Neutral kaon mixing beyond the Standard Model with nf = 2 + 1 chiral fermions. Part 1: bare matrix elements and physical results

Abstract

Abstract:We compute the hadronic matrix elements of the four-quark operators relevant for K 0 −K 0 mixing beyond the Standard Model. Our results are from lattice QCD simulations with n f = 2 + 1 flavours of domain-wall fermion, which exhibit continuum-like chiral-flavour symmetry. The simulations are performed at two different values of the lattice spacing (a ∼ 0.08 and a ∼ 0.11 fm) and with lightest unitary pion mass ∼ 300 MeV. For the first time, the full set of relevant four-quark operators is renormalised non-perturbatively through RI-SMOM schemes; a detailed description of the renormalisation procedure is presented in a companion paper. We argue that the intermediate renormalisation scheme is responsible for the discrepancies found by different collaborations. We also study different normalisations and determine the matrix elements of the relevant four-quark operators with a precision of ∼ 5% or better.

Neutral kaon mixing beyond the Standard Model with n f = 2 + 1 chiral fermions. Part 2: non perturbative renormalisation of the ΔF = 2 four-quark operators

“…This has been confirmed by the update of SWME [18]. Therefore, one of our main conclusions in [1,21] is that the renormalisation procedure is the source of the discrepancy and we suggest to discard the results obtained with exceptional kinematics due to the systematic uncertainty in the pion pole subtraction.…”

“…The latter are RI-SMOM schemes whose precise definitions are given in this work. The N f = 2 + 1 results quoted here are obtained with exactly the same framework apart from the intermediate renormalisation scheme, see [1]. We argue that the difference comes the renormalisation and we suggest to discard the results obtained with the RI-MOM scheme.…”

“…In [1,21], we added another lattice spacing and investigated the origin of the discrepancy. In particular for the non-perturbative renormalisation procedure, in addition to the traditional RI-MOM scheme, we have implemented new intermediate renormalisation schemes, called (γ µ , γ µ ) and (/ q, / q) which satisfy the RI-SMOM condition, and therefore exhibit non-exceptional kinematics.…”

“…We remind the reader that although the renormalisation is performed nonperturbatively, the matching to MS from the RI scheme (R MS←RI (µ)) has to be done using continuum perturbation theory as MS is not possible to implement on the lattice. Accurate matching of lattice operators using the Rome-Southampton technique requires the matching scale µ (given by the magnitude of a momentum µ = p 2 ) to be well-separated from both the scales where non-perturbative effects of QCD such as chiral symmetry-breaking become important and the (inverse) lattice scale where cut-off effects 1 The main reasons are that we do not need to generate new configurations, we can take advangate of multi-loop continuum perturbative computations for the matching to MS, and we can obtain very good statistical accuracy with moderate computer resources. The drawback is that we have to fix the gauge.…”

“…We find that, once converted to MS, the Z-factors computed through these RI-SMOM schemes are in good agreement but differ significantly from the ones computed through the RI-MOM scheme. The RI-SMOM Z-factors presented here have been used to compute the BSM neutral kaon mixing matrix elements in the companion paper [1]. We argue that the renormalisation procedure is responsible for the discrepancies observed by different collaborations, we will investigate and elucidate the origin of these differences throughout this work.…”