Higgs and supersymmetry

Global frequentist fits to the CMSSM and NUHM1 using the MasterCode framework predicted M _h ?119 GeV in fits incorporating the (g?2) _μ constraint and ?126 GeV without it. Recent results by ATLAS and CMS could be compatible with a Standard Model-like Higgs boson around M _h ?125 GeV. We use the previous MasterCode analysis to calculate the likelihood for a measurement of any nominal Higgs mass within the range of 115 to 130 GeV. Assuming a Higgs mass measurement at M _h ?125 GeV, we display updated global likelihood contours in the (m ₀,m _1/2) and other parameter planes of the CMSSM and NUHM1, and present updated likelihood functions for $m_{\tilde{g}}, m_{\tilde{q}_{R}}We perform a determination of the strong coupling constant using the latest ATLAS inclusive jet cross section data, from proton?Cproton collisions at $\sqrt{s}=7~\mathrm{TeV}$ , and their full information on the bin-to-bin correlations. Several procedures for combining the statistical information from the different data inputs are studied and compared. The theoretical prediction is obtained using NLO QCD, and it also includes non-perturbative corrections. Our determination uses inputs with transverse momenta between 45 and 600?GeV, the running of the strong coupling being also tested in this range. Good agreement is observed when comparing our result with the world average at the Z-boson scale, as well as with the most recent results from the Tevatron.     

Phenomenological implications of light stop and higgsinos

We examine the phenomenological implications of light $\tilde t_R $ and higgsinos in the Minimal Supersymetric Standard Model, assuming tan² ??<m _t m _b and heavy $\tilde t_L $ and gauginos. In this simplified setting, we study the contributions to ??m _{B d},?? _K,BR(b??s??),R _b???(Z??bb) /??(Z??hadrons),BR(t??bW), and their interplay.     

Flavoured co-annihilation

In minimal supergravity (mSUGRA) or CMSSM, one of the main co-annihilating partners of the neutralino is the lightest stau, $\tilde{\tau}_1$ . In the presence of flavour violation in the right-handed sector, the co-annihilating partner would be a flavour mixed state. The flavour effect is two-fold: (a) It changes the mass of $\tilde{\tau}_{1}$ , thus modifying the parameter space of the co-annihilation and (b) flavour violating scatterings could now contribute to the cross-sections in the early Universe. In fact, it is shown that for large enough ??~0.2, these processes would constitute the dominant channels in co-annihilation regions. The amount of flavour mixing permissible is constrained by flavour violating ?????? or ????e processes. For ??_RR mass insertions, the constraints from flavour violation are not strong enough in some regions of the parameter space due to partial cancellations in the amplitudes. In mSUGRA, the regions with cancelations within LFV amplitudes do not overlap with the regions of co-annihilations. In non-universal Higgs model (NUHM), however, these regions do overlap leading to significant flavoured co-annihilations. At the LHC and other colliders, these regions can constitute for interesting signals.     

Physics beyond the Standard Model through b → s μ ?+? μ ? transition

A comprehensive study of the impact of new-physics operators with different Lorentz structures on decays involving the b ?? s ?? ^?+? ?? ^? transition is performed. The effects of new vector?Caxial vector (VA), scalar?Cpseudoscalar (SP) and tensor (T) interactions on the differential branching ratios, forward?Cbackward asymmetries (A _FB??s), and direct CP asymmetries of ${\bar B}_{\rm s}^0 \to \mu^+ \mu^-$ , ${\bar B}_{\rm d}^0 \to$ $ X_{\rm s} \mu^+ \mu^-$ , ${\bar B}_{\rm s}^0 \to \mu^+ \mu^- \gamma$ , ${\bar B}_{\rm d}^0 \to {\bar K} \mu^+ \mu^-$ , and ${\bar B}_{\rm d}^0\to {\bar{K}^*} \mu^+ \mu^-$ are examined. In ${\bar B}_{\rm d}^0\to {\bar{K}^*} \mu^+ \mu^-$ , we also explore the longitudinal polarization fraction f _L and the angular asymmetries $A_{\rm T}^{(2)}$ and A _LT, the direct CP asymmetries in them, as well as the triple-product CP asymmetries $A_{\rm T}^{\rm (im)}$ and $A^{\rm (im)}_{\rm LT}$ . While the new VA operators can significantly enhance most of the observables beyond the Standard Model predictions, the SP and T operators can do this only for A _FB in ${\bar B}_{\rm d}^0 \to {\bar K} \mu^+ \mu^-$ .     

