Chasing Shadows: A New Hunt for Quark EDM

Author: Denis Avetisyan

Researchers propose a novel method to detect the elusive electric dipole moment of the strange quark by analyzing asymmetries in particle decays.

The decay of <span class="katex-eq" data-katex-display="false">\gamma^{\ast}</span> into <span class="katex-eq" data-katex-display="false">K^{+}K^{-}\pi^{0}</span> reveals contributions from both standard model processes-mediated by three-gluon annihilation-and, crucially, from electric dipole moment interactions, specifically a strange-quark EDM denoted as <span class="katex-eq" data-katex-display="false">d_{s}</span>, offering a pathway to probe beyond-standard-model physics through the observation of this subtle asymmetry. — The decay of $\gamma^{\ast}$ into $K^{+}K^{-}\pi^{0}$ reveals contributions from both standard model processes-mediated by three-gluon annihilation-and, crucially, from electric dipole moment interactions, specifically a strange-quark EDM denoted as $d_{s}$ , offering a pathway to probe beyond-standard-model physics through the observation of this subtle asymmetry.

A measurement of angular correlations in the K+K-π0 final state from electron-positron collisions could reveal a strange-quark EDM with sensitivity reaching 10^-19 e⋅cm.

The Standard Model, while remarkably successful, offers limited explanation for observed matter-antimatter asymmetry, motivating searches for sources of CP violation beyond its predictions. This paper, ‘Probing Quark Electric Dipole Moment with Topological Anomalies’, explores a novel approach to constrain the strange-quark electric dipole moment (EDM) through measurements of angular correlations in $e^+e^-\to K^+K^-\pi^0$ decays. By leveraging chiral perturbation theory and anomalous couplings arising from a five-dimensional Chern-Simons construction, we estimate sensitivities reaching $10^{-{19}}e\cdot\text{cm}$ at future facilities like Super Tau-Charm and Belle II. Could these hadronic decays provide a complementary pathway to directly probe fundamental CP-violating interactions and refine our understanding of the quark sector?

The Universe’s Imbalance: A Symmetry Broken

The fundamental laws of physics, as currently understood through the Standard Model, suggest an inherent symmetry between matter and antimatter – for every particle, there should be a corresponding antiparticle with identical properties but opposite charges. This implies that the early universe should have produced equal amounts of both. However, observations reveal a startling discrepancy: the universe is overwhelmingly dominated by matter, with very little antimatter remaining. This imbalance isn’t merely a quantitative difference; it’s a profound puzzle challenging the completeness of the Standard Model. The very existence of galaxies, stars, and ultimately, life, hinges on this asymmetry, suggesting that some unknown process favored the creation of matter over antimatter in the nascent universe. Determining the origin of this preference is therefore a central goal in contemporary particle physics, driving the search for physics beyond our current understanding of the cosmos.

The observed prevalence of matter over antimatter in the universe presents a profound challenge to the Standard Model of particle physics, which predicts near-equal creation of both. This discrepancy implies the existence of underlying physical laws not currently accounted for within the established framework. A critical component of any viable explanation involves a phenomenon known as CP violation – a subtle asymmetry in the behavior of particles and their antimatter counterparts. While the Standard Model does permit CP violation, the amount predicted is insufficient to explain the observed matter-antimatter imbalance. Consequently, physicists hypothesize that additional sources of CP violation, originating from physics beyond the Standard Model, are essential to resolve this cosmological puzzle, driving searches for new particles and interactions that could account for the missing asymmetry.

The search for new physics beyond the Standard Model increasingly focuses on electric dipole moments (EDMs), which represent a subtle deviation from predicted symmetry. A fundamental tenet of physics is that particles and their antiparticles should possess identical properties, except for a reversed charge – but any observed EDM would demonstrate a separation between matter and antimatter, directly indicating physics beyond the Standard Model. Experiments meticulously measure the minuscule interaction between a particle’s internal electric charge distribution and an external electric field; because the Standard Model predicts EDMs to be vanishingly small, any non-zero measurement would signify the influence of new particles or interactions. These sensitive probes, utilizing techniques ranging from neutron beams to trapped ions, offer a powerful pathway to unravel the mystery of matter-antimatter asymmetry and potentially reveal the existence of undiscovered forces and particles governing the universe.

Probing Asymmetries: Nucleon and Electron EDMs

Nucleon electric dipole moment (EDM) searches provide a direct probe of charge-parity (CP) violation within the Standard Model and beyond. The Standard Model predicts a very small nucleon EDM, but new sources of CP violation arising from physics beyond the Standard Model could significantly enhance this value. Experiments, such as the ‘Nucleon EDM Search’, aim to measure this tiny moment by observing the interaction of the nucleon’s EDM with an applied electric field. Any non-zero measurement would indicate CP violation in the quark sector, specifically in the complex phase of the Cabibbo-Kobayashi-Maskawa (CKM) matrix or, more likely, from new CP-violating interactions involving as-yet undiscovered particles and forces. The sensitivity of these searches is directly related to the precision with which the nucleon spin polarization and the applied electric field can be controlled and measured.

