Hadronization of

Abstract

The b → ccs transition is usually believed to hadronize predominantly in B → X c D ( * )− s with the D ( * )− s originating from the virtual W . We demonstrate in a variety of independent ways that other hadronization processes cannot be neglected. The invariant mass ofcs has sizable phase-space beyond m D +m K . The rate for B → DD KX could be significant and should not be ignored as was done in previous experimental analyses. We estimate the number of charmed hadrons per B-decay, n c , to be ≈ 1.3 to higher accuracy than obtained in previous investigations. Even though n c is currently measured to be about 1.1, observing a significant B → DD KX would support n c ≈ 1.3. Many testable consequences result, some of which we discuss.Typeset using REVT E X 1 At present, there appears to be a conflict between experiment and theory for fitting both the inclusive semileptonic branching ratio and the number of charmed hadrons per B decay The prime indicates that the corresponding Cabibbo-suppressed mode is included. Experimentally the inclusive semileptonic BR has been measured accurately to be [9]and n c is measured as [9] n c = 1.10 ± 0.06 .A value of B(b → ccs ′ ) ≈ 0.1, suggested by Eqs.(1) and (3), would lead to a theoretical prediction of B(B → Xℓν) that is too large-i.e., inconsistent with its measured value (2).On the other hand, theory predicts n c ≈ 1.3 when the observed semileptonic BR is used as input, which is demonstrated below. Thus a conflict arises between (2) and ( Although this theoretical analysis hints that n c may be larger than currently measured [5][6][7]2,3], it is difficult to draw firm conclusions from this direct calculation of B(b → ccs ′ ) in view of the large uncertainties. 2It should also be stressed at this point, that the experimental determination of B(B → Xℓν) is reliable and accurate. In contrast, the measurement of n c is a sum over the inclusive yields of many charmed hadron species in B decays. It is thus prone to large uncertainties, perhaps larger than currently realized. Figure 1 displays the discrepancy graphically. We discuss now in some detail how the theoretical curve has been generated. Our objective is to draw the most accurate curve of n c versus semi-electronic BR with presently available theoretical calculations. We do not use the prediction for B(b → ccs ′ ) because it involves large errors, but rather proceed as follows. We start withwhere B(b → no charm) is small, typically at the percent level. We taketo account for the small fraction of b → s + no charm [10] and charmless b → u transitions.Furthermore we usewhich is in accordance with the result of Ref.[11] and also agrees with a recent ALEPH measurement [12],The last required ratio is Combining Eqs. (4), (5), (6), (8), the b → ccs ′ branching fraction can be written asIn this relation the very small contribution from b → ucs ′ transitions has been neglected.Eqs. (1) and (9) yield the number of charms per B decay aswhere we note that B(b → ccs ′ ) drops out in the linear relation between n c and B → X c e...

Chiral symmetry breaking, duality in the q channel and b → decays

“…Thus, not only we confirm, exploiting a different line of reasoning, the conclusion of Ref. [7] regarding the abundance of the "wrong" sign D's, but we encounter a menace of "overshooting": the yield of the "wrong" sign D's naturally tends to be too high.…”

“…This transition came under renewed scrutiny recently [7] on purely phenomenological grounds, in an attempt to find a solution of the "branching ratio versus n c problem". In Ref.…”

“…Then, from the measured semileptonic branching ratio of approximately 10.5%, the branching ratio of b →ccs was predicted to be close to 30%, with the corresponding charm yield n c ≈ 1.3. Moreover, using the most naive duality estimates in conjunction with the parton model for b → ccs, it was suggested [7] that approximately 1/2 of b → ccs hadronizes in the channels of the typeB → D ( * )D( * )K X, and only the remaining 1/2 goes to D ( * )D( * ) s X, the channels on which the attention was focused previously. If so, about 15% of theB decays have to end up with the "wrong" sign D's and K's in the final state.…”

“…Due to a relatively small energy release in this transition it is a natural suspect [5,6,7] for duality violations, which might be relevant in the so-called "semileptonic branching ratio versus n c problem" [8]. The model of Ref.…”

The chromomagnetic dipole operator and the B semileptonic branching ratio

“…where [16] Here Γ(b → no charm) is the sum of all B decay widths into charmless final states different from sg. Notice that in eq.…”