Next-to-leading order analysis of $$J/\psi + \gamma $$ production in photon–photon collisions at CEPC

Abstract We systematically investigate the production of $$J/\psi + \gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>J</mml:mi> <mml:mo>/</mml:mo> <mml:mi>ψ</mml:mi> <mml:mo>+</mml:mo> <mml:mi>γ</mml:mi> </mml:mrow> </mml:math> in $$\gamma \gamma $$ <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> collisions within nonrelativistic QCD (NRQCD) factorization, with the direct-photon channel calculated specifically up to the next-to-leading order in $$\alpha _s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> </mml:msub> </mml:math> . Calculations for CEPC energy region show the resolved photon contribution is negligible, while the direct photon process dominates, yielding substantial annual $$J/\psi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>J</mml:mi> <mml:mo>/</mml:mo> <mml:mi>ψ</mml:mi> </mml:mrow> </mml:math> yields. Significant modifications to $$J/\psi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>J</mml:mi> <mml:mo>/</mml:mo> <mml:mi>ψ</mml:mi> </mml:mrow> </mml:math> polarization parameters emerge from color-octet mechanisms, and different NRQCD long distance matrix elements (LDMEs) further yield distinct polarization patterns. Furthermore, the polarization predictions are highly sensitive to the 3 $$P_J^{[8]}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>P</mml:mi> <mml:mi>J</mml:mi> <mml:mrow> <mml:mo>[</mml:mo> <mml:mn>8</mml:mn> <mml:mo>]</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> LDME, while being insensitive to the 1 $$S_0^{[8]}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>S</mml:mi> <mml:mn>0</mml:mn> <mml:mrow> <mml:mo>[</mml:mo> <mml:mn>8</mml:mn> <mml:mo>]</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> and 3 $$S_1^{[8]}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>S</mml:mi> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>[</mml:mo> <mml:mn>8</mml:mn> <mml:mo>]</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> LDMEs. Leveraging the cleaner environment of $$e^+e^-$$ <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> collisions versus hadronic processes, the production of $$J/\psi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>J</mml:mi> <mml:mo>/</mml:mo> <mml:mi>ψ</mml:mi> </mml:mrow> </mml:math> associated with a photon in $$\gamma \gamma $$ <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> collisions provides a high-precision platform to test LDMEs universality and resolve longstanding $$J/\psi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>J</mml:mi> <mml:mo>/</mml:mo> <mml:mi>ψ</mml:mi> </mml:mrow> </mml:math> polarization puzzles.