CalcHEP

The cross-section diverges for double pair production

Asked by AmirFarzan Esmaeili

We are trying to calculate a photon-photon interaction cross-section using the codes calcHEP and compHEP, however we faced some problems. We would be grateful to have your comments and help on this issue.

Our setting and problem is the following: we are trying to compute the double pair production differential and total cross-sections and for the first step we intended to reproduce the results of the paper arXiv: 0812.0859 (by Demidov and Kalashev).

The setting (batch file) in calcHEP3.8.10 is:

model: SM (Feynman Gauge)

process: A,A -> e,E,e,E (For the moment none of the diagrams are excluded)

Structure Func 1 and 2: OFF

First/Second particle momentum: 5[GeV]

Kinematics: We have tried both 12->3,456 ... and 12->34,56 ...

Cuts: 2.25 < E(e) < 2.5 and 0.9 < C(e) < 1.0

Vegas Iteration: we have tried iterations between 5 to 30

Vegas nCall : A wide range of nCalls (between 10k and 5M have been tested)

The problem is that with this setting, the integration does not converge. As it has been mentioned in the calcHEP's documentation, the Vegas integral results are trustable when the errors become less that 1% and the cross-sections at each iteration are close to each other. None of these two happens for the aforementioned settings. On the contrary, the errors fluctuate between 10% and 100% and they don't even smoothly decrease . Also increasing the iterations gives us "Bad Precision" or "Negative Points".

In the next step we modified the regularization. Because some of the diagrams have Z propagators:

56: MZ , wZ , 2

46: MZ , wZ , 2

134: MZ , wZ , 2

and so forth. This also didn't change anything.

For a check, we chose only one squared diagram which didn't include any Z propagators. For this only one squared diagram again we got the same problem for different Vegas iteration numbers and nCalls.

Also, changing the Cuts for this one squared diagram didn't help.

In our last try to solve the problem, we edited the model variables and parameters. We changed the electromagnetic coupling constant to 0.302 and defined the muon mass and electron mass in model variables section and added them in model particles section. This also didn't give better results.

We have tried all of these steps for "Quadruple" and "Long double" computation precision.

Best regards,

AmirFarzan Esmaeili

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Solved by:
Alexander Pukhov
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Revision history for this message
Best Alexander Pukhov (pukhov) said : 		#1

You already wrote us  and I have  answered.

First  answer:

Here the  problem is caused by small mass of electron.

I  guess you use version of model where  electron mass is zero. Then
electron going  in direction of photon leads to singularity in matrix
element.

I propose use   replace electron on tau-letpon

    A,A->l,l,L,L

remove diagrams with virtual  h and Z,

and set in numerical session Ml=5E-4.

Then for large number of  callc ( 10000000 per session) you'll get a
reasonable answer

    1     8.1135E+06   2.01E+00  9565938
    2     8.9928E+06   2.72E+00  9565938
    3     8.6933E+06   1.08E+00  9565938
    4     8.9276E+06   1.67E+00  9565938
    5     9.4802E+06   3.87E+00  9565938
  < >     8.8415E+06   1.13E+00 47829690         5

May be  one can  get  result faster using regularization.

  Second answer

There is another way to get the same  result fast.

A,A->m,M,l,L

where both m and l have mass of  electron.

Then we apply a cut    Y(m,M) > 0 . I mean the pair  m,M  can go
forward, or can go backward.  So, we just reduce result twice and now
have only one pole :  P^2  with P= ( pA - pm-pM)

So, I mean  the main contribution comes form small mass m,M which
flies  forward and exchanges  by photon with l,L which flies backward.

I see  A,A->m,M,l,L  with Y cut get the same cross section as
A,A->l,L,l,L.  Not clear about factor 2. But more likely it is correct.

=========================

Have you  received   these mails?

