Exploring bottom-charmed molecular tetraquarks with the complex scaling method

In this work, we adopt the one-boson exchange model to analyze the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msubsup> <a:mi>D</a:mi> <a:mrow> <a:mo stretchy="false">(</a:mo> <a:mi>s</a:mi> <a:mo stretchy="false">)</a:mo> </a:mrow> <a:mrow> <a:mo stretchy="false">(</a:mo> <a:mo>*</a:mo> <a:mo stretchy="false">)</a:mo> </a:mrow> </a:msubsup> <a:msubsup> <a:mi>B</a:mi> <a:mrow> <a:mo stretchy="false">(</a:mo> <a:mi>s</a:mi> <a:mo stretchy="false">)</a:mo> </a:mrow> <a:mrow> <a:mo stretchy="false">(</a:mo> <a:mo>*</a:mo> <a:mo stretchy="false">)</a:mo> </a:mrow> </a:msubsup> </a:math> interactions from a coupled-channel perspective. For the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>I</k:mi> <k:mo stretchy="false">(</k:mo> <k:msup> <k:mi>J</k:mi> <k:mi>P</k:mi> </k:msup> <k:mo stretchy="false">)</k:mo> <k:mo>=</k:mo> <k:mn>1</k:mn> <k:mo stretchy="false">(</k:mo> <k:msup> <k:mn>1</k:mn> <k:mo>+</k:mo> </k:msup> <k:mo stretchy="false">)</k:mo> </k:math> <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>D</q:mi> <q:msup> <q:mi>B</q:mi> <q:mo>*</q:mo> </q:msup> <q:mo>/</q:mo> <q:msup> <q:mi>D</q:mi> <q:mo>*</q:mo> </q:msup> <q:mi>B</q:mi> <q:mo>/</q:mo> <q:msup> <q:mi>D</q:mi> <q:mo>*</q:mo> </q:msup> <q:msup> <q:mi>B</q:mi> <q:mo>*</q:mo> </q:msup> </q:math> system, employing the complex scaling method, we obtain a loosely bound state and two resonant states located below the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>D</s:mi> <s:msup> <s:mi>B</s:mi> <s:mo>*</s:mo> </s:msup> </s:math> , <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msup> <u:mi>D</u:mi> <u:mo>*</u:mo> </u:msup> <u:mi>B</u:mi> </u:math> , and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:msup> <w:mi>D</w:mi> <w:mo>*</w:mo> </w:msup> <w:msup> <w:mi>B</w:mi> <w:mo>*</w:mo> </w:msup> </w:math> thresholds, respectively. Assuming that the charmoniumlike states <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:msub> <y:mi>Z</y:mi> <y:mi>c</y:mi> </y:msub> <y:mo stretchy="false">(</y:mo> <y:mn>3900</y:mn> <y:mo stretchy="false">)</y:mo> </y:math> and <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:msub> <cb:mi>Z</cb:mi> <cb:mi>c</cb:mi> </cb:msub> <cb:mo stretchy="false">(</cb:mo> <cb:mn>4020</cb:mn> <cb:mo stretchy="false">)</cb:mo> </cb:math> , as well as the bottomoniumlike states <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:msub> <gb:mi>Z</gb:mi> <gb:mi>b</gb:mi> </gb:msub> <gb:mo stretchy="false">(</gb:mo> <gb:mn>10610</gb:mn> <gb:mo stretchy="false">)</gb:mo> </gb:math> and <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"> <kb:msub> <kb:mi>Z</kb:mi> <kb:mi>b</kb:mi> </kb:msub> <kb:mo stretchy="false">(</kb:mo> <kb:mn>10650</kb:mn> <kb:mo stretchy="false">)</kb:mo> </kb:math> , are molecular states near their respective thresholds, we suggest that the predicted states in the <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"> <ob:mi>I</ob:mi> <ob:mo stretchy="false">(</ob:mo> <ob:msup> <ob:mi>J</ob:mi> <ob:mi>P</ob:mi> </ob:msup> <ob:mo stretchy="false">)</ob:mo> <ob:mo>=</ob:mo> <ob:mn>1</ob:mn> <ob:mo stretchy="false">(</ob:mo> <ob:msup> <ob:mn>1</ob:mn> <ob:mo>+</ob:mo> </ob:msup> <ob:mo stretchy="false">)</ob:mo> <ob:msup> <ob:mi>D</ob:mi> <ob:mrow> <ob:mo stretchy="false">(</ob:mo> <ob:mo>*</ob:mo> <ob:mo stretchy="false">)</ob:mo> </ob:mrow> </ob:msup> <ob:msup> <ob:mi>B</ob:mi> <ob:mrow> <ob:mo stretchy="false">(</ob:mo> <ob:mo>*</ob:mo> <ob:mo stretchy="false">)</ob:mo> </ob:mrow> </ob:msup> </ob:math> system could be their bottom-charmed analogs. In addition, we extend our analysis to other <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"> <yb:msubsup> <yb:mi>D</yb:mi> <yb:mrow> <yb:mo stretchy="false">(</yb:mo> <yb:mi>s</yb:mi> <yb:mo stretchy="false">)</yb:mo> </yb:mrow> <yb:mrow> <yb:mo stretchy="false">(</yb:mo> <yb:mo>*</yb:mo> <yb:mo stretchy="false">)</yb:mo> </yb:mrow> </yb:msubsup> <yb:msubsup> <yb:mi>B</yb:mi> <yb:mrow> <yb:mo stretchy="false">(</yb:mo> <yb:mi>s</yb:mi> <yb:mo stretchy="false">)</yb:mo> </yb:mrow> <yb:mrow> <yb:mo stretchy="false">(</yb:mo> <yb:mo>*</yb:mo> <yb:mo stretchy="false">)</yb:mo> </yb:mrow> </yb:msubsup> </yb:math> combinations with various quantum numbers. Our results indicate that, besides the <ic:math xmlns:ic="http://www.w3.org/1998/Math/MathML" display="inline"> <ic:mi>I</ic:mi> <ic:mo stretchy="false">(</ic:mo> <ic:msup> <ic:mi>J</ic:mi> <ic:mi>P</ic:mi> </ic:msup> <ic:mo stretchy="false">)</ic:mo> <ic:mo>=</ic:mo> <ic:mn>1</ic:mn> <ic:mo stretchy="false">(</ic:mo> <ic:msup> <ic:mn>1</ic:mn> <ic:mo>+</ic:mo> </ic:msup> <ic:mo stretchy="false">)</ic:mo> </ic:math> channel, more molecular states with quantum numbers <oc:math xmlns:oc="http://www.w3.org/1998/Math/MathML" display="i