The interplay between grand unified and flavour symmetries in a Pati-Salam x S4 model

Both discrete flavour symmetries and Grand Unified symmetries explain apparent structures in the mass sector of the Standard Model. A model that combines both symmetries is therefore very appealing. We construct a model with the $S_4$ flavour symmetry and the Pati-Salam unification. We show that this model can indeed explain many observable relations between the masses of the quarks and leptons and that it is predictive in the neutrino sector. However, the combination of the two symmetries leads to new complications in the Higgs sector and in the running of the renormalisation group equations.Comment: To appear in the proceedings of PASCOS 2010, the 16th International Symposium on Particles, Strings and Cosmology, Valencia, Spai

Finite Modular Groups and Lepton Mixing

We study lepton mixing patterns which are derived from finite modular groups Gamma_N, requiring subgroups G_nu and G_e to be preserved in the neutrino and charged lepton sectors, respectively. We show that only six groups Gamma_N with N=3,4,5,7,8,16 are relevant. A comprehensive analysis is presented for G_e arbitrary and G_nu=Z2 x Z2, as demanded if neutrinos are Majorana particles. We discuss interesting patterns arising from both groups G_e and G_nu being arbitrary. Several of the most promising patterns are specific deviations from tri-bimaximal mixing, all predicting theta_13 non-zero as favoured by the latest experimental data. We also comment on prospects to extend this idea to the quark sector.Comment: 27 pages + 8 pages of appendices, 1 figur

Erratum: constraining flavour symmetries at the EW scale I: the A4 Higgs potential

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Quark mixing in the discrete dark matter model

We consider a model in which dark matter is stable as it is charged under a Z2 symmetry that is residual after an A4 flavour symmetry is broken. We consider the possibility to generate the quark masses by charging the quarks appropriately under A4. We find that it is possible to generate the CKM mixing matrix by an interplay of renormalisable and dimension-six operators. In this set-up, we predict the third neutrino mixing angle to be large and the dark matter relic density to be in the correct range. However, low energy observables - in particular meson-antimeson oscillations - strongly limit the available parameter space.Comment: 10 pages, 4 figures; version 3 as appeared in Nuclear Physics

Discrete Flavour Symmetries in Light of T2K

We show that a non-vanishing angle theta_13 of order 0.1 can be predicted in the framework of discrete flavour symmetries. We assume that left-handed leptons transform as triplets under a group G_f which is broken in such a way that neutrino and charged lepton sectors remain invariant under the subgroups G_nu and G_e of G_f, respectively. In this limit mixing angles and the Dirac CP violating phase delta_CP are determined. By choosing G_f=Delta(6 n^2) (n=4,8), G_nu=Z_2 x Z_2 and G_e=Z_3 we find sin^2 theta_13=0.045(0.011) for n=4(8). At the same time theta_23 and theta_12 remain close to their experimental best fit values, particularly in the case n=8, where sin^2 theta_23 = 0.424 and sin^2 theta_12 = 0.337. delta_CP is predicted to be 0 or pi so that CP is conserved in our examples.Comment: 1+11 pages, 1 figure; v2: matches journal versio

Constraining flavour symmetries at the EW scale II: the fermion processes

We study the set of models in which the Standard Model symmetry is extended with the avour group

The Interplay Between GUT and Flavour Symmetries in a Pati-Salam x S4 Model

Both Grand Unified symmetries and discrete flavour symmetries are appealing ways to describe apparent structures in the gauge and flavour sectors of the Standard Model. Both symmetries put constraints on the high energy behaviour of the theory. This can give rise to unexpected interplay when building models that possess both symmetries. We investigate on the possibility to combine a Pati-Salam model with the discrete flavour symmetry $S_4$ that gives rise to quark-lepton complementarity. Under appropriate assumptions at the GUT scale, the model reproduces fermion masses and mixings both in the quark and in the lepton sectors. We show that in particular the Higgs sector and the running Yukawa couplings are strongly affected by the combined constraints of the Grand Unified and family symmetries. This in turn reduces the phenomenologically viable parameter space, with high energy mass scales confined to a small region and some parameters in the neutrino sector slightly unnatural. In the allowed regions, we can reproduce the quark masses and the CKM matrix. In the lepton sector, we reproduce the charged lepton masses, including bottom-tau unification and the Georgi-Jarlskog relation as well as the two known angles of the PMNS matrix. The neutrino mass spectrum can present a normal or an inverse hierarchy, and only allowing the neutrino parameters to spread into a range of values between $\lambda^{-2}$ and $\lambda^2$, with $\lambda\simeq0.2$. Finally, our model suggests that the reactor mixing angle is close to its current experimental bound.Comment: 62 pages, 4 figures; references added, version accepted for publication in JHE

Decision Rules for Corporate Investment †

We investigate the decision rules for corporate investment by designing a company value frontier. This company value frontier allows for balancing the financial value and social and environmental impacts. This article develops novel value concepts—ranging from shareholder value to shareholder welfare and integrated value—resulting in varying preferences for social and environmental impacts or values. Next, these preferences are incorporated in investment decision rules. The traditional net present value (NPV) rule optimises only the financial value. We propose a new integrated present value (IPV) decision rule that includes a preference for social and environmental values without neglecting the financial value. By applying the new IPV rule, responsible companies are able to achieve more sustainable outcomes.</p

Beslisregels voor langetermijnwaardecreatie

Toekomstgerichte bedrijven sturen op langetermijnwaardecreatie (LTW) in plaats van alleen op aandeelhouderswaarde. LTW gaat om het beheren en balanceren van verschillende ‘waardedimensies’: financieel, sociaal en ecologisch. Dat vergt beslisregels voor de investeringen van bedrijven. Dit artikel leidt dergelijke beslisregels af door te analyseren wat nodig is voor LTW; en hoe LTW verschilt van aandeelhouderswaardemaximalisatie. Ook schetst het artikel transitietrajecten voor bedrijven die momenteel waardevernietigend zijn op één van de dimensies. Ten slotte introduceert het eenvoudige modellen die het mogelijk maken om specifieke soorten waarde te prioriteren, in overeenstemming met de missie van de onderneming