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We briefly discuss the present status of models of neutrino mixing. Among the existing viable options we review the virtues of Bimaximal Mixing (that could be implemented by an $S_4$ discrete symmetry), corrected by terms arising from the charged lepton mass diagonalization. In particular in a GUT formulation the property of quark lepton "weak" complementarity can be naturally realized. We discuss in some detail two new versions of particular GUT models, one based on $SU(5)$ and one on $SO(10)$ and the associated phenomenology. We compare these approaches based on symmetry to models based on chance, like Anarchy or $U(1)_{FN}$., Comment: 18 pages, 4 figures, Proceedings of the Corfu Summer Institute 2014 "School and Workshops on Elementary Particle Physics and Gravity", 3-21 September 2014 Corfu, Greece

The LHC runs at 7 and 8 TeV have led to the discovery of the Higgs boson at 125 GeV which will remain as one of the major physics discoveries of our time. Another very important result was the surprising absence of any signals of new physics that, if confirmed in the continuation of the LHC experiments, is going to drastically change our vision of the field. Indeed the theoretical criterium of naturalness required the presence of new physics at the TeV scale. At present the indication is that Nature does not too much care about our notion of naturalness. Still the argument for naturalness is a solid one and one is facing a puzzling situation. We review the different ideas and proposals that are being considered in the theory community to cope with the naturalness problem., Comment: 19 pages, no figures. Talk given at the Vulcano Workshop 2014 - Frontier Objects in Astrophysics and Particle Physics. Vulcano island, Italy, May 2014. Typos removed, a few References added

In the last two decades experiments have established the existence of neutrino oscillations and most of the related parameters have by now been measured with reasonable accuracy. These results have accomplished a major progress for particle physics and cosmology. At present neutrino physics is a most vital domain of particle physics and cosmology and the existing open questions are of crucial importance. We review the present status of the subject, the main lessons that we have learnt so far and discuss the great challenges that remain in this field., Comment: 18 pages, 1 figure. Talk presented at the International Conference on Flavor Physics and Mass Generation, Singapore, February 2014. arXiv admin note: substantial text overlap with arXiv:1312.1107, arXiv:1304.5047, arXiv:1111.6421, arXiv:1210.3467, arXiv:hep-ph/0405048

We present a concise outlook of particle physics after the first LHC results at 7-8 TeV. The discovery of the Higgs boson at 126 GeV will remain as one of the major physics discoveries of our time. But also the surprising absence of any signals of new physics, if confirmed in the continuation of the LHC experiments, is going to drastically change our vision of the field. At present the indication is that Nature does not too much care about our notion of naturalness. Still the argument for naturalness is a solid one and we are facing a puzzling situation. We review the established facts so far and present a tentative assessment of the open problems., Comment: 17 pages, 4 figures. Talk given at the Nobel Symposium on LHC results, Krusenberg, Sweden, 3-17 May 2013. Typos corrected, References added

We present a renormalizable non supersymmetric Grand Unified SO(10) model which, at the price of a large fine tuning, is compatible with all compelling phenomenological requirements below the unification scale and thus realizes a minimal extension of the SM, unified in SO(10) and describing all known physics below $M_{GUT}$. These requirements include coupling unification at a large enough scale to be compatible with the bounds on proton decay; a Yukawa sector in agreement with all the data on quark and lepton masses and mixings and with leptogenesis as the origin of the baryon asymmetry of the Universe; an axion arising from the Higgs sector of the model, suitable to solve the strong CP problem and to account for the observed amount of Dark Matter. The above constraints imposed by the data are very stringent and single out a particular breaking chain with the Pati-Salam group at an intermediate scale $M_I\sim10^{11}$ GeV., Comment: references added, minor changes in the text, version to appear in JHEP

We present a concise review of the recent important experimental developments on neutrino mixing (hints for sterile neutrinos, large $\theta_{13}$, possible non maximal $\theta_{23}$, approaching sensitivity on $\delta_{CP}$) and their implications on models of neutrino mixing. The new data disfavour many models but the surviving ones still span a wide range going from Anarchy (no structure, no symmetry in the lepton sector) to a maximum of symmetry, as for the models based on discrete non-abelian flavour groups that can be improved following the indications from the data., Comment: 8 pages, no figures. Talk presented at Les Rencontres de Physique de la Vallee d'Aoste, La Thuile, Italy, February 2013

