Charged current weak production of Δ(1232) induced by electrons and positrons

The charged current weak production of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="normal">Δ</a:mi><a:mo stretchy="false">(</a:mo><a:mn>1232</a:mn><a:mo stretchy="false">)</a:mo></a:math> from the free proton target induced by the electron/positron in the intermediate energy range corresponding to the beam energy available at JLab and Mainz, has been studied. The results for the differential scattering cross section <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mfrac><f:mrow><f:mi>d</f:mi><f:mi>σ</f:mi></f:mrow><f:mrow><f:mi>d</f:mi><f:msup><f:mi>Q</f:mi><f:mn>2</f:mn></f:msup></f:mrow></f:mfrac></f:math>, the angular distribution <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mfrac><h:mrow><h:mi>d</h:mi><h:mi>σ</h:mi></h:mrow><h:mrow><h:mi>d</h:mi><h:msub><h:mi mathvariant="normal">Ω</h:mi><h:mi mathvariant="normal">Δ</h:mi></h:msub></h:mrow></h:mfrac></h:math>, and the total scattering cross section <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>σ</l:mi><l:mo stretchy="false">(</l:mo><l:msub><l:mi>E</l:mi><l:mi>e</l:mi></l:msub><l:mo stretchy="false">)</l:mo></l:math> for both the electron and positron induced processes are presented, for the various energies in the range of 0.5–4 GeV. The cross section <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mi>σ</p:mi><p:mo stretchy="false">(</p:mo><p:msub><p:mi>E</p:mi><p:mi>e</p:mi></p:msub><p:mo stretchy="false">)</p:mo></p:math> is found to be of the order of <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:msup><t:mn>10</t:mn><t:mrow><t:mo>−</t:mo><t:mn>39</t:mn></t:mrow></t:msup><t:mtext> </t:mtext><t:mtext> </t:mtext><t:msup><t:mrow><t:mi>cm</t:mi></t:mrow><t:mrow><t:mn>2</t:mn></t:mrow></t:msup></t:math> for the electron/positron energies in the few GeV range. The availability of electron/positron beams having well-defined energy and direction with very high luminosity of the order of <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:msup><v:mn>10</v:mn><v:mn>38</v:mn></v:msup><v:mo>–</v:mo><v:msup><v:mn>10</v:mn><v:mn>39</v:mn></v:msup><v:mtext> </v:mtext><v:mtext> </v:mtext><v:mrow><v:msup><v:mrow><v:mi>cm</v:mi></v:mrow><v:mrow><v:mo>−</v:mo><v:mn>2</v:mn></v:mrow></v:msup><v:mtext> </v:mtext><v:mtext> </v:mtext><v:msup><v:mrow><v:mi>sec</v:mi></v:mrow><v:mrow><v:mo>−</v:mo><v:mn>1</v:mn></v:mrow></v:msup></v:mrow></v:math>, makes it possible to observe the weak charged current production of <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mi mathvariant="normal">Δ</x:mi><x:mo stretchy="false">(</x:mo><x:mn>1232</x:mn><x:mo stretchy="false">)</x:mo></x:math> and determine the axial vector form factors <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msubsup><cb:mi>C</cb:mi><cb:mi>i</cb:mi><cb:mi>A</cb:mi></cb:msubsup><cb:mo stretchy="false">(</cb:mo><cb:msup><cb:mi>Q</cb:mi><cb:mn>2</cb:mn></cb:msup><cb:mo stretchy="false">)</cb:mo><cb:mo>;</cb:mo><cb:mo stretchy="false">(</cb:mo><cb:mi>i</cb:mi><cb:mo>=</cb:mo><cb:mn>3</cb:mn><cb:mi>–</cb:mi><cb:mn>5</cb:mn><cb:mo stretchy="false">)</cb:mo></cb:math>. The sensitivity of the differential cross section <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mfrac><ib:mrow><ib:mi>d</ib:mi><ib:mi>σ</ib:mi></ib:mrow><ib:mrow><ib:mi>d</ib:mi><ib:msup><ib:mi>Q</ib:mi><ib:mn>2</ib:mn></ib:msup></ib:mrow></ib:mfrac></ib:math> to the subdominant form factors <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:msubsup><kb:mi>C</kb:mi><kb:mn>3</kb:mn><kb:mi>A</kb:mi></kb:msubsup><kb:mo stretchy="false">(</kb:mo><kb:msup><kb:mi>Q</kb:mi><kb:mn>2</kb:mn></kb:msup><kb:mo stretchy="false">)</kb:mo></kb:math> and <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:msubsup><ob:mi>C</ob:mi><ob:mn>4</ob:mn><ob:mi>A</ob:mi></ob:msubsup><ob:mo stretchy="false">(</ob:mo><ob:msup><ob:mi>Q</ob:mi><ob:mn>2</ob:mn></ob:msup><ob:mo stretchy="false">)</ob:mo></ob:math> is found to be strong enough, especially in the low <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:msup><sb:mi>Q</sb:mi><sb:mn>2</sb:mn></sb:msup></sb:math> region, which can be used to determine them phenomenologically and to test the various theoretical models proposed to calculate them.