2007

Constant terms in threshold resummation and the quark form factor

Friot, S., Grunberg, G.

Understand

We verify to order alpha_s^4 two previously conjectured relations, valid in four dimensions, between constant terms in threshold resummation (for Deep Inelastic Scattering and the Drell-Yan process) and the second logarithmic derivative of the massless quark form factor.

The same relations are checked to all orders in the large beta_0 limit; as a byproduct a dispersive representation of the form factor is obtained.
These relations allow to compute in a symmetrical way the three-loop resummation coefficients B_3 and D_3 in terms of the three-loop contributions to the virtual diagonal splitting function and to the quark form factor, confirming results obtained in the literature.

Built on

G. Grunberg, “Renormalization scheme independent QCD and QED: the method of effective charges”
1984
Earlier work this paper cites.
G. Sterman, “Summation of large corrections to short distance hadronic cross-sections”
1987
Earlier work this paper cites.
S. Catani and L. Trentadue, “Resummation of the QCD perturbative series for hard processes”
1989
Earlier work this paper cites.
L. Magnea and G. Sterman, “Analytic continuation of the Sudakov form-factor in QCD”
1990
Earlier work this paper cites.
S. Catani, B. R. Webber and G. Marchesini, “QCD coherent branching and semi-inclusive processes at large- x x ”
1991
Earlier work this paper cites.
P. Ball, M. Beneke and V. M. Braun, “Resummation of ( β 0 α s ) n (\beta_{0}\alpha_{s})^{n} corrections in QCD: Techniques and applications to the tau hadronic width and the heavy quark pole mass”
1995
Earlier work this paper cites.
Ph. Flajolet, X. Gourdon and Ph. Dumas, “Mellin Transforms and Asymptotics : Harmonic sums”
1995
Earlier work this paper cites.
Y. L. Dokshitzer, G. Marchesini and B. R. Webber, “Dispersive Approach to Power-Behaved Contributions in QCD Hard Processes”
1996
Earlier work this paper cites.
S. Catani, “Physical anomalous dimensions at small x”
1997
Earlier work this paper cites.
L. Magnea, “Analytic resummation for the quark form factor in QCD”
2001
Earlier work this paper cites.

Similar

E. Laenen, G. Sterman and W. Vogelsang, “Recoil and threshold corrections in short-distance cross sections”
Original
2001
Cited alongside, same era.
E. Gardi, “Dressed gluon exponentiation”
2002
Cited alongside, same era.
S. Forte and G. Ridolfi, “Renormalization group approach to soft gluon resummation”
2003
Cited alongside, same era.
E. Gardi and R. G. Roberts, “The interplay between Sudakov resummation, renormalons and higher twist in deep inelastic scattering”
2003
Cited alongside, same era.
T. O. Eynck, E. Laenen and L. Magnea, “Exponentiation of the Drell-Yan cross section near partonic threshold in the DIS and MS-bar schemes”
2003
Cited alongside, same era.
S. Moch, J. A. M. Vermaseren and A. Vogt, “The three-loop splitting functions in QCD: The non-singlet case”
2004
Cited alongside, same era.
S. Moch, J. A. M. Vermaseren and A. Vogt, “Higher-order corrections in threshold resummation”
2005
Cited alongside, same era.
S. Moch, J. A. M. Vermaseren and A. Vogt, “The quark form factor at higher orders”
2005
Cited alongside, same era.
S. Moch and A. Vogt, “Higher-order soft corrections to lepton pair and Higgs boson production”
2005
Cited alongside, same era.
V. Ravindran, J. Smith and W. L. van Neerven, “Two-loop corrections to Higgs boson production”
2005
Cited alongside, same era.
G. Grunberg, “Infrared finite coupling in Sudakov resummation”
Cited in the paper.
A. Idilbi, X. d. Ji and F. Yuan, “Resummation of threshold logarithms in effective field theory for DIS, Drell-Yan and Higgs production”
Cited in the paper.

Then

S. Moch, J. A. M. Vermaseren and A. Vogt, “Three-loop results for quark and gluon form factors”
2005
Later among the works it cites.
S. Friot, D. Greynat and E. de Rafael, “Asymptotics of Feynman diagrams and the Mellin-Barnes representation”
2005
Later among the works it cites.
G. Grunberg, “Infrared finite coupling in Sudakov resummation: The precise set-up”
2006
Later among the works it cites.
G. Grunberg, “Evidence for infrared finite coupling in Sudakov resummation”
2006
Later among the works it cites.
E. Laenen and L. Magnea, “Threshold resummation for electroweak annihilation from DIS data”
2006
Later among the works it cites.
V. Ravindran, “Higher-order threshold effects to inclusive processes in QCD”
2006
Later among the works it cites.
A. Idilbi, X. d. Ji, J. P. Ma and F. Yuan, “Threshold resummation for Higgs production in effective field theory”
2006
Later among the works it cites.
V. Ravindran, “On Sudakov and soft resummations in QCD”
2006
Later among the works it cites.
G. Sterman and W. Vogelsang, “Crossed threshold resummation”
2006
Later among the works it cites.
G. Grunberg, “Dispersive approach in Sudakov resummation”
2007
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…