mass energy enables one to reconstruct
the W mass even if one of them decays leptonically. At LEP
two methods have been used to obtain the W mass. In the
first method the measured W–pair production cross sections,
σ(e+e− → W+W−), have been used to determine the W mass
using the predicted dependence of this cross section on MW (see
Fig. 1). At 161 GeV, which is just above the W–pair production
threshold, this dependence is a much more sensitive function of
the W mass than at the higher energies (172 to 209 GeV) at
which LEP has run during 1996–2000. In the second method,
which is used at the higher energies, the W mass has been
determined by directly reconstructing the W from its decay
products.
Each LEP experiment has combined their own mass values
properly taking into account the common systematic errors. In
order to compute the LEP average W mass each experiment
has provided its measured W mass for the qqqq and qq(cid:2)ν(cid:1)
channels at each center-of-mass energy along with a detailed
break-up of errors (statistical and uncorrelated, partially cor-
related and fully correlated systematics [1]) . These have been
properly combined to obtain a preliminary LEP W mass =
80.388±0.035 GeV [2], which includes W mass determination
from W-pair producton cross section variation at threshold. Er-
rors due to uncertainties in LEP energy (9 MeV) and possible
effect of color reconnection (CR) and Bose–Einstein correlations
CITATION: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: http://pdg.lbl.gov)
July 27, 2006 11:28
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)
b 20 LEP
PRELIMINARY
p
(
W YFSWW andRacoonWW
W
σ
18
10
17
16
0 190 195 200 205
160 180 200
√s (GeV)
Figure 1: Measurement of the W-pair produc-
tion cross section as a function of the center–of–
mass energy [1], compared to the predictions
of RACOONWW [3] and YFSWW [4]. The
shaded area represents the uncertainty on the
t√heoretical predictions, estimated to be ±2% for
s < 170 GeV and ranging from 0.7 to 0.4%
above 170 GeV. See full-color version on color
pages at end of book.
(BEC) between quarks fromdifferent W’s(7 MeV) areincluded.
The mass difference between qqqq and qq(cid:2)ν(cid:1) final states (due to
possible CR and BEC effects) is −4±44 MeV.
For completeness we give here also the preliminary LEP
value for the W width: Γ(W) = 2.134±0.079 GeV [2].
The two Tevatron experiments have also carried out the
exercise of identifying common systematic errors and averag-
ing with CERN UA2 data obtain an average W mass [5]=
80.454±0.059 GeV.
July 27, 2006 11:28
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Combining the above W mass values from LEP and hadron
colliders, which are based on all published and unpublished
results, and assuming no common systematics between them,
yields a preliminary average W mass of 80.405±0.030 GeV.
Finally a fit to this directly determined W mass together
with measurements on the ratio of W to Z mass (MW/MZ)
and on their mass difference (MZ –MW) yields a world average
W-boson mass of 80.406±0.029 GeV.
The Standard Model prediction from the electroweak fit,
using Z-pole data plus mtop measurement, gives a W–boson
mass of 80.364±0.021 GeV [1,2].
OUR FIT in the listing below is obtained by combining
only published LEP and p–p Collider results using the same
procedure as above.
References
1. The LEP Collaborations: ALEPH, DELPHI, L3, OPAL,
the LEP Electroweak Working Group, CERN-PH-EP/2005-
051, hep-ex/0511027 (9 November 2005).
2. A. Venturi, “New (almost final) W mass and width results
from LEP”, talk given at “Les Rencontres de Physique de
la Vall´ee d’Aoste”, La Thuile (Italy), 5–11 March 2006.
3. A. Denner et al., Nucl. Phys. B587 67, (2000).
4. S. Jadach et al., Comput. Phys. Comm. 140, 432 (2001).
5. V.M. Abazov et al., Phys. Rev. D70, 092008 (2004).
July 27, 2006 11:28
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EXTRACTION OF TRIPLE GAUGE COUPLINGS
(TGC’S)
