Another Odd Thing About Unparticle Physics

TL;DR

This paper investigates how a scale-invariant unparticle sector leaves imprint through unusual interference with Standard Model amplitudes in $e^+e^-\to\mu^+\mu^-$. By formulating the unparticle propagator with a nontrivial phase $\phi_{d_{\mathcal{U}}}=-(d_{\mathcal{U}}-1)\pi$ and matching Banks-Zaks operators to unparticle operators in an effective field theory, the author computes leading-order interference terms arising from vector and axial-vector couplings $c_{V\mathcal{U}}$ and $c_{A\mathcal{U}}$. The results show that the interference depends strongly on the scaling dimension $d_{\mathcal{U}}$ (especially in the range $1<d_{\mathcal{U}}<2$), producing energy-dependent patterns and a notable case at $d_{\mathcal{U}}=3/2$ where interference is purely with the imaginary part of the SM amplitude. These findings suggest observable deviations in cross sections and asymmetries across collider energies, offering a framework to probe unparticle physics through interference without requiring a detailed microscopic unparticle picture.

Abstract

The peculiar propagator of scale invariant unparticles has phases that produce unusual patterns of interference with standard model processes. We illustrate some of these effects in $e^+e^-\toμ^+μ^-$.

Figures (8)

• Figure 1: The fractional change in total cross-section for $e^+e^-\to\mu^+\mu^-$ versus $\sqrt{s}$ for $d_{\mathcal{U}}=1.1$, $1.3$, $1.5$, $1.7$ and $1.9$ for non-zero $c_{A\mathcal{U}}$ and $c_{V\mathcal{U}}=0$. The dash-length increases with $d_{\mathcal{U}}$.
• Figure 2: The fractional change in total cross-section for $e^+e^-\to\mu^+\mu^-$ versus $\sqrt{s}$ for $d_{\mathcal{U}}=1.1$, $1.3$, $1.5$, $1.7$ and $1.9$ for non-zero $c_{A\mathcal{U}}$ and $c_{V\mathcal{U}}=0$. The dash-length increases with $d_{\mathcal{U}}$. Note the different scales compared to figure \ref{['fig-1']}.
• Figure 3: The fractional change in total cross-section for $e^+e^-\to\mu^+\mu^-$ versus $\sqrt{s}$ for $d_{\mathcal{U}}=1.48$, $1.49$, $1.5$, $1.51$ and $1.52$ for non-zero $c_{A\mathcal{U}}$ and $c_{V\mathcal{U}}=0$. The dash-length increases with $d_{\mathcal{U}}$. Note the different vertical scale compared to figure \ref{['fig-1']}.
• Figure 4: The fractional change in total cross-section for $e^+e^-\to\mu^+\mu^-$ versus $\sqrt{s}$ for $d_{\mathcal{U}}=1.1$, $1.3$, $1.5$, $1.7$ and $1.9$ for non-zero $c_{V\mathcal{U}}$ and $c_{A\mathcal{U}}=0$. The dash-length increases with $d_{\mathcal{U}}$.
• Figure 5: The change in the front-back asymmetry for $e^+e^-\to\mu^+\mu^-$ versus $\sqrt{s}$ for $d_{\mathcal{U}}=1.1$, $1.3$, $1.5$, $1.7$ and $1.9$ for non-zero $c_{A\mathcal{U}}$ and $c_{V\mathcal{U}}=0$. The dash-length increases with $d_{\mathcal{U}}$.