F. Buccella

A new evaluation of the parity violating pion-nucleon coupling

Abstract We evaluate the parity violating pion-nucleon coupling, A π , in the framework of the standard model of weak and electromagnetic interactions, including QCD corrections. We point out that important contributions to A π have been overlooked previously. Taking into account the uncertainties in the determination of the coefficients of the effective Hamiltonian, we find A π = (16–29) ( A π ) C , where ( A π ) C is the prediction of the Cabibbo theory, related to hyperon decay S-wave amplitudes. The sign of A π with respect to the strong pion-nucleon coupling is also determined.

Electromagnetic mass differences of hadrons

SummaryStarting from the Cottingham formula, the problem of the ΔI=1 and ΔI=2 mass differences of the pseudoscalar and vector mesons, (1/2+) baryon octet and (3/2+) decuplet are examined in the framework of Hararis approach. The Born and the transition terms of all these particles are calculated using a «low frequency» limit which comes essentially from the strong suppression of highq2 values in the Cottingham integral due to the form factors; in this limit we find a «universal» relation between both the electric and the magnetic contributions of the Born terms to the two gauge-invariant parts on the forward spin-nonflip amplitude for the Compton scattering. The residue function of the A2 Regge pole β(q2) is calculated via FESR for the Compton scattering of K-mesons. The application of FESR to (p-n) mass difference is critically examined. The connection with the residues of all the other particles is obtained with the use of the «universality» hypothesis for the coupling of A2 Regge pole with mesons and baryons proposed by Cabibbo, Horowitz and Neeman. We find that the inelastic terms thus evaluated give always a contribution of the right sign to the e.m. mass differences. The final numerical results are in striking agreement with experiment.RiassuntoPartendo dalle formule di Cottingham e nel quadro della ipotesi di Harari, viene esaminato il problema delle differenze di massa ΔI=1 e ΔI=2 dei mesoni pseudoscalari e vettoriali, dellottetto barionico (1/2+) e del decupletto (3/2+). I termini di Born e di transizione di tutte queste particelle sono calcolati usando un limite di «bassa frequenza» che deriva sostanzialmente dal rapido annullamento dei fattori di forma che stanno nellintegrale di Cottingham; in questo limite si trova una relazione «universale» per i contributi sia elettrici che magnetici dei termini di Born alle due parti invarianti di gauge dellampiezza di non spin-flip dello scattering Compton in avanti. Il residuo β(q2) del polo di Regge A2 viene calcolato mediante le F.E.S.R. per lo scatering Compton dei mesoni K. Si esamina criticamente la possibilità di applicazione delle F.E.S.R. al calcolo della differenza di massa (p—n). La connessione con i residui di tutte le altre particelle si ottiene con luso dellipotesi di «universalità» per laccoppiamento del polo di Regge A2 con i mesoni e i barioni proposti da Cabibbo, Horowitz e Neeman. Troviamo che i termini inelastici calcolati in questo modo danno sempre un contributo del segno giusto alle differenze di massa elettromagnetica. I risultati numerici finali sono in ottimo accordo con i dati sperimentali.РезюмеИсходя из формулы Коттингама, в рамках подхода Харари, исследуется проблема разностей масс ΔI=1 и ΔI=2 для псевдоскалярных и векторных мезонов, барионного октета (1/2+) и декуплета (3/2+). Вычисляются борновские члены и члены переходов для всех зтих частиц, используя предел «низкой частоты», который происходит, в основном, из сильного подавления больших величинq2 в интеграле Коттингама, благодаря форм-факторам; в зтом пределе мы находим «универсальное» соотношение между обоими вкладами, злектрическим и магнитным, борновских членов в две калибровочно-инвариантные части амплиды рассеяния вперед без переворачивания спина для комптоновского рассеяния. Вычисляются функция вычета для полюса Редже A2 β(q2) через F.E.S.R. для комптоновского рассеяния К-мезонов. Критически изучается применение F.E.S.R. к разности масс (p−n). Получается связь с вычетами всех других часиц при помощи использования гипотезы «универсальности» для связи полюса Редже A2 смезонами и барионами, предложенной Кабиббо, Горовитцем и Нииманом. Мы находим, что неупругие члены, вычисленные таким образом, дают всегда вклад правильиого знака в злектромагнитные разности масс. Окончательные численные результаты находятся в поразительном согласии с экспериментом.

Sum rules for the mixing angles of the baryons in SU(3) ⊗ SU(3) chiral algebra at infinite momentum

Abstract Under the assumption that axial charges couple the baryon octet only to one-particle states belonging to 1, 8, 10 SU(3) representations, sum rules for the mixing angles of the baryon wave function are derived. The results obtained from their saturation are in good agreement with the known electromagnetic properties of nucleons.

