Comments (4)
More details about alternatives will appear later on :)
Alternatives:
- current APFEL (inconsistent approximation of two masses)
- current yadism (consistent approximation, hard cut of charm mass effects above bottom matching)
- possibly with a different bottom matching scale than its mass, to mitigate the effects of the cut (but introducing a trade-off with bottom PDF resummation)
- this proposal
- ACOT (requires encoding perturbative matching, i.e. an expanded EKO in x-space)
- doubly analytical matched FONLL (requires encoding many and lengthy expressions, still to be computed, and approximations)
- outlined in sec. 4.1 of BBR
from yadism.
More about ACOT
As spelled out in BBR sec. 2.3 (summarized in eq. 2.25) ACOT boils down to using PDFs in the
In this way, mass effects are kept in the coefficient functions, while collinear logs are resummed in the PDFs at the same time.
However, if the inverse evolution would unwind exactly the evolution, this would be perfectly equivalent to compute everything in the
Thus, to apply ACOT, the inverse evolution has to be computed at fixed order, in order to preserve the resummed result from PDF evolution. Thus, the two options are:
- compute the fully truncated evolution operator (not even LO exact)
- inline the evolution in the coeff funcs
Usually (personal poor experience from FONLL implementation) the second approach is more convenient, since a large part of
from yadism.
More about doubly matched
Implementing eqs. 4.16-17 in BBR is full of troubles:
- it is declared to be an approximation, since no intrinsic is taken into account
- it is even more an approximation than declared, since terms like
$C_g^{(3)} \otimes K_{gb} \otimes f_b^{(4)}$ (that should appear in the second branch of eq. 4.17) are neglected, and definitely not intrinsic - it is sketchy, since only the subtraction of charm logs is taken into account, but
$B_i^{(5)}(m_c^2, m_b^2)$ contains also bottom mass logs, that are redundant with$C_i^{(5)}(0,0)$ and thus should be subtracted as well, not to be double counted - two mass effects are still neglected, otherwise the whole thing would complicate even more
- computing the double match analytically is feasible, but challenging, since terms starts growing
- even more in the case of FONLL-B and intrinsic
- doing it at N3LO starts being prohibitive
Taking into account the first three points, it is manifest that either this strategy outlines a further approximation, without any clear improvement, or it requires quite some work to be implemented. Taking into account the last two, it is manifest that it does not scale, while the main PR proposal does it much better.
from yadism.
Implementing eqs. 4.16-17 in BBR is full of troubles
while I agree on the statement that this is highly non-trivial, I believe the FONLL expressions (that we would use of course) are given by Eqs. (4.10 - 4.13). Also to say explicitly Eq. (4.3) is already a complicated expression since it already contains a matching (i.e. this C is under the hood already an B).
from yadism.
Related Issues (20)
- Public Interface HOT 1
- drop `gh-pages` HOT 3
- Benchmark Workflow HOT 2
- FONLL-B below charm mass is NNLO instead of NLO HOT 4
- `kDISqThr` is ignored with runner HOT 3
- Minus sign missing in k_qq_loc HOT 2
- Number of active nf in Singlet FONLL HOT 8
- Regression tests fail HOT 2
- Clean up inputcard keys HOT 5
- Light structure functions à la FONLL
- Higher mass effects in heavylight
- Update FONLL docs HOT 1
- New coefficient function library
- Deduplicate scale variations
- Runcard serialization
- TMC in nuclear DIS HOT 1
- Improve documentation
- Drop intrinsic configuration and activate it always
- Fix pydocstyle HOT 1
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from yadism.