Direct-Photon Puzzle in Heavy-Ion Collisions

• Direct-photon puzzle is the challenge of reconciling measured low-pT yields and large azimuthal anisotropies from complex multi-stage photon emissions in heavy-ion collisions.
• It involves contributions from prompt, thermal, pre-equilibrium, hadronic, and jet–medium interaction sources, each affecting the overall photon spectrum differently.
• Experimental results from RHIC and LHC reveal an excess photon yield and unexpectedly high flow, pushing current theoretical models to incorporate multi-channel emission dynamics.

The direct-photon puzzle is the persistent difficulty of constructing a single quantitatively consistent description of direct-photon production in relativistic heavy-ion collisions that reproduces both the measured low-$p_T$ yields and the large azimuthal anisotropies of those photons. In this context, direct photons are all photons not produced by final-state hadron decays; they are emitted from prompt hard processes, thermal QGP and hadronic matter, pre-equilibrium stages, hadronization, and jet–medium interactions. Because they escape the medium essentially without strong final-state interactions, they encode the full space–time history of the collision, but precisely that time integration makes source separation difficult and gives rise to the puzzle (Gale, 2012, David, 2019).

1. Direct photons, excess ratios, and flow observables

In hadronic and nuclear collisions, the inclusive photon yield is decomposed as

$$\gamma_{\text{incl}}=\gamma_{\text{decay}}+\gamma_{\text{dir}},$$

with

$$\gamma_{\text{dir}}=\gamma_{\text{incl}}-\gamma_{\text{decay}}.$$

Decay photons are dominated by hadron decays, especially $\pi^0\to\gamma\gamma$, whereas direct photons include prompt hard photons from $qg\to q\gamma$ and $q\bar q\to g\gamma$, fragmentation photons, thermal photons from the QGP and hadronic gas, pre-equilibrium photons, hadronization photons, and jet–medium photons such as back-scattering and bremsstrahlung (Masson, 2018, Fries et al., 2012).

Experimentally, the direct-photon excess is commonly expressed through

$$R_\gamma=\frac{\gamma_{\text{incl}}}{\gamma_{\text{decay}}},$$

so that

$$\gamma_{\text{dir}}=\left(1-\frac{1}{R_\gamma}\right)\gamma_{\text{incl}}.$$

At low $p_T$, a direct-photon excess is often characterized by an approximate exponential form,

$$\frac{dN_\gamma}{dp_T}\sim e^{-p_T/T_{\text{eff}}},$$

whose inverse slope $$\gamma_{\text{incl}}=\gamma_{\text{decay}}+\gamma_{\text{dir}},$$0 is an effective temperature folded with collective flow. Azimuthal anisotropies are extracted from

$$\gamma_{\text{incl}}=\gamma_{\text{decay}}+\gamma_{\text{dir}},$$1

and the direct-photon harmonics follow from the statistical subtraction

$$\gamma_{\text{incl}}=\gamma_{\text{decay}}+\gamma_{\text{dir}},$$2

These observables define the empirical content of the puzzle: the simultaneous magnitude of the low-$$\gamma_{\text{incl}}=\gamma_{\text{decay}}+\gamma_{\text{dir}},$$3 excess and the unexpectedly large $$\gamma_{\text{incl}}=\gamma_{\text{decay}}+\gamma_{\text{dir}},$$4 and $$\gamma_{\text{incl}}=\gamma_{\text{decay}}+\gamma_{\text{dir}},$$5 (Fan, 2017, Gale, 2012).

2. Experimental establishment at RHIC and the LHC

At RHIC, PHENIX established the canonical form of the puzzle in Au+Au collisions at $$\gamma_{\text{incl}}=\gamma_{\text{decay}}+\gamma_{\text{dir}},$$6 GeV. In central collisions, the low-$$\gamma_{\text{incl}}=\gamma_{\text{decay}}+\gamma_{\text{dir}},$$7 direct-photon yield exhibits an effective inverse slope

