Electroweak precision data and gravitino dark matter

— physics pp. 947–951

Electroweak precision data and gravitino dark matter

S HEINEMEYER

Instituto de Fisica de Cantabria (CSIC-UC), Santander, Spain E-mail: Sven.Heinemeyer@cern.ch

Abstract. Electroweak precision measurements can provide indirect information about the possible scale of supersymmetry already at the present level of accuracy. We review present day sensitivities of precision data in mSUGRA-type models with the gravitino as the lightest supersymmetric particle (LSP). Theχ²fit is based onMW, sin²θeff, (g−2)µ, BR(b → sγ) and the lightest MSSM Higgs boson mass, Mh. We find indications for relatively light soft supersymmetry-breaking masses, offering good prospects for the LHC and the ILC, and in some cases also for the Tevatron.

Keywords. Gravitino dark matter; fit; precision observables.

PACS Nos 12.60.Jv; 14.80.Ly

1. Introduction

We have recently analyzed [1,2] the indications provided by current experimental data concerning the possible scale of supersymmetry (SUSY) within the framework of the minimal supersymmetric extension of the standard model (MSSM), assuming that the soft supersymmetry-breaking scalar massesm0, gaugino massesm_1/2 and tri-linear parameters A0 were each constrained to be universal at the input GUT scale, with the gravitino heavy and the lightest supersymmetric particle (LSP) being the lightest neutralino ˜χ⁰₁(CMSSM). (For other recent analyses, see ref. [3].) However, there are more scenarios for SUSY phenomenology. For example, the gravitino might be the LSP and constitute the dark matter [4], a framework known as the GDM [5].

Supersymmetry may provide an important contribution to loop effects that are rare or forbidden within the standard model. Especially sensitive in this respect are the observables MW and sin²θeff, the loop-induced quantities (g−2)µ and BR(b→sγ), as well as the lightest MSSM Higgs boson mass,Mh(see ref. [6] for a review). Another important constraint is provided by the cold dark matter (CDM) density ΩCDMh² determined by WMAP and other observations. We analyze the precision observables in the context of the GDM, focusing on parameter combina- tions that fulfill 0.094 <ΩCDMh²<0.129 [7]. In order to simplify the analysis in a motivated manner, we furthermore restrict our attention to scenarios inspired by

supergravity (mSUGRA), in which the gravitino mass is constrained to be equal tom0 at the input GUT scale, and the trilinear and bilinear soft supersymmetry- breaking parameters are related by A0 = B0+m0. In the cases we review here, namelyA0/m0= 0,3/4,3−√

3,2, the regions of the (m1/2, m0) plane allowed by cosmological constraints then take the form of wedges located at small values of m0 [5,8].

2. The χ² fit

In this section we review briefly the experimental data set that has been used for the fits. We focus on parameter points that yield the correct value of the cold dark matter density, 0.094<ΩCDMh²<0.129 [7], which is, however, not included in the fit itself. The top quark mass has been fixed to bemt= 172.7 GeV [9], where the experimental uncertainty ofδm^exp_t = 2.9 GeV has been taken into account in the parametric uncertainty (see below). For the other observables we use the following experimental values (see ref. [2] and references therein)

M_W^exp= 80.410±0.032 GeV, sin²θ^exp_eff = 0.23153±0.00016,

a^exp_µ −a^theo,SM_µ = (25.2±9.2)×10⁻¹⁰,

BR(b→sγ) = (3.39^+0.30_−0.27)×10⁻⁴. (1) An update to the most recent experimental values would not change our results in a qualitative manner (see e.g. ref. [10] for an analysis of the dependence on m^exp_t and δm^exp_t ). For Mh we use the complete likelihood information available from LEP [11]. Our starting points are the CLs(Mh) values provided by the final LEP results on the SM Higgs boson search (see figure 9 in [11], where theχ²contribution is obtained by inversion CLs(Mh) (see ref. [2] for details).

Assuming that the five observables listed above are uncorrelated, a χ² fit has been performed with

χ²≡ X4 n=1

µR^exp_n −R^theo_n σn

¶2

+χ²_Mh. (2)

Here R^exp_n denotes the experimental central value of the nth observable (M_W, sin²θeff, (g−2)µ and BR(b → sγ)), R^theo_n is the corresponding GDM prediction andσn denotes the combined error (experimental, parametric, intrinsic, refs [2,6]).

