Experimental sensitivity to the electric dipole moment (EDM) of the electron has improved remarkably in recent years. Consequently, future prospects could probe new physics whose contribution to the electron EDM first arises at three-loop order. Additional SU(2) multiplets with CP-violating Yukawa interactions, which contribute to the electron EDM at three-loop level, is one such testable new physics scenario. In this scenario, the electron EDM is radiatively induced from two contributions: the CP-odd trilinear $\textit{W}$ -boson coupling, called the electroweak-Weinberg operator, and the CP-odd dipole operator of electron. The former and the latter operators are generated at two-loop and three-loop levels, respectively, after integrating out the SU(2) multiplets. Within the same models, according to an analysis based on the Standard Model Effective Field Theory (SMEFT), we previously found that the contribution to the electron EDM from the electroweak-Weinberg operator can be probed in future experiments. However, the one-loop matching condition between the electron EDM and the electroweak-Weinberg operator does not receive a large logarithmic enhancement because the associated anomalous dimension is zero. The CP-odd dipole operator of the electron would contribute to the electron EDM at the same three-loop order as the contribution through the electroweak-Weinberg operator. In this paper, we directly calculate the electron EDM induced by the CP-violating Yukawa interactions of the SU(2) multiplets at $\textit{full}$ three-loop level. A central result is that the full three-loop calculation is a factor of three larger than that of the electroweak-Weinberg operator alone.

Japan

Tatsuya Banno

Junji Hisano

Teppei Kitahara

Kiyoto Ogawa

Naohiro Osamura

Full three-loop electroweak multiplet contributions to the electron electric dipole moment

We study the renormalization of the QCD $\textit{θ}$ angle at the two-loop level focusing on divergent and finite $\textit{CP}$-violating contributions from evanescent operators, using dimensional regularization with the BMHV scheme. When one considers the Lagrangian in $\textit{d}$-dimensional space-time instead of four dimensions in dimensional regularization, evanescent operators that break the chiral symmetry are induced. Consequently, $\textit{T}$-odd and $\textit{P}$-odd fermion loops in the BMHV scheme generate evanescent contributions to the QCD $\textit{θ}$ angle. We carefully classify the evanescent contributions into two types: one originating from the evanescent operators at the one-loop level and the other directly produced by two-loop calculations. We show that renormalization of the parameters in the BMHV scheme keeps removing those unphysical contributions to the QCD $\textit{θ}$ angle at any scale at the two-loop level. We also discuss how the rephasing invariance of the radiative correction to the QCD $\textit{θ}$ angle is realized in the BMHV scheme.

Two-loop corrections to QCD $\textit{θ}$ angle from evanescent operator in the BMHV scheme

In this paper we extend the supersymmetric SU(5) GUTs with the Nelson-Barr (NB) models. The NB models are a candidate for the solution of the strong CP problem. We show that the parameters in the CKM matrix are reproduced while the mass ratios of the down-type quarks and leptons in the second and third generations are explained in the minimal extension.

Moe Kuroda

Extension of SUSY SU(5) GUTs with Nelson-Barr models

Recent progress in the electric dipole moment (EDM) measurements of the electron using the paramagnetic atom or molecule is remarkable. In this paper, we calculate a contribution to the electron EDM at three-loop level, introducing the CP-violating Yukawa couplings of new SU(2) multiplets. At two-loop level, the Yukawa interactions generate a CP-violating dimension-six operator, composed of three SU(2) field strengths, called the electroweak-Weinberg operator. Another one-loop diagram with this operator inserted induces the electron EDM. We derive the matching condition and find that even if new SU(2) particles have masses around the TeV scale, the electron EDM may be larger than the Standard Model (SM) contribution to the paramagnetic atom or molecule EDMs. We also discuss the relation between the Barr-Zee diagram contribution at two-loop level and three-loop one, assuming that the SM Higgs has new Yukawa interactions with the SU(2) multiplets.

Impact of the electroweak Weinberg operator on the electric dipole moment of electron

In this paper, we scrutinize a radiatively generated QCD θ parameter at the two-loop level based on both full analytical loop functions with the Fock-Schwinger gauge method and the effective field theory approach, using simplified models. We observe that the radiatively generated θ parameters at the low energy scale precisely match between them. It provides validity to perturbative loop calculations of the QCD θ parameter with the Fock-Schwinger gauge method. Furthermore, it is also shown that the ordinary Fujikawa method for the radiative θ parameter by using   <math> <mover> <mi>θ</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\theta} $$  = −arg det   <math> <msubsup> <mi>M</mi> <mi>q</mi> <mtext>loop</mtext> </msubsup> </math>  $$ {\mathcal{M}}_q^{\textrm{loop}} $$  does not cover all contributions in the simplified models. But, we also find that when there is a scale hierarchy in CP-violating sector, evaluation of the Fujikawa method is numerically sufficient. As an application, we calculate the radiative θ parameter at the two-loop level in a slightly extended Nelson-Barr model, where the spontaneous CP violation occurs to solve the strong CP problem. It is found a part of the radiative θ parameters cannot be described by the Fujikawa method.

