[Paper Review] New Physics Contributions to the Muon Anomalous Magnetic Moment

Farinaldo S. Queiroz, William Shepherd|arXiv (Cornell University)|Mar 10, 2014

Particle physics theoretical and experimental studies18 citations

TL;DR

This paper analyzes one-loop contributions from simplified models of new physics to the muon anomalous magnetic moment $a_\mu$, providing analytic formulas and a Mathematica code for computing these contributions. It identifies viable new particles—such as neutral scalars at 0.3–2 TeV and doubly charged scalars at 4 TeV—that can explain the observed $g-2$ discrepancy with unit couplings, while deriving stringent $1\sigma$ lower bounds on masses assuming the anomaly is resolved by other means.

ABSTRACT

We consider the contributions of individual new particles to the anomalous magnetic moment of the muon, utilizing the generic framework of simplified models. We also present analytic results for all possible one-loop contributions, allowing easy application of these results for more complete models which predict more than one particle capable of correcting the muon magnetic moment. Additionally, we provide a Mathematica code to allow the reader straightforwardly compute any 1-loop contribution. Furthermore, we derive bounds on each new particle considered, assuming either the absence of other significant contributions to $a_\mu$ or that the anomaly has been resolved by some other mechanism. The simplified models we consider are constructed without the requirement of $SU(2)_L$ invariance, but appropriate chiral coupling choices are also considered. In summary, we found the following particles capable of explaining the current discrepancy, assuming unit couplings: $2$~TeV ($0.3$~TeV) neutral scalar with pure scalar (chiral) couplings, $4$~TeV doubly charged scalar with pure pseudoscalar coupling, $0.3-1$~TeV neutral vector boson depending on what couplings are used (vector, axial, or mixed), $0.5-1$~TeV singly-charged vector boson depending on which couplings are chosen, and $3$~TeV doubly-charged vector-coupled bosons. We also derive the following $1\sigma$ lower bounds on new particle masses assuming unit couplings and that the experimental anomaly has been otherwise resolved: a doubly charged pseudo-scalar must be heavier than $7$~TeV, a neutral scalar than $3$~TeV, a vector-coupled new neutral boson $600$~GeV, an axial-coupled neutral boson $1.5$~TeV, a singly-charged vector-coupled $W^\prime$ $1$~TeV, a doubly-charged vector-coupled boson $5$~TeV, scalar leptoquarks $10$~TeV, and vector leptoquarks $10$~TeV.

Motivation & Objective

• To systematically evaluate all possible one-loop contributions from new particles to the muon anomalous magnetic moment $a_\mu$ using simplified models.
• To provide analytic expressions for all 1-loop diagrams involving new particles, enabling direct application to more complex models.
• To derive model-independent lower bounds on new particle masses assuming the $a_\mu$ anomaly is resolved by other mechanisms or absent.
• To explore the viability of various new particles—scalar, vector, and leptoquark states—with different couplings (scalar, pseudoscalar, vector, axial, chiral) in explaining the current $g-2$ discrepancy.

Proposed method

• Constructs a generic framework of simplified models without requiring $SU(2)_L$ invariance, allowing flexible new particle content.
• Derives analytic expressions for all one-loop contributions to $a_\mu$ from scalar, vector, and leptoquark states with various couplings.
• Uses unit coupling assumptions to estimate the mass scales of new particles that can explain the observed $a_\mu$ discrepancy.
• Applies $1\sigma$ statistical bounds to derive lower limits on new particle masses under the assumption that the anomaly is resolved by other means.
• Develops a Mathematica code to compute any 1-loop contribution efficiently, facilitating application to realistic models.
• Considers chiral and non-chiral coupling structures to assess the impact of fermion helicity and coupling type on $a_\mu$.

Experimental results

Research questions

• RQ1 Which new particles in simplified models can explain the current discrepancy in the muon anomalous magnetic moment with unit couplings?
• RQ2 What are the analytic expressions for all one-loop contributions to $a_\mu$ from new scalar, vector, and leptoquark states with various coupling types?
• RQ3 What are the $1\sigma$ lower bounds on the masses of new particles if the $a_\mu$ anomaly is resolved by some other mechanism?
• RQ4 How do different coupling structures—scalar, pseudoscalar, vector, axial, chiral—affect the size and sign of $a_\mu$ contributions?
• RQ5 What is the minimal mass scale of new particles required to account for the $g-2$ anomaly under conservative assumptions?

Key findings

• A neutral scalar with pure scalar coupling can explain the $a_\mu$ discrepancy if its mass is around 2 TeV, while a chiral-coupled scalar requires only 0.3 TeV.
• A doubly charged scalar with pure pseudoscalar coupling can account for the anomaly if its mass is approximately 4 TeV.
• Neutral vector bosons with vector, axial, or mixed couplings can explain the anomaly for masses between 0.3 and 1 TeV.
• Singly-charged vector bosons with vector coupling can explain the anomaly at masses of 0.5–1 TeV.
• Doubly-charged vector-coupled bosons require a mass of about 3 TeV to resolve the discrepancy.
• The $1\sigma$ lower bounds on new particle masses—assuming the anomaly is resolved by other means—include: 7 TeV for doubly charged pseudo-scalars, 3 TeV for neutral scalars, 600 GeV for vector-coupled neutral bosons, 1.5 TeV for axial-coupled neutral bosons, 1 TeV for singly-charged vector-coupled $W'$, 5 TeV for doubly-charged vector-coupled bosons, and 10 TeV for both scalar and vector leptoquarks.