Proper constituent gluon mass as the final piece to construct hybrid mesons

In this Letter, we propose that a proper constituent gluon mass <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>m</a:mi> <a:mi>g</a:mi> </a:msub> <a:mo>=</a:mo> <a:mn>450</a:mn> <a:mtext> </a:mtext> <a:mtext> </a:mtext> <a:mi>MeV</a:mi> </a:math> can be applied to identify the hybrids composed of quarks and gluons. By investigating the spectra and decay widths of the light hybrids <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mo stretchy="false">(</c:mo> <c:mi>q</c:mi> <c:mover accent="true"> <c:mi>q</c:mi> <c:mo stretchy="false">¯</c:mo> </c:mover> <c:mi>g</c:mi> <c:mo stretchy="false">)</c:mo> </c:math> with <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msup> <i:mi>J</i:mi> <i:mi>P</i:mi> </i:msup> <i:mo>=</i:mo> <i:msup> <i:mn>1</i:mn> <i:mrow> <i:mo>−</i:mo> <i:mo>+</i:mo> </i:mrow> </i:msup> </i:math> , we find the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>π</k:mi> <k:mn>1</k:mn> </k:msub> <k:mo stretchy="false">(</k:mo> <k:mn>1600</k:mn> <k:mo stretchy="false">)</k:mo> </k:math> and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>η</o:mi> <o:mn>1</o:mn> </o:msub> <o:mo stretchy="false">(</o:mo> <o:mn>1855</o:mn> <o:mo stretchy="false">)</o:mo> </o:math> may not be explained as <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msup> <s:mn>1</s:mn> <s:mrow> <s:mo>−</s:mo> <s:mo>+</s:mo> </s:mrow> </s:msup> </s:math> hybrids, simultaneously, and the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msub> <u:mi>η</u:mi> <u:mn>1</u:mn> </u:msub> <u:mo stretchy="false">(</u:mo> <u:mn>1855</u:mn> <u:mo stretchy="false">)</u:mo> </u:math> observed by BESIII may not be a hybrid. In addition, we predict an existence of a hybrid <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:msub> <y:mi>η</y:mi> <y:mn>1</y:mn> </y:msub> <y:mo stretchy="false">(</y:mo> <y:mn>1640</y:mn> <y:mo stretchy="false">)</y:mo> </y:math> , which can be verified by searching the <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:msub> <cb:mi>a</cb:mi> <cb:mn>1</cb:mn> </cb:msub> <cb:mo stretchy="false">(</cb:mo> <cb:mn>1260</cb:mn> <cb:mo stretchy="false">)</cb:mo> <cb:mi>π</cb:mi> </cb:math> channel. Moreover, we suggest the <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:msub> <gb:mi>K</gb:mi> <gb:mn>1</gb:mn> </gb:msub> <gb:mo stretchy="false">(</gb:mo> <gb:mn>1270</gb:mn> <gb:mo stretchy="false">)</gb:mo> <gb:mover accent="true"> <gb:mi>K</gb:mi> <gb:mo stretchy="false">¯</gb:mo> </gb:mover> </gb:math> and <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"> <mb:msub> <mb:mi>K</mb:mi> <mb:mn>1</mb:mn> </mb:msub> <mb:mo stretchy="false">(</mb:mo> <mb:mn>1270</mb:mn> <mb:mo stretchy="false">)</mb:mo> <mb:mi>π</mb:mi> </mb:math> as the golden channels to search for isospin-0 and isospin- <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"> <qb:mfrac> <qb:mn>1</qb:mn> <qb:mn>2</qb:mn> </qb:mfrac> </qb:math> hybrids, respectively.