Implications of heavy quark-diquark symmetry for excited doubly heavy baryons and tetraquarks
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The first search for the doubly heavy $ {{{{\varOmega}_{bc}^{0}}}} $ baryon and a search for the $ {{{{\varXi}_{bc}^{0}}}} $ baryon are performed using $ pp $ collision data collected via the $ {\rm{LHCb}} $ experiment from 2016 to 2018 at a centre-of-mass energy of $ 13 \;{\rm{TeV}} $, corresponding to an integrated luminosity of 5.2 $ \;{\rm{f}}{{\rm{b}}^{ - 1}} $. The baryons are reconstructed via their decays to $ {{{{\varLambda}^+_c}}} {{{{\pi}^-}}} $ and $ {{{{\varXi}^+_c}}} {{{{\pi}^-}}} $. No significant excess is found for invariant masses between 6700 and 7300 $ \;{\rm{MeV}}/{c^2} $, in a rapidity range from 2.0 to 4.5 and a transverse momentum range from 2 to 20 $ \;{\rm{MeV}}/{c} $. Upper limits are set on the ratio of the $ {{{{\varOmega}_{bc}^{0}}}} $ and $ {{{{\varXi}_{bc}^{0}}}} $ production cross-section times the branching fraction to $ {{{{\varLambda}^+_c}}}{{{{\pi}^-}}} $ ( $ {{{{\varXi}^+_c}}}{{{{\pi}^-}}} $) relative to that of the $ {{{{\varLambda}^0_b}}} $ ( $ {{{{\varXi}_{b}^{0}}}} $) baryon, for different lifetime hypotheses, at 95% confidence level. The upper limits range from $ 0.5\times10^{-4} $ to $ 2.5\times10^{-4} $ for the $ {{{{{{{{\varOmega}_{bc}^{0}}}}{{\rightarrow }}{{{{\varLambda}^+_c}}}{{{{\pi}^-}}}}}}} $ ( $ {{{{{{{{\varXi}_{bc}^{0}}}}{{\rightarrow }}{{{{\varLambda}^+_c}}}{{{{\pi}^-}}}}}}} $) decay, and from $ 1.4\times10^{-3} $ to $ 6.9\times10^{-3} $ for the $ {{{{{{{{\varOmega}_{bc}^{0}}}}{{\rightarrow }}{{{{\varXi}^+_c}}}{{{{\pi}^-}}}}}}} $ ( $ {{{{{{{{\varXi}_{bc}^{0}}}}{{\rightarrow }}{{{{\varXi}^+_c}}}{{{{\pi}^-}}}}}}} $) decay, depending on the considered mass and lifetime of the $ {{{{\varOmega}_{bc}^{0}}}} $ ( $ {{{{\varXi}_{bc}^{0}}}} $) baryon.
A symmetry-preserving truncation of the strong-interaction bound-state equations is used to calculate the spectrum of ground-state J=1/2 + , 3/2 + (qq'q")-baryons, where q,q',q"ϵ{u,d,s,c,b}, their first positive-parity excitations and parity partners. Using two parameters, a description of the known spectrum of 39 such states is obtained, with a mean-absolute-relative-difference between calculation and experiment of 3.6(2.7)%. From this foundation, the framework is subsequently used to predict the masses of 90 states not yet seen empirically.
In this paper, the baryonic wave function has been obtained with the Cornell potential, a combination of linear and Coulomb terms, using the hyper-radial Schrödinger equation and an improved variational method while on the other hand, hyperfine interactions are considered, including smeared standard hyperfine term, isospin dependent and spin–isospin dependent terms in order to improve the results. Then, the baryonic Isgur–Wise function in hyperspherical coordinates has been investigated employing both mentioned wave functions. Finally, in particular, the charged radius and the decay width of transition have been reported for both methods and compared with those obtained in experiments or theories.
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We compute the mass, radius and tidal deformability of stars containing phase transitions from hadronic to quark phase(s). These quantities are computed for three types of hadronic envelopes: purely nuclear, hyperonic, and Δ-resonance--hyperon admixed matter. We consider either a single first-order phase transition to a quark phase with a maximally stiff equation of state (EOS) or two sequential first-order phase transitions mimicking a transition from hadronic to a quark matter phase followed by a second phase transition to another quark phase. We explore the parameter space which produces low-mass twin and triplet configurations where equal-mass stars have substantially different radii and tidal deformabilities. We demonstrate that while for purely hadronic stiff EOS the obtained maximum mass is inconsistent with the upper limit on this quantity placed by GW170817, the inclusion of the hyperonic and Δ-resonance degrees of freedom, as well as the deconfinement phase transition at sufficiently low density, produces a configuration of stars consistent with this limit. The obtained hybrid star configurations are in the mass range relevant for the interpretation of the GW170817 event. We compare our results for the tidal deformability with the limits inferred from GW170817 showing that the onset of non-nucleonic phases, such as Δ-resonance--hyperon admixed phase and/or the quark phase(s), are favored by this data if the nuclear EOS is stiff. Also, we show that low-mass twins and especially triplets proliferate the number of combinations of possible types of stars that can undergo a merger event, the maximal number being six in the case of triplets. The prospects for uncovering the first-order phase transition(s) to and in quark matter via measurements of tidal deformabilities in merger events are discussed.
