On the Standard Model prediction for \mathcal{B}(B_{s,d} \to \mu^{+} \mu^{-})

The decay B _s →μ ⁺ μ ^? is one of the milestones of the flavor program at the LHC. We reappraise its Standard Model prediction. First, by analyzing the theoretical rate in the light of its main parametric dependence, we highlight the importance of a complete evaluation of higher-order electroweak corrections, at present known only in the large-m _t limit, and leaving sizable dependence on the definition of electroweak parameters. Using insights from a complete calculation of such corrections for $K\to\pi\nu\bar{\nu}We present O(?? _s ) results on the decays of polarized W ^± and Z bosons into massive quark pairs. The NLO QCD corrections to the polarized decay functions are given up to the second order in the quark mass expansion. We find a surprisingly strong dependence of the NLO polarized decay functions on finite quark mass effects even at the relatively large mass scale of the W ^± and Z bosons. As a main application we consider the decay t??b+W ⁺ involving the helicity fractions ?? _mm of the W ⁺ boson followed by the polarized decay $W^{+}(\uparrow)\to q_{1}\bar{q}_{2}$ for which we determine the O(?? _s ) polar angle decay distribution. We also discuss NLO polarization effects in the production/decay process $e^{+}e^{-}\to Z(\uparrow)\to q\bar{q}$ .     

Forward-backward asymmetry in top quark semileptonic decay

The semileptonic decay of the top quark t → bW⁺ → bl⁺ν_l is analyzed in the rest system of the W. The forward-backward asymmetry of the lepton l⁺ with respect to the heavy quark direction is defined and computed. It is argued that this observable will be an ideal tool to study top quark properties at Tevatron and LHC. Higher order QCD corrections are calculated and their structure is elucidated in some detail.     

Status and prospects of top-quark physics

The top quark is the heaviest elementary particle observed to date. Its large mass of about 173 GeV/c² makes the top quark act differently than other elementary fermions, as it decays before it hadronises, passing its spin information on to its decay products. In addition, the top quark plays an important role in higher order loop corrections to standard model processes, which makes the top-quark mass a crucial parameter for precision tests of the electroweak theory. The top quark is also a powerful probe for new phenomena beyond the standard model.During the time of discovery at the Tevatron in 1995 only a few properties of the top quark could be measured. In recent years, since the start of Tevatron Run II, the field of top-quark physics has changed and entered a precision era. This report summarises the latest measurements and studies of top-quark properties and gives prospects for future measurements at the Large Hadron Collider (LHC).     

Update of the global electroweak fit and constraints on two-Higgs-doublet models

We present an update of the global fit of the Standard Model electroweak sector to latest experimental results. We include new kinematic top quark and W boson mass measurements from the LHC, a \(\sin \!^2\theta ^{\ell }_{\mathrm{eff}}\) result from the Tevatron, and a new evaluation of the hadronic contribution to \(\alpha (M_Z^2)\). We present tests of the internal consistency of the electroweak Standard Model and updated numerical predictions of key observables. The electroweak data combined with measurements of the Higgs boson coupling strengths and flavour physics observables are used to constrain parameters of two-Higgs-doublet models.     

Techniques for the Calculation of Electroweak Radiative Corrections at the One-Loop Level and Results for W-physics at LEP 200

We review the techniques necessary for the calculation of virtual electroweak and soft photonic corrections at the one-loop level. In particular we describe renormalization, calculation of one-loop integrals and evaluation of one-loop Feynman amplitudes. We summarize many explicit results of general relevance. We give the Feynman rules and the explicit form of the counterterms of the electroweak standard model, we list analytical expressions for scalar one-loop integrals and reduction of tensor integrals, we present the decomposition of the invariant matrix element for processes with two external fermions and we give the analytic form of soft photonic corrections. These techniques are applied to physical processes with external W-bosons. We present the full set of analytical formulae and the corresponding numerical results for the decay width of the W-boson and the top quark. We discuss the cross section for the production of W-bosons in e⁺ e⁻ annihilation including all O(x) radiative corrections and finite width effects. Improved Born approximations for these processes are given.     

