<p>Electric dipole moment (EDM) measurements using paramagnetic molecules have significantly advanced over the last decade. Traditionally, these experiments have been analyzed in terms of the electron EDM. However, paramagnetic molecules are also sensitive to hadronic sources of charge-parity (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>) violation, highlighting the need for a new framework to interpret the experimental results. In this Letter, we introduce an effective field theory framework to relate molecular EDMs to the EDMs of neutrons and protons. We identify the dominant contributions through power counting and pinpoint the necessary nuclear matrix elements. As a practical application, we employ the nuclear shell model to calculate these nuclear matrix elements for the polar molecule BaF. Finally, we estimate the limits on the nucleon EDMs set by current molecular EDM experiments.</p>

United States

Wouter Dekens

Netherlands

Jordy de Vries

Lemonia Gialidi

Spain

Javier Menéndez

Heleen Mulder

Beatriz Romeo

Nucleon Electric Dipole Moments in Paramagnetic Molecules through Effective Field Theory

We investigate the properties of the radially excited charged pion, with a specific focus on its electromagnetic form factor (EFF) and its box contribution to the hadronic light-by-light (HLbL) component of the muon's anomalous magnetic moment, $ a_{\mu} $ . Utilizing a coupled non-perturbative framework combining Schwinger-Dyson and Bethe-Salpeter equations, we first compute the mass and weak decay constant of the pion's first radial excitation. Initial results are provided for the Rainbow-Ladder (RL) approximation, followed by an extended beyond RL (BRL) analysis that incorporates meson cloud effects. Building on our previous work, this analysis demonstrates that an accurate description of the first radial excitation can be achieved without the need for a reparametrization of the interaction kernels. Having demonstrated the effectiveness of the truncation scheme, we proceed to calculate the corresponding EFF, from which we derive the contribution of the pion's first radial excitation to the HLbL component of the muon's anomalous magnetic moment, producing $ a_{\mu}^{\pi_1-\text{box}}(\text{RL}) = -(2.03 \pm 0.12) \times 10 ^{-13} $ , $ a_{\mu}^{\pi_1-\text{box}}(\text{BRL}) = $ $ -(2.02 \pm 0.10) \times 10 ^{-13} $ . Our computation also sets the groundwork for calculating related pole contributions of excited pseudoscalar mesons to $ a_{\mu} $ .

Mexico

Angel S. Miramontes

K. Raya

A. Bashir

P. Roig

G. Paredes-Torres

Radially excited pion: electromagnetic form factor and the box contribution to the muon's $\textit{g}$-2 * A. S. Miramontes acknowledges $\textit{Consejo Nacional de Ciencia, Humanidades y Tecnología}$ (CONAHCyT), Mexico, for the financial support received through the program '$\textit{Postdoctorados Nacionales por México}$', additionally, has been partially funded by the 'PROMETEO' programme of the 'Generalitat Valenciana' grant CIPROM/2022/66, and by the Spanish 'Agencia Estatal de Investigación', MCIN/AEI/10.13039/501100011033, through the grants PID2020-113334GB-I00 and PID2023-151418NB-I00. A. Bashir thanks $\textit{Coordinación de la Investigación Científica}$ of the $\textit{Universidad Michoacana de San Nicolás de Hidalgo}$ Grant No. 4.10., CONAHCyT grant CBF2023-2024-3544 and $\textit{Ayudas Beatriz Galindo}$, Spain. P. Roig acknowledges Conahcyt (México) funding through project CBF2023-2024-3226 as well as Spanish support during his sabbatical year through projects MCIN/AEI/10.13039/501100011033, grant PID2020-114473GB-I00, and Generalitat Valenciana grant PROMETEO/2021/071. G. Paredes-Torres acknowledges CONAHCyT, Mexico, for the financial support provided to him through the program '$\textit{Beca de Posgrado en México}$'. The work of A. Bashir and K. Raya is supported by Spanish Ministry of Science and Innovation (MICINN grant no. PID2022-140440NB-C22) and Junta de Andalucía (grant P18-FR-5057)

We investigate the experimental feasibility of detecting second-order double-magnetic dipole (γγ-<math><mi>M</mi><mn>1</mn><mi>M</mi><mn>1</mn></math>) decays from double isobaric analog states (DIAS), which have recently been found to be strongly correlated with the nuclear matrix elements of neutrinoless ββ decay. Using the nuclear shell model, we compute theoretical branching ratios for γγ-<math><mi>M</mi><mn>1</mn><mi>M</mi><mn>1</mn></math> decays and compare them with other competing processes, such as single-γ decay and proton emission, which represent the dominant decay channels. We also estimate the potential competition from internal conversion and internal pair creation, which can influence the decay dynamics. Additionally, we propose an experimental strategy based on using LaBr$_{3}$ scintillators to identify γγ-<math><mi>M</mi><mn>1</mn><mi>M</mi><mn>1</mn></math> transitions from the DIAS amidst the background of the competing processes. Our approach emphasizes the challenges of isolating the rare γγ-<math><mi>M</mi><mn>1</mn><mi>M</mi><mn>1</mn></math> decay and suggests ways to enhance the experimental detection sensitivity. Our simulations suggest that it may be possible to access experimentally γγ-<math><mi>M</mi><mn>1</mn><mi>M</mi><mn>1</mn></math> decays from DIAS, shedding light on the neutrinoless ββ decay nuclear matrix elements.

Italy

Damiano Stramaccioni

Jose Javier Valiente-Dobón

A pathway to unveiling neutrinoless Decay Nuclear Matrix Elements via Decay