Single-top-quark production in the t-channel at NNLO

We present a calculation of t-channel single-top-quark production and decay in the five-flavor scheme at NNLO. Our results resolve a disagreement between two previous calculations of this process that found a difference in the inclusive cross section at the level of the NNLO coefficient itself. We compare in detail with the previous calculations at the inclusive, differential and fiducial level including b-quark tagging at a fixed scale μ = mt. In addition, we advocate the use of double deep inelastic scattering (DDIS) scales (μ2 = Q2 for the light-quark line and μ2 = Q2 + $$ {m}_t^2 $$ m t 2 for the heavy-quark line) that maximize perturbative stability and allow for robust scale uncertainties. All NNLO and NLO⊗NLO contributions for production and decay are included in the on-shell and vertex-function approximation. We present fiducial and differential results for a variety of observables used in Standard Model and Beyond Standard Model analyses, and find an important difference between the NLO and NNLO predictions of exclusive t + n-jet cross sections. Overall we find that NNLO corrections are crucial for a precise identification of the t-channel process.

CONSISTENTLY COMPUTING THE K → π LONG DISTANCE WEAK TRANSITION

First we extract the long-distance (LD) weak matrix element <π|HW|K> from K → 2π, K → 3π, KL→ 2γ, K+→ π+e+e-, K+→ π+μ+μ-and KL→ μ+μ-data and give compatible theoretical estimates. We also link this LD scale to the single-quark-line (SQL) transition scale βWand then test the latter SQL scale against the decuplet weak decay amplitude ratio <π-Ξ0| HW|Ω->/<Ξ-|HW|Ω->. Finally, we study LD KS→ 2γ decay. All of these experimental and theoretical values for <π|HW|K> are in good agreement. We deduce an average value from 11 experimental determinations of <π|HW|K> = (3.59 ± 0.05) × 10-8GeV2, while the theoretical SQL values average to (3.577 ± 0.004) × 10-8GeV2.

SIGNATURES OF SINGLE QUARK LINE WEAK TRANSITIONS

We study the ΔI = 1/2 single quark line transition that occurs in p-wave baryon B → B′π, in radiative Ξ− → Σ−γ, in decuplet Ω− → Ξπ and in kaon K° → ππ weak decays. This leads to five empirical signatures of the single quark line scale. This scale is also predicted from a quark loop model.

APPROXIMATE |∆I| = 1/2 RULE IN K → ππ DECAYS FROM ASYMPTOTIC QUARK-LINE DIAGRAM APPROACH

Approximate |∆I| = 1/2 rule in K → ππ decays is studied from a new dynamical perspective in which quark-line diagrams should only be associated with asymptotic single-hadron matrix elements of [Formula: see text], and not with the whole amplitude. The asymptotic matrix elements of [Formula: see text] taken between ordinary [Formula: see text] mesons are found to satisfy the strict |∆I| = 1/2 rule. However, the contribution of the four-quark (QQ)[Formula: see text] type mesons leads explicitly to a small violation of the selection rule.