Universality and m_X cut effects in B -> Xs l+ l-

TL;DR

The paper addresses how experimental hadronic m_X cuts affect the B -> X_s l+l- rate in the low-q^2 region, where nonperturbative effects overwhelm a straightforward OPE. It introduces a shape-function framework and the universality of cut effects across short-distance operators, enabling predictions of the cut-induced reduction by relating to B -> X_s gamma and B -> X_u l nu processes. The authors develop a soft-collinear effective theory (SCET) based, split-matching calculation including O(α_s) corrections, showing that the cut fractions are universal to within a few percent and providing concrete cut-rate predictions with quantified uncertainties; they discuss strategies to mitigate hadronic uncertainties, such as normalization to related decays. This work strengthens the reliability of using B -> X_s l+l- to search for new physics by controlling hadronic effects from experimental cuts.

Abstract

The most precise comparison between theory and experiment for the B -> Xs l+ l- rate is in the low q^2 region, but the hadronic uncertainties associated with an experimentally required cut on m_X potentially spoil the search for new physics in these decays. We show that a 10-30% reduction of dΓ(B -> Xs l+ l-) / dq^2 due to the m_X cut can be accurately computed using the B -> X_s gamma shape function. The effect is universal for all short distance contributions in the limit m_X^2 << m_B^2, and this universality is spoiled neither by realistic values of the m_X cut nor by alpha_s corrections. Both the differential decay rate and forward-backward asymmetry with an m_X cut are computed.

Figures (3)

• Figure 1: Phase space cuts. A substantial part of the rate for $q_1^2< q^2< q_2^2$ falls in the rectangle bounded by $p_X^+ < p_X^{+{\rm cut}}$.
• Figure 2: $\eta_{ij}(m_X^{\rm cut}, 1\,{\rm GeV}^2, 6\,{\rm GeV}^2)$ as functions of $m_X^{\rm cut}$. The dashed curves show the local OPE result, the solid curves include the leading shape function effects. The uppermost, middle, and lowest curves are $\eta_{00,99}$, $\eta_{79}$, and $\eta_{77}$, respectively.
• Figure 3: $\eta_{00}(m_X^{\rm cut}, 1\,{\rm GeV}^2, 6\,{\rm GeV}^2)$ as a function of $m_X^{\rm cut}$. The orange, green and purple (medium, light, dark) curves show $m_b^{1S} = 4.68\,{\rm GeV}$, $4.63\,{\rm GeV}$, and $4.73\,{\rm GeV}$, respectively.