different me_frame gave different XS in VBS Same-sign WW

In the paper,

The difference is sizeable as well actually.
So I'm not surprised at all. This is actually the reason why we have introduced that parameter in the run_card since this is important for the user to be allowed to define (in a non lorentz invariant way) what longitudinal means.

Cheers,

Olivier

> On 5 Feb 2020, at 11:12, xiao jie <email address hidden> wrote:
>
> New question #688519 on MadGraph5_aMC@NLO:
> https://answers.launchpad.net/mg5amcnlo/+question/688519
>
> Dear MadGraph experts,
>
> I am using MG5 v2.7.0 to simulate VBS same-sign WW process. I test the me_frame this time.
>
> I run two processes, they have same proc_card_mg5.dat:
> set default_unset_couplings 99
> set group_subprocesses Auto
> set ignore_six_quark_processes False
> set loop_optimized_output True
> set loop_color_flows False
> set gauge unitary
> set complex_mass_scheme False
> set max_npoint_for_channel 0
> import model sm
> define p = g u c d s u~ c~ d~ s~
> define j = g u c d s u~ c~ d~ s~
> define l+ = e+ mu+
> define l- = e- mu-
> define vl = ve vm vt
> define vl~ = ve~ vm~ vt~
> import model sm-ckm_no_b_mass
> define p = 21 2 4 1 3 -2 -4 -1 -3 5 -5
> define p = g u c d s b u~ c~ d~ s~ b~
> define j = p
> define l+ = e+ mu+
> define l- = e- mu-
> define vl = ve vm
> define vl~ = ve~ vm~
> generate p p > w+{0} w+{0} j j QED=4 QCD=0
> output vbs_wpwp_ll2
>
> For their run_card.dat, the only difference is one of them uses '1,2 = me_frame' (vbs_wpwp_ll), the other one uses '3,4 = me_frame' (vbs_wpwp_ll2), other settings are same as this page:
> https://github.com/freejiebao/generator/blob/master/MG5CARDS/polarization/vbs_wpwp_ll2/vbs_wpwp_ll2_run_card.dat
>
> I got different XS:
> XS(vbs_wpwp_ll): 0.009639 ± 7.3e-05 pb
> XS(vbs_wpwp_ll2): 0.01476 ± 0.00012 pb
>
> Does someone know the reason why? Because from this paper: https://arxiv.org/pdf/1912.01725.pdf. Different should not have big difference.
>
> Thanks,
> Jie
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Dear Olivier,

Sorry to open this thread again. I have done more detailed study and have an additional question about the 'me_frame'.

I defined following processes:
vbs_wmwm_ll: generate p p > w-{0} w-{0} j j QED=4 QCD=0, w- > l- vl~
vbs_wmwm_lt: generate p p > w-{0} w-{T} j j QED=4 QCD=0, w- > l- vl~
vbs_wmwm_tt: generate p p > w-{T} w-{T} j j QED=4 QCD=0, w- > l- vl~

vbs_wpwp_ll: generate p p > w+{0} w+{0} j j QED=4 QCD=0, w+ > l+ vl
vbs_wpwp_lt: generate p p > w+{0} w+{T} j j QED=4 QCD=0, w+ > l+ vl
vbs_wpwp_tt: generate p p > w+{T} w+{T} j j QED=4 QCD=0, w+ > l+ vl
(ps: I don't know should I define 'vbs_wmwm_tl': p p > w-{T} w-{0} j j, 'vbs_wpwp_tl': p p > w+{T} w+{0} j j, since in the paper https://arxiv.org/pdf/1912.01725.pdf, opposite-sign process should have ll, tl, lt, tt component?
And I have discussed about this here https://answers.launchpad.net/mg5amcnlo/+question/688206)

If I set '[1,2] = me_frame', then I will get cross sections for each process:
vbs_wmwm_ll:0.0000726243 pb
vbs_wmwm_lt:0.000192457 pb
vbs_wmwm_tt:0.000586751 pb

vbs_wpwp_ll:0.000213863 pb
vbs_wpwp_lt:0.000585871 pb
vbs_wpwp_tt:0.00180202 pb

the total cross section is: xs1 = 0.0034535863 pb

If I set '[3,4] = me_frame', then I will get cross sections for each process:
vbs_wmwm_ll2:0.000183671 pb
vbs_wmwm_lt2:0.000516927 pb
vbs_wmwm_tt2:0.000266909 pb

vbs_wpwp_ll2:0.000532552 pb
vbs_wpwp_lt2:0.00155994 pb
vbs_wpwp_tt2:0.000877589 pb

the total cross section is: xs2 = 0.003937588 pb

Because xs1 != xs2, so for different rest frame, even the inclusive cross section can change, do I understand it correctly?

Thanks,
Jie

Hi Jie,

The sum of those processes should not always add to the full unpolarised cross-sections.
(in therefore the sum can also depend of the frame)

They are multiple reason for that:

1) interference between polarization. Since your W will not be exactly onshell, you actually have intereference between the longitudinal and transverse polarization. Such interference can not be computed by our code. Note that if you do not apply ANY cut, this interferences is actually vanishing (for the cross-section but not for the differential distribution)

2) Since your W is allowed to be off-shell, you have a fourth polarization that enter the game.
vbs_wpwp_aa: generate p p > w+{A} w+{A} j j QED=4 QCD=0, w+ > l+ vl
vbs_wpwp_aa: generate p p > w+{A} w+{T} j j QED=4 QCD=0, w+ > l+ vl
vbs_wpwp_aa: generate p p > w+{A} w+{0} j j QED=4 QCD=0, w+ > l+ vl
(and again all the associated interference term)

3) renormalisation and refactorization scale. The default is based on the CKKW-L clustering and based on a diagram by diagram importance sampling. This lead to a sensitivity to the scale in such type of comparison since the actual definition of the scale choice will not be the same for each of the process. You can either use a fix scale or a simpler dynamical scale (like HT/2) to avoid to have such issues during comparison.

Concerning the https://answers.launchpad.net/mg5amcnlo/+question/688206
looks like your are confused about this so I will re-reply to it since for me you were just pointing us a bug.

Hi Olivier,

In 1912.01725, Table 5 and 6 shows the difference is not very large between WW-CM and p-CM frames.

This seems not the case for Jie, e.g. the longitudinal fraction can be 100% different. Do you know why? Is it due to that Jie included W decay while 1912.01725 doesn't?

vbs_wmwm_ll:0.0000726243 pb
vbs_wmwm_ll2:0.000183671 pb

One more question, what is the default frame of polarization evaluation in MG version 24X and 26X? The lab frame or rest frame of particle?

Best,
Qiang

Hi,

This is likely due to scale uncertainty (I believe). We did not use the default dynamical scale choice for our paper.

Cheers,

Olivier