Regular Series

Vol. 46 (2015), No. 11, pp. 2067 - 2412

XXXIX International Conference of Theoretical Physics Matter to the Deepest

A Brief Theory Overview of Higgs Physics at the LHC

Acta Phys. Pol. B 46, 2079 (2015)

page 2079 •


This is a brief review of the theoretical status of Higgs production at the LHC in the Standard Model, with an emphasis on the recent developments and computations. In particular, I focus on both inclusive and differential cross sections for the dominant production mode in the Standard Model, where the theoretical uncertainties induced by the different interplays between top- and bottom-quark effects in the gluon-fusion scattering amplitude are discussed.

NLO Corrections to Hard Process in Parton Shower MC — KrkNLO Method

Acta Phys. Pol. B 46, 2089 (2015)

page 2089 •


A new method of combining an NLO-corrected hard process with an LO parton shower Monte Carlo, nicknamed KrkNLO, was proposed recently. It is simpler than well-established two other methods: MC@NLO and POWHEG. In this contribution, we present some results of extensive numerical tests of the new method for single \(Z\)-boson production at hadron colliders and numerical comparisons with two other methods as well as with NNLO calculations.

Fully Differential Decay Rate of a Standard Model Higgs Boson into Two \(b\)-jets at NNLO

Acta Phys. Pol. B 46, 2097 (2015)

page 2097 •


We present a general method for computing QCD jet cross sections at next-to-next-to-leading order accuracy, called CoLoRFulNNLO. We also discuss how to combine the predictions for the production of a Standard Model Higgs boson and its decay into a \(b\)-quark pair, both computed at the next-to-next-to-leading order accuracy, to predict precisely the kinematic distributions of \(b\)-jets emerging in the process \(pp \to H + X \to b \bar {b} + X\).

Calculation and Application of Off-shell Amplitudes

Acta Phys. Pol. B 46, 2105 (2015)

page 2105 •


Hadron scattering processes involving low values for the fraction of the momentum of the hadrons transfered to the partonic process require factorization prescriptions other than collinear factorization. These admit pdfs with resummed logarithms of this momentum fraction. One of their characteristics is that they provide an explicit transverse momentum to the parton, rendering it off-shell. Consequently, the exact definition and calculation of the matrix element needs special attention. The program AMP4HEF numerically evaluates multi-parton amplitudes and matrix elements with up to two of them off-shell.

Towards \(\mathcal {B}(\bar {B} \rightarrow X_{s} \gamma )\) for an Arbitrary Charm Quark Mass

Acta Phys. Pol. B 46, 2111 (2015)

page 2111 •


Constraints on New Physics from the \(\bar {B} \rightarrow X_{s} \gamma \) branching ratio are very sensitive to uncertainties in the Standard Model prediction. However, some of the dominant \(m_c\)-dependent \(\mathcal {O}(\alpha ^2_{\rm s})\) corrections are currently estimated with the help of an interpolation in the charm quark mass \(m_c\), which causes about \(\pm 3\%\) uncertainty. They need to be calculated for the physical value of \(m_c\). Here, we report on evaluation of all the necessary \(m_c\)-dependent ultraviolet counterterm contributions to the considered corrections.

MBsums — a Mathematica Package for the Representation of Mellin–Barnes Integrals by Multiple Sums

Acta Phys. Pol. B 46, 2117 (2015)

page 2117 •


Feynman integrals may be represented by the Mathematica packages AMBRE and MB as multiple Mellin–Barnes integrals. With the Mathematica package MBsums we transform these Mellin–Barnes integrals into multiple sums.

Simplifying Systems of Differential Equations. The Case of the Sunrise Graph

Acta Phys. Pol. B 46, 2125 (2015)

page 2125 •


Differential equations are one of the most powerful and promising tools for evaluating multi-loop and multi-scale Feynman integrals. We report on a new systematic method for simplifying systems of differential equations. The method is based on the analysis of the integration by parts identities in fixed integer numbers of dimensions. The case of the two-loop massive sunrise is discussed in detail.

The Sunrise Integral Around Two and Four Space-time Dimensions in Terms of Elliptic Polylogarithms

Acta Phys. Pol. B 46, 2131 (2015)

page 2131 •


In this paper, we discuss the solution for the sunrise integral around two and four space-time dimensions in terms of a generalised elliptic version of the multiple polylogarithms. In two space-time dimensions, we obtain a sum of three elliptic dilogarithms. The arguments of the elliptic dilogarithms have a nice geometric interpretation. In four space-time dimensions, the sunrise integral can be expressed with the \(\epsilon ^0\)- and \(\epsilon ^1\)-solution around two dimensions, mass derivatives thereof and simpler terms.

