Hard pion and prompt photon at RHIC, from single to double inclusive production

TL;DR

The paper develops a unified perturbative QCD framework to study high-$p_\perp$ pion and prompt photon production at RHIC, combining NLO calculations in $p$-$p$ with shadowing and an energy-loss model to predict Au-Au quenching. By comparing to PHENIX data, it extracts a plausible medium transport scale $\omega_c$ and estimates a RHIC energy density $\epsilon_{RHIC}$ on the order of $10$–$15$ GeV/fm$^3$, with a corresponding temperature near $0.36$ GeV. The work demonstrates that photons are less quenched than pions due to the direct contribution, and it shows that photon-pion momentum correlations are especially sensitive to medium-modified fragmentation, offering a promising tool to probe fragmentation in nuclear collisions. It also provides projected counting rates for photon-pion correlations, highlighting the potential for future experimental studies to constrain the properties of the produced medium. Overall, the study connects hard probes with medium parameters and motivates further exploration of photon-tagged observables in heavy-ion collisions at RHIC.

Abstract

Single pion and prompt photon large transverse momentum spectra in p-p and Au-Au collisions are computed in perturbative QCD at RHIC energy, s^1/2 = 200 GeV. Next-to-leading order calculations are discussed and compared with p-p scattering data. Subsequently, quenching factors are computed to leading order for both pions and photons within the same energy loss model. The good agreement with PHENIX preliminary data allows for a lower estimate of the energy density reached in central Au-Au collisions, epsilon > 10 GeV/fm^3. Double inclusive photon-pion production in p-p and Au-Au collisions is then addressed. Next-to-leading order corrections prove rather small in p-p scattering. In Au-Au collisions, the quenching of momentum-correlation spectra is seen to be sensitive to parton energy loss processes, which would help to understand how the fragmentation dynamics is modified in nuclear collisions at RHIC.

Figures (11)

• Figure 1: LO (dashed) and NLO (solid) predictions for pions (left) and prompt photons (right) at $p_{_\perp} = 20$ GeV are shown as a function of the renormalization scale, $\mu$ (normalized to $p_{_\perp}$). The factorization scale $M$ and the fragmentation scale $M_F$ are taken to be equal to $\mu$. The optimal scale is chosen so as to minimize the scale dependence of the NLO predictions (see text).
• Figure 2: Single-pion (left) and single-photon (right) invariant cross section at mid-rapidity in $p$--$p$ collisions computed at NLO accuracy, varying simultaneously the factorization, the renormalization and the fragmentation scales from $\mu_{_{{\rm opt}}}/\sqrt{2}$ to $\sqrt{2} \, \mu_{_{{\rm opt}}}$. The PHENIX data for pions Adler:2003pb (9.6% normalization error not shown) and the PHENIX preliminary data for photons Okada:2005in are also shown for comparison. Photons and pions are produced in the $[-0.35;0.35]$ rapidity interval.
• Figure 3: Scale dependence of the NLO predictions for single-pion (left) and single-photon (right) production at RHIC. Predictions varying simultaneously all scales from $\mu_{_{{\rm opt}}}/\sqrt{2}$ to $\sqrt{2} \mu_{_{{\rm opt}}}$ are normalized to the "central" prediction $\mu = M = M_{_F} = \mu_{_{{\rm opt}}}$.
• Figure 4: PHENIX data for single-pion (left) and PHENIX preliminary single-photon data (right) normalized to the NLO predictions. The experimental error bars are shown as solid (statistical) and dashed (statistical plus systematic) lines, and the theoretical systematic uncertainty is shown as a box. The band indicates the 9.6% normalization error in the PHENIX measurements.
• Figure 5: Ratio of Au--Au over $p$--$p$ single-pion (left) and single-photon (right) production cross section. Calculations are done at LO, assuming (i) isospin (solid), (ii) isospin and shadowing (dotted), (iii) isospin, shadowing and energy loss (band) effects (see text for details). The PHENIX preliminary data on the single-pion Isobe:2005pc and single-photon Adler:2005ig production in Au--Au collisions normalized respectively to $p$--$p$ scattering $\pi^0$ data and to the present NLO prompt photon prediction in $p$--$p$ collisions are also shown for comparison.