Abstract
In the Bloch-wave approach to estimate the baryon-number-violating scattering cross section in the standard electroweak theory in the laboratory, we clarify the relation between the single sphaleron barrier and multiple (near periodic) sphaleron barrier cases. We explain how a realistic consideration modifies/corrects the idealized Bloch wave and the resonant tunneling approximation. The basic approach is in part analogous to the well-known triple-$\alpha$ process to form carbon in nucleosynthesis.
Highlights
The SUð2Þ × Uð1Þ electroweak (EW) theory is very well established
We find that σðΔn ≠ 0Þ is no longer exponentially suppressed at E ∼ Esph, so there is a chance that a (B þ L)-violating event may be observed at the Large Hadron Collider (LHC)
Earlier work [19] argued why (B þ L)-violating processes may not be exponentially suppressed for two-particle scattering at energies close to and above the sphaleron energy
Summary
The SUð2Þ × Uð1Þ electroweak (EW) theory is very well established . With the SUð2Þ gauge coupling g ≃ 0.645 (or αW 1⁄4 g2=4π ≃ 1=30), the W-boson mass mW 1⁄4 gv=2 ≃ 80 GeV (where v 1⁄4 246 GeV is the Higgs vacuum expectation value), and the Higgs mass mH 1⁄4 125 GeV all measured, the theory (without further extension) has no free parameters and all dynamics are in principle completely determined. Earlier speculations have argued that such (B þ L)-violating scattering cross section σðEqq; Δn ≠ 0Þ in the laboratory remains exponentially small (see Fig. 1); even if one can reach proton-proton energy of around 50 TeV, with the quarkquark energy Eqq much higher than the sphaleron barrier height of 9 TeV, the event rate is still far too small to be observed [14,15,16,21,22]. The advantage of this viewpoint is the reliability of the extrapolation to higher energies In this approach, we find that σðΔn ≠ 0Þ is no longer exponentially suppressed at E ∼ Esph, so there is a chance that a (B þ L)-violating event may be observed at the Large Hadron Collider (LHC). Appendix C reviews the sphaleron process, in particular the shape of the sphaleron in Minkowski spacetime
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