Calculation of Multi-scale, Multi-loop Integrals Using SecDec 3

Acta Phys. Pol. B 46, 2137 (2015)

page 2137 •


In this paper, the publicly available program SecDec is briefly described. Its main virtues and new features are summarized, including suggestions for an optimal usage of the program.

The Matrix Element Method at Next-to-leading Order Accuracy

Acta Phys. Pol. B 46, 2143 (2015)

page 2143 •


The Matrix Element Method (MEM) has proven beneficial to make maximal use of the information available in experimental data. However, so far it has mostly been used in Born approximation only. In this paper, we discuss an extension to NLO accuracy. As a prerequisite, we present an efficient method to calculate event weights for jet events at NLO accuracy. As illustration and proof of the concept, we apply the method to the extraction of the top-quark mass in \(e^+e^-\) annihilation. We observe significant differences when moving from LO to NLO which may be relevant for the interpretation of top-quark mass measurements at hadron colliders relying on the MEM.

Introducing Loopedia

Acta Phys. Pol. B 46, 2149 (2015)

page 2149 •


Loopedia is a new project for a public database of loop integrals. After stating the goals and desired properties of the project, two possible ways to characterize Feynman graphs are explained here: the Adjacency List and the Nickel Index. Furthermore, a first version of the Loopedia website is presented. It allows for automatic graph generation and the conversion from Adjacency List to Nickel Index.

Searches for Physics/Particles Beyond the Standard Model at the LHC

Acta Phys. Pol. B 46, 2155 (2015)

page 2155 •


One of the main goals of the LHC is a search for phenomena beyond the Standard Model. Some basic aspects of such searches at the ATLAS and the CMS, two universal LHC detectors are recalled. Results of two representative analyses are shown and the importance of the search for dark matter candidates is underlined.

Di-boson Production Beyond NLO QCD and Anomalous Couplings

Acta Phys. Pol. B 46, 2165 (2015)

page 2165 •


In this paper, we review results for several di-boson production processes beyond NLO QCD at high transverse momenta using the VBFNLO Monte Carlo program together with the LOOPSIM method. Additionally, we show for the \(WZ\) production process how higher order QCD corrections can resemble anomalous coupling effects.

Neutrino Portal Dark Matter

Acta Phys. Pol. B 46, 2173 (2015)

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A simple model for dark matter is presented where the main interactions with the Standard Model involve neutrinos.

Meeting Higgs and Electroweak Precision Observables with R-symmetric SUSY

Acta Phys. Pol. B 46, 2179 (2015)

page 2179 •


We briefly review results of a recent calculation of the leading two-loop corrections to the Higgs boson mass in the Minimal R-symmetric Supersymmetric Standard Model.

Leptogluons in Dilepton Production at the LHC

Acta Phys. Pol. B 46, 2185 (2015)

page 2185 •


In the composite models with colored substructure of the fermions, the color singlet leptons are accompanied by a composite color octet partners, which are known as leptogluons. We consider the effect of leptogluons in the dilepton production at the LHC and show that in the reachable parameter range this effect is typically dominated by \(t\)-channel leptogluon exchange (indirect channel). We show that this channel alone can give a sizable contribution to the dimuon production at the LHC for TeV scale values of the invariant mass of \(\mu ^+\mu ^-\) pairs.

Heavy Neutrino Masses and Mixings at the LHC

Acta Phys. Pol. B 46, 2193 (2015)

page 2193 •


The \(pp\to lljj\) process is analysed assuming right-handed currents and heavy Majorana neutrinos. We discuss dependence of the cross section \(\sigma (pp\to lljj)\) on the ratio \(g_{\rm R}/g_{\rm L}\) of right and left gauge couplings. Estimation of the signal strength is given for \(\sqrt {s}=8\) TeV and 14 TeV with \(g_{\rm R}/g_{\rm L}=0.6\) and \(g_{\rm R}/g_{\rm L}=1\).