The search for an electron electric dipole moment (EDM) provides complementary constraints on new physics beyond the Standard Model due to its sensitivity to different contributing factors compared to nucleon EDM searches. While nucleon EDMs are primarily influenced by CP-violating interactions within the quark sector affecting strong interactions, electron EDM measurements are sensitive to both direct CP-violating interactions involving leptons and indirect effects arising from interactions within virtual particles contributing to the electron’s anomalous magnetic moment. These contributions can include interactions with hypothetical particles like heavy bosons or sparticles, offering a distinct avenue to probe beyond-Standard-Model physics not readily accessible through hadronic systems. Furthermore, differing theoretical uncertainties and systematic limitations between nucleon and electron EDM experiments reinforce the value of pursuing both approaches for a comprehensive search for CP violation.

Current experiments searching for electric dipole moments (EDMs) of nucleons and electrons fundamentally depend on the interaction between particle spin and applied electric fields. These searches utilize strong electromagnetic fields – typically generated by atomic or molecular systems – to polarize the spins of the particles under investigation. Precise measurement of these polarized spins, and any precession caused by an EDM interacting with the field, requires sophisticated techniques like Ramsey spectroscopy and magnetic resonance. The sensitivity of these experiments is directly proportional to both the strength of the electric field and the duration of spin coherence, necessitating ultra-high vacuum environments and careful shielding from external magnetic field gradients to minimize decoherence effects. Any observed precession rate is then directly correlated to the magnitude of the particle’s EDM.

Strange Quark CP Violation: The Lambda Hyperon as a Probe

The electric dipole moment (EDM) of the Lambda hyperon serves as a probe for charge-parity (CP) violation within the strange quark sector, a region of the Standard Model not yet fully explored. While the Standard Model predicts a negligible EDM, many beyond-the-Standard-Model theories predict non-zero EDMs, particularly involving new sources of CP violation. The Lambda hyperon is uniquely suited to this search due to its relatively long lifetime and the fact that it contains a strange quark, allowing for enhanced sensitivity to CP-violating effects related to this quark flavor. Measurements of the Lambda EDM, therefore, provide a complementary search for CP violation alongside studies focusing on charm and bottom quarks, potentially revealing new physics if a non-zero value is detected.

The BESIII experiment utilizes $e^+e^-$ collisions to produce and study the Lambda hyperon via the decay of the $J/\psi$ meson. Specifically, the $J/\psi$ decays into $K^+K^-\pi^0$ with a measured branching fraction of $2.88 \times 10^{-3}$ . This decay channel provides a significant source of Lambda hyperons for analysis, enabling precise measurements of its properties. The relatively high branching fraction of this particular $J/\psi$ decay is crucial for achieving sufficient event statistics within the experimental timeframe and allows for a detailed study of the Lambda hyperon’s characteristics.

The measurement of the Lambda hyperon’s electric dipole moment (EDM) is performed by analyzing the angular distribution of its primary decay products, typically a proton and a pion. This analysis requires a precise understanding of the decay dynamics and acceptance corrections, necessitating detailed theoretical calculations of the decay form factors and polarization parameters. The BESIII experiment is designed to achieve a sensitivity of $7.1 \times 10^{-{19}} \text{ e}\cdot\text{cm}$ for the Lambda EDM, based on projected statistics from $J/\psi$ decays and careful control of systematic uncertainties related to detector effects and reconstruction efficiencies. Achieving this sensitivity necessitates modeling the angular acceptance of the detector and accounting for backgrounds that can mimic an EDM signal.

Theoretical Foundations: Chiral Perturbation Theory and Beyond

Chiral Perturbation Theory ( $\chi PT$ ) provides a systematic framework for calculating the electric dipole moment (EDM) of the Lambda baryon, addressing limitations encountered when directly applying Quantum Chromodynamics (QCD) at low energies. As a low-energy effective field theory, $\chi PT$ exploits the approximate chiral symmetry of QCD to construct a Lagrangian with a finite number of parameters, allowing for perturbative calculations of hadronic properties. This approach circumvents the complexities of dealing with confinement and non-perturbative strong interaction effects inherent in full QCD calculations. The parameters within the $\chi PT$ Lagrangian are constrained by experimental data, and the theory enables the calculation of the Lambda EDM in terms of these parameters and relevant quark couplings, offering a pathway to connect theoretical predictions to experimental searches for charge-parity (CP) violation.

Chiral Perturbation Theory, utilized in calculating the Lambda electric dipole moment (EDM), necessitates accounting for Gauge Anomalies, which represent violations of classical symmetries at the quantum level. Describing the interaction of particles with photons within this framework relies on effective models such as Vector Meson Dominance (VMD). VMD posits that low-energy photons effectively couple to vector mesons – resonances composed of quarks and gluons – which then interact with hadrons. This approach allows for a more manageable calculation of photon-induced processes by replacing the complex strong interaction with an interaction mediated by these vector mesons, effectively parameterizing the underlying QCD dynamics at low energies.