Inelastic Character of Solitons of Slowly Varying gKdV Equations

In this paper we study soliton-like solutions of the variable coefficients, the subcritical gKdV equation $$u_t + (u_{xx} -\lambda u + a(\varepsilon x) u^m )_x =0,\quad {\rm in} \quad \mathbb{R}_t\times\mathbb{R}_x, \quad m=2,3\,\, { \rm and }\,\, 4,$$ with ${\lambda\geq 0, a(\cdot ) \in (1,2)}$ a strictly increasing, positive and asymptotically flat potential, and ${\varepsilon}$ small enough. In previous works (Mu?oz in Anal PDE 4:573?C638, 2011; On the soliton dynamics under slowly varying medium for generalized KdV equations: refraction vs. reflection, SIAM J. Math. Anal. 44(1):1?C60, 2012) the existence of a pure, global in time, soliton u(t) of the above equation was proved, satisfying $$\lim_{t\to -\infty}\|u(t) - Q_1(\cdot -(1-\lambda)t) \|_{H^1(\mathbb{R})} =0,\quad 0\leq \lambda<1,$$ provided ${\varepsilon}$ is small enough. Here R(t, x) := Q _c (x ? (c ? ??)t) is the soliton of R _t +? (R _xx ??? R + R ^m ) _x =?0. In addition, there exists ${\tilde \lambda \in (0,1)}$ such that, for all 0?<??? <?1 with ${\lambda\neq \tilde \lambda}$ , the solution u(t) satisfies $$\sup_{t\gg \frac{1}{\varepsilon}}\|u(t) - \kappa(\lambda)Q_{c_\infty}(\cdot-\rho(t)) \|_{H^1(\mathbb{R})}\lesssim \varepsilon^{1/2}.$$ Here ${{\rho'(t) \sim (c_\infty(\lambda) -\lambda)}}$ , with ${{\kappa(\lambda)=2^{-1/(m-1)}}}$ and ${{c_\infty(\lambda)>\lambda}}$ in the case ${0<\lambda<\tilde\lambda}$ (refraction), and ${\kappa(\lambda) =1}$ and c _??(??)?<??? in the case ${\tilde \lambda<\lambda<1}$ (reflection). In this paper we improve our preceding results by proving that the soliton is far from being pure as t ?? +???. Indeed, we give a lower bound on the defect induced by the potential a(·), for all ${{0<\lambda<1, \lambda\neq \tilde \lambda}}$ . More precisely, one has $$\liminf_{t\to +\infty}\| u(t) - \kappa_m(\lambda)Q_{c_\infty}(\cdot-\rho(t)) \|_{H^1(\mathbb{R})}>rsim \varepsilon^{1 +\delta},$$ for any ${{\delta>0}}$ fixed. This bound clarifies the existence of a dispersive tail and the difference with the standard solitons of the constant coefficients, gKdV equation.     

Reanalysis of the mass difference ofB_d^0 - \bar B_d^0 within the Minimal Supersymmetric Standard Modelwithin the Minimal Supersymmetric Standard Model

We present a detailed and complete calculation of the loop corrections to the mass difference $\Delta {{m_{B_d^0 } } \mathord{\left/ {\vphantom {{m_{B_d^0 } } {m_{B_d^0 } }}} \right. \kern-0em} {m_{B_d^0 } }}$ . We include charginos and scalar up quarks as well as gluinos and scalar down quarks on the relevant loop diagrams. We include the mixings of the charginos and of the scalar partners of the left and right handed quarks. We find that the gluino contribution to this quantity is important with respect to the chargino contribution only in a small part of phase space: mainly when the gluino mass is small (～100 GeV) and the symmetry-breaking parameterm _S is below 300 GeV. This contribution is also important for very large values of tanβ (～50) irrespective of the other parameters. Otherwise, the chargino contribution dominates vastly and can be roughly as large as that of the Standard Model. We also present the contribution of the charged Higgs to the mass difference $\Delta {{m_{B_d^0 } } \mathord{\left/ {\vphantom {{m_{B_d^0 } } {m_{B_d^0 } }}} \right. \kern-0em} {m_{B_d^0 } }}$ in the casem _b tanβ?m _t cotβ. This last contribution can be larger than the Standard Model contribution for small values of the Higgs mass and small values of tanβ.     

