 Solution

ID: past-exam-of-the-advanced-quantum-field-theory-for-particle-physics-course-of-the-university-of-oxford/2021/2/a/i/solution

s = (p_{1} + p_{2})^{2}

t = (p_{1} - p_{3})^{2}

and

u = (p_{1} - p_{4})^{2}

. The external on shell relations are

p_{1}^{2} = p_{2}^{2} = m_{e}^{2}

and

p_{3}^{2} = p_{4}^{2} = m_{t}^{2}

p_{3} + p_{4} = p_{1} + p_{2}

, gives

s + t + u = 3 p_{1}^{2} + p_{2}^{2} + p_{3}^{2} + p_{4}^{2} + 2 p_{1} \cdot (p_{2} - p_{3} - p_{4}) = p_{1}^{2} + p_{2}^{2} + p_{3}^{2} + p_{4}^{2} = 2 (m_{e}^{2} + m_{t}^{2}) .

 New to topics? Read the docs here!