The global electroweak fit and constraints on new physics with Gfitter
aa r X i v : . [ h e p - ph ] O c t The global electroweak fit and constraints on newphysics with Gfitter
Dörthe Ludwig ∗ for the Gfitter group DESY Hamburg, Unversity of HamburgE-mail: [email protected]
The thourough investigation of radiative corrections allows to gain information on physics pro-cesses at higher energy scales than those directly accessible by current experiments. As a conse-quence, using electroweak precision measurements in conjunction with state-of-the-art SM pre-dictions e.g. allows the estimation of a preferred mass range for the SM Higgs boson mass.Physics beyond the Standard Model can modify the relations between electroweak observablesand their theoretical predictions. Such effects can be parametrized in terms of effective, so-calledoblique parameters. A global fit of the electroweak SM, as performed with the Gfitter pack-age [1], allows the determination of the oblique parameters and to probe physics models and toset constraints on their free parameters.In this paper we present updated results of the global electroweak SM fit taking into accountthe latest experimental precision measurements and the results of direct Higgs searches fromLEP and Tevatron. Through the formalism of oblique parameters we obtain constraints on BSMmodels with universal and warped extra dimensions. In constrast, taking into account heavy flavorobservables, (g-2) m , and dark matter predictions allows to constrain the parameter space of theminimal supergravity model (mSugra). ∗ Speaker. c (cid:13) Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/ he global electroweak f it and constraints on new physics with Gf itter
Dörthe Ludwig [GeV] H M
100 150 200 250 300 cD L EP exc l u s i on a t % C L T eva t r on exc l u s i on a t % C L s s s Theory uncertaintyFit including theory errorsFit excluding theory errors [GeV] H M
100 150 200 250 300 cD G fitter SM J u l S -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 T -0.4-0.3-0.2-0.100.10.20.30.40.5 H (M [114,1000] GeV ˛ H M 1.1 GeV – = 173.3 t m H M preliminary S -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 T -0.4-0.3-0.2-0.100.10.20.30.40.5 G fitter
SMB A ug Figure 1:
Left:
D c profile as a function of M H for the electroweak fit including results of direct Higgssearches at LEP and Tevatron (shaded areas). Right: Fit result of the oblique parameters. Shown are the68%, 95%, and 99% CL allowed regions in the S - T -plane with U = M H = m t = . M H and m t .
1. The global electroweak fit
In the global electroweak fit predictions for precision observables are compared with the mostrecent measurements done by LEP, SLC, and Tevatron. A detailed list of all data used in the fit canbe found in [1]. The free floating parameters are M Z , M H , m t , m b , m c , D a ( ) had , and a S ( M Z ) where thelatest average for the m t as well as the newly obtained exclusion limits for M H [2] have been used.The fit converges at a c minimum of 16 . ( . ) excluding (including) the direct Higgssearches. The respective p-values based on toy Monte Carlo experiments are 0.23 (0.22) whereno individual pull value exceeds 3 s . One of the most important results of the electroweak fit is theestimation of Higgs mass. The c min is found at M H = . + . − . GeV ( M H = . + . − . GeV) witha 2 s interval of [40.3,159.2] GeV ([114.4, 154.9] GeV). Figure 1 (left) shows the D c profile as afunction of M H for the fit including the direct Higgs searches. The increase of D c at the 95% CLexclusion limits from LEP and Tevatron (shaded areas) is clearly visible.
2. The oblique parameters and constraints on beyond the SM physics models
The main assumption that led to the introduction of the oblique paramters [3] is that high-scale BSM physics appears only through vacuum polarisation corrections. The electroweak fitis sensitive to BSM physics through these oblique corrections which can be described through the
STU parametrization: O meas = O SM ; re f ( M H ; m t ) + c S S + c T T + c U U . The STU parameters measuredeviations from electroweak radiative correction that are expected in the reference SM determinedby the chosen m t and M H .In our analysis the SM reference point is chosen to be at M H =
120 GeV and m t = . S , T , and U are derived from a fit to electroweak observables and are compatible with 0 as illustratedin Fig. 1 (right) showing the 68%, 95%, and 99% CL level allowed regions in the S - T -plane for U =
0. The grey area shows the SM prediction highlighting the logarithmical dependence of S and T on M H . Small values of M H are compatible with data.2 he global electroweak f it and constraints on new physics with Gf itter Dörthe Ludwig S -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 T -0.4-0.3-0.2-0.100.10.20.30.40.5 SM [114, 1000] GeV ˛ H M 1.1 GeV – = 173.3 t m [100, 2000] GeV ˛ -1 R [114, 1000] GeV ˛ H M = 150 GeV H M = 350 GeV H M = 700 GeV H M = 900 GeV H M =300 GeV -1 R=500 GeV -1 R = G e V - R =1500 GeV -1 R One Universal Extra Dimension68%, 95%, 99% CL fit contours=120 GeV, U=0) H (M preliminary S -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 T -0.4-0.3-0.2-0.100.10.20.30.40.5 G fitter
SMB A ug [GeV] H M
