# Threshold energy particle physics

1. ### fabsuk

51
E(threshold enrgy) = M* − M(squared) −m(squared) divided by 2M

Determine the threshold energy for producing a top quark and an anti-top quark when beams
of electrons and positrons of equal energy are made to collide head on.

What do i sub in where and what do i with M*.

Thanks

2. ### malawi_glenn

4,727
How is your M* defined? How is M and m defined?

There is no standard formula or standard notation for these things.

3. ### fabsuk

51
a particle of mass m collides with a stationary particle of mass M, the minimum
energy required to produce a state of mass M* is, in natural units,

4. ### malawi_glenn

4,727
So what do you think you should put in for M and m?

5. ### fabsuk

51
the mass of electron and positron but I dont know which one is stationary,

i.e dont know which corresponds to M and m.

M* must correspond to mass of top quark.

6. ### malawi_glenn

4,727
your formula is for stationary targets, but you have a head on collision. Now do you know any other ways to do this? Have you used invariant mass?

51
8. ### malawi_glenn

4,727
You don't learn physics by memorizing a formula, you must know how to derive things so that they fit your needs.

The web page you have linked to show you how to derive the Threshold energy using s, the invariant mass.

9. ### fabsuk

51
so we are in a centre of mass frame as the particles are both moving ( i am assuming my equation was for lab frame)

so we use a different equation right

are u saying the positron and electron have equal mass.
but then do we use the positron mass or the elctron mass.
If anybody has any ideas, help would really be appreciated.

10. ### malawi_glenn

4,727
you start with the invariant mass, and yes electron and positron has equal mass.

11. ### fabsuk

51
But the invariant mass if the total mass in the equation right
where would i subsitute it,

don't i just subsitute mass of top quark and anti top quark (dont i have had to add them together) for M*

and then substitute electron mass for both M and m.

12. ### malawi_glenn

4,727
sure but don't you want to understand WHY one does all this?

13. ### fabsuk

51
I would love to know but i never get a satisfactory answer .

In many areas of physics i dont completely understand so i end up instead of trying to understand,

I do pattern recognition. ( you can either blame teachers/books for using too much jargon)

Have i done it correctly,(would you add up masses of top and anti top quark)

14. ### malawi_glenn

4,727
use invariant mass:

Left hand side, the eletctron + positron:

we choose labframe; head on collision:

$$s = (\sum_i E_i)^2 - (\sum _i \vec{p}_i)^2 = 4E^2$$

right hand side, we choose the frame where the particles are created at rest.

Now try

15. ### fabsuk

51
Are you trying to derive the equation i have already stated

or are we trying to rearrange the equation to put it in a way we like.

16. ### malawi_glenn

4,727
If one knows how to derive it one knows where to to put in the numbers.