Constituent model of light hybrid meson decays

A model of light hybrid mesons and their strong decays is developed. The model employs a gluonic quasiparticle to describe low energy gluodynamics and uses the QCD Hamiltonian in Coulomb gauge to guide the construction of states and decay amplitudes. We compute the partial widths of the twelve low lying isovector and vector hybrids. Implications of these results on hybrid searches are also made, with the chief conclusions being that direct observation of the vector states will be difficult, that a hybrid <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>π</a:mi><a:mo stretchy="false">(</a:mo><a:mn>1800</a:mn><a:mo stretchy="false">)</a:mo></a:math> has distinctive decay characteristics, a narrow <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>η</e:mi><e:mo stretchy="false">(</e:mo><e:mn>1900</e:mn><e:mo stretchy="false">)</e:mo></e:math> hybrid should exist, an <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>η</i:mi><i:mn>1</i:mn></i:msub><i:mo stretchy="false">(</i:mo><i:mn>1750</i:mn><i:mo stretchy="false">)</i:mo></i:math> should be sought, and that the exotic nature of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msup><m:mi>J</m:mi><m:mrow><m:mi>P</m:mi><m:mi>C</m:mi></m:mrow></m:msup><m:mo>=</m:mo><m:msup><m:mn>2</m:mn><m:mrow><m:mo>−</m:mo><m:mo>+</m:mo></m:mrow></m:msup></m:math> hybrid mesons should be discernible with sufficient data. We argue that the isovector <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>π</o:mi><o:mn>2</o:mn></o:msub></o:math> hybrid has been discovered, giving a total of four possible hybrid mesons, <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>π</q:mi><q:mn>1</q:mn></q:msub><q:mo stretchy="false">(</q:mo><q:mn>1600</q:mn><q:mo stretchy="false">)</q:mo></q:math>, <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>, <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>π</y:mi><y:mo stretchy="false">(</y:mo><y:mn>1800</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>π</cb:mi><cb:mn>2</cb:mn></cb:msub><cb:mo stretchy="false">(</cb:mo><cb:mn>2360</cb:mn><cb:mo stretchy="false">)</cb:mo></cb:math>, which appear to be filling out the low lying hybrid supermultiplet in the expected fashion.