How to Calculate Threshold Energy for Top Quark Production?

[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

 

[malawi_glenn]

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

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

 

[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,

 

[malawi_glenn]

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

 

[fabsuk]

the mass of electron and positron but I don't know which one is stationary,

i.e don't know which corresponds to M and m.

M* must correspond to mass of top quark.

 

[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?

 

[fabsuk]

how would invariant mass equation help

does this website help:

http://www.phys.ufl.edu/~rfield/PHY3063/images/Chapter2_9.pdf

 

[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.

 

[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.

 

[malawi_glenn]

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

 

[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.

 

[malawi_glenn]

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

 

[fabsuk]

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

In many areas of physics i don't 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)

 

[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

 

[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.

 

[malawi_glenn]

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