3 The Standard Model of Electroweak Interactions
43
Fig. 3.3 The three- and four-gauge boson vertices. The cubic coupling is of order g, while the
quartic one is of order g 2
W
+
W
+
W
W
e
+
e
+
e
e
,Z
Fig. 3.4 The three- and four-gauge boson vertices. The cubic coupling is of order g, while the
quartic one is of order g 2
symmetric and C and P conserving couplings. In fact some small corrections are
already induced by the radiative corrections. But, in principle, more important could
be the modifications induced by some new physics effect. The experimental testing
of the triple gauge vertices has been done mainly at LEP2 and at the Tevatron. At
LEP2 the crosssection and angular distributions for the process e + e − → W + W −
have been studied (see Chap. 6).
In Born approximation the Feynman diagrams for the LEP2 process are shown
in Fig. 3.4 [6]. Besides neutrino exchange which only involves the well established
charged current vertex, the triple weak gauge vertices V W − W + V appear in the γ and
Z exchange diagrams. The Higgs exchange is negligible because the electron mass is
very small. The analytic cross section formula in Born approximation can be found,
for example, in Ref. [5]. The experimental data are compared with the SM prediction
in Chap. 6 [7]. The agreement is very good. Note that the sum of all three exchange
amplitudes has a better high energy behaviour. This is due to cancellations among
the amplitudes implied by gauge invariance, connected to the fact that the theory is
renormalizable (the crosssection can be seen as a contribution to the imaginary part
of the e + e − → e + e − amplitude).
The quartic gauge coupling is proportional to g 2 ABC W B W C ADE W D W E .
Thus in the term with A = 3 we have four charged W’s. For A = 1 or two
we have two charged W’s and 2 W 3 ’s, each W 3 being a combination of γ and Z
according to Eq. (3.13). With a little algebra the quartic vertex can be cast in the
form:
V W W V V = ig W W V V [2g μν g λρ − g μλ g νρ − g μρ g νλ ] ,
(3.37)
43
Fig. 3.3 The three- and four-gauge boson vertices. The cubic coupling is of order g, while the
quartic one is of order g 2
W
+
W
+
W
W
e
+
e
+
e
e
,Z
Fig. 3.4 The three- and four-gauge boson vertices. The cubic coupling is of order g, while the
quartic one is of order g 2
symmetric and C and P conserving couplings. In fact some small corrections are
already induced by the radiative corrections. But, in principle, more important could
be the modifications induced by some new physics effect. The experimental testing
of the triple gauge vertices has been done mainly at LEP2 and at the Tevatron. At
LEP2 the crosssection and angular distributions for the process e + e − → W + W −
have been studied (see Chap. 6).
In Born approximation the Feynman diagrams for the LEP2 process are shown
in Fig. 3.4 [6]. Besides neutrino exchange which only involves the well established
charged current vertex, the triple weak gauge vertices V W − W + V appear in the γ and
Z exchange diagrams. The Higgs exchange is negligible because the electron mass is
very small. The analytic cross section formula in Born approximation can be found,
for example, in Ref. [5]. The experimental data are compared with the SM prediction
in Chap. 6 [7]. The agreement is very good. Note that the sum of all three exchange
amplitudes has a better high energy behaviour. This is due to cancellations among
the amplitudes implied by gauge invariance, connected to the fact that the theory is
renormalizable (the crosssection can be seen as a contribution to the imaginary part
of the e + e − → e + e − amplitude).
The quartic gauge coupling is proportional to g 2 ABC W B W C ADE W D W E .
Thus in the term with A = 3 we have four charged W’s. For A = 1 or two
we have two charged W’s and 2 W 3 ’s, each W 3 being a combination of γ and Z
according to Eq. (3.13). With a little algebra the quartic vertex can be cast in the
form:
V W W V V = ig W W V V [2g μν g λρ − g μλ g νρ − g μρ g νλ ] ,
(3.37)