Measurement of the effective leptonic weak mixing angle

Today, at the 42^nd International Conference on High Energy Physics, ICHEP, Prague, Czech Republic, the LHCb collaboration reported a measurement of the effective leptonic weak mixing angle, sin²θ^l_eff, the parameter which is involved in the unification of the electromagnetic and weak forces. The result was obtained from the analysis of the forward-backward asymmetry in the pp→Z/γ^*→μ⁺μ^– process measured in intervals of the difference of the muon pseudorapidities.

The squared sine function of the electroweak mixing angle sin²θ_W^eff was precisely measured by the experiments at the Large Electron-Positron Collider (LEP) in the 1990s. The electrons and positrons were collided at the energy of about 91 GeV at which the Z boson resonance was formed. The Z bosons than decayed into pairs of leptons (e⁺e^–, μ⁺μ^–, τ⁺,τ^–) or pairs of quarks. By determining the electric charge and direction of these decaying particles a quantity called the “forward-backward asymmetry” was measured, and then used to calculate the value of sin²θ_W^eff. The forward-backward asymmetry is related to how often the produced matter particle travels in a similar (“forward”) direction as the incoming matter particle involved in the collision. An important measurement was made also at another electron-positron collider SLAC Linear Collider (SLC) with the detector SLD. The sin²θ_W^eff parameter was determined from the analysis of a so called left-right asymmetry obtained by counting the difference in number of Z bosons produced with two opposite (left and right) spin orientation of colliding electrons using the longitudinally polarized SLC electron beam. The measurement requires no detailed final-state identification. It turned out that the most precise measurements of sin²θ_W^eff, the LEP forward-backward b quark asymmetry (A_FB(b)) and the SLD left-right asymmetry (A_LR), differed by 3.2σ (see a figure from the LEP-SLD electroweak report in which all the details of measurements are explained). This 3.2σ LEP-SLD puzzle has been interpreted by some commentators as an effect driven by new physics. It is a very interesting challenge for measurements at other particle colliders to resolve this puzzle.

Measurements of sin²θ_W^eff have continued at the Tevatron at Fermilab and LHC at CERN. The task is, however, more difficult than at an e⁺e^– collider. The parton (quark and antiquark) distributions inside proton need to be known precisely. At the LHC the Z bosons used in this analysis are produced mainly in the collisions of (valence) quarks with high momentum and (sea) antiquarks with low momentum. The Z bosons then decay into a pair of electrons or muons. The LHCb geometrical acceptance is ideal for this measurement. The incoming quark direction, needed to define the sign of the asymmetry, can be identified correctly 90% of the time.

The figure above shows the forward-backward muon asymmetry A_FB measured by LHCb for 10 different pseudorapidity Δη intervals. The measured values are compared with prediction for different values of sin²θ^l_eff shown with blue and orange mini-lines. The predictions were adjusted to the measured experimental numbers and the result is shown with green mini-lines. The final value of 0.23152±0.0044(stat.)±0.00005(syst.)±0.00022(theory) for sin²θ^l_eff was obtained in this way. The LHCb result is compared in the figure at the left with the results of other experiments and the indirect determination obtained in electroweak fits in which all the other electroweak measurements were used except those of direct sin²θ^l_eff measurements. The significant difference between direct measurements and indirect determination could indicate manifestation of the physics beyond Standard Model. The LHCb result is consistent with other direct measurements and with prediction from the global electroweak fits.

Read more in the LHCb ICHEP presentation and also in the forthcoming paper and CERN seminar presentation.