# Homework Help: Threshold energy particle physics

1. Apr 12, 2009

### fabsuk

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. Apr 13, 2009

### malawi_glenn

How is your M* defined? How is M and m defined?

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

3. Apr 13, 2009

### fabsuk

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. Apr 14, 2009

### malawi_glenn

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

5. Apr 14, 2009

### fabsuk

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. Apr 14, 2009

### malawi_glenn

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?

7. Apr 14, 2009

### fabsuk

Last edited by a moderator: Apr 24, 2017
8. Apr 14, 2009

### malawi_glenn

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. Apr 14, 2009

### fabsuk

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. Apr 14, 2009

### malawi_glenn

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

11. Apr 14, 2009

### fabsuk

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. Apr 14, 2009

### malawi_glenn

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

13. Apr 14, 2009

### fabsuk

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. Apr 14, 2009

### malawi_glenn

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. Apr 14, 2009

### fabsuk

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. Apr 15, 2009

### malawi_glenn

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