First Lattice QCD Study of B-physics With Four Flavors of Dynamical Quarks
Researchers from the three universities of Rome, the universities of Valencia, Paris XI, Groningen, Bonn, and Berlin have formed a team to carry out an extensive study of the physics of mesons containing a beauty quark. The results of this study will allow to address issues relevant for the phenomenology of the so-called flavor sector of the Standard Model (SM) and its possible extensions to New Physics (NP), that are currently under investigation by the LHCb experiment at CERN and will also be studied at the planned super B-factories.
Flavor physics deals, basically, with transitions among quarks induced by the weak interaction. Since quarks are not free particles, the quark mixing can be studied only through the decays of systems made of quarks (namely, mesons and baryons). The structure of such systems is governed by another interaction, the strong one, for which our fundamental theory is the quantum chromodynamics (QCD). In this theory, quarks interact with gluons in a highly non-perturbative way, which can only be properly taken into account by using simulations performed on a discretized space-time lattice.
By using lattice QCD, the aim of the scientists is to calculate from first principles several B-physics observables with unprecedented accuracy based on the use of the gluon configurations produced by the European Twisted Mass Collaboration with four flavors of dynamical quarks (Nf = 2+1+1). These include the non-perturbative effects due to the light mass-degenerate up (u) and down (d) quarks, as well as to the strange (s) and the charm (c) quarks with masses close to their physical values. Such a setup is the closest one to the real world.
The B-physics observables that were computed accurately are:
- the mass of the beauty (b) quark, mb, which is a fundamental parameter of the SM;
- the decay constants of B (=Bu,d) and Bs mesons, fB and fBs, which are basic hadronic parameters entering the theoretical predictions of several B-physics processes. In particular, current studies of the Bs → μ+ μ- decay at LHCb will provide one of the most stringent flavor physics constraints on the NP model building and in that respect fBs will play a very decisive role;
- the bag parameters BBd,s, which, together with the decay constant fBd,s, encode the non-perturbative QCD information about the Bd,s – anti(B)d,s mixing amplitude in the SM. Their accurate determination would help getting information on the entries Vts and Vtd of the Cabibbo-Kobayashi-Maskawa (CKM) matrix describing the quark mixing. Moreover, in most of the NP scenarios, non-SM four-quark operators contribute to the mixing amplitude, and for the quantitative studies of such scenarios the non-SM bag parameters should be computed on the lattice too;
- the form factors of semileptonic B and Bs meson decays, which are indispensable for the reliable extraction of the CKM entries Vub and Vcb, from the detailed experimental studies at LHCb and in Super-B factories. A list of such decay modes includes: B → πℓν, Bs → Kℓν, B → Dℓν, Bs → Dsℓν and the similar modes with a vector meson in the final state;
- the form factors of exclusive b →s ℓ+ℓ- decays, which are currently the major source of (large) uncertainties in exploring the various asymmetries constructed from the full angular analysis of B → K ℓ+ℓ-, B → K* ℓ+ℓ- and Bs → ϕ ℓ+ℓ-modes, that are nowadays intensively studied at LHCb and will also be studied at Super-B and Super-KEKB. These decays, combined with the Bd,s – anti(B)d,s mixing, are the most fertile ground for studying many, if not all, of the NP scenarios.
The present situation of the lattice determinations for some of the quantities of interest in our project is summarized in Figs. 1 and 2, taken from the recent updated publication of the FLAG working group .
In order to get very precise results, the number of lattice points has to be sufficiently large. Therefore the lattice QCD simulations of the present project have been carried out on the HPC Tier-0 systems JUGENE and JUQUEEN of the JSC (Germany) and FERMI of the CINECA (Italy).
The analysis of all the correlation functions calculated in the project is in progress and some preliminary results have been presented already at the recent lattice Conference in Mainz (2013).
Fig. 1. Decay constants of the B and Bs mesons obtained with QCD simulations on the lattice by various collaborations . The results are grouped according to the number of dynamical quark flavors (Nf =2, 2+1 and 2+1+1).
Fig. 2. Compilation of the lattice results for the neutral B and Bs meson mixing matrix elements . Note that till now no results are available for Nf =2+1+1.
 S. Aoki et al. [FLAG working group], Review of lattice results concerning low energy particle physics, arXiv:1310.8555 [hep-lat].
 N. Carrasco et al. [ETM collaboration], A Nf =2+1+1 “twisted” determination of the b-quark mass, fB and fBs, arXiv:1311.2837 [hep-lat].
 N. Carrasco et al. [ETM collaboration], K and D oscillations in the Standard Model from Nf =2+1+1 twisted mass, arXiv:1310.5461 [hep-lat].
Istituto Nazionale di Fisica Nucleare (INFN) - Sezione Roma Tre
Via della Vasca Navale 84, I-00146 Roma/Italy