We replace ordinary chiral SU (3)L × SU (3)R perturbation theory χPT3 by a new theory χPTσ based on a low-energy expansion about an infrared fixed point α IR for 3-flavor QCD. At α IR , the quark condensate qq vac = 0 induces nine Nambu-Goldstone bosons: π, K, η and a 0 ++ QCD dilaton σ. Physically, σ appears as the f0(500) resonance, a pole at a complex mass with real part mK . The ∆I = 1/2 rule for nonleptonic K-decays is then a consequence of χPTσ, with a KSσ coupling fixed by data for K 0 S → γγ and γγ → ππ. We estimate RIR ≈ 5 for the nonperturbative Drell-Yan ratio R = σ(e + e − → hadrons)/σ(e + e − → µ + µ − ) at α IR .

We describe an extension to the SOFTSUSY program that provides for the calculation of the sparticle spectrum in the Next-to-Minimal Supersymmetric Standard Model (NMSSM), where a chiral superfield that is a singlet of the Standard Model gauge group is added to the Minimal Supersymmetric Standard Model (MSSM) fields. Often, a Z 3 symmetry is imposed upon the model. SOFTSUSY can calculate the spectrum in this case as well as the case where general Z 3 violating (denoted as \ Z 3 ) terms are added to the soft supersymmetry breaking terms and the superpotential. The user provides a theoretical boundary condition for the couplings and mass terms of the singlet. Radiative electroweak symmetry breaking data along with electroweak and CKM matrix data are used as weak-scale boundary conditions. The renormalisation group equations are solved numerically between the weak scale and a high energy scale using a nested iterative algorithm. This paper serves as a manual to the NMSSM mode of the program, detailing the approximations and conventions used.

Recent anomalies in the decays of B mesons and the Higgs boson provide hints towards lepton flavor (universality) violating physics beyond the Standard Model. We observe that four-fermion operators which can explain the B-physics anomalies have corresponding analogs in the kaon sector, and we analyze their impact on K → πℓℓ 0 and K → ℓℓ 0 decays ðℓ ¼ μ; eÞ. For these processes, we note the corresponding physics opportunities at the NA62 experiment. In particular, assuming minimal flavor violation, we comment on the required improvements in sensitivity necessary to test the B-physics anomalies in the kaon sector.

We analyze the Callan-Symanzik equations when scale invariance at a nontrivial infrared (IR) fixed point αir is realized in the Nambu-Goldstone (NG) mode. As a result, Green's functions at αir do not scale in the same way as for the conventional Wigner-Weyl (WW) mode. This allows us to propose a new mechanism for dynamical electroweak symmetry breaking where the running coupling α "crawls" towards (but does not pass) αir in the exact IR limit. The NG mechanism at αir implies the existence of a massless dilaton σ, which becomes massive for IR expansions in ǫ ≡ αir − α and is identified with the Higgs boson. Unlike "dilatons" that are close to a WW-mode fixed point or associated with a Coleman-Weinberg potential, our NG-mode dilaton is genuine and hence naturally light. Its (mass) 2 is proportional to ǫβ ′ (4 + β ′ )F −2 σ Ĝ 2 vac, where β ′ is the (positive) slope of the beta function at αir, Fσ is the dilaton decay constant and Ĝ 2 vac is the technigluon condensate. Our effective field theory for this works because it respects Zumino's consistency condition for dilaton Lagrangians. We find a closed form of the Higgs potential with β ′ -dependent deviations from that of the Standard Model. Flavor-changing neutral currents are suppressed if the crawling region α αir includes a sufficiently large range of energies above the TeV scale. In Appendix A, we observe that, contrary to folklore, condensates protect fields from decoupling in the IR limit. CONTENTS

In the framework of the MSSM, we examine several simplified models where only a few superpartners are light. This allows us to study WIMP-nucleus scattering in terms of a handful of MSSM parameters and thereby scrutinize their impact on dark matter direct-detection experiments. Focusing on spin-independent WIMP-nucleon scattering, we derive simplified, analytic expressions for the Wilson coefficients associated with Higgs and squark exchange. We utilize these results to study the complementarity of constraints due to direct-detection, flavor, and collider experiments. We also identify parameter configurations that produce (almost) vanishing cross sections. In the proximity of these so-called blind spots, we find that the amount of isospin violation may be much larger than typically expected in the MSSM. This feature is a generic property of parameter regions where cross sections are suppressed, and highlights the importance of a careful analysis of the nucleon matrix elements and the associated hadronic uncertainties. This becomes especially relevant once the increased sensitivity of future direct-detection experiments corners the MSSM into these regions of parameter space.

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Chiral-scale perturbation theory χPT σ has been proposed as an alternative to chiral SU(3) L × SU(3) R perturbation theory which explains the ∆I = 1/2 rule for kaon decays. It is based on a lowenergy expansion about an infrared fixed point in three-flavor QCD. In χPT σ , quark condensation qq vac = 0 induces nine Nambu-Goldstone bosons: π, K, η and a QCD dilaton σ which we identify with the f 0 (500) resonance. Partial conservation of the dilatation and chiral currents constrains low-energy constants which enter the effective Lagrangian of χPT σ . These constraints allow us to obtain new phenomenological bounds on the dilaton decay constant via the coupling of σ / f 0 to pions, whose value is known precisely from dispersive analyses of ππ scattering. Improved predictions for σ → γγ and the σ NN coupling are also noted. To test χPT σ for kaon decays, we revive a 1985 proposal for lattice methods to be applied to K → π on-shell.

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