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At least 1,297 records · Page 72

Integrated Modeling and Development of Component-Based Embedded Software in Scala

Programming of embedded systems is challenging due to the low-level design patterns normally applied in the implementation of such systems. Furthermore, programming languages normally considered suitable for this level of programming, such as C and C++, are themselves low-level compared to more modern programming languages. We report on an effort exploring modeling and programming of embedded systems in modern high-level programming languages combining object-oriented and functional programming. We present an integration of four separate internal DSLs (libraries), considered useful for embedded program- ming, in the Scala programming language, for programming and testing component-based systems. These include a DSL for defining components and their connections, and a DSL for programming the individual components as hierarchical state machines. Two additional DSLs support testing, and include a DSL for writing temporal logic flavored test oracles for monitoring program executions, and a DSL for rule-based test input generation. The paper discusses the gap between Scala as used here and the needs for embedded systems programming.

Bocchino, Robert↗

Neutrino Oscillations in Supernovae

A (core-collapse) supernova is the final death call of a massive star during which a gigantic amount of a special kind of elementary particles known as neutrinos are released for a brief period of time. An earlier work by the PI and his collaborators has shown that the dense neutrino gas deep inside the supernova can experience "flavor transformation" or "oscillations" in a collective fashion, a macroscopic quantum phenomenon spanning over distances of 100-1000 kilometers. During this process neutrinos of different energies and propagation directions change their identities simultaneously. This phenomenon may be a key to understanding the mechanism of supernova explosion and the origin of many of the chemical elements found on the earth which were produced in the supernovae exploded in the past. The previous understanding of neutrino oscillations in supernovae was based on a stationary 3-dimensional model with 1 spatial dimension and 2 momentum dimensions. In this "neutrino bulb model" neutrinos are emitted from a spherically symmetric surface and they are decoupled from the motion of matter and the production of chemical elements. In order to accurately model the neutrino oscillations in supernovae and determine its physical consequences, sophisticated 7-dimensional (1 temporal dimension + 3 spatial dimensions + 3 momentum dimensions) modelling of neutrino transport must be performed self-consistently together with the hydrodynamic simulation of the flow of energy and matter inside the supernova and with the calculation of the production and destruction of chemical elements through a large nucleosynthesis network. Although it will be long journey to achieve the lofty goal, our project has made important progress in three different fronts towards this goal. In the first front we explored new computing hardware on which the next generation simulation codes may be run. We ported the neutrino bulb code to the platform of Graphics Processing Unit (GPU) and then later developed a new bulb code that can be run on supercomputers equipped with the Intel Xeon CPUs and/or the Xeon Phi coprocessors. In the second front we developed new algorithms that can be used towards computing neutrino oscillations in multi-dimensional models. We have developed a moment expansion method which is approximately 10 times more efficient than the old algorithm. We have also developed numerical codes to solve neutrino oscillations in toy models with two spatial dimensions. In the last front we used analytic methods to study neutrino oscillations in more sophisticated models, e.g. of multiple spatial dimensions and/or with time dependence. By analyzing the neutrino oscillations in toy models with two spacial dimensions we found that the approximate spacial translation symmetry, which is similar to the spherical symmetry in the neutrino bulb model, can be broken spontaneously as neutrino oscillations begin. By analyzing a time-dependent neutrino bulb model we found that certain modes of neutrino oscillations that are suppressed in the stationary model can become active in the time-dependent model. We have also developed theories which give insights to how ordinary matter may affect neutrino oscillations in supernovae and other astrophysical environments.

