REVIEW
Theory of Charmless Inclusive B Decays and the Extraction of V_{ub}
High Energy Physics - Phenomenology · Submitted 11 Apr 2005 · 58 references
Pith's verdict: A load-bearing framework paper with real new technology, but the abstract's claim to have eliminated the dominant uncertainty outruns the tables, where the subleading shape-function band is set by a hand-picked model scale.
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Referee report
The paper
The paper claims
A single fitted shape function is claimed to remove the dominant hadronic uncertainty from inclusive $|V_{ub}|$ extraction, because the same non-perturbative function that shapes the $B^0 to X_s gamma$ photon spectrum also controls the $B^0
The reading
What carries the argument
The machinery is a QCD-factorization formula in which each structure function is a convolution of a hard function, a jet function, and the leading shape function, with renormalization-group evolution resumming the large logarithms between the hard scale $m_b$ and the intermediate scale $sqrt{m_b Lambda_{QCD}}$. Two technical devices carry the interpolation. First, the kinematical power corrections are written in terms of the variable $y = (P_- - P_+)/(M_B - P_+)$, chosen so that the expansion in $1/(M_B - P_+)$ produces terms singular as $y to 0$ that are nevertheless integrable against the $y^2$ behaviour of phase space. Second, the leading shape function is redefined, $hat{S} to hat{S}$, by absorbing a specific linear combination of the subleading shape functions $hat{t}$, $hat{u}$, $hat{v}$ in such a way that its moment relations are unchanged; the same $hat{S}$ then appears in both the photon spectrum and the semileptonic distributions, which is what allows a single experimental fit to serve both processes.
Extended reading notes
Core claim
The central claim is that the triple differential $B^0 to X_u l^- nu$ rate and the $B^0 to X_s gamma$ photon spectrum can be written in a single unified form that is valid in both kinematical regimes and that reduces to the standard OPE result when integrated over wide phase space, up to unknown $O(alpha_s^2)$ terms. The construction is organized as an expansion in inverse powers of the hadronic variable $(M_B - P_+)$ rather than of the partonic momentum, so that the exact phase-space factors cancel the would-be singularities of the expanded structure functions. Because no partonic quantity such as the b-quark mass appears explicitly, the dependence on $m_b$ is carried entirely by the moments of the leading shape function, which the authors argue should be extracted from the $B^0 to X_s gamma$ photon spectrum rather than taken from a mass scheme. They present partial-rate predictions for a range of experimental cuts, and a detailed error budget separating perturbative scale variation, the spread over models of the subleading shape functions, and weak annihilation.
Load-bearing premise
The kinematical power corrections are assigned a strong coupling evaluated at a scale that the authors choose by hand, because the anomalous dimensions that would fix it are not known, so the quoted perturbative error bars rest on an uncomputed input.
Editorial extensions
If this is right
- A fit to the measured $B^0 to X_s gamma$ photon spectrum yields the leading shape function, and hence parameter-free predictions for $B^0 to X_u l^- nu$ partial rates under arbitrary cuts, without recomputing weight functions for each new analysis.
- The b-quark mass and the kinetic-energy parameter are accessed indirectly through the first moments of that shape function, so the same data constrain both the decay distributions and the heavy-quark parameters.
- Imposing a cut at high leptonic invariant mass, $q^2 leq (M_B - M_D)^2$, removes the region where weak annihilation is concentrated, trading about twenty percent of the efficiency for the elimination of that uncertainty.
- The formalism is suited to building an event generator for inclusive charmless semileptonic and radiative decays, since it covers both the endpoint and the wide-phase-space domains with one set of formulae.
- For the most favourable cuts, notably $P_+ leq M_D^2/M_B$, the quoted total theoretical uncertainty is around seven percent, which the authors present as the level at which a $|V_{ub}|$ determination becomes competitive.
Reading between the lines
- The claim is testable as a consistency check rather than a single number: the shape function fitted to the photon spectrum should reproduce measured partial semileptonic rates with the same parameters, so a joint fit that fails to describe both spectra with one function would undercut the interpolation.
- Because the interpolation is exact only up to unknown $O(alpha_s^2)$ terms, the practical size of the residual is an empirical question that a future two-loop calculation of the jet and hard functions would settle directly.
- The strategy is structurally similar to extracting parton distributions from deep inelastic scattering and then predicting other processes; the analogy suggests that the dominant long-run error will migrate from theory to the experimental systematics of the photon-spectrum endpoint region.
- If weak annihilation is indeed confined near $q^2 approx m_b^2$ as argued, then a comparison of charged and neutral $B$ partial rates under identical cuts would give an independent handle on the flavour-non-singlet four-quark matrix elements.
