View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by National Tsing Hua University Institutional Repository PHYSICAL REVIEW D 66, 116008 ͑2002͒ Constraints from electric dipole moments on chargino baryogenesis in the minimal supersymmetric standard model Darwin Chang NCTS and Physics Department, National Tsing-Hua University, Hsinchu 30043, Taiwan, Republic of China and Theory Group, Lawrence Berkeley Lab, Berkeley, California 94720 We-Fu Chang NCTS and Physics Department, National Tsing-Hua University, Hsinchu 30043, Taiwan, Republic of China and TRIUMF Theory Group, Vancouver, British Columbia, Canada V6T 2A3 Wai-Yee Keung NCTS and Physics Department, National Tsing-Hua University, Hsinchu 30043, Taiwan, Republic of China and Physics Department, University of Illinois at Chicago, Chicago, Illinois 60607-7059 ͑Received 9 May 2002; revised 13 September 2002; published 27 December 2002͒ A commonly accepted mechanism of generating baryon asymmetry in the minimal supersymmetric standard model ͑MSSM͒ depends on the CP violating relative phase between the gaugino mass and the Higgsino ␮ term. The direct constraint on this phase comes from the limit of electric dipole moments ͑EDM’s͒ of various light fermions. To avoid such a constraint, a scheme which assumes that the first two generation sfermions are very heavy is usually evoked to suppress the one-loop EDM contributions. We point out that under such a scheme the most severe constraint may come from a new contribution to the electric dipole moment of the electron, the neutron, or atoms via the chargino sector at the two-loop level. As a result, the allowed parameter space for baryogenesis in the MSSM is severely constrained, independent of the masses of the first two generation sfermions. DOI: 10.1103/PhysRevD.66.116008 PACS number͑s͒: 11.30.Er, 11.30.Fs, 12.60.Jv, 98.80.Cq INTRODUCTION BAU. One immediate question is whether or not such a new source of CP violation is already severely experimentally While the standard model of particle physics continues to constrained. It is not surprising that the most severe con- accurately describe a wide array of experimental tests many straints are provided by the current experimental limits of the ͑ ͒ physicists suspect that the next generation of a unified field electric dipole moments EDM’s of the electron (de) and theory will be supersymmetric. This supersymmetric theory the neutron (dn). in its simplest form, the minimal supersymmetric standard Fortunately, the lowest order ͑one-loop͒ contributions to model ͑MSSM͓͒1͔, may help to solve many of the outstand- various EDM’s through chargino mixing can be easily sup- ing problems in the standard model. Two examples of this pressed by demanding that the first two generations of sfer- sort are the coupling-constant-unification problem and the mions be heavier than the third one ͓4,5͔. For example, if observed baryon asymmetry of the universe ͑BAU͒.Itisthe one requires these sfermions to be heavier than 10 TeV, the latter of these two that will be discussed in this paper. one-loop induced EDM’s will be safely small ͓6͔. In fact, It has been demonstrated that the SM is insufficient in such a scenario can even be generated naturally in a more generating a large enough BAU ͓2͔. Particles lighter in mass basic scheme referred to as the more minimal SUSY model but stronger in coupling are needed to make the electroweak ͓7͔. However, despite the enlarged parameter space of the transition more first order. Additionally, a new CP violating MSSM, thanks to all the intricate limits provided by accu- phase is required to generate enough BAU. It is very appeal- mulated data from various collider experiments, there is only ing that the MSSM naturally provides a solution to both a small region of parameters left within the MSSM for such requirements ͓3͔. baryogenesis to work ͓3͔. The top-quark partner, the top squark, which is naturally In this article we wish to point out that even if sfermions lighter than the other squarks, can make the transition more of the first two generations are assumed to be very heavy, first order, while there are plenty of new CP violating phases there are important contributions to the EDM of the electron at our disposal in the soft supersymmetry ͑SUSY͒ breaking at the two-loop level via the chargino sector that strongly