⚛️ phenomenology

Electric Dipole Moments as Precision Probes of CP-Violating Top-Quark Interactions in SMEFT

This paper utilizes the Standard Model Effective Field Theory (SMEFT) to demonstrate how current and future electric dipole moment measurements, particularly of the proton, provide highly sensitive and complementary constraints on CP-violating top-quark interactions by accounting for complex multi-loop effects and renormalization-group evolution.

Original authors: Subhajit Kala, Soumitra Nandi, Sonakshi Saha

Published 2026-09-30

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Subhajit Kala, Soumitra Nandi, Sonakshi Saha

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The universe is filled with matter, yet it should not exist. According to our best understanding of physics, the Big Bang should have created equal amounts of matter and antimatter, which would have immediately annihilated each other, leaving behind only empty light. The fact that we are here, made of solid stuff, implies that a subtle imbalance tipped the scales in favor of matter. To explain this, physicists look for a specific kind of symmetry breaking called CP violation, a process where the laws of physics treat matter and antimatter slightly differently. While the current standard model of particle physics includes a mechanism for this, it is far too weak to account for the vast amount of matter we see today. This gap suggests that new, undiscovered forces or particles are at work, hiding in the interactions of the heaviest known particle, the top quark.

Because these new forces are likely too heavy to be created directly in current particle colliders, scientists must look for their fingerprints in low-energy experiments. One of the most sensitive ways to find them is by measuring the electric dipole moment of particles. Imagine a spinning particle like a tiny magnet; if it also has a separation of positive and negative charge along its axis of spin, it possesses an electric dipole moment. In the standard model, this value is so incredibly small that it is effectively zero. If scientists were to measure a non-zero value, it would be a smoking gun for new physics. Researchers recently performed a comprehensive analysis to see how the top quark's interactions might generate these tiny moments in other particles, using a vast array of experimental data to map out where new physics might be hiding.

The team, working from the Indian Institute of Technology Guwahati, focused on the top quark because of its unique connection to the mechanism that gives particles mass. They asked a simple but profound question: if the top quark interacts with other particles in ways that violate the symmetry between matter and antimatter, how would those effects ripple down to influence the electric dipole moments of electrons, protons, and neutrons? To answer this, they did not just look at one type of experiment. Instead, they built a complete theoretical bridge connecting the high-energy world of the top quark to the low-energy world of precision measurements. This bridge involved calculating how quantum effects at the highest energy scales evolve as they move down to the energy levels where experiments actually take place, accounting for complex interactions that occur at multiple stages.

Their analysis revealed a powerful division of labor between different types of experiments. The most precise measurements to date come from experiments tracking the electric dipole moment of the electron. These experiments, which use heavy molecules to amplify tiny signals, have placed incredibly tight limits on certain types of top quark interactions. Specifically, the electron's behavior is exquisitely sensitive to how the top quark couples to the electromagnetic field and the Higgs boson. The researchers found that current electron measurements already rule out a vast range of possible new physics scenarios, pushing the limits of these interactions to levels that are billions of times smaller than what we can produce in particle accelerators.

However, the electron is not the whole story. The team discovered that other experiments, which measure the electric dipole moments of neutrons and protons, or the moments of heavy atoms like mercury and radium, are sensitive to different kinds of top quark interactions. While the electron is a master detective for electromagnetic couplings, the neutron and proton are uniquely sensitive to interactions involving the strong nuclear force. The researchers showed that if new physics involves the top quark interacting with gluons—the particles that carry the strong force—these effects would be invisible to the electron but would leave a clear, measurable signature in the neutron. This means that relying on just one type of experiment would leave large gaps in our understanding; only by combining data from leptons, nucleons, and atoms can we get a complete picture.

A significant portion of their work involved calculating how these effects change as they travel from the high-energy scale of the top quark down to the scale of the neutron. They found that some interactions, which might seem weak at first glance, become much stronger due to a process called renormalization group evolution, where quantum effects accumulate over different energy scales. They also identified specific pathways where the top quark's influence is transmitted through intermediate particles, creating a chain of effects that eventually alters the properties of the neutron. By including these complex, multi-step processes, they were able to show that future experiments, particularly those aiming to measure the proton's electric dipole moment with high precision, could improve our constraints on these interactions by orders of magnitude.

