Spectrum of scalar and pseudoscalar glueballs from functional methods

Abstract

Abstract We provide results for the spectrum of scalar and pseudoscalar glueballs in pure Yang–Mills theory using a parameter-free fully self-contained truncation of Dyson–Schwinger and Bethe–Salpeter equations. The only input, the scale, is fixed by comparison with lattice calculations. We obtain ground state masses of $$1.9\,\text {GeV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1.9</mml:mn> <mml:mspace/> <mml:mtext>GeV</mml:mtext> </mml:mrow> </mml:math> and $$2.6\,\text {GeV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2.6</mml:mn> <mml:mspace/> <mml:mtext>GeV</mml:mtext> </mml:mrow> </mml:math> for the scalar and pseudoscalar glueballs, respectively, and $$2.6\,\text {GeV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2.6</mml:mn> <mml:mspace/> <mml:mtext>GeV</mml:mtext> </mml:mrow> </mml:math> and $$3.9\,\text {GeV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>3.9</mml:mn> <mml:mspace/> <mml:mtext>GeV</mml:mtext> </mml:mrow> </mml:math> for the corresponding first excited states. This is in very good quantitative agreement with available lattice results. Furthermore, we predict masses for the second excited states at $$3.7\,\text {GeV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>3.7</mml:mn> <mml:mspace/> <mml:mtext>GeV</mml:mtext> </mml:mrow> </mml:math> and $$4.3\,\text {GeV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>4.3</mml:mn> <mml:mspace/> <mml:mtext>GeV</mml:mtext> </mml:mrow> </mml:math> . The quality of the results hinges crucially on the self-consistency of the employed input. The masses are independent of a specific choice for the infrared behavior of the ghost propagator providing further evidence that this only reflects a nonperturbative gauge completion.

Topics & Concepts