Impact of QED backgrounds on light-by-light scattering measurements at $$e^+e^-$$ and $$e^-e^-$$ colliders

Abstract The process of elastic scattering of photons ( $$\gamma \gamma \rightarrow \gamma \gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>γ</mml:mi> <mml:mi>γ</mml:mi> <mml:mo>→</mml:mo> <mml:mi>γ</mml:mi> <mml:mi>γ</mml:mi> </mml:mrow> </mml:math> , light-by-light scattering) has attracted significant interest in recent years as a loop-induced process sensitive to all charged particles. To date, this process has been studied through Delbrück scattering, photon splitting in the nuclear Coulomb field, and ultra-peripheral heavy-ion collisions at the LHC. Future precision measurements are anticipated at high-luminosity $$e^+e^-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>-</mml:mo> </mml:msup> </mml:mrow> </mml:math> colliders (SuperKEKb, FCC, CEPC, ILC, CLIC), their $$e^-e^-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>-</mml:mo> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>-</mml:mo> </mml:msup> </mml:mrow> </mml:math> options, and $$\gamma \gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>γ</mml:mi> <mml:mi>γ</mml:mi> </mml:mrow> </mml:math> colliders based on the backscattering of laser photons. In this paper, we show that background QED processes severely limit the study of elastic light-by-light scattering at $$e^+e^-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>-</mml:mo> </mml:msup> </mml:mrow> </mml:math> colliders. For the $$e^+e^-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>-</mml:mo> </mml:msup> </mml:mrow> </mml:math> case, the main background arises from $$e^+e^-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>e</mml:mi> <mml:mo>-</mml:mo> </mml:msup> </mml:mrow> </mml:math> annihilation into two photons within the detector acceptance after the initial electron and positron emit hard ISR photons at small angles. Since only two photons with a small total transverse momentum are registered in the detector in both cases, this process effectively mimics the $$\gamma \gamma \rightarrow \gamma \gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>γ</mml:mi> <mml:mi>γ</mml:mi> <mml:mo>→</mml:mo> <mml:mi>γ</mml:mi> <mml:mi>γ</mml:mi> </mml:mrow> </mml:math> signal with a significantly larger cross section at high invariant masses. Other relevant background QED processes for both types of collisions are also comprehensively analyzed and discussed.