χ²_Mh denotes the χ² contribution coming from the lightest MSSM Higgs boson mass as described above. For details of the theory evaluations, see refs [6,12–15]

and references therein.

3. Results in the GDM

In figure 1 we show totalχ²as a function ofm and various SUSY particle masses.

0 200 400 600 800 1000 m1/2 [GeV]

0 2 4 6 8 10

χ2 (today)

mSUGRA GDM, µ > 0 A₀/m₀ = 0.00 A₀/m₀ = 0.75 A₀/m₀ = 1.27 A₀/m₀ = 2.00

0 200 400 600 800 1000

m_χ~0 1

[GeV]

0 2 4 6 8 10

χ2 (today)

mSUGRA GDM, µ > 0 A₀/m₀ = 0.00 A₀/m₀ = 0.75 A₀/m₀ = 1.27 A₀/m₀ = 2.00

(a) (b)

0 200 400 600 800 1000

m_χ~0 2

, m_χ~+ 1

[GeV]

0 2 4 6 8 10

χ2 (today)

mSUGRA GDM, µ > 0 A₀/m₀ = 0.00 A₀/m₀ = 0.75 A₀/m₀ = 1.27 A₀/m₀ = 2.00

0 200 400 600 800 1000

m_τ~

1

[GeV]

0 2 4 6 8 10

χ2 (today)

mSUGRA GDM, µ > 0 A₀/m₀ = 0.00 A₀/m₀ = 0.75 A₀/m₀ = 1.27 A₀/m₀ = 2.00

(c) (d)

0 200 400 600 800 1000 1200 1400 1600 1800 2000 m~t

1

[GeV]

0 2 4 6 8 10

χ2 (today)

mSUGRA GDM, µ > 0 A₀/m₀ = 0.00 A₀/m₀ = 0.75 A₀/m₀ = 1.27 A₀/m₀ = 2.00

0 200 400 600 800 1000 1200 1400 1600 1800 2000 mg~ [GeV]

0 2 4 6 8 10

χ2 (today)

mSUGRA GDM, µ > 0 A₀/m₀ = 0.00 A₀/m₀ = 0.75 A₀/m₀ = 1.27 A₀/m₀ = 2.00

(e) (f)

Figure 1. The dependence of the χ² function onm1/2 for GDM scenarios withA0/m0 = 0,0.75,3−√

3 and 2, scanning the regions where the lighter stau ˜τ1 is the NLSP, shown as a function of (a)m1/2, (b)m_χ˜0

1, (c)m_χ˜0 2 and m_χ˜±

1, (d)mτ˜₁, (e)m˜t₁, and (f)m˜g.

and 2 is at m_1/2 ∼ 450 GeV. However, this minimum is not attained for GDM models with largerm0, as they do not reach the low-m_1/2 tip of the GDM wedge.

In general, we see in the different panels of figure 1 that there might be some hope to observe the lightest ˜τ at the Tevatron, that there are good prospects for observing

˜

g and perhaps ˜t1 at the LHC, and that ILC(500) has good prospects for ˜χ⁰₁ and

˜

τ1, though these diminish for largerm0. The ILC(1000) offers much better chances also for largem0. We recall that, in these GDM scenarios, ˜τ1 is the NLSP, and ˜χ⁰₁ is heavier. ˜τ₁ decays into the gravitino and a τ, and is metastable with a lifetime that may be measured in hours, days or weeks.

One feature of the class of GDM scenarios discussed here is that the required value of tanβ increases with m_1/2. Therefore, the preference for relatively small m_1/2 discussed above maps into an analogous preference for moderate tanβ (see ref. [2]). It can be shown that, at the 95% confidence level

300 GeV<∼m1/2<∼800 GeV, 15<∼ tanβ <∼27 (3) in this mSUGRA class of GDM models.

Acknowledgements

The author thanks J Ellis, K A Olive and G Weiglein with whom he derived the results presented here.

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The code is accessible via www.feynhiggs.de