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Scientific Report 2007-2009 Theoretical physics T2. B decay spectra in resummed QCD calculations At present, all experimental data in particle physics are compatible with the current theory of strong and electroweak interactions — the so-called standard model (SM). All the particles predicted by the SM have been discovered, with the exception of the Higgs boson, which will probably be discovered in the next decade at the Large Hadron Collider (LHC) at Cern, Geneve — currently in the first stages of operation. Apart from the Higgs search, a good fraction of present-day research in particle physics involves detailed comparison of experimental data with theoretical distributions of known particles with standard interactions. Weak and electromagnetic interactions of quarks are, in general, largely affected by the accompanying strong interactions effects, described by Quantum Chromodynamics (QCD). Even if someone is not primarily interested in strong interactions, he has to face them in any case as background effects, as for example in Higgs physics at LHC. In order to measure the strenght of the weak coupling of a beauty quark to an up quark — the CKM matrix element V ub — one has to compute for example the lepton energy spectrum in the semileptonic decay B → X u lν l , where X u is any hadron state coming from the fragmentation of the u quark. Let us note that at present there is no theory for any CKM element, but only some consistency relations among them coming from unitarity of the matrix itself, as implied by the SM. Such free parameters are therefore measured by comparing theoretical distributions containing them as unknown quantities, to experimental data. The only analytic tool available at present to compute QCD effects is perturbation theory: the corrections are computed with Feynman diagrams as truncated series in α S , the strong coupling. The latter decreases logarithmically with the energy of the process — asymptotic freedom; for beauty decays α S (m b ) ≃ 0.21. In some regions of phase space of the above decays, experimentally relevant, many-body effects related to infrared divergencies become important: they manifest themselves in an enhancement of the coefficients of αS n in the perturbative series. This effect renders the fixed-order expansion completely unreliable and forces the resummation to all orders in α S of the enhanced terms. A general problem of all-order resummation is that an integration of the QCD coupling constant in the low energy region is involved, in which α S is large and outside the perturbative domain — the old problem of the Landau ghost makes a specific appearence here. As shown in the eighties, this problem cannot be solved inside perturbation theory, because of missing dynamical input from the perturbative phase, and therefore it is necessary to introduce an arbitrary prescription from outside in order to have well-definite predictions for resummed spectra. These conclusions also apply to resummation in heavy flavor decays, as we explicitly found, but are in disagreement with those reached in the past few years by other groups (M. Neubert and coll. for instance). In our modelization of non-perturbative effects, we also equate the on-shell mass of the b quark to the mass of the B meson: m b = m B . That is consistent because the mass of a heavy quark has a much weaker physical meaning that is generally believed nowadays: quarks are confined. If one aims at describing all QCD dynamics at a fundamental level, he has to abandon perturbative QCD, because the latter has always to be supplemented with phenomenological models connecting the fictitious “parton world” with the real “hadron world”. QCD can be computed exactly only with numerical Monte-Carlo methods after regularization on a lattice. In that case, one only deals with bare, regularization dependent, quark masses and with observable hadron masses. A renormalized beauty mass can certainly be defined but it is just conventional and bears to relation to dynamics. A consequence is that one has the freedom to fix m b in a rather arbitrary way and a simple way to implement hadron kinematics in a parton computation is just to identify the unphysical b mass with the physical B mass. Also these assumptions are in disagreement with a large part of the B physics community (M. Neubert and E. Gardi). Many colleagues object that the Operator Product Expansion (OPE) involves m b and not m B and that identifying them would introduce non-vanishing 1/m b corrections. Our reply is that implementing the OPE from first principles, i.e. on a lattice, would give similar problems in the definition of the quark mass as those discussed above, augmented by the specific ultraviolet power divergencies brought in by the small-momentum expansion. We have used the accurate experimental data from B fragmentation to fix the prescription for the QCD coupling constant at low energy [1], from which we have derived our resummed B decay spectra [2]. By comparing the latter with experimental data, we have found some disagreement with electron spectra from the B-factories in the low-energy region, which we interpret as originating from an undersubtracted b → clν l background [2]. We have obtained for V ub the value (3.76 ± 0.13 ± 0.22)10 −3 [3], smaller than the values obtained by the other groups and in good agreement with the determinations coming from lattice QCD (exclusive channels) or from global fits to the SM of the UTfit collaboration. References 1. U. Aglietti et al., Nucl. Phys. B775, 162 (2007). 2. U. Aglietti et al, Nucl. Phys. B768, 85 (2007). 3. U. Aglietti et al., Eur. Phys. J. C59, 831 (2009). 4. U. Aglietti et al., Phys .Lett. B653, 38 (2007). Authors U. Aglietti, G. Corcella, G. Ferrera, A. Renzaglia. <strong>Sapienza</strong> Università di Roma 25 Dipartimento di Fisica
