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LHC Shines on Positivity

Zhen Liu, Kun-Feng Lyu, Tong Arthur Wu

TL;DR

The paper investigates testing positivity bounds of effective field theory at hadron colliders through dimension-8 diphoton operators. It identifies two operator classes—quark-portal and gluon–photon—and derives helicity amplitudes, applying forward-limit positivity to constrain sign combinations of Wilson coefficients. By exploiting interference with the SM in $q\bar{q}\to \gamma\gamma$ and $gg\to \gamma\gamma$, and analyzing the 2D distribution $\mathrm{d}\sigma/(\mathrm{d}\sqrt{\hat{s}}\,\mathrm{d}\Delta y)$ via a binned $\chi^2$ fit, the study projects 95% C.L. bounds for HL-LHC and a future 100 TeV collider on the effective scales $\Lambda/(C^{(8)})^{1/4}$, reaching ~$2$ TeV and ~$5$ TeV respectively (with variations depending on operator mixing). The results show that the diphoton channel can test positivity up to multi-TeV scales and yield strong, principle-driven constraints that complement SMEFT fits. This work thus provides a direct collider probe of fundamental positivity principles in quantum field theory and demonstrates how higher-dimensional operators in the diphoton sector encode the underlying UV physics.

Abstract

We show that hadron colliders have an excellent reach for positivity tests on a class of diphoton operators. Due to the helicity selection rules, the relevant dimension-6 operators either do not contribute or are highly constrained by other experimental observables. We show, for the first time, that the LHC can probe the positivity of the dimension-8 operators involving colored particles. The kinematic differential distributions of the diphoton final states are exploited to perform the $χ^2$ analysis. Through a global fit, the effective scale for these operators can be inclusively probed up to around 2 TeV at HL-LHC and over 5 TeV at future 100 TeV FCC-hh at 95% C.L., providing a powerful test of the positivity bounds up to multi-TeV scale.

LHC Shines on Positivity

TL;DR

The paper investigates testing positivity bounds of effective field theory at hadron colliders through dimension-8 diphoton operators. It identifies two operator classes—quark-portal and gluon–photon—and derives helicity amplitudes, applying forward-limit positivity to constrain sign combinations of Wilson coefficients. By exploiting interference with the SM in and , and analyzing the 2D distribution via a binned fit, the study projects 95% C.L. bounds for HL-LHC and a future 100 TeV collider on the effective scales , reaching ~ TeV and ~ TeV respectively (with variations depending on operator mixing). The results show that the diphoton channel can test positivity up to multi-TeV scales and yield strong, principle-driven constraints that complement SMEFT fits. This work thus provides a direct collider probe of fundamental positivity principles in quantum field theory and demonstrates how higher-dimensional operators in the diphoton sector encode the underlying UV physics.

Abstract

We show that hadron colliders have an excellent reach for positivity tests on a class of diphoton operators. Due to the helicity selection rules, the relevant dimension-6 operators either do not contribute or are highly constrained by other experimental observables. We show, for the first time, that the LHC can probe the positivity of the dimension-8 operators involving colored particles. The kinematic differential distributions of the diphoton final states are exploited to perform the analysis. Through a global fit, the effective scale for these operators can be inclusively probed up to around 2 TeV at HL-LHC and over 5 TeV at future 100 TeV FCC-hh at 95% C.L., providing a powerful test of the positivity bounds up to multi-TeV scale.

Paper Structure

This paper contains 8 sections, 9 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Di-photon Processes
  3. Dimension-6 Operators
  4. Basic set of Dimension-8 Operators
  5. $q\bar{q}\rightarrow \gamma\gamma$ processes
  6. $g g \rightarrow \gamma\gamma$ process
  7. Probing the positivity bound at LHC
  8. Summary and Outlook

Figures (4)

  • Figure 1: Top: invariant mass distribution of the SM background and the interference signal from quark‑photon operators. Bottom: normalized $\Delta y$ distribution. Curves labelled $O_u$ and $O_d$ show the interference term with only the up‑ or down‑quark operator switched on with $C_q=1$ and $\Lambda=2\,\mathrm{TeV}$.
  • Figure 2: Top: invariant mass distribution of the SM background and the interference signal from gluon‑photon operators. Bottom: normalized $\Delta y$ distribution. Curves labelled $O_{g,i}$ show the interference term with the corresponding $C_{g,i}=1$ and $\Lambda=2\,$TeV.
  • Figure 3: The 95% C.L. reach for the effective scale $\Lambda/\left(C_i \right)^{1/4}$ of different operators. Light‑colored bars: individual operator bounds (one operator turned on at a time). Darker bars: marginalized projection with five operators varied simultaneously. Results assume an integrated luminosity of $L=3\,\mathrm{ab}^{-1}$ at 14 TeV and 100 TeV.
  • Figure 4: Projected 95% C.L. contours in representative 2D planes of Wilson coefficients at the 14 TeV HL‑LHC. The blue contour is obtained when five coefficients (all except $C_d$) are floated and the orange contour shows the two‑parameter fit (only the two indicated coefficients are nonzero).