Renormalization and Observables in the Standard Model and Beyond in Higher Orders of Perturbation Theory

doctoral thesis

• Title (croatian): Renormalizacija i opservable u standardnom modelu i izvan njega u višim redovima računa smetnje
• Author: Marija Mađor-Božinović
• Mentor: Amon Ilakovac (mentor)
• Committee member: Kornelija Passek-Kumerički (predsjednik povjerenstva)
• Committee member: Amon Ilakovac (član povjerenstva)
• Committee member: Ivica Friščić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2022-06-14, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics
• Universal decimal classification (UDC): 53 - Physics

Abstract

We study the application of the Breitenlohner–Maison–’t Hooft–Veltman (BMHV) scheme of Dimensional Regularization to the renormalization of massless chiral gauge theories; chiral Yang-Mills theory, and chiral Quantum Electrodynamics, being the main ingredients of the Standard Model, up to one and two-loop level, respectively. We focus on the counterterm structure specific to the BHMV scheme induced by the non-anticommuting Dirac γ_5 matrix and the breaking of the Becchi-Rouet-Stora-Tyutin (BRST) invariance. We find the singular counterterms and BRST symmetry restoring counterterms needed for the complete renormalization of the models. This study is based on the symmetry requirements coming from the Algebraic Renormalization and regularized Quantum Action Principle. We find the Renormalization Group Equations for the Yang-Mills model at the first order within this framework and compare the procedure with standard symmetry-invariant regularizations. For chiral Quantum Electrodynamics, we determine the full structure of symmetry-restoring counterterms up to the 2-loop level and find no discrepancy from the 1-loop level structures. The counterterms have interpretation in terms of restoration of Ward identities that play the role of the benchmark for this 2-loop study. Hence, we prove the correctness of results within this framework, what is the property of a self-consistent scheme. We impose future proposals for the application of the BMHV scheme to phenomenological studies.

Abstract (croatian)

Standardni model fizike elementarnih cestica toliko uspješno objašnjava strukturu materije da je već gotovo desetljećima duboko u tzv. eri preciznosti. Mjerljive opservable precizno se procjenjuju na temelju obrade sada već otprilike dvjesto petabajta dostupnih podataka iz velikih svjetskih sudarivača cestica. Preciznost koja se stalno povećava zahtijeva teorijski dobro postavljene proračune mjerljivih opservabli u visokim redovima računa smetnje. Teorijski izračuni ovih preciznih opservabli u velikoj su mjeri provedeni u dimenzionalnoj regularizaciji (DReg), regularizacijskoj shemi koja je dovela do revolucije u proračunima na visokim redovima. DReg čuva simetrije vektorskih teorija, uključujući Lorentzovu kovarijantnost, baždarnu i BRST invarijantnost i translacijske simetrije. Kada se primjeni na vektorski model, ova shema divergencije proizašle iz računa dijagrama s petljama izolira kao polove koje je moguće otkloniti uvođenjem lokalnih kontraclanova. Zbog svoje teorijske konzistentnosti, praktičnosti i korisnih svojstava dosegla je široku upotrebu u računima i implementirana u računalne kodove koji djelomično automatiziraju račune u višim redovima. ...

• Keywords: anomalies in field theories; BRST symmetry; gauge symmetry; renormalization; perturbation theory; algebraic renormalization; BMHV scheme; chiral theory; Yang-Mills model; quantum electrodynamics; Slavnov-Taylor identities; Ward identities; standard model
• Keywords (croatian): anomalije u teoriji polja; BRST simetrija; baždarna simetrija; renormalizacija; perturbacijska teorija; algebarska renormalizacija; BMHV shema; kiralna teorija; Yang-Millsov model; kvantna elektrodinamika; Slavnov-Taylorovi identiteti; Wardovi identitieti; standardni model
• Language: english
• URN:NBN: urn:nbn:hr:217:427566
• Promotion: 2022
• Study programme: Title: Physics; Study programme type: university; Study level: postgraduate; Academic / professional title: doktor/doktorica znanosti, područje prirodnih znanosti, polje fizika (doktor/doktorica znanosti, područje prirodnih znanosti, polje fizika)
• Type of resource: Text
• Extent: 161 str,
• File origin: Born digital
• Access conditions: Open access
• Created on: 2022-07-04 11:46:10