A brief review is given of $a_{\mu}=(g_{\mu}-2)/2$ as a probe of
supersymmetry and of extra dimensions. It is known since the early to mid
nineteen eightees that the supersymmetric electro-weak correction to $a_{\mu}$
can be as large or larger than the Standard Model electro-weak correction and
thus any experiment that proposes to test the Standard Model electro-weak
correction will also test the supersymmetric correction and constrain
supersymmetric models. The new physics effect seen in the Brookhaven (BNL)
experiment is consistent with these early expectations. Detailed analyses
within the well motivated supergravity unified model show that the size of the
observed difference ($a_{\mu}^{exp}-a_{\mu}^{SM}$) seen at Brookhaven implies
upper limits on sparticle masses in a mass range accessible to the direct
observation of these particles at the Large Hadron Collider. Further, analyses
also show that the BNL data is favorable for the detection of supersymmeteric
dark matter in direct dark matter searches. The effect of large extra
dimensions on $a_{\mu}$ is also discussed. It is shown that with the current
limits on the size of extra dimensions, which imply that the inverse size of
such dimensions lies in the TeV region, their effects on $a_{\mu}$ relative to
the supersymmetric contribution is small and thus extra dimensions do not
produce a serious background to the supersymmetric contribution. It is
concluded that the analysis of the additional data currently underway at
Brookhaven as well as a reduction of the hadronic error will help pin down the
scale of weak scale supersymmetry even more precisely.Comment: 11 pages,Latex.Invited talk at La Thuile,01 conference March
  4-10,200

Nath, Pran

English

arXiv

A brief review is given of $a_{\mu}=(g_{\mu}-2)/2$ as a probe of supersymmetry and of extra dimensions. It is known since the early to mid nineteen eightees that the supersymmetric electro-weak correction to $a_{\mu}$ can be as large or larger than the Standard Model electro-weak correction and thus any experiment that proposes to test the Standard Model electro-weak correction will also test the supersymmetric correction and constrain supersymmetric models. The new physics effect seen in the Brookhaven (BNL) experiment is consistent with these early expectations. Detailed analyses within the well motivated supergravity unified model show that the size of the observed difference ($a_{\mu}^{exp}-a_{\mu}^{SM}$) seen at Brookhaven implies upper limits on sparticle masses in a mass range accessible to the direct observation of these particles at the Large Hadron Collider. Further, analyses also show that the BNL data is favorable for the detection of supersymmeteric dark matter in direct dark matter searches. The effect of large extra dimensions on $a_{\mu}$ is also discussed. It is shown that with the current limits on the size of extra dimensions, which imply that the inverse size of such dimensions lies in the TeV region, their effects on $a_{\mu}$ relative to the supersymmetric contribution is small and thus extra dimensions do not produce a serious background to the supersymmetric contribution. It is concluded that the analysis of the additional data currently underway at Brookhaven as well as a reduction of the hadronic error will help pin down the scale of weak scale supersymmetry even more precisely.A brief review is given of $a_{\mu}=(g_{\mu}-2)/2$ as a probe of supersymmetry and of extra dimensions. It is known since the early to mid nineteen eightees that the supersymmetric electro-weak correction to $a_{\mu}$ can be as large or larger than the Standard Model electro-weak correction and thus any experiment that proposes to test the Standard Model electro-weak correction will also test the supersymmetric correction and constrain supersymmetric models. The new physics effect seen in the Brookhaven (BNL) experiment is consistent with these early expectations. Detailed analyses within the well motivated supergravity unified model show that the size of the observed difference ($a_{\mu}^{exp}-a_{\mu}^{SM}$) seen at Brookhaven implies upper limits on sparticle masses in a mass range accessible to the direct observation of these particles at the Large Hadron Collider. Further, analyses also show that the BNL data is favorable for the detection of supersymmeteric dark matter in direct dark matter searches. The effect of large extra dimensions on $a_{\mu}$ is also discussed. It is shown that with the current limits on the size of extra dimensions, which imply that the inverse size of such dimensions lies in the TeV region, their effects on $a_{\mu}$ relative to the supersymmetric contribution is small and thus extra dimensions do not produce a serious background to the supersymmetric contribution. It is concluded that the analysis of the additional data currently underway at Brookhaven as well as a reduction of the hadronic error will help pin down the scale of weak scale supersymmetry even more precisely