In this lecture, after recalling the basic definitions and facts about the running coupling in QCD, I present a critical discussion of the methods for measuring $\alpha_s$ and select those that appear to me as the most reliably precise, Comment: 16 pages, Proceedings of the Corfu Summer Institute 2012 "School and Workshops on Elementary Particle Physics and Gravity", September 8-27, 2012

The first LHC results at 7-8 TeV, with the discovery of a candidate Higgs boson and the non observation of new particles or exotic phenomena, have made a big step towards completing the experimental confirmation of the Standard Model (SM) of fundamental particle interactions. It is thus a good moment for me to collect, update and improve my graduate lecture notes on Quantum Chromodynamics (QCD) and the theory of Electroweak (EW) Interactions, with main focus on Collider Physics. I hope that these lectures can provide an introduction to the subject for the interested reader, assumed to be already familiar with quantum field theory and some basic facts in elementary particle physics as taught in undergraduate courses., Comment: 174 pages, 62 figures. v2 corrected, augmented and updated

The recent results that $\theta_{13}$ is relatively large, of the order of the previous upper bound, and the indications of a sizable deviation of $\theta_{23}$ from the maximal value are in agreement with the predictions of Anarchy in the lepton sector. The quark and charged lepton hierarchies can then be reproduced in a SU(5) GUT context by attributing non-vanishing $U(1)_{FN}$ charges, different for each family, only to the SU(5) tenplet states. The fact that the observed mass hierarchies are stronger for up quarks than for down quarks and charged leptons supports this idea. As discussed in the past, in the flexible context of $SU(5)\otimes U(1)_{FN}$, different patterns of charges can be adopted going from Anarchy to various types of hierarchy. We revisit this approach by also considering new models and we compare all versions to the present data. As a result we confirm that, by relaxing the extreme ansatz of equal $U(1)_{FN}$ charges for all SU(5) pentaplets and singlets, better agreement with the data than for Anarchy is obtained without increasing the model complexity. We also present the distributions obtained in the different models for the Dirac CP-violating phase. Finally we discuss the relative merits of these simple models., Comment: v1: 12 pages, 3 figures; v2: 13 pages, 3 figures, text improved, matches version accepted for publication; v3: submitted to add an acknowledgment to a network

We present a short review of the LHC results at 7 TeV and their implications on the Standard Model (SM) and on its Supersymmetric (SUSY) extension. In particular we discuss the exclusion range for the SM Higgs mass, the tantalizing hint of an excess at $m_H \sim 125$ GeV, the negative results of searches for SUSY particles (as well as for any other new physics) and the present outlook., Comment: 9 pages, no figures. Talk given at the QCD Session of the Rencontres de Moriond, La Thuile, Italy, March 2012

We review the application of non-Abelian discrete groups to Tri-Bimaximal (TB) neutrino mixing, which is supported by experiment as a possible good first approximation to the data. After summarizing the motivation and the formalism, we discuss specific models, mainly those based on A4 but also on other finite groups, and their phenomenological implications, including the extension to quarks. The recent measurements of \theta_13 favour versions of these models where a suitable mechanism leads to corrections to \theta_13 that can naturally be larger than those to \theta_12 and \theta_23. The virtues and the problems of TB mixing models are discussed, also in connection with lepton flavour violating processes, and the different approaches are compared., Comment: 26 pages, 5 figures, 4 tables. V3 submitted to add an acknowledgment to a network. Review written for the special issue on "Flavor Symmetries and Neutrino Oscillations", published in Fortschritte der Physik - Progress of Physics

