- #1

FilipLand

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## Homework Statement

A Higgs particle of mass M is moving in the z-direction with speed $\Beta_H$c compared to the lab system.

It decays to a b-quark ans anti-b quark, each of mass m. What is the speed and direction of the b-quark compared to the lab-system, if the Higgs system,

(a) it is emitted in the forward direction.

(b) emitted in backwards direction.

(c) is emitted in y direction.

## Homework Equations

Perhaps the lorentz transformation velocities.

$$V_y = \frac{v´_y}{\gamma (1-v´_x\frac{u}{c^2})}$$

Rapidity:

$$\eta (v)=artanh(\frac{v}{c}) $$

$$\eta(v´)= \eta (v´) + \eta(u)$$

## The Attempt at a Solution

I tried to set $$ v_M * M(1-\frac{u^2}{c^2})^-1/2 = (v_b+b_anti-b)*m*(1-\frac{u^2}{c^2})^-1/2$$

which is equivalent to $$(v_b+b_anti-b)*m=v_M * M$$

Tha Higgs particle was coming in z-direction so $$v_M=v_z= \frac{v´_z}{\gamma(1+\frac{v'_x\beta_H}{c})}$$

And v_b and v_anti-b = v_y (in +- direction)

and

$$v_{\pm y}= \frac{v´_y}{\gamma(1\pm v´_x\beta_H/c}$$

Then I can set v´_x =0 for the higgs particle to simplify v_z to $$v_z=\frac{v´_z}{\gamma}$$

But this should be solved using rapidity, i.e velocity addition so I think I'm out on deep water..

Any ideas?

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