CERN Document Server

CERN-TH/2001-124PROBE OF SUSY AND EXTRA DIMENSIONS BYTHE BROOKHAVEN g-2 EXPERIMENTPran NathTheoretical Physics Division, CERN CH 1211, Geneva, SwitzerlandDepartment of Physics, Northeastern University, Boston, MA 02115-5000, USAAbstractA brief review is given of aµ = (gµ − 2)/2 as a probe of supersymmetry and ofextra dimensions. It is known since the early to mid nineteen eightees that thesupersymmetric electro-weak correction to aµ can be as large or larger than theStandard Model electro-weak correction and thus any experiment that proposes totest the Standard Model electro-weak correction will also test the supersymmetriccorrection and constrain supersymmetric models. The new physics effect seen in theBrookhaven (BNL) experiment is consistent with these early expectations. Detailedanalyses within the well motivated supergravity unified model show that the sizeof the observed difference (aexpµ − aSMµ ) seen at Brookhaven implies upper limits onsparticle masses in a mass range accessible to the direct observation of these parti-cles at the Large Hadron Collider. Further, analyses also show that the BNL datais favorable for the detection of supersymmeteric dark matter in direct dark mattersearches. The effect of large extra dimensions on aµ is also discussed. It is shownthat with the current limits on the size of extra dimensions, which imply that theinverse size of such dimensions lies in the TeV region, their effects on aµ relative toPermanent address1the supersymmetric contribution is small and thus extra dimensions do not producea serious background to the supersymmetric contribution. It is concluded that theanalysis of the additional data currently underway at Brookhaven as well as a reduc-tion of the hadronic error will help pin down the scale of weak scale supersymmetryeven more precisely.1. IntroductionThe topics we discuss in this paper consist of the supersymmetric electro-weak effect on aµ,and the implications of the precise Brookhaven (BNL) aµ result for the direct detection ofsupersymmetry at accelerators and in the direct search for dark matter. We will also discussthe effect of extra dimensions on aµ. We begin by reviewing the situation with regard to theStandard Model contribution which consists of aSMµ = aqedµ +ahadµ +aEWµ . The qed correctionshave been computed to O(5) (for a review see Refs.1), the Standard Model electro-weakcorrection is computed to one loop2 and two loop orders3 and isaEWµ (SM) = 15:1(0:4)  10−10 (1)The hadronic contribution from vacuum polarization corrections to O(2)4 and O(3)5 andlight by light scattering contribution6,7 together give4,8 ahadµ = 673:9(6:7) 10−10. The totalStandard Model contribution is then aSMµ =11659159:7 (6:7) 10−10. The recent Brookhavenresult gives a 2:6 difference between experiment and theory9aexpµ − aSMµ = 43(16)  10−10 (2)2. Supersymmetric electro-weak contributionsIt is well known that the anomalous magnetic moment vanishes in the limit of exactsupersymmetry10. The early analyses of aµ in supersymmetric models with broken su-persymmetry are listed in Ref.11. However, the anomalous moment is very sensitive to the2pattern of supersymmetry breaking and thus one needs phenomenologically viable modelsof SUSY breaking for such computations. The supergravity unified model12,13 provides sucha framework and led to the modern analyses of supersymmetric electro-weak correction toaµ14,15. The parameter space of the minimal supergravity model (mSUGRA) at low energyis characterized by the parameters m0; m 12; A0; tan and sign where m0 is the univer-sal scalar mass, m 12is the universal gaugino mass, A0 is the universal trilinear coupling,tan  =< H1 > = < H2 > where, H2 gives mass to the up quarks and H1 gives mass tothe down quarks and leptons, and  is the Higgs mixing parameter which appears in thesuperpotential as H1H2. We reproduce here some of the results of Ref.15 where the first fullone loop analysis of the supersymmetric effect was given. The supersymmetric contributionhere arises from the chargino - sneutrino exchange and from the neutralino - smuon exchangeso that aSUSYµ = aW˜µ + aZ˜µ . The chargino exchange which is typically the larger contributionis given by17aW˜µ =m2µ482A(a)R2m2W˜aF1((mν˜mW˜a)2) +mµ82A(a)R A(a)LmW˜aF2((mν˜mW˜a)2) (3)where AL(AR) are the left(right) chiral amplitudes and are given by17A(1)R = −ep2 sin Wcos γ1; A(1)L = (−1)θemµ cos γ22MW sin W cos (4)A(2)R = −ep2 sin Wsin γ1; A(2)L = −emµ sin γ22MW sin W cos (5)Here γ1 and γ2 are the mixing angles and  = 0( = 1) if the lighter eigenvalue of the charginomass matrix is negative (positive). The supersymmetric electro-weak corrections has severalinteresting features. First under the constraint of radiative breaking of the electro-weaksymmetry one finds that the term proportional to ALAR term in Eq.