The CMSSM and NUHM1 in light of 7 TeV LHC, B s →μ + μ − and XENON100 data

We make a frequentist analysis of the parameter space of the CMSSM and NUHM1, using a Markov Chain Monte Carlo (MCMC) with 95 (221) million points to sample the CMSSM (NUHM1) parameter spaces. Our analysis includes the ATLAS search for supersymmetric jets?+? signals using ～5/fb of LHC data at 7 TeV, which we apply using PYTHIA and a Delphes implementation that we validate in the relevant parameter regions of the CMSSM and NUHM1. Our analysis also includes the constraint imposed by searches for BR(B _s →μ ⁺ μ ^?) by LHCb, CMS, ATLAS and CDF, and the limit on spin-independent dark matter scattering from 225 live days of XENON100 data. We assume M _h ～125 GeV, and use a full set of electroweak precision and other flavour-physics observables, as well as the cold dark matter density constraint. The ATLAS_5/fb constraint has relatively limited effects on the 68 and 95 % CL regions in the (m ₀,m _1/2) planes of the CMSSM and NUHM1. The new BR(B _s →μ ⁺ μ ^?) constraint has greater impacts on these CL regions, and also impacts significantly the 68 and 95 % CL regions in the (M _A ,tanβ) planes of both models, reducing the best-fit values of tanβ. The recent XENON100 data eliminate the focus-point region in the CMSSM and affect the 68 and 95 % CL regions in the NUHM1. In combination, these new constraints reduce the best-fit values of m ₀,m _1/2 in the CMSSM, and increase the global χ ² from 31.0 to 32.8, reducing the p-value from 12 % to 8.5 %. In the case of the NUHM1, they have little effect on the best-fit values of m ₀,m _1/2, but increase the global χ ² from 28.9 to 31.3, thereby reducing the p-value from 15 % to 9.1 %.     

SU(5) andSU(2)×U(1) radiative breakings inN=1 supergravity unified models

Non-minimalSU(5) supergravity GUTs are analyzed in order to obtain theSU(5) andSU(2)×U(1) breakings à la Coleman-Weinberg as dynamical effects generated by the soft breaking terms, residues of supergravityN=1 (minimally coupled). Solutions are found that predict the existence ofSU(2)-triplets andSU(3)-octets as heavy asO(1 TeV). Supersymmetric Higgs masses, of the same order than the gravitino mass, must be introduced for the heavy, Σ(24), and lightH ₁ (2),H ₂ (2) sectors. Imposing the experimental bound \(m_{\tilde g} \gtrsim 60GeV\) , the lower boundsm _3/2?30 GeV, \(m_{\bar e} > 140GeV\) \(m_{\bar u} > 133GeV\) are obtained.     

The static multipole moments of Δ1236(3/2,3/2) from superconvergence inNγ → Δπ scattering

Saturating superconvergence sum rules inNγ→Δπ scattering byN andΔ, we are able to relate the (isoscalar) dipole magnetic moment \(\tilde \mu _\Delta\) and the quadrupole electric moment \(\tilde Q_\Delta\) of the isobarΔ to the electric charge \(\tilde Z_\Delta\) and the dipole magnetic momentμ _N of the nucleonN. The numerical results are: \(\tilde \mu _\Delta \equiv \mu _{\Delta ^ + } + \mu _{\Delta ^0 } = 3.26\) (in unitse/2M)=2.48 (in unitse/2m), and \(\tilde Q_\Delta \equiv Q_{\Delta ^ + } + Q_{\Delta ^0 } = 0.050\) (in unitse/M ²)=0.029 (in unitse/m ²), whereM(m) is the mass ofΔ(N). Neglecting the pion mass and takingM=m,μ _n /μ _p =?2/3, we get theSU ₆ result μ_Δ+=μ _p .     

