Charged current neutrino and antineutrino induced associated particle production from nucleons

In this work, we study the charged-current (anti)neutrino induced associated particle (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>K</a:mi><a:mi mathvariant="normal">Λ</a:mi></a:math>) production (<d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi mathvariant="normal">Δ</d:mi><d:mi>S</d:mi><d:mo>=</d:mo><d:mn>0</d:mn></d:math>) from free nucleons in the energy region of a few GeV, relevant to the (anti)neutrino oscillation experiments with accelerator and atmospheric neutrinos. We employ a model based on effective Lagrangians to evaluate the contributions from the nonresonant and the resonant diagrams. The nonresonant background terms are calculated using a microscopic model derived from the SU(3) chiral Lagrangians. For the resonant contributions, we consider the low-lying spin-<g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mfrac><g:mn>1</g:mn><g:mn>2</g:mn></g:mfrac></g:math> resonances, such as <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>S</i:mi><i:mn>11</i:mn></i:msub><i:mo stretchy="false">(</i:mo><i:mn>1650</i:mn><i:mo stretchy="false">)</i:mo></i:math>, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>P</m:mi><m:mn>11</m:mn></m:msub><m:mo stretchy="false">(</m:mo><m:mn>1710</m:mn><m:mo stretchy="false">)</m:mo></m:math>, <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>P</q:mi><q:mn>11</q:mn></q:msub><q:mo stretchy="false">(</q:mo><q:mn>1880</q:mn><q:mo stretchy="false">)</q:mo></q:math>, and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi>S</u:mi><u:mn>11</u:mn></u:msub><u:mo stretchy="false">(</u:mo><u:mn>1895</u:mn><u:mo stretchy="false">)</u:mo></u:math>, and spin-<y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mfrac><y:mn>3</y:mn><y:mn>2</y:mn></y:mfrac></y:math> resonances, such as <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:msub><ab:mi>P</ab:mi><ab:mn>13</ab:mn></ab:msub><ab:mo stretchy="false">(</ab:mo><ab:mn>1720</ab:mn><ab:mo stretchy="false">)</ab:mo></ab:math> and <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msub><eb:mi>P</eb:mi><eb:mn>13</eb:mn></eb:msub><eb:mo stretchy="false">(</eb:mo><eb:mn>1900</eb:mn><eb:mo stretchy="false">)</eb:mo></eb:math>, which have finite branching ratios to the <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mi>K</ib:mi><ib:mi mathvariant="normal">Λ</ib:mi></ib:math> channel. These resonant contributions are modeled using an effective phenomenological Lagrangian approach, with strong couplings determined from the experimental branching ratios and the decay widths to the <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"><lb:mi>K</lb:mi><lb:mi mathvariant="normal">Λ</lb:mi></lb:math> channel. To fix the parameters of the vector current interaction, the model is first used to reproduce satisfactorily the MAMI@Mainz experimental data on the real photon induced scattering off the nucleon resulting an eta meson in the final state and with the CLAS@JLab data for the <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:mi>K</ob:mi><ob:mi mathvariant="normal">Λ</ob:mi></ob:math> production in the final state. The partial conservation of the axial vector current hypothesis and the generalized Goldberger-Treiman relation are used to fix the parameters of the axial vector interaction. The model is then applied to study the weak production of <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"><rb:mi>K</rb:mi><rb:mi mathvariant="normal">Λ</rb:mi></rb:math> induced by the neutrinos and antineutrinos and predicts the numerical values for the <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"><ub:msup><ub:mi>Q</ub:mi><ub:mn>2</ub:mn></ub:msup></ub:math> distribution <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"><wb:mo stretchy="false">(</wb:mo><wb:mfrac><wb:mrow><wb:mi>d</wb:mi><wb:mi>σ</wb:mi></wb:mrow><wb:mrow><wb:mi>d</wb:mi><wb:msup><wb:mi>Q</wb:mi><wb:mn>2</wb:mn></wb:msup></wb:mrow></wb:mfrac><wb:mo stretchy="false">)</wb:mo></wb:math>, the kinetic energy distribution for the outgoing kaon <ac:math xmlns:ac="http://www.w3.org/1998/Math/MathML" display="inline"><ac:mo stretchy="false">(</ac:mo><ac:mfrac><ac:mrow><ac:mi>d</ac:mi><ac:mi>σ</ac:mi></ac:mrow><ac:mrow><ac:mi>d</ac:mi><ac:msub><ac:mi>p</ac:mi><ac:mi>K</ac:mi></ac:msub></ac:mrow></ac:mfrac><ac:mo stretchy="false">)</ac:mo></ac:math>, and the total scattering cross sections (<ec:math xmlns:ec="http://www.w3.org/1998/Math/MathML" display="inline"><ec:mi>σ</ec:mi></ec:math>) with and without a cut on the center of mass energy <gc:math xmlns:gc="http://www.w3.org/1998/Math/MathML" display="inline"><gc:mi>W</gc:mi></gc:math>. The results presented in this work are relevant for the present and future accelerator experiments like MicroBooNE, T2K, NOvA, MINERvA, SBND, ICARUS, T2-HyperK, and DUNE as well as for the atmospheric neutrino experiments.