[Paper Review] A Proposal to Measure Photon-Photon Scattering

Takehisa Fujita, Naohiro Kanda|arXiv (Cornell University)|May 30, 2011

Advanced Optical Sensing Technologies1 references4 citations

TL;DR

This paper proposes a novel experimental approach to measure photon-photon scattering at low energies, arguing that the $γ + \gamma \rightarrow e^+ + e^-$ process should be measured first as a benchmark for initial state control. It shows the elastic $γ\gamma \rightarrow \gamma\gamma$ cross section is $\sim 10^{37}$ times larger than the Heisenberg-Euler prediction, making it potentially observable if initial collision conditions are mastered.

ABSTRACT

We discuss a possibility to measure the photon-photon scattering cross section at low energy in a theoretical standpoint. The cross section of photon-photon scattering at low energy can be written as $\displaystyle{{dσ\over dΩ} \simeq {α^4\over (12π)^2 ω^2} (3+2\cos^2θ+\cos^4θ)}$ with $ω$ the energy of photon. The magnitude of the cross section at $ω\simeq 1$ eV should be $10^{37}$ times larger than the prediction of Heisenberg and Euler who calculated the photon scattering by the classical picture of field theory. Due to a difficulty of the initial condition of photon-photon reaction process, we propose to first measure $γ+γ ightarrow e^++e^- $ reaction at a few MeV before measuring $γ+γ ightarrow γ+γ$ elastic scattering.

Motivation & Objective

• To address the long-standing experimental challenge of measuring photon-photon scattering due to the difficulty of achieving controlled head-on photon collisions.
• To argue that the $γ + \gamma \rightarrow e^+ + e^-$ process is a necessary experimental precursor to measuring elastic $γ\gamma \rightarrow \gamma\gamma$ scattering.
• To demonstrate that the quantum field theory prediction for $γ\gamma \rightarrow \gamma\gamma$ cross section is vastly larger than the classical Heisenberg-Euler result at low energies.
• To provide a quantitative framework for estimating cross sections in the MeV energy range, enabling experimental planning.

Proposed method

• Proposes using $γ + \gamma \rightarrow e^+ + e^-$ as a control experiment to verify initial state conditions before attempting elastic $γ\gamma \rightarrow \gamma\gamma$ scattering.
• Uses quantum field theory to derive the differential cross section $d\sigma/d\Omega \simeq \alpha^4 / (12\pi)^2 \omega^2 (3 + 2\cos^2\theta + \cos^4\theta)$ for low-energy $γ\gamma \rightarrow \gamma\gamma$ scattering.
• Compares the predicted quantum cross section with the classical Heisenberg-Euler result, showing a $10^{37}$-fold enhancement at $\omega \sim 1$ eV.
• Performs a naive energy extrapolation of $e^+e^-$ scattering cross sections to estimate the scale of $γ\gamma \rightarrow \gamma\gamma$ cross sections at $\sim$2 MeV.
• Analyzes the kinematic and dynamical constraints of photon-photon collisions, emphasizing the need for mechanical focusing due to photons' inability to be at rest.
• Argues that the $γ\gamma \rightarrow e^+e^-$ process is of comparable magnitude to Compton scattering at a few MeV, making it a viable experimental monitor.

Experimental results

Research questions

• RQ1 Why has photon-photon scattering not been experimentally observed despite theoretical predictions?
• RQ2 What is the correct low-energy cross section for $γ\gamma \rightarrow \gamma\gamma$ scattering according to quantum field theory?
• RQ3 Can the $γ + \gamma \rightarrow e^+ + e^-$ process serve as a practical benchmark for validating the initial conditions of a photon-photon scattering experiment?
• RQ4 How does the quantum field theory prediction for $γ\gamma \rightarrow \gamma\gamma$ compare to the classical Heisenberg-Euler result?
• RQ5 What are the experimental challenges in achieving head-on photon-photon collisions, and how can they be mitigated?

Key findings

• The differential cross section for $γ\gamma \rightarrow \gamma\gamma$ scattering at low energy is predicted to be $d\sigma/d\Omega \simeq \alpha^4 / (12\pi)^2 \omega^2 (3 + 2\cos^2\theta + \cos^4\theta)$, which is independent of the electron mass in the low-energy limit.
• At $\omega \sim 1$ eV, the predicted cross section is $10^{37}$ times larger than the Heisenberg-Euler classical result, indicating a dramatic enhancement from quantum effects.
• The cross section for $γ\gamma \rightarrow e^+ + e^-$ at a few MeV is comparable in magnitude to Compton scattering, making it a feasible experimental monitor.
• The estimated differential cross section for $γ\gamma \rightarrow \gamma\gamma$ at $\sim$2 MeV is $\sim 6 \times 10^{-7}$ mb/st, which is smaller than $e^+e^-$ elastic scattering by 7 orders of magnitude but still potentially measurable.
• The main experimental difficulty lies in achieving the precise initial conditions for head-on photon-photon collisions, as photons cannot be at rest and require mechanical focusing.
• The paper concludes that observing $γ\gamma \rightarrow \gamma\gamma$ scattering is feasible once the $γ + \gamma \rightarrow e^+ + e^-$ process is successfully demonstrated as a control experiment.