Assuming the presence of physics beyond the Standard Model (SM) with a characteristic scale M∼O(10)TeV, we investigate the naturalness of the Higgs sector at scales below M using an effective field theory (EFT) approach. We obtain the complete set of higher-dimensional effective operators (at any dimension n≥5) that give the leading one-loop EFT contributions to the Higgs mass with a Wilsonian-like hard cutoff and discuss the (fine-) tuning between these terms and the SM one-loop contribution, which is required in order to alleviate the little hierarchy problem. We then show that this tuning can be translated into a condition for naturalness in the underlying new physics, a condition we denote by "EFT naturalness" and which we express as constraints on the corresponding higher-dimensional operator coefficients up to the scale of the effective action Λ

We examine new aspects of leptoquark (LQ) phenomenology using effective field theory (EFT). We construct a complete set of leading effective operators involving SU(2) singlets scalar LQ and the SM fields up to dimension six. We show that, while the renormalizable LQ-lepton-quark interaction Lagrangian can address the persistent hints for physics beyond the Standard Model in the B-decays $\bar B \to D^{(*)} \tau \bar u$, $\bar B \to \bar K \ell^+ \ell^-$ and in the measured anomalous magnetic moment of the muon, the LQ higher dimensional effective operators may lead to new interesting effects associated with lepton number violation. These include the generation of one-loop sub-eV Majorana neutrino masses, mediation of neutrinoless double-$\beta$ decay and novel LQ collider signals. For the latter, we focus on 3rd generation LQ ($\phi_3$) in a framework with an approximate $Z_3$ generation symmetry, and show that one class of the dimension five LQ operators may give rise to a striking asymmetric same-charge $\phi_3 \phi_3$ pair-production signal, which leads to low background same-sign leptons signals at the LHC. For example, with $M_{\phi_3} \sim 1$ TeV and a new physics scale of $\Lambda \sim 5$ TeV, we expect about $5000$ positively charged $\tau^+ \tau^+$ events via $pp \to \phi_3 \phi_3 \to \tau^+ \tau^+ + 2 \cdot j_b$ ($j_b$=b-jet) at the 13 TeV LHC with an integrated luminosity of 300 fb$^{-1}$. It is interesting to note that, in the LQ EFT framework, the expected same-sign lepton signals have a rate which is several times larger than the QCD LQ-mediated opposite-sign leptons signals, $gg,q \bar q \to \phi_3 \phi_3^* \to \ell^+ \ell^- +X$. We also consider the same-sign charged lepton signals in the LQ EFT framework at higher energy hadron colliders such as a 27 TeV HE-LHC and a 100 TeV FCC-hh.

We suggest a new class of tests for searching for lepton flavor non-universality (LFNU) using ratio observables and based on correlations among the underlying LFNU new physics (NP) effects in several (seemingly independent) di-lepton and single lepton + jet(s) processes. This is demonstrated by studying the effects generated by LFNU 4-Fermi interactions involving 3rd generation quarks. We find that the sensitivity to the scale ($\Lambda$) of the LFNU 4-Fermi operators significantly improves when the correlations among the various di-lepton +jets and single-lepton + jets processes are used, reaching $\Lambda \sim {\cal O}(10)$~TeV at the HL-LHC.