Doubly heavy tetraquark states in a mass splitting model

Abstract

Treating <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>X</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>4140</a:mn> <a:mo stretchy="false">)</a:mo> </a:math> as a compact <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mrow> <e:msup> <e:mrow> <e:mi>J</e:mi> </e:mrow> <e:mrow> <e:mi>P</e:mi> <e:mi>C</e:mi> </e:mrow> </e:msup> <e:mo>=</e:mo> <e:msup> <e:mrow> <e:mn>1</e:mn> </e:mrow> <e:mrow> <e:mo>+</e:mo> <e:mo>+</e:mo> </e:mrow> </e:msup> </e:mrow> </e:math> <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:mi>c</g:mi> <g:mi>s</g:mi> <g:mover accent="true"> <g:mrow> <g:mi>c</g:mi> </g:mrow> <g:mrow> <g:mo stretchy="false">¯</g:mo> </g:mrow> </g:mover> <g:mover accent="true"> <g:mrow> <g:mi>s</g:mi> </g:mrow> <g:mrow> <g:mo stretchy="false">¯</g:mo> </g:mrow> </g:mover> </g:mrow> </g:math> state and using its mass as a reference scale, we systematically estimate the masses of doubly heavy tetraquark states <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>Q</m:mi> <m:mi>Q</m:mi> <m:mover accent="true"> <m:mi>q</m:mi> <m:mo stretchy="false">¯</m:mo> </m:mover> <m:mover accent="true"> <m:mi>q</m:mi> <m:mo stretchy="false">¯</m:mo> </m:mover> </m:math> , where <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mrow> <s:mi>Q</s:mi> <s:mo>=</s:mo> <s:mi>c</s:mi> </s:mrow> </s:math> , <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mrow> <u:mi>b</u:mi> </u:mrow> </u:math> and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mi>q</w:mi> <w:mo>=</w:mo> <w:mi>u</w:mi> </w:math> , <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mrow> <y:mi>d</y:mi> </y:mrow> </y:math> , <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mrow> <ab:mi>s</ab:mi> </ab:mrow> </ab:math> . Their decay properties are studied with a simple rearrangement scheme. Based on our results, the lowest <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:mi>I</cb:mi> <cb:mo stretchy="false">(</cb:mo> <cb:msup> <cb:mi>J</cb:mi> <cb:mi>P</cb:mi> </cb:msup> <cb:mo stretchy="false">)</cb:mo> <cb:mo>=</cb:mo> <cb:mn>0</cb:mn> <cb:mo stretchy="false">(</cb:mo> <cb:msup> <cb:mn>1</cb:mn> <cb:mo>+</cb:mo> </cb:msup> <cb:mo stretchy="false">)</cb:mo> </cb:math> <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:mi>b</ib:mi> <ib:mi>b</ib:mi> <ib:mover accent="true"> <ib:mi>n</ib:mi> <ib:mo stretchy="false">¯</ib:mo> </ib:mover> <ib:mover accent="true"> <ib:mi>n</ib:mi> <ib:mo stretchy="false">¯</ib:mo> </ib:mover> </ib:math> state is a stable tetraquark about 20 MeV below the <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"> <ob:msup> <ob:mover accent="true"> <ob:mi>B</ob:mi> <ob:mo stretchy="false">¯</ob:mo> </ob:mover> <ob:mo>*</ob:mo> </ob:msup> <ob:mover accent="true"> <ob:mi>B</ob:mi> <ob:mo stretchy="false">¯</ob:mo> </ob:mover> </ob:math> threshold. The mass and width of the low-mass <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"> <ub:mn>0</ub:mn> <ub:mo stretchy="false">(</ub:mo> <ub:msup> <ub:mn>1</ub:mn> <ub:mo>+</ub:mo> </ub:msup> <ub:mo stretchy="false">)</ub:mo> </ub:math> <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"> <yb:mi>c</yb:mi> <yb:mi>c</yb:mi> <yb:mover accent="true"> <yb:mi>n</yb:mi> <yb:mo stretchy="false">¯</yb:mo> </yb:mover> <yb:mover accent="true"> <yb:mi>n</yb:mi> <yb:mo stretchy="false">¯</yb:mo> </yb:mover> </yb:math> ( <ec:math xmlns:ec="http://www.w3.org/1998/Math/MathML" display="inline"> <ec:mrow> <ec:mi>n</ec:mi> <ec:mo>=</ec:mo> <ec:mi>u</ec:mi> </ec:mrow> </ec:math> , <gc:math xmlns:gc="http://www.w3.org/1998/Math/MathML" display="inline"> <gc:mrow> <gc:mi>d</gc:mi> </gc:mrow> </gc:math> ) tetraquark are compatible with the <ic:math xmlns:ic="http://www.w3.org/1998/Math/MathML" display="inline"> <ic:msub> <ic:mi>T</ic:mi> <ic:mrow> <ic:mi>c</ic:mi> <ic:mi>c</ic:mi> </ic:mrow> </ic:msub> <ic:mo stretchy="false">(</ic:mo> <ic:mn>3875</ic:mn> <ic:msup> <ic:mo stretchy="false">)</ic:mo> <ic:mo>+</ic:mo> </ic:msup> </ic:math> observed by the LHCb Collaboration. The locations of the lowest <mc:math xmlns:mc="http://www.w3.org/1998/Math/MathML" display="inline"> <mc:mn>0</mc:mn> <mc:mo stretchy="false">(</mc:mo> <mc:msup> <mc:mn>0</mc:mn> <mc:mo>+</mc:mo> </mc:msup> <mc:mo stretchy="false">)</mc:mo> </mc:math> and <qc:math xmlns:qc="http://www.w3.org/1998/Math/MathML" display="inline"> <qc:mn>0</qc:mn> <qc:mo stretchy="false">(</qc:mo> <qc:msup> <qc:mn>1</qc:mn> <qc:mo>+</qc:mo> </qc:msup> <qc:mo stretchy="false">)</qc:mo> </qc:math> <uc:math xmlns:uc="http://www.w3.org/1998/Math/MathML" display="inline"> <uc:mi>b</uc:mi> <uc:mi>c</uc:mi> <uc:mover accent="true"> <uc:mi>n</uc:mi> <uc:mo stretchy="false">¯</uc:mo> </uc:mover> <uc:mover accen

Topics & Concepts