Understand physics of doubly factorized decay processes

[dwiesler]

Looking at e.g. zz.evt of the testfile decays.sin shows, that the momenta of the decayed particles are still given in the restframe of the mother particle. A simple boost back to the lab/cm frame should do the trick.

I hacked a workaround into particles.f90 for writing event files for my own analysis, but this should somehow be repaired more internally.

[Juergen Reuter]

The problem is that the Lorentz transformation with the boost is not applied. This should obviously be done in decay_generate in decays.f90.

[dwiesler]

Current status: I wrote a small subroutine (particle_boost_decay_momenta), which boosts the daughters of the resonant decay particle and is called in particle_set_init_interaction, after the rest of the momenta are set.

WK/JR: maybe you have a look in the attached particles.f90 and decide wether this solution is sufficient.

[Juergen Reuter]

I just add a point which is related to the fact that information is not properly propagated through the decay chain here: As sub-process ID in the LHEF file there always appears the ID of the last decay process, which should be the one of the mother process, so for ID 1: e+ e- -> Z Z , ID 2 Z -> e+ e-, ID3 Z -> uubar from the decay.sin, process ID 3 appears in the LHEF file, while ID 1 should appear. Could be fixed on the same footing, probably.

[dwiesler]

I found several other issues and thus renamed the ticket. Here's a short list of the defects/shortcomings:

1) Momenta of decayed products need to be boosted (solved in the attached particles.f90)

2) Process ID in the LHEFiles gets messed up due to the fact, that it's given by process_store_index, which is incorrect in case of several active 1->2 decay processes (JR mentioned that)

3) Depending on the number of decays in an event, whizard seems to get lost in an endless loop just while writing events to the desired file (after the output '...corresponds to Lumi...'). I will try to give a concrete example i.e. a sindarin file asap.

4) Investigating a fermionic Leptoquarkino decay cascade I found, that the masses set in the upper part of the sindarin file are ignored and the default values from the .mdl files are used, when using the decay module. Removing the boost (my solution of 1) ) revealed a violation of energy conservation in the LHEFiles which led to this assumption.

[dwiesler]

Replying to dwiesler:

4) Investigating a fermionic Leptoquarkino decay cascade I found, that the masses set in the upper part of the sindarin file are ignored and the default values from the .mdl files are used, when using the decay module. Removing the boost (my solution of 1) ) revealed a violation of energy conservation in the LHEFiles which led to this assumption.

Forgot: it only seems to effect the event generation, integration for the corresponding 2->2 process correctly uses the defined values.

[dwiesler]

additional subroutine for boosting decay momenta

[dwiesler]

Replying to dwiesler:

Replying to dwiesler:

4) Investigating a fermionic Leptoquarkino decay cascade I found, that the masses set in the upper part of the sindarin file are ignored and the default values from the .mdl files are used, when using the decay module. Removing the boost (my solution of 1) ) revealed a violation of energy conservation in the LHEFiles which led to this assumption.

Forgot: it only seems to effect the event generation, integration for the corresponding 2->2 process correctly uses the defined values.

Ok, found out that it DOES matter, where additional parameters are defined. Calling the integration of the decay process after the definition of the former is mandatory, solving point 4).

Nevertheless, another one:

5) When using the decay module together with an analysis (e.g. histogram), the content of the histogram is only filled, after a second run of whizard is started, where it reads events out of the raw file whizard.evx. In the first run, the histogram simply stays empty with no entries. This is probably linked with the endless loop of 3).

[dwiesler]

And yet another one:

6) Spin correlation not working in the decay module: I tried setting the keep_correlations logical to .true. and also tried the several factorization modes for the helicities in the simulate call in commands.f90, but none of these seems to have an effect in reproducing effects of spin correlation as the full matrix element does. I assume this is not finished yet?

[kilian]

The error that caused (1) was much more trivial, a flag that was not copied together with the process object. Fixed this in r2075. Have to check the other items ...

[dwiesler]

sample file for cascade decays which should show spin correlation effects

[dwiesler]

missing spincorrelation example

[dwiesler]

dito

[dwiesler]

sample file w/ full matrixelement includign spin correlation effects...

[kilian]

Current status:

1. Missing boost: fixed by r2075
2. Process ID: In r2076, switched to index in process library. This is more transparent to the user, but beware:
   • There may be extra processes in the library from previous runs, unless -r is given
   • If there are several libraries, the index is not unique.
3. Endless loop: could not reproduce this.
4. Parameter settings: was invalid, see above.
5. Event analysis: fixed in r2076.
6. Spin correlations: Partially done in r2089. To catch correlations completely, I have to switch to non-diagonal density matrices in decays (I should have known better ;). Will do this next.

[Juergen Reuter]

WK took it as P1, but didn't rank it up.

[kilian]

Update: spin correlations work now (not yet checked in), code needs some cleanup, then to be combined with new color computation via OMega.

[kilian]

r2140 implements spin correlations. With the flags ?isotropic_decay and ?diagonal_decay the approximations of ignoring spin correlations and keeping only the diagonal entries in density matrices (classical correlations), respectively, are available for each unstable particle. Furthermore, color-flow coefficients are also computed based on spin-correlated matrix elements.

