粒子物理学|Particle Physics代写 6CCP3241代考

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这是一份KCL伦敦大学学院 6CCP3241作业代写的成功案

粒子物理学|Particle Physics代写 6CCP3241代考
问题 1.

The bubble wall will be described by a Higgs field profile sketched in figure 20 ,
$$
H_{i}(z)=\frac{1}{\sqrt{2}} h_{i}(z) e^{i \theta_{i}(z)}
$$
where
$$
\begin{aligned}
&h_{i}(z) \cong\left(\begin{array}{c}
\cos \beta \
\sin \beta
\end{array}\right) h(z) \
&h(z) \cong \frac{v_{c}}{2}\left(1-\tanh \left(\frac{z}{L}\right)\right)
\end{aligned}
$$


证明 .

appears in the potential (5.39), due to $\mathrm{U}(1){y}$ gauge invariance; it can be rewritten as $$ \begin{aligned} V\left(h{1}, h_{2}, \theta\right) &=-\frac{1}{2} \sum_{i} \mu_{i}^{2} h_{i}^{2}-\mu_{3}^{2} \cos (\theta+\phi) h_{1} h_{2} \
&=\frac{1}{8} \sum_{i} \lambda_{i} h_{i}^{4}+\frac{1}{4}\left(\lambda_{3}+\lambda_{4}+\lambda_{5} \cos 2 \theta\right) h_{1}^{2} h_{2}^{2}
\end{aligned}
$$

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6CCP3241 COURSE NOTES :

$$
\left(i \not p-m P_{L}-m^{*} P_{R}\right) \psi=0
$$
using the complex mass
$$
m=\frac{y}{\sqrt{2}} h_{2}(z) e^{i \theta_{2}(z)}
$$
Decompose the Dirac spinor into its chiral components as
$$
\psi=e^{-i E t}\left(\begin{array}{l}
R_{s} \
L_{s}
\end{array}\right) \otimes \chi_{s}
$$