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The theoretical and experimental investigation of exotic hadrons like tetraquarks is an important branch of modern elementary particle physics. In this thesis I investigate different four-quark systems using lattice QCD and search for evidence of stable tetraquark states or resonances.
Lattice QCD as a non-perturbative approach to QCD allows an accurate and reliable determination of the masses of strongly bound hadrons.
However, most tetraquarks appear as weakly bound states or resonances, which makes a theoretical investigation using lattice QCD difficult due to the finite spatial volume. A rigorous treatment of such systems is feasible using the so-called Lüscher method. This allows to calculate the scattering amplitude based on the finite-volume energy spectrum determined in a lattice QCD calculation. Similarly to the analysis of experimental data, this scattering amplitude can be used to determine the binding energies of bound states or the masses and decay widths of resonances in the infinite volume.
In my work I calculate the low-energy energy spectra of different four-quark systems and use - if necessary - the Lüscher method to determine the masses of potential tetraquark states.
I focus on systems consisting of two heavy antiquarks and two light quarks, where at least one of the heavy antiquarks is a bottom quark.
Even though such tetraquarks have not yet been experimentally detected, they are considered promising candidates for particles that are stable with respect to the strong interaction.
A decisive step for successfully calculating low-lying energy levels for such four-quark systems is a carefully chosen set of creation operators, which represent the physical states most accurately. In addition to operators that generate a local structure where all four quarks are located at the same space-time point, I also use so-called scattering operators that resemble two spatially separated mesons. These scattering operators turned out to be relevant for successfully determining the lowest energy levels and are therefore essential, especially if a Lüscher analysis is carried out.
In my work, I considered two different lattice setups to study the four-quark systems $\bar{b}\bar{b}ud$ with $I(J^P)=0(1^+) $, $\bar{b}\bar{b}us$ with $J^P=1^+ $ and $\bar{b}\bar{c}ud$ with $I(J^P)=0(0^+) $ and $I(J^P)=0(1^+) $ and to predict potential tetraquark states. In both setups, I considered scattering operators. While in the first setup I used them only as annihilation operators, in the second setup they were included both as creation and annihilation operators. Additionally, in the second lattice setup, I performed a simplified investigation of the $\bar{b}\bar{b}ud$ system with $I(J^P)=0(1^-) $, which is a potential candidate for a tetraquark resonance. The results of the investigation of the mentioned four-quark systems can be summarized as follows:
For the $ \bar{b}\bar{b}ud $ four-quark system with $ I(J^P)=0(1^+) $ I found a deeply bound ground state slightly more than $ 100\,\textrm{MeV} $ below the lowest meson-meson threshold. The existence of a corresponding $\bar{b}\bar{b}ud$ tetraquark in the infinite volume was confirmed using a Lüscher analysis and possible systematic errors due to the use of lattice QCD were taken into account.
Similar results were obtained for the $ \bar{b}\bar{b}us $ four-quark system with $ J^P=1^+ $. Again, I found a ground state well below the lowest meson-meson threshold, but slightly weaker bound than for the $ \bar{b}\bar{b}ud $ system. Effects due to the finite volume turned out to be negligible for this system, as already predicted for the $ \bar{b}\bar{b}ud $ system. \item For the $ \bar{b}\bar{c}ud $ four-quark systems with $ (J^P)=0(0^+) $ and $ (J^P)=0(1^+) $ I was able to rule out the existence of a deeply bound tetraquark states based on the energy spectrum in the finite volume. However, by means of a scattering analysis using the Lüscher method, I found evidence a broad resonance for both channels.
In the case of the $ \bar{b}\bar{b}ud $ four-quark system with $ I(J^P)=0(1^-) $, I could neither confirm the existence of a resonance, nor rule out its existence with certainty.
In particular, my investigations showed that the results of the two different lattice simulations are consistent. The theoretical prediction of the bound tetraquark states $\bar{b}\bar{b}ud$ and $\bar{b}\bar{b}us$ as well as the tetraquark resonances in the $\bar{b}\bar{c}ud$ system in this work represent an important contribution to the future experimental search for exotic hadrons and can support the discovery of previously unobserved particles.
