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Extracting Chargino/Neutralino Mass View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server PM/98{26 hep-ph/9810214 EXTRACTING CHARGINO/NEUTRALINO MASS PARAMETERS FROM PHYSICAL OBSERVABLES G. MOULTAKA Physique Mathematique et Theorique, UMR{CNRS, Universite Montp ellier I I, F{34095 Montp ellier Cedex 5, France. E-mail: [email protected] Abstract I rep ort on two pap ers, hep-ph/9806279 and hep-ph/9807336, where complemen- tary strategies are prop osed for the determination of the chargino/neutralino sector parameters, M ;M ; and tan , from the knowledge of some physical observables. 1 2 This determination and the o ccurrence of p ossible ambiguities are studied as far as p ossible analytically within the context of the unconstrained MSSM, assuming however no CP-violation. Talk given at the International Conference on High Energy Physics, Vancouver 1998 (to appear in the proceedings) 1 1 Intro duction The gauge b osons and Higgs b osons sup erpartners have every chance to play, in the minimal version of the sup ersymmetric standard mo del (MSSM), an imp ortant part in the rst direct exp erimental evidence for sup ersymmetry, if the latter happ ens to b e linearly realized in nature around the electroweak scale. This would go through the study of the direct pro duction of the light states and their subsequent decays, eventually cascading ; ; down to leptons (or jets) and missing energy [3] [4] [5]. The chargino/neutralino sector is an over-constrained system in the sense that only a few basic parameters in the Lagrangian are needed to determine all the six physical masses and the mixing angles of the various states. The latter determine the couplings to gauge b osons, Higgs b osons and matter fermions, so that various phenomenological tests could be in principle envisaged in the pro cess of exp erimental identi cation. Alternatively, one might hop e that a partial exp erimental knowledge of this sector would be sucient to allow a reasonably unequivo cal reconstruction of the full set of parameters; at stakes, on one hand the determination of the magnitude of the fermion soft susy breaking parame- ters, on the other, the existence of a heavy neutral stable particle, of prime imp ortance to the cold dark matter issue [6]. Furthermore, the sensitivity to tan , the ratio of the twovacuum exp ectation values of the Higgs elds, and to the sup ersymmetric parameter , brings in a further correlation with the other sectors of the MSSM. Hereafter we describ e two strategies: the rst deals with the extraction of M ; and 2 + tan form the study of the lightest chargino pair pro duction and decayine e collisions [1], the second with the extraction of M ;M and form the knowledge of any three ino 1 2 masses and tan [2]. We start by stating the common features to these complementary approaches as well as their sp eci c assumptions. We then highlight the main ingredients of each of them and illustrate some of their results. Finally we show in what sense they eventually complement one another. [Obviously, the reader is referred to [1] and [2] for more details and references. Still, we add some comments at various places of the ongoing presentation, which di er slightly from, and hop efully complete, the latter references.] The reconstruction of the basic parameters of the theory involves generically two steps which can b e sketched as follows: Exp erimental Observables x ? y (I ) Physical Parameters (1.1) x ? y (II) Lagrangian parameters Each of these steps can su er from equivo cal reconstructions due to partial exp erimental knowledge or to theoretical ambiguities. In the present rep ort we concentrate on the theoretical asp ects of b oth steps. 