specular chains treatment when reducing diagram counting

Hi Arian,

You will not gain anything for interferences since you have the same diagram (and therefore the same analytical expression for the square matrix element)
The only difference is that in (3), the BW_cut is not used (while it is in (1) and (2)).
Since
1) this cut ensures to only generate events in the physicaly valid region.
2) (1) and (2) should faster for the event generation,
I would strongly suggest to use (1/2)

Cheers,

Olivier

On Nov 20, 2012, at 8:35 AM, Arian Abrahantes <email address hidden> wrote:

> New question #214747 on MadGraph5:
> https://answers.launchpad.net/madgraph5/+question/214747
>
> Dear MG-team:
>
> I have a question related to the usage of decay chains when two identical particles are produced in intermediate states of a reaction. For instance, take as example the MSSM producing a gluino pair (the usual example MadGraph provide is a particle-anti-particle decay treatment):
>
> import model mssm
> generate g g > go go, go > t t1~ , go > b b1~ @1
> add process g g > go go , go > b b1~ , go > t t1~ @2
> add process g g > b b1~ t t1~ / t1 t2 b1 b2 t b @3
>
> MadGraph give a similar diagram count and shape for all of them (3). However, process 3 is the most general way to obtain "t b t1~ b1~". So, If I would like to use the force decay approach for identical particles which would be the correct way? or to obtain better results (I am thinking on interferences) should I prevent the force decay approach in identical particles in intermediate states?
>
> thanks in advance,
>
> arian
>
> --
> You received this question notification because you are a member of
> MadTeam, which is an answer contact for MadGraph5.

dear Olivier:

thanks for your suggestion. I get the point with the cut issue. Yet, your suggestion: "I would strongly suggest to use (1/2)" means:

1- use either process 1 or 2

or

2- use processes 1 and 2.

the point of being identical particles in intermediate states makes me wonder how symmetric diagram (specially in the channel g g > g > go go -G1-) are handled in this case, actually that may have been the primordial question.

In practice I tried above processes with default param_card

P1: s= 0.046797 ± 0.000378 (pb)

P2: s= 0.046205 ± 0.00058 (pb)

P3: s= 0.050086 ± 0.000543 (pb)

The difference between 1 or 2 and 3 should be provoked by the BW_cut.

best regards and deeply thankful for your help,

arian

secondly, what if still I'd like to decay the squark following this process

suppose

define ne = n1 n2 n3 n4
define ch = x1- x1+ x2- x2+
define wb = w+ w- z a
define sq = ul ur sl sr cl cr dl dr
define av = ne ch wb sq

g g > t t~ t t~ n1 n2 / av QED=2 @1

g g > go go / av , (go > t t1~, t1~ > t n1) , (go > t~ t1, t1 > t n2) @2

g g > go go / av , go > t t~ n1 , go > t t~ n2 / av QED=2 @3

according to your previous suggestion the second case respect the BW_cut for all decays. still diagram counting for process 3 is comparatively higher than process 2.

What makes me reluctant to shorten my diagram generation is, the first process has several non resonant squarks diagrams with a single squarks propagator (actually only one susy particle propagator, which might make them the leading diagrams on the reaction) that depending on the SUSY parameterization might interfer (actually sometimes not visible at bare eyes, let say by comparing only the squark masses).

I can tell you this because I have already made other calculations (p p > b b~ n1 n1) where non-resonant diagrams (p p > b1 > b b~ n 1n1 and p p > b2 > b b~ n1 n1, only one susy particle propagator in the diagram) are leading with respect to double pole diagrams (p p > b1 b1~ > b b~ n1 n1 and p p > b2 b2~ > b b~ n1 n1, two susy particles propagators in diagrams), that's sort of expected. Furthermore for a SUSY parameterization I use, the first case show a large interference if both squarks are included in the calculation. So, I am wondering what might happen now that diagram count in the first process drastically increases and it may include leading diagrams that might be cut away by forcing the decay chain (either process 2 or 3).

dear oliver

thanks for your concern and prompt reply

> process (1) and (2) are equivalent to each other and to (3)
> as you provide as cross-section this proves that the symmetry factor is
> taken into account properly.
>
> so you can use either (1) or (2)
>
>
R: Ok.

> Concerning your second question,
> The difference between (2) and (3) should be only due to the difference
> between
> > (go > t t1~, t1~ > t n1)
> and
> > go > t t~ n1
> (respectively for n2)
>
> The go > t t~ n1 allows to have as well t2 in the propagator and not only
> t1.
> The relevance of such diagram depends of your analysis (and of the mass
> spectrum that you are looking at).
>
>
R: Actually the reason why I need the heavier squark is that sometimes my
spectra is almost degenerated (sq_L=sq_R). So, from your reply I infer that
the BW_cut is well managed by the code in that case.

>
> The concern is indeed valid, but then why do you forbid the presence of a
> large quantity of particles in (1) [all the av]?
> This also removes a huge quantity of diagram (10%) and in that case and
> those diagrams can also have interferences.
>

R: I tried to shorter the example generation that's why I remove those
particles. The most I'll be able to remove in my calculation, because of my
parameterizations, are the first and second generation squarks which are
much heavier than the rest of the particles.