$$\gamma_{\text{incl}}=\gamma_{\text{decay}}+\gamma_{\text{dir}},$$8

well above the pseudo-critical temperature range, while the direct-photon elliptic flow at low $$\gamma_{\text{incl}}=\gamma_{\text{decay}}+\gamma_{\text{dir}},$$9 is large and comparable to that of pions. PHENIX also reported a sizable triangular flow $$\gamma_{\text{dir}}=\gamma_{\text{incl}}-\gamma_{\text{decay}}.$$0, and the low-$$\gamma_{\text{dir}}=\gamma_{\text{incl}}-\gamma_{\text{decay}}.$$1 direct-photon excess shows strong centrality dependence. At higher $$\gamma_{\text{dir}}=\gamma_{\text{incl}}-\gamma_{\text{decay}}.$$2, direct photons are consistent with small or vanishing $$\gamma_{\text{dir}}=\gamma_{\text{incl}}-\gamma_{\text{decay}}.$$3, as expected for prompt photons (Gale, 2012, Fan, 2017).

At the LHC, ALICE supplied the complementary systematics needed to sharpen the interpretation. In pp collisions at $$\gamma_{\text{dir}}=\gamma_{\text{incl}}-\gamma_{\text{decay}}.$$4 and $$\gamma_{\text{dir}}=\gamma_{\text{incl}}-\gamma_{\text{decay}}.$$5 TeV, and in p–Pb collisions at $$\gamma_{\text{dir}}=\gamma_{\text{incl}}-\gamma_{\text{decay}}.$$6 TeV, the double ratio $$\gamma_{\text{dir}}=\gamma_{\text{incl}}-\gamma_{\text{decay}}.$$7 is compatible with unity at very low $$\gamma_{\text{dir}}=\gamma_{\text{incl}}-\gamma_{\text{decay}}.$$8, while at $$\gamma_{\text{dir}}=\gamma_{\text{incl}}-\gamma_{\text{decay}}.$$9 the measurements agree with NLO pQCD. In central Pb–Pb collisions at $\pi^0\to\gamma\gamma$0 TeV, however, ALICE observes a significant low-$\pi^0\to\gamma\gamma$1 excess: $\pi^0\to\gamma\gamma$2 exceeds unity by about $\pi^0\to\gamma\gamma$3–$\pi^0\to\gamma\gamma$4 in the most central events. The derived direct-photon yield is compatible with several hydrodynamic models assuming QGP formation, and the medium effective temperature measured by ALICE is about $\pi^0\to\gamma\gamma$5 higher than that observed by PHENIX at RHIC, consistent with a hotter medium at higher collision energy (Masson, 2018).

These measurements establish a clean hierarchy. Small systems provide no significant low-$\pi^0\to\gamma\gamma$6 excess, high-$\pi^0\to\gamma\gamma$7 photons are described by prompt pQCD baselines, and the excess is tied to large, central A–A systems. The yield side of the direct-photon puzzle is therefore not a trivial artifact of decay subtraction or prompt-photon mis-modeling (Masson, 2018).

3. Why the puzzle arises in dynamical modeling

The theoretical tension is fundamentally temporal. Early QGP stages are hottest and therefore efficient photon emitters, but they carry little collective anisotropy. Late hadronic stages are cooler and less emissive at fixed $\pi^0\to\gamma\gamma$8, but the medium has by then developed strong elliptic and triangular flow. Standard hydrodynamic reasoning therefore predicts that the low-$\pi^0\to\gamma\gamma$9 photon yield should receive a substantial early contribution with small $qg\to q\gamma$0, so the total direct-photon flow should be smaller than hadronic flow. RHIC data violate that expectation: the measured low-$qg\to q\gamma$1 $qg\to q\gamma$2 is positive and as large as that of $qg\to q\gamma$3, while the spectrum simultaneously indicates substantial radiation from hot matter (Gale, 2012).

State-of-the-art calculations that successfully reproduce hadronic soft observables do not remove the discrepancy. Viscous hydrodynamic calculations with QGP and hadronic rates, fluctuating initial conditions, and prompt-photon contributions still underpredict the direct-photon elliptic flow, especially at RHIC. Fluctuating initial conditions and viscous effects are of comparable size, but their net impact is insufficient to bridge the gap. In transport-based decompositions such as PHSD, QGP photons contribute substantially to the low-$qg\to q\gamma$4 yield yet have very small intrinsic $qg\to q\gamma$5, so they dilute the larger anisotropy of hadronic photons; the net result remains below the PHENIX measurement (Bratkovskaya, 2014, Gale, 2018).

