124
G. Altarelli and S. Forte
0
250
500
750
1000
1250
1500
1750
2000
2250
-0.5
0
0.5
-0.5
0
0.5
dV/dp
T
W
[pb/(GeV/ )]
b-space (Ladinsky-Yuan)
p T -space (Ellis-Veseli)
b-space (Arnold-Kauffman)
p QCD O(D s
2
)
(Data-Theory)/Theory
b-space (Ladinsky-Yuan)
F
2
/d.o.f.=14/15
p T -space (Ellis-Veseli)
F
2
/d.o.f.=58/15
b-space (Arnold-Kauffman)
F
2
/d.o.f.=100/15
p T
W
[GeV/ ]
-0.5
0
0.5
0
5 10 15 20 25 30 35 40 45 50
Fig. 4.20 QCD predictions for the W p T distribution compared with recent D0 data at the
Tevatron (
√
s = 1.8 TeV)[49] [40]
presumably the relevant scale is of order k 2
T . So it must be completed by some non
perturbative ansatz or an extrapolation into the soft region. All the formalism has
been extended to NLO accuracy, where one starts from the perturbative expansion
at order α 2
s , and generalises the resummation to also include NLO terms of order
α s (p 2
T ) 2 log m 2
W /p 2
T (see, for example, [40]). The comparison with the data is very
impressive. In Fig. 4.20 we see the p T distribution as predicted in QCD (with a
number of variants that mainly differ in the approach to the soft region) compared
with some recent data at the Tevatron [49].
A great effort is being devoted to the preparation to the LHC. Calculations
for specific processes are being completed. A very important example is Higgs
production via g + g → H . The amplitude is dominated by the top quark loop, as
discussed in Chap. 3 [51]. The NLO corrections turn out to be particularly large [52],
as seen in Fig. 4.21. Higher order corrections can be computed either in the effective
lagrangian approach, where the heavy top is integrated away and the loop is shrunk
down to a point [53] [the coefficient of the effective vertex is known to α 4
s accuracy
[54]], or in the full theory. At the NLO the two approaches agree very well for the
rate as a function of m H [55]. The NNLO corrections have been computed in the
effective vertex approximation [56] (see Fig. 4.21). Beyond fixed order resummation
of large logs were carried out [57]. Also the NLO EW contributions have been
computed [58]. Rapidity (at NNLO) [59] and p T distributions (at NLO) [60] have
also been evaluated. At smaller p T the large logarithms [log(p T /m H )] n have been
G. Altarelli and S. Forte
0
250
500
750
1000
1250
1500
1750
2000
2250
-0.5
0
0.5
-0.5
0
0.5
dV/dp
T
W
[pb/(GeV/ )]
b-space (Ladinsky-Yuan)
p T -space (Ellis-Veseli)
b-space (Arnold-Kauffman)
p QCD O(D s
2
)
(Data-Theory)/Theory
b-space (Ladinsky-Yuan)
F
2
/d.o.f.=14/15
p T -space (Ellis-Veseli)
F
2
/d.o.f.=58/15
b-space (Arnold-Kauffman)
F
2
/d.o.f.=100/15
p T
W
[GeV/ ]
-0.5
0
0.5
0
5 10 15 20 25 30 35 40 45 50
Fig. 4.20 QCD predictions for the W p T distribution compared with recent D0 data at the
Tevatron (
√
s = 1.8 TeV)[49] [40]
presumably the relevant scale is of order k 2
T . So it must be completed by some non
perturbative ansatz or an extrapolation into the soft region. All the formalism has
been extended to NLO accuracy, where one starts from the perturbative expansion
at order α 2
s , and generalises the resummation to also include NLO terms of order
α s (p 2
T ) 2 log m 2
W /p 2
T (see, for example, [40]). The comparison with the data is very
impressive. In Fig. 4.20 we see the p T distribution as predicted in QCD (with a
number of variants that mainly differ in the approach to the soft region) compared
with some recent data at the Tevatron [49].
A great effort is being devoted to the preparation to the LHC. Calculations
for specific processes are being completed. A very important example is Higgs
production via g + g → H . The amplitude is dominated by the top quark loop, as
discussed in Chap. 3 [51]. The NLO corrections turn out to be particularly large [52],
as seen in Fig. 4.21. Higher order corrections can be computed either in the effective
lagrangian approach, where the heavy top is integrated away and the loop is shrunk
down to a point [53] [the coefficient of the effective vertex is known to α 4
s accuracy
[54]], or in the full theory. At the NLO the two approaches agree very well for the
rate as a function of m H [55]. The NNLO corrections have been computed in the
effective vertex approximation [56] (see Fig. 4.21). Beyond fixed order resummation
of large logs were carried out [57]. Also the NLO EW contributions have been
computed [58]. Rapidity (at NNLO) [59] and p T distributions (at NLO) [60] have
also been evaluated. At smaller p T the large logarithms [log(p T /m H )] n have been