Best

      Alexander Pukhov

On 1/9/23 22:50, AmirFarzan Esmaeili wrote:
> New question #704340 on CalcHEP:
> https://answers.launchpad.net/calchep/+question/704340
>
> We are trying to calculate a photon-photon interaction cross-section using the codes calcHEP and compHEP, however we faced some problems. We would be grateful to have your comments and help on this issue.
>
> Our setting and problem is the following: we are trying to compute the double pair production differential and total cross-sections and for the first step we intended to reproduce the results of the paper arXiv: 0812.0859 (by Demidov and Kalashev).
>
>
>
> The setting (batch file) in calcHEP3.8.10 is:
>
> model: SM (Feynman Gauge)
>
> process: A,A -> e,E,e,E (For the moment none of the diagrams are excluded)
>
> Structure Func 1 and 2: OFF
>
> First/Second particle momentum: 5[GeV]
>
> Kinematics: We have tried both 12->3,456 ... and 12->34,56 ...
>
> Cuts: 2.25 < E(e) < 2.5 and 0.9 < C(e) < 1.0
>
> Vegas Iteration: we have tried iterations between 5 to 30
>
> Vegas nCall : A wide range of nCalls (between 10k and 5M have been tested)
>
>
>
> The problem is that with this setting, the integration does not converge. As it has been mentioned in the calcHEP's documentation, the Vegas integral results are trustable when the errors become less that 1% and the cross-sections at each iteration are close to each other. None of these two happens for the aforementioned settings. On the contrary, the errors fluctuate between 10% and 100% and they don't even smoothly decrease . Also increasing the iterations gives us "Bad Precision" or "Negative Points".
>
>
>
> In the next step we modified the regularization. Because some of the diagrams have Z propagators:
>
> 56: MZ , wZ , 2
>
> 46: MZ , wZ , 2
>
> 134: MZ , wZ , 2
>
> and so forth. This also didn't change anything.
>
>
>
> For a check, we chose only one squared diagram which didn't include any Z propagators. For this only one squared diagram again we got the same problem for different Vegas iteration numbers and nCalls.
>
> Also, changing the Cuts for this one squared diagram didn't help.
>
>
>
> In our last try to solve the problem, we edited the model variables and parameters. We changed the electromagnetic coupling constant to 0.302 and defined the muon mass and electron mass in model variables section and added them in model particles section. This also didn't give better results.
>
>
>
> We have tried all of these steps for "Quadruple" and "Long double" computation precision.
>
>
>
> Best regards,
>
>
>
> AmirFarzan Esmaeili
>

Revision history for this message
AmirFarzan Esmaeili (amirfarzan) said : 		#2

Dear Prof. Pukhov

Thanks for your reply. Unfortunately we didn't receive your email, so I had to resend my question here.

For your first solution, I changed the settings as follows:

Interaction: A,A->l,L,l,L
Removed diagrams with virtual h and Z
In the numerical session: Ml->5E-4
First/Second particle momentum: 5[GeV]
Cuts: 2.25 < E(l) < 2.5 and 0.9 < C(l) < 1.0
nCall : 10,000,000

The cross-section converged to the value around 9.8E-02
The cross-section with the same configuration, without the cuts (considering all the energy and angle ranges) also converges to the value matching with the value you obtained, 8.48E+06

However there is a huge difference in the distributions for 0.9<C(l)<1.0. For the first config the range of the distribution is between 0.1 - 100 pb, but for the second one is between 10^5 - 10^9. Here the question is that which one is correct?

For your second solution (all other settings are the same as previous solution), the cross-section converges more efficiently and the distribution is matching with Figure. 1 of the paper arXiv: 0812.0859 (Demidov and Kalashev) if I put the cuts 2.25 < E(l) < 2.5 and 0.9 < C(l) < 1.0.

Also, once more I tried to define electron mass in Edit Model -> Variables and the add it in Edit Model -> Particles (this is similar to your first solution) and this time with 10 diagrams (deleting diagrams containing virtual h and Z) and 10,000,000 ncalls after 10 iterations, the cross-section converged. Although, interestingly, the same configuration, for only one diagram, gives "Negative points" and diverges.

At the end, I think the problem with the convergence is solved, thanks to you, but still I don't know which distribution is correct.

Best regards,

Amir

Revision history for this message
Alexander Pukhov (pukhov) said : 		#3

On 1/11/23 02:55, AmirFarzan Esmaeili wrote:
> Question #704340 on CalcHEP changed:
> https://answers.launchpad.net/calchep/+question/704340
>
> Status: Answered => Open

I asked  help of  I.F. Ginzburg and V.G. Serbo from Novosibirsk. It
appears that    for this processes   there is  a symbolic answer

     sigma  =\frac{\alpha^4}{36 \pi m^2} (175 \zeta(3)- 38)

and this formula reproduces numerical result  obtained by CalcHEP.   But
as it was mentioned by Ginzburg,   to get correct physical result one
has to substitute alpha=1/137, because here all photons are close to
mass shell ( at list their virtualities are smaller than electron
mass).  So this fantastic cross section 8E6 pb  -> (6.5E6pb for
alpha=1/137) is correct.