Combined fit of low energy constraints to minimal supersymmetry and discovery potential at LEP II

Within the Constrained Minimal Supersymmetric Standard Model (CMSSM) it is possible to predict the low energy gauge couplings and masses of the 3. generation particles from a few parameters at the GUT scale. In addition the MSSM predicts electroweak symmetry breaking due to large radiative corrections from Yukawa couplings, thus relating theZ ⁰ boson mass to the top quark mass. From ax ² analysis, in which these constraints can be considered simultaneously, one can calculate the probability for each point in the MSGUT parameter space. The recently measured top quark mass prefers two solutions for the mixing angle in the Higgs sector: tanβ in the range between 1 and 3 or alternatively tanβ≈25?50. For both cases we find a uniquex ² minimum in the parameter space. From the corresponding most probable parameters at the GUT scale, the masses of all predicted particles can be calculated at low energies using the RGE, albeit with rather large errors due to the logarithmic nature of the running of the masses and coupling constants. Our fits include full second order corrections for the gauge and Yukawa couplings, low energy threshold effects, contributions of all (s)particles to the Higgs potential and corrections tom _b from gluinos and higgsinos, which exclude (in our notation) positive values of the mixing parameterμ in the Higgs potential for the large tanβ region. Further constraints can be derived from the branching ratio for the radiative (penguin) decay of theb-quark intosγ and the lower limit on the lifetime of the universe, which requires the dark matter density due to the Lightest Super-symmetric Particle (LSP) not to overclose the universe. For the low tanβ solution these additional constraints can be fulfilled simultaneously for quite a large region of the parameter space. In contrast, for the high tanβ solution the correct value for theb→sγ rate is obtained only for small values of the gaugino scale and electroweak symmetry breaking is difficult, unless one assumes the minimal SU(5) to be a subgroup of a larger symmetry group, which is broken between the Planck scale and the unification scale. In this case small splittings in the Yukawa couplings are expected at the unification scale and electroweak symmetry breaking is easily obtained, provided the Yukawa coupling for the top quark is slightly above the one for the bottom quark, as expected e.g. if the larger symmetry group would be SO(10). For particles, which are most likely to have masses in the LEP II energy range, the cross sections are given for the various energy scenarios at LEP II. For low tanβ the production of the lightest Higgs boson, which is expected to have a mass below 103 GeV, is the most promising channel, while for large tanβ the production of charginos and/or neutralinos covers the preferred parameter space.     

Combined fit of low energy constraints to minimal supersymmetry and discovery potential at LEP II

Within the Constrained Minimal Supersymmetric Standard Model (CMSSM) it is possible to predict the low energy gauge couplings and masses of the 3. generation particles from a few parameters at the GUT scale. In addition the MSSM predicts electroweak symmetry breaking due to large radiative corrections from Yukawa couplings, thus relating theZ ⁰ boson mass to the top quark mass. From ax ² analysis, in which these constraints can be considered simultaneously, one can calculate the probability for each point in the MSGUT parameter space. The recently measured top quark mass prefers two solutions for the mixing angle in the Higgs sector: tan?? in the range between 1 and 3 or alternatively tan????25?50. For both cases we find a uniquex ² minimum in the parameter space. From the corresponding most probable parameters at the GUT scale, the masses of all predicted particles can be calculated at low energies using the RGE, albeit with rather large errors due to the logarithmic nature of the running of the masses and coupling constants. Our fits include full second order corrections for the gauge and Yukawa couplings, low energy threshold effects, contributions of all (s)particles to the Higgs potential and corrections tom _b from gluinos and higgsinos, which exclude (in our notation) positive values of the mixing parameter?? in the Higgs potential for the large tan?? region. Further constraints can be derived from the branching ratio for the radiative (penguin) decay of theb-quark intos?? and the lower limit on the lifetime of the universe, which requires the dark matter density due to the Lightest Super-symmetric Particle (LSP) not to overclose the universe. For the low tan?? solution these additional constraints can be fulfilled simultaneously for quite a large region of the parameter space. In contrast, for the high tan?? solution the correct value for theb??s?? rate is obtained only for small values of the gaugino scale and electroweak symmetry breaking is difficult, unless one assumes the minimal SU(5) to be a subgroup of a larger symmetry group, which is broken between the Planck scale and the unification scale. In this case small splittings in the Yukawa couplings are expected at the unification scale and electroweak symmetry breaking is easily obtained, provided the Yukawa coupling for the top quark is slightly above the one for the bottom quark, as expected e.g. if the larger symmetry group would be SO(10). For particles, which are most likely to have masses in the LEP II energy range, the cross sections are given for the various energy scenarios at LEP II. For low tan?? the production of the lightest Higgs boson, which is expected to have a mass below 103 GeV, is the most promising channel, while for large tan?? the production of charginos and/or neutralinos covers the preferred parameter space.     

