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Register a new userLight fermion masses and chiral freedom
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Authors
Christof Wetterich
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Within the scenario of chiral freedom we compute the quark and lepton masses of the first two generations in terms of their chiral couplings. This allows us to make a rough estimate of the size of the chiral couplings, narrowing down the uncertainty in the chiron contribution to low energy observables, like the anomalous magnetic moment of the muon. We also extract information about the chiron mass which determines the size of possible chiron effects at the LHC.
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A short review of the status of supersymmetric grand unified theories and their relation to the issue of fermion masses and mixings is given.
The boson and fermion particle masses are calculated in a finite quantum field theory. The field theory satisfies Poincare invariance, unitarity and microscopic causality, and all loop graphs are finite to all orders of perturbation theory. The infinite derivative nonlocal field interactions are regularized with a mass (length) scale parameter $Lambda_i$. The $W$, $Z$ and Higgs boson masses are calculated from finite one-loop self-energy graphs. The $W^{pm}$ mass is predicted to be $M_W=80.05$ GeV, and the higher order radiative corrections to the Higgs boson mass $m_H=125$ GeV are damped out above the regulating mass scale parameter $Lambda_H=1.57$ TeV. The three generations of quark and lepton masses are calculated from finite one-loop self-interactions, and there is an exponential spacing in mass between the quarks and leptons.
We perform a non-perturbative chiral study of the masses of the lightest pseudoscalar mesons. In the calculation of the self-energies we employ the S-wave meson-meson amplitudes taken from Unitary Chiral Perturbation Theory (UCHPT) that include the lightest nonet of scalar resonances. Values for the bare masses of pions and kaons are obtained, as well as an estimate of the mass of the eta_8. The former are found to dominate the physical pseudoscalar masses. We then match to the self-energies from Chiral Perturbation Theory (CHPT) to O(p^4), and a robust relation between several O(p^4) CHPT counterterms is obtained. We also resum higher orders from our calculated self-energies. By taking into account values determined from previous chiral phenomenological studies of m_s/hat{m} and 3L_7+L^r_8, we determine a tighter region of favoured values for the O(p^4) CHPT counterterms 2L^r_6-L^r_4 and 2L^r_8-L^r_5. This determination perfectly overlaps with the recent determinations to O(p^6) in CHPT. We warn about a likely reduction in the value of m_s/hat{m} by higher loop diagrams and that this is not systematically accounted for by present lattice extrapolations. We also provide a favoured interval of values for m_s/hat{m} and 3L_7+L^r_8.
Besides the string scale, string theory has no parameter except some quantized flux values; and the string theory Landscape is generated by scanning over discrete values of all the flux parameters present. We propose that a typical (normalized) probability distribution $P({cal Q})$ of a physical quantity $cal Q$ (with nonnegative dimension) tends to peak (diverge) at ${cal Q}=0$ as a signature of string theory. In the Racetrack Kahler uplift model, where $P(Lambda)$ of the cosmological constant $Lambda$ peaks sharply at $Lambda=0$, the electroweak scale (not the electroweak model) naturally emerges when the median $Lambda$ is matched to the observed value. We check the robustness of this scenario. In a bottom-up approach, we find that the observed quark and charged lepton masses are consistent with the same probabilistic philosophy, with distribution $P(m)$ that diverges at $m=0$, with the same (or almost the same) degree of divergence. This suggests that the Standard Model has an underlying string theory description, and yields relations among the fermion masses, albeit in a probabilistic approach (very different from the usual sense). Along this line of reasoning, the normal hierarchy of neutrino masses is clearly preferred over the inverted hierarchy, and the sum of the neutrino masses is predicted to be $sum m_{ u} simeq 0.0592$ eV, with an upper bound $sum m_{ u} <0.066$ eV. This illustrates a novel way string theory can be applied to particle physics phenomenology.
Fermion masses can be generated through four-fermion condensates when symmetries prevent fermion bilinear condensates from forming. This less explored mechanism of fermion mass generation is responsible for making four reduced staggered lattice fermions massive at strong couplings in a lattice model with a local four-fermion coupling. The model has a massless fermion phase at weak couplings and a massive fermion phase at strong couplings. In particular there is no spontaneous symmetry breaking of any lattice symmetries in both these phases. Recently it was discovered that in three space-time dimensions there is a direct second order phase transition between the two phases. Here we study the same model in four space-time dimensions and find results consistent with the existence of a narrow intermediate phase with fermion bilinear condensates, that separates the two asymptotic phases by continuous phase transitions.
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