By running the prospective high-energy e^+e^- collider TESLA in the GigaZ
mode on the Z resonance, experiments can be performed on the basis of more than
10^9 Z events. This will allow the measurement of the effective electroweak
mixing angle to an accuracy of \delta sin^2(theta_W,eff) \approx \pm 10^-5. The
W boson mass is likewise expected to be measurable with an error of \delta M_W
\approx \pm 6 MeV near the W^+W^ threshold. We review the electroweak precision
tests that can be performed with these high precision measurements within the
Standard Model (SM) and its minimal Supersymmetric extension (MSSM). The
complementarity of direct measurements at a prospective linear e^+e^- collider
and indirect constraints following from measurements performed at GigaZ is
emphasized.Comment: 5 pages, 3 figures, talk given by S. Heinemeyer at the 5th
  International Linear Collider Workshop (LCWS 2000), Fermilab, Batavia,
  Illinois, 24-28 Oct 200

Heinemeyer, S.

Weiglein, G.

English

arXiv

Sven Heinemeyer

Crossref

Electroweak precision tests with GigaZ

By running the prospective high-energy $e^+e^−$ collider TESLA in the GigaZ mode on the $Z$ resonance, experiments can be performed on the basis of more than 109 $Z$ events. This will allow the measurement of the effective electroweak mixing angle to an accuracy of $\delta \sin^2 θ_{\mathrm{eff}}≈±1×10^{−5}$. The $W$ boson mass is likewise expected to be measurable with an error of $\delta M_W≈±6$ MeV near the $W^+W^−$ threshold. We review the electroweak precision tests that can be performed with these high precision measurements within the Standard Model (SM) and its minimal Supersymmetric extension (MSSM). The complementarity of direct measurements at a prospective linear $e^+e^−$ collider and indirect constraints following from the measurements performed at GigaZ is emphasized

DESY

By running the prospective high-energy e^+e^- collider TESLA in the GigaZ mode on the Z resonance, experiments can be performed on the basis of more than 10^9 Z events. This will allow the measurement of the effective electroweak mixing angle to an accuracy of \delta sin^2(theta_W,eff) \approx \pm 10^-5. The W boson mass is likewise expected to be measurable with an error of \delta M_W \approx \pm 6 MeV near the W^+W^ threshold. We review the electroweak precision tests that can be performed with these high precision measurements within the Standard Model (SM) and its minimal Supersymmetric extension (MSSM). The complementarity of direct measurements at a prospective linear e^+e^- collider and indirect constraints following from measurements performed at GigaZ is emphasized.By running the prospective high-energy e^+e^- collider TESLA in the GigaZ mode on the Z resonance, experiments can be performed on the basis of more than 10^9 Z events. This will allow the measurement of the effective electroweak mixing angle to an accuracy of \delta sin^2(theta_W,eff) \approx \pm 10^-5. The W boson mass is likewise expected to be measurable with an error of \delta M_W \approx \pm 6 MeV near the W^+W^ threshold. We review the electroweak precision tests that can be performed with these high precision measurements within the Standard Model (SM) and its minimal Supersymmetric extension (MSSM). The complementarity of direct measurements at a prospective linear e^+e^- collider and indirect constraints following from measurements performed at GigaZ is emphasized.By running the prospective high-energy e^+e^- collider TESLA in the GigaZ mode on the Z resonance, experiments can be performed on the basis of more than 10^9 Z events. This will allow the measurement of the effective electroweak mixing angle to an accuracy of \delta sin^2(theta_W,eff) \approx \pm 10^-5. The W boson mass is likewise expected to be measurable with an error of \delta M_W \approx \pm 6 MeV near the W^+W^ threshold. We review the electroweak precision tests that can be performed with these high precision measurements within the Standard Model (SM) and its minimal Supersymmetric extension (MSSM). The complementarity of direct measurements at a prospective linear e^+e^- collider and indirect constraints following from measurements performed at GigaZ is emphasized.By running the prospective high-energy e^+e^- collider TESLA in the GigaZ mode on the Z resonance, experiments can be performed on the basis of more than 10^9 Z events. This will allow the measurement of the effective electroweak mixing angle to an accuracy of \delta sin^2(theta_W,eff) \approx \pm 10^-5. The W boson mass is likewise expected to be measurable with an error of \delta M_W \approx \pm 6 MeV near the W^+W^ threshold. We review the electroweak precision tests that can be performed with these high precision measurements within the Standard Model (SM) and its minimal Supersymmetric extension (MSSM). The complementarity of direct measurements at a prospective linear e^+e^- collider and indirect constraints following from measurements performed at GigaZ is emphasized.By running the prospective high-energy e+e− collider TESLA in the GigaZ mode on the Z resonance, experiments can be performed on the basis of more than 109 Z events. This will allow the measurement of the effective electroweak mixing angle to an accuracy of δ sin2 θeff≈±1×10−5. The W boson mass is likewise expected to be measurable with an error of δMW≈±6 MeV near the W+W− threshold. We review the electroweak precision tests that can be performed with these high precision measurements within the Standard Model (SM) and its minimal Supersymmetric extension (MSSM). The complementarity of direct measurements at a prospective linear e+e− collider and indirect constraints following from the measurements performed at GigaZ is emphasized

