arXiv subjects
Publications and source records attributed to Thomas Mannel.
In this talk some of the theoretical aspects of $b \to s γ$ transitions are discussed. The focus is on inclusive decays, since these can be computed more reliably. Topics covered are (1) perturbative QCD corrections, (2) non-perturbative contributions and (3) effects of ``new physics'' in these decays.
We point out that a simple test of the mechanism of CP violation can be performed by a measurement of the CP asymmetries in exclusive and inclusive radiative rare decays. We show that the rate asymmetries $ΔΓ= Γ(B^- \to f γ) - Γ(B^+ \to \bar{f} γ)$} for certain final states $f$ can be predicted in a theoretically clean way. Some implications for $b \to s \ell^+ \ell^-$ decays are discussed.
Employing the SU(2) isospin symmetry of strong interactions and estimates borrowed from effective field theory, we explore the impact of new physics on the decays $B^\pm\to ϕK^\pm$ and $B_d\to ϕK_S$ in a model-independent manner. To this end, we introduce - in addition to the usual mixing-induced CP asymmetry in $B_d\to ϕK_S$ - a set of three observables, which may not only provide smoking-gun signals for new-physics contributions to different isospin channels, but also valuable insights into hadron dynamics. Imposing dynamical hierarchies of amplitudes, we discuss various patterns of these observables, including also scenarios with small and large rescattering processes. Whereas the $B\toϕK$ system provides, in general, a powerful tool to search for indications of new physics, there is also an unfortunate case, where such effects cannot be distinguished from those of the Standard Model.
We construct the higher twist structure functions that describe inclusive b hadron decays in regions of phase space where the hadronic decay products carry high energy but have low invariant mass. We show that, for B meson decays, there are four new non-vanishing matrix elements of non-local operators. We show that to subleading twist these decays are parametrized in terms of four functions. We compute the tree-level matching for a general heavy-to-light current and apply it to B -> X_s gamma. Using a simple model for these functions we estimate the subleading twist contributions to this decay.
We present a model-independent parametrization of the $B^\pm\to J/ψK^\pm$, $B_d\to J/ψK_S$ decay amplitudes by taking into account the constraints that are implied by the isospin symmetry of strong interactions. Employing estimates borrowed from effective field theory, we explore the impact of physics beyond the Standard Model and introduce -- in addition to the usual mixing-induced CP asymmetry $A_{CP}^{mix}$ in $B_d\to J/ψK_S$ -- a set of three observables, allowing a general analysis of possible new-physics effects in the $B\to J/ψK$ system. Imposing a dynamical hierarchy of amplitudes, we argue that one of these observables may already be accessible at the first-generation $B$-factories, whereas the remaining ones will probably be left for second-generation $B$ experiments. However, in the presence of large rescattering effects, all three new-physics observables may be sizeable. We also emphasize that a small value of $A_{CP}^{mix}$ could be due to new-physics effects arising at the $B\to J/ψK$ decay-amplitude level. In order to establish such a scenario, the observables introduced in this paper play a key role.
We discuss the non-perturbative and the radiative corrections to inclusive B decays from the point of view known from QED corrections to high energy e^+ e^- processes. Here the leading contributions can be implemented through the so called ``radiator function'' which corresponds to the shape function known in heavy hadron decays. In this way some new insight into the origin of the shape function is obtained. As a byproduct, a parameterization of the radiatively corrected shape function is suggested which can be implemented in Monte Carlo studies of inclusive heavy hadron decays.
One-particle inclusive CP asymmetries in the decays of the type B -> D(*) X are considered in the framework of a QCD based method to calculate the rates for one-particle inclusive decays.
We discuss one-particle inclusive B decays in the limit of heavy b and c quarks. Using the large-N_C limit we factorize the non-leptonic matrix elements, and we employ a short distance expansion. Modeling the remaining nonperturbative matrix elements we obtain predictions for various decay channels and compare them with existing data.
