Pierre Ramond-Journeys Beyond the Standard Model

In summary, the conversation is about diagonalizing a quadratic form in order to find the mass of η and ##\pi^0## pions, which is produced by a term that breaks the Chiral Symmetry ##SU_L(3)\times SU_R(3)##. The desired result is 5.48, but the attempt at a solution using standard orthogonal diagonalization resulted in an incorrect expression for ##\pi^0## mass. However, after taking the Taylor expansion for the square root at ##m_s>>m_{u,d}##, the correct answer was obtained.
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Homework Statement


I want to diagonalize the quadratic form
$$ m_0((m_u+m_d)\pi^3\pi^3+\frac{2}{\sqrt{3}}(m_u-m_d)\pi^3\pi^8+\frac{1}{3}(m_u+m_d+4m_s)\pi^8\pi^8)$$
which can be found under equation 5.47, in order to get the mass of the η and ##\pi^0## pions. This quadratic form is produced by the term that breaks the Chiral Symmetry ##SU_L(3)\times SU_R(3) ##

Homework Equations


I want to know how to produce the result 5.48 as i am unable till now to do the calculation.

The Attempt at a Solution


I tried to diagonalize the expression using the standard procedure of orthogonal diagonalization. After doing all the calculations i get for the ##\pi^0##: $$m^2_{\pi^0} = m_0\bigg(m_u+m_d-\frac{(m_u-m_d)^2}{2\sqrt{m^2_u+m^2_d+m^2_s-m_um_d-m_um_s-m_dm_s}+2m_s-m_u-m_d}\bigg)$$

which is incorrect. Can anyone help me to figure out what i am doing wrong.
Thank you very much!
 
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  • #2
Actually i found it. Taking the taylor expansion for the square root at ##m_s>>m_{u,d}## produces the right answer! Thank you very much!
 

1. Who is Pierre Ramond?

Pierre Ramond is a theoretical physicist and professor at the University of Florida. He is best known for his contributions to the development of the Standard Model of particle physics and his work on supersymmetry and superstring theory.

2. What is the Standard Model?

The Standard Model is a theory in physics that describes the fundamental particles and their interactions that make up the universe. It includes three of the four fundamental forces of nature (excluding gravity) and has been successful in predicting and explaining a wide range of phenomena in particle physics.

3. What are "Journeys Beyond the Standard Model"?

"Journeys Beyond the Standard Model" refers to the theoretical exploration and development of ideas that go beyond the Standard Model of particle physics. This includes theories such as supersymmetry, grand unified theories, and superstring theory, which aim to address the limitations and unanswered questions of the Standard Model.

4. What contributions has Pierre Ramond made to the study of "Journeys Beyond the Standard Model"?

Pierre Ramond has made numerous contributions to the field of "Journeys Beyond the Standard Model." He is known for his work on supersymmetry, which proposes a symmetry between particles with different spin, and for his contributions to superstring theory, which suggests that particles are not point-like but rather tiny strings vibrating at different frequencies.

5. How has the study of "Journeys Beyond the Standard Model" advanced our understanding of the universe?

The study of "Journeys Beyond the Standard Model" has advanced our understanding of the universe by providing potential explanations for phenomena that cannot be accounted for by the Standard Model. These theories have also pushed the boundaries of our knowledge and allowed for the exploration of new concepts such as extra dimensions and the unification of the fundamental forces of nature.

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