CERN Document Server

BNL–HET–00/47CERN–TH/2000-370hep-ph/0012364Electroweak Precision Tests with GigaZ S. Heinemeyer1 yand G. Weiglein2 z1 HET, Brookhaven Natl. Lab., Upton, New York 11973, USA2 CERN, TH Division, CH-1211 Geneva 23, SwitzerlandAbstract. By running the prospective high-energy e+e− collider TESLA in the GigaZmode on the Z resonance, experiments can be performed on the basis of more than109 Z events. This will allow the measurement of the eective electroweak mixing angleto an accuracy of δ sin2 θeff  110−5. The W boson mass is likewise expected to bemeasurable with an error of δMW  6 MeV near the W+W− threshold. We reviewthe electroweak precision tests that can be performed with these high precision mea-surements within the Standard Model (SM) and its minimal Supersymmetric extension(MSSM). The complementarity of direct measurements at a prospective linear e+e−collider and indirect constraints following from measurements performed at GigaZ isemphasized.) Talk given by S. Heinemeyer at the 5th International Linear Collider Workshop (LCWS 2000),Fermilab, Batavia, Illinois, 24-28 Oct 2000y) email: Sven.Heinemeyer@bnl.govz) email: Georg.Weiglein@cern.chElectroweak Precision Tests at GigaZSven Heinemeyer and Georg WeigleinyHET, Brookhaven Natl. Lab., Upton, New York 11973, USAyCERN, TH Division, CH-1211 Geneva 23, SwitzerlandAbstract. By running the prospective high-energy e+e− collider TESLA in the GigaZmode on the Z resonance, experiments can be performed on the basis of more than109 Z events. This will allow the measurement of the eective electroweak mixingangle to an accuracy of δ sin2 θeff  110−5. The W boson mass is likewise expectedto be measurable with an error of δMW  6 MeV near the W+W− threshold. Wereview the electroweak precision tests that can be performed with these high precisionmeasurements within the Standard Model (SM) and its minimal Supersymmetric ex-tension (MSSM). The complementarity of direct measurements at a prospective lineare+e− collider and indirect constraints following from the measurements performed atGigaZ is emphasized.I THEORETICAL BASISThe prospective high-energy e+e− linear collider TESLA can be operated on theZ boson resonance by adding a bypass to the main beam line [1]. Due to thehigh luminosity, L = 7  1033cm−2s−1, about 2  109 Z events per year can begenerated, which will be referred to as the “GigaZ” mode. By using the Blondelscheme, this results in a measurement of the effective leptonic mixing angle, sin2 θeff ,of about δ sin2 θeff  1  10−5 [2]. Increasing the collider energy to the W -pairthreshold, about O(106) W bosons can be generated resulting in a measurement ofthe W mass of δMW  6 MeV [3]. This increase of precision in sin2 θeff and MWopens new opportunities for high precision physics in the electroweak sector [4,5].In this paper we compare the theoretical predictions for MW and sin2 θeff in theStandard Model (SM) and the Minimal Supersymmetric Standard Model (MSSM)with the expected experimental uncertainties. In order to calculate the W -bosonmass in the SM and the MSSM we useM2W = M2Z/2[1 +(4piα/(p2GFM2Z) (1 + ∆r))1/2], (1)where the loop corrections are summarized in ∆r. The quantity sin2 θeff is definedthrough the effective couplings gfV and gfA of the Z boson to fermions:sin2 θeff = 1/(4 jQf j)[1− Re gfV /Re gfA], (2)where the loop corrections are contained in gfV,A. The theoretical input for MW andsin2 θeff is described in detail in Ref. [5]. It involves corrections up to O(α2) [6] andO(αα2s) [7] in the SM and up to O(ααs) in the