Analyticity, Shapes of Semileptonic Form Factors, and B to pi l nu

C. Glenn Boyd (Carnegie Mellon University); Martin J. Savage (University of Washington)

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Analyticity, Shapes of Semileptonic Form Factors, and B to pi l nu

C. Glenn Boyd (Carnegie Mellon University), Martin J. Savage (University of Washington)

High Energy Physics - Phenomenology · Submitted 11 Feb 1997

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The authors' main claim Moments of the dispersion relations are shown to provide substantially tighter constraints on the f_+ (t) form factor describing B -> pi l nu than the unweighted dispersion relation alone.

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arXiv IDhep-ph/9702300 (version 1)

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CitationC. Glenn Boyd (Carnegie Mellon University), Martin J. Savage (University of Washington). "Analyticity, Shapes of Semileptonic Form Factors, and B to pi l nu." arXiv:hep-ph/9702300 (1997). https://pith.science/paper/K6WX4FBH

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We give a pedagogical discussion of the physics underlying dispersion relation-derived parameterizations of form factors describing B -> pi l nu and B -> D l nu. Moments of the dispersion relations are shown to provide substantially tighter constraints on the f_+ (t) form factor describing B -> pi l nu than the unweighted dispersion relation alone. Heavy quark spin symmetry relations between the B -> pi l nu and B^* -> pi l nu form factors enables such constraints to be tightened even further.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We give a pedagogical discussion of the physics underlying dispersion relation-derived parameterizations of form factors describing B -> pi l nu and B -> D l nu.	contribution 0.84	0.75	0.08	asserted 0.71
s1	Moments of the dispersion relations are shown to provide substantially tighter constraints on the f_+ (t) form factor describing B -> pi l nu than the unweighted dispersion relation alone.	result 0.97	0.79	0.43	asserted 1.00
s2	Heavy quark spin symmetry relations between the B -> pi l nu and B^* -> pi l nu form factors enables such constraints to be tightened even further.	result 0.67	0.39	0.20	asserted 0.97

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Original abstract

We give a pedagogical discussion of the physics underlying dispersion relation-derived parameterizations of form factors describing B -> pi l nu and B -> D l nu. Moments of the dispersion relations are shown to provide substantially tighter constraints on the f_+ (t) form factor describing B -> pi l nu than the unweighted dispersion relation alone. Heavy quark spin symmetry relations between the B -> pi l nu and B^* -> pi l nu form factors enables such constraints to be tightened even further.

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References

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Cited by 14 Pith papers

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

$B \to \rho \ell \bar{\nu}$ resonance form factors from $B \to \pi\pi \ell \bar{\nu}$ in lattice QCD
hep-lat 2025-01 accept novelty 7.0 of 10

First lattice QCD calculation of B to rho semileptonic form factors with the rho treated as a resonant pi-pi state, using the Lellouch-Luscher formalism.
Precision Corrections to Dispersive Bounds on Form Factors
hep-ph 1997-05 conditional novelty 7.0 of 10

Adding higher hadronic channels and two-loop QCD to the dispersive bound lets each B to D and B to D* form factor be parameterized by one coefficient at the few-percent level, and invalidates a prior slope-curvature relation.
Combined analysis of semileptonic $B$ decays to $D$ and $D^*$: $R(D^{(*)})$, $|V_{cb}|$, and new physics
hep-ph 2017-03 accept novelty 6.0 of 10

Fitting light-lepton B to D(*) decay data with heavy-quark symmetry yields R(D)=0.299±0.003 and R(D*)=0.257±0.003, keeping the roughly 4-sigma tension with measurements.
$|V_{ub}|$ from $B\to\pi\ell\nu$ decays and (2+1)-flavor lattice QCD
hep-lat 2015-03 conditional novelty 6.0 of 10

Combining a new four-lattice-spacing QCD calculation of the B to pi form factor with BaBar and Belle data yields |Vub| = (3.72 +/- 0.16) x 10^-3, with lattice and experimental uncertainties now equal in size.
Lattice QCD calculation of form factors describing the rare decays $B \to K^* \ell^+ \ell^-$ and $B_s \to \phi \ell^+ \ell^-$
hep-lat 2013-10 accept novelty 6.0 of 10

Full-QCD lattice calculations with 2+1 dynamical quark flavors and NRQCD bottom quarks determine the B to K* and Bs to phi form factors at low recoil with roughly 5 percent total systematic uncertainty.