(3) dominates, andfurther this term itself is dominated by the light chargino exchange contribution. As isevident from Eq.(4) the light chargino exchange term carries with it a signature and becauseof that one finds a strong correlation between the sign of  and the sign of aSUSYµ . Thus onefinds that quite generally that aSUSYµ > 0;  > 0, and aSUSYµ < 0;  < 0 (in the standard sign3convention18) except when tan   116,17. Second we also note that the dominant ALARterm in Eq.(3) has a coupling proportional to 1= cos. Because of this aµ increases linearlywith tan for large tan16,17. As will be discussed in Sec.3 the effects of extra dimensionson aµ is relatively small19, so their contribution to aµ does not pose a serious backgroundto the supersymmetric electro-weak contribution. The effect of the phases was analyzed inRef.20 and it is found that the supersymmetric contribution to aµ is a very sensitive functionof the phases and their inclusion in the analysis can change both the sign and the magnitudeof the supersymmetric contribution.After the recent BNL experimental result became available9 a large number of investi-gations exploring the implications of the result for supersymmetry have been reported21–26.In the analysis of Ref.21 under the assumption of CP conservation and setting aSUSYµ =aexpµ − aSMµ , it is found as anticipated16,17 that the BNL data determines the sign of  andone finds21 sign() = +1. Further, using the 2 error corridor of Eq.(2) one finds thatthe data implies upper bounds on the sparticle masses. Thus within mSUGRA one finds21mW˜  650GeV; mν˜  1:5TeV and m1/2  800GeV; m0  1:5TeV , for tan   55. Theseresults imply that the sparticles should become visible at the LHC and perhaps even atRUNII of the Tevatron. Additionally one finds that the  sign implied by the BNL datais the sign which least restricts the supersymmetry parameter space under the b ! s + γconstraint27 and is also the one preferred in dark matter analyses. Thus the determinationby the Brookhaven data that the sign of  is positive is encouraging from the point of viewof search for supersymmetric dark matter21. Further, as discussed above the CP violatingphases associated with soft SUSY parameters can generate large contributions to aµ andaffect both the magnitude and the sign of aµ20. The above sensitivity of aµ implies that theBNL data, i.e., Eq.(2), can provide a strong constraint on the phases. This indeed turns outto be the case and one finds that as much as sixty to ninety percent of the parameter spaceof the CP violating phases can be eliminated by the BNL data25.43. Effect of large extra dimensions on aµNext we discuss the implications of large extra dimensions28 on aµ(for a recent review seeRef.29). This class of models can arise from compactifications of Type I string theory and inmodels of this type the string scale and even the fundamental Planck scale can be quite low,i.e., in the vicinity of a few TeV28. For specificity we shall consider the case with one largeextra dimension compactified on S1=Z2 with compactification radius R where we assumethat the inverse radius MR = 1=R is O(TeV ). In this model the resulting spectrum aftercompactification contains massless modes with N=1 supersymmetry in 4D, which preciselyform the spectrum of MSSM in 4D and the massive Kaluza-Klein (KK) modes form N=2multiplets in 4D. The Kaluza-Klein excitations generate corrections to the Fermi constant30and one finds for the above model GF = GSMF (1+pi23M2WM2R). With the current error corridor onGSMF one finds MR  3TeV. Large extra dimensions affect the value of aµ from contributionsvia the excitations of W; Z; γ and the KK correction to aµ is given by19(∆aµ)extra = 9m2µM2R+GFm2µ6p2(− 512+43(sin2W − 14)2)(M2Z −M2WM2R) (6)The relative minus sign between the M2Z and the M2W terms in the last brace in Eq.