Scientific Report 2007-2009 Theoretical physics T3. Flavor, CP violation and Matter-Antimatter asymmetry The past decade has seen tremendous progress in the study of flavor and CP violation. B-factories have collected and analyzed an impressive amount of experimental data, that led to the confirmation of the Cabibbo- Kobayashi-Maskawa (CKM) mechanism for flavor and CP violation. While sizable New Physics (NP) contributions may still hide in b → s penguin decays [1], the bulk of CP violation in the K and B sectors can be correctly accounted for within the Standard Model (SM), with possible new sources of flavor and CP violation being confined to the level of 20-30% corrections [2]. If NP is of Minimal Flavor Violation (MFV) type, however, its contributions can be much larger without spoiling the consistency with experimental data. Until one year ago, MFV extensions of the SM seemed phenomenologically very appealing, although they give only a description of the NP flavor structure and not a solution to the origin of flavor. However, the recent Tevatron experiments presented their first measurement of CP violation in B s → J/Ψϕ decays, showing a discrepancy from the SM expectation at the level of three standard deviations. If this indication is confirmed, it will represent a major breakthrough in flavor physics and in model building, leaving behind MFV models and pointing to a more fundamental origin of flavor mixing. It would also open up very interesting perspectives for the LHCb experiment, which may become a primary source of indirect NP signals and a gold mine for the determination of NP flavor couplings. In any case, it is of the utmost importance to be ready to study in detail the possible signals of a non-MFV NP at the Large Hadron Collider (LHC) experiments. Concerning the theoretical evaluation of hadronic flavor and CP violation at low energies, most of the relevant processes have been computed in all known extensions of the SM, including the Minimal Supersymmetric Standard Model (MSSM), extra-dimensional models, composite Higgs theories, etc. The Particle Theory Group (PTG) in Rome has given major contributions in these directions, pioneering the study of NP contributions to flavor and CP violation beyond the leading order in QCD. One of the fundamental results achieved by the PTG is the calculation of ∆F = 2 hadronic matrix elements in Lattice QCD, with the computation of Next-to-Leading order (NLO) anomalous dimensions for the most general ∆F = 2 operator basis and the calculation of the NLO matching for these operators in the MSSM. Working in tight collaboration with experimental physicists, the UTfit collaboration, of which Guido Martinelli was one of the founders, has a world-leading role in performing combined analyses of flavor and CP violation in the SM and beyond. It has developed efficient tools to simultaneously constrain the CKM matrix and the NP contributions to ∆F = 2 processes. These tools, η 1 0.5 0 -0.5 -1 ε K β V ub V cb -1 -0.5 0 0.5 1 Figure 1: Constraints on the Wolfenstein parameters ¯ρ and ¯η from the Unitarity Triangle analysis [2]. combined with the model-specific ones for the known theoretical extensions of the SM, will form the starting point for the implementation of flavor and CP violation constraints on the NP Lagrangian. The missing ingredients (additional processes and/or new models) will be implemented in this framework. The PTG has also pioneered the phenomenology of non-leptonic decays, devising several strategies to estimate the SM uncertainty in a reliable, mostly data-driven way, as well as new methods to extract short-distance information from non-leptonic decays. The extraction from experiments of useful phenomenological information on the SM and/or NP fundamental parameters may require an accurate knowledge of the relevant hadronic matrix elements of the effective weak Hamiltonian, which can be evaluated in Lattice QCD. The PTG in Rome is part of an important large-scale lattice collaboration, the European Twisted-Mass Collaboration. Thanks to the use of the ApeNext machines of INFN the PTG in Rome has a world-leading role in LQCD simulations and has provided accurate determinations of many important hadronic quantities, like: 1) light, strange and charm quark masses; 2) the decay constants of K-, D- and B-mesons; 3) the vector and scalar form factors relevant in the semileptonic decays of K-, D- and B-mesons relevant for the determination of the entries of the CKM matrix; 4) the bag parameters of the kaon relevant for the study of CP violation in the SM as well as in NP scenarios. The future research activity of the PTG will continue along this lines, to keep up with the experimental results and to estimate the uncertainties in any NP model singled out by direct searches at the LHC. References 1. M. Bona et al. PMC Phys. A3, 6 (2009) 2. M. Bona et al. J. High Energy Phys. 0803, 049 (2008) Authors R. Contino, E. Franco 1 , G. Martinelli, L. Silvestrini 1 γ ∆m d ∆m s α ∆md ρ <strong>Sapienza</strong> Università di Roma 26 Dipartimento di Fisica
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