Duan, Huaiyu↗

Peccei-Quinn symmetry and nucleon decay in renormalizable SUSY SO(10)

We suggest simple ways of implementing Peccei-Quinn (PQ) symmetry to solve the strong CP problem in renormalizable SUSY SO(10) models with a minimal Yukawa sector. Realistic fermion mass generation requires that a second pair of Higgs doublets survive down to the PQ scale. We show how unification of gauge couplings can be achieved in this context. Higgsino mediated proton decay rate is strongly suppressed by a factor of (M PQ /M GUT ) 2 , which enables all SUSY particles to have masses of order TeV. With TeV scale SUSY spectrum, $p → \bar{ν}K^+$ decay rate is expected to be in the observable range. Lepton flavor violating processes µ → eγ decay and µ - e conversion in nuclei, induced by the Dirac neutrino Yukawa couplings, are found to be within reach of forthcoming experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The Future Circular Collider: a Summary for the US 2021 Snowmass Process

In this white paper for the 2021 Snowmass process, we give a description of the proposed Future Circular Collider (FCC) project and its physics program. The paper summarizes and updates the discussion submitted to the European Strategy on Particle Physics. After construction of an approximately 90 km tunnel, an electron-positron collider based on established technologies allows world-record instantaneous luminosities at center-of-mass energies from the Z resonance up to tt thresholds, enabling a rich set of fundamental measurements including Higgs couplings determinations at the sub percent level, precision tests of the weak and strong forces, and searches for new particles, including dark matter, both directly and via virtual corrections or mixing. Among other possibilities, the FCC-ee will be able to (i) indirectly discover new particles coupling to the Higgs and/or electroweak bosons up to scales around 7 and 50 TeV, respectively; (ii) perform competitive SUSY tests at the loop level in regions not accessible at the LHC; (iii) study heavy-flavor and tau physics in ultra-rare decays beyond the LHC reach, and (iv) achieve the best potential in direct collider searches for dark matter, sterile neutrinos, and axion-like particles with masses up to around 90 GeV. The tunnel can then be reused for a proton-proton collider, establishing record center-of-mass collision energy, allowing unprecedented reach for direct searches for new particles up to the around 50 TeV scale, and a diverse program of measurements of the Standard Model and Higgs boson, including a precision measurement of the Higgs self-coupling, and conclusively testing weakly-interacting massive particle scenarios of thermal relic dark matter.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

A light Higgs at the LHC and the B-anomalies

After the Higgs discovery, the LHC has been looking for new resonances, decaying into pairs of Standard Model (SM) particles. Recently, the CMS experimen observed an excess in the di-photon channel, with a di-photon invariant mass of about 96 GeV. This mass range is similar to the one of an excess observed in the search for the associated production of Higgs bosons with the Z neutral gauge boson at LEP, with the Higgs bosons decaying to bottom quark pairs. On the other hand, the LHCb experiment observed a discrepancy with respect to the SM expectations of the ratio of the decay of B -mesons to K -mesons and a pair of leptons, \( {R}_{K^{\left(\ast \right)}}=BR\left(B\to {K}^{\left(\ast \right)}{\mu}^{+}{\mu}^{-}\right)/BR\left(B\to {K}^{\left(\ast \right)}{e}^{+}{e}^{-}\right) \) . This observation provides a hint of the violation of lepton-flavor universality in the charged lepton sector and may be explained by the existence of a vector boson originating form a \( U{(1)_{L_{\mu}}}_{-{L}_{{}_{\tau }}} \) symmetry and heavy quarks that mix with the left-handed down quarks. Since the coupling to heavy quarks could lead to sizable Higgs di-photon rates in the gluon fusion channel, in this article we propose a common origin of these anomalies identifying a Higgs associated with the breakdown of the \( U{(1)_{L_{\mu}}}_{-{L}_{{}_{\tau }}} \) symmetry and at the same time responsible to the quark mixing, with the one observed at the LHC. We also discuss the constraints on the identification of the same Higgs with the one associated with the bottom quark pair excess observed at LEP.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The Palomar Transient Factory Core-collapse Supernova Host-galaxy Sample. I. Host-galaxy Distribution Functions and Environment Dependence of Core-collapse Supernovae

