Question

Draw possible Feynman diagrams for the following phenomena: a) protons scattering off each other b) neutron beta decays to a proton: \(n \rightarrow p+e^{-}+\bar{\nu}_{e}\).

Short answer

Question: Draw Feynman diagrams for the following phenomena: a) protons scattering off each other and b) neutron beta decay. Answer: a) For protons scattering off each other, the interaction is mediated by the strong force carried by gluons. A simple Feynman diagram depicts two incoming protons exchanging a gluon between two quarks (e.g., \(u_1\) and \(u_3\)) and two outgoing protons. b) For neutron beta decay, the process is mediated by the weak nuclear force, involving the emission of a W- boson from a down quark. The diagram depicts an incoming neutron, the emission of a W- boson that transforms the down quark into an up quark, forming a proton, and the decay of the W- boson into an electron and an electron antineutrino.

Step-by-step solution

Proton Scattering

To draw the Feynman diagram for protons scattering off each other, we need to consider their internal structure. A proton is composed of two up quarks and one down quark. The interaction between quarks in protons is mediated by the exchange of gluons, which are the carriers of the strong force. In this case, we can consider a simple case where one quark from each proton interacts via the exchange of a gluon. It is important to note that there are many possible diagrams for the scattering process, but we will draw a particular one. The diagram will have the following features: - Two incoming protons (labeled as \(p_1\) and \(p_2\)) with their quark content (\(u_1, u_2, d\) for \(p_1\) and \(u_3, u_4, d'\) for \(p_2\)). - The exchange of a gluon (labeled as \(g\)) between, for instance, \(u_1\) and \(u_3\). - Two outgoing protons (labeled as\(p_1'\) and \(p_2'\)) with their quark content (\(u_2, u_3', d\) for \(p_1'\) and \(u_4, u_1', d'\) for \(p_2'\)).

Neutron Beta Decay

To draw the Feynman diagram for neutron beta decay, we need to consider the weak nuclear force mediated by W bosons. The process is characterized by the transition of a down quark in the neutron into an up quark, resulting in the transformation of a neutron into a proton. Simultaneously, an electron and an antineutrino are emitted. The diagram will have the following features: - An incoming neutron (labeled as \(n\)) and its quark content (\(u, d, d\)). - The emission of a W- boson (labeled as \(W^-\)) from the down quark. - The transformation of the down quark into an up quark and subsequent formation of a proton (labeled as \(p\)) and its quark content (\(u, u, d'\)). - The W- boson decays into an electron (labeled as \(e^-\)) and an electron antineutrino (labeled as \(\bar{\nu}_e\)).

Key concepts

Proton Scattering

Proton scattering is a fascinating phenomenon in particle physics where protons collide and interact with each other. Protons, found in the nucleus of an atom, are composed of smaller particles known as quarks. Each proton consists of two up quarks and one down quark. When protons scatter, these quarks interact via the exchange of particles called gluons, which serve as the intermediaries for the strong nuclear force.

• In a Feynman diagram representation of proton scattering, visualize two paths that represent the incoming protons.
• Inside these paths, show the quarks they are composed of, such as up and down quarks.
• Include a line between these paths representing a gluon, indicating the interaction between quarks from different protons.
• The diagram also shows outgoing protons with possibly different paths showing their new configurations post-collision.

Understanding this helps in realizing how subatomic particles behave and interact at fundamental levels during high-energy collisions.

Neutron Beta Decay

Neutron beta decay is a type of radioactive decay where a neutron transforms into a proton. This process is a prime example of the weak nuclear force at work, one of the four fundamental forces of nature. During beta decay:

• A neutron, typically comprising one up quark and two down quarks, converts one of its down quarks into an up quark. This change results in a proton, which has two up quarks and one down quark.
• An essential part of this process is the emission of a W- boson, a particle that mediates the weak force.
• The W- boson quickly decays into an electron and an electron antineutrino, conserving charge and lepton number.

The study of neutron beta decay provides significant insights into the processes that govern particle transformation and has implications for understanding nuclear reactions in the universe.

Quarks

Quarks are the fundamental building blocks of matter in the universe. They are elementary particles that combine in various ways to form protons and neutrons, the components of atomic nuclei. Quarks come in six "flavors": up, down, charm, strange, top, and bottom.

• In protons and neutrons, only up and down quarks are relevant, which are the lightest and most common quark types.
• These quarks are held together by the strong nuclear force, mediated by gluons.
• Quarks carry fractional electric charges, with up quarks carrying a charge of +2/3 and down quarks a charge of -1/3.
• They never exist independently but are always found in groups of two (mesons) or three (baryons like protons and neutrons).

Quarks are integral to the structure of matter and a crucial part of understanding particle physics.

Gluon Exchange

Gluons are the carriers of the strong nuclear force, which is the force that binds quarks together inside protons, neutrons, and other hadrons. In proton scattering events, as mentioned earlier, gluons facilitate the interaction between the quarks of colliding protons.

• Gluons are massless and carry a "color charge" that allows them to bind quarks together.
• They work much like photons do for the electromagnetic force, but their interactions are more complex due to the color charge.
• When quarks in different protons exchange gluons, this leads to the transfer of momentum, resulting in the scattering of protons.

Studying gluon exchange helps physicists understand how strong force functions at fundamental levels, revealing insights about the stability of atomic nuclei and the behavior of particles under extreme conditions.

Weak Nuclear Force

The weak nuclear force is one of the four fundamental forces and is responsible for processes like beta decay. It is much weaker than the strong force but plays a crucial role in the universe's functioning.

• It acts at a very short range, about 0.1% of the diameter of a typical atomic nucleus.
• This force is mediated by exchange particles known as W and Z bosons, with the W boson involved in neutron beta decay.
• Unlike other forces, it can change the type of quark, enabling the transformation of particles such as changing a neutron into a proton.
• The weak nuclear force is responsible for the fusion reactions in the sun that provide energy for life on Earth.

Understanding the weak nuclear force reveals much about the fundamental aspects of particle transformations and the forces that govern particle interactions in the universe.