The standard model and beyond

Foreword, A. Salam using quark and lepton masses to guess the scalar spectrum, S. Weinberg fermion masses in the standard model, I.H. Lee and S.D. Drell wave packet tunnelling and the Buttiker precession time, F.E. Low and P.F. Mende delta-function potentials in two and three-dimensional quantum mechanics, R. Jackiw emergence of spinor from flux and lattice hopping, A. Zee atomic physics constraints on the existence of ultralight, ultraweak gauge bosons, G. Feinberg and J. Sucher theories with signal-locality and their experimental tests, V. Singh and S.M. Roy higher order contributions to delta r, S. Fanchiotti and A. Sirlin symmetry in strings and particle physics, L. Dolan flavour and spin content of the proton, Riazuddin and Fayyazuddin origin of masses in the standard model, R.N. Mohapatra revitalizing grand unification, Q. Shafi polarized inclusive scattering from high-spin targets, P. Hoodbhoy constraints in dynamical symmetry breaking mechanism from elecroweak data, A. Ali and G. Degrassi from the quark model to the standard model - ten fateful years in particle physics, M.A.B. Beg dynamical isospin symmetry breaking and seesaw mechanism in extended technicolour, A. Hernandex-Galeana and A. Zepeda random matrix formulation of the fractional quantum hall effect, D.J.E. Callaway the gravitational force in general relativity, A. Qadir.

Although there have been a number of very fine experiments probing the nature of CP violation, even after 25 years we don't know whether we understand the basic theory involved. We do not know if CP violation is a profound clue to physics beyond the Standard Model and to the origin of the baryon asymmetry, or a trivial accident involving (for example) diagonalizing a mass matrix of quarks or Higgs scalars or neutralinos or squarks. The Standard Model can give a satisfactory description of CP violation in kaon decays to pions without any other contribution, if the phase angle in the CKM matrix is fairly large. The Standard model description of e and e I depends on some poorly known parameters. Some of those, such as m,, will be better known soon. Unfortunately, the hadronic matrix elements that enter are not well known, and may not be for a long time. Better measurements of e and e I will provide valuable input to eventually understanding the origin of CP violation, but unless the hadronic matrix elements can be calculated, measurements of e and e ~ can never give us real confidence that we understand CP violation. In particular, they may never be able to tell us whether a second source of CP violation, about the same size as the Standard Model one, is present. Most people do not expect the Standard Model to be the sole source of CP violation, for very general reasons. Although the Standard Model describes the world accessible to experiment so far, it leaves unanswered many questions and it is conceptually unsatisfactory. Everyone believes that new physics will appear to help explain why the weak scale is where it is, why there are families, and so on. Every form of new physics that has been thought of so far involves new sets of particles whose interactions will normally have phase factors. That all the new phase angles which enter the more complete theory should be zero would seem to be a miraculous coincidence. These particles could come in the Higgs sector, and/or be supersymmetric partners, and/or leptoquarks, and/or new gauge bosons, or new quarks, or other objects. It cannot be emphasized enough that if the Standard Model were the only origin of CP violation it would be a remarkable fact that would require explanation. Indeed, if the view of a number of people that the excess baryon number of the universe is generated at the weak scale is correct, either new sources of CP violation must exist that are larger than the CP violation in K decay, or that source must have a rapid growth with energy. Given this situation, it is extremely important to find new ways to get information about the source of CP violation. Even if very accurate experiments

A Z′ gauge boson with mass around the (few) TeV scale is a popular example of physics beyond the Standard Model (SM) and can be a fascinating remnant of a Grand Unified Theory (GUT). Recently, Z′ models with non-universal couplings to the SM fermions due to extra vector-like states have received attention as potential explanations of the present RK, RK⁎ anomalies; this includes GUT model proposals based on the SO(10) group. In this paper we further develop GUT models with a flavour non-universal low scale Z′ and clarify several outstanding issues within them. First, we successfully incorporate a realistic neutrino sector (with linear and/or inverse low scale seesaw mechanism), which was so far a missing ingredient. Second, we investigate in detail their compatibility with the RK, RK⁎ anomalies; we find that the anomalies do not have a consistent explanation within such models. Third, we demonstrate that these models have other compelling phenomenological features; we study the correlations between the flavour violating processes of μ→3e and μ–e conversion in a muonic atom, showing how a GUT imprint could manifest itself in experiments.