The Price of Unification Signatures in a SO(10) Model With Left-right Symmetry Broken at the Highest Scale

We construct a unified model with symmetry breaking pattern SO(10) → SO(6) × SO(4) → SU(3) × SU(2) × U(1) → SU3 ×U(1) with Higgs in the 210 + 126 + 10 representations, which is consistent with the lower bound on τp → e+ + π0 and with the experimental values of sin2ϑw and αs. It is not difficult to adjust the parameters in the scalar potential in such a way as to expect mντ ≈ 10 eV, while drastic conditions are required to expect τNN

The Majoron and left-handed neutrino masses in SU(5)

Abstract We consider the spontaneous breaking of B − L in SU(5) in connection with left-handed neutrino masses. We show that the ensuing Goldstone boson, “the majoron”, is harmless. The low-energy predictions are the same as in the SU(2) L × U(1) majoron model which, in particular, predicts the existence of doubly and singly charged scalars, with masses ≲250 GeV and with a mass ratio of √2. Going to SU(5), one would expect these scalars to escape to the grand unified mass. This does not happen and, surprisingly, even the ratio √2 is preserved.

Lower hadron states classification and SU(3) ⊗ SU(3) chiral algebra approximate saturation

Abstract A classification scheme for hadrons is proposed, which fits well with the experimental π-N resonances. Under the hypothesis of SU(3) ⊗ SU(3) chiral algebra approximate saturation, GA and α = D/D + F are evaluated in terms of the squares of the axial coupling constants; their value is in good agreement with experiment. Further model dependent predictions are obtained for the mixing angles of the baryon wave function and for the branching ratios of the predicted strange resonances. The values of the mixing angles are in agreement with what we expect from the e.m. structure of the nucleons.

Stability of spontaneous symmetry breaking in SO(10)

Abstract The stability of the breaking of SO(10) into SO(6) × SO(4) with Higgs in the 54 representation is studied in the range of scales 1016–1019 GeV. One finds constraints on the parameters of the potential.

Spontaneously broken SU(5) symmetries and 1-loop effects in the early universe

This paper studies the 1-loop effective potential and spontaneous-symmetry-breaking pattern for SU(5) gauge theory in de Sitter spacetime. Curvature effects modify the flat-space effective potential by means of a very complicated special function previously derived in the literature. An algebraic technique already developed by Buccella et al. to study spontaneous symmetry breaking of SU(n) for renormalizable polynomial potentials is here generalized, for SU(5), to the much more difficult case of a de Sitter background. A detailed algebraic and numerical analysis provides a better derivation of the stability of the extrema in the maximal subgroups SU(4)*U(1), SU(3)*SU(2)*U(1), SU(3)*U(1)*U(1)*R311, SU(2)*SU(2)*U(1)*U(1)+R2211, where R311 and R2211 discrete symmetries select particular directions in the corresponding two-dimensional strata. One thus obtains a deeper understanding of the result, previously found with a different numerical analysis, predicting the slide of the inflationary Universe into either the SU(3)*SU(2)*U(1) or SU(4)*U(1) extremum. Interestingly, using this approach, one can easily generalize all previous results to a more complete SU(5) tree-level potential also containing cubic terms.

Octonions and subalgebras of the exceptional algebras

The vector space of the generators of E8 is realized in terms of 3×3 traceless matrices, two independent sets of octonions imaginary units, and the two G2 acting on them. In this way one gets an appropriate framework to describe in a simple way how exceptional algebras and their fundamental representations transform under their subalgebras.

The fifth interaction and baryon mass differences

SummaryThe problem of theSU3-breaking mass splittings and their connection with the electromagnetic ones has been re-examined by using the «fifth interaction» Lagrangian proposed by Ne’eman to interpret the high-energy large-angle proton-proton scattering data, in the framework of the approach suggested by Harari and Segré. Satisfactory results are found for the mass differences andF/D ratio which support the Ne’eman model and provide a justification for the use of a secondorder perturbation formula even for the medium-strong interaction.RiassuntoIl problema delle differenze di massa fra barioni dovute alla rottura diSU3 e la loro connessione con le differenze di massa elettromagnetiche è stato riesaminato usando la lagrangiana della «quinta interazione» proposta da Ne’eman, per interpretare i dati dello scattering protone-protone ad alta energia ed a grandi angoli, e seguendo l’approccio suggerito da Harari e Segré. Si trovano risultati soddisfacenti per le differenze di massa e per il rapportoF/D, che danno una conferma del modello di Ne’eman e giustificano l’uso al secondo ordine della formula perturbativa anche per le interazioni semi-forti.РезюмеЗаново исследуется продлема расщеплений масс нарушенииSU3 и ее связь с электромагнитными расщеплениями, посредством использования Лагранжиана «пятого взаимодействия», предложенного Нееманом для интерпретации данных протон-протонного рассеяния на большие углы при высоких энергиях, в рамках подхода, предложенного Харари и Сегре. Найдены удовлетворительные результаты для разностей масс иF/D отношения, которые подтверздают модель Неемана и обеспечивют оправдание для использования пертурбационной формулы второго порядка, даже для срэдне-сильного взаимодействия.