The origin of proton mass from J/$${\Psi }$$ photo-production data
Rong Wang, Xurong Chen, Jarah Evslin
Abstract
Abstract The trace of the stress tensor characterizes the transformation of a theory under rescaling. In quantum chromodynamics (QCD), this trace contains contributions from the bare masses of the quarks and also from a purely quantum effect, called the QCD trace anomaly. It affects all masses in the theory. We present an estimation of the QCD trace anomaly from the near-threshold $$\hbox {J}/{\Psi }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>J</mml:mtext> <mml:mo>/</mml:mo> <mml:mi>Ψ</mml:mi> </mml:mrow> </mml:math> photo-production data of the GlueX experiment, at JLab. We apply a vector meson dominance model to describe the photo-production of $$\hbox {J}/{\Psi }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtext>J</mml:mtext> <mml:mo>/</mml:mo> <mml:mi>Ψ</mml:mi> </mml:mrow> </mml:math> and a running strong coupling which includes the nonperturbative effects in the low $$\mu ^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>μ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> region. Despite the large uncertainty, we find that the experimental data favors a small value of the trace anomaly parameter $$b=0.07\pm 0.17$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>b</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.07</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.17</mml:mn> </mml:mrow> </mml:math> . We report the resulting proton mass decompositions at $$\mu ^2=0.41\hbox { GeV}^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>μ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.41</mml:mn> <mml:mspace/> <mml:msup> <mml:mtext>GeV</mml:mtext> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> and $$\mu ^2=4\hbox { GeV}^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>μ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> <mml:mspace/> <mml:msup> <mml:mtext>GeV</mml:mtext> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> .