Further study on excited $$ {\Xi}_{QQ^{\prime }} $$ via photoproduction at CEPC and FCC-ee

A bstract Within the framework of NRQCD, the photoproduction of doubly heavy baryons Ξ cc , Ξ bc , Ξ bb and their P -wave excited states has been systematically investigated. The production mechanism is that a color anti-triplet or sextuplet diquark ⟨ QQ ′ ⟩ is first produced, and then evolved into a corresponding doubly heavy baryon $$ {\Xi}_{QQ^{\prime }} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Ξ</mml:mi> <mml:msup> <mml:mi>QQ</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:msub> </mml:math> via the subprocess γ + γ → ⟨ QQ ′ ⟩[ n ] + $$ {\overline{Q}}^{\prime } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mover> <mml:mi>Q</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mo>′</mml:mo> </mml:msup> </mml:math> + $$ \overline{Q} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>Q</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> → $$ {\Xi}_{QQ^{\prime }} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Ξ</mml:mi> <mml:msup> <mml:mi>QQ</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:msub> </mml:math> + $$ {\overline{Q}}^{\prime } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mover> <mml:mi>Q</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mo>′</mml:mo> </mml:msup> </mml:math> + $$ \overline{Q} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>Q</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> . Here, Q (′) denotes the heavy quark b or c , [ n ] is the color and spin quantum number of intermediate diquark, which can be $$ {\left[^3{S}_1\right]}_{\overline{\textbf{3}}/\textbf{6}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mfenced> <mml:mmultiscripts> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mprescripts/> <mml:none/> <mml:mn>3</mml:mn> </mml:mmultiscripts> </mml:mfenced> <mml:mrow> <mml:mover> <mml:mn>3</mml:mn> <mml:mo>¯</mml:mo> </mml:mover> <mml:mo>/</mml:mo> <mml:mn>6</mml:mn> </mml:mrow> </mml:msub> </mml:math> and $$ {\left[^1{S}_0\right]}_{\overline{\textbf{3}}/\textbf{6}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mfenced> <mml:mmultiscripts> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mprescripts/> <mml:none/> <mml:mn>1</mml:mn> </mml:mmultiscripts> </mml:mfenced> <mml:mrow> <mml:mover> <mml:mn>3</mml:mn> <mml:mo>¯</mml:mo> </mml:mover> <mml:mo>/</mml:mo> <mml:mn>6</mml:mn> </mml:mrow> </mml:msub> </mml:math> for S -wave states, or $$ {\left[^1{P}_1\right]}_{\overline{\textbf{3}}/\textbf{6}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mfenced> <mml:mmultiscripts> <mml:msub> <mml:mi>P</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mprescripts/> <mml:none/> <mml:mn>1</mml:mn> </mml:mmultiscripts> </mml:mfenced> <mml:mrow> <mml:mover> <mml:mn>3</mml:mn> <mml:mo>¯</mml:mo> </mml:mover> <mml:mo>/</mml:mo> <mml:mn>6</mml:mn> </mml:mrow> </mml:msub> </mml:math> and $$ {\left[^3{P}_J\right]}_{\overline{\textbf{3}}/\textbf{6}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mfenced> <mml:mmultiscripts> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>J</mml:mi> </mml:msub> <mml:mprescripts/> <mml:none/> <mml:mn>3</mml:mn> </mml:mmultiscripts> </mml:mfenced> <mml:mrow> <mml:mover> <mml:mn>3</mml:mn> <mml:mo>¯</mml:mo> </mml:mover> <mml:mo>/</mml:mo> <mml:mn>6</mml:mn> </mml:mrow> </mml:msub> </mml:math> with J = 0, 1, 2 for P -wave states. Predictions for the cross sections, differential distributions, and theoretical uncertainty have been analyzed. The results indicate that, at $$ \sqrt{s} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> </mml:math> = 91 GeV, the contribution of photoproduction for P -wave Ξ cc , Ξ bc , and Ξ bb is approximately 2 . 19%, 4 . 23%, 1 . 26% of the contribution for S -wave, respectively. As the collision energy increase