Discrete flavour groups have been studied in connection with special patterns of neutrino mixing suggested by the data, such as Tri-Bimaximal mixing (groups A4, S4...) or Bi-Maximal mixing (group S4...) etc. We review the predictions for sin(\theta_13) in a number of these models and confront them with the experimental measurements. We compare the performances of the different classes of models in this respect. We then consider, in a supersymmetric framework, the important implications of these flavour symmetries on lepton flavour violating processes, like \mu -> e gamma and similar processes. We discuss how the existing limits constrain these models, once their parameters are adjusted so as to optimize the agreement with the measured values of the mixing angles. In the simplified CMSSM context, adopted here just for indicative purposes, the small tan(beta) range and heavy SUSY mass scales are favoured by lepton flavour violating processes, which makes it even more difficult to reproduce the reported muon g-2 discrepancy., Comment: 45 pages, 16 figures, 3 tables; V3 submitted to add an acknowledgment to a Network

In the last years we have learnt a lot about neutrino masses and mixings. Neutrinos are not all massless but their masses are very small. Probably masses are small because neutrinos are Majorana particles with masses inversely proportional to the large scale M of lepton number (L) violation, which turns out to be compatible with the GUT scale. We have understood that there is no contradiction between large neutrino mixings and small quark mixings, even in the context of GUTs and that neutrino masses fit well in the SUSY GUT picture. Out of equilibrium decays with CP and L violation of heavy RH neutrinos can produce a B-L asymmetry, then converted near the weak scale by instantons into an amount of B asymmetry compatible with observations (baryogenesis via leptogenesis). It appears that active neutrinos are not a significant component of Dark Matter in the Universe. A long list of models have been formulated over the years to understand neutrino masses and mixings. With the continuous improvement of the data most of the models have been discarded by experiment. The surviving models still span a wide range going from a maximum of symmetry, with discrete non-abelian flavour groups, to the opposite extreme of anarchy., Comment: 27 pages, 2 figures. Lectures given at the 2011 Ettore Majorana International School of Subnuclear Physics, Erice, June 2011

This is a Concluding Talk, not a Summary of the Conference. I will discuss some of the highlights that particularly impressed me (a subjective choice) and make some comments on the status and the prospects of neutrino mass and mixing., Comment: 9 pages, 1 figure. Concluding Talk at the XIV International Workshop on "Neutrino Telescopes" Venice, Italy, March 15-18, 2011

Recently SO(10) models with type-II see-saw dominance have been proposed as a promising framework for obtaining Grand Unification theories with approximate Tri-bimaximal (TB) mixing in the neutrino sector. We make a general study of SO(10) models with type-II see-saw dominance and show that an excellent fit can be obtained for fermion masses and mixings, also including the neutrino sector. To make this statement more significant we compare the performance of type-II see-saw dominance models in fitting the fermion masses and mixings with more conventional models which have no built-in TB mixing in the neutrino sector. For a fair comparison the same input data and fitting procedure is adopted for all different theories. We find that the type-II dominance models lead to an excellent fit, comparable with the best among the available models, but the tight structure of this framework implies a significantly larger amount of fine tuning with respect to other approaches., Comment: 24 pages, References and minor wording changes added

We present a short summary of our present knowledge and understanding of neutrino masses and mixing., Comment: 15 pages, 2 figures. Talk given at the Quarks, Strings and the Cosmos - Hector Rubinstein Memorial Symposium, August 09-11, 2010, AlbaNova, Stockholm, Sweden

I present a concise review of the major issues and challenges in particle physics at the start of the LHC era. After a brief overview of the Standard Model and of QCD, I will focus on the electroweak symmetry breaking problem which plays a central role in particle physics today. The Higgs sector of the minimal Standard Model is so far just a mere conjecture that needs to be verified or discarded by the LHC. Probably the reality is more complicated. I will summarize the motivation for new physics that should accompany or even replace the Higgs discovery and a number of its possible forms that could be revealed by the LHC., Comment: 17 pages. From talks given at the 22nd Rencontres de Blois on Particle Physics and Cosmology, Blois, France, July 15-20, 2010, at the Symposium on High Energy Strong Interactions, Kyoto, Japan, August 9 -13, 2010 and at the LHC days in Split, Split, Croatia, October 4-9, 2010

I present a concise review of the Higgs problem which plays a central role in particle physics today. The Higgs of the minimal Standard Model is so far just a conjecture that needs to be verified or discarded at the LHC. Probably the reality is more complicated. I will summarize the motivation for New Physics that should accompany or even replace the Higgs discovery and a number of its possible forms that could be revealed by the LHC, Comment: 17 pages, 3 figures, Talk presented at the Corfu Summer Institute: School and Workshop on the Standard Model and Beyond - Standard Cosmology, Corfu, Greece, August 31 - September 6, 2009 A few references added.