Several thousand core-collapse supernovae (CCSNe) of different flavors have been discovered so far. However, identifying their progenitors has remained an outstanding open question in astrophysics. Studies of SN host galaxies have proven to be powerful in providing constraints on the progenitor populations. In this paper, we present all CCSNe detected between 2009 and 2017 by the Palomar Transient Factory. This sample includes 888 SNe of 12 distinct classes out to redshift z ≈ 1. We present the photometric properties of their host galaxies from the far-ultraviolet to the mid-infrared and model the host-galaxy spectral energy distributions to derive physical properties. The galaxy mass function of Type Ic, Ib, IIb, II, and IIn SNe ranges from 105 to 1011.5 M o˙, probing the entire mass range of star-forming galaxies down to the least-massive star-forming galaxies known. Moreover, the galaxy mass distributions are consistent with models of star-formation-weighted mass functions. Regular CCSNe are hence direct tracers of star formation. Small but notable differences exist between some of the SN classes. Type Ib/c SNe prefer galaxies with slightly higher masses (i.e., higher metallicities) and star formation rates than Type IIb and II SNe. These differences are less pronounced than previously thought. H-poor superluminous supernovae (SLSNe) and SNe Ic-BL are scarce in galaxies above 1010 M o˙. Their progenitors require environments with metallicities of < 0.4 and < 1 solar, respectively. In addition, the hosts of H-poor SLSNe are dominated by a younger stellar population than all other classes of CCSNe. Our findings corroborate the notion that low metallicity and young age play an important role in the formation of SLSN progenitors.

79 ASTRONOMY AND ASTROPHYSICS↗

Effects of gamma-Radiation on Select Lipids and Antioxidants

Radiation encountered on an extended duration space mission (estimates of 3 Sieverts for a mission to Mars) poses a threat not only to human health, but also to the quality, nutritional value, and palatability of the food system. Free radicals generated by radiation interaction with foods may initiate many unwanted reactions including: 1) autoxidation in lipids that alters flavor, odor, and concentrations of essential fatty acids, and 2) depletion of antioxidants food products and dietary supplements. Studies have shown that antioxidants may provide long term health protection from oxidative stress caused by radiation exposure; therefore, consumption of antioxidants will be important. Stability of essential fatty acids is also important for astronauts long-term health status. The objectives of this study were to characterize the effects of low dose gamma-radiation on lipids and antioxidants by monitoring oxidation and reducing power, respectively, in model systems. Select oils and antioxidants were exposed to levels of gamma-radiation ranging from 0 to 1000 Gy (1 Gy = 1 Sv) using a Gammacell 220 and stored at ambient or elevated temperatures (65 C) for up to 3 months prior to analysis. A Fricke dosimeter was used to verify differences between the radiation doses administered. Primary and secondary products of lipid oxidation in soybean and peanut oils were monitored using conjugated diene and 2-thiobarbituric acid (TBARs) assays. Changes in fatty acid composition and formation and vitamin E levels were also measured. The reducing power of antioxidant compounds, including vitamins C and E and beta-carotene, was determined using the ferric reducing antioxidant power (FRAP) assay. Significant differences (alpha =0.05) were present between all radiation doses tested using the Fricke dosimeter. Increasing radiation doses above 3 Sv resulted in significantly (alpha =0.05) elevated levels of oxidation and free fatty acids in soybean and peanut oils. Decreases in concentrations of essential fatty acids upon increasing radiation doses were also observed. Increasing radiation doses caused significant (alpha =0.05) decreases in reducing power and hence the effectiveness of vitamins C and E as well as beta-carotene. This work establishes a need for quantifying the effects of space relevant radiation doses in the development of a food system for an extended duration mission and for identifying threshold radiation levels that will impact the useful shelf-life of the variety of foods that will be sent. Eventual rancidity of lipids and the loss of antioxidant bioprotective effects are major concerns for the acceptability and nutritional profile of a food system.

Gandolph, Jacob↗

Different flavors of exact-factorization-based mixed quantum-classical methods for multistate dynamics

Here, the exact factorization approach has led to the development of new mixed quantum-classical methods for simulating coupled electron–ion dynamics. We compare their performance for dynamics when more than two electronic states are occupied at a given time, and analyze: (1) the use of coupled versus auxiliary trajectories in evaluating the electron–nuclear correlation terms, (2) the approximation of using these terms within surface-hopping and Ehrenfest frameworks, and (3) the relevance of the exact conditions of zero population transfer away from nonadiabatic coupling regions and total energy conservation. Dynamics through the three-state conical intersection in the uracil radical cation as well as polaritonic models in one dimension are studied.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