Electroweak radiative corrections toe + e −→γZ 0

We calculated the explicit analytic expressions for the electroweak radiative corrections to the differential cross sectione ⁺ e ^?→γZ ⁰ to one-loop in the framework of the Glashow-Salam-Weinberg model. Special attention is payed to the dependence on the Higgs and top quark masses.     

Electroweak one-loop corrections to the decay of the charged vector boson

The electroweak radiative corrections to the decay widths of theW-boson, Γ \((W \to l\bar v,\bar ud,\bar cs)\) , have been calculated in the standard theory. The results are presented in terms of an electroweak form factorρ ^W and their dependence onm _t , andM _H (masses oft-quark and higgs boson) is studied. Typically,ρ ^W ?1 is of an order of one percent. The differenceρ _lv ^W ?ρ _qq′ ^W is negligible, 0.046%. The calculational scheme used is described in detail.     

Electroweak corrections to the observables of W-boson production at RHIC

The processes of the single W-production in hadron-hadron collisions are suggested for investigation of the nucleon spin. An approach is proposed for the determination of quark spin densities at low x. The lowest order electroweak radiative corrections to the observable quantities are calculated. The numerical calculations of the cross sections and the single spin asymmetries taking into consideration the electroweak corrections at RHIC energies have been made.     

The width of theZ boson

We present a detailed discussion of the electroweak radiative corrections to the partial decay widths of theZ boson into lepton and quark pairs (q≠t) and to the total width for 5 flavors. The results are only very weakly dependent on the Higgs mass. The top mass dependence leads to sizable variations ofΓ _z which have to be taken into account for precision experiments at thee ⁺ e ^? colliders LEP and SLC.     

A novel approach to confront electroweak data and theory

A novel approach to study electroweak physics at one-loop level in generic SU(2)_L×U(1)_Y theories is introduced. It separates the 1-loop corrections into two pieces: process specific ones from vertex and box contributions, and universal ones from contributions to the gauge boson propagators. The latter are parametrized in terms of four effective form factors $\bar e^2 (q^2 ), \bar s^2 (q^2 ), \bar g_Z^2 (q^2 )$ and $\bar g_W^2 (q^2 )$ corresponding to the γγ, γZ,ZZ andWW propagators. Under the assumption that only the Standard Model contributes to the process specific corrections, the magnitudes of the four form factors are determined atq ²=0 and atq ²=m _Z ² by fitting to all available precision experiments. These values are then compared systematically with predictions of SU(2)_L×U(1)_Y theories. In all fits α _s (m _Z ) and $\bar \alpha (m_Z^2 )$ are treated as external parameters in order to keep the interpretation as flexible as possible. The treatment of the electroweak data is presented in detail together with the relevant theoretical formulae used to interpret the data. No deviation from the Standard Model has been identified. Ranges of the top quark and Higgs boson masses are derived as functions of α _s (m _Z ) and $\bar \alpha (m_Z^2 )$ . Also discussed are consequences of the recent precision measurement of the left-right asymmetry at SLC as well as the impact of a top quark mass and an improvedW mass measurement.     

Higgs production at the LHC: an update on cross sections and branching ratios

New theoretical and experimental information motivates a re-examination of the Standard Model Higgs production rates at the LHC pp collider. We present calculations of the relevant cross sections and branching ratios, including recently calculated QCD next-to-leading order corrections, new parton distributions fitted to recent HERA structure function data, and new values for electroweak input parameters, in particular for the top quark mass. Cross sections are calculated at two collider energies, √s = 10 TeV and 14 TeV.     

Electroweak precision observables in the MSSM with non-minimal flavor violation

The leading corrections to electroweak precision observables in the MSSM with non-minimal flavor violation (NMFV) are calculated and the effects on M _W and are analyzed. The corrections are obtained by evaluating the full one-loop contributions from the third and second generation scalar quarks, including the mixing in the scalar top and charm, as well as in the scalar bottom and strange sector. Furthermore the leading corrections to the mass of the lightest MSSM Higgs-boson, m _h , is obtained. The electroweak one-loop contribution to M _W can amount up to 140 MeV and up to 70 x 10^-5 for , allowing one to set limits on the NMFV parameters. The corrections for m _h are not significant for moderate generation mixing.Received: 1 July 2004, Published online: 13 October 2004     

Flavor changing Z0 decay and the top quark

The flavor changing neutral current decay of the Z⁰ boson into charge $\text{2}\text{3}$ quarks in the standard three generation SU(2)_L × U(1) theory of electroweak interactions has been studied. This process occurs first at one-loop order, where it has been calculated without approximation. The possibility of producing the as yet undiscovered top quark by this decay has been considered. The branching ratios are extremely small, independent of the top quark mass and plausible quark mixing matrices if there are three generations, making it unlikely that the top quark will be produced by this mechanism. However, a massive fourth bottom quark could increase the rates.     

