The Isgur-Wise Function in the BPS Limit

Abstract

From sum rules in the heavy quark limit of QCD, using the non-forward amplitude, we demonstrate that if the slope ρ 2 = −ξ ′ (1) of the Isgur-Wise function ξ(w) attains its lower bound 3 4 (as happens in the BPS limit proposed by Uraltsev), the IW function is completely determined, given by the function ξ(w) = 2 w + 1 3/2 .

Lattice measurement of the Isgur–Wise functions τ1/2 and τ3/2<

“…To make a long story short, a series of sum rules [9]- [14] have been derived from QCD, all indicating that τ 3/2 should be significantly larger than τ 1/2 . These sum rules relate the τ j form factors, as well as form factors related to excitations, to derivatives of the ground state Isgur-Wise function ξ and allow to bound the latter derivatives in an efficient and useful way [15]- [17]. Not only does the slope of ξ verify ρ 2 > 3/4 but also the curvature and even higher derivatives are bound.…”

SEMILEPTONIC DECAY OF Bc MESON INTO $c\bar c$ STATES IN A QCD POTENTIAL MODEL

“…We have taken the prescription of the strong coupling constant of ref. [28,40], which contains a QCD cut off parameter Λ QCD constrained in the region 382 MeV ≤ Λ QCD ≤ 430 MeV by the theoretical bounds on Isgur-Wise function [41,42]. We 1.44 [16] have taken the limiting values of the scales for our computation with the same parameters b and c from our previous work [39](i.e.…”

“…The physically plausible range of effective Λ QCD can be deduced from the allowed range of the slope and curvature of the I-W function. Considering the theoretical bounds on slope 3/4 ≤ ρ 2 < 1.51 [41,42] and curvature C ≥ 5ρ 2 4 [42] of the I-W function, we obtained an allowed range of Λ QCD in the model as 382MeV ≤ Λ QCD ≤ 430MeV for B meson [43]. We extend this theoretical bounds for B c meson and compute the slope and curvature of the Isgur Wise function.…”

Holographic models of the scalar sector of QCD

“…As a consequence, the chiral condensate Σ is proportional to m q at odds with what happens in QCD. This shortcoming does not appear in the Hard Wall model where the coefficients of z and z 3 terms of v(z) are independent [6,7] and in an improved Soft Wall model [8] .…”

“…The correlator (7) shows the presence of a discrete set of poles, corresponding to the poles of the Euler function ψ, with masses m 2 Sn = c 2 (4n + 6) for all radial states labeled by n. The residues correspond to the scalar meson decay constants F 2 Sn = R k 16c 4 (n + 1) = Nc π 2 c 4 (n + 1) where the overall factor R/k is fixed by matching (7) in the short-distance limit q 2 → +∞, expanded in powers of 1/q 2 , with the QCD perturbative contribution [4] : R k = Nc 16π 2 . Thus, scalar mesons turn out to be heavier than vector mesons (for which m 2 ρn = c 2 (4n + 4) [2] ) if a 0 (980) and f 0 (980) are identified as the lightest scalar mesons.…”