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Bounds on Supersymmetry from Electroweak Precision Analysis

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Bounds on Supersymmetry from Electroweak Precision Analysis SLAC{PUB{7634 UPR{788{T January, 1998 Bounds on Sup ersymmetry from Electroweak Precision Analysis Jens Erler DepartmentofPhysics and Astronomy UniversityofPennsylvania Philadelphia, PA 19104 Damien M. Pierce Stanford Linear Accelerator Center Stanford University Stanford, CA 94309 Abstract The Standard Mo del global t to precision data is excellent. The Minimal Sup ersym- metric Standard Mo del can also t the data well, though not as well as the Standard Mo del. At b est, sup ersymmetric contributions either decouple or only slightly decrease 2 the total , at the exp ense of decreasing the numb er of degrees of freedom. In general, regions of parameter space with large sup ersymmetric corrections from light sup erpart- ners are asso ciated with p o or ts to the data. We contrast results of a simple (oblique) approximation with full one-lo op results, and show that for the most imp ortant observ- ables the non-oblique corrections can be larger than the oblique corrections, and must b e taken into account. We elucidate the regions of parameter space in b oth gravity- and gauge-mediated mo dels which are excluded. Signi cant regions of parameter space are excluded, esp ecially with p ositive sup ersymmetric mass parameter . We give a com- plete listing of the b ounds on all the sup erpartner and Higgs b oson masses. For either sign of , and for all sup ersymmetric mo dels considered, we set a lower limit on the mass of the lightest CP{even Higgs scalar, m 78 GeV. Also, the rst and second h generation squark masses are constrained to b e ab ove 280 (325) GeV in the sup ergravity (gauge-mediated) mo del. Submitted to Nuclear Physics B D.M.P. is supp orted by Department of Energy contract DE{AC03{76SF00515. 1 Intro duction For more than a decade, ideas involving sup ersymmetry (SUSY) have b een among the most p opular extensions of the Standard Mo del (SM), having the greatest p otential to solve its shortcomings such as the gauge hierarchy problem and the lack of a quantized version of grav- ity. Indeed, all sup erstring theories necessarily contain quantum gravity and sup ersymmetry. Moreover, very recently, using arguments based on various dualities and sup ersymmetry, all sup erstring theories as well as 11 dimensional sup ergravity seem to be connected nonp ertur- batively [1], suggesting a uni ed theory in which sup ersymmetry is one of the indisp ensable key elements. The idea of sup ersymmetric uni cation is further supp orted by the observation of gauge coupling uni cation [2] two orders of magnitude b elow the reduced Planck scale, p 18 M = 8 2 10 GeV, the natural sup ergravity scale. P Taken together this implies a strong motivation to investigate the phenomenological conse- quences of low energy sup ersymmetry. In this pap er we present a systematic study of precision observables in the minimal sup ersymmetric standard mo del (MSSM) in an attempt to nd favorable and/or excluded regions in SUSY parameter space. We do this in two scenarios for how sup ersymmetry breaking is conveyed to the observable sector. In the \minimal sup ergravity" mo del [3] sup ersymmetry breaking is transmitted from a hidden sector to the observable sector via gravitational interactions. Sup ersymmetry is sp ontaneously broken in the hidden sector at a scale [4]. In p opular mo dels which invoke 2 1=3 13 gaugino condensation [5], (M M =8) 10 GeV. Since gravityis avor blind, it SU SY P is assumed that the explicit soft breaking terms in the observable sector are universal at the sup ergravity scale. In simple mo dels of gauge mediation [6] there is a sup ersymmetry breaking sector which gives rise to b oth an F -term, F , and a vacuum exp ectation value, X , of a standard mo del X singlet eld. This eld is coupled to the vector-like \messenger elds", M , through a sup erp o- M . The generated soft mass term for a given sup erpartner tential interaction of the form X M 5 is prop ortional to F =X 4M = 10 GeV, and grows with the square of its gauge X Z couplings. Therefore sleptons are much lighter than squarks and the gluino is heavier than charginos and neutralinos. In b oth cases the generated soft terms are suciently avor universal that all avor chang- ing neutral current (FCNC) e ects are adequately suppressed. However, in the minimal su- p ergravity mo del it must b e implicitly assumed that universality is not sp oiled by the Kahler p