This is the core logic of the puzzle: any mechanism that enhances early emission tends to support the yield and slope but suppress the flow, whereas any mechanism that shifts weight to late times tends to raise $qg\to q\gamma$6 but risks undershooting the yield or softening the spectrum. The empirical coexistence of both features forces a nontrivial redistribution of photon sources in space–time (David, 2019).

4. Proposed mechanisms and partial resolutions

One major class of responses emphasizes the late hadronic and near-$qg\to q\gamma$7 region. In hadronic transport, mesonic channels such as $qg\to q\gamma$8 and $qg\to q\gamma$9, together with $q\bar q\to g\gamma$0- and $q\bar q\to g\gamma$1-mediated processes, increase the hadronic photon rate relative to older $q\bar q\to g\gamma$2-only descriptions. A finite $q\bar q\to g\gamma$3-meson width significantly enhances $q\bar q\to g\gamma$4 at low and intermediate photon energies. Because these photons are emitted late, when collective flow is already strong, they are natural carriers of large $q\bar q\to g\gamma$5. The non-equilibrium SMASH implementation was presented explicitly as a first step toward quantifying whether an enhanced hadronic afterburner can help resolve the direct photon flow puzzle, not as a completed solution (Schäfer et al., 2020).

A second proposal separates thermal equilibration from chemical equilibration. In the two-time-scale picture, hydrodynamics starts at $q\bar q\to g\gamma$6 fm/$q\bar q\to g\gamma$7, but full QGP chemical equilibration is delayed to $q\bar q\to g\gamma$8 fm/$q\bar q\to g\gamma$9. The medium is then thermalized but gluon-dominated during the early stage, so photon emission is suppressed when the temperature is highest and the flow anisotropy is smallest. In this construction the direct-photon spectrum is only weakly affected, while the direct-photon $$R_\gamma=\frac{\gamma_{\text{incl}}}{\gamma_{\text{decay}}},$$0 is significantly increased because a larger fraction of photons are emitted later, when the medium already carries sizeable flow (Liu, 2015).

A third line of work isolates additional non-thermal or semi-thermal sources rather than modifying the bulk evolution alone. Jet-tagged back-scattering photons from $$R_\gamma=\frac{\gamma_{\text{incl}}}{\gamma_{\text{decay}}},$$1 and $$R_\gamma=\frac{\gamma_{\text{incl}}}{\gamma_{\text{decay}}},$$2 in the QGP were proposed as a measurable away-side signal below the trigger-jet energy, sensitive to both medium temperature and jet energy loss. These photons are important for source decomposition and QGP tomography, but that program does not claim to solve the full direct-photon puzzle by itself (Fries et al., 2012). More recently, photon production from gluon splitting and fusion induced by a magnetic field during the pre-equilibrium stage was shown to reproduce a significant fraction of the PHENIX excess yield for 20–30% centrality, with splitting dominating over fusion at low photon energies. That mechanism was presented as a plausible contribution to the yield side of the puzzle, while a consistent calculation of the associated $$R_\gamma=\frac{\gamma_{\text{incl}}}{\gamma_{\text{decay}}},$$3 remains ongoing (Ayala et al., 26 Mar 2026).

Taken together, these proposals suggest that the puzzle is unlikely to have a single-channel resolution. A plausible implication is that the observed photons receive non-negligible contributions from several stages—near-$$R_\gamma=\frac{\gamma_{\text{incl}}}{\gamma_{\text{decay}}},$$4 hadronic radiation, chemically delayed QGP emission, and selected pre-equilibrium or jet–medium channels—whose relative weights are still unsettled.

5. Constraints from modern theory and related electromagnetic probes

Recent lattice-QCD input constrains one of the most straightforward escape routes, namely a large arbitrary enhancement of the QGP photon rate. At $$R_\gamma=\frac{\gamma_{\text{incl}}}{\gamma_{\text{decay}}},$$5 MeV, lattice calculations of two moments of the photon spectrum yield

$$R_\gamma=\frac{\gamma_{\text{incl}}}{\gamma_{\text{decay}}},$$6

whereas integrating the full LO AMY rate gives a corresponding range $$R_\gamma=\frac{\gamma_{\text{incl}}}{\gamma_{\text{decay}}},$$7–$$R_\gamma=\frac{\gamma_{\text{incl}}}{\gamma_{\text{decay}}},$$8. The lattice central value is lower than, but compatible with, LO weak coupling. Since the NLO correction is positive, this result disfavors a dramatic enhancement of the hard QGP photon emissivity at $$R_\gamma=\frac{\gamma_{\text{incl}}}{\gamma_{\text{decay}}},$$9. This pushes phenomenology away from explanations that simply amplify the early QGP rate and toward scenarios with stronger late-time or near-$$\gamma_{\text{dir}}=\left(1-\frac{1}{R_\gamma}\right)\gamma_{\text{incl}}.$$0 contributions (Krasniqi et al., 15 May 2025).

