Displaced $B_c^-$ mesons as an inclusive signature of weakly decaying double beauty hadrons

The recent discovery, by the LHCb collaboration, of the $\Xi_{cc}^{++}$ doubly charmed baryon, has renewed interest in the spectroscopy of doubly heavy hadrons. Experimentally, however, searches for such states appear highly challenging. The reconstructed final states tend to involve multiple heavy flavoured (beauty or charm) hadrons, so the yield for any exclusive decay mode will be suppressed to unobservably low levels by the product of several branching fractions, each of which is typically $10^{-3}$--$10^{-2}$. Noting that decays of double beauty hadrons are the only possible source of $B_c^-$ mesons that are displaced from the primary vertices of proton-proton collisions at the LHC, a more promising inclusive search strategy is proposed.


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This discovery has prompted various theoretical predictions for the production and decay properties of other doubly heavy states. Interestingly, these have not been confined to baryonic states. Various recently discovered "exotic" hadrons, which do not fit into the conventional scheme of qq mesons and qqq baryons, have led to several different interpretations including models based on tightly bound tetraquarks (see, for example, refs. [4][5][6] for reviews). Several authors have predicted the existence of a bbūd tetraquark state with mass below the threshold for decay to a pair of beauty mesons [7][8][9][10][11][12][13]. 1 It is possible that the bbūs and bbds tetraquarks are also stable against strong and electromagnetic decays. Since these tetraquarks can only decay weakly, they are expected to have comparable lifetimes to the ground state double beauty baryons, i.e. ∼ 0.4-0.8 ps [14][15][16].
Double beauty hadrons bbx, where x is either a quark or an anti-diquark, can be produced in high energy collisions such as those at the LHC where, assuming non-negligible lifetimes, they will travel a measurable distance before decaying. Typical estimates for the production cross-sections are O(1 nb) [17]. Since the accumulated data sample at LHCb (ATLAS and CMS) already exceeds 8 (150) fb −1 , with increases of over an order of magnitude anticipated in the HL-LHC era, it might be assumed that prospects for discovery are good. Unfortunately, branching fractions for heavy flavour decays to even the most abundant final states are typically 10 −2 -10 −3 . Exclusive reconstruction of double beauty hadrons will inevitably involve a chain of such decays. It is also relevant that the final states will involve many particles, leading to lower reconstruction efficiencies. Consequently, the yields that can be obtained are expected to be suppressed to unobservably low levels.
This motivates the development of inclusive search strategies. An important realisation, in this respect, is that weak decays of double beauty hadrons are the only possible source of B − c mesons that are displaced from, i.e. do not originate directly from, the primary vertices of the LHC collisions. This is a simple consequence of the facts that: (i) all fundamental Standard Model particles heavier than the b quark decay instantaneously, and do not produce a displaced vertex; (ii) any hadron containing both b andb constituent quarks will decay via strong and electromagnetic interactions and hence not have a measurable lifetime. Displaced B − c mesons can therefore only be produced 2 when one of the beauty quarks in a bbx hadron decays via a b →c transition and the producedc antiquark hadronises with the remaining b quark as shown in figure 1. The b → ccs transition will be dominant, since amplitudes for b → ccd, b → ucs and b → ucd processes involve smaller CKM matrix elements. The inclusion of charge conjugate processes is implied throughout this paper.
The signature of displaced B − c mesons is quite attractive experimentally, especially for the LHCb experiment which can exploit its precision vertex detector to separate signal 1 Some of these predictions predate the Ξ ++ cc discovery, in two cases quite considerably so. The experimental data have, however, put the theory on much firmer ground.