> Furthemore since you have off-shell contribution, they are no a priori
> reason to assume that you can neglect those interferences.
>
>
R: So I will have to take a diagram sample and see what happens. Once more
thanks for your help and suggestions,

best regards,

arian

> Cheers,
>
> Olivier
>
>
> On Nov 20, 2012, at 11:55 AM, Arian Abrahantes <
> <email address hidden>> wrote:
>
> > Question #214747 on MadGraph5 changed:
> > https://answers.launchpad.net/madgraph5/+question/214747
> >
> > Arian Abrahantes gave more information on the question:
> > secondly, what if still I'd like to decay the squark following this
> > process
> >
> > suppose
> >
> > define ne = n1 n2 n3 n4
> > define ch = x1- x1+ x2- x2+
> > define wb = w+ w- z a
> > define sq = ul ur sl sr cl cr dl dr
> > define av = ne ch wb sq
> >
> > g g > t t~ t t~ n1 n2 / av QED=2 @1
> >
> > g g > go go / av , (go > t t1~, t1~ > t n1) , (go > t~ t1, t1 > t n2) @2
> >
> > g g > go go / av , go > t t~ n1 , go > t t~ n2 / av QED=2 @3
> >
> > according to your previous suggestion the second case respect the BW_cut
> > for all decays. still diagram counting for process 3 is comparatively
> > higher than process 2.
> >
> > What makes me reluctant to shorten my diagram generation is, the first
> > process has several non resonant squarks diagrams with a single squarks
> > propagator (actually only one susy particle propagator, which might make
> > them the leading diagrams on the reaction) that depending on the SUSY
> > parameterization might interfer (actually sometimes not visible at bare
> > eyes, let say by comparing only the squark masses).
> >
> > I can tell you this because I have already made other calculations (p p
> >> b b~ n1 n1) where non-resonant diagrams (p p > b1 > b b~ n 1n1 and p p
> >> b2 > b b~ n1 n1, only one susy particle propagator in the diagram) are
> > leading with respect to double pole diagrams (p p > b1 b1~ > b b~ n1 n1
> > and p p > b2 b2~ > b b~ n1 n1, two susy particles propagators in
> > diagrams), that's sort of expected. Furthermore for a SUSY
> > parameterization I use, the first case show a large interference if both
> > squarks are included in the calculation. So, I am wondering what might
> > happen now that diagram count in the first process drastically increases
> > and it may include leading diagrams that might be cut away by forcing
> > the decay chain (either process 2 or 3).
> >
> > --
> > You received this question notification because you are a member of
> > MadTeam, which is an answer contact for MadGraph5.
>
> --
> If this answers your question, please go to the following page to let us
> know that it is solved:
>
> https://answers.launchpad.net/madgraph5/+question/214747/+confirm?answer_id=3
>
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>
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>

Thanks Olivier Mattelaer, that solved my question.

Dear oliver:

I have given a second thought on this issue. It actually came after your suggestion of forcing decays over the full diagram generation and knowing that there might be interesting diagrams left aside. So my question is: which would be the most accurate procedure to generate complex final states where decaying particle appear in other internal lines -non-resonant diagrams- as well.

For instance:

import model sm
generate g g > t t~ , t > b w+ , t~ > b~ w- @1
add process g g > b b~ w- w+ @2
output test-sm-tt -f

Process 1, set the off-shell top-quark production and subsequent decay (BW_cut is considered)
Process 2, generates all possible diagrams of the first depicted final states.

At this point worth saying that diagrams not present in 1 are of the same QCD/QED order in the coupling (QED=2 QCD=2)

Xsection of process 1 do not match with those of similar diagrams in Process 2. For instance,

gg -> g -> tt~ -> bwbw (channel-S diagram)

(1) xs = 49.46 pb
(2) xs = 51.39 pb

even fixing factorization and renormalization scales, there are differences among these values. Thus, I presume and as you pointed out previously, the BW_cut make the difference here.

The rest of diagrams in process 2, those not included in process 1, contributes significantly if compared to example above (about 34 pb resumed in diagrams as 14 and 15 in process 2) and they are not supposed to be discarded in an accurate xsection calculation. And, despite of the fact that those diagrams may alter the b-quark distribution in the event since they are not fully correlated to the top-quark as it happens in events generated in Process 1. I agree that in this example this type of diagrams contributes about 5% of the xsection and they could be discarded but other processes, models and simulations (specially with off-shell particles in final states) may have different correlation.

How can I take the largest advantage of MG (i.e. accurateness in event simulation)? For instance in this event generation, I cam e with different solutions:

1- should I force top-quark decay in process 1 and in process 2 just take diagrams not generated by process 1. If I am correct the latter would have to be done manually?

