Can we reach the Zeptouniverse with rare K and B s,d decays?

Abstract

The Large Hadron Collider (LHC) will directly probe distance scales as short as 10−19 m, corresponding to energy scales at the level of a few TeV. In order to reach even higher resolutions before the advent of future high-energy colliders, it is necessary to consider indirect probes of New Physics (NP), a prime example being ΔF = 2 neutral meson mixing processes, which are sensitive to much shorter distance scales. However ΔF = 2 processes alone cannot tell us much about the structure of NP beyond the LHC scales. To identify for instance the presence of new quark flavour-changing dynamics of a left-handed (LH) or right-handed (RH) nature, complementary results from ΔF = 1 rare decay processes are vital. We therefore address the important question of whether NP could be seen up to energy scales as high as 200 TeV, corresponding to distances as small as $$ \mathcal{O}\left(1{0}^{-21}\right)\mathrm{m} $$ — the Zeptouniverse — in rare K and B s,d decays, subject to present ΔF = 2 constraints and perturbativity. We focus in particular on a heavy Z ′ gauge boson. If restricted to purely LH or RH Z ′ couplings to quarks, we find that rare K decays, in particular $$ {K}^{+}\to {\pi}^{+}\nu \overline{\nu} $$ and $$ {K}_L\to {\pi}^0\nu \overline{\nu} $$ , allow us to probe the Zeptouniverse. On the other hand rare B s and B d decays, which receive stronger ΔF = 2 constraints, allow us to reach about 15 TeV. Allowing for both LH and RH couplings a loosening of the ΔF = 2 constraints is possible, and we find that the maximal values of M Z′ at which NP effects could be found that are consistent with perturbative couplings are approximately 2000 TeV for K decays and 160 TeV for rare B s,d decays. Because Z ′ exchanges in the B s,d → μ + μ − rare decays are helicity suppressed, we also consider tree-level scalar exchanges for these decays, for which we find that scales close to 1000 TeV can be probed for the analogous pure and combined LH and RH scenarios. We further present a simple idea for an indirect determination of M Z′ that could be realised at the next linear e + e − or μ + μ − collider and with future precise flavour data.