MUonE sensitivity to new physics explanations of the muon anomalous magnetic moment

The MUonE experiment aims at a precision measurement of the hadronic vacuum polarization contribution to the muon g – 2, via elastic muon-electron scattering. Since the current muon g – 2 anomaly hints at the potential existence of new physics (NP) related to the muon, the question then arises as to whether the measurement of hadronic vacuum polarization in MUonE could be affected by the same NP as well. In this work, we address this question by investigating a variety of NP explanations of the muon g – 2 anomaly via either vector or scalar mediators with either flavor-universal, non-universal or even flavor-violating couplings to electrons and muons. We derive the corresponding MUonE sensitivity in each case and find that the measurement of hadronic vacuum polarization at the MUonE is not vulnerable to any of these NP scenarios.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

$Ξ$ 𝑐 → $Ξ$ form factors from lattice QCD with domain-wall quarks: A new piece in the puzzle of $Ξ^0_𝑐$ decay rates

We present a lattice quantum chromodynamics (QCD) determination of the vector and axial-vector form factors that describe the charm-baryon semileptonic decays Ξ 𝑐 → Ξ⁢ℓ + ⁢𝜈 ℓ . The calculation uses a domain-wall action for the up, down, and strange quarks, and an anisotropic clover action for the charm quark. We use four ensembles of gauge-field configurations generated by the RBC and UKQCD collaborations, with lattice spacings between 0.111 and 0.073 fm and pion masses ranging from 420 to 230 MeV. We present Standard Model predictions for the decay rates and branching fractions of Ξ$^0_𝑐$ → Ξ$^−_𝑐$⁢ℓ + ⁢𝜈 ℓ and Ξ$^+_𝑐$ → Ξ$^0_𝑐$⁢ℓ + ⁢𝜈 ℓ for ℓ =𝑒, 𝜇. In particular, we obtain Γ⁡(Ξ$^0_𝑐$ → Ξ − ⁢𝑒 + ⁢𝜈 𝑒 )/|𝑉 𝑐⁢𝑠 | 2 = 0.2515⁢(73) ps −1 and ℬ⁡(Ξ$^0_𝑐$ → Ξ − ⁢𝑒 +⁢ 𝜈 𝑒 ) = 3.58⁢(12)%. These values are higher than those predicted by a previous lattice calculation and substantially higher than the experimentally measured values, but consistent with expectations from approximate 𝑆⁢𝑈⁡(3) flavor symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Interplaying mechanisms behind single inclusive jet suppression in heavy-ion collisions

The suppression factor for single inclusive jets in Pb + Pb collisions at the Large Hadron Collider (LHC) has a weak dependence on the transverse momentum $p_T$ and remains almost the same at two colliding energies, $\sqrt{s}$ = 2.76 and 5.02 TeV, though the central rapidity density of bulk hadrons increases by about 20%. Here, this phenomenon is investigated within the linear Boltzmann transport (LBT) model, which includes elastic and inelastic processes based on perturbative QCD for both jet shower and recoil medium partons as they propagate through a quark-gluon plasma (QGP). With the dynamic evolution of the QGP given by the 3 + 1 D CLVisc hydrodynamic model with event-by-event fully fluctuating initial conditions, single inclusive jet suppression in Pb + Pb collisions from LBT agrees well with experimental data. The weak $ \sqrt{s} $ and $p_T$ dependence of the jet suppression factor at LHC are found to result directly from the $ \sqrt{s} $ dependence of the initial jet $p_T$ spectra and slow $p_T$ dependence of the jet energy loss. Contributions from jet-induced medium response, influence of radial expansion, both of which depend on jet-cone size, and jet flavor composition all conjoin to give a slow $p_T$ dependence of jet energy loss and the single jet suppression factor R AA , their dependence on $\sqrt{s}$ , and jet-cone size. Single inclusive jet suppression at $\sqrt{s}$ = 200 GeV is also predicted that actually decreases slightly with p T in the $p_T$< 50 GeV/c range because of the steeper initial jet spectra though the $p_T$ dependence of the jet energy loss is weaker than that at LHC.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Searching for New Physics with Flavor Violating Observables

