Next-to-next-to-leading logarithms in four-fermion electroweak processes at high energy

Abstract

We sum up the next-to-next-to-leading logarithmic virtual electroweak corrections to the high energy asymptotics of the neutral current four-fermion processes for light fermions to all orders in the coupling constants using the evolution equation approach. From this all order result we derive finite order expressions through next-to-next-to leading order for the total cross section and various asymmetries. We observe an amazing cancellation between the sizable leading, next-to-leading and next-to-next-toleading logarithmic contributions at TeV energies.PACS numbers: 12.38.Bx, 12.38.Cy, 12.15.Lk Experimental and theoretical studies of electroweak interactions have traditionally explored the range from very low energies, e.g. through parity violation in atoms, up to energies comparable to the masses of the W -and Z-bosons, e.g. at LEP or the Tevatron. The advent of multi-TeV-colliders like the LHC or a future linear electron-positron collider during the present decade will give access to a completely new energy domain.Once the characteristic energies s are far larger than the masses of the W -and Z-bosons, M W,Z , multiple soft and collinear gauge boson emission is kinematically possible. Conversely, exclusive reactions like electron-positron (or quark-antiquark) annihilation into a pair of fermions or gauge bosons will receive large negative corrections from virtual gauge boson emission. These double logarithmic "Sudakov" corrections [1,2] proportional to powers of g 2 ln 2 (s/M 2 W,Z ) are dominant at high energies and thus have to be controlled in higher orders to arrive at reliable predictions.The importance of large logarithmic corrections for electroweak reactions at high energies in one-loop approximation which may well amount to ten or even twenty percent was noticed already several years ago [3,4]. The need for a resummation of higher orders of these doublelogarithmic terms in the context of electroweak interactions was first emphasized in [5] which also contains a first discussion of this resummation. In particular, it was shown that the double logarithms do not depend on the details of the mechanism of the gauge boson mass generation. The issue is complicated by the appearance of massive (W , Z) and massless (γ) gauge bosons in the SU L (2) × U(1) theory, which necessarily have to be treated on a different footing. A complete analysis of this problem in the double or leading logarithmic (LL) approximation by the systematic separation of soft (ω γ ≤ M) and hard (ω γ ≥ M) photons was given in [6]. In two loops the results of this approach essentially based on the concept of infrared evolution equations have been confirmed by explicit calculations in [7].The large coefficient in front of the single logarithmic term in the one-loop corrections to the electroweak amplitudes (see, e.g. [8]) suggests that subleading terms play an important role also in higher orders, as long as realistic energies of order TeV are under consideration. Motivated by this observation a systematic evaluation of the next-to-leading...

Electroweak corrections to W-boson pair production at the LHC

“…However, this approach is only justified for energies of order M W or M Z . As is well known from earlier investigations [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], EW corrections increase with the squared logarithm of the energy, and may reach several tens of percent for energies accessible at the LHC. In view of their strong dependence both on energy and scattering angle, they will induce significant distortions in transverse-momentum and rapidity distributions and consequently may well mimic "New Physics" and hence must be carefully taken into account.…”

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“…A careful analysis shows that for pure photonic correctionsà (2) (m e , λ) can be constructed of the two-loop corrections to the form factor and the products of the one-loop contributions. Note that the corrections have matrix structure in the chiral amplitude basis [18]. We have checked that in dimensional regularization the structure of the infrared divergences of the auxiliary amplitude obtained in this way agrees with the one given in Refs.…”

NNLOPS accurate Drell-Yan production

“…Furthermore electroweak corrections have been the subject of intensive studies [6][7][8][9][10][11]. Electroweak Sudakov effects become more important at large invariant mass [9,[12][13][14], a region that was already interesting at run I and which will be explored even more during the next LHC run. Version 3 of…”