Studies of $X(3872)$ and $\psi(2S)$ production in $p\bar{p}$ collisions at 1.96 TeV

TL;DR

This study analyzes the production mechanisms of the $X(3872)$ and $ ext{psi}(2S)$ states in proton-antiproton collisions at 1.96 TeV, comparing results with LHC data and testing models of their internal structure.

Contribution

It provides the first detailed comparison of prompt and nonprompt production fractions of $X(3872)$ and $ ext{psi}(2S)$ at Tevatron energies and tests the soft-pion production hypothesis for $X(3872)$.

Findings

Nonprompt fraction $f_{NP}$ for $ ext{psi}(2S)$ increases with transverse momentum.

$f_{NP}$ for $X(3872)$ is constant within uncertainties.

The prompt to nonprompt production ratio for $X(3872)$ decreases significantly from Tevatron to LHC.

Abstract

We present various properties of the production of the $X(3872)$ and $\psi(2S)$ states based on 10.4 fb$^{-1}$ collected by D0 experiment in Tevatron $p \bar p$ collisions at $\sqrt{s}$ = 1.96 TeV. For both states, we measure the nonprompt fraction $f_{NP}$ of the inclusive production rate due to decays of $b$-flavored hadrons. We find the $f_{NP}$ values systematically below those obtained at the LHC. The $f_{NP}$ fraction for $\psi(2S)$ increases with transverse momentum whereas for the X(3872) it is constant within large uncertainties, in agreement with the LHC results. The ratio of prompt to nonprompt $\psi(2S)$ production, $(1 - f_{NP}) / f_{NP}$, decreases only slightly going from the Tevatron to the LHC, but for the $X(3872)$ this ratio decreases by a factor of about 3. We test the soft-pion signature of the $X(3872)$ modeled as a weakly-bound charm-meson pair by studying the production of the $X(3872)$ as a function of the kinetic energy of the $X(3872)$ and the pion in the $X(3872)\pi$ center-of-mass frame. For a subsample consistent with prompt production, the results are incompatible with a strong enhancement in the production of the $X(3872)$ at small kinetic energy of the $X(3872)$ and the $\pi$ in the $X(3872)\pi$ center-of-mass frame expected for the $X$+soft-pion production mechanism. For events consistent with being due to decays of $b$ hadrons, there is no significant evidence for the soft-pion effect but its presence at the level expected for the binding energy of 0.17 MeV and the momentum scale $\Lambda=M(\pi)$ is not ruled out.