In this talk, I review the status and prospects of several low energy flavor observables that are highly sensitive to New Physics effects. In particular I discuss the implications for possible New Physics in b {yields} s transitions coming from the recent experimental results on the B{sub s} mixing phase, the branching ratio of the rare decay B{sub s} {yields} {mu}{sup +}{mu}{sup -}, and angular observables in the B {yields} K* {mu}{sup +}{mu}{sup -} decay. Also the recent evidence for direct CP violation in singly Cabibbo suppressed charm decays and its interpretation in the context of New Physics models is briefly discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Up, down, and strange nucleon axial form factors from lattice QCD

Here, we report a calculation of the nucleon axial form factors $G_A^q(Q^2)$ and $G_P^q(Q^2)$ for all three light quark flavors $q\in\{u,d,s\}$ in the range $0\leq Q^2\lesssim 1.2\text{ GeV}^2$ using lattice QCD. Our work was done using a single ensemble with pion mass 317 MeV and made use of the hierarchical probing technique to efficiently evaluate the required disconnected loops. We perform nonperturbative renormalization of the axial current, including a nonperturbative treatment of the mixing between light and strange currents due to the singlet-nonsinglet difference caused by the axial anomaly. The form factor shapes are fit using the model-independent $z$ expansion. From $G_A^q(Q^2)$, we determine the quark contributions to the nucleon spin and axial radii. By extrapolating the isovector $G_P^{u-d}(Q^2)$, we obtain the induced pseudoscalar coupling relevant for ordinary muon capture and the pion-nucleon coupling constant. We also found that the disconnected contributions to $G_P$ form factors are large, and give an interpretation based on the dominant influence of the pseudoscalar poles in these form factors.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Search for flavor changing neutral current interactions of the top quark in final states with a photon and additional jets in proton-proton collisions at s = 13 TeV

A search for the production of a top quark in association with a photon and additional jets via flavor changing neutral current interactions is presented. The analysis uses proton-proton collision data recorded by the CMS detector at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb - 1 . The search is performed by looking for processes where a single top quark is produced in association with a photon, or a pair of top quarks where one of the top quarks decays into a photon and an up or charm quark. Events with an electron or a muon, a photon, one or more jets, and missing transverse momentum are selected. Multivariate analysis techniques are used to discriminate signal and standard model background processes. No significant deviation is observed over the predicted background. Observed (expected) upper limits are set on the branching fractions of top quark decays: B ( t → u γ ) < 0.95 × 10 - 5 ( 1.20 × 10 - 5 ) and B ( t → c γ ) < 1.51 × 10 - 5 ( 1.54 × 10 - 5 ) at 95% confidence level, assuming a single nonzero coupling at a time. The obtained limit for B ( t → u γ ) is similar to the current best limit, while the limit for B ( t → c γ ) is significantly tighter than previous results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Lepton universality violation with lepton flavor conservation in B-meson decays

Anomalies in semileptonic B-meson decays present interesting patterns that might be revealing the shape of the new physics to come. Under the assumption that neutrino and charged lepton mass terms are the only sources of flavor violation and given the hierarchy between the two, we find that charged lepton universality violation without charged lepton flavor violation naturally arises. This can account for a deficit of B + → K + μμ over B + → K + ee decays with new physics coupled predominantly to muons and a new physics scale of a few TeV. A generic prediction of this scenario is a large enhacement of tauonic B decay rates that, in particular, could accommodate an excess in B → D (*) τ ν. For the most part, the study is carried out in an effective field theory framework with an underlying SU(2) L × U(1) Y symmetry that emphasizes the model-independent correlations between low- and high-energy observables. As an example, a connection between B-decays and top physics is pointed out. To complement the discussion, all possible (spin 0 and 1) leptoquark models are matched to the low-energy field theory so that the effective analysis can be used to survey these candidates for new physics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Higgs-confinement transitions in QCD from symmetry protected topological phases

