Centre-of-momentum frame analysis of $$\eta $$ production in DUNE

Abstract A deep understanding of neutrino-nucleus interaction is crucial for the precise measurement of neutrino oscillation parameters and cross section measurements. Various nuclear effects, such as initial state effects (IS) and final state interactions (FSI), make neutrino interactions more complicated. To probe the impacts of the nuclear effects, a separate study of FSI and IS is required. A set of variables known as centre-of-momentum (c.m.) variables ( $$\theta _{c.m.}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>θ</mml:mi> <mml:mrow> <mml:mi>c</mml:mi> <mml:mo>.</mml:mo> <mml:mi>m</mml:mi> <mml:mo>.</mml:mo> </mml:mrow> </mml:msub> </mml:math> and $$E_{c.m.}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mrow> <mml:mi>c</mml:mi> <mml:mo>.</mml:mo> <mml:mi>m</mml:mi> <mml:mo>.</mml:mo> </mml:mrow> </mml:msub> </mml:math> ) provides a unique approach to isolate the FSI effect with minimal sensitivity to IS. This work presents the importance of c.m. variables in neutrino-induced eta ( $$\eta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>η</mml:mi> </mml:math> ) meson production in the DUNE near detector. $$\theta _{c.m.}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>θ</mml:mi> <mml:mrow> <mml:mi>c</mml:mi> <mml:mo>.</mml:mo> <mml:mi>m</mml:mi> <mml:mo>.</mml:mo> </mml:mrow> </mml:msub> </mml:math> is an important parameter to improve the FSI modeling, while $$E_{c.m.}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mrow> <mml:mi>c</mml:mi> <mml:mo>.</mml:mo> <mml:mi>m</mml:mi> <mml:mo>.</mml:mo> </mml:mrow> </mml:msub> </mml:math> helps in isolating high-purity neutrino-Hydrogen events. The study of $$\eta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>η</mml:mi> </mml:math> production in neutrino interactions helps in understanding the theoretical descriptions of higher resonance states.