Original abstract
We present ``state-of-the-art'' theoretical expressions for the triple differential B->X_u l^- nu decay rate and for the B->X_s gamma photon spectrum, which incorporate all known contributions and smoothly interpolate between the ``shape-function region'' of large hadronic energy and small invariant mass, and the ``OPE region'' in which all hadronic kinematical variables scale with M_B. The differential rates are given in a form which has no explicit reference to the mass of the b quark, avoiding the associated uncertainties. Dependence on m_b enters indirectly through the properties of the leading shape function, which can be determined by fitting the B->X_s gamma photon spectrum. This eliminates the dominant theoretical uncertainties from predictions for B->X_u l^- nu decay distributions, allowing for a precise determination of |V_{ub}|. In the shape-function region, short-distance and long-distance contributions are factorized at next-to-leading order in renormalization-group improved perturbation theory. Higher-order power corrections include effects from subleading shape functions where they are known. When integrated over sufficiently large portions in phase space, our results reduce to standard OPE expressions up to yet unknown O(alpha_s^2) terms. Predictions are presented for partial B->X_u l^- nu decay rates with various experimental cuts. An elaborate error analysis is performed that contains all significant theoretical uncertainties, including weak annihilation effects. We suggest that the latter can be eliminated by imposing a cut on high lepton invariant mass.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We present ``state-of-the-art'' theoretical expressions for the triple differential B->X_u l^- nu decay rate and for the B->X_s gamma photon spectrum, which incorporate all known contributions and smoothly interpolate between the ``shape-function region'' of large hadronic energy and small invariant mass, and the ``OPE region'' in which all hadronic kinematical variables scale with M_B. The differential rates are given in a form which has no explicit reference to the mass of the b quark, avoiding the associated uncertainties. Dependence on m_b enters indirectly through the properties of the leading shape function, which can be determined by fitting the B->X_s gamma photon spectrum. This eliminates the dominant theoretical uncertainties from predictions for B->X_u l^- nu decay distributions, allowing for a precise determination of |V_{ub}|. In the shape-function region, short-distance and long-distance contributions are factorized at next-to-leading order in renormalization-group improved perturbation theory. Higher-order power corrections include effects from subleading shape functions where they are known. When integrated over sufficiently large portions in phase space, our results reduce to standard OPE expressions up to yet unknown O(alpha_s^2) terms. Predictions are presented for partial B->X_u l^- nu decay rates with various experimental cuts. An elaborate error analysis is performed that contains all significant theoretical uncertainties, including weak annihilation effects. We suggest that the latter can be eliminated by imposing a cut on high lepton invariant mass.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present ``state-of-the-art'' theoretical expressions for the triple differential B->X_u l^- nu decay rate and for the B->X_s gamma photon spectrum, which incorporate all known contributions and smoothly interpolate between the ``shape-function region'' of large hadronic energy and small invariant mass, and the ``OPE region'' in which all hadronic kinematical variables scale with M_B. | contribution 1.00 | 0.92 | 0.13 | asserted 1.00 |
| s1 | The differential rates are given in a form which has no explicit reference to the mass of the b quark, avoiding the associated uncertainties. | method 0.54 | 0.89 | 0.07 | asserted 1.00 |
| s2 | Dependence on m_b enters indirectly through the properties of the leading shape function, which can be determined by fitting the B->X_s gamma photon spectrum. | method 0.81 | 0.44 | 0.06 | asserted 0.83 |
| s3 | This eliminates the dominant theoretical uncertainties from predictions for B->X_u l^- nu decay distributions, allowing for a precise determination of |V_{ub}|. | interpretation 0.88 | 0.73 | 0.72 | asserted 0.98 |
| s4 | In the shape-function region, short-distance and long-distance contributions are factorized at next-to-leading order in renormalization-group improved perturbation theory. | method 0.90 | 0.65 | 0.04 | asserted 1.00 |
| s5 | Higher-order power corrections include effects from subleading shape functions where they are known. | contribution 0.42 | 0.69 | 0.03 | asserted 0.97 |
| s6 | When integrated over sufficiently large portions in phase space, our results reduce to standard OPE expressions up to yet unknown O(alpha_s^2) terms. | result 0.51 | 0.82 | 0.05 | asserted 0.99 |
| s7 | Predictions are presented for partial B->X_u l^- nu decay rates with various experimental cuts. | result 0.59 | 0.90 | 0.04 | asserted 1.00 |
| s8 | An elaborate error analysis is performed that contains all significant theoretical uncertainties, including weak annihilation effects. | contribution 0.51 | 0.93 | 0.05 | asserted 1.00 |
| s9 | We suggest that the latter can be eliminated by imposing a cut on high lepton invariant mass. | future work 0.64 | 0.47 | 0.10 | hedged possibility 0.99 |
What was examined, and what was not
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Figures
Figures reproduced from arXiv:hep-ph/0504071 by the authors.
References
How later papers used it
59 later papers cite it
2 later papers by other authors are listed below: 1 used its method or tool and 1 compared its own results with it.
Uses its method or tool 1 of 10 papers with this label
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Determined weights using this paper's BLNP model to study the model dependence of the DFN shape function and possible effects of next-to-next-to-leading order corrections in α_s.
Search for $B^+ \to \mu^+\, \nu_\mu$ and $B^+ \to \mu^+\, N$ with inclusive tagging (2019) · 0.97 · paraphrased: the licence does not allow quoting
Compares with it 1 of 7 papers with this label
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Compared the state-of-the-art OPE results from the BLNP approach of this paper with its own results at the level of cumulative distributions.
