We estimate the size of the hadronic matrix elements of CP-violating three-gluon and four-gluon Weinberg operators using sum-rule techniques. In the three-gluon case, we are able to reproduce the expressions given in earlier works, while the four-gluon results obtained in this article are new. Our paper therefore represents the first systematic study of contributions to the electric dipole moment of the neutron due to CP-violating dimension-six and dimension-eight operators. We provide many details on both the derivation of the sum rules as well as the analysis of the uncertainties that plague our final predictions.Here G A µν is the QCD field strength tensor,G A µν = 1/2 µνρλ G A ρλ with 0123 = +1 denotes its dual, f ABC are the fully anti-symmetric structure constants of SU(3) and c ABCD denote the colour structures defined in (5.20). Lacking the expertise in LQCD as well as the needed computer resources, we will present estimates of the hadronic matrix elements of the operators in (1.1) using QCD sum-rule techniques. In the case of the dimension-six contribution O 6 such a calculation has already been performed in [40], but the latter publication does not provide details on the actual computation making an independent reevaluation worthwhile. Our determination of the hadronic matrix elements of the dimension-eight term O 8 is instead new. Both results will be used in a companion paper [59], where we derive model-independent bounds on CP-violating Higgs-gluon interactions in BSM scenarios with vanishing or highly suppressed light-quark Yukawa couplings.Our work is organised as follows. After briefly reviewing the basic idea behind the sum-rule determinations of the hadronic matrix elements of O 6 and O 8 , we discuss in Section 3 the phenomenological side of the sum rules. The operator product expansion (OPE) computation of the dimension-six and dimension-eight contributions is described in Section 4 and Section 5, respectively. The matching and the numerical analysis of the sum rules are performed in Section 6. We conclude in Section 7. Technical details are relegated to several appendices. General idea behind the sum rulesThe central object for the derivation of the sum-rule estimates for the hadronic matrix elements of operators of the type (1.1) is the following correlation function Π(q 2 ) = i d 4 x e iqx Ω T η(x)η(0) Ω EM,O k , (2.1)

We estimate the form factors that parametrise the hadronic matrix elements of proton-to-pion transitions with the help of light-cone sum rules. These form factors are relevant for semi-leptonic proton decay channels induced by baryon-number violating dimension-six operators, as typically studied in the context of grand unified theories. We calculate the form factors in a kinematical regime where the momentum transfer from the proton to the pion is space-like and extrapolate our final results to the regime that is relevant for proton decay. In this way, we obtain estimates for the form factors that show agreement with the state-of-the-art calculations in lattice QCD, if systematic uncertainties are taken into account. Our work is a first step towards calculating more involved proton decay channels where lattice QCD results are not available at present.

We investigate CP-violating interactions involving the Higgs boson and gluons within an effective field theory approach, focusing on the specific class of new-physics scenarios where the Yukawa couplings of light quarks are zero or strongly suppressed compared to the standard-model expectations. We compute the contributions of the most relevant higher-dimensional operators of Weinberg type to the electric dipole moment of the neutron (nEDM), which are induced by Feynman diagrams that involve an effective CP-violating Higgs-gluon coupling and top-quark loops. The resulting nEDM sensitivities and prospects are discussed and compared to the existing and expected LHC bounds. We find that future nEDM searches can set non-trivial constraints on CP-violating Higgs-gluon interactions even if the Higgs only couples to the third generation of quarks.

Using light-cone sum rule techniques, we estimate the form factors which parametrise the hadronic matrix elements that are relevant for semi-leptonic three-body proton decays. The obtained form factors allow us to determine the differential rate for the decay of a proton (p) into a positron (e+), a neutral pion (π0) and a graviton (G), which is the leading proton decay channel in the effective theory of gravitons and Standard Model particles (GRSMEFT). The sensitivity of existing and next-generation neutrino experiments in detecting the p → e+π0G signature is studied and the phenomenological implications of our computations for constraints on the effective mass scale that suppresses the relevant baryon-number violating GRSMEFT operator are discussed.