|Vub| and Constraints on the Leading-Twist Pion Distribution Amplitude from B → πlν

Using new experimental data on the leptonic mass spectrum of B → πlν, we simultaneously determine |Vub| and constrain a π 2 and a π 4 , the first two Gegenbauer moments of the pion’s leading-twist distribution amplitude. We find |Vub| = (3.2 ± 0.1 ± 0.1 ± 0.3) × 10 , where the first error is experimental, the second comes from the shape of the form factor in q and the third is a 8% uncertainty from the normalisation of the form factor. We also find a2 (1GeV) = 0.19± 0.19 and a π 4 (1GeV) ≥ −0.07. submitted to Physics Letters B [email protected] [email protected] |Vub| is one of the least well-known elements of the CKM quark-mixing matrix. A more precise determination of this parameter will not only greatly improve the constraints on the unitarity triangle, but also provide a stringent test of the CKM mechanism of flavour structure and CP violation. In this letter, we determine |Vub| from the exclusive semileptonic decay B → πlν, based on the invariant lepton-mass spectrum recently reported by BaBar [1] and the light-cone sum rule calculations of the relevant form factor in Ref. [2]. The hadronic matrix element relevant for B → πlν is given by 〈π(pπ)|ūγμb|B(pB)〉 = ( pB + pπ − q mB −m 2 π q2 ) μ f+(q ) + mB −m 2 π q2 qμ f0(q ), (1) where the form factors f+,0 depend on q 2 ≡ (pB −pπ) , the invariant mass of the lepton-pair, with 0GeV ≤ q ≤ (mB −mπ) 2 = 26.4GeV. f+ is the dominant form factor, i.e. the only one needed for calculating the spectrum in q, dΓ dq2 (B → πlνl) = GF |Vub| 2 192πmB λ(q)|f+(q )| (2) for massless leptons; λ(q) = (mB +m 2 π−q )−4mBm 2 π is the usual phase-space factor. The determination of |Vub| from B → πlν requires theoretical input on f+, which has been the subject of many a calculation using various methods, in particular quark models [3], QCD sum rules on the light-cone (LCSRs) [2, 4, 5] and lattice simulations [6]. The challenge for theory is twofold: the region of applicability of theoretical calculations is, in most cases, restricted to part of the full physical phase-space; a calculation of f+ for, say, small values of q is, however, not sufficient, as experimental data on the decay spectrum are still very scarce, so that any meaningful extraction of |Vub| necessitates the extrapolation of the form factor to all q. LCSR calculations, for instance, are valid for large pion momentum, which translates into small to moderate q < ∼ 14GeV , whereas lattice calculations are restricted to small pion momentum, corresponding to large q > ∼ 15GeV . Extrapolations rely either on a model for the q-dependence of f+, like vector meson dominance or the parametrisation advocated by Becirevic and Kaidalov [7], or dispersive bounds on the form factor, which have been studied for instance in Ref. [8]. The BaBar collaboration has measured the spectral decay distribution in 5 bins in q [1], which is a significant improvement over previous results reported for 3 bins [9], and allows one, for the first time, to assess the validity of various parametrisations of the q-dependence of f+ like • vector meson dominance (VMD); • the parametrisation of Becirevic and Kaidalov (BK) [7]; • the extended BK parametrisation used by Ball and Zwicky (BZ) [2]. All these parametrisations can be motivated from the exact representation of f+ in terms of a dispersion relation, f+(q ) = Resq2=m2 B f+(q ) q2 −mB∗ + 1 π ∫ ∞ (mB+mπ) dt Im f+(t) t− q2 − iǫ , (3)