Revised March 2006 by C. Caso (University of Genova) and
A. Gurtu (Tata Institute).
Fourteen independent couplings, 7 each for ZWW and
γWW, completely describe the VWW vertices within the
most general framework of the electroweak Standard Model
(SM) consistent with Lorentz invariance and U(1) gauge in-
variance. Of each of the 7 TGC’s, 3 conserve C and P in-
dividually, 3 violate CP, and one TGC violates C and P
individually while conserving CP. Assumption of C and P con-
servation and electromagnetic gauge invariance reduces the
independent VWW couplings to five: one common set [1,2] is
(κγ,κZ,λγ,λZ,g1Z), where κγ = κZ = g1Z = 1 and λγ = λZ
= 0 in the Standard Model at the tree level. The parameters
κZ and λZ are related to the other three due to constraints
of gauge invariance as follows: κZ = g1Z − (κγ − 1)tan2θW
and λZ = λγ, where θW is the weak mixing angle. The W
magnetic dipole moment, µW, and the W electric quadrupole
moment, qW, are expressed as µW = e (1+κγ +λγ)/2MW and
qW = −e (κγ −λγ)/MW2 .
Precision measurements of suitable observables at LEP1 has
already led to an exploration of much of the TGC parameter
space. At LEP2 the VWW coupling arises in W-pair produc-
tion via s-channel exchange or in single W production via the
radiation of a virtual photon off the incident e+ or e−. At the
TEVATRON hard photon bremsstrahlung off a produced W
or Z signals the presence of a triple gauge vertex. In order to
extract the value of one TGC the others are generally kept fixed
to their SM values.
References
1. K. Hagiwara et al., Nucl. Phys. B282, 253 (1987).
2. G. Gounaris et al., CERN 96-01 p. 525.
CITATION: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: http://pdg.lbl.gov)
July 27, 2006 11:28
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EXTRACTION OF ANOMALOUS ZZγ, Zγγ, AND
ZZV NEUTRAL COUPLINGS
Revised March 2006 by C. Caso (University of Genova) and
A. Gurtu (Tata Institute).
In the reaction e+e− → Zγ, deviations from the Standard
Model for the Zγγ∗ and ZγZ∗ couplings may be described
in terms of 8 parameters, hV (i = 1,4; V = γ,Z) [1]. The
i
parameters hγ describe the Zγγ∗ couplings and the param-
i
eters hZ the ZγZ∗ couplings. In this formalism hV and hV
i 1 2
lead to CP-violating and hV and hV to CP-conserving effects.
3 4
All these anomalous contributions to the cross section increase
rapidly with center-of-mass energy. In order to ensure unitarity,
these parameters are usually described by a form-factor rep-
resentation, hV(s) = hV/(1 + s/Λ2)n, where Λ is the energy
i i◦
scale for the manifestation of a new phenomenon and n is a
sufficiently large power. By convention one uses n = 3 for hV
1,3
and n = 4 for hV . Usually limits on hV’s are put assuming
2,4 i
some value of Λ (sometimes ∞).
Above the e+e− → ZZ threshold, deviations from the
Standard Model for the ZZγ∗ and ZZZ∗ couplings may be
described by means of four anomalous couplings fV (i =
i
4,5;V = γ,Z) [2]. As above, the parameters fγ describe the
i
Zγγ∗ couplings and the parameters fZ the ZZZ∗ couplings.
i
The anomalous couplings fV lead to violation of C and P
5
symmetries while fV introduces CP violation.
4
All these couplings hV and fV are zero at tree level in the
i i
Standard Model.
References
1. U. Baur and E.L. Berger Phys. Rev. D47, 4889 (1993).
2. K. Hagiwara et al., Nucl. Phys. B282, 253 (1987).
CITATION: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: http://pdg.lbl.gov)
July 27, 2006 11:28
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ANOMALOUS W/Z QUARTIC COUPLINGS
Revised March 2006 by C. Caso (University of Genova) and
A. Gurtu (Tata Institute).
The Standard Model predictions for WWWW, WWZZ,
WWZγ, WWγγ, and ZZγγ couplings are small at LEP,
but expected to become important at a TeV Linear Collider.