I present a concise review of where we stand in particle physics today. First, I will discuss QCD, then the electroweak sector and finally the motivations and the avenues for new physics beyond the Standard Model., Comment: 17 pages. Concluding talk given at the XXIV International Symposium on Lepton Photon Interactions at High Energies (Lepton Photon 2009), Hamburg, Germany, 17-22 August 2009

We review the application of non abelian discrete groups to the theory of neutrino masses and mixing, which is strongly suggested by the agreement of the Tri-Bimaximal mixing pattern with experiment. After summarizing the motivation and the formalism, we discuss specific models, based on A4, S4 and other finite groups, and their phenomenological implications, including lepton flavor violating processes, leptogenesis and the extension to quarks. In alternative to Tri-Bimaximal mixing the application of discrete flavor symmetries to quark-lepton complementarity and Bimaximal Mixing is also considered., Comment: 54 pages, 3 figures, minor changes in the text and references added

I will present here my perception on the status of Deep Inelastic Scattering physics, as I have further developed it during this Workshop, together with a number of comments on the results that have impressed me most during this week. I will emphasize a number of open problems and of critical areas. Finally I conclude with some projections and auspices for the future of the field., Comment: 18 pages, 10 figures. Talk given at the XVI Int. Workshop on Deep Inelastic Scattering and Related Subjects; Madrid, Spain, 26-30 April, 2009

We report on recent progress towards quantitative phenomenology of small x resummation of deep-inelastic structure functions. We compute small x resummed K-factors with realistic PDFs and estimate their impact in the HERA kinematical region. These K-factors, which match smoothly to the fixed order NLO results, approximately reproduce the effect of a small x resummed PDF analysis. Typical corrections are found to be of the same order as the NNLO ones, that is, a few percent, but with opposite sign. These results imply that resummation corrections could be relevant for a global PDF analysis, especially with the very precise combined HERA dataset., Comment: 7 pages, 8 figures, proceedings of 17th International Workshop on Deep Inelastic Scattering (DIS 2009), Madrid, 26-30 Apr 2009

We present a very concise summary of the status of our knowledge and understanding of neutrino masses and mixing., Comment: 12 pages, 1 figure. Talk given at the Rencontres de Physique de la Vallee d'Aoste, La Thuile, Aosta Valley (Italy). March 1-7, 2009

The data on neutrino mixing are at present compatible with Tri-Bimaximal (TB) mixing. If one takes this indication seriously then the models that lead to TB mixing in first approximation are particularly interesting and A4 models are prominent in this list. However, the agreement of TB mixing with the data could still be an accident. We discuss a recent model based on S4 where Bimaximal mixing is instead valid at leading order and the large corrections needed to reproduce the data arise from the diagonalization of charged leptons. The value of $\theta_{13}$ could distinguish between the two alternatives., Comment: 21 pages. Talk at the 13th International Workshop on Neutrino Telescopes, Venice, March 10-13, 2009

We present a see-saw $A_4$ model for Tri-Bimaximal mixing which is based on a very economical flavour symmetry and field content and still possesses all the good features of $A_4$ models. In particular the charged lepton mass hierarchies are determined by the $A_4\times Z_4$ flavour symmetry itself without invoking a Froggatt-Nielsen U(1) symmetry. Tri-Bimaximal mixing is exact in leading order while all the mixing angles receive corrections of the same order in next-to-the-leading approximation. As a consequence the predicted value of $\theta_{13}$ is within the sensitivity of the experiments which will take data in the near future. The light neutrino spectrum, typical of $A_4$ see-saw models, with its phenomenological implications, also including leptoproduction, is studied in detail., Comment: 20 pages, 2 figures

I present a concise review of where we stand in particle physics today. First, I will discuss the status of the Standard Model, its open problems and the expected answers from the LHC. Then I will briefly review the avenues for New Physics that can be revealed by the LHC., Comment: 25 pages, 7 figures. Talk given at the Conference "The Legacy of Edoardo Amaldi in Science and Society", Rome, Italy, October 23-25, 2008

