MadGraph5_aMC@NLO

Madweight: transfer function for hadronic taus

Asked by Ben Brunt

Dear Madgraph forum,

I've been working for a while to try and distinguish z/h->tautau->lephad events based on their Madweight weight.
To begin with, I was calculating weights for the fully-decayed processes, e.g.
generate p p > z > ta+ ta-, ta+ > l+ vl vt~, ta- > vt j j
running over truth events generated by Madgraph from the same process.
The weights returned for the ztautau process in this case form a single broad peak, which seems reasonable.

The above gave some promising results, but is obviously not physically reasonable (in almost all cases the two "jets" are not resolvable).
I've since been calculating weights for the process
generate p p > z > ta+ ta-, ta+ > l+ vl vt~
attempting to match to a "hadronic tau" object in the lhco.

The problem comes in defining a transfer function for the tau, in order to account for the missing momentum in going from a "true tau" to the "visible hadronic tau". I've tried a couple of different approaches, but the weights returned have some odd features.

To begin with, I tried to come up with an energy transfer function based on a three-body decay of a stationary tau. The strategy in the transfer function is then to boost the "visible" tau to the rest frame of the "true" tau and return a weight from the distribution of the "jj" energy. The TF is unform in theta and phi, since these are folded into the energy TF through the Lorentz transform.
To test the phase space calculation, I "generated" tau decays by drawing from the phase space distributions and boosting to match the "true tau" momentum in Madgraph events. The phase-space "visible tau" distributions match the Madgraph events pretty well. There are some small angular differences which I think are due to spin correlations (and I can see no way to include in a TF).

Running over the Madgraph ztautau events using this transfer function gives a weight distribution with some interesting features. The weights are now split between two well-separated peaks - a large one and a smaller one, the smaller having weights several orders of magnitude smaller. And almost all discrimination between Z and Higgs events has been lost.

In an attempt to work out where this extra peak is coming from, it occurred to me that this energy transfer function is rather unlike a typical resolution function, in that it has a very long tail of events where the visible tau has a small proportion of the true tau energy.
To check the effect of tail events, I looked at the weight distribution for those events with the smallest ratio of vis_tau / true_tau energies. These events are strongly biased towards appearing in the smaller, low-weight peak.
Increasing the "characteristic width" of the energy transfer function helped somewhat, but even with a very large width the tail events are biased towards this low peak.

As another approach, I tried boosting the Madgraph events to the rest frame of the true tau and fitting the "visible tau" energy distribution. Implementing this in the transfer function instead of the phase-space-decay distribution above gives very similar results.

I'd be very grateful if someone could take the time to read through the above and comment whether I'm going about this in a silly way, and if there's a better approach that I'm missing.

Thanks,
Ben

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Olivier Mattelaer (olivier-mattelaer) said : 		#1

Hi Ben,

> I’d be very grateful if someone could take the time to read through the above and comment whether I'm going about this in a silly way, and if there's a better approach that I'm missing.

I’ve read it and it seems reasonable even if I confess that I’m not sure to fully understand what you are doing.
My only suggestion would be to check the literature, I remember that some other people investigate the transfer function of the tau, three or four years ago.
Their work should be now documented in the literature.

Cheers,

Olivier

> On Jul 30, 2016, at 12:02, Ben Brunt <email address hidden> wrote:
>
> New question #313074 on MadGraph5_aMC@NLO:
> https://answers.launchpad.net/mg5amcnlo/+question/313074
>
> Dear Madgraph forum,
>
> I've been working for a while to try and distinguish z/h->tautau->lephad events based on their Madweight weight.
> To begin with, I was calculating weights for the fully-decayed processes, e.g.
> generate p p > z > ta+ ta-, ta+ > l+ vl vt~, ta- > vt j j
> running over truth events generated by Madgraph from the same process.
> The weights returned for the ztautau process in this case form a single broad peak, which seems reasonable.
>
> The above gave some promising results, but is obviously not physically reasonable (in almost all cases the two "jets" are not resolvable).
> I've since been calculating weights for the process
> generate p p > z > ta+ ta-, ta+ > l+ vl vt~
> attempting to match to a "hadronic tau" object in the lhco.
>
> The problem comes in defining a transfer function for the tau, in order to account for the missing momentum in going from a "true tau" to the "visible hadronic tau". I've tried a couple of different approaches, but the weights returned have some odd features.
>
> To begin with, I tried to come up with an energy transfer function based on a three-body decay of a stationary tau. The strategy in the transfer function is then to boost the "visible" tau to the rest frame of the "true" tau and return a weight from the distribution of the "jj" energy. The TF is unform in theta and phi, since these are folded into the energy TF through the Lorentz transform.
> To test the phase space calculation, I "generated" tau decays by drawing from the phase space distributions and boosting to match the "true tau" momentum in Madgraph events. The phase-space "visible tau" distributions match the Madgraph events pretty well. There are some small angular differences which I think are due to spin correlations (and I can see no way to include in a TF).
>
> Running over the Madgraph ztautau events using this transfer function gives a weight distribution with some interesting features. The weights are now split between two well-separated peaks - a large one and a smaller one, the smaller having weights several orders of magnitude smaller. And almost all discrimination between Z and Higgs events has been lost.
>
> In an attempt to work out where this extra peak is coming from, it occurred to me that this energy transfer function is rather unlike a typical resolution function, in that it has a very long tail of events where the visible tau has a small proportion of the true tau energy.
> To check the effect of tail events, I looked at the weight distribution for those events with the smallest ratio of vis_tau / true_tau energies. These events are strongly biased towards appearing in the smaller, low-weight peak.
> Increasing the "characteristic width" of the energy transfer function helped somewhat, but even with a very large width the tail events are biased towards this low peak.
>
> As another approach, I tried boosting the Madgraph events to the rest frame of the true tau and fitting the "visible tau" energy distribution. Implementing this in the transfer function instead of the phase-space-decay distribution above gives very similar results.
>
> I'd be very grateful if someone could take the time to read through the above and comment whether I'm going about this in a silly way, and if there's a better approach that I'm missing.
>
> Thanks,
> Ben
>
> --
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