Exotic hadrons with heavy quark and antiquark in lattice QCD

Šadl, Mitja (author), Prelovšek, Saša (mentor)

In the past two decades, experiments have revealed a rich hadronic spectrum, including exotic states that cannot be easily explained by the quark model. Studying these states requires non-perturbative methods. In this thesis, we employ lattice QCD, the only reliable first-principles approach for examining the non-perturbative aspects of QCD. We perform two lattice studies of exotic hadrons with a heavy $\bar{Q}Q$ pair, specifically charmonium-like ($\bar cc \bar qq$) and bottomonium-like ($\bar bb \bar qq$) tetraquarks with $I=1$, where numerous decay channels pose the biggest challenge. The most notable examples of these tetraquarks observed in experiments are the $Z_c$ ($\bar cc \bar qq$) and $Z_b$ ($\bar bb \bar qq$) states. In the study of charmonium-like states, we extract finite-volume spectra for states with $J^{PC}=1^{+\pm}$. This is the first simulation of these channels employing more than one volume and frames with nonzero total momentum. The resulting eigenenergies are compatible or just slightly shifted down with respect to non-interacting meson-meson energies. We extract the scattering amplitudes for $1^{+\pm}$, where both channels contain a virtual pole slightly below the threshold if $D\bar D^*$ is assumed to be decoupled from other channels. We also perform a coupled channel analysis of $J/\psi \pi$ and $D\bar D^*$ scattering with $1^{+-}$ within an effective field theory framework. The $J/\psi \pi$ and $D\bar D^*$ line shapes and eigenenergies from several lattice QCD simulations, including ours, are fitted simultaneously. Our findings suggest that the employed effective field theory can reasonably reconcile the peaks in the experimental line shapes and the lattice energies, although those lie close to non-interacting energies. The lattice study of the $\bar bb\bar qq$ systems employs static bottom quarks. Previous studies reveal that the potential between $B$ and $\bar{B}^*$ in the channel that couples to $\Upsilon\pi$ is very attractive. Our simulation considers three complementary channels for the first time. Spectra of the $\bar bb \bar qq$ system are extracted as a function of separation between $b$ and $\bar b$. The eigenenergies do not show sizable deviation from the $\bar bb+\bar qq$ and $\bar bq+\bar qb$ non-interacting energies. The resulting $B\bar{B}^*$ potential related to the channel coupled to $\eta_b\rho$ is not attractive, except slightly at small separation. The two mentioned potentials suggest that the linear combination of both may cause the existence of $Z_b$.

• Language: English
• Keywords: quantum chromodynamics on the lattice, hadron spectroscopy, hadron, exotic meson, tetraquark, meson molecule, heavy quarks, resonance, scattering
• Work type: Doctoral dissertation
• Typology: 2.08 - Doctoral Dissertation
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2024
• PID: 20.500.12556/RUL-162860
• COBISS.SI-ID: 209950211
• Publication date in RUL: 28.09.2024

Secondary language

• Language: Slovenian
• Title: Eksotični hadroni s težkim kvarkom in antikvarkom v kvantni kromodinamiki na mreži

Abstract

V zadnjih dveh desetletjih smo priča mnogim eksperimentalnim odkritjem novih hadronov, vključno z eksotičnimi, ki jih ne moremo preprosto opisati s kvarkovskim modelom. Raziskovanje teh stanj zahteva neperturbativne metode. V tej doktorski disertaciji uporabimo edino zanesljivo metodo preiskovanja hadronov, ki temelji na osnovni teoriji: kvantno kromodinamiko na mreži. Opisani sta dve študiji eksotičnih hadronov s težkim kvarkom in antikvarkom ($\bar{Q}Q$), natančneje, čarmoniju ($\bar cc \bar qq$) in botomoniju ($\bar bb \bar qq$) podobnih tetrakvarkov z izospinom 1. Največji izziv predstavlja množica njihovih razpadnih kanalov. Najpomembnejši primeri teh tetrakvarkov, opaženih v poskusih, so stanja $Z_c$ ($\bar cc \bar qq$) in $Z_b$ ($\bar bb \bar qq$). V delu, ki je posvečen čarmoniju podobnim stanjem, izluščimo lastne energije v končnem volumnu za stanja z $J^{PC}=1^{+\pm}$. Gre za prvo simulacijo teh kanalov, ki je izvedena na več kot enem volumnu in vključuje tudi sistem z neničelno skupno gibalno količino. Dobljene lastne energije so enake ali kvečjemu malo manjše kot neinteragirajoče energije dveh mezonov. Za oba kanala $1^{+\pm}$ iz energij določimo sipalni amplitudi, ki vsebujeta virtualni pol tik pod pragom $D\bar D^*$. Pri tem predpostavimo, da je sipanje $D\bar D^*$ razklopljeno od ostalih kanalov. V okviru efektivne teorije polja analiziramo tudi sklopljeno sipanje kanalov $J/\psi \pi$ in $D\bar D^*$ z $1^{+-}$. Sočasno prilagajamo parametre, ki opisujejo eksperimentalni porazdelitvi invariantnih mas za $J/\psi \pi$ in $D\bar D^*$ ter lastne energije več simulacij na mreži, vključno z našo. Rezultati nakazujejo, da lahko uporabljena efektivna teorija polja hkrati opiše vrhove eksperimentalnih porazdelitev dogodkov in energije iz mreže, čeprav te ležijo blizu neinteragirajočih nivojev. V študiji sistema $\bar bb\bar qq$ uporabimo statična kvarka $b$ in $\bar{b}$. Raziskave so pokazale, da je potencial med $B$ in $\bar{B}^*$ v kanalu, ki se sklaplja na $\Upsilon\pi$, zelo privlačen. Naša simulacija obravnava tri komplementarne kanale. Spektre sistema $\bar bb \bar qq$ določimo kot funkcijo razdalje med $b$ in $\bar b$. Lastne energije ne pokažejo velikih odstopanj od neinteragirajočih energij $\bar bb+\bar qq$ in $\bar bq+\bar qb$. Dobljeni potencial med $B$ in $\bar{B}^*$ je za kanal, ki se sklaplja na $\eta_b\rho$, minimalno privlačen pri majhnih razdaljah in neprivlačen drugod. Iz obeh omenjenih potencialov sklepamo, da je obstoj stanja $Z_b$ posledica linearne kombinacije obeh potencialov.

• Keywords: kvantna kromodinamika na mreži, spektroskopija hadronov, hadron, eksotičen mezon, tetrakvark, molekula mezonov, težki kvarki, resonanca, sipanje