200 300 400 500 600 700 800 900 1000 [ G e V ] - R One Universal Extra Dimension68%, 95%, 99% CL fit contours (allowed) preliminary [GeV] H M
200 300 400 500 600 700 800 900 1000 [ G e V ] - R G fitter
SMB A ug Figure 2:
Left: Comparison in the S-T-plane between CL contours from fits to the electroweak precisiondata and predictions of the UED model. For illustration some benchmark points are depicted. With increas-ing compactification scale the ST values converge to the SM predictions. Right: Contours of 68%, 95% and99% CL obtained from scans of fits with fixed variable pairs R − and M H . Extra dimension models
The universal extra dimension model (UED) [4] allows all SM particles to propagate into theextra dimensions. Their compactification leads to Kaluza-Klein (KK) modes. The free parametersof this model are the number of extra dimensions d UED which is fixed to one in our analysis and thecompactification scale R − where R is the size of the extra dimension. The S , T , and U parametersmainly depend R − , M H , and m t . The result is illustrated in Fig. 2 (left). The blue region indicatesthe S - T -parameter space allowed for various parameter sets in the UED model. For large com-pactification it approaches the SM prediction. Only small M H are allowed. If the compactificationbecomes smaller the BSM contribution needs to be compensated by larger M H . A comparison withelectroweak precision data allows the exclusion of R − <
300 GeV and M H >
800 GeV as can beseen in Fig. 2(right) in which the 68%, 95%, and 99% CL allowed regions are shown.A different higher-dimensional approach has been proposed by Randall and Sundrum[5]. Thegeometry of this model is characterized by one warped extra dimension confined by two three-branes, one of them containing the SM fields. The generation of the weak scale from a larger scaleis achieved by introducing a warp factor altering the known four-dimensional metric. The inverseof the warp factor L and the Kaluza-Klein scale M KK are free model parameters. In a slightlyextended version of the original minimal model SM gauge bosons and fermions can propagate inthe five-dimensional warped bulk region [6]. Figure 3 (left) shows again in blue the allowed regionin the S - T -plane. For large values of L high M KK values are preferred by the data. However, thehigher M H the lower M KK values can be compensated.
3. Minimal Supergravity
Minimal supergravity is one of the most investigated supersymmetry models by current col-lider experiments. One highly constraining breaking mechanism suggests that the breaking is me-diated by the gravitational interaction. Some of the free parameters of this model are m ( ) , themass of scalar particles (fermions) at the GUT scale, and tan b , the ratio of the two Higgs vacuum3 he global electroweak f it and constraints on new physics with Gf itter Dörthe Ludwig S -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 T -0.4-0.3-0.2-0.100.10.20.30.40.5 SM [114, 1000] GeV ˛ H M 1.1 GeV – = 173.3 t m [0.5, 10] TeV ˛ KK M [5, 37] ˛ L = 10 TeV KK M = 3 TeV KK M = 2 TeV KK M = 250 GeV) H (M L = L = L = Randall-Sundrum68%, 95%, 99% CL fit contours=120 GeV, U=0) H (M preliminary S -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 T -0.4-0.3-0.2-0.100.10.20.30.40.5 G fitter
SMB A ug [GeV] m [ G e V ] m = 10 b tan = - 400 A LSP t~ no EWSB(1) theoretically allowed(2) + LEP limits(3) + heavy flavor-2) m (4) + (g(5) + dark matterMinimal SuperGravity [GeV] m [ G e V ] m preliminary G fitter
SMB J u l Figure 3:
Left: Comparison in the S-T-plane between CL contours from fits to the electroweak precisiondata and predictions from models with one warped extra dimensions. For illustration several benchmarkpoints are depicted. Right: Contours of 68% CL obtained from scans with fixed m − m pairs taking intoaccount constraints from (2) LEP (blue), (3)heavy flavor (green), (4) ( g − ) m (orange), and (5) dark matter(purple). expectation values. Figure 3 (right) shows the constraints on m and m . Whereas the impact ofthe LEP and heavy flavor data do not severely limit these two parameters the ( g − ) m and darkmatter measurements clearly favor small values.
4. Conclusion
The global electroweak fit shows an excellent agreement of the SM with data. Includingthe latest experimental results from Tevatron for m t , M W , and M H results in a c min at M H = . + . − . GeV. However, this result may change if BSM physics is present. For many new physicsmodel contributions from a larger Higgs mass could be compensated and be still compatible withcurrent data. A more detailed list including the Littlest Higgs model, warped extra dimensions withcustodial symmetry and a fourth generation model can be found in [1]. As the LHC and Tevatroncontribute further to the electroweak precision measurements tighter constraints might be set onmany BSM models. Therefore, a continuous development of the electroweak fit and the obliqueparameters will be carried out.
References [1] H. Flächer et al.,
Eur. Phys. J. C, Phys. Rev. D , 381 (1991)[4] T. Appelquist and H. Yee, Phys. Rev. D , 055002 (2003); I. Gogoladze and C. Macesanu, Phys.Rev. D , 093012 (2006).[5] L. Randall and R. Sundrum, Phys. Rev. Lett. , 3370 (1999).[6] S.Casagrande et al., JHEP (2008) 094.(2008) 094.