On the Role of Prompt Photons in the Anisotropic Emission of Direct Photons -- Direct Photons from Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV with IP-Glasma Initial Condition

Using a (3+1)-dimensional viscous hydrodynamic model with IP-Glasma initial conditions, this study demonstrates that accurately accounting for prompt photon contributions resolves the long-standing discrepancy between theoretical predictions and experimental measurements of direct photon anisotropic flow in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV.

The Gist

Imagine two heavy gold atoms smashing into each other at nearly the speed of light. This collision creates a tiny, super-hot fireball of matter known as a Quark-Gluon Plasma (QGP). As this fireball expands and cools, it emits light in the form of photons.

The paper by Fu-Ming Liu investigates a specific mystery: Why does the light coming out of this explosion flow in a specific, lopsided pattern?

Here is a breakdown of the paper's story, using simple analogies:

1. The Two Types of "Light Bulbs"

The authors explain that the light (photons) coming from this collision comes from two very different sources, acting like two different types of light bulbs in a room:

• The "Flashbulbs" (Prompt Photons): These are created instantly at the very moment the gold atoms crash. They are like a camera flash going off. Because they are created instantly and travel so fast, they don't interact with the messy, expanding fireball. They fly straight out in all directions equally. In physics terms, they are isotropic (the same in every direction) and contribute zero to the "flow" or shape of the light.
• The "Glowing Embers" (Thermal Photons): These are created continuously as the hot fireball expands and cools down. Imagine a campfire where the embers are glowing. As the fireball spins and stretches, these embers get pushed around, creating a specific shape or "flow" in the light they emit. These are the ones responsible for the lopsided patterns (called elliptic and triangular flow).

2. The Big Puzzle

For a long time, scientists had a problem. When they measured the light from these collisions, the "flow" (how lopsided the light was) was huge.

When they tried to calculate this using their best computer models, the "glowing embers" (thermal photons) didn't seem to produce enough flow to match the real data. It was as if the model predicted a gentle breeze, but the experiment showed a hurricane. Scientists were confused: How can the light flow so strongly?

3. The Missing Ingredient: The "Flashbulb" Count

The authors realized the problem wasn't with the "glowing embers" calculation, but with how they were counting the "flashbulbs" (prompt photons).

Think of it like a crowd of people holding signs.

• Some people hold signs that say "Flow" (Thermal photons).
• Some people hold blank signs (Prompt photons).

If you want to measure how much the crowd is moving in a specific direction, you have to ignore the people with blank signs. However, if you overestimate how many people are holding blank signs, you dilute the average. You think the crowd is less organized than it actually is.

The Paper's Discovery:
Previous studies had overestimated the number of "flashbulbs" (prompt photons). Because they thought there were so many blank signs, they calculated that the "Flow" signs were being drowned out, leading to a low flow prediction.

The authors recalculated the "flashbulbs" more carefully. They found there were fewer prompt photons than previously thought.

4. The Solution

When they corrected the count:

1. The "blank signs" (prompt photons) were fewer.
2. This meant the "Flow signs" (thermal photons) made up a larger percentage of the total light.
3. Because the thermal photons naturally have a strong flow, and they now make up a bigger chunk of the total, the average flow of the entire light matched the experimental data perfectly.

5. The Results

• The Shape: The paper shows that their new model matches the real-world data from the RHIC accelerator (where gold atoms are smashed) very well.
• The Flow: They successfully explained the "elliptic flow" (an oval shape) and "triangular flow" (a triangle shape) of the light without needing to invent new physics.
• The Takeaway: The "large flow" observed in experiments isn't a mystery anymore. It's simply because we were previously counting too many "flashbulbs" (prompt photons), which masked the strong flow coming from the "glowing embers" (thermal photons).

In short: The paper fixes a math error in how we count the "instant" light versus the "hot fireball" light. Once the count is right, the theory finally explains why the light from these atomic collisions flows in such a strong, specific pattern.

Technical Summary

1. Problem Statement

The paper addresses a long-standing challenge in heavy-ion collision physics: the simultaneous description of experimental data for both hadrons and direct photons (specifically their yields, elliptic flow $v_2$, and triangular flow $v_3$).

• The "Photon Flow Puzzle": Previous theoretical calculations (e.g., by the Paquet group using IP-Glasma initial conditions and viscous hydrodynamics) successfully described hadron data but significantly underpredicted the observed elliptic ($v_2$) and triangular ($v_3$) flow of direct photons measured at RHIC.
• The Discrepancy: Theoretical models predicted that thermal photons (emitted from the hot medium) would have high flow, but the inclusion of prompt photons (emitted at the initial collision) was thought to dilute this flow. However, previous calculations suggested that even with prompt photons, the resulting total direct photon flow was too low to match experimental data, or conversely, that the measured flow was "too large" to be explained by standard thermal models.
• Objective: To resolve this discrepancy by rigorously calculating the contribution of prompt photons and determining how their yield affects the observed anisotropic flow of total direct photons.

2. Methodology

The authors employ a comprehensive (3+1)-dimensional viscous hydrodynamic framework coupled with a specific initial condition and a two-component photon emission model.

• Collision System & Initial Conditions:

  • System: Au+Au collisions at $\sqrt{s_{NN}} = 200$ GeV.
  • Initial Condition: IP-Glasma model, which describes the initial energy-momentum distribution based on the color glass condensate framework.
  • Hydrodynamics: The evolution of the hot, dense matter is simulated using the EPOS3102 framework, solving relativistic viscous hydrodynamic equations. The system evolves from an initial time $\tau_0 = 0.4$ fm/c through the Quark-Gluon Plasma (QGP) and Hadronic Gas (HG) phases until freeze-out.