China

Closer look at the matching condition for radiative QCD θ parameter

We consider electrically neutral complex-vector particles <math><mi>V</mi></math> below the GeV mass scale that, from a low-energy perspective, couple to the photon via higher-dimensional form factor interactions. We derive ensuing astrophysical constraints by considering the anomalous energy loss from the Sun, Horizontal Branch, and Red Giant stars as well as from SN1987A that arise from vector pair production in these environments. Under the assumption that the dark states <math><mi>V</mi></math> constitute dark matter, the bounds are then complemented by direct and indirect detection as well as cosmological limits. The relic density from freeze-out and freeze-in mechanisms is also computed. On the basis of a UV-complete model that realizes the considered effective couplings, we also discuss the naturalness of the constrained parameter space, and provide an analysis of the zero mass limit of <math><mi>V</mi></math>.

Austria

Xiaoyong Chu

Germany

Alejandro Ibarra

United States

Jui-Lin Kuo

CERN

Josef Pradler

Multipole vector dark matter below the GeV scale

When the QCD axion is absent in full theory, the strong CP problem has to be explained by an additional mechanism, e.g., the left-right symmetry. Even though tree-level QCD   <math> <mover> <mi>θ</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\theta} $$  parameter is restricted by the mechanism, radiative corrections to   <math> <mover> <mi>θ</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\theta} $$  are mostly generated, which leads to a dangerous neutron electric dipole moment (EDM). The ordinary method for calculating the radiative   <math> <mover> <mi>θ</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\theta} $$  utilizes an equation   <math> <mover> <mi>θ</mi> <mo>¯</mo> </mover> <mo>=</mo> <mo>−</mo> <mo>arg</mo> <mspace width="0.25em"></mspace> <mo>det</mo> <msubsup> <mi>m</mi> <mi>q</mi> <mtext>loop</mtext> </msubsup> </math>  $$ \overline{\theta}=-\arg\ \det {m}_q^{\textrm{loop}} $$  based on the chiral rotations of complex quark masses. In this paper, we point out that when full theory includes extra heavy quarks, the ordinary method is unsettled for the extra quark contributions and does not contain its full radiative corrections. We formulate a novel method to calculate the radiative corrections to   <math> <mover> <mi>θ</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\theta} $$  through a direct loop-diagrammatic approach, which should be more robust than the ordinary one. As an application, we investigate the radiative   <math> <mover> <mi>θ</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\theta} $$  in the minimal left-right symmetric model. We first confirm a seminal result that two-loop level radiative   <math> <mover> <mi>θ</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\theta} $$  completely vanishes (corresponding to one-loop corrections to the quark mass matrices). Furthermore, we estimate the size of a non-vanishing radiative   <math> <mover> <mi>θ</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\theta} $$  at three-loop level. It is found that the resultant induced neutron EDM is comparable to the current experimental bound, and the expected size is restricted by the perturbative unitarity bound in the minimal left-right model.

Atsuyuki Yamada

Novel loop-diagrammatic approach to QCD θ parameter and application to the left-right model

Abstract We review proton decay in the SUSY SU(5) GUTs assuming the mini-split SUSY breaking model. In the mini-split SUSY breaking model, the squark and slepton masses are O(10$^{(2 − 3)}$) TeV while the gaugino masses are O(1) TeV. As the result, even the minimal SUSY SU(5) GUT is still viable in the model. We present the motivation of the mini-split SUSY model and discuss the future prospects of proton decay searches in the SUSY SU(5) GUTs.

Proton decay in SUSY GUTs

In this paper, we derive a simplified formula of electric dipole moments (EDMs) of a fermion. In the Standard Model, it is well-known that non-trivial cancellations between some rainbow-type diagrams induced by W boson exchanges occur in the calculation of the neutron EDM at the two-loop level due to the gauge symmetry. The fermion self-energy and the vertex correction are related through the Ward-Takahashi identity, and this relation causes the exact cancellation of the EDM. We derive EDM formulas for a more general setup by introducing the form factors for the fermion self-energy and the vertex correction so that the derived formulas can be applicable to a larger class of models. We conclude that the non-zero EDM contributions are induced from rainbow-type diagrams with the chirality flipping effects for internal fermions. We also discuss the other possible generalization of the EDM calculation which is applicable to the other classes of models.

Motoko Fujiwara

Takashi Toma

Vanishing or non-vanishing rainbow? Reduction formulas of electric dipole moment

We study gamma-ray line signatures from electroweakly interacting non-abelian spin-1 dark matter (DM). In this model, Z 2-odd spin-1 particles including a DM candidate have the SU(2) L  triplet-like features, and the Sommerfeld enhancement is relevant in the annihilation processes. We derive the annihilation cross sections contributing to the photon emission and compare with the SU(2) L  triplet fermions, such as Wino DM in the supersymmetric Standard Model. The Sommerfeld enhancement factor is approximately the same in both systems, while our spin-1 DM predicts the larger annihilation cross sections into γγ/Zγ modes than those of the Wino by   <math> <mfrac> <mn>38</mn> <mn>9</mn> </mfrac> </math>  $$ \frac{38}{9} $$ . This is because a spin-1 DM pair forms not only J = 0 but also J = 2 partial wave states where J denotes the total spin angular momentum. Our spin-1 DM also has a new annihilation mode into Z 2-even extra heavy vector and photon, Z′γ. For this mode, the photon energy depends on the masses of DM and the heavy vector, and thus we have a chance to probe the mass spectrum. The latest gamma-ray line search in the Galactic Center region gives a strong constraint on our spin-1 DM. We can probe the DM mass for ≲ 25.3 TeV by the Cherenkov Telescope Array experiment even if we assume a conservative DM density profile.