Decay chain vs intermediate state syntax

Hi Will,

> I am trying to understand if there is any difference between using a decay chain syntax vs an intermediate state syntax, if both end up giving me the same set of diagrams. I understand that in both cases you force the intermediate particles to be on-shell (the on-shellness being defined by bwcutoff).

Only the decay chain syntax force the particle to on-shell, the intermediate only ask for a particle of that type to be in the s-channel.

> For example, if I have a higgs EFT, and I want to generate higgs decaying to two Z decaying each decaying to two leptons, which of the following would be “preferred"?

The preferred way for this case is
h > l+ l- l+ l-
Which includes all relevant diagram (and some interfering diagram as well)
Alternatively, you can assume a Z to be on shell in your analysis and in that case you can restrict your generation to
h > l+ l- z , z > l+ l-
In that case you need to take a “small” bwcut value to avoid double counting.

> h > z > l+ l- l+ l- / l+ l- #the exclusion of l+ l- from internal legs is to exclude the “+ l-, l- > l- z, z > l+ l- " like decay chains

This one is not valid since they are no good reason to not include some of the diagram that you exclude with your syntax.
(At least as long as you do not prove that the interference between the diagram is indeed negligeable which is not clear to me)

> h > z z, z > l+ l- #doesn’t include interference between final state leptons though….

This one is clearly not valid since 2*MZ>MH, so you can not put both Z on shell.

> Finally, if I did:
>
> h > z > e+ e- mu+ mu- / l+ l-
> h > z z, z > e+ e-, z > mu+ mu-
>
> What is the difference, if any? Mg5 suggests the former is 1 process with 1 diagram, and the latter is 1 process with 3 diagrams, so I’m guessing there is a difference here, even though in both cases the z bosons are 'on shell' ....

This is just due to a different way to generate the diagram for the two cases. In the decay chain syntax, each part of the process is generated independently by the code, this is why you have 3 diagram:
h > z z : 1 diagram
z > e+ e- : 1 diagram
z > mu+ mu- : 1 diagram

When you do the “output” command those diagram will be merge and you will get the physical number of diagram (in this case 1).

Cheers,

Olivier

On 04 Feb 2015, at 09:41, Will <email address hidden> wrote:

> New question #261658 on MadGraph5_aMC@NLO:
> https://answers.launchpad.net/mg5amcnlo/+question/261658
>
> Hello,
>
> I am trying to understand if there is any difference between using a decay chain syntax vs an intermediate state syntax, if both end up giving me the same set of diagrams. I understand that in both cases you force the intermediate particles to be on-shell (the on-shellness being defined by bwcutoff).
>
> For example, if I have a higgs EFT, and I want to generate higgs decaying to two Z decaying each decaying to two leptons, which of the following would be "preferred"?
>
> h > z > l+ l- l+ l- / l+ l- #the exclusion of l+ l- from internal legs is to exclude the "+ l-, l- > l- z, z > l+ l- " like decay chains
> h > z z, z > l+ l- #doesn't include interference between final state leptons though....
>
> Or are neither of these a good option?
>
> Finally, if I did:
>
> h > z > e+ e- mu+ mu- / l+ l-
> h > z z, z > e+ e-, z > mu+ mu-
>
> What is the difference, if any? Mg5 suggests the former is 1 process with 1 diagram, and the latter is 1 process with 3 diagrams, so I'm guessing there is a difference here, even though in both cases the z bosons are 'on shell' ....
>
> Cheers
> Will
>
>
>
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Thanks for answering quickly... just a few follow up questions....

I didn't know that intermediate particles in the a > b > c syntax were not constrained to be on-shell, so thanks - not sure where I read it made it to be on-shell. And this is saying that my final example of:

h > z > e+ e- mu+ mu- / l+ l-
h > z z, z > e+ e-, z > mu+ mu-

despite having the same diagram differ in that the former includes off-shell z whereas the latter (ignoring fact that it's kinematically impossible) requires on-shell z? Is the former therefore preferred to the latter (again, supposing Mz < Mh/2)?

h > z z was a bad example because of the mass restriction, so suppose I have a "y" particle which is like a z except it is light enough to be pair produced on-shell by a higgs ... this is not far from the scenario I am actually working with. And lets suppose that someone has used another generator to calculate: h > l+ l- l+ l- / y (all diagrams not involving y particles). Can I establish what would be the best way to proceed to supply a sample of events simulating the missing diagrams that do involve y particles....