The study also looked at scenarios where the top quark interacts with lighter quarks in ways that change their flavor, a process known as flavor violation. In these cases, the researchers found that experiments are not sensitive to a single interaction strength but rather to the product of two different couplings. They demonstrated that current data already places severe limits on these combinations, effectively closing the door on many theoretical models that proposed such interactions. Furthermore, they extended their analysis to consider even more complex, higher-dimensional interactions that might arise from theories beyond the standard model. They showed that the precision of modern electric dipole moment experiments is so high that it can already probe these exotic, higher-order effects, providing a window into physics that is far beyond the reach of direct particle collisions.

Ultimately, this work provides a unified map of how the top quark could be the source of the universe's matter-antimatter imbalance. It demonstrates that the search for new physics is not a single hunt but a coordinated effort across many different laboratories and particle types. The electron, the neutron, and heavy atoms each act as a different kind of sensor, tuned to detect specific types of symmetry breaking. The researchers concluded that while current limits are already formidable, the next generation of experiments holds the promise of either discovering these new interactions or pushing the boundaries of the standard model even further. By systematically connecting the heavy top quark to the lightest particles, they have shown that the smallest measurements in the lab can reveal the deepest secrets of the cosmos.

Technical Summary: Electric Dipole Moments as Precision Probes of CP-Violating Top-Quark Interactions in SMEFT

Problem Statement
The observed matter-antimatter asymmetry of the Universe requires sources of CP violation beyond those provided by the Standard Model (SM) Cabibbo-Kobayashi-Maskawa (CKM) matrix. The top quark, due to its large mass and connection to electroweak symmetry breaking, is a prime candidate for hosting new CP-violating interactions. While previous phenomenological studies have explored specific classes of top-quark interactions (e.g., flavor-conserving dipole or Yukawa couplings) using low-energy Electric Dipole Moment (EDM) observables, a systematic framework incorporating the full range of EDM measurements and the complete chain of low-energy operators induced by top-quark interactions has been lacking. The challenge lies in consistently connecting high-energy CP-violating top-quark interactions in the Standard Model Effective Field Theory (SMEFT) to low-energy EDM observables, accounting for the complex interplay of renormalization-group evolution (RGE), operator mixing, and threshold effects.

Methodology
The authors perform a comprehensive analysis within the SMEFT framework, truncating the expansion at dimension-six. They systematically categorize all dimension-six operators involving the top quark, including flavor-conserving neutral currents, flavor-violating charged and neutral currents, and relevant four-fermion and dipole interactions.

The core methodology involves a multi-scale evolution and matching procedure connecting the New Physics (NP) scale ( $\Lambda_{NP} = 1$ TeV) to the hadronic scale ( $\mu_{had} \approx 2$ GeV):

SMEFT Running: The Wilson coefficients (WCs) are evolved from $\Lambda_{NP}$ to the electroweak scale ( $\mu_{EW}$ ) using leading-logarithmic (LL) RGEs, incorporating the anomalous dimension matrices for SMEFT operators.
Electroweak Matching: At $\mu_{EW}$ , heavy SM degrees of freedom (top, Higgs, $W$ , $Z$ ) are integrated out. The authors perform matching onto the Weak Effective Theory (WET)/Low-Energy Effective Theory (LEFT) operators, including contributions up to two-loop order. This includes finite Barr-Zee diagrams and sequential one-loop effects.
WET Running and Thresholds: Below $\mu_{EW}$ , operators are evolved to $\mu_{had}$ . This stage incorporates QCD corrections, heavy-quark (charm, bottom) threshold corrections, and the mixing of heavy-quark chromoelectric dipole moments (CEDMs) into the Weinberg three-gluon operator and light-quark EDMs/CEDMs.
Hadronic Matching: Finally, the low-energy WET coefficients are matched to physical observables, including lepton EDMs ( $d_e, d_\mu, d_\tau$ ), nucleon EDMs ( $d_n, d_p$ ), CP-odd pion-nucleon couplings ( $\bar{g}_0, \bar{g}_1$ ), and diamagnetic atomic EDMs ( $^{199}\text{Hg}, ^{129}\text{Xe}, ^{171}\text{Yb}, ^{225}\text{Ra}$ ).

