Renormalization pseudo-scalar meson theory

In summary, there are various methods and resources available for understanding renormalization in the pseudo-scalar meson theory, including the work of Kenneth G. Wilson, research papers, and different approaches such as dimensional regularization or lattice regularization.
  • #1
kryshen
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Imagine the vertex correction diagram in the pseudo-scalar meson theory.

The amplitude for this diagram is UV divergent. In order to get rid of this divergence we apply regularization technique and obtain the expression with the UV cut-off parameter. The usual practice is that we expand the result in series and extract the finite part for this expression.

In QED this series expansion is performed at zero 3-momenta of participating particles, as the QED coupling constant is obtained from the low-energy experiments.

In the pseudo-scalar meson theory the g_piNN coupling constant is obtained at the chyral limit of QCD (m_pi =0). Therefore, I was advised to make renormalization at zero 4-momentum of participating pion.

Could annybody here give me some links where the renormalization of pseudo-scalar meson theory is discussed? Your opinion on the question is wellcome.
 
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  • #2


Renormalization in the pseudo-scalar meson theory can be a complex topic, but I can provide some resources that may be helpful in understanding it better.

Firstly, I would recommend looking into the work of Kenneth G. Wilson, who pioneered the concept of renormalization in quantum field theory. His book "Renormalization Group and Critical Phenomena" is a great resource for understanding the basics of renormalization.

Additionally, there are many papers and articles discussing renormalization in the context of the pseudo-scalar meson theory. Some examples include "Renormalization of the Pseudoscalar Meson Theory" by A. A. Vladimirov and "Renormalization Group Analysis of the Pseudoscalar Meson Theory" by J. M. Pawlowski.

It is also important to note that there are different approaches to renormalization in the pseudo-scalar meson theory, such as the use of dimensional regularization or lattice regularization. So it may be helpful to explore different methods and see which one best fits your research.

I hope this helps and good luck with your studies!
 
  • #3


Renormalization in pseudo-scalar meson theory is an important aspect of understanding the behavior of these particles in the strong interaction regime. The vertex correction diagram in this theory, as in any other quantum field theory, is UV divergent. This means that the amplitude for this diagram becomes infinite when the momentum of the particles involved approaches infinity. In order to make sense of this calculation, we need to apply a regularization technique to control the divergences.

One common approach is to introduce a UV cut-off parameter, which effectively limits the momentum of the particles and makes the calculation finite. However, this introduces a dependence on the cut-off parameter in the final result, which is undesirable. To address this issue, we perform a series expansion and extract the finite part of the expression, which is the physically relevant quantity.

In QED, this series expansion is usually performed at zero 3-momenta, as the QED coupling constant is obtained from low-energy experiments. However, in the pseudo-scalar meson theory, the coupling constant g_piNN is obtained at the chiral limit of QCD, where the pion mass is zero. Therefore, it is advised to perform renormalization at zero 4-momentum of the participating pion.

As for resources on the renormalization of pseudo-scalar meson theory, there are several textbooks and articles that discuss this topic in detail. Some recommended resources include "Quantum Field Theory" by Mark Srednicki, "The Quantum Theory of Fields" by Steven Weinberg, and "Renormalization Methods: A Guide for Beginners" by John C. Collins. Additionally, there are several online lecture notes and videos available on this topic. It is always helpful to consult with your professors or colleagues who have expertise in this area for further guidance and clarification.
 

1. What is Renormalization Pseudo-Scalar Meson Theory?

Renormalization Pseudo-Scalar Meson Theory is a mathematical framework used to describe the interactions between subatomic particles called mesons. It is a type of quantum field theory that uses the concept of renormalization to account for the effects of virtual particles and infinite terms in calculations.

2. How does Renormalization Pseudo-Scalar Meson Theory work?

In Renormalization Pseudo-Scalar Meson Theory, the interactions between mesons are described by a Lagrangian, which is a mathematical function that represents the potential energy of the system. The Lagrangian is then used to calculate the probability amplitudes for different particle interactions. The concept of renormalization is then used to remove infinite terms from these calculations, resulting in finite and meaningful results.

3. What is the significance of Renormalization Pseudo-Scalar Meson Theory?

Renormalization Pseudo-Scalar Meson Theory is a crucial tool in understanding the behavior of subatomic particles and their interactions. It has been used to successfully predict and explain experimental results in particle physics, and is an essential component of the Standard Model of particle physics.

4. What are some applications of Renormalization Pseudo-Scalar Meson Theory?

Renormalization Pseudo-Scalar Meson Theory has many applications in particle physics research, including the study of strong nuclear forces, the behavior of hadrons, and the properties of subatomic particles. It is also used in the development of new theoretical models and in the interpretation of experimental data.

5. What are the limitations of Renormalization Pseudo-Scalar Meson Theory?

Like any scientific theory, Renormalization Pseudo-Scalar Meson Theory has its limitations. It is not able to fully describe all interactions between subatomic particles, and there are still many unanswered questions in the field of particle physics. Additionally, the calculations involved in this theory can be complex and difficult to interpret, making it a challenging subject for non-experts to understand.

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