# Inconsistent results at high energies for the process pp->hh

Dear Calchep team,

We try to obtain the consistent cross section results for the process p,p->h,h  between Calchep and the literature. Previously, we discussed the similar inconsistency problem with you. Your suggestion solved the problem (RQCDh -> 1). Now, we check this process for different energies (\sqrt{s}=7,8,13,14,27 and also 100 TeV). For small energies, Calchep gives the consistent results with the literature. However, for 27 TeV and 100 TeV energies, large difference between  the literature and Calchep results. What is the problem? How we can solve this inconsistency?

For example; \sqrt{s}=8 TeV Calchep gives 9.46 and in literature it is 9.44. -> Consistent

\sqrt{s}=27 TeV Calchep gives 243, on the other hand in literature it is 140 -> Inconsistent

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 Revision history for this message Alexander Belyaev (alexander.belyaev) said on 2021-01-02: #1

Dear Nurhan,
could you send us reference to the source of the cross section
calculation for  \sqrt{s}=27 TeV
I would like to see details how it was calculated  and make detailed
comparison with CalcHEP one.
Thank you,
Sasha

On 02/01/2021 09:45, Nurhan Karahan wrote:
> New question #694758 on CalcHEP:
>
> Dear Calchep team,
>
> We try to obtain the consistent cross section results for the process p,p->h,h  between Calchep and the literature. Previously, we discussed the similar inconsistency problem with you. Your suggestion solved the problem (RQCDh -> 1). Now, we check this process for different energies (\sqrt{s}=7,8,13,14,27 and also 100 TeV). For small energies, Calchep gives the consistent results with the literature. However, for 27 TeV and 100 TeV energies, large difference between  the literature and Calchep results. What is the problem? How we can solve this inconsistency?
>
> For example; \sqrt{s}=8 TeV Calchep gives 9.46 and in literature it is 9.44. -> Consistent
>
> \sqrt{s}=27 TeV Calchep gives 243, on the other hand in literature it is 140 -> Inconsistent
>
>

--
______________________________________________________________________
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
______________________________________________________________________

 Revision history for this message Nurhan Karahan (ckarahan) said on 2021-01-02: #2

Here the link that we use as the source of the cross section.

https://twiki.cern.ch/twiki/bin/view/LHCPhysics/LHCHXSWGHH

In this page in the part 1 of Latest recommendations for gluon fusion" the first table shows the cross sections for different energies.

For 7,8,13 and 14 TeV energies we obtained the consistent results by setting RQCDh=1 as you suggested before.

 Revision history for this message Alexander Pukhov (pukhov) said on 2021-01-02: #3

Let me write my comment.

Here  the leading  contribution comes from point-like GGhh vertex.

This vertex appears in Lagrangian to restore SU(2) gauge invariance
broken by  GGh. At the level of Lagrangian we have added effective vertex

F^2 H^2

where F is the gluon field strength tensor and H is  the Higgs doublet.
Indeed, here we expect contribution of  t-quark  loop diagram, our
point-like vertex is an approximation for mTop->infty.

F^2 H^2 leads to increasing cross section and brakes unitarity at 20TeV,
but definitely it becomes wrong for smaller energies. So, we do not
expect correct result  when  we are close to unitarity limit for GGhh
operator.

Other point. Our GGh vertex is normalized on Higgs mass. Generally such
vertex has to contain  GG^2 coupling which is fixed on Mh scale. To make
GG 'alive' in our Lagrangian we have to restore running GG. For this
case we have to add to hGG and hhGG vertices the following couplings

GG^2/GGMh2  and GG^4/GGMh2^2

where GGMh2=alphaQCD(Mh)*4*pi

When running GG is restored for

G,G -> h,h cross section with cteq6l1 and Pcm=14TeV

I get  0.18pb.     Yes, It is larger than 0.14, but  for the reason
explained  above. In general it looks reasonable.

Best

Alexander Pukhov

On 1/2/21 4:25 PM, Alexander Belyaev wrote:
> Question #694758 on CalcHEP changed:
>
>
> Alexander Belyaev proposed the following answer:
> Dear Nurhan,
> could you send us reference to the source of the cross section
> calculation for  \sqrt{s}=27 TeV
> I would like to see details how it was calculated  and make detailed
> comparison with CalcHEP one.
> Thank you,
> Sasha
>
>
>
> On 02/01/2021 09:45, Nurhan Karahan wrote:
>> New question #694758 on CalcHEP:
>>
>> Dear Calchep team,
>>
>> We try to obtain the consistent cross section results for the process p,p->h,h  between Calchep and the literature. Previously, we discussed the similar inconsistency problem with you. Your suggestion solved the problem (RQCDh -> 1). Now, we check this process for different energies (\sqrt{s}=7,8,13,14,27 and also 100 TeV). For small energies, Calchep gives the consistent results with the literature. However, for 27 TeV and 100 TeV energies, large difference between  the literature and Calchep results. What is the problem? How we can solve this inconsistency?
>>
>> For example; \sqrt{s}=8 TeV Calchep gives 9.46 and in literature it is 9.44. -> Consistent
>>
>> \sqrt{s}=27 TeV Calchep gives 243, on the other hand in literature it is 140 -> Inconsistent
>>
>>

 Revision history for this message Nurhan Karahan (ckarahan) said on 2021-01-02: #4

Yes, for 14 TeV it seems reasonable result.

in the reference that I sent its link with my previous message, for 14 TeV the cross section ~36.7 fb. What is the source of the cross section value for 14 TeV (0.14 pb) mentioned by you above.

