Two Photon DecayEdit

Two photon decay refers to a category of electromagnetic transitions in which an excited quantum state returns to a lower-energy state through the simultaneous emission of two photons. This process stands in contrast to the more familiar single-photon transitions and arises from higher-orders in quantum electrodynamics (QED). Because certain transitions are forbidden as one-photon processes by angular-momentum and parity conservation, two-photon emission provides a crucial channel for de-excitation in a variety of systems, from simple atoms to subatomic particles. The study of two-photon decays has yielded precise tests of QED, offered insight into the structure of hadrons, and helped illuminate how fundamental symmetries manifest in electromagnetic interactions.

Two photon decay appears in several physical contexts: - In atomic physics, the canonical example is the metastable hydrogen 2s state decaying to the 1s ground state via two photons. This transition is forbidden as a one-photon electric dipole (E1) process but proceeds as a second-order two-photon emission, with characteristic energy sharing and angular correlations of the photon pair. - In particle physics, the neutral pion (pion) decays predominantly into two photons, a process tied to the axial anomaly in quantum chromodynamics (QCD) and serving as a stringent test of the interplay between QED and hadronic structure. - In heavy quarkonium and other meson systems, certain 0++ or 2++ states can decay to two photons, providing laboratories for testing perturbative and nonperturbative aspects of QCD. - In the electroweak sector and Higgs physics, decays to two photons (for example, the Higgs boson decaying to two photons) are experimentally clean channels that help determine fundamental couplings and loop effects.

Overview

Two-photon decays are described by second-order perturbation theory in the electromagnetic coupling, reflecting the fact that two photons are emitted in a single transition event. The transition amplitude involves a sum over intermediate states and carries information about the quantum numbers of the initial and final states, as well as about the spectrum of allowed intermediate configurations. The total energy carried by the two photons equals the energy difference between the initial and final states, while the individual photon energies can vary, subject to energy conservation and the available phase space.

Key features of two-photon decays include: - Selection rules: For many transitions, a one-photon channel is forbidden by angular momentum or parity considerations, while a two-photon channel remains allowed. This makes two-photon decays an important de-excitation pathway when other routes are suppressed. - Photon correlations: The two photons are not emitted independently; their energies, directions, and polarizations exhibit correlations that encode the quantum numbers of the transition and, in some cases, the entanglement between the photons. - Sensitivity to structure and higher-order effects: Because the process probes higher-order QED and, in hadronic cases, the structure of the participating states, precise measurements of two-photon decay rates contribute to tests of fundamental theories and their symmetries.

In atomic systems, the hydrogen 2s → 1s two-photon decay is the prototype and has been studied extensively both theoretically and experimentally. In particle physics, the π0 → γγ decay is a cornerstone for understanding anomalies and the role of chiral symmetry in QCD. In broader contexts, two-photon decays serve as clean electromagnetic probes that complement single-photon transitions in testing the limits of current theories.

Atomic systems: hydrogen 2s → 1s and related transitions

The prototypical two-photon atomic decay is the 2s state of the hydrogen atom transitioning to the 1s ground state. The single-photon E1 transition between these two states is forbidden by angular-momentum and parity constraints, so the decay proceeds almost entirely through the simultaneous emission of two photons. The rate for this two-photon decay is small compared with allowed one-photon transitions, yet it is large enough to be observable and serves as a precise testbed for QED.

Rate and lifetime: The two-photon decay rate for hydrogen 2s → 1s is approximately 8 s^-1, corresponding to a lifetime on the order of 10^-1 seconds for the 2s state. The exact value depends on the level of theory and the inclusion of higher-order corrections, but it is a well-established benchmark in atomic theory.
Energy sharing and angular distributions: Because the total energy difference ΔE is fixed, the two photons share energy in a continuous distribution. The angular and polarization correlations reflect the initial and final-state quantum numbers and the intermediate-state contributions that mediate the transition.
Entanglement and fundamental tests: The two photons from the 2s → 1s decay can exhibit polarization entanglement, making the process a natural platform for studies of quantum correlations and tests of fundamental symmetries in light-mield interactions.