2- a trick to remove only the diagrams like those depicted in process 1 from process 2?.

best regards and thanks for your help,

arian

Hello Arian,

> I have given a second thought on this issue. It actually came after your
> suggestion of forcing decays over the full diagram generation and
> knowing that there might be interesting diagrams left aside. So my
> question is: which would be the most accurate procedure to generate
> complex final states where decaying particle appear in other internal
> lines -non-resonant diagrams- as well.
>
> For instance:
>
> import model sm
> generate g g > t t~ , t > b w+ , t~ > b~ w- @1
> add process g g > b b~ w- w+ @2
> output test-sm-tt -f
>
> Process 1, set the off-shell top-quark production and subsequent decay (BW_cut is considered)
> Process 2, generates all possible diagrams of the first depicted final states.
>
> At this point worth saying that diagrams not present in 1 are of the
> same QCD/QED order in the coupling (QED=2 QCD=2)
>
> Xsection of process 1 do not match with those of similar diagrams in
> Process 2. For instance,
>
> gg -> g -> tt~ -> bwbw (channel-S diagram)
>
> (1) xs = 49.46 pb
> (2) xs = 51.39 pb
>
> even fixing factorization and renormalization scales, there are
> differences among these values. Thus, I presume and as you pointed out
> previously, the BW_cut make the difference here.

Please note that the "cross section" for a "diagram" has no physical meaning. The "diagram" is just a representation of the phase space parameterization used for the corresponding integration channel. So you need to compare full (or differential) cross sections.

> The rest of diagrams in process 2, those not included in process 1,
> contributes significantly if compared to example above (about 34 pb
> resumed in diagrams as 14 and 15 in process 2) and they are not supposed
> to be discarded in an accurate xsection calculation. And, despite of the
> fact that those diagrams may alter the b-quark distribution in the event
> since they are not fully correlated to the top-quark as it happens in
> events generated in Process 1. I agree that in this example this type of
> diagrams contributes about 5% of the xsection and they could be
> discarded but other processes, models and simulations (specially with
> off-shell particles in final states) may have different correlation.

See above. To get a feeling for the importance of off-shell diagrams in this process, you need to either set bwcutoff very large (e.g., 200) so your difference is not simply due to the cut-away part of the Breit-Wiegner, or generate the process (1) using the syntax
generate p p > t t~ > b b~ w+ w-

I would be quite surprised if off-shell diagrams are relevant in this case, except possibly in specific phase space regions (such as where b b~ are very close in phase space, the typical gluon splitting region). Or, of course if you force the tops to be offshell using, e.g., a large cut on the invariant mass of the b and w.

> How can I take the largest advantage of MG (i.e. accurateness in event
> simulation)? For instance in this event generation, I cam e with
> different solutions:
>
> 1- should I force top-quark decay in process 1 and in process 2 just
> take diagrams not generated by process 1. If I am correct the latter
> would have to be done manually?

What you can do is to run
p p > b b~ w+ w- $ t t~
which forbids *near-onshell tops from the integration channels where the top is an s-channel resonance* (see the MG5 UpdateNotes). This allows you to combine the two processes without double counting (assuming you keep bwcutoff at a reasonable value, e.g. 15 or lower).
Note that actually removing diagrams is not gauge invariant in general and is therefore not recommended.

All the best,
Johan

dear johan:

thanks for your prompt and accurate reply.

What you can do is to run
> p p > b b~ w+ w- $ t t~
> which forbids *near-onshell tops from the integration channels where the
> top is an s-channel resonance* (see the MG5 UpdateNotes). This allows you
> to combine the two processes without double counting (assuming you keep
> bwcutoff at a reasonable value, e.g. 15 or lower).
>

R: This is very interesting and, indeed, answers my question.

> Note that actually removing diagrams is not gauge invariant in general and
> is therefore not recommended.
>
>
R: That's why I was looking a compromise in event generation between
forcing decay procedure (which eliminates many many diagrams hence gauge
invariance may play some role) and the rest of possible diagrams for a
given final state.

I am in a situation where for MSSM actually the non-resonant diagrams of a
given final state are the leading ones (including interferences) over the
most simpler choice let's say the type of diagrams related to the forced
decay of the sparticle (the type of processes discussed along this thread).
This answers from you it is really-really helpful, sorry if I had to go all
this way to actually find "the correct question".

best regards and deeply thankful,

arian

> All the best,
> Johan
>
> --
> You received this question notification because you asked the question.
>

dear johan

>
> I would be quite surprised if off-shell diagrams are relevant in this
> case, except possibly in specific phase space regions (such as where b
> b~ are very close in phase space, the typical gluon splitting region).
> Or, of course if you force the tops to be offshell using, e.g., a large
> cut on the invariant mass of the b and w.
>

I do have the scenario and model where this kind of situation may arise,
mostly due to diagram interference and effective models. Unfortunately, I
should not post it here but we can discussed it privately -likely that my
thesis depend on it ;-)-. Either way you may get a feeling of my work from
here (http://arxiv.org/abs/1209.5214 -nowadays it is under revision by
EPJC-),

best regards,

arian