Charmonia in an unquenched quark model

Abstract

In this work, we study the charmonium spectrum within an unquenched quark model including coupled-channel effects. In couple-channel calculations, we include all of the opened charmed meson channels with the once-subtracted method, meanwhile we adopt a suppressed factor to soften the hard vertices given by the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mmultiscripts> <a:mrow> <a:msub> <a:mrow> <a:mi>P</a:mi> </a:mrow> <a:mrow> <a:mn>0</a:mn> </a:mrow> </a:msub> </a:mrow> <a:mprescripts/> <a:none/> <a:mrow> <a:mn>3</a:mn> </a:mrow> </a:mmultiscripts> </a:mrow> </a:math> model in the high momentum region. We obtain a good description of both the masses and widths for the well-established states in the charmonium spectrum. Furthermore, we give predictions for the higher <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>S</c:mi> </c:math> -, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>P</e:mi> </e:math> -, and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>D</g:mi> </g:math> -wave charmonium states up to mass region of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mo>∼</i:mo> <i:mn>5.0</i:mn> <i:mtext> </i:mtext> <i:mtext> </i:mtext> <i:mi>GeV</i:mi> </i:math> . The magnitude of mass shifts due to the coupled-channel effects is estimated to be about <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mrow> <k:mn>10</k:mn> <k:mi>s</k:mi> </k:mrow> </k:math> MeV. Although many decay channels are opened for the higher charmonium states, they are relatively narrow states. Their widths scatter in the range of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mrow> <m:mo>∼</m:mo> <m:mn>10</m:mn> <m:mi>s</m:mi> <m:mi>–</m:mi> <m:mn>100</m:mn> <m:mtext> </m:mtext> <m:mtext> </m:mtext> <m:mi>MeV</m:mi> </m:mrow> </m:math> . Many charmoniumlike states, such as <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>χ</o:mi> <o:mrow> <o:mi>c</o:mi> <o:mn>1</o:mn> </o:mrow> </o:msub> <o:mo stretchy="false">(</o:mo> <o:mn>4274</o:mn> <o:mo stretchy="false">)</o:mo> </o:math> , <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msub> <s:mi>χ</s:mi> <s:mrow> <s:mi>c</s:mi> <s:mn>0</s:mn> </s:mrow> </s:msub> <s:mo stretchy="false">(</s:mo> <s:mn>3915</s:mn> <s:mo stretchy="false">)</s:mo> </s:math> , <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:msub> <w:mi>χ</w:mi> <w:mrow> <w:mi>c</w:mi> <w:mn>0</w:mn> </w:mrow> </w:msub> <w:mo stretchy="false">(</w:mo> <w:mn>4500</w:mn> <w:mo stretchy="false">)</w:mo> </w:math> , <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:msub> <ab:mi>χ</ab:mi> <ab:mrow> <ab:mi>c</ab:mi> <ab:mn>0</ab:mn> </ab:mrow> </ab:msub> <ab:mo stretchy="false">(</ab:mo> <ab:mn>4700</ab:mn> <ab:mo stretchy="false">)</ab:mo> </ab:math> , <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:mi>X</eb:mi> <eb:mo stretchy="false">(</eb:mo> <eb:mn>4160</eb:mn> <eb:mo stretchy="false">)</eb:mo> </eb:math> , <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:mi>X</ib:mi> <ib:mo stretchy="false">(</ib:mo> <ib:mn>4350</ib:mn> <ib:mo stretchy="false">)</ib:mo> </ib:math> , <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"> <mb:mi>Y</mb:mi> <mb:mo stretchy="false">(</mb:mo> <mb:mn>4500</mb:mn> <mb:mo stretchy="false">)</mb:mo> </mb:math> , and <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"> <qb:mi>ψ</qb:mi> <qb:mo stretchy="false">(</qb:mo> <qb:mn>4660</qb:mn> <qb:mo stretchy="false">)</qb:mo> <qb:mo>/</qb:mo> <qb:mi>Y</qb:mi> <qb:mo stretchy="false">(</qb:mo> <qb:mn>4710</qb:mn> <qb:mo stretchy="false">)</qb:mo> </qb:math> , can be accommodated by the charmonium spectrum when the unquenched coupled-channel effects are carefully considered. Published by the American Physical Society 2024

Topics & Concepts