(6)arises because the Fermi constant must be normalized to take account of the KK correction.Numerically the effects of the KK states is small, i.e.,aextraµ =aSUSYµ  O(10−2) (7)Thus extra dimensions do not create a serious background to the SUSY contribution. Theeffect of extra dimensions could be enhanced in some models which, however, do not appearto be very natural31. Similar results are expected in models with strong gravity32 since thefundamental Planck scale M from the recent gravity experiment33 is constrained so thatM  3:5TeV and this scale may be as high as 50-100 TeV from studies of graviton emissioninto large extra compact dimensions from a hot supernova core using the SN1987A data34.We note, however, that although the extra dimensions are invisible in g-2 experiment their5effects could still become visible at accelerators with large enough energies29,35,36. Additionalanalyses within the framework of extra dimensions can be found in Ref.37.4. ConclusionSUSY provides the most natural explanation of the difference aexpµ − aSMµ seen at BNL. Theeffect was already predicted within the framework of SUGRA models where it was knownsince the early to mid nineteen eightees that the supersymmetric correction could be aslarge or larger than the Standard Model electro-weak correction15. A detailed analysis ofthe implications of the BNL experiment in mSUGRA shows that if the size of the new physicseffect seen by Brookhaven persists it would imply the existence of sparticles accessible at theLHC. Further, if SUSY is the right explanation of the difference seen in the BNL experiment,then the existence of a Higgs field as a fundamental field (as opposed to a composite field) isimplied. In SUGRA unified models there is an upper limit of about 130 GeV for the lightestneutral Higgs boson within the usual naturalness limits on sparticle masses38 and thus oneexpects this Higgs boson to become visible at RUNII of the Tevatron with appropriateintegrated luminosity. Additionally the possibility of finding a sparticle at RUNII is notexcluded. It is also found that the BNL data imposes impressive constraints on the phasesof soft SUSY breaking parameters eliminating a large part of the parameter space of thesephases. The effect of extra space-time dimensions on aµ was also discussed and it is concludedthat extra dimensions do not generate an effect comparable to the supersymmetric electro-weak effect. There are other possibilities not discussed here such as of a light higgs39,lepto-quarks, composite models, techni-color and extra gauge bosons as possible sources fora large correction to aµ (for a general review of these see Czarnecki and Marciano in Ref.26and for a model independent analysis see Ref.40). However, of all the scenarios mentionedabove the possibility that the observed effect is arising from supersymmetry appears to usto be the most compelling.In the coming months additional data collected in runs in the year 2000 will be analyzed6and one expects that the experimental error will reduce further. The central issue of courseis the size of the difference aexpµ − aSMµ and the associated error corridor. Here the crucialquestion concerns the size of the hadronic correction and the error associated with it. Sincemuch of the error arises in the energy domain of less than 2 GeV in the e+e− ! hadronscross section more accurate data in this region will certainly help reduce the errors8. An-other sensitive issue is the light by light contribution to the hadronic error. Although acomputation of this correction relies entirely on theoretical models, it is comforting thattwo independent analyses6,7 are in agreement on the overall sign and also in fair agreementon the magnitude of this contribution. These issues are expected to be explored in greaterdepth in the coming months and along with the expected more accurate experimental mea-surement of aµ at Brookhaven, the revised version of Eq.(2) will pin down the scale of weakscale supersymmetry even more precisely.5. AcknowledgementsThe work reported here is a review of the collaborative work with Richard Arnowitt, AliChamseddine, and T.C. Yuan in the early nineteen eightees when the modern analysis of g-2was carried out, of the more recent works with Utpal Chattopadhyay and Tarek Ibrahim,and of the work with Masahiro Yamaguchi on the effect of large extra dimensions on g-2.This research was supported in part by the NSF grant PHY-9901057.7REFERENCES1: A. Czarnecki and W.J. Marciano, Nucl. Phys. (Proc. Suppl.) B76, 245(1999).2: K. Fujikawa, B. W. Lee, and A. I. Sanda, Phys. Rev. D6, 2923 (1972); R. Jackiw and S.Weinberg, Phys. Rev. D5, 2473 (1972); G. Altarelli, N. Cabbibo, and L. Maiani, Phys.Lett. B40, 415 (1972); I. Bars and M. Yoshimura, Phys. Rev. D6, 374 (1972); W. A.Bardeen, R. Gastmans, and B. E. Lautrup, Nucl. Phys. B46, 315 (1972).3: A. Czarnecki and W.J. Marciano, Phys.Rev. Lett. 76, 3267(1996); Phys. Rev. D52,R2619(1995); S. Peris, M.Perrottet, and E. de Rafael, Phys. Lett. B355, 523(1995); G.Degrassie and G.F. Giudice, Phys. Rev. D58, 053007(1998).4: M. Davier and A. Hocker, Phys. Lett. B435, 427(1998).5: B. 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Probe of SUSY and Extra Dimensions by the Brookhaven g-2 Experiment

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