Ratio of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>γ</mml:mi> <mml:mo>/</mml:mo> <mml:msup> <mml:mi>π</mml:mi> <mml:mn>0</mml

<jats:p> We study the dependence of neutrino-induced <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>γ</a:mi> <a:mo>/</a:mo> <a:msup> <a:mi>π</a:mi> <a:mn>0</a:mn> </a:msup> </a:math> production ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mover accent="true"> <c:msub> <c:mi>ν</c:mi> <c:mi>μ</c:mi> </c:msub> <c:mrow> <c:mo stretchy="false">(</c:mo> <c:mo>−</c:mo> <c:mo stretchy="false">)</c:mo> </c:mrow> </c:mover> <c:mo>+</c:mo> <c:mi>A</c:mi> <c:mo stretchy="false">→</c:mo> <c:mover accent="true"> <c:msub> <c:mi>ν</c:mi> <c:mi>μ</c:mi> </c:msub> <c:mrow> <c:mo stretchy="false">(</c:mo> <c:mo>−</c:mo> <c:mo stretchy="false">)</c:mo> </c:mrow> </c:mover> <c:mo stretchy="false">(</c:mo> <c:mi>μ</c:mi> <c:mo stretchy="false">)</c:mo> <c:mo>+</c:mo> <c:mi>γ</c:mi> <c:mo>/</c:mo> <c:msup> <c:mi>π</c:mi> <c:mn>0</c:mn> </c:msup> <c:mo>+</c:mo> <c:mi>X</c:mi> </c:math> ) on the target nucleus <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mi>A</n:mi> </n:math> , in the <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mi mathvariant="normal">Δ</p:mi> </p:math> resonance mass region. Our conclusion is based on experimental data for <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msup> <s:mi>π</s:mi> <s:mn>0</s:mn> </s:msup> </s:math> production rates at photon-nucleus interactions from the A2 Collaboration at the Mainz MAMI accelerator. We assume that <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mi mathvariant="normal">Δ</u:mi> </u:math> resonance decays are independent of the production mechanism (via photon, Z, or W boson). In neutral current (NC) interactions, the <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:mn>1</x:mn> <x:msup> <x:mi>π</x:mi> <x:mn>0</x:mn> </x:msup> <x:mo>+</x:mo> <x:mi>X</x:mi> </x:math> production scales as <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:msup> <z:mi>A</z:mi> <z:mrow> <z:mn>2</z:mn> <z:mo>/</z:mo> <z:mn>3</z:mn> </z:mrow> </z:msup> </z:math> . In contrast, photons from <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:mi mathvariant="normal">Δ</bb:mi> </bb:math> decays typically escape the nucleus, resulting in a cross-section proportional to the atomic number <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:mi>A</eb:mi> </eb:math> . Thus, in NC interactions, the ratio of <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:mi>γ</gb:mi> </gb:math> production to <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:msup> <ib:mi>π</ib:mi> <ib:mn>0</ib:mn> </ib:msup> </ib:math> production is proportional to <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"> <kb:msup> <kb:mi>A</kb:mi> <kb:mrow> <kb:mn>1</kb:mn> <kb:mo>/</kb:mo> <kb:mn>3</kb:mn> </kb:mrow> </kb:msup> </kb:math> . In charged current (CC) <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"> <mb:mrow> <mb:mrow> <mb:msub> <mb:mrow> <mb:mi>ν</mb:mi> </mb:mrow> <mb:mrow> <mb:mi>μ</mb:mi> </mb:mrow> </mb:msub> </mb:mrow> <mb:mtext>−</mb:mtext> </mb:mrow> </mb:math> ( <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"> <ob:msub> <ob:mover accent="true"> <ob:mi>ν</ob:mi> <ob:mo stretchy="true">¯</ob:mo> </ob:mover> <ob:mi>μ</ob:mi> </ob:msub> </ob:math> )-induced production of <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"> <sb:msup> <sb:mi mathvariant="normal">Δ</sb:mi> <sb:mo>+</sb:mo> </sb:msup> </sb:math> ( <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"> <vb:msup> <vb:mi mathvariant="normal">Δ</vb:mi> <vb:mn>0</vb:mn> </vb:msup> </vb:math> ) will be proportional to the number of neutrons (protons) in the nucleus. After <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"> <yb:mi mathvariant="normal">Δ</yb:mi> </yb:math> decay, due to the charge universality in strong interactions, the suppression factor for <bc:math xmlns:bc="http://www.w3.org/1998/Math/MathML" display="inline"> <bc:msup> <bc:mi>π</bc:mi> <bc:mn>0</bc:mn> </bc:msup> </bc:math> escaping the nucleus must also follow <dc:math xmlns:dc="http://www.w3.org/1998/Math/MathML" display="inline"> <dc:msup> <dc:mi>A</dc:mi> <dc:mrow> <dc:mo>−</dc:mo> <dc:mn>1</dc:mn> <dc:mo>/</dc:mo> <dc:mn>3</dc:mn> </dc:mrow> </dc:msup> </dc:math> , as in NC interactions. We predict the ratio of the <fc:math xmlns:fc="http://www.w3.org/1998/Math/MathML" display="inline"> <fc:mi>γ</fc:mi> <fc:mo>/</fc:mo> <fc:msup> <fc:mi>π</fc:mi> <fc:mn>0</fc:mn> </fc:msup> </fc:math> production rates in NC and CC interactions and for <hc:math xmlns:hc="http://www.w3.org/1998/Math/MathML" display="inline"> <hc:msub> <hc:mi>ν</hc:mi> <hc:mi>μ</hc:mi> </hc:msub> </hc:math> and <jc:math xmlns:jc="http://www.w3.org/1998/Math/MathML" display="inline"> <jc:msub> <jc:mover accent="true"> <jc:mi>ν</jc:mi> <jc:mo stretchy="false">¯</jc:mo> </jc:mover> <jc:mi>μ</jc:mi> </jc:msub> </jc:math> beams: argon target, <nc:math xmlns:nc="http://www.w3.org/1998/Math/MathML" display="inline"> <nc:mo>∼</nc:mo>