⚛️ phenomenology

A Compatibility Check: Low-Scale Chiral $U(1)_X$ Theories Vs. $(g-2)_e$ Anomaly

This paper demonstrates that three specific low-scale, anomaly-free chiral Abelian extensions of the Standard Model are completely incompatible with the observed electron anomalous magnetic moment ( $(g-2)_e$ ) anomaly when combined with existing experimental constraints.

Original authors: Bibhabasu De

Published 2026-08-10

📖 3 min read🧠 Deep dive

CC BY 4.0

Original authors: Bibhabasu De

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

Imagine the universe as a giant, intricate video game. For decades, the best players have been using a rulebook called the Standard Model to predict how every particle behaves. This rulebook is incredibly accurate, explaining how the tiny building blocks of matter stick together and interact. But just like any good game, there are glitches. Sometimes, the particles don't act quite the way the rulebook says they should. One of the most famous glitches involves the "electron," a tiny particle that spins like a top. Scientists have measured how fast it spins with extreme precision, and the number they get doesn't match the number the rulebook predicts. It's a tiny difference, but in the world of physics, a mismatch this big is like finding a ghost in your living room—it means there's a hidden rule or a secret character in the game that we haven't discovered yet.

To fix these glitches, physicists propose "Beyond the Standard Model" theories. These are like adding new expansion packs to the game, introducing new forces and particles to explain the weird behavior. One popular idea is to add a new, invisible force carrier called a $Z'$ boson. Think of this $Z'$ as a new type of messenger that can talk to electrons but ignores other things. The paper you are about to read investigates a specific, fancy version of this idea where the new force treats the left-spinning and right-spinning versions of particles differently. This is called a "chiral" theory. The big question is: Can this specific new force explain the electron's spin glitch without breaking the rest of the game?

This paper acts like a rigorous quality control inspector for three specific versions of this "chiral $Z'$ " theory. The author, led by Bibhabasu De, took three popular models (labeled BM1, BM2, and BM3) that had previously been suggested as potential solutions to the electron glitch. They ran a massive compatibility check, asking a simple but deadly question: "Can these models explain the electron's weird spin and survive all the other strict rules of the universe?"

The answer, unfortunately for these specific theories, is a hard no. The author found that while these models could theoretically fix the electron's spin problem, doing so requires the new force to be strong enough to break other, well-established rules of physics. Specifically, the models clash with a measurement called the " $\rho$ parameter," which acts like a ruler for the masses of the universe's force-carrying particles. If the models are tuned to fix the electron, the ruler breaks. Furthermore, the author checked the models against data from massive underground detectors (like XENONnT and LZ) that hunt for invisible particles. They found that the "safe zones" where the models might have worked are completely blocked off by these existing experiments.

In short, the paper concludes that these three specific chiral $Z'$ theories are completely ruled out. They cannot simultaneously explain the electron's anomaly and respect the known laws of physics. While this doesn't mean the electron glitch is solved, it does mean that this particular family of solutions is dead. The author suggests that to find a real answer, physicists might need to try different types of models, perhaps ones that treat different particles differently or include even more new particles, but for now, these three specific ideas have been sent back to the drawing board.

Technical Summary: A Compatibility Check of Low-Scale Chiral $U(1)_X$ Theories vs. the $(g-2)_e$ Anomaly

Problem Statement
The Standard Model (SM) remains robust regarding strong and electroweak interactions but fails to address phenomena such as dark matter, neutrino oscillations, and matter-antimatter asymmetry. While vector-like $U(1)_X$ extensions (where left- and right-handed fermions share charges) are well-studied, chiral $U(1)_X$ extensions (where chiral fermions carry different charges) remain less explored. These chiral models require additional fermions to cancel gauge anomalies and non-trivial Higgs transformations to preserve Yukawa invariance, leading to mass mixing between the SM $Z$ boson and a new $Z'$ boson.

Recent experimental updates have highlighted a significant discrepancy in the electron anomalous magnetic moment, $(g-2)_e$ , while the muon anomaly has been ruled out at current precision levels. The central problem addressed in this work is whether the low-scale parameter spaces of three specific, anomaly-free chiral $U(1)_X$ benchmark models (BMs)—previously constrained by neutrino scattering experiments—can simultaneously accommodate the observed $(g-2)_e$ discrepancy without violating existing electroweak precision data.