Potential and limitations of machine-learning approaches to inclusive $|V_{ub}|$ determinations (2021) · 0.98 · paraphrased: the licence does not allow quoting
How the literature uses it
54 arXiv papers cite this in 98 sentences
Papers citing it · 61 sentences without a confident label
Uses its method or tool 9 papers
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Specifically, we have used the earlier calculations by De Fazio and Neubert [ref] and Kagan and Neubert [ref] , and the more comprehensive approaches by Lange, Neubert and Paz [ref] , Gambino, Giordano, Ossola and Uraltsev [ref] , and Andersen and Gardi [ref] .
Measurement of the inclusive electron spectrum from B meson decays and determination of |Vub| · Conclusions · 0.87
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For the inclusive contribution, we use two different calculations: the De Fazio and Neubert (DFN) model [ref] (with $m_b^KN = (4.66 ±0.04) GeV$, $a^KN = 1.3 ±0.5$) and the Bosch-Lange-Neubert-Paz (BLNP) model [ref] (with $m_b^SF = 4.61 GeV$, $μ_π^2 SF = 0.20 GeV^2$).
First Simultaneous Determination of Inclusive and Exclusive $\left|V_{ub}\right|$ · Introduction · 0.87
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The four predictions are: - BLNP: The prediction of Bosch, Lange, Neubert, and Paz (short BLNP) of Ref. [ref] provides a prediction at next-to-leading-order accuracy in terms of the strong coupling constant $α_s$ and incorporates all known corrections.
Measurements of Partial Branching Fractions of Inclusive $B \to X_u \, \ell^+\, \nu_{\ell}$ Decays with Hadronic Tagging · $||$ Determination · 0.80
Uses its data or values 2 papers
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The above contribution to the hadronic tensor is: [equation] where [equation] The subleading shape functions are defined as: [equation] and [equation] where $k$, $l$ are color indices, $S$ in equation ([ref]) is a soft Wilson line defined in [ref] (not to be confused with the leading order shape function $S(ω)$!), $[x,y]≡S(x)S^†(y)$, $L_h^(2)$ is the next-to-leading term in the expansion of the HQET Lagrangian, and [equation] The second type of terms, namely the kinematical power corrections, can be found in [ref] , where they were called $F^kin$.
Subleading Jet Functions in Inclusive B Decays · Review · 0.80
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PDG [ref] quotes again quite different values for the inclusive (see [ref] ) and exclusive (e.g. [ref] ) determination based on data from Babar and Belle [ref] : [equation] However, now the effect on quantities like $ΔM_q$ arising from this difference is minor [ref] compared to the ambiguities arising from different values of $|V_cb|$, therefore will not discuss the current determinations in more detail.
High precision in CKM unitarity tests in $b$ and $c$ decays · $V_ub$ · 0.95
Compares with it 5 papers
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From the above discussion we can conclude that, compared to BLNP analysis in [ref] , where $μ_i=1.5$ GeV, the net effect of the NNLO corrections is to lower the central values for partial rates by around $15$–$20%$, while at the same time reducing the perturbative uncertainty on the scale $μ_h$.
NNLO corrections to B --> X_u l nu and the determination of |V_ub| · Impact of NNLO corrections on central values and errors · 0.99
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Our results are compatible with the most recent Heavy Flavour Averaging Group (HFAG) average for $|V_ub|$ from inclusive decays [ref] [equation] where the two values refer to two different theoretical frameworks [ref] , respectively, currently employed by HFAG.
Inclusive semileptonic B decays and the determination of |V_ub| · Introduction · 0.95
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The distributions are compared to the hybrid MC and the fully inclusive DFN [ref] and BLNP [ref] predictions with model parameters listed in Table [ref].
Measurement of Differential Branching Fractions of Inclusive ${B \to X_u \, \ell^+\, \nu_{\ell}}$ Decays · Introduction · 1.00
Cites it as background 15 papers
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Until this summer, the most complete theoretical analysis of inclusive $B̅→X_u l ν̅_l$ spectra was based on calculations described in [ref] and referred to as the BLNP approach.
QCD Calculations of Decays of Heavy Flavor Hadrons · Inclusive determination of $|V_ub|$ · 0.84
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Different approaches to this factorization have been put forth in the literature, going under the names of BLNP [ref] , GGOU [ref] , and the dressed-gluon exponentiation [ref] .
NNLO corrections to B --> X_u l nu and the determination of |V_ub| · Introduction · 0.99
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The basic two-parameter functional forms proposed in the literature [ref] are F(k_+) = N (Λ̅-k_+)^a e^b k_+ θ(Λ̅-k_+) (exponential) F(k_+) = N (Λ̅-k_+)^a e^-b (Λ̅-k_+)^2 θ(Λ̅-k_+) (gaussian) F(k_+) = N (Λ̅-k_+)^a/cosh[b (Λ̅-k_+)] θ(Λ̅-k_+) (hyperbolic) F(k_+) = N e^-a (Λ̅-k_+ + b/Λ̅-k_+)^2 θ(Λ̅-k_+) (roman)
Inclusive semileptonic B decays and the determination of |V_ub| · Functional forms · 0.93
Discussion
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