We search for an axion-like particle (ALP) a through the process ψ(3686)→π+π−J/ψ, J/ψ→γa, a→γγ in a data sample of (2.71±0.01)×109 ψ(3686) events collected by the BESIII detector. No significant ALP signal is observed over the expected background, and the upper limits on the branching fraction of the decay J/ψ→γa and the ALP-photon coupling constant gaγγ are set at 95% confidence level in the mass range of 0.165≤ma≤2.84GeV/c2. The limits on B(J/ψ→γa) range from 8.3×10−8 to 1.8×10−6 over the search region, and the constraints on the ALP-photon coupling are the most stringent to date for 0.165≤ma≤1.468GeV/c2.
Using data samples with an integrated luminosity of 22.42 fb−1 collected by the BESIII detector operating at the BEPCII storage ring, we measure the cross sections of the $e^{+}e^{-}\rightarrow\etaJ/\psi$ process at center-of-mass energies from 3.808 to 4.951 GeV. Three structures are observed in the line shape of the measured cross sections. A maximum-likelihood fit with ψ(4040), two additional resonances, and a non-resonant component is performed. The mass and width of the first additional state are (4219.7±2.5±4.5)MeV/c2 and (80.7±4.4±1.4)MeV, respectively, consistent with the ψ(4230). For the second state, the mass and width are (4386±13±17)MeV/c2 and (177±32±13)MeV, respectively, consistent with the ψ(4360). The first uncertainties are statistical and the second ones are systematic. The statistical significance of ψ(4040) is 8.0σ and those for ψ(4230) and ψ(4360) are more than 10.0σ.
Using a sample of (10087±44)×106 J/ψ events, which is about fifty times larger than that was previously analyzed, a further investigation on the J/ψ→γ3(π+π−) decay is performed. A significant distortion at 1.84 GeV/c2 in the line-shape of the 3(π+π−) invariant mass spectrum is observed for the first time, which is analogous to the behavior of X(1835) and could be resolved by two overlapping resonant structures, X(1840) and X(1880). The new state X(1880) is observed with a statistical significance of 14.7σ. The mass and width of X(1880) are determined to be 1882.1±1.7±0.7 MeV/c2 and 30.7±5.5±2.4 MeV, respectively, which indicates the existence of a pp¯ bound state.
Based on (10.09±0.04)×109 J/ψ events collected with the BESIII detector operating at the BEPCII collider, a partial wave analysis of the decay J/ψ→ϕπ0η is performed. We observe for the first time two new structures on the ϕη invariant mass distribution, with statistical significances of 24.0σ and 16.9σ; the first with JPC = 1+−, mass M = (1911 ± 6 (stat.) ± 14 (sys.))~MeV/c2, and width Γ= (149 ± 12 (stat.) ± 23 (sys.))~MeV, the second with JPC = 1−−, mass M = (1996 ± 11 (stat.) ± 30 (sys.))~MeV/c2, and width Γ = (148 ± 16 (stat.) ± 66 (sys.))~MeV. These measurements provide important input for the strangeonium spectrum. In addition, the f0(980)−a0(980)0 mixing signal in J/ψ→ϕf0(980)→ϕa0(980)0 and the corresponding electromagnetic decay J/ψ→ϕa0(980)0 are measured with improved precision, providing crucial information to understand the nature of a0(980)0 and f0(980).
