Compositeness above the electroweak scale and a proposed test at LHCb

I review attempts to construct models of partial compositeness from strongly coupled gauge theories. A few minimal assumptions allow one to isolate a small number of representative models. After presenting the main idea, I discuss a recent proposal to detect a light pseudo-scalar, predicted in all these models, at the LHCb detector.

BSM master formula for ε′/ε in the WET basis at NLO in QCD

As an important step towards a complete next-to-leading (NLO) QCD analysis of the ratio ε′/ε within the Standard Model Effective Field Theory (SMEFT), we present for the first time the NLO master formula for the BSM part of this ratio expressed in terms of the Wilson coefficients of all contributing operators evaluated at the electroweak scale. To this end we use the common Weak Effective Theory (WET) basis (the so-called JMS basis) for which tree-level and one-loop matching to the SMEFT are already known. The relevant hadronic matrix elements of BSM operators at the electroweak scale are taken from Dual QCD approach and the SM ones from lattice QCD. It includes the renormalization group evolution and quark-flavour threshold effects at NLO in QCD from hadronic scales, at which these matrix elements have been calculated, to the electroweak scale.

Minimal scenario of criticality for electroweak scale, neutrino masses, dark matter, and inflation

We propose a minimal model that can explain the electroweak scale, neutrino masses, Dark Matter (DM), and successful inflation all at once based on the multicritical-point principle (MPP). The model has two singlet scalar fields that realize an analogue of the Coleman–Weinberg mechanism, in addition to the Standard Model with heavy Majorana right-handed neutrinos. By assuming a $$Z_2 $$ Z 2 symmetry, one of the scalars becomes a DM candidate whose property is almost the same as the minimal Higgs-portal scalar DM. In this model, the MPP can naturally realize a saddle point in the Higgs potential at high energy scales. By the renormalization-group analysis, we study the critical Higgs inflation with non-minimal coupling $$\xi |H|^2 R$$ ξ | H | 2 R that utilizes the saddle point of the Higgs potential. We find that it is possible to realize successful inflation even for $$\xi =25$$ ξ = 25 and that the heaviest right-handed neutrino is predicted to have a mass around $$10^{14}$$ 10 14 $$\mathrm{GeV}$$ GeV to meet the current cosmological observations. Such a small value of $$\xi $$ ξ can be realized by the Higgs-portal coupling $$\lambda _{SH}\simeq 0.32$$ λ SH ≃ 0.32 and the vacuum expectation value of the additional neutral scalar $$\langle \phi \rangle \simeq 2.7$$ ⟨ ϕ ⟩ ≃ 2.7 TeV, which correspond to the dark matter mass 2.0 TeV, its spin-independent cross section $$1.8\times 10^{-9}$$ 1.8 × 10 - 9 pb, and the mass of additional neutral scalar 190 GeV.

Weak scale right-handed neutrino as pseudo-Goldstone fermion of spontaneously broken $$ \mathrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} $$

Possibility of a Right-Handed (RH) neutrino being a Goldstone fermion of a spontaneously broken global U(1) symmetry in a supersymmetric theory is considered. This fermion obtains mass from the supergravity effects leading to a RH neutrino at the electroweak scale with a mass similar to the gravitino mass. A prototype model realizing this scenario contains just three gauge singlet superfields needed for the type I seesaw mechanism. Masses of the other two neutrinos are determined by the U(1) breaking scale which too can be around the electroweak scale. Light neutrinos obtain their masses in this scenario through (a) mixing with the RH neutrinos (type I seesaw), (b) mixing with neutralinos (R-parity breaking), (c) indirectly through mixing of the RH neutrinos with neutralinos, and (d) radiative corrections. All these contributions are described by the same set of a small number of underlying parameters and provide a very constrained and predictive framework for the neutrino masses which is investigated in detail for various choices of U(1) symmetries. It is found that flavour independent U(1) symmetries cannot describe neutrino masses if the soft supersymmetry breaking terms are flavour universal and one needs to consider flavour dependent symmetries. Considering a particular example of Lμ− Lτ symmetry, it is shown that viable neutrino masses and mixing can be obtained without introducing any flavour violation in the soft sector. The leptonic couplings of Majoron are worked out in the model and shown to be consistent with various laboratory, astrophysical and cosmological constraints. The neutrino data allows sizeable couplings between the RH neutrinos and Higgsinos which can be used to probe the pseudo-Goldstone fermion at colliders through its displaced decay vertex.

