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

1. Oct 16, 2016

### 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? $$\Psi(x^\mu, y) \int \,dx^4 \int \,dy \sqrt{-g} \frac{1}{M_5^3} \bar{\Psi_i}^{(0)}\Psi_j^{(0)} \bar{\Psi_k}^{(0)} \Psi_l^{(0)} \equiv \int \,dx^4 \Psi(x^\mu, y) H \frac{1}{M_4^2} \bar{\Psi_i}^{(0)}\Psi_j^{(0)} \bar{\Psi_k}^{(0)} \Psi_l^{(0)}$$

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2. Oct 21, 2016

### Staff: Admin

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

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