otential. Recently, a number of articles [7] examined whether sup ersymmetry has the p otential to describ e the data b etter than the SM. The conclusions in the armative were mainly driven by R (see section 2), which at times was more than 3 higher than SM exp ectations. Lo ops b involving light charginos and top squarks could account for a large part of the discrepancy for low tan , provided the e ect was not canceled by charged-Higgs lo ops. For large tan , large shifts could be obtained from lo ops containing b ottom quarks and light neutral Higgs b osons, and to a lesser extent from neutralino/b ottom-squark lo ops. However, more recent analyses nd the measured value of R closer to the SM prediction (the discrepancy is 1:3 ), b and at the same time direct limits on sup erpartner masses have increased. Now, even if one is able to nd a region of parameter space where the R discrepancy is alleviated, the decrease b 2 in the overall is not signi cant. Also, in those regions of parameter space one typically 1 FB nds that the discrepancy in A (b) is made worse. In the sp eci c high-scale mo dels of sup ersymmetry breaking we consider in this pap er, the largest p ossible shift in R is less than b 1 . It follows that R now plays a much smaller role, and sup ersymmetric mo dels can no b 2 longer yield signi cantly smaller values of than the SM. 1 Therefore, in this work we take a di erent p oint of view and fo cus on elucidating the excluded regions of sup ersymmetry parameter space. We present a complete one-lo op analysis of sup ersymmetry, combined with a state of the art SM calculation. Input data are as of August 1997. In Section 2 we give a short overview of the inputs and observables we use. For reference we p erform a global t to the SM, and comment on some of the deviating observables. Section 3 describ es the parameter spaces of the sup ersymmetric mo dels in more detail, and reviews recent direct limits on sup erpartner masses. We compare the oblique approximation [12] with the full calculation in some detail. We present our results in Section 4 and our conclusions in Section 5. 2 Overview Within the SM we p erform a global t to a total of 31 observables listed b elow. We include 3 full one-lo op radiative corrections [13]; full QCD corrections up to O ( ); higher order QCD s corrections when enhanced by b eta function e ects; mixed electroweak/QCD corrections of 2 O ( ) with the exception of non-leading sp ecial vertex corrections to Z ! bb decays ; and s 2 O ( ) corrections when enhanced, e.g. by large top mass e ects or large logarithms. The Fermi constant, G , and the ne structure constant, , are taken as xed inputs. The ve t parameters are the strong coupling constant, ; the contribution of the ve light s (5) quarks to the photon vacuum p olarization function, ; and the masses of the Z -b oson, had M , the Higgs scalar, M , and the top quark, m . Alternatively, one may x M as well, since Z H t Z its relative error is now comparable to that of G . Wehavechosen to leave it free, b ecause the Z -mass measurement is correlated with other observables. In practice, the di erence b etween the two treatments is numerically insigni cant. We have organized the measurements into seven groups: 9 lineshap e observables The mutually correlated LEP observables [16] are determined from a common t to the Z lineshap e and the leptonic forward-backward asymmetries. They include the Z -b oson p ole mass M , the total Z -width , the hadronic p eak cross section, Z Z 12 ee had 0 = ; had 2 2 M Z Z and, for each lepton avor, ` = e, , , the ratios R = = , and the p ole asymme- ` had `` 1 First results of this kind of analysis were presented in Ref. [8]. 2 These have b een calculated very recently and shown to b e quite small compared to the analogous correc- tions to the lighter quark vertices [15]. 2 FB tries, A (`). denotes the partial Z width into x. De ning x f 2 1 4Q sin f e A = ; f f f 2 4 2 1 4Q sin +8Q sin f e f e f 2 where sin is the e ective weak mixing angle for fermion f at the Z scale, we have e 3 FB A (f )= A A : e f 4 3 further LEP asymmetries FB These are the p olarization, P ( ) = A , its forward-backward asymmetry, P ( ) = FB A , and the hadronic charge asymmetry, hQ i, which is quoted as a measurement of e 2 e sin [16]. e 6 heavy avor observables The mutually correlated heavy avor observables from LEP and SLC [16] are the ratios FB R = = ; the forward-backward p ole asymmetries, A (q) (LEP); and the com- q qq had FB bined left-right forward-backward asymmetries, A (q )=A (SLC), each for q = b; c.
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