Methodology
The paper analyzes three benchmark models (BM1, BM2, BM3) derived from general anomaly-free chiral $U(1)_X$ frameworks. The methodology proceeds as follows:

Model Construction: The SM gauge group is extended by a chiral $U(1)_X$ symmetry. Anomaly cancellation conditions (triangle and mixed gauge-gravitational) are solved to determine the $X$ -charges of SM fermions and three additional right-handed SM-singlet fermions ( $\psi_k$ ). An SM-singlet scalar $\Phi$ is introduced to spontaneously break the $U(1)_X$ symmetry independently of the electroweak scale.
Gauge Sector and Mixing: The spontaneous symmetry breaking induces mixing between the SM $Z$ boson and the new $Z'$ boson. The physical mass eigenstates and the mixing angle $\theta_X$ are derived. The deviation of the $\rho$ parameter from its SM value ( $\rho_{SM}=1$ ) is calculated as a function of the gauge coupling $g_X$ and the $Z'$ mass ( $M_{Z'}$ ).
$(g-2)_e$ Calculation: The paper calculates the one-loop BSM corrections to the electron anomalous magnetic moment ( $a_e$ ) arising from $Z$ and $Z'$ exchange. The total correction is defined as $\Delta a_e = a_e^Z + a_e^{Z'} - a_e^{Z_{SM}}$ , subtracting the SM $Z$ contribution to isolate the new physics effect. The calculation utilizes chiral couplings ( $S_L, S_R$ ) derived from the model's charge assignments.
Constraint Analysis: The allowed parameter space ( $M_{Z'}$ $M_{Z^{'}}$ vs. $g_X$ $g_{X}$ ) is tested against three sets of constraints:
- Electroweak precision data (specifically the $\rho$ parameter).
- Existing neutrino scattering bounds (E $\nu$ ES and CE $\nu$ NS) from experiments like TEXONO, COHERENT, XENONnT, LZ, and PandaX-4T.
- The observed discrepancy in the electron anomalous magnetic moment, specifically using the Rubidium-87 based SM prediction which shows a $2.4\sigma$ deviation ( $\Delta a_e^{Rb}$ ), as the Cesium-133 result ( $1.6\sigma$ ) is considered less significant.

Key Contributions and Results

Anomaly-Free Benchmark Models: The study utilizes three specific models (BM1, BM2, BM3) corresponding to different solutions of the anomaly cancellation equations, ensuring the models are theoretically consistent and renormalizable.
Decoupling Behavior: The analysis confirms that the BSM contribution to $(g-2)_e$ exhibits a decoupling nature, decreasing as the new physics scale ( $M_{Z'}$ ) increases. The contribution is dominated by the $Z'$ exchange due to significant cancellation between the $Z$ and SM $Z$ contributions.
Positive Correction: For the considered models, the vector and axial-vector couplings result in a positive correction to $a_e$ across the entire parameter space. Consequently, the models can only address the discrepancy if the experimental value is higher than the SM prediction, specifically aligning with the Rubidium-87 result ( $\Delta a_e^{Rb}$ ), which is used to derive meaningful constraints.
Exclusion Limits:
- Electroweak Constraints: The $\rho$ parameter imposes strict upper limits on $g_X$ (e.g., $g_X > 1.82 \times 10^{-3}$ is excluded for BM1).
- $(g-2)_e$ Compatibility: To satisfy the observed $(g-2)_e$ anomaly, the models require specific combinations of $g_X$ and $M_{Z'}$ that push the parameter space into regions already excluded by the $\rho$ parameter or neutrino scattering experiments.
- Comprehensive Exclusion: When the constraints from neutrino scattering experiments (DARWIN, XENONnT, etc.) are combined with the $(g-2)_e$ requirement, no viable parameter space remains. The regions capable of explaining the electron anomaly are completely ruled out by existing detector bounds.

Significance and Claims
The paper claims that the considered flavor-blind chiral $U(1)_X$ models, when tested against the $(g-2)_e$ anomaly in complementarity with existing neutrino scattering data, are completely ruled out as self-sufficient New Physics theories.

The author emphasizes that while these models were previously constrained by neutrino experiments, the inclusion of the $(g-2)_e$ anomaly provides a "stringent exclusion limit" that leaves no surviving parameter space. The work concludes that these specific chiral extensions cannot simultaneously satisfy the electron magnetic moment discrepancy and current experimental bounds. The author modestly suggests that future viability might only be possible through an augmented particle spectrum, further extension of the gauge symmetry, or by adopting flavor-specific chiral theories, none of which are explored in the current analysis.

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