In the recent literature, constraints on the CKM angle $γ$ arising from the branching ratios for $B^\pm\toπ^\pm K$ and $B_d\toπ^\mp K^\pm$ decays received a lot of attention. An important theoretical limitation of the accuracy of these bounds is due to rescattering effects, such as $B^+\to\{π^0K^+\}\toπ^+K^0$. We point out that these processes are related to penguin topologies with internal up quark exchanges and derive SU(2) isospin relations among the $B^+\toπ^+K^0$ and $B_d^0\toπ^-K^+$ decay amplitudes by defining ``tree'' and ``penguin'' amplitudes in a proper way, allowing the derivation of generalized bounds on the CKM angle $γ$. We propose strategies to obtain insights into the dynamics of penguin processes with the help of the decays $B_{u,d}\to K\bar{K}$ and $B^\pm\toπ^\pm K$, derive a relation among the direct CP-violating asymmetries arising in these modes, and emphasize that rescattering effects can be included in the generalized bounds on $γ$ completely this way. Moreover, we have a brief look at the impact of new physics.
In the infinite mass limit for a heavy quark its spin decouples from the QCD dynamics, which leads to the heavy-quark spin symmetry. After a short discussion of spin symmetry some applications are considered.
Measurements of the combined branching ratios for $B^\pm \to π^\pm K$ and $B_d \to π^\mp K^\pm$ allow interesting constraints on the CKM angle $γ$, the ratio $r \equiv |T'|/|P'|$ of the current-current and penguin operator contributions to $B_d \to π^\mp K^\pm$, and the CP asymmetry in that decay. Present CLEO results for these branching ratios indicate where problems with consistency of the Standard Model may arise in the future. In this paper we discuss scenarios of new physics in these decays and investigate their implications for the above constraints.
Motivated by recent CLEO measurements of $B\toπK$ modes, we investigate their implications for the CKM angle $γ$ and a consistent description of these decays within the Standard Model. Interestingly it turns out that already the measurement of the combined branching ratios $B^\pm\toπ^\pm K$ and $B_d\toπ^\mp K^\pm$ allows to derive stringent constraints on $γ$ which are complementary to the presently allowed range for that angle. This range, arising from the usual fits of the unitarity triangle, is typically symmetric around $γ= 90^\circ$, while our method can in principle exclude a range of this kind. Consistency within the Standard Model implies furthermore bounds on the ratio $r\equiv|T'|/|\tilde P|$ of the current-current and penguin operator contributions to $B_d\toπ^\mp K^\pm$, and upper limits for the CP-violating asymmetry arising in that decay. Commonly accepted means to estimate $r$ yield values at the edge of compatibility with the present CLEO measurements.
A short review of a few selected topics in Heavy Quark Effective Theory is given. Applications to exclusive decays are discussed.
We reanalyze the decay $B_d\toπ^+π^-$ without assuming dominance of QCD penguins with internal top-quark exchanges. In that case the weak phase of the $\bar b \to\bar d$ QCD penguin amplitude is not related in a simple way to the CKM angle $β$. Nevertheless it is still possible to extract the CKM angle $α$ in a transparent and almost model-independent way from the time-dependent CP-violating asymmetry of the transition $B_d\toπ^+π^-$. Aside from that CP asymmetry this approach needs as an input only amplitudes of decays with branching ratios of order $10^{-5}$ and will thus be well within reach at future $B$-factories.
An effective theory approach to heavy quarkonia decays based on the $1/m_Q$ expansion is introduced. Its application to decays in which the two heavy quarks annihilate is discussed.
In this series of lectures the basic ideas of the $1/m_Q$ expansion in QCD ($m_Q$ is the mass of a heavy quark) are outlined. Applications to exclusive and inclusive decays are given.
We construct an effective Lagrangian for the hadronic decays of a heavy excited $s$-wave-spin-one quarkonium into its ground state. We show that reasonable fits to the measured invariant mass spectra in the $J/ψ$ and $Υ$ systems can be obtained working in the chiral limit. The mass dependence of the various terms in the Lagrangian is discussed on the basis of a quark model.
Assuming so called global duality we argue that it is very likely that local duality needed to obtain results for the hadronic width of heavy meson decays within the $1/m_Q$ expansion holds. Hence, if the discrepancy between experiment and the theory concerning charm counting, the semileptonic branching fraction and the lifetimes of $b$ hadrons persist, it may be taken as a hint at some qualitatively new effect in (nonperturbative) QCD or even as a new physics.