Vacuum Stability from Vector Dark Matter

Acta Phys. Pol. B 46, 2199 (2015)

page 2199 •


We study a model of vector dark matter with the complex scalar Higgs portal. Renormalisation group equations at the 2-loop level are used to analyse perturbativity and stability of the vacuum. We impose experimental and theoretical constraints on the model, and find regions in the parameter space consistent with the dark matter relic abundance inferred from the Planck data and bounds on DM-nucleon scattering cross section from XENON and LUX experiments.

Radius Stabilization and Dark Matter with a Bulk Higgs in Warped Extra Dimension

Acta Phys. Pol. B 46, 2205 (2015)

page 2205 •


We employ an SU\((2)\) bulk Higgs doublet as the stabilization field in the Randall–Sundrum model with appropriate bulk and brane-localized potentials. The gauge hierarchy problem can be solved for an exponentially IR-localized Higgs background field with mild values of fundamental parameters of the 5D theory. We consider an IR–UV–IR background geometry with the 5D SM fields in the bulk such that all the fields have even and odd towers of KK-modes. The zero-mode 4D effective theory contains all the SM fields plus a stable scalar, which serves as a dark matter candidate.

Status and Prospects of \(e^+e^-\) Linear Collider Projects

Acta Phys. Pol. B 46, 2213 (2015)

page 2213 •


This article gives a short overview of the ILC and CLIC \(e^+e^-\) linear collider projects and reviews key motivations of future \(e^+e^-\) collider projects.

New Circular \(e^+e^-\) Accelerators at the Energy Frontier

Acta Phys. Pol. B 46, 2221 (2015)

page 2221 •


In recent years, the idea of construction of a new circular \(e^+e^-\) collider collecting data at the energy frontier has been materialised in two proposals: the FCC-ee at CERN and CEPC in China. Both projects are reviewed and the selected highlights of their physics programme are presented.

High-precision Luminosity at \(e^+ e^-\) Colliders: Theory Status and Challenges

Acta Phys. Pol. B 46, 2227 (2015)

page 2227 •


We review the state of the art of the theory predictions available for the Bhabha process in QED, paying particular attention to the implementation of the theoretical ingredients into Monte Carlo generators used for high-precision luminosity measurements at present and future \(e^+ e^-\) colliders. The challenges posed by per mille normalization at present flavor factories, as well as by the precision tag at the \(10^{-4}\) level for future \(e^+ e^-\) facilities, are also discussed.

S-matrix Approach to the \(Z\) Resonance

Acta Phys. Pol. B 46, 2235 (2015)

page 2235 •


The proposed \(e^+e^-\)-collider FCC-ee aims at an unprecedented accuracy for \(e^+e^-\) collisions into fermion pairs at the \(Z\) peak, based on about \(10^{13}\) events. The S-matrix approach to the \(Z\)-boson line shape allows the model-independent quantitative description of the reaction \(e^+e^- \to {\bar f}f\) around the \(Z\) peak in terms of few parameters, among them the mass \(M_Z\) and width \({\mit \Gamma }_Z\) of the \(Z\) boson. While weak and strong corrections remain “black”, a careful theoretical description of the photonic interactions is mandatory. I introduce the method and describe applications and the analysis tool SMATASY/ZFITTER.

News on Muon \((g-2)\)

Acta Phys. Pol. B 46, 2243 (2015)

page 2243 •


Recent new results on the SM and the SUSY prediction for the muon \((g-2)\) are briefly reviewed, and a SUSY scenario with particularly large contributions is discussed.

Hadronic Contributions to \((g-2)_\mu \) and \(\alpha _{\rm QED}(M_Z^2)\)

Acta Phys. Pol. B 46, 2251 (2015)

page 2251 •


We review recent developments in the evaluations of the muon anomalous magnetic moment, putting some emphasis on the leading-order had-ronic contribution to it. We also discuss related quantities such as the QED gauge coupling at the \(Z\)-pole \(\alpha _{\rm QED}(M_Z^2)\) and the running QED gauge coupling \(\alpha _{\rm QED}(q^2)\) as a function of \(q^2\).

