Question about the "negative points" and breaking gauge invariance.

Dear Qiji Xin,

since you have been using t'Hoof-Feynman gauge in calchep,
there are unphysical states of photons or gluon with negative norm which
gives you negative cross section.
The amplitude squared is of course positive but is is being multiplied
to unphysical photon polarisations.
In case of gauge invariance is preserved unphysical photon states are
cancelled with the contribution from ghosts,
but if the gauge invariance is broken, which is your case -- then
cancellation does not take place and you are getting negative cross
sections.

If you chose Unitary(Physical) gauge -- then you will be not getting
negative numbers.
But remember that your results is not gauge invariant

Regards,
Alexander

On 12/09/18 23:37, Qiji Xin wrote:
> New question #673769 on CalcHEP:
> https://answers.launchpad.net/calchep/+question/673769
>
> Hi,
>
> I am calculating the cross for a process that has 7 diagrams before squared.
> I would like to see the contribution from single diagram and squared, so I delete other 6 diagrams.
> Then the MC integration returns me result with "negative points".
> >From the previous question in this forum I found it is due to breaking the gauge invariance (GI).
>
> The "negative points" is as large as 20% at low s (CM energy), decreass s, and disappears at high s.
> I also find the percentage only depends on energy, not on the "nCalls". So the percentage should have some physical reason instead of numerical.
>
> So could you explain what determines the percentage of the "negative points"?
> Also could you explain something more about the "negative points" and "gauge invariance"?
>
> Thanks!
>
>

--
______________________________________________________________________
Prof. Alexander S Belyaev (<email address hidden>)
https://www.hep.phys.soton.ac.uk/content/alexander-belyaev

School of Physics & Astronomy, University of Southampton
Office 5047, SO17 1BJ, TEL: +44 23805 98509, FAX: +44 23805 93910
.....................................................................
Particle Physics Department, Rutherford Appleton Laboratory
Didcot, OX11 0QX, TEL: +44 12354 45562, FAX: +44 12354 46733
.....................................................................
CERN, CH-1211 Geneva 23, Switzerland
Office 40/1-B20, Mailbox: E27910, TEL: +41 2276 71642
______________________________________________________________________

Dear Alexander,

Thanks for your answer!

Yes the single diagram is not gauge invariant. But it may be useful to see which one dominate at a certain s.

So what's the percentage of the negative points, as I mentioned before, mean? What determines the percentage? I guess the smaller percentage means the result is more physical.

Also, for my goal to see the contribution and dominance of single diagram at certain range of s, it is better to use t'Hooft-Feynman gauge or Unitary gauge?

Thanks very much!

Best,
Qiji

Dear Qiji,

On 14/09/18 02:57, Qiji Xin wrote:
> Question #673769 on CalcHEP changed:
> https://answers.launchpad.net/calchep/+question/673769
>
> Status: Answered => Open
>
> Qiji Xin is still having a problem:
> Dear Alexander,
>
> Thanks for your answer!
>
> Yes the single diagram is not gauge invariant. But it may be useful to
> see which one dominate at a certain s.
>
> So what's the percentage of the negative points, as I mentioned before,
> mean? What determines the percentage? I guess the smaller percentage
> means the result is more physical.
No, this is not correct.
And please define what do you mean under "more physical"

>
> Also, for my goal to see the contribution and dominance of single
> diagram at certain range of s, it is better to use t'Hooft-Feynman gauge
> or Unitary gauge?

It does not matter which gauge you choose.

The contribution from one
diagram can be 1000 ,
from other -1001
and from another one is 10

So first two diagrams will cancel each other, so contribution from 1+2 << 3

So, how you would judge which one is the most important?!

There is no generic advice, but I can try to give some :-)

1 What you should do is to chose the gauge invariant subset of
giagrams(if possible)
2. Work in Unitary gauge, where squared diagrams are positive
3. Check the size of the interference between diagrams you are interested in

Regards,
Alexander

>
> Thanks very much!
>
> Best,
> Qiji
>

--
Prof. Alexander S Belyaev (<email address hidden>)
https://www.hep.phys.soton.ac.uk/content/alexander-belyaev

School of Physics & Astronomy, University of Southampton, Office: 5047
SO17 1BJ, TEL.: +44 (0)23 8059 8509; FAX.: +44 (0)23 8059 3910
.....................................................................
Particle Physics Department, Rutherford Appleton Laboratory, Didcot,
OX11 0QX, TEL.: +44 (0)1235 445562; FAX.: +44 (0)1235 446733
.....................................................................
CERN: Office: 40 1-B20 Mailbox: E27910; ccid: 532076
TEL: +41 22 76 71642
______________________________________________________________________

Dear Alexander,

Thanks!

>
> Thanks for your answer!

> So what's the percentage of the negative points, as I mentioned before,
> mean? What determines the percentage? I guess the smaller percentage
> means the result is more physical.

>> No, this is not correct.
>> And please define what do you mean under "more physical"

I think I should say I guess the smaller percentage means the result is more robust instead of physical? I say this because I saw in a previous question (https://answers.launchpad.net/calchep/+question/349730) you said "would not put much attention to 10^-8% negative numbers".
So could you say something about what determines the percentage of the negative points, for the xsec from a single gauge-breaking diagram? Briefly is fine.

And thanks very much for your other advice!

Dear Qiji Xin,

looks like your last question on this issue was not answered,

here it is

> I think I should say I guess the smaller percentage means the result is more robust instead of physical?
This is correct.
> I say this because I saw in a previous question (https://answers.launchpad.net/calchep/+question/349730) you said "would not put much attention to 10^-8% negative numbers".
> So could you say something about what determines the percentage of the negative points, for the xsec from a single gauge-breaking diagram? Briefly is fine.

As we have written in the CalcHEP manual and CalcHEP paper, introduction
of the width in the tree-level calculation strictly speaking always
breaks gauge invariance since it (the width)  is related to higher order
calculations. This violation is negligible (almost always) if you
consider the full set of diagrams and one should be very careful with
removing some sets of diagrams. The percentage of the negative cross
section in the t'Hooft feynman gauge reflects the level of such violation.

This is it.

For further details, please read CalcHEP manual, CalcHEP paper or textbooks.

Regards,

Alexander

>
> And thanks very much for your other advice!

>
--
______________________________________________________________________
Prof. Alexander S Belyaev (<email address hidden>)
https://www.hep.phys.soton.ac.uk/content/alexander-belyaev

School of Physics & Astronomy, University of Southampton
Office 5047, SO17 1BJ, TEL: +44 23805 98509, FAX: +44 23805 93910
.....................................................................
Particle Physics Department, Rutherford Appleton Laboratory
Didcot, OX11 0QX, TEL: +44 12354 45562, FAX: +44 12354 46733
.....................................................................
CERN, CH-1211 Geneva 23, Switzerland
Office 40/1-B20, Mailbox: E27910, TEL: +41 2276 71642
______________________________________________________________________

Thank you so much Alexander! Very helpful answers!