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$Υ(nS)$ and $χ_b(nP)$ production at hadron colliders in nonrelativistic QCD

H. Han, Y. Q. Ma, C. Meng, H. S. Shao, Y. J. Zhang, K. T. Chao

TL;DR

This paper applies NLO NRQCD to hadron-collider production of $Υ(nS)$ and $χ_b(nP)$ (n=1,2,3), incorporating full feeddown from higher states. By fitting yield data from LHC experiments, it extracts the relevant LDMEs, including combinations $M_{0,r_0}^{Υ(nS)}$ and $M_{1,r_1}^{Υ(nS)}$ and the ratios $r_{nP}$ for $χ_b(nP)$. Using these LDMEs, it predicts the polarizations $λ_θ$ of prompt $Υ(nS)$ and finds good agreement with CMS measurements, notably attributing the $Υ(3S)$ polarization to substantial $χ_b(3P)$ feeddown. The results provide a coherent description of both cross sections and polarizations at large $p_T$ and highlight the importance of accurate feeddown treatment in bottomonium production.

Abstract

$Υ(nS)$ and $χ_b(nP)$ (n=1,2,3) production at the LHC is studied at next-to-leading order in $α_s$ in nonrelativistic QCD. Feeddown contributions from higher $χ_b$ and $Υ$ states are all considered for lower $Υ$ cross sections and polarizations. The long distance matrix elements (LDMEs) are extracted from the yield data, and then used to make predictions for the $Υ(nS)$ polarizations, which are found to be consistent with the measured polarization data within errors. In particular, the $Υ(3S)$ polarization puzzle can be understood by a large feeddown contribution from $χ_b(3P)$ states. Our results may provide a good description for both cross sections and polarizations of prompt $Υ(nS)$ and $χ_b(nP)$ production at the LHC.

$Υ(nS)$ and $χ_b(nP)$ production at hadron colliders in nonrelativistic QCD

TL;DR

This paper applies NLO NRQCD to hadron-collider production of and (n=1,2,3), incorporating full feeddown from higher states. By fitting yield data from LHC experiments, it extracts the relevant LDMEs, including combinations and and the ratios for . Using these LDMEs, it predicts the polarizations of prompt and finds good agreement with CMS measurements, notably attributing the polarization to substantial feeddown. The results provide a coherent description of both cross sections and polarizations at large and highlight the importance of accurate feeddown treatment in bottomonium production.

Abstract

and (n=1,2,3) production at the LHC is studied at next-to-leading order in in nonrelativistic QCD. Feeddown contributions from higher and states are all considered for lower cross sections and polarizations. The long distance matrix elements (LDMEs) are extracted from the yield data, and then used to make predictions for the polarizations, which are found to be consistent with the measured polarization data within errors. In particular, the polarization puzzle can be understood by a large feeddown contribution from states. Our results may provide a good description for both cross sections and polarizations of prompt and production at the LHC.

Paper Structure

This paper contains 4 sections, 7 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Feeddown and $\chi_b(nP)$
  3. Prompt $\Upsilon(nS)$ production
  4. Summary

Figures (4)

  • Figure 1: Differential $p_T$ cross sections for the experimental windows of ATLAS, CMS and CDF. From left to right: $\Upsilon(1S)$, $\Upsilon(2S)$, $\Upsilon(3S)$. The contributions from direct production are denoted by dashed lines, while those from feeddown by dashed-dotted lines. The $\chi_{b1}(nP)-\Upsilon(nS)$ and $\chi_{b2}(nP)-\Upsilon(nS)$ feeddown contributions are denoted by the solid and dotted lines, respectively. The experimental data are taken from Refs. Aad:2012dlqChatrchyan:2013ynaAcosta:2001gv.
  • Figure 2: The fractions of $\Upsilon(mS)~(m=1,2,3)$ production originating from $\chi_b(nP)~(n=1,2,3;~n\geq m)$ feeddown contributions, denoted as $R_{\Upsilon(mS)}^{\chi_b(nP)}$ (in units of percentage). From left to right: $R_{\Upsilon(1S)}^{\chi_b(1P)}$, $R_{\Upsilon(2S)}^{\chi_b(2P)}$, $R_{\Upsilon(1S)}^{\chi_b(2P)}$ in the first row and $R_{\Upsilon(3S)}^{\chi_b(3P)}$, $R_{\Upsilon(2S)}^{\chi_b(3P)}$, $R_{\Upsilon(1S)}^{\chi_b(3P)}$ in the second row. Our predictions are denoted by the blue bands, while those obtained by using parameters in Ref.Gong:2013qka are denoted by the yellow bands. Experimental data are taken from Ref.Aaij:2014caa.
  • Figure 3: The ratio of differential cross sections of $\chi_{b2}(1P)$ to $\chi_{b1}(1P)$ for the experimental windows of CMS. The blue band is our NLO results with the extracted value of $r_{1P}$ in Tab. \ref{['rnp-fit']} and the yellow band is obtained by using parameters in Ref.Gong:2013qka. Experimental data are taken from Ref.Khachatryan:2014ofa
  • Figure 4: The polarization parameter $\lambda_\theta$ in the helicity frame for the experimental widows at the LHC. From left to right: $\Upsilon(1S)$, $\Upsilon(2S)$, $\Upsilon(3S)$. The contributions from direct production are denoted by dashed lines, while those from feeddown by dashed-dotted lines. The total results are denoted by the blue bands. The experimental data are taken from Ref.Chatrchyan:2012woa.