Relativistic flux-tube model predictions from charmed mesons to double-charmed baryons

Utilizing comprehensive experimental data on charmed mesons, we systematically investigate masses of the higher radial and orbital excitations of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>D</a:mi> </a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>D</c:mi> <c:mi>s</c:mi> </c:msub> </c:math> meson families using the relativistic flux-tube model. Our study employs mass splitting induced by spin-dependent interactions within the j-j coupling scheme. Our predicted masses align well with the experimental measurements for the well-established <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>D</e:mi> </e:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>D</g:mi> <g:mi>s</g:mi> </g:msub> </g:math> states. However, anomalous resonances such as <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msub> <i:mi>D</i:mi> <i:mrow> <i:mi>s</i:mi> <i:mn>0</i:mn> </i:mrow> </i:msub> <i:mo stretchy="false">(</i:mo> <i:mn>2317</i:mn> <i:mo stretchy="false">)</i:mo> </i:math> and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msub> <m:mi>D</m:mi> <m:mrow> <m:mi>s</m:mi> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo stretchy="false">(</m:mo> <m:mn>2460</m:mn> <m:mo stretchy="false">)</m:mo> </m:math> do not align with conventional meson states within our theoretical framework. We also study strong decays using an effective Lagrangian formalism that combines heavy-quark symmetry with chiral dynamics, focusing on two-body modes into a charmed meson plus a light pseudoscalar ( <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>π</q:mi> </q:math> , <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>K</s:mi> </s:math> , <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mi>η</u:mi> </u:math> ). Using the combined constraints from masses and decay patterns we propose spectroscopic assignments for several recently observed resonances, including <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:msub> <w:mi>D</w:mi> <w:mn>2</w:mn> </w:msub> <w:mo stretchy="false">(</w:mo> <w:mn>2740</w:mn> <w:msup> <w:mo stretchy="false">)</w:mo> <w:mn>0</w:mn> </w:msup> </w:math> , <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:msubsup> <ab:mi>D</ab:mi> <ab:mn>3</ab:mn> <ab:mo>*</ab:mo> </ab:msubsup> <ab:mo stretchy="false">(</ab:mo> <ab:mn>2750</ab:mn> <ab:mo stretchy="false">)</ab:mo> </ab:math> , <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:msub> <eb:mi>D</eb:mi> <eb:mn>0</eb:mn> </eb:msub> <eb:mo stretchy="false">(</eb:mo> <eb:mn>2550</eb:mn> <eb:msup> <eb:mo stretchy="false">)</eb:mo> <eb:mn>0</eb:mn> </eb:msup> </eb:math> , <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:msubsup> <ib:mi>D</ib:mi> <ib:mn>1</ib:mn> <ib:mo>*</ib:mo> </ib:msubsup> <ib:mo stretchy="false">(</ib:mo> <ib:mn>2600</ib:mn> <ib:msup> <ib:mo stretchy="false">)</ib:mo> <ib:mn>0</ib:mn> </ib:msup> </ib:math> , <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"> <mb:msubsup> <mb:mi>D</mb:mi> <mb:mn>1</mb:mn> <mb:mo>*</mb:mo> </mb:msubsup> <mb:mo stretchy="false">(</mb:mo> <mb:mn>2760</mb:mn> <mb:msup> <mb:mo stretchy="false">)</mb:mo> <mb:mn>0</mb:mn> </mb:msup> </mb:math> , <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"> <qb:msubsup> <qb:mi>D</qb:mi> <qb:mi>J</qb:mi> <qb:mo>*</qb:mo> </qb:msubsup> <qb:mo stretchy="false">(</qb:mo> <qb:mn>3000</qb:mn> <qb:mo stretchy="false">)</qb:mo> </qb:math> , <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"> <ub:msub> <ub:mi>D</ub:mi> <ub:mi>J</ub:mi> </ub:msub> <ub:mo stretchy="false">(</ub:mo> <ub:mn>3000</ub:mn> <ub:mo stretchy="false">)</ub:mo> </ub:math> , <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"> <yb:msubsup> <yb:mi>D</yb:mi> <yb:mn>2</yb:mn> <yb:mo>*</yb:mo> </yb:msubsup> <yb:mo stretchy="false">(</yb:mo> <yb:mn>3000</yb:mn> <yb:mo stretchy="false">)</yb:mo> </yb:math> , <cc:math xmlns:cc="http://www.w3.org/1998/Math/MathML" display="inline"> <cc:msubsup> <cc:mi>D</cc:mi> <cc:mrow> <cc:mi>s</cc:mi> <cc:mn>1</cc:mn> </cc:mrow> <cc:mo>*</cc:mo> </cc:msubsup> <cc:mo stretchy="false">(</cc:mo> <cc:mn>2860</cc:mn> <cc:msup> <cc:mo stretchy="false">)</cc:mo> <cc:mo>±</cc:mo> </cc:msup> </cc:math> , and <gc:math xmlns:gc="http://www.w3.org/1998/Math/MathML" display="inline"> <gc:msubsup> <gc:mi>D</gc:mi> <gc:mrow> <gc:mi>s</gc:mi> <gc:mn>3</gc:mn> </gc:mrow> <gc:mo>*</gc:mo> </gc:msubsup> <gc:mo stretchy="false">(</gc:mo> <gc:mn>2860</gc:mn> <gc:msup> <gc:mo stretchy="false">)</gc:mo> <gc:mo>±</gc:mo> </gc:msup> </gc:math> . We also identify <kc:math xmlns:kc="http://www.w3.org/1998/Math/MathML" display="inline"> <kc:msub> <kc:mi>D</kc:mi> <kc:mrow> <kc:mi>s</kc:mi> <kc:mi>J</kc:mi> </kc:mrow> </kc:msub> <kc:mo stretchy="false">(</kc:mo> <kc:mn>3040</kc:mn> <kc:msup> <kc:mo stretchy="false">)</kc:mo> <kc:mo>+</kc:mo> </kc:msup> </kc:math> as a <oc:math xmlns:oc="http://www.w3.org/1998/Math/MathML" display="inline"> <oc:mn>2</oc:mn> <oc:mi>P</oc:mi> <