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Heavy-quark symmetry implies stable heavy tetraquark mesons $Q_iQ_j\overline{q}_k\overline{q}_l$ In the limit of very heavy quarks Q, novel narrow doubly heavy tetraquark states (DHTQ) must exist. HQS relates DHTQ mass to masses of a doubly heavy baryon, heavy-light baryon, and heavy-light meson. The lightest double-beauty states composed of $bb \overline{u} \overline{d}$, $bb \overline{u}\overline{s}$, and $bb \overline{d} \overline{s}$ will likely be stable against strong decays. Heavier $bb\overline{q}_k \overline{q}_l$ states, $cc \overline{q}_k \overline{q}_l$ states, and mixed $bc \overline{q}_k \overline{q}_l$ states, will likely dissociate into pairs of heavy-light mesons. Some might be seen as \double- avor" resonances near threshold. Observing a weakly decaying double-beauty state would establish the existence of tetraquarks and illuminate the role of heavy color-$\overline{3}$ diquarks as hadron constituents.
Double-heavy hadrons can decay into pairs of heavy hadrons through transitions from confining Born-Oppenheimer potentials to heavy-hadron-pair potentials with the same Born-Oppenheimer quantum numbers. The states of the double-heavy hadron are constrained by a Born-Oppenheimer exclusion principle from the identical heavy quarks. The states of a pair of identical heavy hadrons are constrained by exclusion principles from identical particles. The transitions are also constrained by conservation of angular momentum and parity. From these constraints, we derive model-independent selection rules for decays of double-heavy hadrons into pairs of heavy hadrons. The coupling potentials are expressed as sums of products of Born-Oppenheimer transition amplitudes and angular-momentum coefficients. If there is a single dominant Born-Oppenheimer transition amplitude, it factors out of the coupling potentials between double-heavy hadrons in the same Born-Oppenheimer multiplet and pairs of heavy hadrons in specific heavy-quark-spin-symmetry multiplets and out of the corresponding partial decay rates. As examples, we discuss the Born-Oppenheimer potentials and multiplets for conventional double-heavy baryons and for double-heavy tetraquark mesons. We also discuss the relative partial decay rates for conventional double-heavy baryons into pairs of heavy hadrons.
Heavy-quark symmetry implies stable heavy tetraquark mesons $Q_{i}Q_{j}\overline{q}_{k}\overline{q}_{l}$. in the limit of very heavy quarks Q, novel narrow double heavy tetraquark state (DHTQ) must exist. HQS relates DHTQ mass to masses of a doubly heavy baryon, heavy-light baron, and heavy-light meson. The lightest double-beauty states composed of $bb\overline{ud}$, $bb\overline{us}$, and $bb\overline{ds}$ will likely be stable against strong decays. Heavier $bb\overline{q}_{k}\overline{q}_{l}$ states, $cc\overline{q}_{k}\overline{q}_{l}$ states, and mixed $bc{q}_{k}\overline{q}_{l}$ states, will likely dissociate into pairs of heavy-light mesons. Some might be seen as "double-flavor" resonances near threshold. Observing a weakly decaying double-beauty state would establish the existence of tetraquarks and illuminate the role of heavy color-$\overline{3}$ diquarks as hadron constituents.
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A precise measurement of the differential cross sections dσ/dΩ and the linearly polarized photon beam asymmetry Σ 3 for Compton scattering on the proton below pion threshold has been performed with a tagged photon beam and almost 4π detector at the Mainz Microtron. The incident photons were produced by the recently upgraded Glasgow-Mainz photon tagging facility and impinged on a cryogenic liquid hydrogen target, with the scattered photons detected in the Crystal Ball/TAPS setup. Using the highest statistics Compton scattering data ever measured on the proton along with two effective field theories (both covariant baryon and heavy-baryon) and one fixed-t dispersion relation model, constraining the fits with the Baldin sum rule, we have obtained the proton electric and magnetic polarizabilities with unprecedented precision: α E1 = 10.99 ± 0.16 ± 0.47 ± 0.17 ± 0.34, β M1 = 3.14 ± 0.21 ± 0.24 ± 0.20 ± 0.35; in units of 10 -4 fm 3 where the errors are statistical, systematic, spin polarizability dependent, and model dependent.
We use a symmetry-preserving truncation of meson and baryon bound-state equations in quantum field theory in order to develop a unified description of systems constituted from light and heavy quarks. In particular, we compute the spectrum and leptonic decay constants of ground-state pseudoscalar and vector mesons: q'(q) over bar, Q'(Q) over bar, with q', q = u, d, s and Q', Q = c, b, and the masses of J P = 3/2 + baryons and their first positive-parity excitations, including those containing one or more heavy quarks. This Poincare covariant analysis predicts that such baryons have a complicated angular momentum structure. For instance, the ground states are all primarily S wave in character, but each possesses P -, D - and F -wave components, with the P -wave fraction being large in the qqq states, and the first positive-parity excitation in each channel having a large D -wave component, which grows with increasing current-quark mass, but also exhibits features consistent with a radial excitation. In conclusion, the configuration space extent of all such baryons decreases as the mass of the valence-quark constituents increases.
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