Mass matrices and eigenstates for scalars / pseudoscalars; indirect CP violation, mass hierarchies and symmetry breaking

I study indirect CP violation for neutral kaons, and extend it to large values of the CP-violating parameter (taken to be real). I show how and at which condition there can exist a continuous set of basis in which the kinetic and mass terms in the Lagrangian can be diagonalized simultaneously. An ambiguity results for the mass spectrum, which then depends on the basis. In particular, for fixed (positive) (mass)^2 of the CP eigenstates K^0_1, K^0_2, and for certain ranges of values of the CP-violating parameter, a negative (mass)^2 can arise in the CP-violating basis. Under certain conditions, even a small perturbation, by lifting the ambiguity, can strongly alter the pattern of masses. These investigations extend in a natural way to indirect CP violation among a set of Higgs-like doublets. The C-odd commutator [K^0, K^0 bar], or its equivalent for Higgs multiplets, plays an important role. The condition for its vanishing and its consequences are among the main concerns of this work.Comment: LaTeX2e, 35 pages, 10 postscript figures + 1 log

Binary systems of neutral mesons in Quantum Field Theory

Quasi-degenerate binary systems of neutral mesons of the kaon type are investigated in Quantum Field Theory (QFT). General constraints cast by analyticity and discrete symmetries P, C, CP, TCP on the propagator (and on its spectral function) are deduced. Its poles are the physical masses; this unambiguously defines the propagating eigenstates. It is diagonalized and its spectrum thoroughly investigated. The role of ``spurious'' states, of zero norm at the poles, is emphasized, in particular for unitarity and for the realization of TCP symmetry. The K_L-K_S mass splitting triggers a tiny difference between their CP violating parameters \epsilon_L and \epsilon_S, without any violation of TCP. A constant mass matrix like used in Quantum Mechanics (QM) can only be introduced in a linear approximation to the inverse propagator, which respects its analyticity and positivity properties; it is however unable to faithfully describe all features of neutral mesons as we determine them in QFT, nor to provide any sensible parameterization of eventual effects of TCP violation. The suitable way to diagonalize the propagator makes use of a bi-orthogonal basis; it is inequivalent to a bi-unitary transformation (unless the propagator is normal, which cannot occur here). Problems linked with the existence of different ``in'' and ``out'' eigenstates are smoothed out. We study phenomenological consequences of the differences between the QFT and QM treatments. The non-vanishing of semi-leptonic asymmetry \delta_S - \delta_L does not signal, unlike usually claimed, TCP violation, while A_TCP keeps vanishing when TCP is realized. We provide expressions invariant by the rephasing of K0 and K0bar.Comment: 44 pages, 2 figures. Version to appear in Int. J. Mod. Phys.

Using an online collaboration platform to facilitate group work

The onset of COVID-19 necessitated moving three large-enrolment introductory engineering and IT subjects online after just one week of face to face teaching. All three subjects focus on facilitating students' learning through group work to solve a self-identified problem. Considering a key Subject Learning Outcome is 'to collaborate effectively in team processes', group work is integral to the aims of these subjects. Studies for both online and face-to-face group work identify the influence educators play in achieving successful learning outcomes and group satisfaction; for example, the importance of group work management (Xu, Du & Fan, 2015). While many challenges faced in online group work in education are common to face-to-face teaching (Roberts & McInnerney, 2007), it has been shown that "distance does matter" (Olson & Olson, 2000). The challenge was to facilitate the same level of cooperation between students and enable them to build teamwork skills without face-to-face interaction with teammates or educators. PURPOSE OR GOAL Moving three early-year subjects of approximately 600 students each onto an online collaboration platform over a short period provided new challenges. This paper will discuss the aspects of our transition to online group work that worked well, and those that did not, from the perspective of students and tutors. These insights into best-practice online learning will inform how teaching can shift into blended learning in 2021. METHODOLOGY Focus groups were conducted with students from one second-year and two first-year subjects. In these focus groups, students discussed their experiences of working in a group environment and how this experience can be improved. The comments from student feedback surveys and students’ comments from the SPARKplus peer assessments were also used. In addition, feedback on classes and materials were taken from tutors and compared to the students' view of the online classes. Transcripts and comments were analysed to identify recurrent themes. OUTCOMES Students had mixed feelings about the transition to online classes. Despite the use of many different strategies, issues with engagement remain. However, some strategies have emerged that motivate the students, while successful ways for groups to work together were discovered. Our research also indicates that the use of a learning platform which facilitates instant student discussion is worth further investigation for online classes. CONCLUSIONS/RECOMMENDATIONS/SUMMARY Online classes make it more challenging to engage students in group work based learning. However, careful fostering of group team spirit helps to lessen individual isolation. Some students thrive from the provision of instant feedback through an interactive learning platform. In future work, focus groups need to be conducted with students who achieved lower marks or dropped out of the subject to understand the issues they faced. More attention needs to be paid to the tutor perspective and how activities can be better adapted to student needs. KEYWORDS Transition online, group work, student engagement

On the η\eta and f1_1(1420) Couplings to the Nucleon

We consider neutral pseudoscalar, $\eta$, and axial vector, $f_1(1420)$, mesons in the OZI-rule-respecting flavor basis, $\lbrace (\bar s s), {1\over \sqrt{2}}(\bar u u + \bar d d)\rbrace$, and suggest a scenario for their coupling to the nucleon. Within this framework, the non--strange parts of the $\eta N$ and f$_1 N$ couplings are modeled by means of triangular $a_0\pi N$, and $K K^* (\Lambda /\Sigma)$ vertices, while the strange ones partly proceed via Goldberger-Treiman relations, which have been concluded solely on the grounds of current universality. The suggested model explains the observed suppression of the $\eta N$ coupling with respect to the constituent quark model expectations, and predicts the coupling of $f_1$ to the nucleon.Comment: appears in Int. J. Mod. Phys. A (in press