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Charmless B-decays in Soft-Collinear Effective Theory

Principal Investigator: Guido Bell (Siegen)
Participating Researchers: Thorsten Feldmann (Siegen), Björn O. Lange (Siegen), Jan Piclum (Siegen)

B-meson decays into light (charmless) hadrons play a central role in testing the Cabibbo-Kobayashi-Maskawa (CKM) mechanism of quark flavour mixing and CP violation. Within the Standard Model (SM), charmless B-decays are mediated by rare b→ u quark transitions or by loop-induced b→ d/s decays that are sensitive to effects from new heavy particles beyond the SM. The phenomenology of charmless B-decays is extremely rich, ranging from semileptonic B→ Xu decays to nonleptonic B→Kπ, radiative B→ Xsγ and electroweak penguin B→K(∗)ll decays.

Most of the charmless B-meson decays will be scrutinized at the Large Hadron Collider (LHC) and the super-flavour factory Belle~II in the next few years. A meaningful inter\-pretation of the experimental data requires to control the underlying hadronic matrix elements in Quantum Chromodynamics (QCD). The heavy quark expansion as well as its field-theoretical incarnation in terms of effective field theories (EFTs) provide a systematic framework to compute the hadronic matrix elements in a twofold expansion in ΛQCD/ mb and αs(mb).

At leading power in the heavy quark expansion the hadronic matrix elements factorize into perturbatively calculable coefficient functions and process-independent hadronic parameters. The factorization is particularly involved for decays with energetic, massless particles in the final state (with respect to the B-meson rest frame). The energetic (collinear) degrees of freedom prevent a local operator product expansion, and one is left with convolutions of hard-scattering kernels with nonlocal hadronic matrix elements. The relevant effective theory is called Soft-Collinear Effective Theory (SCET) and one distinguishes between two different versions, SCETI and SCETII, depending on the physical context.

SCETI is the appropriate effective theory for inclusive B-meson decays as B→ Xu and B→ Xsγ. Experimental cuts constrain the measurements of the decay spectra to the endpoint region in which the invariant mass of the hadronic system is small. The factorization of the differential decay rates in the endpoint region is well established. SCETI also provides the means to resum parametrically large logarithms to all orders in perturbation theory based on renormalization group (RG) techniques.

The theoretical understanding of exclusive B-decays, as B→Kπ or B→K(∗)ll at large hadronic recoil, within SCETII is currently incomplete. The problem is related to the separation of the various (soft and collinear) long-distance modes which result in endpoint-divergent convolution integrals. At present, one typically tries to circumvent this problem by absorbing the endpoint-sensitive contributions into hadronic parameters which are not factorized but treated as nonperturbative inputs. While such a procedure limits the application of the EFT techniques, a better understanding of the endpoint dynamics is desirable. In particular, it would open the path for studying power corrections to exclusive B-decays — a problem of primary importance for nonleptonic B-decays as well as for the precision angular analysis of B→K(∗)ll decays.

The current project aims at improving the SCET techniques in various respects. First and foremost, the factorization of short- and long-distance effects in SCETII applications to exclusive B-meson decays will be revisited. In the last few years, there has been substantial progress in understanding SCETII factorization theorems for collider physics observables. The new techniques go under the names collinear anomaly and rapidity renormalization group, and the current project aims at transferring these techniques to B-physics applications. In addition, RG properties of nonperturbative input parameters — the shape function for inclusive B-decays and light-cone distribution amplitudes (LCDAs) for exclusive B-decays — will be investigated. The project also intends to derive new factorization theorems as well as to refine their perturbative input by computing the relevant hard and jet functions to higher orders.