We review the current status of small x resummation of evolution of parton distributions and of deep-inelastic coefficient functions. We show that the resummed perturbative expansion is stable, robust upon different treatments of subleading terms, and that it matches smoothly to the unresummed perturbative expansions, with corrections which are of the same order as the typical NNLO ones in the HERA kinematic region. We discuss different approaches to small x resummation: we show that the ambiguities in the resummation procedure are small, provided all parametrically enhanced terms are included in the resummation and properly matched., Comment: 12 pages, 12 figures; LaTeX with espcrc2.sty. Talk given at the 2008 Ringberg workshop "New Trends in HERA Physics"

We consider future experiments to detect CP violation in neutrino oscillations and discuss how to test that all asymmetries are indeed described in terms of the single leptonic Jarlskog invariant as predicted in the absence of new physics effects., Comment: 28 pages, 15 figures, references added, version to appear in NPB

In these lectures I start by briefly reviewing the status of the electroweak theory, in the Standard Model and beyond. I then discuss the motivation and the possible avenues for new physics, on the brink of the LHC start., Comment: 35 pages, 8 figures. Lectures given at the Lake Louise Winter Institute, Lake Louise, Alberta, Canada, 18-23 February 2008

We summarize our recent results on small x resummation in full QCD with n_f quark flavours and discuss their phenomenological impact in the extraction of parton distributions from present day structure function data and their extrapolation to the kinematics relevant for future colliders such as the LHC., Comment: 6 pages, 3 figures: proceedings contribution for 8th International Symposium on Radiative Corrections (RADCOR), Florence, October 2007

We discuss a grand unified model based on SUSY SU(5) in extra dimensions and on the flavour group A4xU(1) which, besides reproducing tri-bimaximal mixing for neutrinos with the accuracy required by the data, also leads to a natural description of the observed pattern of quark masses and mixings., Comment: 19 pages

We extend our previous results on small-x resummation in the pure Yang--Mills theory to full QCD with nf quark flavours, with a resummed two-by-two matrix of resummed quark and gluon splitting functions. We also construct the corresponding deep-inelastic coefficient functions, and show how these can be combined with parton densities to give fully resummed deep-inelastic structure functions F_2 and F_L at the next-to-leading logarithmic level. We discuss how this resummation can be performed in different factorization schemes, including the commonly used MSbar scheme. We study the importance of the resummation effects by comparison with fixed-order perturbative results, and we discuss the corresponding renormalization and factorization scale variation uncertainties. We find that for x below 0.01 the resummation effects are comparable in size to the fixed order NNLO corrections, but differ in shape. We finally discuss the phenomenological impact of the small-x resummation, specifically in the extraction of parton distribution from present day experiments and their extrapolation to the kinematics relevant for future colliders such as the LHC, Comment: 45 pages, 16 figures, plain TeX with harvmac

We present a concise review of models for neutrino masses and mixings with particular emphasis on recent developments and current problems. We discuss in detail attempts at reproducing approximate tri-bimaximal mixing starting from discrete symmetry groups, notably A4. We discuss the problems encountered when trying to extend the symmetry to the quark sector and to construct Grand Unified versions., Comment: Two lectures given at the Summer Institute 2007, 3-10 August 2007, Fuji-Yoshida, Japan 27 pages, 3 figures

We present some recent developments on model building for neutrino masses and mixings. In particular, we review tri-bimaximal neutrino mixing derived from discrete groups, notably A4. We discuss the problems encountered with extending the symmetry to the quark sector and with Grand Unification., Comment: Talk presented at the XII International Workshop on Neutrino Telescopes, March 6-9, 2007, Venice, Italy. 23 pages, 2 figures

We present a concise review of model building for neutrino masses and mixings, with special emphasis on recent developments., Comment: Lectures given at the 61st Scottish Universities Summer School in Physics, St.Andrews, Scotland, 8-23 August 2006. 27 pages, 2 figures

We briefly review the status of the electroweak theory, in the Standard Model and beyond, on the brink of the LHC start., Comment: Lecture given at the SLAC Summer Institute, July 2006