Based on (10.09±0.04)×109 J/ψ events collected with the BESIII detector operating at the BEPCII collider, a partial wave analysis of the decay J/ψ→ϕπ0η is performed. We observe for the first time two new structures on the ϕη invariant mass distribution, with statistical significances of 24.0σ and 16.9σ; the first with JPC = 1+−, mass M = (1911 ± 6 (stat.) ± 14 (sys.))~MeV/c2, and width Γ= (149 ± 12 (stat.) ± 23 (sys.))~MeV, the second with JPC = 1−−, mass M = (1996 ± 11 (stat.) ± 30 (sys.))~MeV/c2, and width Γ = (148 ± 16 (stat.) ± 66 (sys.))~MeV. These measurements provide important input for the strangeonium spectrum. In addition, the f0(980)−a0(980)0 mixing signal in J/ψ→ϕf0(980)→ϕa0(980)0 and the corresponding electromagnetic decay J/ψ→ϕa0(980)0 are measured with improved precision, providing crucial information to understand the nature of a0(980)0 and f0(980).
Using 7.33 fb−1 of e+e− collision data collected by the BESIII detector at center-of-mass energies between 4.128 and 4.226~GeV, we observe for the first time the decay D±s→ωπ±η with a statistical significance of 7.6σ. The measured branching fraction of this decay is (0.54±0.12±0.04)%, where the first uncertainty is statistical and the second is systematic.
Evidence for the singly Cabibbo suppressed decay Λ+c→pπ0 is reported for the first time with a statistical significance of 3.7σ based on 6.0 fb−1 of e+e− collision data collected at center-of-mass energies between 4.600 and 4.843 GeV with the BESIII detector at the BEPCII collider. The absolute branching fraction of Λ+c→pπ0 is measured to be (1.56+0.72−0.58±0.20)×10−4, which distinctly exceeds the upper limit measured by Belle experiment. Combining with the branching fraction of Λ+c→nπ+, (6.6±1.3)×10−4, the ratio of the branching fractions of Λ+c→nπ+ and Λ+c→pπ0 is calculated to be 3.2+2.2−1.2. As an important input for the theoretical models describing the decay mechanisms of charmed baryons, our result indicates that the non-factorizable contributions play an essential role and their interference with the factorizable contributions should not be significant. In addition, the absolute branching fraction of Λ+c→pη is measured to be (1.63±0.31stat±0.11syst)×10−3, which is consistent with previous measurements.
Evidence for the singly Cabibbo suppressed decay Λ+c→pπ0 is reported for the first time with a statistical significance of 3.7σ based on 6.0 fb−1 of e+e− collision data collected at center-of-mass energies between 4.600 and 4.843 GeV with the BESIII detector at the BEPCII collider. The absolute branching fraction of Λ+c→pπ0 is measured to be (1.56+0.72−0.58±0.20)×10−4. Combining with the branching fraction of Λ+c→nπ+, (6.6±1.2±0.4)×10−4, the ratio of the branching fractions Λ+c→nπ+ and Λ+c→pπ0 is calculated to be 4.2+2.2−1.9; this is an important input for the understanding of the decay mechanisms of charmed baryons. In addition, the absolute branching fraction of Λ+c→pη is measured to be (1.63±0.31stat±0.11syst)×10−3, which is consistent with previous measurements.
Based on 4.5 fb−1 data taken at seven center-of-mass energies ranging from 4.600 to 4.699 GeV with the BESIII detector at the BEPCII collider, we measure the branching fractions of Λ + c → Σ + + hadrons relative to Λ + c → Σ +π +π −. Combining with the world average branching fraction of Λ + c → Σ +π +π −, their branching fractions are measured to be (0.377 ± 0.042 ± 0.020 ± 0.021)% for Λ + c → Σ +K+K−, (0.200 ± 0.023 ± 0.011 ± 0.011)% for Λ + c → Σ+K+π−, (0.414 ± 0.080 ± 0.030 ± 0.023)% for Λ + c → Σ +φ and (0.197 ± 0.036 ± 0.009 ± 0.011)% for Λ + c → Σ +K+K−(non-φ). In all the above results, the first uncertainties are statistical, the second are systematic and the third are from external input of the branching fraction of Λ + c → Σ +π +π −. Since no signal for Λ + c → Σ +K+π−π 0 is observed, the upper limit of its branching fraction is determined to be 0.13% at the 90% confidence level.