bb̅ud̅ four-quark systems in the Born-Oppenheimer approximation: prospects and challenges

Abstract

We summarize previous work onbbud four-quark systems in the Born-Oppenheimer approximation and discuss first steps towards an extension to the theoretically more challenging bbud system. Strategies to identify a possibly existing bbud bound state are discussed and first numerical results are presented. MotivationA number of mesons observed in experiment, e.g. at the LHCb or at Belle, are tetraquark candidates. Examples are the charged states Z b (10610) and Z b (10650), cf. e.g. [1]. They are bottomonium-like, which can be concluded from their masses and decay products. However, they also carry electric charge, which means they must include additional quarks. It is most likely that these additional quarks are a light quark-antiquark pair. So the quark content of the Z b states is assumed to be bbud/bbdū. Investigating heavy-heavy-light-light four-quark systems with Lattice QCD and within the Born-Oppenheimer approximationFour-quark states bbqq are object of experimental and theoretical research. The theoretical investigation of such systems is, for reasons which will be described below, very challenging. Four-quark statesbbqq with q ∈ {u, d, s, c, } are theoretically more straightforward to investigate. These states have not yet been measured experimentally. However, it is interesting to study them e.g. to be able to make predictions for experiment and to gain conceptual insight of four-quark states. Previous studies ofbbqq and bbqq systems can be found e.g. in [2][3][4][5][6][7][8][9][10].To investigate binding of four-quarksbbud and bbud, respectively, we work in the so-called Born-Oppenheimer approximation [11]. We first consider the b quarks to be static. Consequently, the heavy quark spin decouples from the system. We consider u/d quarks with a finite mass. The central element of the investigation is the potential of the two static quarks in the presence of the lighter quarks which we compute using Lattice QCD. We extract potentials V(r) from correlation functions C(t, r) = Ω| O † (t)O(0) |Ω ∝ t large exp(−V(r)t).(1) Speaker,

$Z_b$ tetraquark channel and $B\bar B^*$ interaction

“…where the BB * and B * B * largely dominate Z b (10610) and Z b (10650) decays, respectively. The only preliminary lattice QCD study of these states has been reported in [4,5] and will be briefly reviewed below. No other lattice results are available since this channel present a severe challenge.…”

“…In the present study we consider simplified Born-Oppenheimer approximation, inspired by the study of this system in [4,5]. This approach is based on distinction between heavy and light degrees of freedom and finds enormous application in molecular physics.…”

“…The only previous lattice study of this system [4] presents preliminary results based on Fock components BB * and ϒπ(0). The presence of states ϒπ( p = 0) was mentioned in [5], but not included in the simulation.…”

Opportunities in Flavour Physics at the HL-LHC and HE-LHC

“…This seems to be in accordance with the absence of additional energy eigenstates in [632,643], but more work based on the more rigorous Lüscher's method is needed. An indication for the Z b below the B B * threshold was found using static b quarks, but Υπ states with non-zero pion momentum must be incorporated before drawing any firm conclusion [644].…”

Bottomonium resonances with I=0 from lattice QCD correlation functions with static and light quarks

“…Refs. [35,36]). Therefore, we decided to first explore the simpler I = 0 case, where corresponding high-quality lattice QCD potentials are provided by the string breaking computation of Ref.…”