Probing the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> neutrino model in the SHiP experiment

We present the first comprehensive sensitivity study of the Search for Hidden Particles (SHiP) experiment to sterile neutrino oscillations using all three types of neutrinos, employing a Feldman-Cousins method with a parametric bootstrap to account for systematic uncertainties. In contrast to earlier studies that focused only on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:msub> <a:mrow> <a:mi>ν</a:mi> </a:mrow> <a:mrow> <a:mi>τ</a:mi> </a:mrow> </a:msub> </a:mrow> </a:math> disappearance, we include both appearance and disappearance channels across all active flavors. We also investigate the dual-baseline configuration, which complements the existing near scattering and neutrino detector (SND) at 27 m with an additional far SND at 120 m. The near SND only configuration can probe mixing parameters of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mo stretchy="false">|</c:mo> <c:msub> <c:mrow> <c:mi>U</c:mi> </c:mrow> <c:mrow> <c:mi>α</c:mi> <c:mn>4</c:mn> </c:mrow> </c:msub> <c:msup> <c:mrow> <c:mo stretchy="false">|</c:mo> </c:mrow> <c:mrow> <c:mn>2</c:mn> </c:mrow> </c:msup> <c:mo>≳</c:mo> <c:mn>0.1</c:mn> </c:mrow> </c:math> near <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:mi mathvariant="normal">Δ</g:mi> <g:msubsup> <g:mrow> <g:mi>m</g:mi> </g:mrow> <g:mrow> <g:mn>41</g:mn> </g:mrow> <g:mrow> <g:mn>2</g:mn> </g:mrow> </g:msubsup> <g:mo>∼</g:mo> <g:msup> <g:mrow> <g:mn>10</g:mn> </g:mrow> <g:mrow> <g:mn>3</g:mn> </g:mrow> </g:msup> <g:mtext> </g:mtext> <g:mtext> </g:mtext> <g:msup> <g:mrow> <g:mi>eV</g:mi> </g:mrow> <g:mrow> <g:mn>2</g:mn> </g:mrow> </g:msup> </g:mrow> </g:math> , with a reduction of normalized systematic uncertainties from 20% to 10% improving sensitivity by roughly a factor of two. Moreover, the inclusion of far SND significantly enhances the sensitivity by a factor of 2 to 10 depending on the flavor and the systematic uncertainty. If two active flavors are mixed with a sterile flavor, a cancelation between neutrino appearance and disappearance generates kinks in the sensitivity curves, while those kinks disappear with far SND.