radiative Bhabha scattering

Asked by Ulrike Schnoor on 2019-10-15

Dear Whizard authors,

we want to generate events for the process ee-> ee gamma, which is a background to monophoton signatures if both of the electrons are either very soft or stay in the beam pipe. This means ideally no cuts can be placed on the electrons, only on the photon. Requirements on the photon do also bias the electron kinematics a bit, but nevertheless we do not get a convergence with Whizard if no electron cuts are applied. I think this is expected because there are singularities which are only cancelled at higher order.
How can we know in a well-defined way what is the part of the cross section we are missing when we apply cuts on the electrons? Can we generate a sample with a cut on the electron theta and energy that removes the singularity and still be somewhat sure that we are not missing too much of a contribution? Is there a way to get the higher order in Whizard or do you know some other tool that can do it?

An example sindarin can be found here:

Thanks for any advice!
Ulrike & Philipp & Jean-Jacques

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Wolfgang Kilian (whkilian) said : #1

Hi Ulrike, after several tests, here is how to approach this:

(1) With such low Q^2 at high energy, double-precision numerics is insufficient. Numerical noise dominates the results.

You may use either quadruple precision (16byte) or extended precision (10byte) instead. The former is safe, but it is an order of magnitude slower, at least. The latter (currently only available for gfortran) is as fast as double, but with less precision than quadruple. From my tests, extended seems to be sufficient, but the results can always be cross-checked with quadruple.

This has to be set when configuring whizard before compilation: --with-precision=extended or --with-precision=quadruple. You need a separate executable, switching precision at run-time is not possible.

(2) Since the typical Q^2 values for this process can become very small, convergence of the phase-space adaptation is somewhat improved by setting
    phs_q_scale = 1e-4 GeV
(or so, default is 10 GeV)

There is also phs_e_scale (default 10 GeV) to consider. In the example, the photon energy cut is 10 GeV, so the default should be fine.

(3) With extended precision and phs_q_scale, you may verify that the results converge reasonably well if CIRCE2 is switched OFF. (I.e., only ISR). To check this, I used 30 iterations with 100k calls each. Fewer iterations may be sufficient.

(4) If you switch CIRCE2 ON again, the results do not converge that well. Apparently, the generator mode of CIRCE2 prohibits precise adaptation to this extreme phase space. Nevertheless, the setup should yield a useful result and event samples, albeit with low efficiency. (You may consider doing the study without beamstrahlung first and only later assess the perturbation effect of adding beamstrahlung.)

Wolfgang Kilian (whkilian) said : #2

A possible cause: the momenta generated by the CIRCE module inside WHIZARD are apparently massless, even if the original beam momenta were massive. For almost all physics questions, this property is irrelevant. Here, it might have lead to the observed divergence.

It may be necessary to review the handling of particle masses vs. structure functions/spectra.

Wolfgang Kilian (whkilian) said : #3

There is an additional question whether ISR should be convoluted with the process.

In the vicinity of the Coulomb singularity (which this process has if the matrix-element photon is soft/collinear), the ISR approximation by a structure function is questionable at best. The ISR approximation requires switching the electron from space-like (exact ME) to time-like (factorized) in a region where the amplitude has a power-like dependence on the offshellness.

Apart from the CIRCE problem mentioned above, it appears as if any extra photons have to be generated explicitly here, and ISR should remain switched off altogether.

Can you help with this problem?

Provide an answer of your own, or ask Ulrike Schnoor for more information if necessary.

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