Kolya: an open-source package for inclusive semileptonic B decays

1- The manuscript presents a useful code for flavor physics.
2- It is timely, and a useful addition to existing codes.

1- The writing could be improved for better clarity and to avoid misunderstandings (see report for details).
2- There are several typographical errors, such as:
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The manuscript presents an open-source program dedicated to the B -> X_c l nu inclusive decay. It calculates the total rate and the kinematic moments within the Standard Model and also includes new physics parametrizations. This work is a useful and timely contribution to the existing tools and can be accepted for publication once the points outlined below are addressed.

-The code presented in this manuscript is very specific, focusing solely on the B -> X_c l nu inclusive decay, and does not cover all semileptonic B decays. For instance, neutral current decays are not included. Therefore, the title: "Kolya: an open-source package for inclusive semileptonic B decays" is misleading and should be revised to accurately reflect the scope of the code. This revision should also be applied to the abstract and throughout the main body of the manuscript.

- For *all* the equations, every quantity that appears must be defined, and the corresponding values should be provided where applicable. For example, in Eqs. (9) and (10), it should be specified that the Q_ij​ are the moments, the value of n_f​ (the number of active quarks) should be given, the scale mu_s should be provided, and so on.

- In Eq. (11), the authors provide a hard-coded value for the short-distance radiative corrections, A_ew = 1.01435, and cite a paper from 1978. First, a correct citation should be provided to clarify the source of this value. Second, it is generally not a good practice to hard-code numerically specific corrections, as this may introduce inconsistencies, particularly with respect to the input values used.

- On page 6, it is stated that the scale at which the Wilson coefficients of the HQET Lagrangian are matched onto QCD is mu_b​. Is this a typo?

- The higher-order QCD corrections for the moments are not implemented in their exact form, but instead are approximated using Chebyshev two-dimensional grids, which is useful for fast numerical evaluations. However, could there be regions where this approximation might not work well?

- In Eqs. (30) and (31), no uncertainty is assigned to the fit functions. What is the reason?

- The explanation in the last paragraph of page 13 (following Eq. (32)) is unclear.

- After Eq. (34), it is stated: "to be conservative, we assume a 1% uncertainty on all data points for which no uncertainty was given". This choice seems somewhat arbitrary and not very satisfying in my opinion.

- At the end, the non-BLM corrections to the h2 and h3 are not included. I found the reasoning for this to be quite confusing.

- In section 4 for the BSM extensions, the C_i are assumed to be real. Why?

- Still in Section 4 (BSM extensions), it is unclear what exactly is implemented. From reading this brief section, I assume it refers to a parametrization at the level of the effective Lagrangian. However, for example, what is meant by: "we implement the tree-level contributions in an exact form". What specific expressions are being referred to here? Are any particular new physics models considered?

Ask for major revision

1. Excellent documentation of the underlying formulas used to evaluate the various observables.
2. Useful and timely provision of a standard code to predict observables in inclusive B decays.

1. Minor weaknesses in the documentation, addressed in the detailed report.

The writeup discussed a novel and highly useful piece of open source software for the calculation of observables in inclusive B meson decay.
The physics basis for the code is very well documented. Simple examples are provided as part of the manuscript, with more complex examples available from the Gitlab repository.

I think this paper should be accepted for publication, pending some minor corrections and addendums listed under "requested changes".

Moreover, I have the following comments on the interface / code / package. Addressing the following should *not* be considered a prerequisite for accepting the paper.

- kolya is not (yet?) installable from PyPI. I would highly recommend uploading a Python wheel to pypi, to facilitate the installation process.

- Importing kolya ("import kolya") for the first time takes a very long time (longer than 14min on my laptop (Intel i7-1360P)). Based on the comments in the installation section of the paper, I suspect this is due to the just-in-time compilation using numba. I recommend reconsidering the use of numba and consider the use of cython instead. This would enable building a natively-compiled backend code only once.

- Inspecting an object, such as return value of "par = kolya.parameters.physical_parameters()" can be achieved using the "show()" method. While useful, it is not very python-like. I highly recommend adding a Jupyter / IPython / Python representation to the classes that the users are going to be exposed most. In Jupyter, this would allow to simply "display(par)", which is done automatically if only the object is invoked at the end of a Jupyter cell.

- The HQE parameters ("kolya.parameters.HQE_Parameters") do not have sensible default values. I recommend adding a function (similar to FLAG2024 for the general parameter class that provided sensible default values.)

- I am a bit puzzled by the handling of the Wilson coefficients. Why is Vcb, which is also a parameter in the EFT Lagrangian, not part of the object parametrizing the Lagrangian? (I.e., wc) When I change Vcb, I implicitly change the definition of all Wilson coefficients.

1. The authors mention in the abstract that kolya ``can be used in an interactive Jupyter notebook session''. This is of course true for most Python libraries. My question is: has it been designed to use in a Jupyter notebook? I think the answer is "no" at the present. I would remove this line from the abstract.

2. The 2nd sentence below eq. (11) starts with a mathematical symbol.

3. Below eq. (41), the dependence of the observables on the ratio m_c/m_b is discussed. The trick used to make the expressions more managable is quite neat. I think the text would benefit from a comment on the numerical equivalence of this approach and evaluation f at the value of m_c^pole/m_b^pole as determined from the kinematic / MSbar masses. If there is no numerical equivalencen, it would be useful to understand what precision is achieved by the replacement.

4. It should be documented that the Wilson coefficient parameters are only parametrizing the BSM contribution to the effective Lagrangian, i.e., it is C_V_L^BSM, and the code uses C_V_L = 1.0 * A_ew + C_V_L^BSM. Crucial question: Is the electroweak correction included for BSM contributions? This should also be documented.

Ask for minor revision