2 Another conceivable source of displaced B − c mesons would be from weak decays of triply heavy bqcc tetraquark states, where q ∈ u, d. However, even if such a state is stable against strong decays, its production rate will be tiny, its branching fraction for decays to final states involving B − c mesons will be small, and its lifetime will be very short. This potential contribution is therefore considered to have negligible impact on the proposed measurement strategy. from (prompt) background [18,19]. Moreover, when the B − c → J/ψ π − , J/ψ → µ + µ − decay chain is used there are only three final state particles to be reconstructed, and the J/ψ → µ + µ − signal helps to suppress backgrounds, so that high efficiency can be achieved. The branching fraction for this B − c decay is also relatively large, typically expected to be a few percent [20]. Its exact value is not known since the B − c production cross-section is unmeasured. The ratio has been measured by LHCb in the fiducial range p T (B) < 20 GeV and 2.0 < y(B) < 4.5 [21] (units in which c = 1 are used throughout this paper). Here, f c and f u are the fragmentation fractions for B − c and B − mesons, respectively, while p T and y denote the component of momentum transverse to the beam direction and the rapidity. This result and the prediction for B (B − c → J/ψ π − ) are consistent with the expectation that fc fu ∼ O 10 −3 . In spite of this low production rate, a yield of 3325 ± 73 B − c → J/ψ π − decays has been obtained in 2 fb −1 of proton-proton collision data at centre-of-mass energy √ s = 8 TeV, recorded at LHCb [22]. This is significantly larger than the yields reconstructed in other decay modes, and the B − c → J/ψ π − channel will therefore be the focus of this study. The [23], with a yield about half as large as that for B − c → J/ψ π − , may also contribute useful sensitivity to an experimental analysis.
The expected yield of displaced B − c mesons is given by the product of the following factors, where order-of-magnitude estimated (indicated by "∼") or known values are given in parentheses: the bbx hadron production cross-section (∼ 1 nb), the branching fractions for its inclusive decay to final states containing B − c mesons (∼ 10%) and for the subsequent ploited this approach to measure the bb production rate in different collision environments. In these analyses, the prompt and displaced J/ψ mesons are typically separated by fitting the distribution of a pseudo-proper decay time variable, where z J/ψ and z PV are the respective positions of the J/ψ decay vertex and the primary vertex, and p z J/ψ is the component of the J/ψ momentum, along the beam direction. This approach cannot however be used to study displaced B − c mesons, as the non-negligible B − c lifetime of ∼ 0.5 ps [24,25] causes the production and decay vertices to be separated. An alternative variable, the impact parameter (IP) can be used to identify displaced B − c mesons, as illustrated in figure 2. Due to the non-negligible lifetime of the bbx hadron, the momentum vector of the produced B − c meson will not point back directly at the primary vertex, i.e. the IP will be non-zero. The use of the IP to separate displaced and prompt production has previously been used to identify displaced charm hadrons produced in b hadron decays [26][27][28]. 3 As shown in figure 3, the displaced component is clearly visible at higher IP values, despite the relative yields of displaced and prompt D 0 mesons being approximately 1 : 20. This signal-to-background ratio is somewhat more favourable than expected for displaced B − c mesons, however better alignment has led to improvement of the LHCb IP resolution since the analysis shown in figure 3 was performed, and further improvement is expected with the upgraded vertex locator to be installed before data taking in 2021 [19,29].
In addition to the lifetime and momentum of the weakly decaying double beauty hadron, the shape of the IP distribution for displaced B − c mesons depends on the mo-JHEP01(2019)019 mentum released in the decay (i.e. the value Q, which is the difference between the decaying hadron mass and the sum of the final state particle masses). In the limit of small Q value, the momentum vectors of the B − c meson and its parent particle will be collinear, and hence small IP values will be obtained. For double beauty baryon decays producing a B − c meson through a b → ccs transition, the final state must contain a charm-strange baryon (m Ξc ∼ 2.47 GeV), while for double beauty tetraquark decays a DK combination (m D + m K ∼ 2.36 GeV) must be present. Thus, a similar maximum Q value is obtained in both cases: assuming a bbx mass of 10.5 GeV, Q max ∼ 1.8 GeV. This is sufficient to obtain a significantly non-zero IP value.
In order to understand how the unknown properties of the bbx hadrons, in particular their masses and lifetimes, affect the IP distribution and hence the feasibility of the proposed analysis approach, a study based on a simple simulation of bbūd tetraquarks has been performed. The kinematic properties, within the LHCb acceptance, are assumed to be the same as those for B mesons, i.e. approximately flat in pseudorapidity and having an exponential distribution in p T with mean 5 GeV [30]. Decay to the B − c D + K − final state, uniform over phase space, is assumed, with subsequent B − c → J/ψ π − , J/ψ → µ + µ − transitions. Transverse momentum requirements, similar to those in other studies of B − c mesons at LHCb [22], are imposed on the final-state particles.
