Precision corrections to dispersive bounds on form factors

Abstract

We present precision corrections to dispersion relation bounds on form factors in bottom hadron semileptonic decays and analyze their effects on parameterizations derived from these bounds. We incorporate QCD two-loop and nonperturbative corrections to the two-point correlator, consider form factors whose contribution to decay rates is suppressed by lepton mass, and implement more realistic estimates of truncation errors associated with the parameterizations. We include higher resonances in the hadronic sum that, * boyd@fermi.phys.cmu.edu † bgrinstein@ucsd.edu ‡ rlebed@ucsd.edu 1 together with heavy quark symmetry relations near zero recoil, further tighten the sum rule bounds. Utilizing all these improvements, we show that each of the six form factors inB → Dℓν andB → D * ℓν can be described with 3% or smaller precision using only the overall normalization and one unknown parameter. A similar one-coefficient parameterization of one of the Λ b → Λ c ℓν form factors, together with heavy quark symmetry relations valid to order 1/m 2 , describes the differential baryon decay rate in terms of one unknown parameter and the phenomenologically interesting quantityΛWe discuss the validity of slope-curvature relations derived by Caprini and Neubert, and present weaker, corrected relations. Finally, we present sample fits of current experimentalB → D * ℓν andB → Dℓν data to the improved one-parameter expansion.

Consistency constraints on ms from QCD dispersion relations and chiral perturbation theory in Kℓ3 decays

“…, a N }, with the remaining infinite set bounded in magnitude and forming a theoretical truncation error [7], δ N : 4) which means that the form factor fit to these parameters using (2.5) has a theoretical uncertainty no larger than δ N . The kinematic parameter t s is used to minimize the size of this already small truncation error [1,5]. Equation (4.4) makes it clear that this minimization occurs when z = 0 lies within the kinematic range chosen for the fit, t ∈ [t min , t max ]; from (2.4) one sees that this can occur only if t s also assumes some value in this range.…”

“…Recently, attention has increased due to studies of bounds obtained on form factors from heavy hadron semileptonic decays, which can be used in concert with Heavy Quark Effective Theory to isolate the CKM elements |V cb | and |V ub | (see [1] for a compilation of references). Such studies were initially motivated by the 1981 paper of Bourrely, Machet, and de Rafael [2], which first applied the basic method of equating the dispersion integral over hadronic form factors to its perturbative QCD evaluation in the deep Euclidean region, in that paper for the case of K ℓ3 decays.…”

“…Because the dispersive bound uses QCD to constrain the shape of each hadronic form factor (as a function of momentum transfer), one can use the experimentally measured form factors to obtain limits on QCD parameters such as the quark masses; however, until this data is available, one can use precisely the same method to take the form factor from a given model or calculation as being correct, and discover limits on values of the QCD parameters for which the shape of the form factor is consistent with the dispersive bounds. 1 In particular, we use the one-loop corrected chiral perturbation theory (χPT) result of Gasser and Leutwyler [4] for the scalar form factor in K ℓ3 decays. The scalar form factor is especially interesting because it contributes to the scalar current correlator, which is proportional to (m s − m u ) 2 (i.e., vanishing for flavor-conserving processes), and is thus more sensitive to quark mass values.…”

Extraction of |Vcb| from B → D(∗)ℓνℓ and the Standard Model predictions of R(D(∗))

“…At the moment, the most precise determinations of |V cb | from inclusive [6,7] and exclusive decays [8] differ from each other at ≈ 3σ confidence level (CL). Recently it has been shown that the CapriniLellouch-Neubert (CLN) [9] and Boyd-Grinstein-Lebed (BGL) [10] parameterizations lead to different results for the exclusive determinations of |V cb | [11,12]. In their analysis they have used up-to-date lattice calculations of the form factors along with the available experimental results from Belle [13].…”

Bounds on the derivatives of the Isgur–Wise function from sum rules in the heavy quark limit of QCD

“…In the case of the slope and the curvature, the lower bounds (29) and (33) are complementary to the upper bounds obtained from unitarity constraints [10], [11].…”