Heavy quarkonia in non-relativistic quantum chromodynamics
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2019Copyright
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Quarkonium-hiukkaset ovat saman makulajin kvarkki-antikvarkkiparista muodostuvia sidottuja tiloja. Tässä työssä käydään läpi epärelativistiseksi kvanttiväridynamiikaksi kutsuttavaa efektiivistä kenttäteoriaa, jota voidaan käyttää raskaiden kvarkkien muodostamien quarkonium-hiukkasten kuvaamiseen. Teoriaa kuvaava Lagrangen funktio johdetaan alimmissa kertaluvuissa, ja sitä käytetään johtamaan eri operaattorien skaalautuminen kvarkin nopeuden suhteen. Skaalaussääntöjen avulla johdetaan tämän jälkeen arviot eri Fock-tilojen suuruuksille quarkoniumissa.
Orbitaalista kvanttilukua L=0 vastaavien quarkonium-hiukkasten hajoamisleveydet kirjoitetaan potenssisarjana kvarkin nopeuden suhteen. Hajoamisleveyksien yhtälöissä esiintyy tuntemattomia vakioita, jotka esiintyvät myös quarkoniumin inklusiivisen tuoton vaikutusaloissa. Näiden tuntemattomien vakioiden yhteys quarkoniumin aaltofunktioon käydään myös läpi.
Hajoamisleveyksien lausekkeista saatavia arvoja tutkitaan eri kertaluvuissa kvarkin nopeuden suhteen. Havaitaan, että potenssisarjan suppeneminen on hidasta ja riippuu hajoamisprosessista.
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Quarkonia are bound states of a quark-antiquark pair having the same flavour. In this work, we go through how the effective field theory of non-relativistic quantum chromodynamics (NRQCD) can be used to describe quarkonia formed by heavy quarks. The Lagrangian describing the theory is derived at lowest orders and used to determine the velocity-scaling of different operators. The velocity-scaling rules are then used to estimate contributions of different Fock states in quarkonia.
We then describe the decay of S-wave quarkonia by writing the decay widths as power series in the velocity of the quark. The equations for the decay widths contain unknown constants that also appear in the inclusive cross sections of quarkonium production, and their connection to the quarkonium wave function is also shown.
The results for the decay widths at different orders of the quark velocity are studied. It is found that the convergence of the power series is slow, with the convergence depending on the decay process.
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