This paper presents a search for a new Z′ vector gauge boson with the ATLAS experiment at the Large Hadron Collider using pp collision data collected at sqrt{s} = 13 TeV, corresponding to an integrated luminosity of 139 fb−1. The new gauge boson Z′ is predicted by Lμ − Lτ models to address observed phenomena that can not be explained by the Standard Model. The search examines the four-muon (4μ) final state, using a deep learning neural network classifier to separate the Z′ signal from the Standard Model background events. The di-muon invariant masses in the 4μ events are used to extract the Z′ resonance signature. No significant excess of events is observed over the predicted background. Upper limits at a 95% confidence level on the Z′ production cross-section times the decay branching fraction of pp → Z′μμ → 4μ are set from 0.31 to 4.3 fb for the Z′ mass ranging from 5 to 81 GeV. The corresponding common coupling strengths, gZ′, of the Z′ boson to the second and third generation leptons above 0.003 – 0.2 have been excluded.

The generation of the fermion mass hierarchy in the standard model of particle physics is a long-standing puzzle. The recent discoveries from neutrino physics suggest that the mixing in the lepton sector is large compared to the quark mixings. To understand this asymmetry between the quark and lepton mixings is an important aim for particle physics. In this regard, two promising approaches from the theoretical side are grand unified theories and family symmetries. In this paper we try to understand certain general features of grand unified theories with Abelian family symmetries by taking the simplest $SU(5)$ grand unified theory as a prototype. We construct an $SU(5)$ toy model with $U(1{)}_{F}\ensuremath{\bigotimes}{\mathbb{Z}}_{2}^{\ensuremath{'}}\ensuremath{\bigotimes}{\mathbb{Z}}_{2}^{\ensuremath{'}\ensuremath{'}}\ensuremath{\bigotimes}{\mathbb{Z}}_{2}^{\ensuremath{'}\ensuremath{'}\ensuremath{'}}$ family symmetry that, in a natural way, duplicates the observed mass hierarchy and mixing matrices to lowest approximation. The system for generating the mass hierarchy is through a Froggatt-Nielsen type mechanism. One idea that we use in the model is that the quark and charged lepton sectors are hierarchical with small mixing angles while the light neutrino sector is democratic with larger mixing angles. We also discuss some of the difficulties in incorporating finer details into the model without making further assumptions or adding a large scalar sector.

We propose a new scenario for early cosmology, where inflationary de Sitter phase dynamically occurs. The effect emerges as a result of dynamics of the topologically nontrivial sectors in expanding universe. Technically the effect can be described in terms of the auxiliary fields which effectively describe the dynamics of the topological sectors in a gauge theory. Inflaton in this framework is an auxiliary topological non-propagating field with no canonical kinetic term, similar to known topologically ordered phases in condensed matter systems. We explain many deep questions in this framework using the so-called weakly coupled "deformed QCD" toy model.While this theory is weakly coupled gauge theory, it preserves all the crucial elements of strongly interacting gauge theory, including confinement, nontrivial $\theta$ dependence, degeneracy of the topological sectors, etc. We discuss a specific realization of these ideas using a scaled up version of QCD, coined as \qcd, with the scale M_{PL}\gg \Lbar\gg \sqrt[3]{M_{EW}^2M_{PL}}\sim 10^8 {\mathrm{GeV}}. If no other fields are present in the system de Sitter phase will be the final destination of evolution of the universe. If other interactions are present in the system, the inflationary de Sitter phase lasts for a finite period of time. The inflation starts from the thermal equilibrium state long after the \qcd -confinement phase transition at temperature T_{i}\sim \Lbar\sqrt{\frac{\Lbar}{M_{PL}}}. The end of inflation is triggered by the coupling with gauge bosons from the Standard Model. The corresponding interaction is unambiguously fixed by the triangle anomaly. Number of e-folds in the \qcd-inflation framework is determined by the gauge coupling constant at the moment of inflation, and estimated as N_{\rm inf}\sim \alpha_s^{-2}\sim 10^2.

A fully dynamical origin for the masses of weak gauge bosons and heavy quarks of the Standard Model is considered. Electroweak symmetry breaking and the gauge boson masses arise from new strong dynamics, which leads to the appearance of a composite scalar in the spectrum of excitations. In order to generate mass for the Standard Model fermions, we consider extended gauge dynamics, effectively represented by four fermion interactions at presently accessible energies. By systematically treating these interactions, we show that they lead to a large reduction of the mass of the scalar resonance. Therefore, interpreting the scalar as the recently observed 125 GeV state, implies that the mass originating solely from new strong dynamics can be much heavier, of the order of 1 TeV. The couplings of the scalar resonance with the Standard Model gauge bosons and fermions are evaluated, and found to be compatible with the current LHC results.

