EPA dependence on epa_mass

Roberto, sorry we didn't have the chance to sit down in Sendai. Did you try to run the same setting with an epa_x_min of the order of 0.01 or 0.001?

Hi there, sorry but I thought this was a dropped case, maybe misunderstood.
Anyhow, yes I have tried larger x cuts and there is a dependence on that x _min value.

\gamma\gamma\to b\bar{b} 3 TeV inclusive
3 = lpp1 photon from electron 6 pb
beams = "e-", "e+" => epa, x_{min}=0.001 epa_mass=501 keV 3.76(2) pb
beams = "e-", "e+" => epa, x_{min}=0.001 epa_mass=105 MeV 1.518(7) pb
x_{min}=0.01 epa_mass=501 keV 0.237(1)
x_{min}=1e-4 epa_mass=501 keV 7.77(6) pb
x_{min}=1e-4 epa_mass=105 MeV 3.06(2) pb
x_{min}=1e-5 epa_mass=501 keV 9.06(10) pb
x_{min}=1e-6 epa_mass=501 keV 9.20(10) pb
x_{min}=1e-10 epa_mass=501 keV 9.13(12) pb
x_{min}=1e-10 epa_mass=105 MeV 3.59(4) pb
x_{min}=1e-10 epa_mass=105 MeV epa_q_min=105 MeV isr_mass=105 MeV 0.602(4) pb

It clearly saturates when x_min becomes small enough that all the phase space for bottom pair creation is included in the range. The issue that I see is that the scaling with the epa_mass is too weak compared to the log I was expecting. Am I expecting the wrong thing?

Thanks for providing those details! There may be in issue with the EPA formulas or their implementation that got unnoticed. There are inconsistent results also elsewhere. I'll try to investigate this more closely.

Dear Roberto,
it took a long time for me to chime in here, but recently by a different issue I was dragged into looking into the details of the EPA, and the best reference still is the 1974 report by Budnev, Ginzburg, et al. There are two places where the dependence on the electron mass comes in, both via the same variable. In deriving the EPA one makes a calculation where the phase space integral leads to an integration over the photon virtuality. The lower bound is definitely a kinematic limit, that is proportional, but not equal (!) to the electron mass; indeed it is given by m^2 x^2/(1-x), where x is the ratio of the photon energy over the electron energy. As Budnev studied, taken this explicit lower bound is always a good description, while the upper bound depends a lot more on the usage of the EPA. E.g. for low-energy photo-production of hadrons it is a hadronic variable like the rho or phi mass, for high-energy production of BSM particles it would be something like sqrt(s) or sqrt(s) * (1-x). Now, the lower bound enters the EPA in three places: the leading logarithm that can be found in Eq. (6.17) of the Budnev report, or the 1990 paper by Cahn/Jackson or the textbook calculation by Peskin/Schroeder. Secondly, the second logarithm in Eq. (6.17) of Budnev. And in the power correction term that is given by qmin^2/qmax^2 (last term of Eq. (6.17) in Budnev). Note that there in the prefactor me^2 cancels out between the explicit dependence and the 1/qmin^2. WHIZARD traditionally implemented Eq. (6.17) from the Budnev report which appears to be the best solution for low-x simulations like hadron backgrounds in the tails. For high-x this second logarithm is an "overshooting" in precision, and instead the approximation in Eq. (6.16e) (and its q^2 integral) should be taken, leading to a formula without the second logarithm of Eq. (6.17). Now (end of May 2020) we implemented a switch to choose between five different incarnations of the EPA which is documented in the manual. This is in the nightly builds coming out Jun 1st -> Jun 2nd, and will be released in june in v2.8.3 of WHIZARD. However, a thorough modern study of the applicability of the EPA in which incarnation is still missing, as Budnev studied only cases up to O(10 GeV). Some literature of the early 90s inlcuded studies for LEP1 and early stages of LEP2, but such a study is still lacking.
Cheers,
    JRR

Seems to be solved now.