ELECTROWEAK VECTOR BOSON PRODUCTION IN JOINT RESUMMATION. Page: 2 of 5
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threshold 2,3 and in the recoil 4'5'6'7 case.
However, resummation of recoil and threshold corrections separately can lead to opposite ef-
fects, i.e. suppression or enhancement of the partonic cross section, respectively. A full analysis
of soft gluon effects in transverse momentum distributions do-/dQ2 dQT should therefore take
these two types of corrections simultaneously into account. A joint treatment of these correc-
tions was proposed in'8. It relies on a novel refactorization of short-distance and long-distance
physics at fixed transverse momentum and energy 1. Similarly to standard threshold and recoil
resummation, exponentiation of logarithmic corrections occurs in the impact parameter b space,
Fourier-conjugated to transverse momentum QT space, and Mellin-N moment space, conjugated
to z space. This time both transforms are present, resulting in a final expression which obeys
energy and transverse momentum conservation. Consequently, phenomenological evaluation of
the joint resummation expressions requires providing prescriptions for inverse transforms from
N and b spaces. This also involves specifying a border between resummed perturbation the-
ory and the nonperturbative regime, by analyzing and parameterizing nonperturbative effects.
Moreover, to fully define the expressions a procedure for matching between the fixed-order and
the resummed result needs to be specified. In the following talk we will discuss these topics in
The jointly resummed cross section
In the framework of joint resummation i we derive the following expression at next-to-leading
logarithmic accuracy for electroweak annihilation 1,9:
da Q9 dN T_N db EiQTr
dQ2 dQ a a CIN _A J (T)2
X Ca/A(Q, b, N, t, pF) exp EP (N, b, Q, p) Ca/B(Q, b, N, , PF) , (1)
where Q( ) denotes the Born cross section, T = Q2/S, and Q is the invariant mass of the produced
boson. The flavour-diagonal Sudakov exponent EU, at the next-to-leading logarithmic (NLL)
accuracy in N and b was derived in 9:
Eaa(N, b, Q, P, AF) = - f E Aa a k) n +B(sk) 2
Dependence on the renormalization scale is implicit in Eq. (2) through the expansion of as(kT)
in powers of a (p). Eaf has the classic form of the Sudakov exponent in the recoil-resummed
QT distribution for electroweak annihilation, with the A and B functions defined as perturbative
series in ni '6 The coefficients in the expansion of these functions are the same as in the
pure QT resummation and are known from comparison with fixed-order calculations 10,11,12; at
the NLL only the logarithmic terms with A('), B(1) and A(2) coefficients contribute,
A = CF , B,-
C2) = T6 K2) 10
Aa C A TRNF (3)
The quantity (N. b) organizes the logarithms of N and b in joint resummation 9
(N, b) = b + (4)
where it is a constant and we define
N = Ye^E , (5)
b> bQ&'*/2 . (61
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KULESZA,A.; STERMAN,G. & VOGELSANG,W. ELECTROWEAK VECTOR BOSON PRODUCTION IN JOINT RESUMMATION., article, March 16, 2002; Upton, New York. (digital.library.unt.edu/ark:/67531/metadc736445/m1/2/: accessed June 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.