The analysis considers both flavor-conserving ( $p=r=3$ ) and flavor-violating ( $p \neq r$ ) scenarios, utilizing an "up-aligned" basis to minimize explicit CKM dependence in top-quark interactions.

Key Contributions

Systematic Mapping: The paper provides the first systematic and essentially complete mapping between the full set of CP-violating top-quark SMEFT interactions and low-energy EDM measurements.
New Calculations: While some specific contributions (e.g., one-loop $C_{uG}^{33}$ to hadronic EDMs) exist in literature, the authors perform new calculations for the leading EDM contributions associated with a broad class of flavor-violating top-quark operators (dipole, Higgs-current, and Yukawa interactions) and determine the loop orders at which they enter.
Sequential Mechanisms: The work highlights and quantifies the importance of sequential one-loop effects induced by RGE. For instance, it demonstrates how certain operators (e.g., $O_{lequ}^{(1)}$ ) contribute to EDMs not through direct matching but via mixing into other operators followed by subsequent matching, effectively acting as two-loop contributions with logarithmic enhancements.
Complementarity Analysis: The study explicitly quantifies the complementarity between leptonic (electron, muon, tau) and hadronic (neutron, proton, atomic) EDMs in constraining different operator structures.

Results
The authors derive constraints on the imaginary parts of the SMEFT Wilson coefficients at $\Lambda = 1$ TeV using current experimental limits and projected future sensitivities:

Leptonic EDMs: The electron EDM ( $d_e$ ) provides the strongest constraints on flavor-conserving electroweak dipole operators ( $C_{uB}^{33}, C_{uW}^{33}$ ) and semileptonic operators ( $C_{lequ}^{(3)}$ ), reaching sensitivities of $O(10^{-12})$ TeV $^{-2}$ for semileptonic tensor operators. These constraints are significantly enhanced by double-logarithmic RGE effects.
Hadronic EDMs: Hadronic observables dominate the sensitivity to operators generating quark EDMs, CEDMs, and the Weinberg operator. The top chromodipole operator ( $C_{uG}^{33}$ ) is primarily constrained by the neutron EDM via the Weinberg operator ( $O(10^{-3})$ TeV $^{-2}$ ). Charged-current dipole operators ( $C_{dW}^{13}$ ) are tightly constrained by the pion-nucleon coupling $\bar{g}_1$ ( $O(10^{-7})$ TeV $^{-2}$ ).
Flavor-Violating Interactions: For flavor-changing neutral currents (FCNC), EDMs constrain products of couplings rather than individual coefficients. Products of opposite-chirality $tuX$ couplings are constrained to $O(10^{-8}-10^{-7})$ , while $tuH $–$ tuY$ combinations are constrained to $O(10^{-5}-10^{-4})$ .
Future Projections: The authors show that future proton EDM searches ( $d_p \sim 10^{-29}$ e cm) could significantly strengthen constraints on several CP-violating top-quark interactions, particularly those mediated by the Weinberg operator, potentially improving bounds by one to two orders of magnitude compared to current Barr-Zee limits.
Dimension-Eight Extension: The analysis is extended to dimension-eight SMEFT operators, demonstrating that current EDM precision can probe these higher-dimensional interactions, with the electron EDM providing the strongest bounds on semileptonic and electroweak dipole structures.

Significance
The paper claims that its primary significance lies in providing a unified, comprehensive assessment of the indirect sensitivity of EDM observables to the CP-violating top-quark sector. By incorporating the complete chain of quantum effects—from high-scale matching to low-energy hadronic physics—the study demonstrates that leptonic and hadronic EDMs are highly complementary. Leptonic EDMs are most sensitive to operators generating leptonic dipoles via Barr-Zee or RGE mixing, while hadronic EDMs are essential for probing gluonic sources of CP violation (Weinberg operator) and quark CEDMs. The work establishes that future precision EDM experiments, particularly proton EDM searches, will be crucial for exploring previously uncharted regions of the SMEFT parameter space related to top-quark CP violation.

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