MSSM [8].In the SM the Higgs boson mass is a free parameter. Contrary to this, in theMSSM the masses of the neutral CP-even Higgs bosons are calculable in termsof the other MSSM parameters. The largest corrections arise from the t–t˜-sector,where the dominant contribution reads ∆m2h  m4t/M2W log(m2t˜1 m2t˜2/m4t ). mt˜1 andmt˜2 denote the two stop mass eigenstates. θt˜ will later denote the t˜ mixing angle.Since the one-loop corrections are known to be very large, we use the currently mostprecise two-loop result based on explicit Feynman-diagrammatic calculations [9],where the numerical evaluation is based on Ref. [10]. The relevant observablestogether with their uncertainties at various colliders and their current experimentalvalue can be found in Tab. 1.TABLE 1. Expected precision at various colliders for sin2 θeff , MW , mt andthe (lightest) Higgs boson mass, Mh. \now" refers to the present accuracyobtained at LEP, SLD and the Tevatron RunI. \LHC" here and in the fol-lowing also includes Tev. RunII. See Ref. [5] for a detailed list or references.now LHC LC GigaZ current central valueδ sin2 θeff(105) 17 17 6 1.3 0.23146δMW [MeV] 37 15 15 6 80.436 GeVδmt [GeV] 5.1 2 0.2 0.13 174.3 GeVδMH [MeV] { 200 50 50 {II COMPARISON OF SM AND MSSMIn Fig. 1 the theoretical predictions for MW and sin2 θeff obtained in the SM andthe MSSM are compared with their experimental values. In the left plot of Fig. 1the bands in the mt–MW plane allowed in the SM and the MSSM are compared tothe (prospective) experimental precisions at LEP/Tevatron, LHC/LC and GigaZ.The SM band arises from the unknown value of the Higgs boson mass, where theupper boundary is obtained from the lower bound set by LEP, MH > 113 GeV [11].The band in the MSSM is due to the unknown masses of the SUSY particles. Theupper boundary corresponds to light SUSY, the lower boundary corresponds toheavy SUSY, i.e. the MSSM is SM like. In the overlap area the SM has a Higgsboson in the SUSY range, i.e. MH < 130 GeV. The plot shows a slight preferenceof the present data for the MSSM at the 68% CL.The right plot of Fig. 1 shows the MW–sin2 θeff plane. The allowed area in the SMand the MSSM is compared with the experimental precision at LEP/SLD/Tevatron,LHC/LC and GigaZ. For the SM area, the Higgs boson mass has been variedbetween 113 GeV  MH  400 GeV. The top quark mass has been varied between170 GeV  mt  180 GeV. Both models possess an allowed parameter space atthe 68% CL.165 170 175 180 185mt [GeV]80.2080.3080.4080.5080.60MW [GeV]SMMSSMMH = 113 GeVMH = 400 GeVlight SUSYheavy SUSYexperimental errors:LEP2/TevatronLHC/LCGigaZ80.20 80.25 80.30 80.35 80.40 80.45 80.50MW [GeV]0.23050.23100.23150.23200.2325sin2θ effSM (mH = 113 ... 400 GeV)mt = 170 ... 180 GeVMSSMexperimental errors:LEP2/SLD/TevatronLHC/LCGigaZFIGURE 1. The theoretical prediction of MW and sin2 θeff is compared to the experimentalmeasured values with the current LEP/SLD/Tevatron precision and with the prospective accu-racies at the LHC/LC and at GigaZ.III INDIRECT CONSTRAINTS FROM GIGAZOften the indirect constraints on observables obtained at GigaZ could be com-plementary to their direct measurements at the Tevatron RunII, the LHC or at anLC. As an example we present an analysis for the scalar top sector. The directinformation on the stop sector parameters, mt˜1 and θt˜, can be obtained from theprocess e+e− ! t˜1t˜1 to a precision of O(1%) [12]. These direct measurements canbe combined with the indirect information from requiring consistency of the MSSMwith a precise measurement of the Higgs