We show that the A4 discrete symmetry that naturally leads to tri-bimaximal neutrino mixing can be simply obtained as a result of an orbifolding starting from a model in 6 dimensions. This particular orbifolding has four fixed points where 4 dimensional branes are located and the tetrahedral symmetry of A4 connects these branes. In this approach A4 appears after the reduction from six to four dimensions as a remnant of the 6D space-time symmetry. A previously discussed supersymmetric version of A4 is reinterpreted along these lines., Comment: 16 pages, 2 figures

At the School I gave three lectures on neutrino masses and mixings. Much of the material covered in my first two lectures is written down in a review on the subject that I published not long ago with F. Feruglio \cite{rev}. Here, I make a relatively short summary (with updates) of the content of my first two lectures, referring to our review for a more detailed presentation, and then I expand on the content of the third lecture which was dedicated to recent work on A4 models of tri-bimaximal neutrino mixing which were not covered in the review., Comment: Lectures given at IPM-LHP06, Tehran, Iran; PSN: IPM-LHP06-sch. 14 pages, 1 figure Typos corrected, one reference added

We present a concise review of where we stand in particle physics today. First we discuss QCD, then the electroweak sector and finally the motivations and the avenues for new physics beyond the Standard Model., Comment: 20 pages, to appear in the Proceedings of IFAE 2006, Pavia, Italy

We summarize recent progress in the resummation of perturbative evolution at small x. We show that the problem of incorporating BFKL small x logs in GLAP evolution is now completely solved, and that the main effect of small x resummation is to reduce the growth of the gluon at small x in the HERA and LHC regions., Comment: 5 pages, 4 figures, talk at DIS2006

We present a small x resummation for the GLAP anomalous dimension and its corresponding dual BFKL kernel, which includes all the available perturbative information and nonperturbative constraints. Specifically, it includes all the information coming from next-to-leading order GLAP anomalous dimensions and BFKL kernels, from the constraints of momentum conservation, from renormalization-group improvement of the running coupling and from gluon interchange symmetry. The ensuing evolution kernel has a uniformly stable perturbative expansion. It is very close to the unresummed NLO GLAP kernel in most of the HERA kinematic region, the small x BFKL behaviour being softened by momentum conservation and the running of the coupling. Next-to-leading corrections are small thanks to the constraint of gluon interchange symmetry. This result subsumes all previous resummations in that it combines optimally all the information contained in them., Comment: 44 pages, 12 figures, plain TeX with harvmac. Final version, to be published in Nucl. Phys. B. Discussion of integrated vs. unintegrated pdfs added, see eqns. 5.5-5.7, 6.26-6.29. Figures 6-12 updated

We discuss a class of models of neutrino masses and mixings with inverse hierarchy based on a broken U(1)_F flavour symmetry with charge L_e-L_\mu-L_\tau for lepton doublets and arbitrary right-handed charges. The symmetry breaking sector receives separate contributions from flavon vev breaking terms and from soft mass breaking in the right handed Majorana sector. The model is able to reproduce in a natural way all observed features of the charged lepton mass spectrum and of neutrino masses and mixings (even with arbitrarily small \theta_{13}), with the exception of a moderate fine tuning which is needed to accomodate the observed small value of r = Delta m^2_{sol} / Delta m^2_{atm}., Comment: 8 pages, no figures (v2: references added; version accepted by JHEP;)

We formulate and discuss a 4-dimensional SUSY version of an A4 model for tri-bimaximal neutrino mixing which is completely natural. We also study the next-to-the-leading corrections and show that they are small, once the ratios of A4 breaking VEVs to the cutoff are fixed in a specified interval. We also point out an interesting way of presenting the A4 group starting from the modular group. In this approach, which could be interesting in itself as an indication on a possible origin of A4, the lagrangian basis where the symmetry is formulated coincides with the basis where the charged leptons are diagonal. If the same classification structure in A4 is extended from leptons to quarks, the CKM matrix coincides with the unit matrix in leading order and a study of non leading corrections shows that the departures from unity of the CKM matrix are far too small to accomodate the observed mixing angles., Comment: 21 pages, 1 figure; added section on a see-saw realization; version to appear on Nucl. Phys. B