• Direct Photon Sources:
  The total direct photon yield is treated as the sum of two distinct components:

  1. Prompt Photons: Emitted during the initial hard scattering of partons (quarks and gluons) before thermalization.
     • Calculation: Calculated to Next-to-Leading Order (NLO) using the MRST 2001 parton distribution functions (PDFs) with EKS98 nuclear shadowing corrections.
     • Key Assumption: Prompt photons have a long mean free path and escape the medium without interaction. Consequently, they are emitted isotropically in the azimuthal angle, contributing zero to $v_2$ and $v_3$.
  2. Thermal Photons: Emitted throughout the expansion of the QGP and HG phases.
     • Calculation: Emission rates ($\Gamma$) are calculated using the AMY rate for the QGP phase and parameterized rates for the HG phase (e.g., $\pi+\rho \to \pi+\gamma$).
     • Flow Generation: These photons inherit the collective flow velocity of the medium, generating non-zero $v_2$ and $v_3$.

• Flow Calculation & Event Plane:

  • The flow harmonics ($v_n$) are calculated relative to the event plane, reconstructed using charged hadrons from the freeze-out stage.
  • Two rapidity windows for event plane determination were tested: a wide window ($-5 \le \eta \le 5$) and a narrow mid-rapidity window ($-1 \le \eta \le 1$).
  • Mixing Formula: Since prompt photons have $v_n = 0$, the total direct photon flow ($v_n^{dir}$) is a weighted average:
    $$v_n^{dir} = \frac{N_{th}}{N_{th} + N_{pr}} \times v_n^{th}$$
    Where $N_{th}$ and $N_{pr}$ are the yields of thermal and prompt photons, respectively.

3. Key Contributions

• Re-evaluation of Prompt Photon Yields: The authors identify a critical overestimation of prompt photon yields in previous literature (specifically the Paquet group). Their calculation shows prompt photon yields are significantly lower (by an order of magnitude at $p_T \approx 1$ GeV/c and a factor of four at $p_T \approx 2$ GeV/c) than previously reported.
• Resolution of the Flow Puzzle: By correcting the prompt photon yield, the authors demonstrate that the "dilution" of thermal flow is less severe than previously thought. This allows the theoretical $v_2$ and $v_3$ of total direct photons to align with experimental data without requiring exotic physics or excessive corrections.
• Systematic Comparison: The study provides a direct, side-by-side comparison of spectra and flow coefficients across three centrality bins (0-20%, 20-40%, 40-60%) using the same IP-Glasma initial conditions as previous studies but with a revised prompt photon calculation.

4. Results

• Transverse Momentum ($p_T$) Spectra:

  • The calculated total direct photon spectra show excellent agreement with experimental data from STAR and PHENIX across all centrality bins.
  • Low $p_T$: Dominated by thermal photons.
  • High $p_T$: Dominated by prompt photons.
  • The agreement at high $p_T$ validates the reliability of the prompt photon calculation.

• Elliptic Flow ($v_2$) and Triangular Flow ($v_3$):

  • 20-40% Centrality: The calculated $v_2$ and $v_3$ of direct photons show excellent agreement with PHENIX data.
  • 0-20% (Central) Centrality: The model slightly underpredicts the data, but the discrepancy is significantly reduced compared to previous models.
  • 40-60% (Peripheral) Centrality: The model slightly overpredicts the data.
  • Crucial Finding: The measured $v_2$ of direct photons is no longer "too large" to be explained by standard thermal models. The previous "puzzle" arose because earlier models overestimated the prompt photon fraction, which artificially suppressed the predicted total flow.

• Comparison with Paquet et al.:

  • The authors' thermal photon results are consistent with Paquet et al. for $p_T < 2$ GeV/c.
  • However, due to the lower prompt photon yield in this study, the thermal component dominates the total yield up to $p_T \approx 4$ GeV/c. Consequently, the total direct photon $v_2$ follows the thermal curve more closely, resulting in higher values that match the data, whereas Paquet's higher prompt yield forced the total $v_2$ down to values below the data.

• Event Plane Sensitivity:

  • The choice of rapidity window for event plane reconstruction affects the results, particularly in peripheral collisions (low multiplicity). A wider window ($-5 \le \eta \le 5$) provides a more accurate reaction plane estimate, leading to slightly different flow values compared to a narrow window.

5. Significance

This paper fundamentally shifts the understanding of direct photon anisotropy in heavy-ion collisions.

1. Validation of Standard Models: It demonstrates that standard viscous hydrodynamics with IP-Glasma initial conditions, when combined with a rigorously calculated prompt photon component, can simultaneously describe hadron and photon data (yields and flow).
2. Resolution of the "Large Flow" Anomaly: It resolves the paradox where experimental $v_2$ seemed too large for theory. The anomaly was an artifact of overestimating the prompt photon contribution.
3. Methodological Impact: The work highlights the critical sensitivity of flow observables to the precise calculation of prompt photon yields. It suggests that future analyses must carefully constrain prompt photon contributions to avoid misinterpreting thermal medium properties.
4. Framework for Future Studies: The successful application of this framework at RHIC energies provides a robust baseline for interpreting direct photon data at the LHC and future facilities like the EIC.