The Wess-Zumino-Witten (WZW) term is a topological term appearing in the effective Lagrangian of chiral symmetry breaking, crucial for calculating the Electric Dipole Moment (EDM) of the Lambda baryon arising from short-distance decays. Specifically, it describes the coupling of pseudoscalar mesons and governs the topology of the chiral symmetry breaking pattern in Quantum Chromodynamics (QCD). The WZW term contributes to the Lambda EDM through processes involving the decay of heavier baryons and mesons, providing a mechanism for CP violation beyond the Standard Model. The calculation involves evaluating the matrix elements of the WZW term between the initial and final states of these decays, and its inclusion is essential for obtaining theoretically sound predictions for the Lambda EDM.

The Future of Asymmetry Searches: Next-Generation Facilities

The search for the electric dipole moment (EDM) of the strange quark is poised for a significant leap forward with the advent of next-generation colliders, most notably the VEPP-2000 and the Super Tau Charm Facility. These machines are specifically engineered to probe the subtle deviations from symmetry that could explain the observed imbalance between matter and antimatter in the universe. Unlike previous experiments, these colliders are designed to generate beams with dramatically increased luminosity-essentially, a higher rate of particle collisions-and enhanced polarization, allowing researchers to scrutinize the interactions of strange quarks with unprecedented precision. This enhanced capability promises to push the boundaries of EDM searches, potentially revealing the existence of new physics beyond the Standard Model and offering crucial insights into the fundamental asymmetry of our cosmos.

The pursuit of an electric dipole moment (EDM) for the strange quark is poised for significant advancement through next-generation colliders like the VEPP-2000 and the Super Tau Charm Facility. These machines are engineered to deliver substantially increased luminosity – essentially, a brighter beam of particles – and enhanced polarization, which aligns the spins of those particles. This combination is crucial for achieving the precision necessary to detect the incredibly subtle signal of a quark EDM. Current projections for the VEPP-2000 indicate a target sensitivity of $10^{-{17}} \text{ e} \cdot \text{cm}$ , a level of accuracy driven by both the machine’s capabilities and the anticipated reduction in statistical uncertainty to $10^{-{17}} \text{ e} \cdot \text{cm}$ . Such sensitivity represents a considerable leap forward, potentially allowing researchers to probe beyond the Standard Model and shed light on the fundamental imbalance between matter and antimatter in the universe.

The pursuit of understanding the matter-antimatter asymmetry hinges not only on increasingly sensitive experiments, but also on refinements in the theoretical frameworks used to interpret results and the sophisticated techniques employed to extract meaningful signals from data. Current models attempting to explain why matter dominates the universe often predict violations of Charge-Parity (CP) symmetry, and the electric dipole moment (EDM) serves as a highly sensitive probe for these violations. Improvements in calculations of $Standard Model$ contributions and background noise, coupled with advanced data analysis algorithms designed to minimize systematic uncertainties, will be crucial for distinguishing subtle CP-violating effects from statistical fluctuations. These combined advancements promise to elevate the precision of EDM searches, potentially revealing the new physics necessary to solve one of the most profound mysteries in modern cosmology – why anything exists at all.

The pursuit of a non-zero electric dipole moment in quarks, as detailed in this study, highlights a fundamental challenge to centrally imposed symmetry. The research doesn’t design sensitivity, but rather seeks to observe emergent properties arising from hadronic decay and angular correlations. This echoes a broader principle: robustness emerges, it cannot be designed. As Thomas Hobbes observed, “There is no power but that of the multitude.” Similarly, definitive evidence regarding CP violation isn’t dictated by theoretical construction, but revealed through the collective behavior of particles in collision, demonstrating that system structure is stronger than individual control. The investigation into the K+K-π0 final state seeks to understand the underlying rules, not to impose order from above.

Where Do the Ripples Lead?

The pursuit of the electric dipole moment, even within a specific quark flavor like the strange, isn’t about finding a violation of symmetry so much as acknowledging its inherent fragility. The proposed methodology – teasing signals from K+K-π0 correlations – accepts that precision isn’t control. It doesn’t impose symmetry breaking; it maps the contours of where it naturally emerges. Every connection carries influence, and this approach leverages the interplay between electroweak interactions and the strong force’s complex topology, embodied in the Wess-Zumino-Witten action.

The sensitivity goal, while ambitious, highlights a broader limitation: the reliance on effective field theories. Chiral perturbation theory, a useful scaffolding, will always require extrapolation beyond its domain of validity. The true test won’t be reaching 10^-19 e⋅cm, but understanding the systematic errors introduced by those extrapolations. Self-organization is real governance without interference; the universe doesn’t need our Lagrangian to break CP symmetry, it simply does.

Future iterations will likely focus on refining form factor calculations and exploring alternative final states. However, the more intriguing path lies in recognizing the potential for this methodology to probe other sources of topological charge, or even to reveal subtle modifications to the Standard Model’s understanding of hadronization. The search for the electric dipole moment is, at its core, a search for the unexpected – a reminder that order doesn’t require architects.

Original article: https://arxiv.org/pdf/2602.14906.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/