Outside the Standard Model framework such possible couplings,
a0,ac,an, are expressed in terms of the following dimension-6
operators [1,2];
L06 = −16eΛ22 a0 Fµν FµνW(cid:2)α ·W(cid:2)α
Lc6 = −16eΛ22 ac Fµα FµβW(cid:2)β ·W(cid:2)α
Ln6 = −i16eΛ22 an(cid:3)ijk Wµ(iα) Wν(j) W(k)αFµν
L(cid:1)06 = −16eΛ22 (cid:1)a0 Fµν F(cid:1)µνW(cid:2)α ·W(cid:2)α
L(cid:1)n6 = −i16eΛ22 (cid:1)an(cid:3)ijk Wµ(iα) Wν(j) W(k)αF(cid:1)µν
where F,W are photon and W fields, L0 and Lc conserve C,
6 6
P separately (L(cid:1)0 conserves only C) and generate anomalous
6
W+W−γγ and ZZγγ couplings, Ln violates CP (L(cid:1)n violates
6 6
both C and P) and generates an anomalous W+W−Zγ cou-
pling, and Λ is an energy scale for new physics. For the ZZγγ
coupling the CP-violating term represented by Ln does not con-
6
tribute. These couplings are assumed to be real and to vanish
at tree level in the Standard Model.
Within the same framework as above, a more recent de-
scription of the quartic couplings [3] treats the anomalous parts
of the WWγγ and ZZγγ couplings separately leading to two
sets parameterized as aV/Λ2 and aV/Λ2, where V = W or Z.
0 c
At LEP the processes studied in search of these quartic
couplings are e+e− → WWγ, e+e− → γγνν, and e+e− →
Zγγ and limits are set on the quantities aW0 /Λ2,aWc /Λ2,an/Λ2.
The characteristics of the first process depend on all the three
couplings whereas those of the latter two depend only on the
two CP-conserving couplings. The sensitive measured variables
are the cross sections for these processes as well as the energy
and angular distributions of the photon and recoil mass to the
photon pair.
CITATION: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: http://pdg.lbl.gov)
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References
1. G. Belanger and F. Boudjema, Phys. Lett. B288, 201
(1992).
2. J.W. Stirling and A. Werthenbach, Eur. Phys. J. C14, 103
(2000);
J.W. Stirling and A. Werthenbach, Phys. Lett. B466, 369
(1999);
A. Denner et al., Eur. Phys. J. C20, 201 (2001);
G. Montagna et al., Phys. Lett. B515, 197 (2001).
3. G. Belanger et al., Eur. Phys. J. C13, 103 (2000).
July 27, 2006 11:28
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THE Z BOSON
Revised April 2006 by C. Caso (University of Genova) and
A. Gurtu (Tata Institute).
Precision measurements at the Z-boson resonance using
electron–positron colliding beams began in 1989 at the SLC and
at LEP. During 1989–95, the four LEP experiments (ALEPH,
DELPHI, L3, OPAL) made high-statistics studies of the pro-
duction and decay properties of the Z. Although the SLD
experiment at the SLC collected much lower statistics, it was
able to match the precision of LEP experiments in determining
the effective electroweak mixing angle sin2θW and the rates of
Z decay to b- and c-quarks, owing to availability of polarized
electron beams, small beam size and stable beam spot.
TheZ-bosonpropertiesreportedinthissectionmaybroadly
be categorized as:
• The standard ‘lineshape’ parameters of the Z con-
sisting of its mass, MZ, its total width, ΓZ, and its
partial decay widths, Γ(hadrons), and Γ((cid:2)(cid:2)) where
(cid:2) = e,µ,τ,ν;
• Z asymmetries in leptonic decays and extraction of
Z couplings to charged and neutral leptons;
• Theb-andc-quark-relatedpartialwidthsandcharge
asymmetries which require special techniques;
• Determination of Z decay modes and the search for
modes that violate known conservation laws;
• Average particle multiplicities in hadronic Z decay;
• Z anomalous couplings.
Details onZ-parameter andasymmetries determination and
the study of Z → bb,cc at LEP and SLC are given in this note.
The standard ‘lineshape’ parameters of the Z are deter-
mined from an analysis of the production cross sections of these
final states in e+e− collisions. The Z → νν(γ) state is identified
directly by detecting single photon production and indirectly
by subtracting the visible partial widths from the total width.
