Extremely high-energy bremsstrahlung in matter

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This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are running a marathon through a crowded, chaotic city. This is what happens when an electron (a tiny particle of electricity) zooms through a piece of matter, like a block of gold or a puff of air.

The Old Story: The "Crowded City" Effect

For decades, physicists understood that as these electrons run faster and faster, they tend to trip and stumble. When they stumble, they lose energy by shooting out a flash of light (a photon). This is called bremsstrahlung (German for "braking radiation").

In 1934, scientists calculated how often this happens. But in the 1950s, they discovered a weird glitch: The faster you run, the more you get suppressed.

Here is the analogy:
Imagine you are trying to throw a ball (the photon) while running. To throw it properly, you need a few seconds of uninterrupted space to build up your momentum. This is called the "formation time."

Slow runner: You have plenty of space to throw the ball before you hit a wall. You throw it easily.
Super-fast runner: Because you are moving so fast, the "throwing motion" takes a very long time to complete. You end up running through the whole city block while still in the middle of your throwing motion.
The Problem: While you are trying to throw, you bump into other people (atoms in the material). These bumps knock you off balance. Because you are constantly getting bumped while you are trying to throw, you can't finish the throw properly. The result? You throw the ball much less often than you should. This is the famous Landau-Pomeranchuk-Migdal (LPM) effect. It's like the crowd is so dense that your super-speed actually stops you from doing your job.

The New Twist: The "Disappearing Act"

For a long time, physicists thought this "crowd suppression" was the whole story. But in this new paper, the authors (Arnold, Bautista, Elgedawy, and Iqbal) realized there was a second, hidden rule that changes everything at extremely high energies.

They noticed that sometimes, the photon (the ball you are trying to throw) doesn't just wait for you to finish throwing it. It disappears before you even finish!

Here is the new analogy:

You are the electron, running super fast.
You start the motion to throw a photon.
Because you are moving so incredibly fast, the photon you are "creating" is so energetic that, almost instantly, it turns into a brand new pair of particles (an electron and a positron) before it can even fully exist as a photon.
The Surprise: In the old theory, this "disappearing act" was thought to make the suppression worse (like the crowd getting even more annoying).
The Discovery: The authors found the opposite is true! When the photon turns into a pair of particles, it breaks the rhythm of the crowd.

Think of it like a dance. The "crowd" (the atoms) was successfully stopping you from dancing because they kept stepping on your toes during your long dance move. But suddenly, your partner (the photon) vanishes and turns into two new dancers. This sudden change shatters the pattern the crowd was using to stop you.

The Result: Instead of being suppressed, the electron is suddenly allowed to lose energy again! The "disappearing act" actually rescues the electron from the suppression. It's like the crowd stops stepping on your toes because the dance floor suddenly changed.

Why Does This Matter?

The "Deep Freeze" vs. The "Thaw": The old theory predicted that at ultra-high energies, the rate of energy loss would drop to almost zero (a deep freeze). This new paper shows that at the very highest energies, the rate "thaws" out and goes back up.
Future Experiments: We haven't seen this yet because we don't have particle accelerators fast enough to reach these "super-fast" speeds where the photon turns into a pair so quickly. However, the authors suggest that if we build a massive new collider (like the proposed Future Circular Collider), we might finally see this effect.
Cosmic Rays: This helps us understand what happens when giant cosmic rays from deep space hit our atmosphere. They might be behaving differently than we thought, creating more showers of particles than our old models predicted.

In a Nutshell

For 70 years, we thought that running super fast through matter made you stop throwing light because the crowd kept bumping you. This paper says: "Wait! If you run fast enough, the light you are trying to throw turns into something else, and that actually helps you get the crowd off your back, letting you throw again!"

It's a correction to our understanding of how the universe behaves at the very edge of what is possible.

1. Problem Statement

The paper addresses a qualitative incompleteness in the theory of bremsstrahlung ( $e \to e\gamma$ ) for extremely high-energy electrons passing through ordinary matter.

The LPM Effect: Historically, the Landau-Pomeranchuk-Migdal (LPM) effect describes the suppression of bremsstrahlung at high energies. This occurs because the quantum formation time ( $t_{\text{form}}$ ) of the photon exceeds the mean free time between elastic scatterings in the medium. Multiple scatterings during this formation time interfere destructively, suppressing the radiation rate compared to the standard Bethe-Heitler (BH) prediction.
The Overlooked Mechanism: In 1964, Galitsky and Gurevich suggested that at extremely high energies, the formation time becomes so long that the emitted photon itself undergoes medium-induced pair production ( $\gamma \to e\bar{e}$ ) before the bremsstrahlung process is complete. They qualitatively argued this would cause further suppression of the rate.
The Conflict: The authors' previous work (Ref. [13]) demonstrated that Galitsky and Gurevich were incorrect regarding the direction of this effect. Instead of further suppression, the subsequent pair production disrupts the coherence required for the LPM suppression, thereby enhancing the bremsstrahlung rate.
The Gap: The previous analysis was limited to the regime where the photon energy $k_\gamma \gg E_{\text{LPM}}$ (where $E_{\text{LPM}}$ is the medium-dependent energy scale). This paper extends the analysis to the full range of ultra-relativistic energies, specifically covering the region where $k_\gamma \lesssim E_{\text{LPM}}$ , requiring the inclusion of the electron mass ( $m$ ) and the medium-induced photon mass ( $m_\gamma$ , the "dielectric effect").

