A Question about a Paper I recently read (about P+ decay)

[bubbadoobop]

So I just read a paper called Fermion masses, mixings and proton decay in a Randall–Sundrum model (it's in Physics Letters B 498(3-4):256–262, but you can also find it at arXiv:hep-ph/0010195v2). Anyways, there us an equation in it [Pg. 8, 4.14] $$ \int \,dx^4 \int \,dy \sqrt{-g} \frac{1}{M_5^3} \bar{\Psi_i}^{(0)}\Psi_j^{(0)} \bar{\Psi_k}^{(0)} \Psi_l^{(0)} \equiv \int \,dx^4 \frac{1}{M_4^2} \bar{\Psi_i}^{(0)}\Psi_j^{(0)} \bar{\Psi_k}^{(0)} \Psi_l^{(0)}$$ So, if we were to make this dependent on the field decomposition equation [Pg. 2, 2.4] $$ \Psi(x^\mu, y) = \frac{1}{\sqrt{2\pi R}} \sum_{n = 0}^ \infty \Psi^{(n)}(x^\mu) f_n(y)) $$ and the Hamiltonian of a system (H), couldn't the more realistic equation be? $$\Psi(x^\mu, y) \int \,dx^4 \int \,dy \sqrt{-g} \frac{1}{M_5^3} \bar{\Psi_i}^{(0)}\Psi_j^{(0)} \bar{\Psi_k}^{(0)} \Psi_l^{(0)} \equiv \int \,dx^4 \Psi(x^\mu, y) H \frac{1}{M_4^2} \bar{\Psi_i}^{(0)}\Psi_j^{(0)} \bar{\Psi_k}^{(0)} \Psi_l^{(0)}$$

 

[AndyW]

Thank you for sharing your thoughts on the paper "Fermion masses, mixings and proton decay in a Randall–Sundrum model." It is always exciting to see people engaging with scientific research and trying to understand it in a deeper way.

I agree that the equation you mentioned, 4.14 on page 8, is interesting and worth exploring further. It relates to the field decomposition equation on page 2, and as you pointed out, it could potentially lead to a more realistic equation if we incorporate the Hamiltonian of a system (H).

However, I would like to caution that it is important to fully understand the context and assumptions of the paper before making any conclusions or proposing alternative equations. The Randall-Sundrum model is a theoretical framework for understanding the hierarchy problem in particle physics, and it makes certain assumptions about the nature of extra dimensions. Therefore, any equations derived within this model should be interpreted within that context.

Furthermore, the paper itself is quite complex and requires a strong background in theoretical physics to fully understand. So, while your idea is interesting, I would suggest consulting with a more experienced physicist before pursuing it further.

In any case, I appreciate your enthusiasm for the subject and your willingness to engage with scientific research. Keep up the curiosity and passion for science!