Direct chargino–neutralino production at the LHC: interpreting the exclusion limits in the complex MSSM

We re-assess the exclusion limits on the parameters describing the supersymmetric (SUSY) electroweak sector of the MSSM obtained from the search for direct chargino–neutralino production at the LHC. We start from the published limits obtained for simplified models, where for the case of heavy sleptons the relevant branching ratio, $\mathrm {BR}(\tilde{\chi}^{0}_{2} \to \tilde{\chi}^{0}_{1} Z)$ , is set to one. We show how the decay mode $\tilde{\chi}^{0}_{2} \to \tilde{\chi}^{0}_{1} h$ , which cannot be neglected in any realistic model once kinematically allowed, substantially reduces the excluded parameter region. We analyze the dependence of the excluded regions on the phase of the gaugino soft SUSY-breaking mass parameter, M ₁, on the mass of the light scalar tau, $m_{{\tilde{\tau}_{1}}}$ , on tanβ as well as on the squark and slepton mass scales. Large reductions in the ranges of parameters excluded can be observed in all scenarios. The branching ratios of charginos and neutralinos are evaluated using a full NLO calculation for the complex MSSM. The size of the effects of the NLO calculation on the exclusion bounds is investigated. We furthermore assess the potential reach of the experimental analyses after collecting 100 fb^?1 at the LHC running at 13 TeV.     

Layered structure of superfluid4He at supercritical motion

Landau’s criterion plays an important role in the theory of superfluidity. According to this criterion, superfluid motion is possible if \(\tilde \varepsilon \left( p \right) \equiv \varepsilon \left( p \right) + pV > 0\) along the curve of the spectrum?(p) of excitations. For⁴He it means thatv<v _c,v _c≈60 m/sec.v _s is equal to the tangent of the slope to the roton part of the spectrum. The question of what happens to the liquid when this velocity is exceeded, as far as we know, remains unclear. We shall show that for small excesses abovev _c a one-dimensional periodic structure appears in the helium. A wave vector of this structure oriented opposite to the flow and equal toρ _c/h whereρ _c is the momentum at the tangent point. The quantity \(\tilde \varepsilon \left( p \right)\) is the energy of excitation in the liquid moving with velocity v. Inequality of Landau ensures that \(\tilde \varepsilon \) is positive. If \(\tilde \varepsilon \) becomes negative, then the boson distribution function \(n\left( {\tilde \varepsilon } \right)\) becomes negative, indicating the impossibility of thermodynamic equilibrium of the ideal gas of rotons; therefore the interaction between them must be taken into account. The final form of the energy operator is $$\hat H = \int {\left\{ {\hat \psi + \tilde \varepsilon \left( p \right)\hat \psi + \tfrac{g}{2}\hat \psi + \hat \psi + \hat \psi \hat \psi } \right\}} d^3 x, g \sim 2 \cdot 10^{ - 38} erg.cm.$$ Then we can seek the rotonψ-operator in the formψ=ηexp(i p _c r/h), determiningη from the condition that the energy is minimized. The result is (η)²=(v?v _c)ρ _c/g, forv>v _c. The plane waveψ corresponds to a uniform distribution of rotons. It leads, however, to a spatial modulation of the density of the helium, since the density operator \(\hat n\) contains a term which is linear in the operator \(\psi :\hat n = n_0 + \left( {n_0 } \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} {A \mathord{\left/ {\vphantom {A {\hat \psi \to \hat \psi ^ + }}} \right. \kern-0em} {\hat \psi \to \hat \psi ^ + }}\) ), where |A|²～ρ _c ² /2m?(ρ _c). Finally we find that the density of helium is modulated according to the law $$\frac{{n - n_0 }}{{n_0 }} = \left[ {\frac{{\left| A \right|^2 \left( {\nu - \nu _c } \right)\rho _c }}{{n_0 g}}} \right]^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \sin \rho _c x \approx 2,6\left[ {\frac{{\nu - \nu _c }}{{\nu _c }}} \right]^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \sin \rho _c x$$ . This phenomenon can be observed, in principle, in the experiments on scattering ofx-rays in moving helium.     

Z c (4025) as the hadronic molecule with hidden charm

We have studied the loosely bound $D^{*}\bar{D}^{*}$ system. Our results indicate that the recently observed charged charmonium-like structure Z _c (4025) can be an ideal $D^{*}\bar{D}^{*}$ molecular state. We have also investigated its pionic, dipionic, and radiative decays. We stress that both the scalar isovector molecular partner Z _c0 and three isoscalar partners ${\tilde{Z}}_{c0,c1,c2}$ should also exist if Z _c (4025) is a $D^{*}\bar{D}^{*}$ molecular state in the framework of the one-pion-exchange model. Z _c0 can be searched for in the channel e ⁺ e ^?→Y→Z _c0(4025)(ππ)_P-wave where Y can be Y(4260) or any other excited 1^?? charmonium or charmonium-like states such as Y(4360), Y(4660), etc. The isoscalar $D^{*}\bar{D}^{*}$ molecular states ${\tilde{Z}}_{c0,c2}$ with 0⁺(0⁺⁺) and 0⁺(2⁺⁺) can be searched for in the three pion decay channel $e^{+}e^{-}\to Y \to {\tilde{Z}}_{c0,c2} (3\pi)^{I=0}_{\text{P-wave}}$ . The isoscalar molecular state ${\tilde{Z}}_{c1}$ with 0^?(1^+?) can be searched for in the channel ${\tilde{Z}}_{c1}\eta$ . Experimental discovery of these partner states will firmly establish the molecular picture.     