The algorithm uses rejection to select a decay cascade with unit weight, appropriate for unweighted events. Two related issues remain:

1. Decay cascades for weighted events (no rejection)
2. Meaningful normalization of matrix elements, so the decay-cascade event samples implement an approximation to the full, non-factorized process (cross section and distributions).

These remaining issues have lower priority.

[dwiesler]

Not sure wether this is still to be solved (i.e. belongs to point 2 of the remaining issues), but the attached example file casc_dec.sin still doesnt show spin correlations in the invariant mass of lepton and quark.

[kilian]

Replying to dwiesler:

Not sure wether this is still to be solved (i.e. belongs to point 2 of the remaining issues), but the attached example file casc_dec.sin still doesnt show spin correlations in the invariant mass of lepton and quark.

Have you checked the effect in the non-factorized process? I did this before the code was refurbished, and the effect was rather small. But I'll recheck now that spin correlations should be in the decay module.

[dwiesler]

Replying to kilian:

Replying to dwiesler:

Not sure wether this is still to be solved (i.e. belongs to point 2 of the remaining issues), but the attached example file casc_dec.sin still doesnt show spin correlations in the invariant mass of lepton and quark.

Have you checked the effect in the non-factorized process? I did this before the code was refurbished, and the effect was rather small. But I'll recheck now that spin correlations should be in the decay module.

Yes I have, and this is what the second example file casc_res.sin is for. The difference is also visible in the added images.

I took this example from Peter Richardson paper on spin correlations: ​http://arxiv.org/abs/hep-ph/0110108

[kilian]

Modified script for observing spin correlations in squark decays

[kilian]

Plots showing spin correlations in squark decay

[kilian]

I just attached my version of Daniel's example. It looks like everything is ok now.

It would be worthwhile to actually reproduce all results in the Richardson paper. This is quite useful.

[kilian]

With r2152, I made sure that decay configurations are coordinated with each other. Furthermore, the 'unstable' and 'stable' commands now accept argument list. It is recommended to declare a set of particles as unstable/stable together, to avoid multiple rescans that keep consistency in the decay store.

[dwiesler]

Replying to kilian:

I just attached my version of Daniel's example. It looks like everything is ok now.

It would be worthwhile to actually reproduce all results in the Richardson paper. This is quite useful.

My examples now also work, the algorithm shows good agreement with the full ME for this process.

I'll try to confirm the other examples from the R-paper...

[dwiesler]

I found some strange behaviour for the SM ttbar production example, demonstrated in the attached new sindarin file:

In the process e+e- -> ttbar -> b e+ nu_e tbar I first compared the factorized 3body decay (t -> b e+ nu_e) to the full ME as in the R-paper and afterwards tried an additional step and also factorized the intermediate Wplus decay (t -> b Wp -> b e+ nu_e).

Observing the distribution of the angle of the top and the outgoing positron (as in Fig.10 in R-paper) these two approaches differ by a fair amount. While the 3body decay-factorized process nicely approximates the full ME, an additional intermediate factorization of the Wplus decay gives a stronger tail and lower maximum.

The question now is wether this is a physical contribution due to some (offshell/polarization ?) effects unknown to me or the spin correlation still has problems when multiple factorizations w/ vectorlike intermediate states are present (the squark decay example from above work's fine though). I'll have a look at some papers governing top quark spin correlations in decays.

Other than that, the (unpolarized) MSSM test seem to be fine so far.

[dwiesler]

sindarin file w/ strange top decay behaviour, see also the pdf

[dwiesler]

strange behaviour of angular distribution w/ two factorized decays

[Juergen Reuter]

In my opinion, the only open issue is the understanding of the doubly-factorized SM process ee -> t (t -> (W -> ev) b). Otherwise, the technical issues are resolved. Shouldn't we add this to "VALIDATION" and close this one?

[Juergen Reuter]

The only open issue is the physics case of the doubly factorized top decay.

[dwiesler]

Revisiting this problem, I found that the angles I compared in the first top decay example were not precisely the same ones as in the R-paper. Now, using the correct angles together w/ inital state polarizations, the difference between the 2x2 body and 1x3 body factorized decay processes looks negligible, visible in the attached Plots (compare to Figs 10b and 11b in R-paper).

The discrepancy in the above case for the first given example remains strange nonetheless. As the default casc_dec.sin susy case also is a doubly factorized process, which also correctly reproduces the full ME, the culprit obviously is this special (single) top decay.

[dwiesler]

2x2 body to 1x3body comparison, correctly reproducing R-paper results

[dwiesler]

same as above, w/ comparison to full 6body ME result corresponding to Fig11b

[Juergen Reuter]

When the Scottish smoke clears and our paper is finished DW will rerun the code and check whether there is still a discrepancy left, presumably not. If not, we will close it.

[dwiesler]

top decaying w/ no visible difference between one and two factorizations

[dwiesler]

There's still lots of smoke, but I found some time to have another look at the problem and reran everything from scratch with the result, that everything's fine now! I'll attach a pdf as proof and close the ticket for good!

[Juergen Reuter]

Milestone renamed