We present a fit to precision electroweak data in the standard model (SM) extended by an additional vector boson, ${Z}^{\ensuremath{'}}$, with suppressed couplings to the electron compared to the $Z$ boson, with couplings to the $b$-quark, and with mass close to the mass of the $Z$ boson. This scenario provides an excellent fit to forward-backward asymmetry of the $b$-quark measured on the $Z$-pole and $\ifmmode\pm\else\textpm\fi{}2\text{ }\text{ }\mathrm{GeV}$ off the $Z$-pole, and to lepton asymmetry, ${A}_{e}$, obtained from the measurement of left-right asymmetry for hadronic final states, and thus it removes the tension in the determination of the weak mixing angle from these two measurements. It also leads to a significant improvement in the total hadronic cross-section on the $Z$-pole and ${R}_{b}$ measured at energies above the $Z$-pole. We explore in detail properties of the ${Z}^{\ensuremath{'}}$ needed to explain the data and present a model for ${Z}^{\ensuremath{'}}$ with required couplings. The model preserves standard model Yukawa couplings; it is anomaly-free and can be embedded into grand unified theories. It allows a choice of parameters that does not generate any flavor violating couplings of the ${Z}^{\ensuremath{'}}$ to standard model fermions. Out of standard model couplings, it only negligibly modifies the left-handed bottom quark coupling to the $Z$ boson and the third column of the Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix. Modifications of standard model couplings in the charged lepton sector are also negligible. It predicts an additional down-type quark, $D$, with mass in the few hundred GeV range, and an extra lepton doublet, $L$, possibly much heavier than the $D$-quark. We discuss signatures of the ${Z}^{\ensuremath{'}}$ at the Large Hadron Collider and calculate the ${Z}^{\ensuremath{'}}b$ production cross-section, which is the dominant production mechanism for the ${Z}^{\ensuremath{'}}$.

We show that in an $SU(2)\otimes U(1)$ model with a DSF-like invisible axion it is possible to obtain (i) the convergence of the three gauge coupling constants at an energy scale near the Peccei-Quinn scale; (ii) the correct value for $\sin^2\hat{\theta}_W(M_Z)$; (iii) the stabilization of the proton by the cyclic $Z_{13}\otimes Z_3$ symmetries which also stabilize the axion as a solution to the strong CP problem. Concerning the convergence of the three coupling constants and the prediction of the weak mixing angle at the $Z$-peak, this model is as good as the minimal supersymmetric standard model with $\mu_{\rm SUSY}=M_Z$. We also consider the standard model with six and seven Higgs doublets. The main calculations were done in the 1-loop approximation but we briefly consider the 2-loop contributions.

In the standard model (SM), the Cabibbo-Kobayashi-Maskawa (CKM) matrix is the only origin of flavor violations (FVs). On the other hand, in general, there are a lot of sources of the FVs in a physics beyond the SM, through the diagonalizing matrices which make Yukawa matrices diagonal. Although most of the diagonalizing matrices are unknown ones, grand unified theories (GUTs) can fix these matrices. In particular, if we consider a GUT model based on the SO(10) group, these diagonalizing matrices are strongly related to each other because of the matter unification. However, this unification causes the problem on the realization of measured SM fermion masses and mixing angles. Up to now, many people showed that supersymmetric (SUSY) threshold corrections can solve this problem, especially unfavorable fermion mass relations. In this paper, we show that how these SUSY threshold corrections affect unknown diagonalizing matrices. Since these contributions are also related to the FVs induced by SUSY particles, we can estimate the maximal effect to the diagonalizing matrices. We found that the (1, 3) and (3, 1) elements of diagonalizing matrices for quarks can be as large as the corresponding mixing angle of the CKM matrix. Moreover, we found that the higher SUSY scale can predict the larger mixing angles, although strong cancellation between the Higgs mass parameters is needed to realize the electroweak symmetry breaking.

We study signals at the LHC for the Kaluza-Klein (KK) excitations of electroweak charged gauge bosons in the framework of the standard model (SM) fields propagating in the bulk of a warped extra dimension. Such a scenario can solve both the Planck-weak and flavor hierarchy problems of the SM. There are two such charged states in this scenario with couplings to light quarks and leptons being suppressed relative to those in the SM, whereas the couplings to top/bottom quarks are enhanced, similar to the case of electroweak neutral gauge bosons previously studied. However, unlike the case of electroweak neutral gauge bosons, there is no irreducible QCD background (including pollution from possibly degenerate KK gluons) for decays to top+bottom final states so that this channel is useful for the discovery of the charged states. Moreover, decays of electroweak charged gauge bosons to longitudinal W, Z and Higgs are enhanced just as for the neutral bosons. However, unlike for the neutral gauge bosons, the purely leptonic (and hence clean) decay mode of the WZ is fully reconstructible so that the ratio of the signal to the SM (electroweak) background can potentially be enhanced by restricting to the resonance region more efficiently. Wemore » show that such final states can give sensitivity to 2(3) TeV masses with an integrated luminosity of 100(300) fb{sup -1}. We emphasize that improvements in discriminating a QCD jet from a highly boosted hadronically decaying W, and a highly boosted top jet from a bottom jet will enhance the reach for these KK particles, and that the signals we study for the warped extra dimensional model might actually be applicable also to a wider class of nonsupersymmetric models of electroweak symmetry breaking.« less

