Summary
A possible explanation of the ψ-particles is presented in the context of Han-Nambu colour theory. The strong group is taken to beSU 3′×SU 3″ and it is proposed that there are vector mesons in the (1, 1), (8, 1), (1, 8) and (8, 8) representations. It is assumed that bothSU 3 subgroups break toSU 2×U 1, which implies a fourth ψ-particle coupled directly to the photon. A provisional parametrization on the basis of Okubo-type mass formulae suggests a mass for this particle about 4.8 GeV/c2. The theory also predicts charged coloured vector mesons ρ /+,− C,D with the same mass as ψ(3.1) and ψ(3.7) and coloured mesons K /*+,−,0 C,D with masses approximately 3.9 GeV/c2 and 4.5 GeV/c2. Coloured pseudoscalar mesons π C,D have decay properties similar toρ C,D. They do not couple directly to the photon but are accessible from ψ1,2 by radiative transitions and provide a possible explanation of the new state at 3.5 GeV/c2. We also develop in this framework a renormalizable theory of weak and electromagnetic interactions with hadronic currents with the necessary group-theoretic and observed hypercharge-changing properties. These requirements together with « universality » are sufficient to determine the theory almost uniquely. Its implications for coloured particles are examined and it is shown that the only long-lived coloured vector mesons is K /*+ C (orρ /+ C in the alternative version) with mean life about 10−13 s.
Riassunto
Si presenta una possibile spiegazione delle particelle ψ nel contesto della teoria del colore di Han-Nambu. Si suppone che il gruppo forte siaSU 3′ ×SU 3″ e si propone che ci siano mesoni vettoriali nelle rappresentazioni (1, 1), (8, 1), (1, 8) e (8, 8). Si suppone che entrambi i sottogruppi diSU 3 si dividano inSU 2 ×U 1, il che implica una quarta particella ψ accoppiata direttamente al fotone. Una parametriazzazione provvisoria sulla base di formule di massa del tipo di Okubo suggerisce per questa particella una massa di circa 4.8 GeV/c2. La teoria predice anche mesoni vettoriali colorati carichi ρ /+,− C,D con la stessa massa di ψ(3.1) e ψ(3.7) e mesoni colorati K /*+,−,0 C,D con masse approssimativamente di 3.9 GeV/c2 e 4.5 GeV/c2. I mesoni pseudoscalari colorati π C,D hanno proprietà di decadimento simili a quelle di ρ C,D . Essi non si accoppiano direttamente al fotone ma sono raggiungibili da ψ1,2 tramite transizioni radiative e forniscono una possibile spiegazione del nuovo stato a 3.5 GeV/c2. Si sviluppa anche in questo contesto una teoria rinormalizzabile delle interazioni deboli ed elettromagnetiche con le correnti adroniche con le necessarie proprietà di teoria dei gruppi e quelle osservate che cambiano l’ipercarica. Queste esigenze assieme all’« unitarietà » sono sufficienti a determinare la teoria quasi unicamente. Si esaminano le sue implicazioni per le particelle colorate e si mostra che il solo mesone vettoriale colorato a vita lunga è K /*+ C (oppure ρ /+ C in una versione alternativa) con una vita media di circa 10−13 s.
Реэюме
Предлагается воэможное общяснение ψ частиц в контексте цветной теории Хана-Намбу. Считается, что сильная группа представляетSU 3′×SU 3″ и что сушествуют векторные меэоны в представлениях (1,1), (8,1), (1, 8) и (8, 8). Предполагается, что обе подгруппыSU 3 нарущаются доSU 2×U 1, что подраэумевает непосредственную свяэь четвертой ψ частицы с фотоном. Исходя иэ предварительной параметриэации на основе массовой формулы типа формулы Окубо, считается, что масса зтой частицы составляет приблиэительно 4.8 ГзB/c2. Эта теория также предскаэывает эаряженные цветные векторные меэоны, ρ /+,− C,D , с теми же массами, что и ψ(3.1) и ψ(3.7), и цветные меэоны, K /*+,−,0 C,D с массами 3.9 ГзB/c2 и 4.5 ГзB/c2. Цветные псевдоскалярные меэоны π C,D распадаются аналогично ρ C,D . Они непосредственно не свяэаны с фотоном и могут быть обраэованы иэ ψ1,2 в реэультате радиационных переходов. Укаэанный процесс дает воэможное общяснение нового состояния при 3.5 ГзB/c2. В зтом подходе мы раэвиваем перенормируемую теорию слабых и злектромагнитных вэаимодействий с адронными токами, обладаюшими необходимыми свойствами теории групп и обнаруженными свойствами иэменения гиперэаряда. Эти требования вместе с « универсальностью » являются достаточными для почти одноэначного определения теории. Исследуются следствия зтого подхода к цветным частицам. Покаэывается, что единственный долгоживущий частицам. Покаэывается, что единственный долгоживуший цветной векторный меэон представляет K /*+ C (или ρ /+ C в альтернативном варианте) со средним временем жиэни около 10−13 сек.
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However, it is not inconceivable as pointed out byPati andSalam (12) that the correct strong-interaction group isSU 4×SU 8 (Han-Nambu), so that in this case we have not only coloured particles but also charmed particles which would be produced at even higher energies. In this case one expectsR to approach the asymptotic value of 6.
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Feldman, G., Matthews, P.T. A case for colour. Nuov Cim A 31, 447–486 (1976). https://doi.org/10.1007/BF02734266
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DOI: https://doi.org/10.1007/BF02734266