The equivalent photon approximation in one- and two-photon exchange processes
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2022Copyright
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Tässä opinnäytetyössä johdetaan ekvivalentti fotoniapproksimaatio ja siihen liittyvä ekvivalentti fotonijakauma yhden ja kahden fotonivaihdon prosesseissa helisiteettipohjaista menetelmää käyttäen kvanttikenttäteorian viitekehyksessä. Johtamiset esitetään yksityiskohtaisemmin kuin kirjallisuudessa yleensä. Fotonijakaumien yleisiä muotoja tarkastellaan spin-0- ja spin-1/2-hiukkasille käyttäen kvantti- ja skalaarikvanttisähködynamiikan yleisiä verteksirakenteita. Kolme protonin dipolimuototekijöihin perustuvaa fotonijakaumaa johdetaan ja niitä sovelletaan myoniparituottoon protoni-protoni-törmäyksissä. Ekvivalentin fotoniapproksimaation avulla saatua myoniparin invarianttia massaspektriä verrataan saman observaabelin tarkkaan laskuun kokonaismassakeskipiste-energioilla √s = 200 GeV ja √s = 13 TeV. Tarkka lasku lasketaan ilman approksimaatioita johtavaan kertalukuun ja sitä integroidaan numeerisesti Monte-Carlo-menetelmin, ja sen nähdään vastaavan hyvin ATLAS-kokeessa saatuja tuloksia. Tulosten perusteella jakauma, jossa sekä protonin massa että sen anomaalinen magneettinen momentti on jätetty huomiotta, on tarkempi kuin jakauma, jossa vain protonin anomaalinen magneettinen momentti on jätetty huomiotta. Tulokset osoittavat myös, että sekä protonin massan että sen anomaalisen magneettisen momentin huomioiva jakauma yliarvio tarkkaa laskua alle 4 %, tarjoten siten erinomaisen approksimaation invariantin massaspektrin laskemiseen myoniparituotossa molemmilla energioilla.
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In this thesis, the equivalent photon approximation and the associated equivalent photon distribution are derived in one- and two-photon exchange processes using a helicity-based method in the framework of quantum field theory. The derivations are presented in more detail than is usually found in the literature. The general forms of the photon distributions for spin-0 and spin-1/2 particles are examined using the general vertex structure of quantum electrodynamics and scalar quantum electrodynamics. A total of three photon distributions based on the dipole form factors of the proton are derived and applied to muon-pair production in proton-proton collisions. The invariant-mass spectrum of the muon pair obtained using the equivalent photon approximation is compared to a full calculation of the same observable at total center-of-mass energies √s = 200 GeV and √s = 13 TeV. The full calculation is obtained at leading order without any approximations and numerically integrated using Monte-Carlo methods, and is found to be in good agreement with an experimental measurement by ATLAS. The results show that the distribution neglecting both the mass and the anomalous magnetic moment of the proton gives more accurate results than the distribution neglecting only the anomalous magnetic moment of the proton. The results also indicate that the distribution including both the mass and the anomalous magnetic moment of the proton overestimates the full calculation by less than 4 %, thus providing an excellent approximation to the calculation of the invariant-mass spectrum in the muon-pair production process at both energies.
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