Constraints on supersymmetry from LHC data on SUSY searches and Higgs bosons combined with cosmology and direct dark matter searches

The ATLAS and CMS experiments did not find evidence for Supersymmetry using close to 5/fb of published LHC data at a center-of-mass energy of 7 TeV. We combine these LHC data with data on $B^{0}_{s}\to \mu^{+}\mu^{-}$ (LHCb experiment), the relic density (WMAP and other cosmological data) and upper limits on the dark matter scattering cross sections on nuclei (XENON100 data). The excluded regions in the constrained Minimal Supersymmetric SM (CMSSM) lead to gluinos excluded below 1270 GeV and dark matter candidates below 220 GeV for values of the scalar masses (m ₀) below 1500 GeV. For large m ₀ values the limits of the gluinos and the dark matter candidate are reduced to 970 GeV and 130 GeV, respectively. If a Higgs mass of 125 GeV is imposed in the fit, the preferred SUSY region is above this excluded region, but the size of the preferred region is strongly dependent on the assumed theoretical error.     

Heavy gluino and squark decays atp \bar p collider

The recent limits, \(m_{\tilde g} , m_{\tilde q} \gtrsim 40\) , GeV for gluino and squark masses obtained from experiments at the collider are based on jet +p _T analysis, in the hypothesis that the gluino or the squark decays into photino+quarks with a branching ratio near to one. We show that this hypothesis is generally not justified for higher masses of the gluino and the squarks, 50 GeV \( \lesssim m_{\tilde g,\tilde q} \lesssim \) 150 GeV, relevant to present and future \(\bar p\) colliders. In an interesting range of the parameters we study the different decay modes and the related signatures, among which isolated leptons or photons in the final states.     

Likelihood analysis of the sub-GUT MSSM in light of LHC 13-TeV data

We describe a likelihood analysis using MasterCode of variants of the MSSM in which the soft supersymmetry-breaking parameters are assumed to have universal values at some scale \(M_\mathrm{in}\) below the supersymmetric grand unification scale \(M_\mathrm{GUT}\), as can occur in mirage mediation and other models. In addition to \(M_\mathrm{in}\), such ‘sub-GUT’ models have the 4 parameters of the CMSSM, namely a common gaugino mass \(m_{1/2}\), a common soft supersymmetry-breaking scalar mass \(m_0\), a common trilinear mixing parameter A and the ratio of MSSM Higgs vevs \(\tan \beta \), assuming that the Higgs mixing parameter \(\mu > 0\). We take into account constraints on strongly- and electroweakly-interacting sparticles from \(\sim 36\)/fb of LHC data at 13 TeV and the LUX and 2017 PICO, XENON1T and PandaX-II searches for dark matter scattering, in addition to the previous LHC and dark matter constraints as well as full sets of flavour and electroweak constraints. We find a preference for \(M_\mathrm{in}\sim 10^5\) to \(10^9 \,\, \mathrm {GeV}\), with \(M_\mathrm{in}\sim M_\mathrm{GUT}\) disfavoured by \(\Delta \chi ^2 \sim 3\) due to the \(\mathrm{BR}(B_{s, d} \rightarrow \mu ^+\mu ^-)\) constraint. The lower limits on strongly-interacting sparticles are largely determined by LHC searches, and similar to those in the CMSSM. We find a preference for the LSP to be a Bino or Higgsino with \(m_{\tilde{\chi }^0_{1}} \sim 1 \,\, \mathrm {TeV}\), with annihilation via heavy Higgs bosons H / A and stop coannihilation, or chargino coannihilation, bringing the cold dark matter density into the cosmological range. We find that spin-independent dark matter scattering is likely to be within reach of the planned LUX-Zeplin and XENONnT experiments. We probe the impact of the \((g-2)_\mu \) constraint, finding similar results whether or not it is included.     