Pion Form Factor Measurement at BESIII

Acta Phys. Pol. B 46, 2261 (2015)

page 2261 •


We extract the \(e^+e^-\rightarrow \pi ^+\pi ^-\) cross section in the energy range between 600 and 900 MeV, exploiting the method of initial state radiation. The measurement is based on an integrated luminosity of 2.93 fb\(^{-1}\), taken at a center-of-mass energy of 3.773 GeV with the BESIII detector. The cross section is measured with a systematic uncertainty of 0.9%. We extract the pion form factor \(|F_\pi |^2\) as well as the contribution to the leading order hadronic vacuum polarization contribution to \((g-2)_\mu \). We find this value to be \(a_\mu ^{\pi \pi ,{\rm LO}}(600\)–900 MeV\()=(370.0\pm 2.5_{\rm stat}\pm 3.3_{\rm sys})\times 10^{-10}\).

Low Energy Hadron Physics with carlomat_3.0

Acta Phys. Pol. B 46, 2267 (2015)

page 2267 •


carlomat_3.0, a new version of the metaprogram for generating codes for Monte Carlo calculations of the leading order cross sections and simulations of multiparticle reactions, is dedicated to the description of the processes \(e^+e^-\to {\rm hadrons}\) at low center-of-mass energies in the framework of effective models, such as the Resonance Chiral Theory and the Hidden Local Symmetry model, or the model of the electromagnetic interaction of nucleons. The program offers a number of new options which give the user a better control over the effective models implemented.

\(\chi _{c_1}\) and \(\chi _{c_2}\) Production in \(e^+ e^-\) Annihilation

Acta Phys. Pol. B 46, 2273 (2015)

page 2273 •


Electromagnetic production of \(\chi _{c_1}\) and \(\chi _{c_2}\) states in \(e^+ e^-\) annihilation is discussed in the frame of a quarkonium model.

Bound Muon Decay

Acta Phys. Pol. B 46, 2279 (2015)

page 2279 •


We summarize the recent progress in evaluation of radiative corrections to bound muon decay spectrum. Calculated corrections reconcile the TWIST measurement with the theoretical prediction. Corrections in the endpoint region of the spectrum affect the sensitivity of the muon electron conversion searches.

Towards First Physics at Belle II

Acta Phys. Pol. B 46, 2285 (2015)

page 2285 •


The next-generation B-factory Belle II at the upgraded KEKB accelerator, SuperKEKB, is aiming to start physics data taking in 2018. The broad physics program covers e.g. physics with \(B\) and \(D\) mesons, \(\mu \) and \(\tau \) leptons as well as measurements using the method of radiative returns and direct searches for New Physics. Among these analyses, there is the search for a Dark Photon decaying into light dark matter or leptons, and the precision measurement of the muon pair asymmetry that both have demanding requirements for the trigger system and the latter also for precision QED theory.

Recent Results on Neutrino Cross Sections in the Intermediate Energy Range

Acta Phys. Pol. B 46, 2291 (2015)

page 2291 •


Knowledge of neutrino–nucleus cross sections is very important for the neutrino oscillation measurements. The requirements for understanding neutrino interactions are becoming even greater which is due to the oscillation experiments entering the era of precision measurements. The goal of this document is to review the recent results on neutrino–nucleus cross sections. The article covers the most important experimental results from the intermediate neutrino energy regime (10s MeV–10s GeV) which were published or reported throughout the years 2013–2015.

Neutrinos and LHC Physics

Acta Phys. Pol. B 46, 2301 (2015)

page 2301 •


Neutrino mass models constitute well motivated scenarios of Beyond-the-Standard-Model physics. The interplay between low energy searches and high energy LHC physics provides us with an effective approach to rule out, constrain or pinpoint such models. In this report, we give a brief overview of examples where LHC searches can help to determine the mechanism of light neutrino mass generation and potentially falsify baryogenesis mechanisms.

Radiative Origin of Neutrino Masses

Acta Phys. Pol. B 46, 2311 (2015)

page 2311 •


Mechanisms for Majorana neutrino mass generation can be classified according to the level at which the Weinberg operator is generated. The different possibilities can be sorted in “canonical” tree-level and loop-induced realizations, the latter being motivated by their potential experimental testability. Here, we discuss the one- and two-loop cases, paying special attention to systematic classification schemes, whose aim is that of constructing a full picture for neutrino mass generation.

Higgs Boson(s) in the Minimal Left–Right Model

Acta Phys. Pol. B 46, 2317 (2015)

page 2317 •


We discuss the scalar sector of the minimal Left–Right model, going through a comprehensive analysis of the relevant theoretical constraints on the parameter space from low energy processes and perturbativity. As a consequence, the anatomy of the Higgs boson(s) is drawn in the parametric space of the model, giving rise to a possible Lepton Number Violating (LNV) channel in the standard-like Higgs boson decay. The process could probe the origin of the neutrino masses and parity restoration at the LHC even beyond other direct searches.

