14.6 Particle Annihilation

Introduction

According to Einstein's mass-energy equivalence principle ($E=m{c}^2$), mass can be converted into energy, and energy can be converted into mass. A dramatic demonstration of this principle is particle annihilation, the process that occurs when a particle of matter collides with its corresponding antiparticle. In this interaction, their masses are completely converted into a burst of pure energy, typically in the form of high-energy photons or, under certain conditions, new particles.

Electron-Positron Annihilation

This is the most common and well-studied example of annihilation. When an electron ($e^{-}$) meets its antiparticle, the positron ($e^{+}$), they annihilate each other.

• Process: The collision results in the disappearance of both the electron and the positron, and their combined mass is converted into energy.
• Products: This energy is typically released as two gamma-ray photons ($\gamma$).

$e^{-}+e^{+}\to \gamma +\gamma$

• Conservation of Momentum: Two photons are produced instead of one to conserve momentum. In the center-of-mass frame of the initial pair, the total momentum is zero. A single photon would have momentum, violating the conservation laws. Two photons emitted in opposite directions can have a net momentum of zero.

• Applications: This process is the basis for Positron Emission Tomography (PET) scans in medicine. In high-energy physics, particle accelerators like the LHC at CERN smash electrons and positrons together at high speeds, using the immense energy from their annihilation to create new and exotic particles.

Annihilation of Matter into New Matter

Annihilation doesn't always result in photons. The energy released can also be converted back into the mass of a different particle-antiparticle pair, especially in high-energy collisions.

• Quark-Antiquark Annihilation:
  • When a quark and its corresponding antiquark (e.g., an up quark and an anti-up quark) collide, they can annihilate.
  • This annihilation produces a highly energetic virtual particle, such as a gluon.
  • This gluon can then decay, using its energy to form a new pair of heavier particles, such as a top quark and an anti-top quark.
  • This process is a key way that particle accelerators create and study heavy, unstable particles.

Detecting Annihilation Products: The Resistive Plate Chamber (RPC)

Observing the products of annihilation requires sophisticated particle detectors. The Resistive Plate Chamber (RPC) is a type of gaseous detector widely used in high-energy physics experiments, especially for tracking muons, which are often produced in particle collisions.

• Features:
  • High Detection Efficiency: Over 95% efficiency in detecting passing particles.
  • Excellent Time Resolution: Can determine the timing of a particle's passage to within a nanosecond.
  • High Rate Capability: Can handle hundreds of particle hits per square centimeter per second.
  • Cost-Effective: Relatively cheap and easy to construct over large areas.
• Applications: RPCs are crucial components of detectors in major experiments, including CMS and ALICE at CERN's LHC, where they help identify and track particles emerging from high-energy collisions and annihilations.

Possible Questions and Answers

Q: Can annihilation produce particles other than photons?

A: Yes. In high-energy environments like particle accelerators, the energy from an annihilation event can be converted into a new pair of matter-antimatter particles, which can even be heavier than the original pair.

Q: What is the fundamental principle behind particle annihilation?

A: The fundamental principle is Einstein's mass-energy equivalence, $E=m{c}^2$, which states that mass can be converted directly into energy.