Extensions of the Standard Model with an Abelian gauge group are constrained by gauge anomaly cancellation, so that only a limited number of possible charge assignments is allowed without the introduction of new chiral fermions. For flavour universal charges, couplings of the associated hidden photon to Standard Model fermions are flavour conserving at tree-level. We show explicitly that even the flavour specific charge assignments allowed by anomaly cancellation condition lead to flavour conserving tree-level couplings of the hidden photon to quarks and charged leptons \emph{if} the CKM or PMNS matrix can be successfully reconstructed. Further, loop-induced flavour changing couplings are strongly suppressed. As a consequence, the structure of the Majorana mass matrix is constrained and flavour changing tree-level couplings of the hidden photon to neutrino mass eigenstates are identified as a means to distinguish the $U(1)_{B-L}$ gauge boson from any other anomaly-free extension of the Standard Model without new chiral fermions. We present a comprehensive analysis of constraints and projections for future searches for a $U(1)_{B-3L_i}$ gauge boson, calculate the reach of resonance searches in $B$ meson decays and comment on the implications for non-standard neutrino interactions.

In grand unified theories based on extended (rank >4) gauge groups, the new gauge interactions require new fermions to ensure anomaly cancellation. We analyze the two kinds of new physics effects that are naturally present in these models: (i) the effects of the new neutral gauge bosons; (ii) the effects of a mixing of the known fermions with the new ones. Concentrating in particular on ${\mathrm{E}}_{6}$ and SO(10) models, we perform a global analysis of the electroweak data to constrain simultaneously these two new physics effects, and we pay particular attention to their reciprocal interplay. Our set of experimental results includes the data at the CERN ${e}^{+}{e}^{\ensuremath{-}}$ collider LEP on the $Z$ decay widths and fermion asymmetries, low-energy neutral-current experiments (atomic parity violation, $\ensuremath{\nu}$ scattering), the $W$-boson mass ${M}_{W}$, as well as charged-current measurements such as the various tests of the universality of the $W$-lepton couplings and the constraints on unitarity of the Cabibbo-Kobayashi-Maskawa matrix. We derive stringent bounds on the ${Z}_{0}\ensuremath{-}{Z}_{1}$ mixing ($|\ensuremath{\varphi}|\ensuremath{\lesssim}0.02$), on the fermion mixing parameters (${sin}^{2}{\ensuremath{\xi}}_{i}\ensuremath{\lesssim}0.01$ in most cases), and on the mass of the new gauge boson (${M}_{{Z}^{\ensuremath{'}}}>170\ensuremath{-}350$ GeV, depending on the model). In many observables the different sources of new physics induce comparable effects that can compensate each other. We confront the results derived by considering only one effect at a time with the results of a joint analysis, and we point out which of the existing bounds are relaxed and which ones remain unaffected.

New heavy gauge bosons exist in many models of new physics beyond the standard model of particle physics. Discovery of these W^\prime and Z^\prime resonances and the establishment of their spins, couplings, and other quantum numbers would shed light on the gauge structure of the new physics. The measurement of the polarization of the SM fermions from the gauge boson decays would decipher the handedness of the coupling of the new states, an important relic of the primordial new physics symmetry. Since the top quark decays promptly, its decay preserves spin information. We show how decays of new gauge bosons into third generation fermions (W^\prime \to tb, Z^\prime\to t\bar{t}) can be used to determine the handedness of the couplings of the new states and to discriminate among various new physics models.

Using the model independent average neutron rms radius of $^{133}\text{Cs}$ and $^{127}\text{I}$ obtained from the analysis of the coherent elastic neutrino-nucleus scattering data of the COHERENT experiment, we remove the long-standing $1.5\,\sigma$ tension between the Standard Model prediction and the weak mixing angle measurement from the atomic parity violation (APV) in caesium. The updated APV result becomes $\sin^2 \vartheta_{\textrm{W}}=0.239{}^{+0.006}_{-0.007}$, to be compared with the Standard Model prediction at low momentum transfer, $\sin^2 \vartheta_{\text{W}}^{\textrm{SM}} = 0.23857(5)$. Moreover, exploiting the fact that the APV result is highly sensitive to the caesium neutron rms radius, $R_{n}$, and assuming that the Standard Model is correct, we combine the APV and the COHERENT measurements in order to get a better determination of $R_{n}$. The value of $R_{n}=5.42\pm 0.31\,\textrm{fm}$ is obtained, improving significantly the current uncertainty. This result allows to infer a meaningful value of the caesium neutron skin, the difference between the neutron and proton distribution radii, equal to $\Delta R_{np}=0.62\pm 0.31\,\text{fm}$, showing for the first time a $2\, \sigma$ deviation from zero.