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Unitarity bounds on charged/neutral state mass ratio

Wei-Ming Chen, Yu-tin Huang, Toshifumi Noumi, Congkao Wen

TL;DR

This work studies how unitarity and analyticity constraints from quantum gravity shape the low-energy spectrum in three dimensions. By deriving an infinite set of forward-limit positivity (Hankel) bounds on EFT coefficients, the authors show that a light charged state with $|z|>1$ cannot exist in isolation and must be accompanied by lighter states, typically neutral. Introducing neutral or additional light states modifies the bounds, potentially permitting large $|z|$ only when accompanied by sufficiently light neutral partners; this yields a quantitative relation $|z|\le a_{\text{symp}}(\beta)$ that grows with the neutral-to-charged mass ratio $\beta$. The results connect UV completion of quantum gravity to the pattern of light states and hint at bounds that could constrain neutrino masses in the 3D SM scenario.

Abstract

In this letter, we study the implications of unitary completion of quantum gravity on the low energy spectrums, through an infinite set of unitarity bounds on the forward-limit scattering amplitudes. In three dimensions, we find that light states with charge-to-mass ratio $z$ greater than $1$ can only be consistent if there exists other light states, preferably neutral. Applied to the compactification of the Standard Model, where the low energy couplings are dominated by the electron with $|z|\sim 10^{22}$, this provides a novel understanding of the need for light neutrinos.

Unitarity bounds on charged/neutral state mass ratio

TL;DR

This work studies how unitarity and analyticity constraints from quantum gravity shape the low-energy spectrum in three dimensions. By deriving an infinite set of forward-limit positivity (Hankel) bounds on EFT coefficients, the authors show that a light charged state with cannot exist in isolation and must be accompanied by lighter states, typically neutral. Introducing neutral or additional light states modifies the bounds, potentially permitting large only when accompanied by sufficiently light neutral partners; this yields a quantitative relation that grows with the neutral-to-charged mass ratio . The results connect UV completion of quantum gravity to the pattern of light states and hint at bounds that could constrain neutrino masses in the 3D SM scenario.

Abstract

In this letter, we study the implications of unitary completion of quantum gravity on the low energy spectrums, through an infinite set of unitarity bounds on the forward-limit scattering amplitudes. In three dimensions, we find that light states with charge-to-mass ratio greater than can only be consistent if there exists other light states, preferably neutral. Applied to the compactification of the Standard Model, where the low energy couplings are dominated by the electron with , this provides a novel understanding of the need for light neutrinos.

Paper Structure

This paper contains 7 sections, 36 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The WGC from weakly interacting matter
  3. Unitarity bounds on the forward amplitude
  4. Constraints on light states
  5. The addition of light state $\frac{m_e}{m_0}>1$
  6. Outlook
  7. Acknowledgements

Figures (3)

  • Figure 1: The plot of $b$ with respect to different values of charged to neutral state mass ratio $\beta$, with $\beta=(0,\frac{1}{4},\frac{5}{4},\frac{9}{4},\frac{13}{4})$ from top to bottom. Note that $\beta=0$ corresponds to the case where one has an isolated charged state.
  • Figure 2: The plot of $a$ with respect to different values of charged to neutral state mass ratio $\beta$, increasing from bottom to top. We see that at sufficiently large $n$ it asymptotes to a fixed value, denoted as $a_{asymp}(\beta)$.
  • Figure 3: the cut diagrams for the extraction of triangle and bubble coefficients: (a) triple-cut (b) double-cut. All exposed lines are put on-shell.