>
> AmirFarzan Esmaeili is still having a problem:
> Dear Prof. Pukhov
>
> Thanks for your reply. Unfortunately we didn't receive your email, so I
> had to resend my question here.
>
> For your first solution, I changed the settings as follows:
>
> Interaction: A,A->l,L,l,L
> Removed diagrams with virtual h and Z
> In the numerical session: Ml->5E-4
> First/Second particle momentum: 5[GeV]
> Cuts: 2.25 < E(l) < 2.5 and 0.9 < C(l) < 1.0
> nCall : 10,000,000
>
> The cross-section converged to the value around 9.8E-02
> The cross-section with the same configuration, without the cuts (considering all the energy and angle ranges) also converges to the value matching with the value you obtained, 8.48E+06

     Here I have a quite different result.   Distribution over C(l)   is
concentrated in very small region  C(l)>1-1E-7.  So, cut for C(l) does
not  change result. But distribution over E(l) is almost flat.

So, the cut for E(l)  changes result according to dE(l) interval - about
40 times.

May be c(l) < 1 works wrongly here because of lost of precision. It
should not be so, but I'll check.

>
> However there is a huge difference in the distributions for
> 0.9<C(l)<1.0. For the first config the range of the distribution is
> between 0.1 - 100 pb, but for the second one is between 10^5 - 10^9.
> Here the question is that which one is correct?
>
> For your second solution (all other settings are the same as previous
> solution), the cross-section converges more efficiently and the
> distribution is matching with Figure. 1 of the paper arXiv: 0812.0859
> (Demidov and Kalashev) if I put the cuts 2.25 < E(l) < 2.5 and 0.9 <
> C(l) < 1.0.
>
> Also, once more I tried to define electron mass in Edit Model ->
> Variables and the add it in Edit Model -> Particles (this is similar to
> your first solution) and this time with 10 diagrams (deleting diagrams
> containing virtual h and Z) and 10,000,000 ncalls after 10 iterations,
> the cross-section converged. Although, interestingly, the same
> configuration, for only one diagram, gives "Negative points" and
> diverges.

      Here we have  electromagnetic interactions of two dipoles created
by  dissociation of incoming photon.   For each couple up/down electrons
cross section is infinite. But we get a finite result because of  mutual
screening.  So,  keeping only one diagram  we expect problems.

Best

     Alexander Pukhov

PS: I did not read  arXiv: 0812.0859  and do not know how they treat
obtained result.

I ask Ginzburg  about reference on formula  for total cross section
which initially was written by Serbo. He promised to send,  but  now I
have not it.

>
> At the end, I think the problem with the convergence is solved, thanks
> to you, but still I don't know which distribution is correct.
>
> Best regards,
>
> Amir
>

Revision history for this message
Alexander Pukhov (pukhov) said : 		#4

Total cross section

H. Cheng and T. T. Wu, Phys. Rev. D1 (1970) 3414;
L.N. Lipatov and G.V. Frolov, Yad. Fiz. 13 (1971) 588

Differential cross section

E.A. Kuraev, L.N. Lipatov and M.I. Strikman, ZhETF 66 (1974) 838

E.A. KURAEV, A. SCHILLER' and V.G. SERBO. Nuclear Physics B256 (1985) 189-210

Best
      Alexander Pukhov

On 1/11/23 02:55, AmirFarzan Esmaeili wrote:
> Question #704340 on CalcHEP changed:
> https://answers.launchpad.net/calchep/+question/704340
>
> Status: Answered => Open
>
> AmirFarzan Esmaeili is still having a problem:
> Dear Prof. Pukhov
>
> Thanks for your reply. Unfortunately we didn't receive your email, so I
> had to resend my question here.
>
> For your first solution, I changed the settings as follows:
>
> Interaction: A,A->l,L,l,L
> Removed diagrams with virtual h and Z
> In the numerical session: Ml->5E-4
> First/Second particle momentum: 5[GeV]
> Cuts: 2.25 < E(l) < 2.5 and 0.9 < C(l) < 1.0
> nCall : 10,000,000
>
> The cross-section converged to the value around 9.8E-02
> The cross-section with the same configuration, without the cuts (considering all the energy and angle ranges) also converges to the value matching with the value you obtained, 8.48E+06
>
> However there is a huge difference in the distributions for
> 0.9<C(l)<1.0. For the first config the range of the distribution is
> between 0.1 - 100 pb, but for the second one is between 10^5 - 10^9.
> Here the question is that which one is correct?
>
> For your second solution (all other settings are the same as previous
> solution), the cross-section converges more efficiently and the
> distribution is matching with Figure. 1 of the paper arXiv: 0812.0859
> (Demidov and Kalashev) if I put the cuts 2.25 < E(l) < 2.5 and 0.9 <
> C(l) < 1.0.
>
> Also, once more I tried to define electron mass in Edit Model ->
> Variables and the add it in Edit Model -> Particles (this is similar to
> your first solution) and this time with 10 diagrams (deleting diagrams
> containing virtual h and Z) and 10,000,000 ncalls after 10 iterations,
> the cross-section converged. Although, interestingly, the same
> configuration, for only one diagram, gives "Negative points" and
> diverges.
>
> At the end, I think the problem with the convergence is solved, thanks
> to you, but still I don't know which distribution is correct.
>
> Best regards,
>
> Amir
>