On the perturbative side, the leading-order QCD photon rate has also been generalized to non-equilibrium media with LPM resummation in a real-time formalism. That development provides a more systematic treatment of non-equilibrium QGP emission than small $$\gamma_{\text{dir}}=\left(1-\frac{1}{R_\gamma}\right)\gamma_{\text{incl}}.$$1 corrections alone, but the 2018 theory update explicitly states that the photon flow puzzle remains, particularly at RHIC, even within state-of-the-art IP-Glasma + viscous hydrodynamics + hadronic cascade modeling (Gale, 2018).

Dileptons provide an independent cross-check on the same space–time history. The same electromagnetic current correlator governs both real and virtual photons, and dilepton measurements constrain in-medium vector spectral functions, hadronic broadening, and the average temperature of QGP radiation in the intermediate-mass region. A unified description of photons and dileptons is therefore not optional: any large modification introduced to solve the photon puzzle must remain compatible with dilepton spectra and inferred temperatures (Gale, 2012, Scheid, 30 Sep 2025).

6. Broader extensions and open problems

A newer extension of the puzzle concerns global systematics. Low-$$\gamma_{\text{dir}}=\left(1-\frac{1}{R_\gamma}\right)\gamma_{\text{incl}}.$$2 direct-photon yields integrated over $$\gamma_{\text{dir}}=\left(1-\frac{1}{R_\gamma}\right)\gamma_{\text{incl}}.$$3 in PHENIX follow a multiplicity scaling with exponent $$\gamma_{\text{dir}}=\left(1-\frac{1}{R_\gamma}\right)\gamma_{\text{incl}}.$$4, while STAR, using $$\gamma_{\text{dir}}=\left(1-\frac{1}{R_\gamma}\right)\gamma_{\text{incl}}.$$5, finds $$\gamma_{\text{dir}}=\left(1-\frac{1}{R_\gamma}\right)\gamma_{\text{incl}}.$$6. ALICE heavy-ion data are presently consistent with both within uncertainties. At the same time, ALICE measurements in pp at $$\gamma_{\text{dir}}=\left(1-\frac{1}{R_\gamma}\right)\gamma_{\text{incl}}.$$7 TeV find a direct-photon fraction $$\gamma_{\text{dir}}=\left(1-\frac{1}{R_\gamma}\right)\gamma_{\text{incl}}.$$8 of about $$\gamma_{\text{dir}}=\left(1-\frac{1}{R_\gamma}\right)\gamma_{\text{incl}}.$$9–$p_T$0 both in minimum-bias and in high-multiplicity events, so the onset of a thermal-like photon component in small systems remains unclear (Scheid, 30 Sep 2025).

The unresolved problems are therefore multiple. Any successful description must reproduce the absence of a low-$p_T$1 excess in pp and p–A baselines, the $p_T$2–$p_T$3 low-$p_T$4 excess in central Pb–Pb, the RHIC inverse slope $p_T$5 MeV, the approximately $p_T$6 higher effective temperature observed by ALICE at the LHC, and the large low-$p_T$7 $p_T$8 and non-zero $p_T$9 seen at RHIC and the LHC (Masson, 2018, Fan, 2017). The remaining degrees of freedom are the relative importance of near-$$\frac{dN_\gamma}{dp_T}\sim e^{-p_T/T_{\text{eff}}},$$0 hadronic emission, chemical non-equilibrium, pre-equilibrium dynamics, magnetic-field effects, jet–medium channels, and the detailed form of the QGP emissivity itself. The direct-photon puzzle thus remains a stringent test of whether heavy-ion phenomenology can provide a single coherent account of electromagnetic radiation across the full space–time evolution of the QGP (David, 2019, Scheid, 30 Sep 2025).