Gravitational tests of electroweak relaxation

We consider a scenario in which the electroweak scale is stabilized via the relaxion mechanism during inflation, focussing on the case in which the back-reaction potential is generated by the confinement of new strongly interacting vector-like fermions. If the reheating temperature is sufficiently high to cause the deconfinement of the new strong interactions, the back-reaction barrier then disappears and the Universe undergoes a second relaxation phase. This phase stops when the temperature drops sufficiently for the back-reaction to form again. We identify the regions of parameter space in which the second relaxation phase does not spoil the successful stabilization of the electroweak scale. In addition, the generation of the back-reaction potential that ends the second relaxation phase can be associated to a strong first order phase transition. We then study when such transition can generate a gravitational wave signal in the range of detectability of future interferometer experiments.

Leading logs in QCD axion effective field theory

The axion is much lighter than all other degrees of freedom introduced by the Peccei-Quinn mechanism to solve the strong CP problem. It is therefore natural to use an effective field theory (EFT) to describe its interactions. Loop processes calculated in the EFT may however explicitly depend on the ultraviolet cutoff. In general, the UV cutoff is not uniquely defined, but the dimensionful couplings suggest to identify it with the Peccei-Quinn symmetry-breaking scale. An example are K+ → π+ + a decays that will soon be tested to improved precision in NA62 and KOTO and whose amplitude is dominated by the term logarithmically dependent on the cutoff. In this paper, we critically examine the adequacy of using such a naive EFT approach to study loop processes by comparing EFT calculations with ones performed in complete QCD axion models. In DFSZ models, for example, the cutoff is found to be set by additional Higgs degrees of freedom and to therefore be much closer to the electroweak scale than to the Peccei-Quinn scale. In fact, there are non-trivial requirements on axion models where the cutoff scale of loop processes is close to the Peccei-Quinn scale, such that the naive EFT result is reproduced. This suggests that the existence of a suitable UV embedding may impose restrictions on axion EFTs. We provide an explicit construction of a model with suitable fermion couplings and find promising prospects for NA62 and IAXO.

Electroweak axion string and superconductivity

We study the axion strings with the electroweak gauge flux in the DFSZ axion model and show that these strings, called the electroweak axion strings, can exhibit superconductivity without fermionic zeromodes. We construct three types of electroweak axion string solutions. Among them, the string with W-flux can be lightest in some parameter space, which leads to a stable superconducting cosmic string. We also show that a large electric current can flow along the string due to the Peccei-Quinn scale much higher than the electroweak scale. This large current induces a net attractive force between the axion strings with the same topological charge, which opens a novel possibility that the axion strings form Y-junctions in the early universe.

Low energy effective field theory operator basis at d ≤ 9

We obtain the complete operator bases at mass dimensions 5, 6, 7, 8, 9 for the low energy effective field theory (LEFT), which parametrize various physics effects between the QCD scale and the electroweak scale. The independence of the operator basis regarding the equation of motion, integration by parts and flavor relations, is guaranteed by our algorithm [1, 2], whose validity for the LEFT with massive fermions involved is proved by a generalization of the amplitude-operator correspondence. At dimension 8 and 9, we list the 35058 (756) and 704584 (3686) operators for three (one) generations of fermions categorized by their baryon and lepton number violations (∆B, ∆L), as these operators are of most phenomenological relevance.

Heavy $$Z^\prime $$ bosons in the secluded $$U(1)^\prime $$ model at hadron colliders

We study $$Z^{\prime }$$ Z ′ phenomenology at hadron colliders in an $$U(1)^{\prime }$$ U ( 1 ) ′ extended MSSM. We choose a $$U(1)^{\prime }$$ U ( 1 ) ′ model with a secluded sector, where the tension between the electroweak scale and developing a large enough mass for $$Z^{\prime }$$ Z ′ is resolved by incorporating three additional singlet superfields into the model. We perform a detailed analysis of the production, followed by decays, including into supersymmetric particles, of a $$Z^{\prime }$$ Z ′ boson with mass between 4 and 5.2 TeV, with particular emphasis on its possible discovery. We select three different scenarios consistent with the latest available experimental data and relic density constraints, and concentrate on final signals with $$2\ell +\not \! \! E_{T}$$ 2 ℓ + ⧸ E T , $$4\ell +\not \! \! E_{T}$$ 4 ℓ + ⧸ E T and $$6\ell +\not \! \! E_{T}$$ 6 ℓ + ⧸ E T . Including the SM background from processes with two, three or four vector bosons, we show the likelihood of observing a $$Z^\prime $$ Z ′ boson is not promising for the HL-LHC at 14 TeV. While at 27 and 100 TeV, the situation is more optimistic, and we devise specific benchmark scenarios which could be observed.