Masses of positive- and negative-parity hadron ground-states, including those with heavy quarks
Pei-Lin Yin, Zhu-Fang Cui, Craig D. Roberts, Jorge Segovia
Abstract
Abstract A symmetry-preserving treatment of a vector $$\times $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>×</mml:mo> </mml:math> vector contact interaction is used to compute spectra of ground-state $$J^P = 0^\pm , 1^\pm $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>J</mml:mi> <mml:mi>P</mml:mi> </mml:msup> <mml:mo>=</mml:mo> <mml:msup> <mml:mn>0</mml:mn> <mml:mo>±</mml:mo> </mml:msup> <mml:mo>,</mml:mo> <mml:msup> <mml:mn>1</mml:mn> <mml:mo>±</mml:mo> </mml:msup> </mml:mrow> </mml:math> $$(f{\bar{g}})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>f</mml:mi> <mml:mover> <mml:mrow> <mml:mi>g</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> mesons, their partner diquark correlations, and $$J^P=1/2^\pm , 3/2^\pm $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>J</mml:mi> <mml:mi>P</mml:mi> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:msup> <mml:mn>2</mml:mn> <mml:mo>±</mml:mo> </mml:msup> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> <mml:mo>/</mml:mo> <mml:msup> <mml:mn>2</mml:mn> <mml:mo>±</mml:mo> </mml:msup> </mml:mrow> </mml:math> ( fg h ) baryons, where $$f,g,h \in \{u,d,s,c,b\}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>,</mml:mo> <mml:mi>g</mml:mi> <mml:mo>,</mml:mo> <mml:mi>h</mml:mi> <mml:mo>∈</mml:mo> <mml:mo>{</mml:mo> <mml:mi>u</mml:mi> <mml:mo>,</mml:mo> <mml:mi>d</mml:mi> <mml:mo>,</mml:mo> <mml:mi>s</mml:mi> <mml:mo>,</mml:mo> <mml:mi>c</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mo>}</mml:mo> </mml:mrow> </mml:math> . Results for the leptonic decay constants of all mesons are also obtained, including scalar and pseudovector states involving heavy quarks. The spectrum of baryons produced by this chiefly algebraic approach reproduces the 64 masses known empirically or computed using lattice-regularised quantum chromodynamics with an accuracy of 1.4(1.2)%. It also has the richness of states typical of constituent-quark models and predicts many baryon states that have not yet been observed. The study indicates that dynamical, nonpointlike diquark correlations play an important role in all baryons; and, typically, the lightest allowed diquark is the most important component of a baryon’s Faddeev amplitude.