2. Methodology

The authors perform a full quantum-mechanical calculation of the energy loss rate $d\Gamma/dx_\gamma$ (where $x_\gamma = k_\gamma/E$ ), extending Migdal's formalism to include overlapping pair production.

Formalism: The calculation is adapted from techniques used in QCD LPM studies. The medium is characterized by the transport coefficient $\hat{q}$ , which relates the mean squared transverse momentum kick to the time traversed.
Approximations:
- The medium is assumed large and homogeneous (ignoring edge effects).
- Calculations are performed to leading-log order in the atomic screening logarithm.
- The atomic number $Z$ is assumed large ( $Z \gg 1$ ), neglecting $1/Z$ suppressed effects.
- Only pure QED processes are considered (photo-nuclear processes are ignored as they dominate only above $\sim 10^{20}$ eV).
Key Innovation: Unlike previous studies that treated bremsstrahlung and pair production as distinct sequential events, this work computes the rate for the initial electron to lose a fraction of its energy, naturally accounting for the interference between the $e \to e\gamma$ formation and the subsequent $\gamma \to e\bar{e}$ disruption.
Definitions:
- LPM Rate: The original Migdal rate (without pair production disruption).
- LPM' Rate: The new rate calculated in this paper, including the effects of overlapping pair production.
- Dielectric Effect: The modification of the soft-photon limit due to the effective photon mass $m_\gamma$ in the medium.

3. Key Contributions

Extension to Lower Energies: The analysis is extended from the ultra-high energy limit ( $k_\gamma \gg E_{\text{LPM}}$ ) down to $k_\gamma \lesssim E_{\text{LPM}}$ . This necessitates the inclusion of the electron mass $m$ and the dielectric effect ( $m_\gamma$ ), which were previously negligible.
Correction of Galitsky-Gurevich: The paper confirms and quantifies that the "disruption" of the LPM effect by pair production leads to a significant enhancement of the radiation rate, not suppression.
Comprehensive Phase Diagram: The authors map out the full parameter space of electron energy ( $E$ ) and photon energy ( $k_\gamma$ ), identifying distinct physical regimes and the boundaries between them.
Analytic Formulas: The paper provides limiting formulas for the differential energy loss rate in various asymptotic regions (Table I) and defines the parametric boundaries between these regions (Table II).

4. Results

The paper presents a contour plot (Fig. 2b) of the ratio $\text{LPM}'/\text{BH}$ (modified rate vs. Bethe-Heitler) and Fig. 3 showing the enhancement ratio $\text{LPM}'/\text{LPM}$ .

Physical Regimes Identified:

Region 1 (Bethe-Heitler): Low energy or high photon fraction where LPM suppression is negligible.
Region 2 (Deep LPM): The standard LPM suppression regime where the rate is suppressed by $\sqrt{k_\gamma/E}$ .
Region 3 (Dielectric): Soft photon region modified by the medium-induced photon mass.
Region 4 (Disruption Regime): The core discovery. Here, the formation time is long enough for pair production to occur.
- Region 4a: Previously studied ( $k_\gamma \gg E_{\text{LPM}}$ ). The rate is enhanced by a factor proportional to $\Gamma_{\text{pair}} t_{\text{form}}$ .
- Region 4b & 5: New regimes at lower energies ( $k_\gamma \lesssim E_{\text{LPM}}$ ). The enhancement persists but follows different logarithmic scaling laws involving $m$ and $m_\gamma$ .
Enhancement Mechanism: In Region 4, the limiting formulas can be physically interpreted as the medium-induced pair production rate ( $\Gamma_{\text{pair}}$ ) multiplied by an effective Weizsäcker-Williams probability distribution for finding a photon component in the electron. The pair production effectively "cuts" the formation time, preventing the full destructive interference of the LPM effect.

Quantitative Findings:

The enhancement factor $S_{\text{extra}}$ can be large when $t_{\text{form}} \gg 1/\Gamma_{\text{pair}}$ .
The transition between suppression (Region 2) and enhancement (Region 4) is smooth but significant.
The "dielectric effect" (Region 3 and 5) modifies the soft-photon behavior, creating a distinct boundary where the photon mass $m_\gamma$ becomes relevant.

5. Significance and Outlook

Theoretical Impact: This work resolves a decades-old ambiguity regarding the interplay between LPM suppression and pair production. It establishes that at extremely high energies, the LPM effect is not a monotonic suppression but is subject to a "recovery" or enhancement due to the finite lifetime of the photon in the medium.
Experimental Relevance:
- Current experiments (SLAC, CERN) operate in the standard LPM suppression regime (Region 2) and have not yet probed the enhancement region (Region 4).
- The paper suggests that future facilities, such as a proposed 50 TeV proton beam (e.g., FCC-hh) capable of generating $\sim$ 50 TeV electron beams, could reach the parameter space (marked by the open circle in Fig. 3) where this enhancement is observable.
Future Work: The authors note that for future experimental verification, calculations must be refined to handle finite target thickness (as the formation length and pair-production mean free path become comparable in the enhancement region) and to separate the contributions of overlapping processes more precisely.

In summary, the paper provides a complete, leading-logarithmic QED description of bremsstrahlung in matter at ultra-high energies, revealing that the LPM effect is fundamentally altered by the possibility of the emitted photon converting into a pair before the radiation process is complete, leading to a significant enhancement of the energy loss rate.