Elliptic anisotropy measurement of the f<inf>0</inf>(980) hadron in proton-lead collisions and evidence for its quark-antiquark composition

Abstract

Despite the f<jats:sub>0</jats:sub>(980) hadron having been discovered half a century ago, the question about its quark content has not been settled: it might be an ordinary quark-antiquark (<jats:inline-formula> <jats:alternatives> <jats:tex-math>$${{\rm{q}}}\overline{{{\rm{q}}}}$$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> <mml:mover> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> </jats:alternatives> </jats:inline-formula>) meson, a tetraquark (<jats:inline-formula> <jats:alternatives> <jats:tex-math>$${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{q}}}\overline{{{\rm{q}}}}$$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> <mml:mover> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>q</mml:mi> <mml:mover> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> </jats:alternatives> </jats:inline-formula>) exotic state, a kaon-antikaon (<jats:inline-formula> <jats:alternatives> <jats:tex-math>$${{\rm{K}}}\overline{{{\rm{K}}}}$$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>K</mml:mi> <mml:mover> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> </jats:alternatives> </jats:inline-formula>) molecule, or a quark-antiquark-gluon (<jats:inline-formula> <jats:alternatives> <jats:tex-math>$${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{g}}}$$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> <mml:mover> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>g</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula>) hybrid. This paper reports strong evidence that the f<jats:sub>0</jats:sub>(980) state is an ordinary <jats:inline-formula> <jats:alternatives> <jats:tex-math>$${{\rm{q}}}\overline{{{\rm{q}}}}$$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> <mml:mover> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> </jats:alternatives> </jats:inline-formula> meson, inferred from the scaling of elliptic anisotropies (<jats:italic>v</jats:italic> <jats:sub>2</jats:sub>) with the number of constituent quarks (<jats:italic>n</jats:italic> <jats:sub>q</jats:sub>), as empirically established using conventional hadrons in relativistic heavy ion collisions. The f<jats:sub>0</jats:sub>(980) state is reconstructed via its dominant decay channel f<jats:sub>0</jats:sub>(980) → <jats:italic>π</jats:italic> <jats:sup>+</jats:sup> <jats:italic>π</jats:italic> <jats:sup>−</jats:sup>, in proton-lead collisions recorded by the CMS experiment at the LHC, and its <jats:italic>v</jats:italic> <jats:sub>2</jats:sub> is measured as a function of transverse momentum (<jats:italic>p</jats:italic> <jats:sub>T</jats:sub>). It is found that the <jats:italic>n</jats:italic> <jats:sub>q</jats:sub> = 2 (<jats:inline-formula> <jats:alternatives> <jats:tex-math>$${{\rm{q}}}\overline{{{\rm{q}}}}$$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> <mml:mover> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> </jats:alternatives> </jats:inline-formula> state) hypothesis is favored over <jats:italic>n</jats:italic> <jats:sub>q</jats:sub> = 4 (<jats:inline-formula> <jats:alternatives> <jats:tex-math>$${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{q}}}\overline{{{\rm{q}}}}$$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> <mml:mover> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>q</mml:mi> <mml:mover> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> </jats:alternatives> </jats:inline-formula> or <jats:inline-formula> <jats:alternatives> <jats:tex-math>$${{\rm{K}}}\overline{{{\rm{K}}}}$$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>K</mml:mi> <mml:mover> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> </jats:alternatives> </jats:inline-formula> states) by 7.7, 6.3, or 3.1 standard deviations in the <jats:italic>p</jats:italic> <jats:sub>T</jats:sub> < 10, 8, or 6 GeV/<jats:italic>c</jats:italic> ranges, respectively, and over <jats:italic>n</jats:italic> <jats:sub>q</jats:sub> = 3 (<jats:inline-formula> <jats:alternatives> <jats:tex-math>$${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{g}}}$$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> <mml:mover> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>g</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula> hybrid state) by 3.5 standard deviations in the <jats:italic>p</jats:italic> <jats:sub>T</jats:sub> < 8 GeV/<jats:italic>c</jats:italic> range. This result represents the first determination of the quark content of the f<jats:sub>0</jats:sub>(980) state, made possible by using a novel approach, and paves the way for similar studies of other exotic hadron candidates.