Study of nucleon and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">Δ</mml:mi></mml:math> resonances from a systematic analysis of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" displa

A systematic analysis of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>K</a:mi><a:mo>*</a:mo></a:msup><a:mi mathvariant="normal">Σ</a:mi></a:math> photoproduction off proton is performed with all the available differential cross section data. We carry out a strategy different from the previous studies of these reactions, where, instead of fixing the parameters of the added resonances from PDG or pentaquark models, we add the resonance with a specific <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msup><d:mi>J</d:mi><d:mi>P</d:mi></d:msup></d:math> and leave its parameters to be determined from the experimental data. When adding only one resonance, the best result is to add a <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msup><f:mi>N</f:mi><f:mo>*</f:mo></f:msup><f:mo stretchy="false">(</f:mo><f:mn>3</f:mn><f:mo>/</f:mo><f:msup><f:mn>2</f:mn><f:mo>−</f:mo></f:msup><f:mo stretchy="false">)</f:mo></f:math> around 2097 MeV, which substantially reduces the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msup><j:mi>χ</j:mi><j:mn>2</j:mn></j:msup></j:math> per degree of freedom to 1.35. There are two best solutions when adding two resonances, one is to add one <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msup><l:mi>N</l:mi><l:mo>*</l:mo></l:msup><l:mo stretchy="false">(</l:mo><l:mn>3</l:mn><l:mo>/</l:mo><l:msup><l:mn>2</l:mn><l:mo>−</l:mo></l:msup><l:mo stretchy="false">)</l:mo></l:math> and one <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:msup><p:mi>N</p:mi><p:mo>*</p:mo></p:msup><p:mo stretchy="false">(</p:mo><p:mn>7</p:mn><p:mo>/</p:mo><p:msup><p:mn>2</p:mn><p:mo>−</p:mo></p:msup><p:mo stretchy="false">)</p:mo></p:math>, the other is to add one <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:msup><t:mi>N</t:mi><t:mo>*</t:mo></t:msup><t:mo stretchy="false">(</t:mo><t:mn>3</t:mn><t:mo>/</t:mo><t:msup><t:mn>2</t:mn><t:mo>−</t:mo></t:msup><t:mo stretchy="false">)</t:mo></t:math> and one <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:msup><x:mi mathvariant="normal">Δ</x:mi><x:mo>*</x:mo></x:msup><x:mo stretchy="false">(</x:mo><x:mn>7</x:mn><x:mo>/</x:mo><x:msup><x:mn>2</x:mn><x:mo>−</x:mo></x:msup><x:mo stretchy="false">)</x:mo></x:math>, leading the <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msup><cb:mi>χ</cb:mi><cb:mn>2</cb:mn></cb:msup></cb:math> per degree of freedom to be 1.10 and 1.09, respectively. The mass values of the <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msup><eb:mi>N</eb:mi><eb:mo>*</eb:mo></eb:msup><eb:mo stretchy="false">(</eb:mo><eb:mn>3</eb:mn><eb:mo>/</eb:mo><eb:msup><eb:mn>2</eb:mn><eb:mo>−</eb:mo></eb:msup><eb:mo stretchy="false">)</eb:mo></eb:math> in the two resonance solutions are both near 2070 MeV. Our solutions indicate that the <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mn>3</ib:mn><ib:mo>/</ib:mo><ib:msup><ib:mn>2</ib:mn><ib:mo>−</ib:mo></ib:msup></ib:math> nucleon resonance around 2080 MeV is strongly coupled with the <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:msup><kb:mi>K</kb:mi><kb:mo>*</kb:mo></kb:msup><kb:mi mathvariant="normal">Σ</kb:mi></kb:math> final state and support the molecular picture of <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"><nb:mi>N</nb:mi><nb:mo stretchy="false">(</nb:mo><nb:mn>2080</nb:mn><nb:mo>,</nb:mo><nb:mn>3</nb:mn><nb:mo>/</nb:mo><nb:msup><nb:mn>2</nb:mn><nb:mo>−</nb:mo></nb:msup><nb:mo stretchy="false">)</nb:mo></nb:math>.