2 2 CDDKZ and KM common features The ino sector is considered in b oth [1] (referred to as CDDKZ) and [2] (KM) with the following assumptions: No reference to mo del-dep endent assumptions ab out physics at energies much higher than the electroweak scale, like the GUT scale, and their p ossible implication on the parameters of this sector. [Thus the study is mainly carried out in the unconstrained MSSM, but any mo del-assumptions can b e easily overlaid.] R-parity conservation; CP-conservation in the ino sector; This assumption is here only for practical rea- sons and should be eventually removed in future studies in order to cop e with the p ossibility to deal with (complex) phases [7]; CDDKZ and KM cho ose M > 0. This is of course a mere convention due to the 2 partial phase freedom through rede nition of elds, the only physical signs b eing the relative ones among M ;M and as one can easily see from the relevant terms 1 2 in the Lagrangian. (also tan is taken p ositive and the term convention is that of ref.[[8 ]].) Let us now recall brie y the basic ingredients of the ino mass matrices. The physical charginos (resp. neutralinos) are mixtures of charged (resp. neutral) higgsino and gaugino comp onents. The chargino mass matrix reads: ! p M 2m sin 2 W p M = (2.2) C 2m cos W It has a sup ersymmetric contribution coming from the term in the sup erp otential, the higgsino comp onent, a contribution from the soft susy breaking wino mass term, and o - diagonal terms due to the electroweak symmetry breaking. Since M is not symmetric one C needs two indep endent unitary matrices for the diagonalization. This is but the re ection of the fact that there are two indep endent mixings involving separately the two higgsino SU (2) doublets. The eigenvalues are most easily obtained from the diagonalization of L y M M giving the squares of the chargino masses: C C 1 2 2 2 2 M = [M + +2m 2 W 2 1;2 q (2.3) 2 2 2 2 2 2 (M + +2m ) 4(M m sin 2 ) ] 2 2 W W On the other hand, the angles ; de ning the two indep endent left- and right- L R chiral mixings among the winos and higgsinos in the four comp onent Dirac representation are given by 3 2 2 2 M 2m cos 2 2 W cos 2 = 2 2 L 2 2 2(M m )M 2 W 1 p 2m (M cos + sin ) 2 2 W sin 2 = 2 2 L 2 2 2(M m )M 2 W 1 (2.4) 2 2 2 M +2m cos 2 2 W cos 2 = 2 2 R 2 2 2(M m )M 2 W 1 p 2 2m (M sin + cos ) 2 W sin 2 = 2 2 R 2 2 2(M m )M 2 W 1 where M is the lightest chargino mass given by eq.(2.3). This form of the mixing 1 angles is such that the eigenvalues of M are always p ositive de nite. C The neutralino mass matrix corresp onds to bilinear terms in the photino, zino and neutral higgsino two-comp onent elds. It receives contributions from the term, the soft mass terms of the gaugino SU (2) triplet (M ) and singlet (M ), while the mixing among L 2 1 states is triggered by the electroweak symmetry breaking: 1 0 M 0 m s cos m s sin 1 Z w Z w C B 0 M m c cos m c sin C B 2 Z w Z w C M = B N A @ m s cos m c cos 0 (2.5) Z w Z w m s sin m c sin 0 Z w Z w In contrast with M , M is symmetric so that it can be diagonalized with one C N 1 unitary matrix. On the other hand the eigenmasses are not p ositive de nite . Finally we note that in general the diagonalization of M cannot be achieved through a similarity N transformation, unless all three parameters M ;M and are real. This will be a key 1 2 p oint in the algorithm we present for the reconstruction of the parameters in the neutralino sector. 3 Sp eci c features 3.1 CDDKZ + + The lightest chargino can b e pro duced in pairs in e e collisions, at LEPI I [4] or NLC 1 [5] energies, through and Z s-channel exchange as well as sneutrino t-channel exchange. The pro duction cross section will thus dep end on the chargino mass m , the sneutrino 1 mass m and the mixing angles, eq.(2.4), which determine the couplings of the chargino ~ states to the Z and the sneutrino. The unp olarized total cross section is illustrated in g.1 with three representative cases of higgsino, gaugino or mixed content of the lightest 1 For more details ab out the ino sector see for instance [8],[9] and references therein. 4 2 4 √ s=200 GeV 3 [pb] [pb] 1 2 tot tot σ σ 1 0 0 150 300 450 600 0 200 400 600 800 √ s [GeV] Sneutrino Mass (a) (b) Figure 1: Total cross section for the charginos pair pro duction for a representative set of M ;, solid line gaugino case, dashed line higgsino case, dot-dashed line mixed case. In 2 (a) m = 200GeV . (taken from ref.[1]) ~ chargino mass. The sharp rise near threshold should allow a precise determination of the chargino mass. Also the sensitivity to the sneutrino mass with the typical destructive interference in the gaugino and mixed cases necessitates the knowledge of this parameter.
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