I I I , ' University of Trondheim UNIT Theoretical Physics Seminar in Trondheim No 8 1992 Limits on supersymmetry masses from the anomalous magnetic moment of leptons Olav F. Syljuåsen Haakon A. Olsen Institute of Physics University of Trondheim, AVH, N-7055 Dragvoll, Norway ISSN 0365-2459 April 1992 Abstract Lower limits on slepton and photino masses mt and mp are obtained from the experimenta] values of the anomalous magnetic moments of the electron and muon. Typical values are m's > 1.5 GeV, mj > 15 GeV for mp < m, and mp > 22 GeV for mj < mp. The present large experimental uncertainty in the r anomalous magnetic moment prevents any statement about the mass of the T slepton. 1 We study in the present paper the effect of supersymmetric quantum electro­ dynamics upon the most accurately known quantum electrodynamic quantity, the anomalous magnetic moment. The supersymmetric quantum electrodynamic La- grangian density may in the four-component (Dirac) representation be written in the compact form: CSQED = —^F^"" + <? (il"Du - mi) $ + D;<plD"<f1-ml<^Vi+ DlWn-mtøn (1) + 2* ('V^* - mr) A + itxji (yr, + 75^,) A - 1'eA tø - 75^) ip with D„ = 3„ + ie.4„, mi the lepton mass, f\ and <^j the scalar and pseudoscalar components of the slepton field and A the (Majorana) photino field. The masses in, and mp which break supersymmetry are the slepton and photino masses respectively. We find that the anomalous magnetic moment due to the supersymmetry photiDO- slepton intermediate states, Fig.l, is given by the simple formula a r1 i'(l — x) asvMm.^p) =—/ <k , , /.,—,% ',,, > (2) w Jo iJ + (j5jJ- })x + m*[l — x) where m, and mT are the scaled masses mi mi Equation (2) shows that for unbroken supersymmetry, m, = mi, mT = 0, the su- persymmetric anomalous magnetic moment asvsr (1,0) = -f;, which is except for the sign exactly the same a* the lowest order quantum electrodynamic contribution "QED — f;- This means that the total theoretical anomalous magnetic moment "i* m aQED + «SVSf (*) 2 would vanish to lowest order, a result which was first obtained by Ferrara and Remiddi1. This is the strongest argument against unbroken supersyminetry. From Eq.(2) follows that for m, > mj, the physically acceptable region of supersymmetric masses asusr(ms,mp) < 0. (5) This shows that an experimental value of the anomalous magnetic moment aexp larger than the theoretical QED value O.QED cannot be accounted for by the super- symmetric contribution alone. This is a general and non-trivial result. It can be shown that the same is true for axion contributions to an. For the case of interest, mj or m* much larger than one, we find aSusy(ms,mp) = -f(ft^ft;), {\ {< - $™W, - 2*j) + 2^|jln^} (6) Typical values are asuM^O) = -j^jj; «st/sy(l,mp) = -^; ««,„(*..*.) = ~j~ (?) A criterion for obtaining the lower limits of slepton and photino masses is taken to be \asvsv\ < \a,xr - "QED\ (8) We use the experimental values2,3'* a'„T = 1 159 652 138.4(±4.3) x 10"" a»„f = 1 165 937(±12)xl0-« a,T„ = 5.2(±4.8) x 10-3 3 and the corresponding theoretical values5' 12 a'QED = 1 159 652 140(±28) x KT 9 a"QED = 1 165 919.20(±1.91) x 10" 3 a££D = 1.1773(±0.0003) x 10" Figure 2 gives the combined slepton-photino mass limits. Specific values are for m] > 1.5 GeV ; mj > 15 GeV. (9) These constraints are consistent with results obtained from high energy experiments. Recent high energy experiments at CERN8 give constraints on slepton masses m,e,mj> 40 GeV, (10) model dependent, with mv assumed to be less than 30 GeV. The corresponding lower limit for the photino mass for m, 4Z. mp is mp>22GeV. (11) No information on photino mass constraints have been obtained from high energy experiments. For the case of r the present uncertainly in the experimental value of the anoma­ lous magnetic moment is too large to make predictions for constraints on the r slepton mass. One finds for r, lasvsvl ^ 4-0 x 10~3 which is true for any value of 4 mj as may be shown from Eq.(2). Improvements in the accuracies in the experimental and theoretical values of the anomalous magnetic moments would improve the constraints on the slepton and photino masses. Improvements of the accuracy for the muon by one order of mag­ nitude would bring the mass constraint on the smuon mass beyond the level of the present high energy experiments. Apparently these precision low energy experiments may be of value comparable to the high energy experiments. 5 References [1] S.Ferrara and E.Remiddi, Phys.Lett. B53, 347 (1974). See also P.A.Éminov, Sov.J.Nucl.Phys. 51, 346 (1990). [2] R.S.Van Dyck Jr., P.B.Schwinberg and H.G.Dehmelt, Phys.Rev.Lett. 59, 26 (19S7). [3] J.Bailey et aJ. CERN Muon Storage Ring Collab. , Phys.Lett. B68, 191 (1977). [4] R.Marshall, Rep.Prog.Phys. 52, 1329 (1989). [5] T.Kinoshita and W.B.Lindquist, Phys.Rev.D 42, 636 (1990). [6] T.Kinoshita,B.Nizic and Y.Okamoto, Phys.Rev.D 41, 593 (1990). [7] M.A.Samuel,G.Li end R.Mendel, Phys.Rev.Lett. 67, 668 (1991). See also S.Narison, J.Phys. 64, 1849 (1978). [8] L3 Collab., B.Adeva et ai., Phys.Lett. B233, 530 (1989); ALEPH Collab., D.Decamp et a/., Phys.Lett. B236, 86 (1990); OPAL Collab., M.Z.Akrawy et a/., Pbys.I.ott. B240, 261 (1990); ALEPH Collab., P.Abreu et a/., Phys.Lett. B247, 157 (1990). 6 Figure captions Figure 1. The QED-SUSY vertex, involving the exchange of a photino and a scalar 1^1 or a pseudoscalar <p2- Figure 2. Allowed region for the masses m*s and mp. Smuons and photinos in the allowed region do not contradict the g — 2 experiment of muons. Mass values for the m'-mp diagram are obtained by multiplication with 0.0942. All mass values are in GeV. 7 1 s M \ -f ©• \ mp 20 - allowed 15 - 10 - forbidden 5 - 1 1 1 1 1 M r. 2.5 7.5 10 12.5 15 m" Figure 2. .