In gauge theories with fundamental matter there is typically no sharp way to distinguish confining and Higgs regimes, e.g. using generalized global symmetries acting on loop order parameters. It is standard lore that these two regimes are continuously connected, as has been explicitly demonstrated in certain lattice and continuum models. We point out that Higgsing and confinement sometimes lead to distinct symmetry protected topological (SPT) phases -- necessarily separated by a phase transition -- for ordinary global symmetries. We present explicit examples in 3+1 dimensions, obtained by adding elementary Higgs fields and Yukawa couplings to QCD while preserving parity P and time reversal T. In a suitable scheme, the confining phases of these theories are trivial SPTs, while their Higgs phases are characterized by non-trivial P- and T-invariant theta-angles θ f , θ g = π for flavor or gravity background gauge fields, i.e. they are topological insulators or superconductors. Finally, we consider conventional three-flavor QCD (without elementary Higgs fields) at finite U(1) B baryon-number chemical potential μ B , which preserves P and T. At very large μ B , three-flavor QCD is known to be a completely Higgsed color superconductor that also spontaneously breaks U(1) B . We argue that this high-density phase is in fact a gapless SPT, with a gravitational theta-angle θ g = π that safely co-exists with the U(1) B Nambu-Goldstone boson. We explain why this SPT motivates unexpected transitions in the QCD phase diagram, as well as anomalous surface modes at the boundary of quark-matter cores inside neutron stars.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Beyond ferryl-mediated hydroxylation: 40 years of the rebound mechanism and C–H activation

Since our initial report in 1976, the oxygen rebound mechanism has become the consensus mechanistic feature for an expanding variety of enzymatic C–H functionalization reactions and small molecule biomimetic catalysts. For both the biotransformations and models, an initial hydrogen atom abstraction from the substrate (R–H) by high-valent iron-oxo species (Fe n =O) generates a substrate radical and a reduced iron hydroxide, [Fe n-1 –OH ·R]. This caged radical pair then evolves on a complicated energy landscape through a number of reaction pathways, such as oxygen rebound to form R–OH, rebound to a non-oxygen atom affording R–X, electron transfer of the incipient radical to yield a carbocation, R + , desaturation to form olefins, and radical cage escape. These various flavors of the rebound process, often in competition with each other, give rise to the wide range of C–H functionalization reactions performed by iron-containing oxygenases. In this review, we first recount the history of radical rebound mechanisms, their general features, and key intermediates involved. We will discuss in detail the factors that affect the behavior of the initial caged radical pair and the lifetimes of the incipient substrate radicals. Several representative examples of enzymatic C–H transformations are selected to illustrate how the behaviors of the radical pair [Fe n-1 –OH ·R] determine the eventual reaction outcome. Finally, we discuss the powerful potential of “radical rebound” processes as a general paradigm for developing novel C–H functionalization reactions with synthetic, biomimetic catalysts. We envision that new chemistry will continue to arise by bridging enzymatic “radical rebound” with synthetic organic chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Search for Z' bosons decaying to pairs of heavy Majorana neutrinos in proton-proton collisions at $ \sqrt{s} $ = 13 TeV

A search for the production of pairs of heavy Majorana neutrinos (N ℓ ) from the decays of Z' bosons is performed using the CMS detector at the LHC. The data were collected in proton-proton collisions at a center-of-mass energy of $\sqrt s$ = 13 TeV, with an integrated luminosity of 138 fb –1 . The signature for the search is an excess in the invariant mass distribution of the final-state objects, two same-flavor leptons (e or μ) and at least two jets. No significant excess of events beyond the expected background is observed. Upper limits at 95% confidence level are set on the product of the Z' production cross section and its branching fraction to a pair of N ℓ , as functions of N ℓ and Z' boson masses (m N ℓ and m Z' , respectively) for m Z' from 0.4 to 4.6 TeV and m N ℓ from 0.1 TeV to m Z' /2. In the theoretical framework of a left-right symmetric model, exclusion bounds in the m N ℓ -m Z' plane are presented in both the electron and muon channels. The observed upper limit on m Z' reaches up to 4.42 TeV. These are the most restrictive limits to date on the mass of N ℓ as a function of the Z' boson mass.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