Actually, we study on a BSM model for the process pp-> hh at high energies (14 TeV AND 100 TeV). Before going on with our BSM model, we want to check the consistency of SM results in Calchep with the literature. For 14 TeV it seems that we can study our BSM in Calchep. But for 100 TeV is not there a way to solve this inconsistency?

 Revision history for this message Alexander Belyaev (alexander.belyaev) said on 2021-01-02: #5

Dear Nurhan,

the difference between CalcHEP result and the one from Higgs working
group is the difference
between EFT result  and exact result, obtained by integration of the top
and bottom loops.

They cannot be equal in general. For 8 TeV collider this approximation
works well
while starting from 14TeV and up the approximation does  not work well
and its accuracy is getting worse with the collider energy increase.
There is non-unitary growth with the energy increase as Sasha Pukhov noted.
Fo 100 TeV collider the difference is factor of 4 meaning that this
approximation completely breaks down.

The only solution is to introduce the exact box and triangle vertices in
CalcHEP
and involve them into the integration.
This can be potentially done using LoopTools library, but this approach
also requires CalcHEP to evaluate vertices  for each momenta
configuration during integration. CalcHEP can not do this at the moment.
This is one of the things on TODO list  in some near future.

Regards,
Sasha Belyaev

On 02/01/2021 18:55, Nurhan Karahan wrote:
> Question #694758 on CalcHEP changed:
>
>
> Nurhan Karahan is still having a problem:
>
> Yes, for 14 TeV it seems reasonable result.
>
> in the reference that I sent its link with my previous message, for 14
> TeV the cross section ~36.7 fb. What is the source of the cross section
> value for 14 TeV (0.14 pb) mentioned by you above.
>
> Actually, we study on a BSM model for the process pp-> hh at high
> energies (14 TeV AND 100 TeV). Before going on with our BSM model, we
> want to check the consistency of SM results in Calchep with the
> literature. For 14 TeV it seems that we can study our BSM in Calchep.
> But for 100 TeV is not there a way to solve this inconsistency?
>

--
______________________________________________________________________
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
______________________________________________________________________

 Revision history for this message Alexander Pukhov (pukhov) said on 2021-01-03: #6

sqrt(s)        7     8        13       14    27     100

http            6.5      9.4        31        36   139    1224

cteq6l1       5        7.5        28        40    165    2500

cteq10       4.6      6.7        23        28    128    1790

The last two lines present CalcHEP results with scale M(h,h)/2 (
according to https).

1) Not so bad  agreement with NNLO

2) There is a dependence on structure function. I am not sure that the
two ones used by be me are good for sqrt(s)=100TeV

3)  Before 27TeV cross section  is proportion to s.

4) ponit-like GGhh realized in CalcHEP should work untill sqrt(s) ~ 2
Mtop ~ 1TeV. But unitarity limit is broken at 20TeV.

Best

Alexander Pukhov

On 1/3/21 12:15 AM, Alexander Belyaev wrote:
> Question #694758 on CalcHEP changed:
>
>
> Alexander Belyaev proposed the following answer:
> Dear Nurhan,
>
> the difference between CalcHEP result and the one from Higgs working
> group is the difference
> between EFT result  and exact result, obtained by integration of the top
> and bottom loops.
>
> They cannot be equal in general. For 8 TeV collider this approximation
> works well
> while starting from 14TeV and up the approximation does  not work well
> and its accuracy is getting worse with the collider energy increase.
> There is non-unitary growth with the energy increase as Sasha Pukhov noted.
> Fo 100 TeV collider the difference is factor of 4 meaning that this
> approximation completely breaks down.
>
> The only solution is to introduce the exact box and triangle vertices in
> CalcHEP
> and involve them into the integration.
> This can be potentially done using LoopTools library, but this approach
> also requires CalcHEP to evaluate vertices  for each momenta
> configuration during integration. CalcHEP can not do this at the moment.
> This is one of the things on TODO list  in some near future.
>
>
> Regards,
> Sasha Belyaev
>
>
> On 02/01/2021 18:55, Nurhan Karahan wrote:
>> Question #694758 on CalcHEP changed:
>>
>>
>> Nurhan Karahan is still having a problem:
>>
>> Yes, for 14 TeV it seems reasonable result.
>>
>> in the reference that I sent its link with my previous message, for 14
>> TeV the cross section ~36.7 fb. What is the source of the cross section
>> value for 14 TeV (0.14 pb) mentioned by you above.
>>
>> Actually, we study on a BSM model for the process pp-> hh at high
>> energies (14 TeV AND 100 TeV). Before going on with our BSM model, we
>> want to check the consistency of SM results in Calchep with the
>> literature. For 14 TeV it seems that we can study our BSM in Calchep.
>> But for 100 TeV is not there a way to solve this inconsistency?
>>