Within an experimental analysis, the B − c IP would be determined from a full vertex fit of the three tracks, accounting for the covariance matrices of their position and momentum measurements, which is beyond the scope of the current study. Instead, the IP resolution is assumed to be dominated by the coordinate resolution of the B − c vertex, so that the IP resolution can be obtained as the uncertainty of the weighted average of the IP values for the three tracks. The per-track IP resolution is taken to be that obtained by LHCb with data collected in 2012, i.e. σ(IP x,y ) [µm] = 11.6 + 23.4/(p T [ GeV]) [19]. The shapes obtained for a range of relevant parameters are shown in figure 4. It can be seen that, for bbx lifetimes above about 0.5 ps, the distribution for displaced B − c hadrons extends to significantly higher IP values than that for prompt production.
The shape of the IP distribution for prompt B − c mesons is given purely by the resolution function, since the underlying true distribution is a delta function. Given the expected signal-to-background ratio of around 1 : 100, the sensitivity of the analysis will depend critically on the detector IP resolution -it must be as precise as possible to separate prompt and displaced production, and must be well-known to avoid potentially large systematic uncertainties. It should be stressed that the IP distribution for prompt B − c mesons shown in figure 4 is based on a simple study containing several approximations, and therefore is not expected to provide an accurate description of the real experimental situation, particularly in the tails. It will be crucial in an experimental analysis that a suitable control mode can be used to study the resolution function. Fortunately, the IP resolution for B − c → J/ψ π − decays can be studied in data using the B − → J/ψ K − decay as a control sample. Contributions from non-prompt B − mesons can be reduced by requiring production in narrow B * * 0 s → B − K + decays [31,32] where the associated K + track is required to originate from the primary vertex. Therefore, systematic uncertainties due to the tail of the resolution function should be controllable.
While the IP is a powerful variable that illustrates how prompt and displaced B − c mesons can be separated, there is also additional information that could potentially be JHEP01(2019)019 exploited to improve the sensitivity in an experimental analysis. The better separation of prompt and displaced components at higher transverse momentum could be exploited by studying the two-dimensional distribution of IP and p T . The per-candidate estimated uncertainty on the IP measurement could alternatively be used in the analysis to enhance the sensitivity; at LHCb, this is usually done by constructing a χ 2 variable. Similarly, better separation is expected at larger values of the distance between the PV and the B − c decay vertex. Determining the optimal analysis approach would be an important aspect of experimental study. It must be noted that whilst the signature of displaced B − c mesons would be sufficient to indicate double beauty hadron production, it would provide only limited information about the properties of those hadrons. The yield is related to the production cross-section times the inclusive branching fraction for decay to final states containing B − c mesons, summed over all weakly decaying bbx hadrons. Therefore, with improved predictions for these crosssections and branching fractions, it could be possible to test whether only double beauty baryons are contributing, or if there is evidence for double beauty tetraquark production. The shape of the distribution depends on the mass, lifetime and kinematic properties of the bbx hadrons, averaged over all the contributing species. Hence with predictions for two of these, the third could potentially be inferred. Moreover, an observation of bbx hadron production from an inclusive analysis would be likely to lead to insights as to how further information could be obtained, for example on which exclusive decays may be most accessible.
Finally, it is worthwhile to consider if any other inclusive signatures of displaced heavy flavour hadrons can be used similarly. Secondary B mesons can only be produced in decays of doubly heavy hadrons, with beauty charm hadron decays likely to be the dominant source. Indeed, the B − c → B 0 s π − decay has already been observed [33]. However, the Q value for B meson production in B − c or Ξ bc decays is relatively small, making it harder to separate signal from prompt production through the IP distribution. This effect also exists, but is less pronounced, for b baryon production, so a search for displaced Λ 0 b baryons as an inclusive signature of beauty charm hadrons could potentially be interesting. (Secondary Λ 0 b production through Ξ − b → Λ 0 b π − is possible [34] but has a very low Q value and hence no significant contribution to the IP.) Another exciting possibility for the long term is that displaced Ξ cc baryons could also be used to search for these states. In these cases a reconstructed muon produced through semileptonic decay could potentially be used to tag the signal and reduce the prompt background significantly.
In conclusion, displaced B − c mesons provide a distinctive signature of the production of double beauty hadrons. There appear to be reasonable prospects for the detection of such a signal with the large data samples accumulated by the LHCb detector and its planned upgrades, since excellent IP resolution is a feature of this experiment.

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Belyaev, Steve Blusk, Alex Bondar, Mat Charles, Vladimir Gligorov, Jibo He and Mika Vesterinen for helpful comments. This work is supported by the Science and Technology Facilities Council.
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