[HELP]What is the difference between renormalized mass and the running mass

[piggy1983]

What is the difference between renormalized mass and the running mass? And physical mass,pole mass?

 

[blechman]

"renormalized mass" (also called "physical mass" sometimes) is the mass parameter AFTER you have subtracted your UV divergences.

"running mass" is a funny, and somewhat misleading, term. It is a mass that is a function of the energy. Roughly speaking, when you compute cross sections, you often find your answer involves logarithms that are large (for example, log(Q/m) where Q is the CM energy and m is the mass - if you're talking about scattering 1 GeV mass particles at the LHC, for example, this is a large ratio). These large logs can cause trouble, since if they get too large, they detroy perturbation theory! So using something called "Renormalization group" we can sum up these logs into functions we call "running couplings" (including mass).

As a simple example of how this works, think of calculating something in perturbation theory. You get an answer:

$$1+x+x^2+x^3$$

Now this is perturbation theory, so you know this should not make sense if x > 1. But you might also recognize this series as $(1-x)^{-1}$, which is valid for MUCH larger x (!) So you "resum" the series into this form and your calcuation will be valid for larger x. These resummed quantities are called "running couplings", but really they're just factors in cross sections and lifetimes.

Pole mass: this is a SPECIFIC renormalization scheme where you define your renormalized mass to be the place where the propogator $(p^2-m_{\rm pole}^2)^{-1}$ blows up.

Hope that helps!

 

[sir-pinski]

Renormalized mass and running mass are both concepts in quantum field theory that describe the effective mass of a particle. However, they differ in the way they are calculated and their physical interpretation.

Renormalized mass is the mass of a particle that has been adjusted or "renormalized" to account for the effects of quantum fluctuations. In other words, it is the mass that is observed experimentally and takes into account the interactions of the particle with its surrounding environment. This mass is usually defined at a specific energy scale or momentum transfer, and it can vary depending on the energy scale at which it is measured.

On the other hand, running mass is a theoretical concept that takes into account the effects of quantum corrections on the mass of a particle. It is calculated by considering the mass at different energy scales and taking into account the changes due to quantum fluctuations. Running mass is a continuous function of the energy scale and can change significantly as the energy scale increases.

Both renormalized mass and running mass are related to the physical mass and pole mass of a particle. Physical mass is the mass that is observed in experiments, while pole mass is a theoretical concept that describes the mass of a particle in a simplified, idealized scenario. In general, physical mass and pole mass are not equal, and their relationship depends on the specific particle and the theoretical framework being used.

In summary, renormalized mass and running mass describe the effective mass of a particle in different ways, while physical mass and pole mass are related to these concepts but have different meanings and interpretations.