Show 9 more citing papers

The B -> pi l nu semileptonic form factor from three-flavor lattice QCD: A model-independent determination of |V(ub)|
hep-lat 2008-11 conditional novelty 6.0 of 10

A combined lattice-QCD and BABAR analysis yields |Vub| = 3.38 ± 0.36 × 10⁻³ using a model-independent z-expansion fit, the first such determination to include a continuum extrapolation.
Unitarity bounds and form-factor predictions for $B$-meson decays
hep-ph 2026-05 unverdicted novelty 5.0 of 10

Reviews unitarity bounds for B-meson form factors, shows standard methods apply rigorously only to B→π, develops GG parametrization for general cases, and delivers combined-analysis predictions with public supplementa...
The $\pi\gamma \to \pi\pi$ transition and the $\rho$ radiative decay width from lattice QCD
hep-lat 2018-07 conditional novelty 5.0 of 10

Lattice QCD yields the pi-gamma to pi-pi transition amplitude across photon virtuality and dipion mass, and from its rho-pole residue the photocoupling |G_rho-pi-gamma| = 0.0802(32)(20), roughly 1.6 times the experime...
Revisiting $B\to D \ell \nu$
hep-ph 2016-06 conditional novelty 5.0 of 10

Combining 2015 lattice form factors with Belle and BaBar spectra gives |Vcb| = 40.49(97) x 10^-3 from B to D l nu and the Standard Model prediction R(D) = 0.299(3).
$B \to \pi \ell \nu$ and $B_s \to K \ell \nu$ form factors and $|V_{ub}|$ from 2+1-flavor lattice QCD with domain-wall light quarks and relativistic heavy quarks
hep-lat 2015-01 accept novelty 5.0 of 10

A domain-wall plus relativistic-heavy-quark lattice calculation determines the B to pion and Bs to K form factors and, combined with BaBar and Belle data, yields |Vub| = 3.61(32) x 10^-3.
B -> K^* Form Factors from Flavor Data to QCD and Back
hep-ph 2013-08 accept novelty 5.0 of 10

Form factor ratios extracted from B to K-star dilepton angular data at low recoil, combined with heavy-quark symmetry and LCSR input, yield Standard-Model-consistent predictions for A_FB and P'_5.
Form Factors for Lambda_b -> Lambda Transitions in SCET
hep-ph 2011-11 conditional novelty 5.0 of 10

In the large-recoil limit all ten Lambda_b to Lambda form factors collapse to one soft function, estimated here at roughly 0.38 with about 50 percent hadronic uncertainty, plus a sub-percent hard-collinear correction.
Theoretical and Phenomenological Constraints on Form Factors for Radiative and Semi-Leptonic B-Meson Decays
hep-ph 2010-04 accept novelty 5.0 of 10

Two-term series expansions, constrained by newly computed NLO tensor-current dispersive bounds, describe B to K, rho, K* and phi form factors across the whole decay region and reproduce lattice points not used in the fits.
Lattice QCD inputs to the CKM unitarity triangle analysis
hep-ph 2009-10 conditional novelty 5.0 of 10

Averaging 2+1 flavor lattice QCD matrix elements and fitting the CKM unitarity triangle yields a 2-3 sigma tension, interpretable as new physics in neutral kaon mixing.

How the literature uses it

30 arXiv papers cite this in 39 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 20 sentences without a confident label

Uses its method or tool 15 papers

Following Ref. [ref] , we compactly express the outer functions of the form factors in a general form: [equation] with $𝒩 = (+ )^a (- )^b$ and [equation] The coefficient $a$–$g$ are listed in Table [ref].

Dispersive bounds for local form factors in $\Lambda_b \to \Lambda$ transitions · Outer functions · 0.97
Once we have continuum values for the form factors, we extrapolate them over the entire physical range of $q^2$ using a fit to a $z$-expansion [ref] .

Exclusive semileptonic $B_s\to K \ell \nu$ decays on the lattice · z-expansions of form factors · 1.00
For an analytic ansatz for the $q^2$-shape of the form factors we employ the Series Expansion (SE) [ref] .

Extracting $B \to K^*$ Form Factors from Data · Introduction · 1.00

Cites it as background 3 papers

The analyses of the experimental data from BELLE [ref] , BABAR [ref] , CLEO [ref] and BESIII [ref] on $D →π(K) e(μ) ν$ decays are based on a variety of parameterizations for the shape of the vector form factor $f_+^D π(K)(q^2)$, like effective pole models, inspired by either dispersion relations [ref] or heavy-quark expansion arguments [ref] , the $z$-expansion method [ref] or even relativistic quark model predictions [ref] .

Extraction of $|V_{cd}|$ and $|V_{cs}|$ from experimental decay rates using lattice QCD $D \to \pi(K) \ell \nu$ form factors · Introduction · 0.86
They were first used for the kaon form factor and have also successfully been applied to exclusive $B→π$ [ref] and $B→D^(∗)$ [ref] form factors[See also applications [ref] of the dispersive matrix method [ref] .].

Dispersive bounds for local form factors in $\Lambda_b \to \Lambda$ transitions · Two-point correlation functions and OPE representation · 0.86
Since exclusive semileptonic branching fractions can precisely determine CKM matrix elements, there is a sizeable body of work discussing accurate parametrizations for form factor shapes [ref] .

Lattice QCD calculation of form factors describing the rare decays $B \to K^* \ell^+ \ell^-$ and $B_s \to \phi \ell^+ \ell^-$ · Form factor shape · 0.95

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