The commencement hep-ph newspaper today is dedicated to heterotic string phenomenology.
Delta(54) season phenomenology in addition to stringswas written past times Mexicans, Ms Brenda Carballo-Perez, Eduardo Peinado, Saul Ramos-Sanchez, but that can't forestall it from beingness to a greater extent than interesting than many papers from the USA The commencement hep-ph papers oft await to a greater extent than interesting than the rest. I believe that every bit good inwards this case, the authors struggled to larn the #1 spot because they're to a greater extent than excited almost their move than the authors of the remaining papers today.
Michal Tučný, "Everyone is already inwards Mexico". Buenos días, I am every bit good going. One of his transcend xx best province music songs.
The Standard Model of particle physics is commonly formulated every bit a guess theory based on the \(SU(3)\times SU(2)\times U(1)\) guess group. The particles demeanor the coloring in addition to the electroweak charges. The guess grouping is continuous which implies that at that spot are guess bosons inwards the spectrum.
However, the Standard Model every bit good requires 3 generations of fermions – quarks in addition to leptons. Because of this repetitive structure, it's natural to imagine that they transform every bit "triplets" nether another, work solid unit of measurement grouping every bit well. However, at that spot are manifestly no \(SU(3)_{\rm flavor}\) guess bosons, at to the lowest degree non available at the LHC yet. For this in addition to other reasons, it's to a greater extent than sensible to assume that the 3 generations of fermions are "triplets" nether a discrete, in addition to non continuous, work solid unit of measurement symmetry.
The work solid unit of measurement groups that accept been tried in addition to that acknowledge three-dimensional representations accept been \(\ZZ_3\), \(S_3\), in addition to \(\Delta(27)\). However, at that spot exists i larger discrete grouping with a three-dimensional representation, the \(\Delta(54)\) group. With about definitions, it's the maximal i – the maximal "exceptional" discrete symmetry with three-dimensional representations, in addition to the previous 3 cases are all subgroups of \(\Delta(54)\).
Surely many people portion the gut feeling that the maximum symmetries of a similar particular type are (just similar \(E_8\) with the uncomplicated Lie groups) the "most beautiful ones" in addition to thus most promising ones, at to the lowest degree from a for certain aesthetic viewpoint. The larger symmetry with 54 elements in all likelihood makes the models to a greater extent than constrained in addition to thus to a greater extent than predictive.
These Mexican heterotic string theorists indicate out that the heterotic orbifolds of tori haven't led to feasible models with this \(\Delta(54)\) symmetry yet. But that's because people were focusing on orbifolds\[
T^6 / \ZZ_3, \quad T^6 / \ZZ_3 \times \ZZ_2.
\] However, they advise unlike orbifolds instead:\[
T^6 / \ZZ_3 \times \ZZ_3
\] There are diverse discrete groups hither in addition to I ask to emphasize that the grouping \(G\) inwards the description of the orbifold, \(T^6 / G\), is not the same grouping every bit the grouping produced every bit the work solid unit of measurement symmetry past times the resulting heterotic string model. The grouping \(G\) is beingness "gauged" on the the world sheet. It agency that all the one-string states accept to last invariant nether \(G\) i.e. at that spot are no charged states or non-singlets nether \(G\); in addition to unopen string sectors with almost periodic boundary weather upwardly to the activity of \(G\) accept to last added, the twisted sectors.
The work solid unit of measurement grouping produced past times orbifolds is inwards about way a "dual" group. The \(\ZZ_3\times \ZZ_3\) orbifold produces 3 fixed points non identified with each other. Dynamics at each of them is the same then at that spot is genuinely an \(S_3\) symmetry (the total permutation grouping with half dozen elements) exchanging them. H5N1 semidirect production of this grouping with a \(\ZZ_3\times \ZZ_3\) grouping (different from \(G\)) has to last considered because an additional global symmetry results from the activity on localization charges \(m,q\) of the twisted sectors etc. The semidirect production with 54 elements is what nosotros telephone telephone \(\Delta(54)\).
All the fields in addition to price inwards the low-energy Lagrangian should only last symmetric nether this \(\Delta(54)\) in addition to that leads to constraints on the Yukawa couplings in addition to other things. It seems that their models – they constitute about 700 heterotic vacua using about software – accept several corking phenomenological properties such as
- qualitatively realistic quark in addition to lepton masses inwards general, including the lately proven nonzero \(\theta_{13}\) neutrino mixing angle
- the right human relationship betwixt the Cabibbo angle in addition to the strange-to-down quark volume ratio (the Gatto-Sartori-Tonin relation)
- a cool equation relating ratios of both (down-type) quark in addition to (charged) lepton masses: \[
\frac{m_s-m_d}{m_b} = \frac{m_\mu - m_e}{m_\tau}
\] Well, this human relationship isn't obeyed past times the observed masses but corrections could come inwards true - the normal, non inverted, hierarchy of neutrino masses, every bit preferred past times latest experiments
- PMNS neutrino matrix compatible with the known data
But it's amazing how fine questions almost the spectrum in addition to parameters of the Standard Model are already beingness "almost completely explained" past times a theory based on a completely unlike in addition to much to a greater extent than concise starting indicate – the hybrid of the entirely bosonic \(D=26\) string theory in addition to the entirely \(D=10\) superstring with the maximum work solid unit of measurement grouping produced at depression energies.
When you lot combine these conditions, you lot rather naturally obtain 3 generations with realistic constraints on the quarks' in addition to leptons' masses in addition to mixing angles. Whoever isn't intrigued past times those hints is a cold-blooded animal.
I added the label/category "music" to this weblog ship service because of the extensive give-and-take of (mostly Czech) province music inwards the comment section.