Meeting on Shape Function Parameters ************************************ Connection Details ================== When: July 07, 2004, 07:00 AM PDT Call: 510-665-5437 Meeting ID: 8160 Discussion Items ================ o Central values and errors of shape function parameters - BABAR - BELLE o Error on mb (see e.g. hep-ex/0404017) o AOB Material ======== o Some theoretical aspects o BABAR's note: ps pdf and the other plots as eps A B and as pdf A B o Belle's SF extraction: ps pdf Present ======= KEK: Toru Iijima, Hidekazu Kakuno, Tadao Nozaki, Yoshi Sakai Melbourne: Elisabetta Baberio, Antonio Limosani Dresden: Heiko Lacker, Kerstin Tackmann Frascati: Ikaros Bigi Heidelberg: Urs Langenegger Cornell: Stefan Bosch, Bjoern Lange, Gil Paz SLAC: Riccardo Faccini, Bob Kowalewski, Francesca di Lodovico Summary ======= In the following SF = shape function; dF/N = de Fazio/Neubert 1. Short theoretical statement ------------------------------ Stefan emphasized that there *is* a relation between *SF moments* and HQET parameters. The HQET parameters are universal quantities and can be extracted from many different experiments like inclusive b -> c l nu decays, b -> s gamma decays, or Upsilon spectroscopy. They can be extracted using different (physical) mass schemes, like the kinetic mass or the 1PS mass. A proper physical scheme for the moments of the SF is the SF mass scheme introduced in section 5.2 of hep-ph/0402094 where also its relations to other physical mass schemes are given. The knowledge of two moments of the shape function (like m_b and mu_pi^2) constrains model-building of the SF but does not determine its functional form. Once a complete theoretical treatment of the b -> s gamma photon spectrum is available, we'll have crucial information on the functional form of the SF. Ric raised the point whether we should just resort to using dF/N to unfold the measured spectra and quote partial branching fractions only, from which the extraction of Vub would be done with MC generators but more directly at the order available for a calculation and scheme. The point here is that dF/N is curretnly the only triple-differential MC generator covering the entire phase space. Improvements to dF/N are work in progress (Bjoern). 2. Belle: B-> s gamma analysis and extraction of SF parameters -------------------------------------------------------------- Tadao discussed the note sent around before the meeting and linked above and proposed a weighted average of the central values extracted from the Belle and CLEO, independently using positive and negative variations. He raised the point of the "old" parametrizations of the B -> s gamma photon spectra. There was a clarifying discussion as what the "extreme1 e_1" and "extreme2 e_2" points in table 2 of the Belle note are: They correspond to the upper left and lower right extreme points on the contours shown in fig 4 of that note. Ikaros inquired into the large uncertainty on mu_pi^2, as the range between 0.23 and 0.96 seems "absurdly" large. The reply stated that the current data of the B->s gamma photon spectrum do not provide sensivity to this parameter in the parametrizations used. The extraction of the SF parameters will be publicly available from the HFAG webpages. In addition, it will be posted to hep-ex by BELLE. 3. Miscellaneous issues ----------------------- Ric again raised the point of the combination of Belle's result with CLEO's in order to go beyond the weighted average. The summary of the discussion is that Belle will provide a functional form of the delta Chi2 in the relevant parameter space by next week. We'll try to get the same information from CLEO and eventually from BABAR. This information will be made available on the HFAG webpages. As the quoted error on Vub should represent a 68%CL, the agreement was to use the delta Chi2 = 2.3 contour. Because delta Chi2 = 1 was used in the last average, we'll remark about this. After the meeting, BABAR statisticians are in disagreement: I think that it has been done correctly using the deltaChisq=1 contour. In a linear approximation (ie, keeping linear order in a Taylor series expansion of Vub in mb,a), the Vub variable picks out a direction in the mb,a plane. The "basis vector" in Vub direction is a rotation of the mb,a coordinates. The 68% confidence interval of the rotated "basis vector" corresponds to taking the extreme points (ie, remaximizing likelihood wrt to the orthogonal directon) on the error ellipse along that direction. This interval gets scaled appropriately when Vub is computed. A way to check that everything is behaving as hoped is to use the Belle deltachisq=1 contour to read off Var(mb), Var(a), Cov(mb,a), and compute: Var(Vub) ~ (dVub/dmb)^2 Var(mb) + (dVub/da)^2 Var(a) + 2 (dVub/dmb) (dVub/da) Cov(mb,a) Ric raised another point whether not separating out the exclusive component is right. The discussion showed that also BELLE uses a fully inclusive mass distribution for there SF parameter determination. The theoretical advice here is that this is the correct approach, including the resonant component adds an ad-hoc model dependence and the advantages are not clear. Ikaros raised two more points: (1) A cautionary note: the universality of the distribution or shape functions holds only to leading order in 1/m_Q; thus only in leading order can you measure it in b -> s gamma and use it in b -> u l nu. There are nonperturbative contributions in order 1/m_Q -- unlike for fully integrated rates, where they arise only in order 1/m_Q^2 -- that affect b-> s gamma and b-> u l nu differently; furthermore the connection to observables becomes much more scheme dependent then. Those 1/m_Q corrections are not known (yet). (2) Just to be more specific and accurate, it should always be stated whether the energies and energy cuts are given for the Y(4S) rest frame or the B meson rest frame. 4. Improvement of charmless semileptonic rate -> |Vub| ------------------------------------------------------ There was agreement that the measurement of the b->c l nu moments by BABAR should be used to improve the extraction of Vub from the total charmless semileptonic rate, which previously had been "fixed" at the CERN CKM workshop. This is currenty under discussion in BABAR, Urs will send out a note once that is settled. 5. Action Items --------------- 1. Belle will circulate their delta Chi2 function by next week 2. We will ask CLEO for the same information. And inquire about the delta Chi2 = 1. 3. The HFAG webpage will be updated to contain the information necessary for each experiment to perform the SF systematic uncertainty as soon as possible. 4. Urs will circulate a short note on the extraction of Vub from the full charmless semileptonic rate based parameters mu_pi^2 and mb as determined in the b->c l nu moments measurements by BABAR.