Constraints on the Higgs Sector from Radiative Mass Generation of Neutrinos

Acta Phys. Pol. B 46, 2323 (2015)

page 2323 •


Adding a single gauge singlet and a second Higgs doublet to the original Standard Model allows an explanation of the observed smallness of the neutrino masses using the seesaw mechanism. This model predicts two neutral fermions with vanishing mass. But the one-loop contribution to the neutral fermion masses due to the second Higgs doublet lifts this degeneracy and allows to fit the model parameters to the observed neutrino mass differences. We present the determination of the additional Yukawa couplings that appear in our model by requiring that our model predicts the correct mass differences and mixings in the neutrino sector.

NuWro Monte Carlo Generator of Neutrino Interactions — First Electron Scattering Results

Acta Phys. Pol. B 46, 2329 (2015)

page 2329 •


NuWro Monte Carlo generator of events is presented. It is a numerical environment containing all necessary ingredients to simulate interactions of neutrinos with nucleons and nuclei in realistic experimental situation in wide neutrino energy range. It can be used both for data analysis as well as studies of nuclear effects in neutrino interactions. The first results and functionalities of eWro — module of NuWro dedicated to electron–nucleus scattering — are also presented.

Is It Possible to Recover the Correct Theory of Gravity from Cosmology?

Acta Phys. Pol. B 46, 2335 (2015)

page 2335 •


We briefly present the concept of determining the true theory of gravitation using cosmological observations and criticize it.

The Influence of the Symmetry Energy on the Structure of Hyperon Stars

Acta Phys. Pol. B 46, 2343 (2015)

page 2343 •


The analysis of the density dependence of the nuclear symmetry energy in strangeness-rich nuclear matter was done. Calculations were performed on the basis of models with significant differences in the vector meson sector.

Impact of the Strangeness on the Structure of a Neutron Star

Acta Phys. Pol. B 46, 2351 (2015)

page 2351 •


The comparative analysis of the impact of strangeness on the structure and evolution of a neutron star was performed on the basis of two theoretical models. These models are indistinguishable for the density range relevant for the outer core of a neutron star. However, they gave qualitatively different results for the hyperon core of a neutron star.

full authors' list

A. Woszczyna, S. Kubis, W. Czaja, Z.A. Golda, P. Plaszczyk, M. Kutschera

Oppenheimer and Bondi Limits: the Case of the Singular Conformal Curvature

Acta Phys. Pol. B 46, 2357 (2015)

page 2357 •


Spherically symmetric, gravitating configurations built of the regularly distributed gas in equilibrium still admit a singular Weyl curvature. In contrast to the Black Holes, the singularity located in the center of the gas cloud is naked — forms the repulsive point-like gravity source. Configurations of this kind can exceed both the Oppenheimer limit and the Bondi limit.

Clusters of Galaxies as a Tool in Cosmology

Acta Phys. Pol. B 46, 2363 (2015)

page 2363 •


Using the data comprising measurements of the gas mass fraction \(f_{\rm gas}\) for 42 hot and dynamically relaxed galaxy clusters with redshift spanning the range of \(0.05 \lt z \lt 1.1\), collected and analysed by Allen (2008) from the Chandra X-ray observations, we obtained constraints on the matter density parameter \({\mit \Omega }_{\rm m}\) and baryonic matter density parameter \({\mit \Omega }_{\rm b}\). In our calculations, we took into account two most popular cosmological scenarios: quintessence model in which dark energy equation of state is constant and the model in which cosmic equation of state evolves with redshift according to Chevalier–Polarski–Linder (CPL) parametrization. Our results for quintessence model: \({\mit \Omega }_{\rm m} = 0.301 \pm 0.086\), \({\mit \Omega }_{\rm b} = 0.042 \pm 0.011\) as well as for time-varying CPL scenario: \({\mit \Omega }_{\rm m} = 0.268 \pm 0.094\), \({\mit \Omega }_{\rm b} = 0.038 \pm 0.012\) are in a very good agreement with the latest Planck results. This demonstrates that galaxy clusters can be an excellent tool to constrain the values of relevant cosmological parameters.

