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Chapter 12: Problem 20

Baryon conservation and lepton conservation are laws used frequently by particle physicists to decide whether a reaction involving elementary particles is possible or not. Explain how these laws are applied to make such determinations.

Short Answer

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Question: Explain how baryon conservation and lepton conservation laws are used by particle physicists to determine if a reaction involving elementary particles is possible. Answer: Particle physicists apply baryon conservation and lepton conservation laws to determine the possibility of a reaction involving elementary particles. They first determine the baryon and lepton numbers for each particle involved in the reaction. Next, they compare the total baryon and lepton numbers before the reaction with the total baryon and lepton numbers after the reaction. If the numbers are conserved (i.e., the total before equals the total after), then the reaction is possible according to these laws. For example, in the case of beta decay, both baryon and lepton numbers are conserved, making the reaction possible according to baryon and lepton conservation laws.

Step by step solution

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1. Understanding Baryon Conservation and Lepton Conservation Laws

Baryon conservation law states that the total number of baryons (particles like protons and neutrons) in a reaction must remain constant before and after the reaction. Similarly, lepton conservation law states that the total number of leptons (particles like electrons, muons, and neutrinos) must also remain constant before and after the reaction. These conservation laws are derived from the observation that reactions involving elementary particles do not create or destroy baryons and leptons.
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2. Checking Baryon and Lepton Numbers

To apply these conservation laws to determine if a reaction is possible, we need to check the baryon and lepton numbers (B and L) for each particle involved in the reaction. This is simply the count of baryons or leptons associated with the particle. For example, a proton has a baryon number of +1 and a lepton number of 0, while an electron has a baryon number of 0 and a lepton number of -1. Antiparticles have opposite baryon and lepton numbers to their corresponding particles.
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3. Applying Conservation Laws to the Reaction

Once we have determined the baryon and lepton numbers for each particle involved in the reaction, we can apply the conservation laws. To do this, we must compare the total baryon and lepton numbers before the reaction (on the left side of the reaction equation) with the total baryon and lepton numbers after the reaction (on the right side of the reaction equation). If the numbers are conserved (i.e., the total before equals the total after), then the reaction is possible according to these laws.
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4. Example: Beta Decay

As an example, let's consider the beta decay reaction, in which a neutron decays into a proton, an electron, and an electron antineutrino: n -> p + e- + (v_e)^{bar} The baryon and lepton numbers for each particle are: - n (neutron): B = +1, L = 0 - p (proton): B = +1, L = 0 - e- (electron): B = 0, L = -1 - (v_e)^{bar} (electron antineutrino): B = 0, L = +1 Comparing the total baryon and lepton numbers before and after the reaction: - Baryon numbers: 1 = 1 (conserved) - Lepton numbers: 0 = -1 + 1 (conserved) Since both baryon and lepton numbers are conserved, the beta decay reaction is possible according to the baryon and lepton conservation laws.

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