Inclusion in this analysis of the forward-backward asymmetry
(0,(cid:1))
of charged leptons, A , of the τ polarization, P(τ), and
FB
its forward-backward asymmetry, P(τ)fb, enables the separate
CITATION: W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006) (URL: http://pdg.lbl.gov)
July 27, 2006 11:28
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determination of the effective vector (g ) and axial vector (g )
V A
couplings of the Z to these leptons and the ratio (g /g ) which
V A
is related to the effective electroweak mixing angle sin2θW
(see the “Electroweak Model and Constraints on New Physics”
Review).
Determination of the b- and c-quark-related partial widths
and charge asymmetries involves tagging the b and c quarks
for which various methods are employed: requiring the pres-
ence of a high momentum prompt lepton in the event with
high transverse momentum with respect to the accompanying
jet; impact parameter and lifetime tagging using precision ver-
tex measurement with high-resolution detectors; application of
neural-network techniques to classify events as b or non-b on
a statistical basis using event–shape variables; and using the
presence of a charmed meson (D/D∗) or a kaon as a tag.
Z-parameter determination
LEP was run at energy points on and around the Z
mass (88–94 GeV) constituting an energy ‘scan.’ The shape
of the cross-section variation around the Z peak can be de-
scribed by a Breit-Wigner ansatz with an energy-dependent
total width [1–3]. The three main properties of this distri-
bution, viz., the position of the peak, the width of the
distribution, and the height of the peak, determine respec-
tively the values of MZ, ΓZ, and Γ(e+e−) × Γ(ff), where
Γ(e+e−) and Γ(ff) are the electron and fermion partial widths
of the Z. The quantitative determination of these parameters
is done by writing analytic expressions for these cross sections
in terms of the parameters and fitting the calculated cross sec-
tions to the measured ones by varying these parameters, taking
properly into account all the errors. Single-photon exchange
(σ0) and γ-Z interference (σ0 ) are included, and the large
γ γZ
(∼25 %) initial-state radiation (ISR) effects are taken into ac-
count by convoluting the analytic expressions over a ‘Radiator
Function’ [1–5] H(s,s(cid:2)). Thus for the process e+e− → ff:
(cid:1)
σf(s) = H(s,s(cid:2)) σf0(s(cid:2)) ds(cid:2) (1)
σ0(s) =σ0 +σ0 +σ0 (2)
f Z γ γZ
July 27, 2006 11:28
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12π Γ(e+e−)Γ(ff) s Γ2
σ0 = Z (3)
Z M2 Γ2 (s−M2)2 + s2Γ2/M2
Z Z Z Z Z
4πα2(s)
σ0 = Q2Nf (4)
γ 3s f c
√
σγ0Z =− 2 2α(s) (QfGFNcfGVe GVf)
3
(s−M2)M2
× Z Z (5)
(s−M2)2 +s2Γ2/M2
Z Z Z
where Qf is the charge of the fermion, Ncf = 3 for quarks and
1 for leptons and Gf is the vector coupling of the Z to the
V
fermion-antifermion pair ff.
Since σ0 is expected to be much less than σ0, the LEP
γZ Z
Collaborations have generally calculated the interference term
in the framework of the Standard Model. This fixing of σ0
γZ
leads to a tighter constraint on MZ and consequently a smaller
error on its fitted value. It is possible to relax this constraint
and carry out the fit within the S-matrix framework which is
briefly described in the next section.
In the above framework, the QED radiative corrections have
been explicitly taken into account by convoluting over the ISR
and allowing the electromagnetic coupling constant to run [6]:
α(s) = α/(1 − ∆α). On the other hand, weak radiative cor-
rections that depend upon the assumptions of the electroweak
theory and on the values of Mtop and MHiggs are accounted
for by absorbing them into the couplings, which are then
called the effective couplings GV and GA (or alternatively the
effective parameters of the (cid:9) scheme of Kennedy and Lynn [7].
Gf andGf arecomplexnumbers withsmallimaginaryparts.
V A
As experimental data does not allow simultaneous extraction
of both real and imaginary parts of the effective couplings, the
convention gf = Re(Gf) and gf = Re(Gf) is used and the
A A V V
imaginary parts are added in the fitting code [4].
Defining
gf ·gf
Af = 2(gf)2V+(Agf)2 (6)
V A
the lowest-order expressions for the various lepton-related
(0,(cid:1))
asymmetries on the Z pole are [8–10] AFB = (3/4)AeAf,
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