Enhanced subleading structure functions in semileptonic B decay

TL;DR

This paper analyzes subleading structure-function effects in the endpoint region of B→X_uℓν decays, where the OPE organizes in Λ_QCD/[m_b(1−y)] and nonperturbative smearing becomes important. Focusing on two dominant contributions—smearing of the λ_2 δ(1−y) term from the one-gluon matrix element and smearing of four-quark operator contributions—the authors show that endpoint spectra can receive several percent corrections to the total rate and up to large corrections in the endpoint bins. They implement a shape-function formalism with a simple f(k_+) model to quantify these effects and discuss how they impact the extraction of |V_{ub}|, including the use and limitations of the B→X_sγ input for shaping the endpoint region. The work highlights that precise measurements near the endpoint are essential to control subleading nonperturbative corrections and to reliably determine |V_{ub}|, potentially enabling observations of these effects with improved data, or allowing a measurement that sidesteps some of these uncertainties if measurements extend to lower E_ℓ.

Abstract

The charged lepton spectrum in semileptonic $B\to X_u \ell\barν$ decay near maximal lepton energy receives important corrections from subleading structure functions that are formally suppressed by powers of $Λ_{QCD}/m_b$ but are enhanced by numerical factors. We investigate the series of higher order terms which smear over a region of width $ΔE_\ell \sim Λ_{QCD}$ near the endpoint the contributions proportional to $δ(E_\ell - m_b/2)$ times (i) the matrix element of the chromomagnetic operator, and (ii) four-quark operators. These contribute to the total rate at the few percent level, but affect the endpoint region much more significantly. Implications for the determination of $|V_{ub}|$ are discussed.

Figures (2)

• Figure 1: The one-gluon matrix element.
• Figure 2: Time ordered product that yields four-quark operators and higher dimension terms.