Scattering of particles with spin in lattice QCD

Skerbiš, Urša (author), Prelovšek, Saša (mentor)

Quantum chromodynamics (QCD) is an area of particle physics investigating strong interaction and its phenomena. Perturbative QCD works very well at energies above 1 GeV. At energies below 1 GeV $\alpha_s$ is not much smaller than one and one cannot use perturbative treatment. In this energy region, a nonperturbative approach, including Lattice quantum chromodynamics (Lattice QCD), should be used. Most of the hadrons are hadronic resonances, and they can decay under strong interaction. Strong decays of the resonances can be studied through the scattering of hadrons on the lattice. Recent experiments have discovered multiple hadronic resonances with exotic quark structures - tetraquarks and pentaquarks. The scattering of hadrons and hadron spectroscopy is an area of Lattice QCD that we explore in this thesis. Hadronic resonances can decay into pairs of hadrons with or without spin. In order to study a scattering of two hadrons with spin one needs operators that create/annihilate two particles with spin in the desired quantum channel. Two hadron operators are used to extract the eigenenergies of the lattice. We construct operators for simulating the scattering of two hadrons with spin on the lattice. Three methods are shown to give consistent operators. Explicit expressions for operators are given for all irreducible representations. The total momentum of two hadrons is restricted to zero, since parity is a good quantum number in this case. We review the derivation of the relation between the scattering amplitude for twohadron scattering and eigenenergies from the lattice simulation originally proposed by Lüscher. The Lüscher relation is derived for the scattering of particles without spin from the point of view of QFT. Relation is later generalized for the system with nonzero spin. We predict eigenenergies for the scattering of the nucleon and $J/\psi$ meson if experimental $P_c$ resonance is coupled only to this channel. We perform the Lattice QCD simulation of $NJ/\psi$ and $N\eta_c$ scattering at $m_{\pi} \approx$266MeV in channels with all possible $J^P$. This presents the frst simulation at 4,1 - 4,5 GeV energies where pentaquarks reside. We explore the fate of $P_c$ in the one-channel approximation. The energies of eigenstates are extracted for the nucleon-charmonium system at zero total momentum for all quantum numbers, i.e. six lattice irreducible representations. No significant energy shifts are observed. The number of observed lattice eigenstates agrees with the number of states expected for noninteracting charmonium and nucleon. Our lattice data suggest that the hidden charm pentaquark $P_c$ is not coupled only to one channel (the $J/\psi$N or $\eta_cN$), but is probably a consequence of coupled channels effects or significant interaction in other channels (i.e. charmed meson and charmed baryon).

• Language: English
• Keywords: LQCD, hadrons, spectroscopy, scattering with spin, elastic scattering, operators, pentaquark
• Work type: Doctoral dissertation
• Typology: 2.08 - Doctoral Dissertation
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2021
• PID: 20.500.12556/RUL-126934
• COBISS.SI-ID: 54316547
• Publication date in RUL: 11.05.2021

Secondary language

• Language: Slovenian
• Title: Sipanje delcev s spinom v kromodinamiki na mreži

Abstract

Kvantna kromodinamika (QCD) je področje fizike osnovnih delcev, ki opisuje močno interakcijo ter njene pojave. Perturbativna QCD deluje odlično za energije večje od 1 GeV, kjer je sklopitvena konstanta αs veliko manjša od ena. Pri nižjih energijah perturbativnega razvoja ne moremo uporabiti in zato potrebujemo neperturbativne pristope k reševanju. Eden izmed mogočih pristopov je kvantna kromodinamika na mreži (LQCD). Hadroni so večinoma resonance, ki lahko razpadajo preko močne interakcije. Na mreži močne razpade raziskujemo kot sipanje hadronov. V preteklih letih so eksperimenti odkrili veliko eksotičnih hadronov (tetra- in penta-kvarkov). Sipanje hadronov in hadronska spektroskopija sta prodročji kvantne kromodinamike na mreži (LQCD), ki ju raziskujemo v tej tezi. Hadronske resonance lahko razpadejo v pare hadronov s spinom ali brez njega. Za raziskovanje sipanja dveh hadronov potrebujemo operatorje, ki kreirajo in anihilirajo ustrezno dvohadronsko stanje. Dvohadronske operatorje uporabimo v simulacijah na mreži. V tej tezi na tri načine izračunamo dvohadronske operatorje za sipanje delcev s spinom. Vse tri metode za izračun dajo konsistentne rezultate, kar tudi pokažemo. Navedemo operatorje s skupno gibalno količino nič za sipanje v vseh nerazcepnih upodobitvah oktahedralne grupe $O^{(2)}_h$. Izračunani operatorji so omejeni na primere s skupno gibalno količino nič, saj je za tak primer parnost dobro kvantno število. Povzamemo izpeljavo povezave med dvo-hadronsko sipalno amplitudo in lastnimi energijami izračunanimi na mreži, ki jo je originalno izpeljal Lüscher. Z uporabo kvantne teorije polja izračunamo povezavo za sipanje delcev brez spina ter jo nato posplošimo na primer za sipanje delcev s spinom. Izpeljano povezavo uporabimo za napoved lastnih energij sistema $N - J/\psi$ za primer, ko je resonanca $P_c$ sklopljena le s tem sipalnim kanalom. Na mreži s pionsko maso $m_{\pi}\approx$266MeV simuliramo sipanje nukleona in mezona $J/\psi$ ter nukleona in mezona $\eta_c$. Simuliramo sipanje z vsemi mogočimi vrtilnimi količinali $J^P$ v vseh nerazcepnih upodobitvah oktahedralne grupe. Prvi opravimo simulacije na energijskemu območju pentakvarkov $P_c$. $P_c$ raziskujemo v eno-kanalnemu približku. Iz sistema s skupno gibalno količino nič izluščimo energije lastnih stanj v vseh šestih nerazcepnih upodobitvah. Ne opazimo nobenega energijskega premika, število opaženih stanj se ujema s številom, ki ga predvideva neinteragirajoča limita za sipanje nukleona in čarmonija. Najverjetnejša razlaga naših rezultatov je, da pentakvark $P_c$ ni sklopljen le na en sipalni kanal ($J/\psi - N$ ali $\eta_c - N$), ampak je verjetno posledica sklopljenega sipanja ali občutne interakcije v drugih kanalih (npr. čaroben mezon in čaroben barijon).

• Keywords: kvantna kromodinamika na mreži, hadroni, spektroskopija, sipanje s spinom, elastično sipanje, pentakvark