Summary
The question of whether the masses of fermions and vector mesons can be generated by the spontaneous breakdown of gauge symmetries in field theories without scalar mesons is discussed. Working with the models proposed by Cornwall-Norton and Jackiw-Johnson, we are able to demonstrate that the dynamical generation of masses is a viable possibility in such theories. We calculate the vector-mesonfermion mass ratio by using nonperturbative and nonasymptotic solutions to the Dyson-Schwinger equations, in terms of the coupling constants of the field theories. Our results are true modulo renormalization and complications stemming from the axial vector anomaly.
Riassunto
Si discute se le masse dei fermioni e dei mesoni vettoriali si possano generare dalla violazione spontanea delle simmetrie di gauge nelle teorie di campo senza mesoni scalari. Utilizzando i modelli proposti da Cornwall-Norton e Jackiw-Johnson, si può dimostrare che la generazione dinamica delle masse è una valida possibilità in queste teorie. Si calcola il rapporto fra la massa del mesone vettoriale e quella del fermione usando le soluzioni non perturbative e non asintotiche delle equazioni di Dyson-Schwinger in termini delle costanti di accoppiamento delle teorie di campo. I risultati sono la rinormalizzazione esatta in modulo e alcune complicazioni derivanti dall'anomalia assiale vettoriale.
Резюме
Обсуждается вопрос, могут ли массы фермионов и векторных мезонов быть образованы в результате спонтанного нарушения калибровочных симметрий в теориях поля без скалярных мезонов. Используя модели, предложенные Корнволом-Нортоном и Джакивом-Джонсоном, мы можем показать, что динамическое образование масс является возможным в таких теориях. Мы вычисляем отношение масс векторного мезона и фермиона, используя непертурбационные и неасимптотические решения уравнений Дайсона-Швингера, в терминах постоянных связей полевых теорий. Полученные результаты представляют значение модуля перенормировки и осложнения, происходящие из аксиально-векторной аномалии.
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Work supported, in part, by Arizona State University Faculty Grant-in-Aid.
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Acharya, R., Narayanaswamy, P. & Nigam, B.P. Spontaneous breakdown of gauge symmetries sans scalar mesons. Nuov Cim A 65, 125–146 (1981). https://doi.org/10.1007/BF02902133
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DOI: https://doi.org/10.1007/BF02902133