Confronting current NLO parton fragmentation functions with inclusive charged-particle spectra at hadron colliders

TL;DR

The paper evaluates NLO pQCD predictions for inclusive, unidentified charged-hadron spectra against collider data from RHIC, Tevatron, and the LHC across a wide energy range. It reveals that current parton-to-hadron fragmentation functions, particularly the gluon-to-hadron component, tend to be too hard, causing systematic overpredictions by up to a factor of two at pT > 10 GeV/c, with large scale uncertainties at lower pT. Through comparisons of multiple FF sets, the study argues for refitting gluon FFs using high-pT LHC/Tevatron data where perturbative calculations are reliable, to achieve better universality and predictive power. It also highlights potential nonperturbative effects at low pT and the need for NNLO corrections, suggesting a focused region (pT > ~10 GeV/c) for future global FF fits.

Abstract

The inclusive spectra of charged particles measured at high transverse momenta ($p_T\gtrsim$2GeV/c) in proton-proton and proton-antiproton collisions in the range of center-of-mass energies $\sqrt{s}=200-7000$GeV are compared with next-to-leading order perturbative QCD calculations using seven recent sets of parton-to-hadron fragmentation functions (FFs). Accounting for the uncertainties in the scale choices and in the parton distribution functions, we find that most of the theoretical predictions tend to overpredict the measured LHC and Tevatron cross sections by up to a factor of two. We identify the currently too-hard gluon-to-hadron FFs as the probable source of the problem, and justify the need to refit the FFs using the available LHC and Tevatron data in a region of transverse momenta, $p_T\gtrsim$10GeV/c, which is supposedly free from additional non-perturbative contributions and where the scale uncertainty is only modest.

Figures (6)

• Figure 1: Top: Charged-hadron fragmentation functions as a function of $z$ for $u$-quarks (left) and gluons (right) at $Q=20\,\rm{GeV}$. Bottom: Ratio between different FFs over the Kretzer FFs.
• Figure 2: Normalized cross section for charged-hadron production as a function of $z$ for $\sqrt{s}~=~900\,\rm{GeV}$ (left) and $\sqrt{s}=7000\,\rm{GeV}$ (right) for $p_{_{\rm T}}=5\,\rm{GeV/c}$ (solid) and $p_{_{\rm T}}=20\,\rm{GeV/c}$ (dashed) at midrapidity, obtained with Kretzer (dark blue) and dss (orange) FFs.
• Figure 3: Relative contributions of quark (dashed) and gluon (solid) fragmentation to the inclusive charged-hadron cross section at $\sqrt{s}=900\,\rm{GeV}$ (left) and $\sqrt{s}=7000\,\rm{GeV}$ (right) at midrapidity, obtained with Kretzer (dark blue) and dss (orange) FFs.
• Figure 4: Top: Charged-hadron invariant cross sections measured as a function of $p_{_{\rm T}}$ by CMS Chatrchyan:2011avCMS:2012aa at $\sqrt{s}=0.9 \, {\rm TeV}$ (green diamonds), $\sqrt{s}=2.76 \, {\rm TeV}$ (red squares), and $\sqrt{s}=7 \, {\rm TeV}$ (blue circles), compared to NLO calculations with dssdeFlorian:2007hc (left) and Kretzer (right) Kretzer:2000yf FFs. The point-to-point systematic and statistical errors are indicated by colored rectangles and error bars. Bottom: Ratio between the data and the respective calculations. The boxes at the beginning of the $p_{_{\rm T}}$-axis mark the luminosity uncertainties of each measurement.
• Figure 5: Ratio of the inclusive charged-hadron spectra measured by CMS (circles) Chatrchyan:2011avCMS:2012aa, ALICE Abelev:2013ala (diamonds), CDF (squares) Aaltonen:2009ne, and UA1 (triangles) Albajar:1989an at $\sqrt{s}$ = 900--7000 GeV, over the corresponding NLO calculations using the Kretzer FFs. The curves show the NLO predictions obtained with other FF sets: kkp (pink scarcely dashed), dss (green dashed), bfgw (brown long-dashed), hkns (purple dashed-dotted), akk08 (yellow dotted-dashed), and akk05 (red long-dashed short-dashed) relative to Kretzer FFs. The point-to-point systematic and statistical errors are indicated by colored rectangles (gray for CMS and CDF, brown for ALICE, green for UA1) and error bars. The boxes at the beginning of the $p_{_{\rm T}}$-axis mark the overall normalization uncertainty. The light-blue bands correspond to the scale uncertainty envelopes while the dark-blue ones indicate the variations derived from the ct10nlo PDF error sets. The hkns uncertainties are shown by the light-brown bands.