First I could generate:

h > l+ l- l+ l- (1)

Then I generate:

h > y > l+ l- l+ l- (2)
h > l+ l- l+ l- / y (3)

And if I find, in terms of cross-sections, that (1) = (2)+(3) can I conclude that interference terms between diagrams with and without y particles are negligible? Then I can just take my MC sample from (2), which is preferable to doing:

h > y y, y > l+ l- l+ l-

because this doesn't include off-shell y and doesn't include interference terms from other diagrams involving y (e.g. h > l+ l-, l+ > y l-, y > l+ l-)

Sorry it's got quite specific/detailed, I just don't want to get caught out :-). I think in summary what I'm wondering is if:

u+ u- > e+ e- = u+ u- > z, z > e+ e- + u+ u- > e+ e- $ z

(I read that is true on one of the magdgraph tutorials) then how valid is it to say:

u+ u- > e+ e- = u+ u- > z > e+ e- + u+ u- > e+ e- / z

Cheers
Will

Hi,

> u+ u- > e+ e- = u+ u- > z, z > e+ e- + u+ u- > e+ e- $ z
>
> (I read that is true on one of the magdgraph tutorials)

This is indeed mostly correct. (you actually miss the interference in the on shell region but this one is expected to be negligeable)

> then how valid
> is it to say:
>
> u+ u- > e+ e- = u+ u- > z > e+ e- + u+ u- > e+ e- / z

This miss the interference on the full phase-space including the tail where such interference are not negligeable.

Cheers,

Olivier

On 04 Feb 2015, at 14:06, Will <email address hidden> wrote:

> Question #261658 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/261658
>
> Status: Answered => Open
>
> Will is still having a problem:
> Thanks for answering quickly... just a few follow up questions....
>
> I didn't know that intermediate particles in the a > b > c syntax were
> not constrained to be on-shell, so thanks - not sure where I read it
> made it to be on-shell. And this is saying that my final example of:
>
> h > z > e+ e- mu+ mu- / l+ l-
> h > z z, z > e+ e-, z > mu+ mu-
>
> despite having the same diagram differ in that the former includes off-
> shell z whereas the latter (ignoring fact that it's kinematically
> impossible) requires on-shell z? Is the former therefore preferred to
> the latter (again, supposing Mz < Mh/2)?
>
>
> h > z z was a bad example because of the mass restriction, so suppose I have a "y" particle which is like a z except it is light enough to be pair produced on-shell by a higgs ... this is not far from the scenario I am actually working with. And lets suppose that someone has used another generator to calculate: h > l+ l- l+ l- / y (all diagrams not involving y particles). Can I establish what would be the best way to proceed to supply a sample of events simulating the missing diagrams that do involve y particles....
>
> First I could generate:
>
> h > l+ l- l+ l- (1)
>
> Then I generate:
>
> h > y > l+ l- l+ l- (2)
> h > l+ l- l+ l- / y (3)
>
> And if I find, in terms of cross-sections, that (1) = (2)+(3) can I
> conclude that interference terms between diagrams with and without y
> particles are negligible? Then I can just take my MC sample from (2),
> which is preferable to doing:
>
> h > y y, y > l+ l- l+ l-
>
> because this doesn't include off-shell y and doesn't include
> interference terms from other diagrams involving y (e.g. h > l+ l-, l+ >
> y l-, y > l+ l-)
>
>
> Sorry it's got quite specific/detailed, I just don't want to get caught out :-). I think in summary what I'm wondering is if:
>
> u+ u- > e+ e- = u+ u- > z, z > e+ e- + u+ u- > e+ e- $ z
>
> (I read that is true on one of the magdgraph tutorials) then how valid
> is it to say:
>
> u+ u- > e+ e- = u+ u- > z > e+ e- + u+ u- > e+ e- / z
>
>
>
> Cheers
> Will
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.