Phase space for off-shell decays of resonances

[Juergen Reuter]

There still seem to be several problems concerning the W2 phase space! Consider the problem by the Dresden people.

Problem: Finding the Higgs resonance in a far off-shell set-up in WW fusion.

[kilian]

This might be a general problem with the parameterization of off-shell decays.

[Juergen Reuter]

Discussion with the experimentalists: this defect should be solved until the release 2.0.7, March 18.

[kilian]

OK, this was a tricky one. At least, I now understand the problem.

In the off-shell Higgs decay, the upper limit for the W* mass in the decay is mH - mW (the other W being on shell). This is 50 GeV for the given kinematics. In theory.

However, in practice the Higgs is resonant, but not forced on-shell. Hence the actual maximum allowed W* mass is the collider c.m. energy. Since Whizard generates squared masses, the ratio (mH-mW)/sqrts is squared.

In the phase-space channel which has the appropriate structure (Higgs resonance with off-shell decay), the decay events therefore populate only a tiny fraction of the initial range. VAMP can adapt to that, but it needs several iterations, and there is a chance that the interesting region is not found at all. Thus the Higgs-decay kinematics is sometimes discarded, and it gets worse if increased collider energy.

Even if I force Whizard to find it (by manually restricting the phs channels), there is a huge loss of efficiency if an event happens to fall just above the last bin boundary. This is an effect of the discretization. The result are fluctuations in the reweighting efficiency of order 100.

The lesson is that off-shell decays require a special mapping of the phase space of their decay products, which is different from the on-shell counterpart. I'll try to find an implementation.

[Juergen Reuter]

Thanks, WK, for the efforts up to now. I guess event for ILC and CLIC physics this is of utmost importance!

[Juergen Reuter]

WK has potentially found a working parameterization ("Karte"). He has to finish implementation and testing...

[kilian]

Update: I have two alternative implementations of the new 'step' mapping, which handles phase space that is effectively populated only up to some resonance mass. They seem to be working fine, but I'll do some more testing before making this the default.

Some modification in cascades.f90 is also required, to enforce 'phs_keep_nonresonant=true' for the relevant cases.

[kilian]

Sindarin input (off-shell Higgs at LHC)

[kilian]

WHIZARD output (10x1M for adaptation), 3 different mapping settings

[kilian]

WHIZARD output (20x100k for adaptation), 3 different mapping settings

[kilian]

Seems to work now.

I attach a test case: pp -> u d e- e+ mu- mu+, in a setting which contains a narrow Higgs with off-shell decay (in VBS scattering). The previous setup fails to find the Higgs resonance in phase space and yields a wrong result, even with high statistics (10x1M for adaptation). The new setting succeeds. If the statistics is lowered (20x200k for adaptation), the first mapping implementation (exponential) also fails, while the second one (hyperbolic) is more robust.

Still, with 200k per iteration more than 10 iterations are required before the off-shell Higgs is described by the adapted phase space. This should be kept in mind. (100k are still ok, but even more iterations needed.)

The new setup requires ?phs_keep_nonresonant=true, which results in a larger number of phs channels. In cases where no off-shell decays are present, the user may turn this off to speed things up. However, I change the default here to be on the safe side.

I make the new setup the default in r3741 and close the ticket, fingers crossed ...