Bloch-Nordsieck Violating Electroweak Corrections to Inclusive TeV Scale Hard Processes

Abstract

We point out that, since the colliders' initial states ( e(+)e(-),pp, p&pmacr;,ellipsis) carry a definite non-Abelian flavor, electroweak radiative corrections to inclusive hard cross sections at the TeV scale are affected by peculiar Bloch-Nordsieck violating double logs. We recall the setup of soft cancellation theorems, and we analyze the magnitude of the noncanceling terms in the example of electron-positron annihilation into hadrons.

Infrared-sensitive Physics in QCD and in Electroweak Theory

“…However, with the advent of TeV scale accelerators, we shall soon have access to energies which are much larger than the symmetry breaking scale (say, the W mass) which may act as infrared cutoff and thus give rise to parametrically large infrared logarithms in the energy dependence, in addition to the ones of collinear origin. That this is indeed the case was first remarked in the late nineties [17] and soon applied to inclusive observables [18]. The failure of the BN theorem is due again to the nonabelian nature of electroweak theory, where now no averaging over flavour is possible, because the initial state consists of electrons, protons, and so on, each of them having a nontrivial weak isospin charge.…”

“…The analysis of such inclusive double logarithms [18] involves form factors of type (1), where now µ 2 is cutoff by the EW scale M 2 W ≃ M 2 Z = M 2 and the Casimir C a refers to the isospin I representation a = I = 0, 1, ... in the t-channel of the lepton-antilepton overlap matrix. For instance, the combinations σ e − ν ± σ e − e + correspond to I = 0 (I = 1), so that…”

Sudakov Electroweak effects in transversely polarized beams

“…The analysis of the electroweak IR singularities for the fermionic sector in presence of polarized initial states is interesting since the final result comes from the interplay of two distinct effects. On one hand, left fermions are free nonabelian charges and this produces uncanceled double logs in inclusive quantities; this phenomenon, related to the SU(2) sector, has been called "Bloch-Nordsieck violation" [10]. On the other hand, a transversely polarized fermion is a coherent superposition of left and right fermions, which have different gauge charges; this produces a different but related effect which is present also in a purely abelian U(1) theory [18].…”

Electroweak corrections and Bloch-Nordsieck violations in 2-to-2 processes at the LHC

“…In contrast, when fully inclusive final states are studied, the effect of virtual corrections is expected to be at least partially compensated by the effect of real electroweak gauge boson emission. Nevertheless, and as we shall discuss in detail below, the cancellation is not expected to be exact due to violation of the Bloch-Nordsieck (BN) theorem even for fully inclusive observables, see for example [8][9][10][11]. The BN violation originates from the non-abelian nature of the electroweak charges in the initial partonic state and is related to electroweak symmetry breaking.…”

“…For the u( 8) in the soft W limit. The prefactor of each of the logarithms is determined by the couplings/charge of the quark involved.…”