Longitudinally polarised W bosons
Hi, I'm investigating the production of longitudinally polarised W bosons at sqrt(s)=13 TeV with MG 3.4.2 and the LO sm UFO. In particular, I'm interested in applications of the Goldstone boson equivalence theorem (GBET), which states that at high enough energies (E_W>>M_W) the probability of emission of a longitudinally polarised W boson becomes equivalent to that of a Goldstone boson. Therefore I would expect it to vanish for light quarks in the u d~ > w+ and c s~ > w+ processes, since the yukawas would be 0.
I run three independent event generations:
1. generate p p > w+ --> xsec = 8.36e+04 +- 77.94 pb
2. generate p p > w+{T} --> xsec = 8.36e+04 +- 77.94 pb
3. generate p p > w+{0} --> error
in run 3. I get the following error message:
"Survey return zero cross section.
Typical reasons are the following:
1) A massive s-channel particle has a width set to zero.
2) The pdf are zero for at least one of the initial state particles
or you are using maxjetflavor=4 for initial state b:s.
3) The cuts are too strong.
Please check/correct your param_card and/or your run_card."
I don't think any of these reasons apply here, so am I really just seeing a vanishing cross section for the production of a longitudinally polarised W boson? I would expect to get *some* W bosons produced close to at rest, and therefore by the GBET a small but non-zero cross section...
Interestingly, if I now generate ttW at LO (exactly the same diagrams, with an extra gluon->ttbar emission from an ISR quark), I get
1. generate p p > t t~ w+ --> xsec = 0.2352 +- 0.0001772 pb
2. generate p p > t t~ w+{T} --> xsec = 0.1848 +- 0.0001151 pb
3. generate p p > t t~ w+{0} --> xsec = 0.0502 +- 3.573e-05 pb
and now there is a non-vanishing longitudinal component. The cross sections from 2. and 3. add up to that from 1., so I presume there is negligible interference. Looking at the distribution of the energy of the W boson, the longitudinally polarised sample 3. does peak at lower values and decreases initially faster than the transversely polarised one, but never fully vanishes, even at very high energies.
Am I doing something wrong here, or perhaps misunderstanding the consequences of the GBET?
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