Charge raising weak current

[indigojoker]

I am baffled by what exactly it means to have the following (ingoing, outgoing) lepton pair configuration: $$(0,\nu_L e_R^+)$$ and $$(e_L^- \bar{\nu}_R,0)$$

This specific question was asked in Halzen and Martin exercise 12.3.

How is it possible to have 0 in going particles and a neutrino and electron going out? I know that an ingoing right-handed antineutrino is the same as a out going lefthanded neutrino, etc, but just trying to grasp what exactly this $$(0,\nu_L e_R^+)$$ and $$(e_L^- \bar{\nu}_R,0)$$ configuration means physically is confusing.

Did Halzen and Martin specifically give this example just to show one can switching ingoing and outgoing particles without looking at its physical consequences?

 

[LightHero]

In this particular case, the (0,\nu_L e_R^+) and (e_L^- \bar{\nu}_R,0) configuration is referring to a process in which an incoming electron and antineutrino interact to produce an outgoing neutrino and positron. It is important to remember that the particle types are labelled according to their handedness, with the subscripts L and R denoting left-handed and right-handed particles, respectively. This means that the incoming lepton pair consists of a left-handed electron (e_L^-) and a right-handed antineutrino (\bar{\nu}_R), while the outgoing lepton pair consists of a left-handed neutrino (\nu_L) and a right-handed positron (e_R^+). Therefore, the (0,\nu_L e_R^+) and (e_L^- \bar{\nu}_R,0) configuration simply describes the process of an incoming electron and antineutrino decaying into an outgoing neutrino and positron.

 

[sir-pinski]

The (0,\nu_L e_R^+) and (e_L^- \bar{\nu}_R,0) configuration refers to a weak interaction process where a charged current is involved. In a weak interaction, there are two types of currents - the charged current and the neutral current. The charged current involves the exchange of a W boson, while the neutral current involves the exchange of a Z boson.

In this specific configuration, the first pair (0,\nu_L e_R^+) refers to an incoming neutrino and an outgoing electron, while the second pair (e_L^- \bar{\nu}_R,0) refers to an incoming electron and an outgoing antineutrino. This configuration is possible in a charged current weak interaction, where the incoming particles are a lepton and an antineutrino, while the outgoing particles are a lepton and a neutrino. This process can also be depicted as (l_i,\bar{\nu_i}) \rightarrow (l_f,\nu_f), where l_i and l_f represent the initial and final leptons respectively.

The reason for this specific configuration is that in a charged current weak interaction, the W boson can change the flavor of the incoming lepton and produce an outgoing lepton with a different flavor. This is known as lepton flavor violation. In this case, the incoming electron is converted into a neutrino, while the outgoing electron is produced from the decay of the W boson.

Halzen and Martin may have given this example to show the concept of lepton flavor violation and how it can be represented in terms of incoming and outgoing particles. It is important to understand the physical consequences of this configuration, as it plays a crucial role in understanding various weak interaction processes.