Production mechanisms of isoscalar pseudotensor mesons in pion and kaon induced reactions

The recent observation of the X(2600) resonance by the BESIII Collaboration has motivated a renewed interest in the spectroscopy of light mesons, particularly pseudotensor states. However, a significant theoretical gap exists in the poorly explored spectrum of isoscalar pseudotensor mesons, where several predicted radial excitations remain unobserved. To address this, we investigate the production of four such states [ <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>η</a:mi> <a:mn>2</a:mn> </a:msub> <a:mo stretchy="false">(</a:mo> <a:mn>4</a:mn> <a:mi>D</a:mi> <a:mo stretchy="false">)</a:mo> </a:math> , <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msubsup> <e:mi>η</e:mi> <e:mn>2</e:mn> <e:mo>′</e:mo> </e:msubsup> <e:mo stretchy="false">(</e:mo> <e:mn>2</e:mn> <e:mi>D</e:mi> <e:mo stretchy="false">)</e:mo> </e:math> , <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msubsup> <i:mi>η</i:mi> <i:mn>2</i:mn> <i:mo>′</i:mo> </i:msubsup> <i:mo stretchy="false">(</i:mo> <i:mn>3</i:mn> <i:mi>D</i:mi> <i:mo stretchy="false">)</i:mo> </i:math> , and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msubsup> <m:mi>η</m:mi> <m:mn>2</m:mn> <m:mo>′</m:mo> </m:msubsup> <m:mo stretchy="false">(</m:mo> <m:mn>4</m:mn> <m:mi>D</m:mi> <m:mo stretchy="false">)</m:mo> </m:math> ] employing an effective Lagrangian approach combined with Regge trajectory phenomenology to describe the high-energy behavior of the reactions. Our calculations reveal a distinct production selectivity: the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msub> <q:mi>η</q:mi> <q:mn>2</q:mn> </q:msub> <q:mo stretchy="false">(</q:mo> <q:mn>4</q:mn> <q:mi>D</q:mi> <q:mo stretchy="false">)</q:mo> </q:math> state is more prominent in pion induced ( <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msup> <u:mi>π</u:mi> <u:mo>−</u:mo> </u:msup> <u:mi>p</u:mi> <u:mo stretchy="false">→</u:mo> <u:msub> <u:mi>η</u:mi> <u:mn>2</u:mn> </u:msub> <u:mi>n</u:mi> </u:math> ) reactions, whereas the <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:msubsup> <x:mi>η</x:mi> <x:mn>2</x:mn> <x:mo>′</x:mo> </x:msubsup> <x:mo stretchy="false">(</x:mo> <x:mn>2</x:mn> <x:mi>D</x:mi> <x:mo>,</x:mo> <x:mn>3</x:mn> <x:mi>D</x:mi> <x:mo>,</x:mo> <x:mn>4</x:mn> <x:mi>D</x:mi> <x:mo stretchy="false">)</x:mo> </x:math> states are preferentially produced in kaon induced ( <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:msup> <bb:mi>K</bb:mi> <bb:mo>−</bb:mo> </bb:msup> <bb:mi>p</bb:mi> <bb:mo stretchy="false">→</bb:mo> <bb:msub> <bb:mi>η</bb:mi> <bb:mn>2</bb:mn> </bb:msub> <bb:mi mathvariant="normal">Λ</bb:mi> </bb:math> ) processes. Moreover, the total cross sections for these states exhibit characteristic peaks at specific beam momenta, providing clear kinematic windows for their discovery. This study provides the first comprehensive theoretical predictions for the production cross sections of these predicted mesons, offering crucial guidance for future experimental searches.