Building the Cosmological Models vs. Different Models of Set Theory

Acta Phys. Pol. B 46, 2369 (2015)

page 2369 •


We use the ‘local weakening of logic in a space-time’ as a mathematical tool suitable also for building cosmological models. One obtains the extensions of the regular space-time solutions of Einstein equations towards solutions with certain space-time singularities. Such space-time models are also natural for addressing the renormalization questions of various quantum field theories. We discuss some examples.

The Structure of the Real Line in Quantum Mechanics and Cosmology

Acta Phys. Pol. B 46, 2375 (2015)

page 2375 •


We discuss the recently proposed model, where the spacetime in large scales is parametrized by the usual real line \(\mathbb {R}\), while at small (quantum mechanical) scales, the space is parametrized by the real numbers \(\mathbb {R}_M\) from some formal model \(M\) of Zermelo–Fraenkel set theory. We argue that the set-theoretic forcing is an important ingredient of the shift from micro- to macroscale. The set \(\mathbb {R}_M\), describing the space at the Planck era, is merely a meager subset of \(\mathbb {R}\). It is Lebesgue non-measurable and all its measurable subsets have Lebesgue measure 0. According to this, the contributions to the cosmological constant from the zero-point energies of quantum fields vanish. Moreover, the emerged irregularities in the real line can be considered as the source of the primordial quantum fluctuations.

Recent Results from NA61/SHINE

Acta Phys. Pol. B 46, 2381 (2015)

page 2381 •


The main physics goals of the NA61/SHINE programme on strong interactions are the study of the properties of the onset of deconfinement and the search for signatures of the critical point of strongly interacting matter. These goals are pursued by performing an energy (beam momentum 13–158\(A\) GeV/\(c\)) and system size (\(p+p\), \(p\)+Pb, Be+Be, Ar+Sc, Xe+La) scan. This publication reviews results and plans of NA61/SHINE. In particular, recent inclusive spectra and new results on fluctuations and correlations of identified hadrons in inelastic \(p+p\) and centrality selected Be+Be interactions at the SPS energies are presented. The energy dependence of quantities inspired by the Statistical Model of the Early Stage (kink, horn and step) show unexpected behaviour in \(p+p\) collisions. The NA61/SHINE results are compared with the corresponding data of other experiments and model predictions.

The Past, Present and Future of LAr-TPC Neutrino Experiments

Acta Phys. Pol. B 46, 2387 (2015)

page 2387 •


Liquid Argon Time Projection Chambers (LAr-TPCs) is an exciting class of detectors designed for registration of very rare events, such as neutrino interactions or nucleon decay. They offer a good detection efficiency, excellent background rejection, bubble chamber quality images, very good particle identification and calorimetric reconstruction of particle’s deposited energy. These capabilities made LAr-TPCs a very promising choice for neutrino physics experiments. In this paper, an overview of past, present and future neutrino experiments based on LAr-TPC technology is presented.

Towards Neutrino Mass Origin

Acta Phys. Pol. B 46, 2393 (2015)

page 2393 •


We discuss the possibility of probing the origin of neutrino mass at the LHC. To this end, we focus on processes mediated by the Higgs boson, in particular on its rare decay to a pair of heavy right-handed neutrinos. Probing the mass origin is possible when heavy neutrino mass is protected by an extended gauge symmetry, such as Left–Right symmetry. In this case, the Higgs triplet that provides the heavy neutrino mass mixes with the SM one. We discuss the collider features, relevant backgrounds and a set of selection criteria which enhance the sensitivity, including a cut on the heavy neutrino vertex displacement.

The Flavour Problem and the Family Symmetry Beyond the Standard Model

Acta Phys. Pol. B 46, 2399 (2015)

page 2399 •


In the framework of a two Higgs doublet model, we try to explain lepton masses and mixing matrix elements assuming that neutrinos are Dirac particles. Discrete family symmetry groups, which are subgroups of U(3) up to the order of 1025 are considered. Like in the Standard Model with one Higgs doublet, we found that discrete family symmetries do not give satisfactory answer to these basic questions in the flavour problem.

Roots of Unity and Lepton Mixing Patterns from Finite Flavour Symmetries

Acta Phys. Pol. B 46, 2407 (2015)

page 2407 •


The classification of lepton mixing matrices from finite residual symmetries is reviewed, with emphasis on the role of vanishing sums of roots of unity for the solution of this problem.


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