Electroweak instantons/sphalerons at VLHC?

There is a close analogy between electroweak instanton-induced baryon plus lepton number (B + L) violating processes in Quantum Flavor Dynamics (QFD) and hard QCD instanton-induced chirality violating processes in deep-inelastic scattering. In view of the recent information about the latter both from lattice simulations and from the H1 experiment at HERA, it seems worthwhile to reconsider electroweak B + L violation at high energies. We present a state of the art evaluation of QFD instanton-induced parton-parton cross-sections, as relevant at future high energy colliders in the hundreds of TeV regime, such as the projected Very Large Hadron Collider (VLHC). We find that the cross-sections are unobservably small in a conservative fiducial kinematical region inferred from the above mentioned QFD–QCD analogy. An extrapolation – still compatible with lattice results and HERA – beyond this conservative limit indicates possible observability at VLHC. 1. The Standard Model of electroweak (Quantum Flavor Dynamics (QFD)) and strong (QCD) interactions is remarkably successful and describes quantitatively a wealth of data accumulated over the last decades. This success is largely based on the possibility to apply ordinary perturbation theory to the calculation of hard, short-distance dominated scattering processes, since the relevant gauge couplings are small. There is, however, a class of processes which – even for small gauge couplings – can not be described by ordinary perturbation theory. These processes are associated with axial anomalies [1] and manifest themselves as anomalous violation of baryon plus lepton number (B + L) in QFD and chirality (Q5) in QCD [2]. They are induced by topological fluctuations of the non-Abelian gauge fields, notably by instantons [3]. Such topological fluctuations and the anomalous processes induced by them are crucial ingredients for an understanding of a number of non-perturbative issues in the Standard Model. Indeed, QCD instantons have been argued to play an important role in various long-distance aspects of QCD, such as giving a possible solution to the axial U(1) problem [2] or being at work in SU(nf ) chiral symmetry breaking [4] (for reviews, see Ref. [5]). In QFD, on the other hand, similar topological fluctuations of the gauge fields and the associated B + L violating processes are very important at high temperatures [6] and have therefore a crucial impact on the evolution of the baryon and lepton asymmetries of the universe (see Ref. [7] for a review). A very interesting, albeit unsolved question is whether manifestations of such topological fluctuations might be directly observable in high-energy scattering at present or future colliders (for a short review, see Ref. [8]). This question has been raised originally in the late eighties in the context of QFD [9, 10]. But, despite considerable theoretical [11, 12, 13, 14] and phenomenological [15, 16] efforts, the actual size of the cross-sections in the relevant, tens of TeV energy regime was never established (for reviews, see Refs. [7, 17]). Meanwhile, the focus switched to quite similar QCD instanton-induced hard scattering processes in deep-inelastic scattering [18, 19], which are calculable from first principles within instanton-perturbation theory [20], yield sizeable rates for observable final state signatures in the fiducial regime of the latter [21, 22, 23, 24], and are actively searched for at HERA [25]. Moreover, larger-size QCD instantons, beyond the semi-classical, instanton-perturbative regime, might well be responsible for the bulk of inelastic hadronic processes and build up soft diffractive scattering [26]. In view of the close analogy of QFD and hard QCD instanton-induced processes in deep-inelastic scattering [19], emphasized throughout this letter, and of the recent information about the latter both from lattice simulations [27, 22, 24] and from experiment [25], recalled and elaborated on below, it seems worthwhile to reconsider electroweak B+L violation at high energies. We therefore present in this letter a state of the art evaluation of QFD instanton-induced parton-parton crosssections – quite analogous to the one presented in Ref. [21] for QCD instanton-induced processes –, as relevant at future high energy colliders in the hundreds of TeV regime, such as the projected Eurasian Long Intersecting Storage Ring (ELOISATRON) [28] or the Very Large Hadron Collider (VLHC) [29]. This goes along with a discussion of the implications of the lattice and HERA results – via the above mentioned QFD–QCD analogy – for the fate of electroweak B + L violation in high energy collisions.