Regge trajectories and mass spectrum of heavy tetraquarks

Abstract In this work, we calculated the masses of the ground and radial excited states of heavy tetraquarks in the framework of the nonrelativistic quark model for two wave states nS and nP. The potential used is the parabolic potential plus the spin term, and the method we used to solve the Schrödinger equation is the NU method. The Regge trajectories in the $$(n_{r}, M^{2})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>n</mml:mi> <mml:mi>r</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:msup> <mml:mi>M</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> plane are linear and we obtained the parameters $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> and $$\beta _{0}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>β</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> for each state. The results are in good agreement with the available experimental data and we predicted the structures of tetraquarks X (4.500), X (4.700), X (4.740), X (6.900), X (7.200), Y (4.230), Y (4.660), and $$Z_b(10.650)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Z</mml:mi> <mml:mi>b</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>10.650</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> .