Other atomic examples include higher-lying states in hydrogen and other simple atoms where single-photon decays are forbidden and two-photon channels provide the leading de-excitation path. The theoretical framework for these processes relies on second-order QED and the sum over a complete set of intermediate states, with results that are sensitive to the structure of the atom and to radiative corrections arising in high-precision measurements.

Particle physics: π0 decay and related two-photon processes

The neutral pion (π0) decays to two photons with a rate that dominates its decay width. This two-photon decay is not merely a straightforward electromagnetic transition; it is intimately connected to the axial anomaly in QCD, a quantum effect that breaks a classical symmetry and thereby enables processes forbidden at tree level.

π0 → γγ and the axial anomaly: The decay π0 → γγ proceeds through a quantum anomaly that links the chiral properties of quarks to electromagnetic interactions. The observed rate agrees with the predictions once the anomaly is properly incorporated, providing a striking confirmation of the interplay between QED and the nonperturbative structure of the strong interaction.
Decay width and lifetime: The decay width Γ(π0 → γγ) is of order 10^-8 eV, corresponding to a mean lifetime on the order of 10^-17 seconds. The two-photon final state provides a clean experimental signature in collider and fixed-target experiments.
Tests of QCD and symmetry: Precise measurements of the π0 two-photon width test low-energy theorems, chiral perturbation theory, and the impact of the axial anomaly. Experiments have pursued increasingly precise determinations of the width to confront the predictions of effective field theories describing the light meson sector.
Related two-photon processes: In addition to π0, other neutral mesons such as η and η' also decay to two photons, though with different rates that reflect their quark content and mixing. Heavier mesons and quarkonium states (e.g., charmonium and bottomonium) can decay to two photons as well, providing complementary laboratories for testing perturbative and nonperturbative QCD.

In the broader landscape, Higgs boson decays to two photons (H → γγ) play a pivotal role in establishing the properties of the Higgs sector. This channel, via loop-induced processes, is sensitive to contributions from particles that couple to the Higgs field and to the overall structure of the Standard Model.

Theoretical framework

Two-photon decays are naturally described within QED as a higher-order electromagnetic process. The transition amplitude is computed using second-order perturbation theory, involving a sum over intermediate states that can couple to the initial state via a single photon at each step. The rate is proportional to the square of this amplitude and to the available two-photon phase space.

Atomic transitions: For atomic systems like hydrogen, the calculation combines the electronic structure with the multiphoton emission dynamics. The two-photon decay rate depends on matrix elements linking the initial and intermediate states and on the spectral distribution of the emitted photons.
Hadronic and meson decays: For π0 → γγ, the process arises from the axial anomaly, a nonperturbative effect that cannot be captured by a naive perturbative expansion alone. The anomaly provides a robust prediction for the decay amplitude regardless of some of the nonperturbative complexities of QCD, and it is augmented by chiral perturbation theory and higher-order corrections.
General lessons: Two-photon decays illustrate how higher-order processes extend the reach of electromagnetic interactions into regimes where selection rules restrict simpler decay channels. They also highlight how quantum correlations, gauge invariance, and symmetry principles shape observable outcomes.

Experimental observations and implications

Experimental investigations of two-photon decays span atomic physics, meson spectroscopy, and collider-based particle physics. Advances in photon detectors, calorimetry, and high-resolution spectroscopy have enabled precise measurements of decay rates, photon energy distributions, and angular correlations. These observations serve multiple roles: - Validation of theory: Matching experimental decay rates and distributions to QED predictions in atoms, or to anomaly-based predictions in meson decays, provides stringent tests of the underlying theories. - Probes of structure: The sensitivity of two-photon decays to intermediate-state contributions and to hadronic structure makes them valuable probes of quantum states and their couplings. - Benchmark channels: Clean two-photon final states (especially in Higgs physics) act as important channels for extracting couplings and for searching for deviations that could indicate new physics.

Experimental results have, for the most part, reinforced the standard picture: well-understood two-photon processes align with the expectations from QED and the QCD anomaly, while remaining rich enough to reveal subtle higher-order effects and structure-dependent corrections.