Three loop corrections to electroweak precision observables in the large Higgs mass limit

The Glashow-Salam-Weinberg Model is presently <br>the most comprehensive formulation of a theory of the unified <br>electroweak interaction, theoretically consistent and in agreement <br>with all experimentally known phenomena of electroweak origin, <br>with the exception of the evidence of neutrino mixing. <br>During the eleven years of data collection at the Large Electron Positron <br>Collider (LEP) at CERN in Geneva, the Electroweak sector of the Standard <br>Model (EWSM), based on a spontaneously broken SU(2)_L \times U(1)_Y gauge <br>symmetry, has been experimentally tested at the level <br>of quantum corrections by precise measurement of several observables. <br>The direct observation of the predicted top quark at the proton-antiproton <br>collider Tevatron at Fermilab in 1994 with a mass determination <br>(now at m_t= 174.3+- 3.4 GeV) that impressively <br>matches the mass range indirectly obtained via the radiative corrections calculated in the framework of the Electroweak Standard Model, strengthened <br>our belief in it as the theory that correctly describes electroweak <br>phenomena. <br>The only ingredient predicted by this model that has not <br>been seen yet is the Higgs particle. The direct search <br>at LEP has only provided us with a lower limit on the mass <br>of the Standard Model Higgs boson excluding the region below 114.4 GeV. <br>The precision of present day experiments even makes it possible to put <br>limits on the Higgs mass through its influence in radiative corrections, <br>which grow logarithmically with the Higgs boson mass at <br>the one loop level. The global fit of <br>the experimental data to the Standard Model favors a light Higgs boson <br>( m_H less or equal to 285 GeV one-sided 95 % Confidence Level (CL)). <br>However the situation is not completely satisfactory, as there is a <br>difference of about 3.2 \sigma between the two most precise <br>determinations of the electroweak mixing angle , ie the one <br>based on the measurement of the b-quark forward-backward asymmetry <br>A_{FB}^{0,b} at LEP on the one hand, and the one based on measurements of <br>the leptonic asymmetry parameter A_l at SLD on the other. <br>The value of the Higgs mass preferred by the b-quark data is around 0.5 TeV, <br>while the leptonic asymmetry data and the <br>W-boson mass point to a value which is slightly below <br>the lower bound from the direct searches. With the recent measurements <br>of the W-mass and top mass from the Tevatron this is well within <br>statistics. <br>The discrepancy between these two precise measurements suggests that <br>the possibility of a heavy Higgs boson is not ruled out. <br>Since the center of mass energies of present colliders do not allow <br>to probe the region of a heavy Higgs boson, <br>the sensitivity of radiative corrections <br>to physical observables to a heavy Higgs boson mass becomes an important <br>tool in setting upper and lower limits on m_H. <br>For a light Higgs boson, the Higgs mass dependence <br>of the theoretical predictions is mainly due to one-loop radiative <br>corrections to the gauge boson propagators. These one-loop corrections <br>depend on m_H logarithmically. However, <br>because the Higgs self-interaction \lambda is proportional to <br>m_H^2, there are higher order radiative corrections which grow like <br>powers of m_H in the limit m_H going to infinity, eventually overcoming <br>their relative suppression by powers of the fine <br>structure constant \alpha. Such higher order <br>corrections could become important if the Higgs boson is very heavy. <br>At the two-loop level, the leading corrections are proportional to <br>m_H^2, but the numerical coefficient of these terms turns out to <br>be very small, <br>and therefore, they are not important for m_H less than a few TeV. <br>However, it has been suggested that the smallness of the two-loop corrections <br>may be somewhat accidental. If this is true, then one <br>may expect larger corrections to appear at the three loop level. <br>In this thesis, we investigate the leading three-loop corrections <br>to three electroweak observables, namely the electroweak <br>\rho-parameter, the effective leptonic weak mixing angle <br>defined in terms of couplings of the Z-boson to leptons, <br>and the W-boson mass. This investigation will allow us to check whether <br>a heavy Higgs boson could behave like a light Higgs boson by giving <br>a similar effect in loop corrections to the previously mentioned <br>electroweak observables. The sign and the size of the leading three-loop <br>corrections to these observables play a crucial role in either confirming <br>this possibility or ruling it out completely.

Author dc:creator

• Boughezal, Radja

Contributors dc:contributor

• Bij, Jochum van der

• radiative corrections, electroweak physics

Repository record source_url

https://freidok.uni-freiburg.de/data/2004

OAI identifier oai:identifier

oai:freidok.uni-freiburg.de:2004