Charm Mass Dependence of the $\CO(\alpha_s^2 n_f)$ Correction to Inclusive $B\rightarrow X_c e\bar\nu_e$ Decay

Mark B. Wise; Martin J. Savage; Michael Luke

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Charm Mass Dependence of the $\CO(\alpha_s^2 n_f)$ Correction to Inclusive $B\rightarrow X_c e\bar\nu_e$ Decay

Michael Luke, Martin J. Savage, Mark B. Wise

High Energy Physics - Phenomenology · Submitted 26 Oct 1994

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The authors' main claim This result provides an estimate of the size of the two-loop correction, which is found to be about 50\% of the one-loop correction.

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arXiv IDhep-ph/9410387 (version 1)

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CitationMark B. Wise, Martin J. Savage, Michael Luke. "Charm Mass Dependence of the $\CO(\alpha_s^2 n_f)$ Correction to Inclusive $B\rightarrow X_c e\bar\nu_e$ Decay." arXiv:hep-ph/9410387 (1994). https://pith.science/paper/URJTAW4A

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.25 · human participants 0.01 · controlled comparison 0.19 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.96 · mentions code or data availability 0.01.

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We compute the $\alpha_s^2 n_f$ perturbative QCD contribution to semileptonic B decay, including the finite mass of the charm quark. This result provides an estimate of the size of the two-loop correction, which is found to be about 50\% of the one-loop correction. We use these results to set the scale for the one-loop correction using the scheme of Brodsky, Lepage and Mackenzie and find a BLM scale of $\mu_{\rm BLM} = 0.13\, m_b$, when the inclusive semileptonic rate is expressed in terms of the $b$ and $c$ quark pole masses and the \msbar strong coupling. The two loop correction lies roughly midway between that obtained at $m_c=0$ and that obtained in the Shifman-Voloshin limit $m_b, m_c\gg m_b-m_c\gg\Lambda_{\rm QCD}$ while the corresponding BLM scale is somewhat closer to that obtained in the former case.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We compute the $\alpha_s^2 n_f$ perturbative QCD contribution to semileptonic B decay, including the finite mass of the charm quark.	contribution 1.00	0.97	0.10	asserted 1.00
s1	This result provides an estimate of the size of the two-loop correction, which is found to be about 50\% of the one-loop correction.	result 0.92	0.95	0.49	asserted 0.93
s2	We use these results to set the scale for the one-loop correction using the scheme of Brodsky, Lepage and Mackenzie and find a BLM scale of $\mu_{\rm BLM} = 0.13\, m_b$, when the inclusive semileptonic rate is expressed in terms of the $b$ and $c$ quark pole masses and the \msbar strong coupling.	result 0.86	0.96	0.21	asserted 1.00
s3	The two loop correction lies roughly midway between that obtained at $m_c=0$ and that obtained in the Shifman-Voloshin limit $m_b, m_c\gg m_b-m_c\gg\Lambda_{\rm QCD}$ while the corresponding BLM scale is somewhat closer to that obtained in the former case.	result 0.59	0.89	0.17	asserted 0.85

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from simulation or computation 0.62.

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Original abstract

We compute the $\alpha_s^2 n_f$ perturbative QCD contribution to semileptonic B decay, including the finite mass of the charm quark. This result provides an estimate of the size of the two-loop correction, which is found to be about 50\% of the one-loop correction. We use these results to set the scale for the one-loop correction using the scheme of Brodsky, Lepage and Mackenzie and find a BLM scale of $\mu_{\rm BLM} = 0.13\, m_b$, when the inclusive semileptonic rate is expressed in terms of the $b$ and $c$ quark pole masses and the \msbar strong coupling. The two loop correction lies roughly midway between that obtained at $m_c=0$ and that obtained in the Shifman-Voloshin limit $m_b, m_c\gg m_b-m_c\gg\Lambda_{\rm QCD}$ while the corresponding BLM scale is somewhat closer to that obtained in the former case.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Third order corrections to the semi-leptonic \boldmath{$b\to c$} and the muon decays
hep-ph 2020-11 accept novelty 7.0 of 10

The three-loop QCD corrections to b to c semileptonic decay are computed and found to be below 1 percent in the kinetic scheme, with companion results for b to u and for third-order QED corrections to muon decay.
Factorization for Power Corrections to B->Xs gamma and B-> Xu e nu
hep-ph 2004-09 conditional novelty 7.0 of 10

New four-quark shape functions enter B -> Xu l nu and B -> Xs gamma endpoint spectra with a 4 pi alpha_s enhancement, potentially adding a large uncertainty to inclusive |Vub| extractions.
Naive nonabelianization and resummation of fermion bubble chains
hep-ph 1994-11 conditional novelty 6.0 of 10

Summing all one-loop vacuum-polarization bubbles into one-loop QCD corrections turns BLM scale ambiguity into a renormalon uncertainty, and shows the pole mass and top width are renormalon-dominated at low orders.
Climbing NLO and NNLO Summits of Weak Decays: 1988-2023
hep-ph 2011-02 accept novelty 2.0 of 10

A 35-year chronicle of next-to-leading and next-to-next-to-leading order QCD corrections to weak decays, with reference tables, an eight-class taxonomy of correction structures, and personal anecdotes.

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5 arXiv papers cite this in 6 sentences

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Cites it as background 2 papers

The Wilson coefficient $C^Γ_Q̅Q$ has been calculated to the $𝒪(α_s^3)$ order [ref] , where the highest order calculation has been done recently [ref] .

Determination of $|V_{cb}|$ using N$^3$LO perturbative corrections to $\Gamma(B \to X_c \ell \nu)$ and 1S masses · Introduction · 0.85
In the free-quark approximation, corrections up to $O(α_s^2)$ are available [ref] together with the leading $β_0$ terms at higher orders [ref] , where $β_0$ is the one-loop coefficient of the QCD beta function.

Third order corrections to the semi-leptonic \boldmath{$b\to c$} and the muon decays · Introduction · 0.91

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