boson mass, mh, and the electroweak pre-cision observables. This is shown in Fig. 2, where the allowed parameter spaceaccording to measurements of mh, MW and sin2 θeff are displayed in the plane ofthe heavier stop mass, mt˜2 , and j cos θt˜j for the accuracies at a LC with and withoutthe GigaZ option and at the LHC (see Tab. 1). For mt˜1 the central value and exper-imental error of mt˜1 = 180 1.25 GeV are taken for LC/GigaZ, while for the LHCan uncertainty of 10% in mt˜1 is assumed. The other parameters have been chosenaccording to the mSUGRA reference scenario 2 [13], with the following accuracies:MA = 257 10 GeV, µ = 263 1 GeV, M2 = 150 1 GeV, mg˜ = 496 10 GeV.For the top-quark mass an error of 0.2 GeV has been used for GigaZ/LC and of2 GeV for the LHC. For tan β a lower bound of tanβ > 10 has been taken. For thefuture theory uncertainty of mh from unknown higher-order corrections an errorof 0.5 GeV has been assumed. The central values for MW and sin2 θeff have beenchosen in accordance with a non-zero contribution to the precision observables fromSUSY loops.As one can see in Fig. 2, the allowed parameter space in the mt˜2–j cos θt˜j plane issignificantly reduced from the LHC to the LC, in particular in the GigaZ scenario.Using the direct information on j cos θt˜j from Ref. [12] allows an indirect determi-nation of mt˜2 with a precision of better than 5% in the GigaZ case. By comparingthis indirect prediction for mt˜2 with direct experimental information on the massof this particle, the MSSM could be tested at its quantum level in a sensitive andhighly non-trivial way.400 600 800 1000m t2 ~ [GeV]0.40.60.81.0|cosθ t~|LHCLCGigaZmh = 115 GeV, ∆mhtheo = 0.5 GeVMW = 80.426 GeV, sin2θeff = 0.23127m t1 ~ = 180 GeV, ∆m t1 ~ = 18 / 1.25 GeVMA = 257 +− 10 GeVµ = 263 +− 1 GeV tanβ > 101 σ errorsdirect measurementat the LCFIGURE 2. Indirect constraints on the MSSM parameter space in the mt˜2{j cos θt˜j plane frommeasurements of mh, MW , sin2 θeff , mt and mt˜1 in view of the prospective accuracies for theseobservables at a LC with and without GigaZ option and at the LHC. The direct information onthe mixing angle from a measurement at the LC is indicated together with the correspondingindirect determination of mt˜2 .REFERENCES1. R. Brinkmann, Talk at the ECFA/DESY Linear Collider Workshop, Orsay 1999.2. R. Hawkings and K. Mo¨nig, EPJdirect C8 (1999) 1.3. G. Wilson, Proceedings, Linear Collider Workshop, Sitges 1999.4. S. Heinemeyer, Th. Mannel and G. Weiglein, hep-ph/9909538.5. J. Erler, S. Heinemeyer, W. Hollik, G. Weiglein and P.M. Zerwas, Phys. Lett. B486(2000) 125.6. A. Freitas et al., Phys. Lett. B495 (2000) 338; A. Freitas et al., hep-ph/0007129.7. K. Chetyrkin, J. H. Ku¨hn and M. Steinhauser, Phys. Rev. Lett. 75 (1995) 3394.8. A. Djouadi, P. Gambino, S. Heinemeyer, W. Hollik, C. Ju¨nger and G. Weiglein,Phys. Rev. Lett. 78 (1997) 3626; Phys. Rev. D57 (1998) 4179.9. S. Heinemeyer, W. Hollik and G. Weiglein, Phys. Rev. D58 (1998) 091701; Phys.Lett. B440 (1998) 296; Eur. Phys. Jour. C9 (1999) 343.10. S. Heinemeyer, W. Hollik and G. Weiglein, Comp. Phys. Comm. 124 (2000) 76;hep-ph/0002213 (http://www.feynhiggs.de)11. S. Andringa et al., ALEPH 2000-074 CONF 2000-051, DELPHI 2000-148 CONF447, L3 Note 2600, OPAL Technical Note TN661.12. A. Bartl, H. Eberl, S. Kraml, W. Majerotto and W. Porod, hep-ph/9909378;M. Berggren, R. Kera¨nen, H. Nowak and A. Sopczak, hep-ph/9911345.13. http://wwwhephy.oeaw.ac.at/susy/lcws.html

Electroweak Precision Tests with GigaZ

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