Electroweak radiative corrections toe + e −→γγ

The explicit analytic expressions for the electroweak radiative corrections to the differential cross sectione ⁺ e ^?→γγ are calculated to one-loop in the framework of the Glashow-Salam-Weinberg model for relativistic energies. Special attention is given to the influence of the parametersM _Z ,M _W on these corrections.     

Higgs boson bremsstrahlung in top quark decay

In top quark decay a neutral Higgs boson may be emitted in bremsstrahlung from the top quark or from the W-boson. We evaluate the branching fraction for this hitherto overlooked t→H⁰bW⁺ decay mode, where the W⁺ can be virtual or real. It has the standard model values of 0.02%, 0.2%, 0.8% for m_t=50, 100, 200 GeVand m_H=10 GeV.     

Precise prediction for the mass of the lightest Higgs boson in the MSSM

The leading diagrammatic two-loop corrections are incorporated into the prediction for the mass of the lightest Higgs boson, m_h, in the Minimal Supersymmetric Standard Model (MSSM). The results, containing the complete diagrammatic one-loop corrections, the new two-loop result and refinement terms incorporating leading electroweak two-loop and higher-order QCD contributions, are discussed and compared with results obtained by renormalization group calculations. Good agreement is found in the case of vanishing mixing in the scalar quark sector, while sizable deviations occur if squark mixing is taken into account.     

The radiative corrections to the electroweak parameters in the dominant fermion-loop approximation

A simple treatment of the dominant radiative corrections to theW ^± andZ ⁰ mass formulae due to fermion-loop corrections to the propagator is given, including the possibility of a very massive top quark,m _t >M _w . A thorough comparison with the results of the complete (SU(2) _L ×U(1) _Y ) one-loop calculations is presented. Using α,G _μ andM _z as input, we find excellent agreement with the complete one-loop calculations (withm _HIGGS?100GeV) for all values ofm _t within an expected error ofΔM _W ?(α/2πM _W ?100MeV) inM _W andΔs _W ² ?0.002 in the weak angle,s _w ² . Technically we differ from previous work in diagonalizing the γZ propagator for arbitrary values ofq ², thus allowing for extensive use of the notion of “running” coupling constants and masses. We also give a simple and closed formula for the radiative corrections to be applied tos _w ² (accurate within an expected error ofΔs _w ² ?0.002), when extractings _W ² ?0.002), when extractings _W ² from neutrino scattering experiments. As a strategy for future precision tests of the electroweak theory, we suggest attempting to isolate and to test directly the “new physics” of boson loops and other new phenomena by comparing with and looking for deviations (larger thanΔM _W ?(α/2π)M _w ) from the predictions of the dominant fermion-loop calculation.     

DKP oscillator in the presence of magnetic field in (1+2)-dimensions for spin-zero and spin-one particles in noncommutative phase space

In view of the discovery of a new boson by the ATLAS and CMS Collaborations at the LHC, we present an update of the global Standard Model (SM) fit to electroweak precision data. Assuming the new particle to be the SM Higgs boson, all fundamental parameters of the SM are known allowing, for the first time, to overconstrain the SM at the electroweak scale and assert its validity. Including the effects of radiative corrections and the experimental and theoretical uncertainties, the global fit exhibits a p-value of 0.07. The mass measurements by ATLAS and CMS agree within 1.3σ with the indirect determination $M_{H}=94^{\,+25}_{\,-22}~\mathrm{GeV}$ . Within the SM the W boson mass and the effective weak mixing angle can be accurately predicted to be M _W =80.359±0.011 GeV and $\sin ^{2}\theta ^{\ell }_{{\rm eff}}= 0.23150\pm 0.00010$ from the global fit. These results are compatible with, and exceed in precision, the direct measurements. For the indirect determination of the top quark mass we find $m_{t}= 175.8^{\:+2.7}_{\:-2.4}~ \mathrm {GeV}$ , in agreement with the kinematic and cross-section-based measurements.