Theoretical prediction of cosmological constant Λ in Veneziano ghost theory of QCD

Based on the Veneziano ghost theory of QCD, we predict the cosmological constant ??, which is related to energy density of cosmological vacuum by $ \Lambda = \frac{{8\pi G}} {3}\rho _\Lambda $ . In the Veneziano ghost theory, the vacuum energy density ?? _?? is expressed by absolute value of the product of quark vacuum condensate and quark current mass: $ \rho _\Lambda = \frac{{2N_f H}} {{m_{\eta '} }}c|m_q < 0|:\bar qq:|0 > | $ . We calculate the quark local vacuum condensates ??0|: $ \bar q $ q: |0?? by solving Dyson-Schwinger Equations for a fully dressed confining quark propagator S _f (p) with an effective gluon propagator G _???? ^ab (q). The quark current mass m _q is predicted by use of chiral perturbation theory. Our theoretical result of ??, with the resulting ??0|: 471-4 q: |0?? = ?(235 MeV)³ and light quark current mass m _q ? 3.29?C6.15 MeV, is in a good agreement with the observable of the ?? ?? 10^?52 m^?2 used widely in a great amount of literatures.     

Charged particle and π0 multiplicity distributions and the annihilation properties of\bar p p interactions at 70 GeV/c

The elastic and inelastic \(\bar p\) p cross sections at 70 GeV/c have been determined in an experiment performed at CERN using BEBC equipped with a TST. The topological cross sections were measured and the moments of the inelastic multiplicity distribution are 〈n _c 〉=6.16±0.09, 〈n _c 〉/D=2.04±0.05 andf ₂ ^cc =2.97±0.03. The average number of Dalitz pairs per inelastic event is (3.12±0.09)×10^?2. Assuming that these all arise from π⁰ decay the average π⁰ multiplicity is \(\langle n_{\pi ^0 } \rangle = 2.71 \pm 0.14\) . The \(\bar p\) p?pp cross section differences lead to an annihilation cross section σ _A = 4.42±0.41 mb and the moments of the annihilation multiplicty distribution are 〈n _A 〉=8.0±0.3, 〈n _A 〉/D=2.5±0.2 andf ₂ ^A?? =?1.4±0.3. An independent check of σ _A was made by investigating fast forward charged and neutral secondary interactions in the TST and in the surrounding neon-hydrogen mixture, and gives a value σ _A = 5.0±1.6 mb. The ratio of fast \(\bar n\) to \(\bar p\) production in non-annihilation interactions at 70 GeV/c is found to be 0.45±0.11.     

SupersymmetricZ 0 decay into lepton-antilepton and two photinos

Working in a softly broken supersymmetricSU(2)×U(1) standard model with the photino as lightest SUSY-particle \((m_{\bar \gamma } \leqq 10GeV)\) differential and total rates for the decay \(Z^0 \to l^ + l^ - \tilde \gamma \tilde \gamma \) as functions of various parameters of the model are presented. The decay involves intermediate scalar leptons and the total rate strongly depends on their masses. The results indicate that for a scalar lepton mass less than 70GeV this process might still be seen at SLC and CERN LEP I.     

Electroweak parameters from a high statistics neutrino nucleon scattering experiment

The final results from the WA 1/2 neutrino experiment in the 1984 CERN 160 GeV narrow band beam are presented. The ratiosR _ν and \(R_{\bar v} \) of neutral to charged current interaction rates of neutrinos and antineutrinos in iron are measured to beR _ν=0.3072±0.0033 and \(R_{\bar v} \) =0.382±0.016. A value of the electroweak parameter sin² θ _w = 1 ?m _W ² /m _Z ² is extracted fromR _ν. The result is sin² θ _w =0.228+0.013(m _c ?1.5)±0.0003 (theor.) wherem _c is the mass of the charmed quark in GeV form _t =60 GeV,M _H =100 GeV, ρ=1. CombiningR _ν and \(R_{\bar v} \) one obtains a value for ρ=0.991+0.023(m _c ?1.5)±0.020(exp.). Alternatively,R _ν and \(R_{\bar v} \) yield a precise value of the ratio of intermediate vector boson massesm _W /m _Z =0.880?0.007(m _c ?1.5)±0.002(exp.)±0.002(theor.). Comparison of these results with those from direct measurements of the vector boson masses are presented. In a model-independent analysis the left- and right-handed neutral current coupling constants,g _L ² andg _R ² , are determined.