sector. In particular, it has been shown that the most likely constrain the chargino sector as the source for BAU in the scenario is to make use of the relative phase between the soft MSSM. Similar contributions to the quark EDM also exist SUSY breaking gaugino mass and the ␮ term of the but the resulting constraint turns out to be relatively weaker. Higgsino sector ͓3͔. In this case, the BAU is generated While this is not the first time that two-loop contributions through the scattering of the charginos on the bubble wall. have been found to be more important than the one-loop The CP violation is provided by the chargino mixing. It turns ones ͓8–12͔, this chargino contribution and its relevance to out that in most parameter space of the MSSM a nearly BAU was never treated fully. maximal CP violating phase is needed to generate enough In the case of chargino contributions, the two-loop contri- 0556-2821/2002/66͑11͒/116008͑8͒/$20.0066 116008-1 ©2002 The American Physical Society CHANG, CHANG, AND KEUNG PHYSICAL REVIEW D 66, 116008 ͑2002͒ bution is dominant because the one-loop contribution is sup- pressed when the sfermions are heavy. This aspect is similar to those in Refs. ͓8,12͔. In addition, the present case of a large CP violating phase in the chargino mixing and the light Higgs scalar, which is necessary to obtain a large baryon asymmetry, is also the same cause of the large EDM. There- fore, the resulting severe EDM constraint is very difficult to avoid in the mechanism of chargino baryogenesis by tuning parameters. THE MODEL AND COUPLINGS Before we outline the physics of the chargino mixing in supersymmetric models we will set forth our conventions. We assume the minimal set of two Higgs doublets. Let the FIG. 1. A two-loop diagram of the EDM of the electron, or ⌽ ϭϪ ⌽ superfield d(Y 1) couple to the d-type field and u(Y quarks. The chargino runs in the inner loop. ϭ1) to the u-type ͑see Ref. ͓11͔ for our convention͒. The chargino fields are combinations of those of the W-ino The complex mixing amplitudes are written in terms of the ␻ϩ ϩ ␺ ϭ ␻ϩ ϩ T S P ( L,R) and the Higgsino (huL,dR). Denote L ( L ,huL) real couplings g and g . In the same spirit, the complex ϩ ϩ and ¯␺ ϭ(¯␻ ¯,h ). The chargino mass term, ϪL C neutral Higgs fields are decomposed into the real and imagi- R R dR M ␸0ϭ 0ϩ 0 ϭ 0 ϭ¯␺ ␺ nary components q hq iaq (q u,d). Note that hd and RM C L in our convention, becomes 0 hu mix in a CP conserving fashion at the tree level, and so do ͱ ␤ a0 and a0 : M 2 2M Wsin u d M ϭͩ ͪ , ͑1͒ C ͱ ␤ ␮ i␾ 0 0 0 0 2M Wcos e h hu G au ͩ ͪ ϭRͩ ͪ , ͩ ͪ ϭSͩ ͪ , ͑4͒ H0 h0 A0 a0 where M 2 is the SUL(2) gaugino mass. Note that we choose d d a CP violating complex Higgsino mass ␮ei␾. The scalar ⌽ ⌽ cos ␣ Ϫsin ␣ sin ␤ Ϫcos ␤ components Hu ,Hd of u , d have real vacuum expectation Rϭͩ ͪ Sϭͩ ͪ ͑ ͒ ͱ ͱ ␤ϭ ␣ ␣ , ␤ ␤ . 5 values vu / 2,vd / 2, respectively, and tan vu /vd . sin cos cos sin We use the biunitary transformation to obtain the diagonal D † mass matrix M ϭUЈM U with eigenvalues m␹ ,m␹ for The EDM calculation involves the Higgs boson propagators, C 1 2 ␹ ␹ which are defined as the eigenfields 1 , 2. The CP violating chargino mixing can contribute to the fermion EDM through the chargino- ͗␸ ␸† ͘ ϭ q,qЈ ͑ 2Ϫ 2 ͒ sfermion loop. Detailed analyses of such contributions can q p2 i͚ Zϩ,␴ / p M ␴ , qЈ ␴ be found in the literature ͓5͔. As noted in the Introduction, such contributions can be tuned to be small by making the sfermions heavy ͓6͔͑typically of 10 TeV or larger͒. Here we ͗␸ ␸ ͘ ϭ q,qЈ ͑ 2Ϫ 2 ͒ ͑ ͒ q qЈ p2 i͚ ZϪ,␴ / p M ␴ . 6 are interested in contributions to the EDM of a fermion that ␴ are still important even with very heavy sfermions. For this we find that the leading contribution is from diagrams of the The Z factors can be shown to be real at the leading order type in Fig. 1. with the explicit forms To evaluate the diagram, we examine gauge couplings of d,d u,u d,d u,u Z ϭZ ϭcos2␣, Z ϭZ ϭϮcos2␤, 0ϭ ϩ␸ ͱ Ϯ,H Ϯ,h Ϯ,G Ϯ,A the Higgs bosons, Hq (vq q)/ 2, d,d u,u 2 d,d u,u 2 ZϮ ϭZϮ ϭsin ␣, ZϮ ϭZϮ ϭϮsin ␤, g ,h ,H ,A ,G L ϭ ¯␹ ͓ Ј † ␸0 ϩ Ј † ␸0 ͔␹ ϩ Y ͚ iR Ui␻Uhj u* UihU␻ j d* jL H.c. ͱ2 ij 1 1 Zu,d ϭ sin 2␣ϭϪZu,d , Zu,d ϭϮ sin 2␤ϭϪZu,d , ͑2͒ Ϯ,H 2 Ϯ,h Ϯ,A 2 Ϯ,G Only the diagonal couplings in the chargino basis are rel- d,u u,d ZϮ ␴ϭZϮ ␴ for ␴ϭh,H,A,G. evant to the simple diagrams in Fig.