Revision history for this message
AmirFarzan Esmaeili (amirfarzan) said : 		#5

Dear Prof. Pukhov,

During these days I took many runs of the code to be sure that I'm understanding the results correctly. Basically, a good part of our problems is solved, thanks to you.

However, I noticed that for the case that we set the interaction to A,A->m,M,l,L with both m and l mass set to electron mass, I can get two different results. Suppose this setting:

A,A->m,M,l,L
removing diagrams with h, Z
Ml=electron mass
Mm=electron mass
No cuts are applied

The cross-section for this setting for some runs converges to 6.45E+06 pb and for some other runs converges to 1.29E+07( = 2 * 6.45E+06 )
But for both of these cases the distributions are reasonable. I mean for the case (cross-sec =1.29E+07 ) the distribution of the rapidity Y(l,L )has two peaks (one forward scattering and the other backward scattering), but for the case (cross-sec =6.45E+06 ), Y(l,L) has only one peak around 10GeV (forward scattered) and Y(m,M) has the other peak around -10GeV (backward scattered). But I don't understand why the scenario of the results can change run by run. However, always realizing the correct cross-section with respect to the number of Feynman diagrams and the distributions is possible.

Either way, I think our main problem is solved.

Again thank you for your help and for your time.

Best regards,

Amir

Revision history for this message
AmirFarzan Esmaeili (amirfarzan) said : 		#6

Thanks Alexander Pukhov, that solved my question.

Revision history for this message
Alexander Pukhov (pukhov) said : 		#7

On 1/17/23 20:25, AmirFarzan Esmaeili wrote:
> Question #704340 on CalcHEP changed:
> https://answers.launchpad.net/calchep/+question/704340
>
> Status: Answered => Solved
>
> AmirFarzan Esmaeili confirmed that the question is solved:
> Dear Prof. Pukhov,
>
> During these days I took many runs of the code to be sure that I'm
> understanding the results correctly. Basically, a good part of our
> problems is solved, thanks to you.
>
> However, I noticed that for the case that we set the interaction to
> A,A->m,M,l,L with both m and l mass set to electron mass, I can get two
> different results. Suppose this setting:
>
> A,A->m,M,l,L
> removing diagrams with h, Z
> Ml=electron mass
> Mm=electron mass
> No cuts are applied
>
> The cross-section for this setting for some runs converges to 6.45E+06 pb and for some other runs converges to 1.29E+07( = 2 * 6.45E+06 )
> But for both of these cases the distributions are reasonable. I mean for the case (cross-sec =1.29E+07 ) the distribution of the rapidity Y(l,L )has two peaks (one forward scattering and the other backward scattering), but for the case (cross-sec =6.45E+06 ), Y(l,L) has only one peak around 10GeV (forward scattered) and Y(m,M) has the other peak around -10GeV (backward scattered). But I don't understand why the scenario of the results can change run by run. However, always realizing the correct cross-section with respect to the number of Feynman diagrams and the distributions is possible.

I  wrote you that we need a cut Y(m,M)> 0 to void doubling.

The reason of instability is the following. At first step Vegas (   MC
routine)  does not see a real  region of phase space where ME is
concentrated. If  the cut for Y is not applied the region consists of
two separated parts.  Vegas can find one of then or both.

I indeed first time see example where a difference between  first
iteration and the final answer is so large.  Appearance of symbolic
answer which allows to check result is a good point here.

Best

     Alexander Pukhov

>
> Either way, I think our main problem is solved.
>
> Again thank you for your help and for your time.
>
> Best regards,
>
> Amir
>

Revision history for this message
AmirFarzan Esmaeili (amirfarzan) said : 		#8

Thank you so much.

I understood what is going on.

Best regards,

Amir