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Determining SUSY Parameters from Chargino Pair Production

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Determining SUSY Parameters from Chargino Pair Production Corfu Summer Institute on Elementary Particle Physics, 1998 PROCEEDINGS Determining SUSY Parameters from Chargino Pair Production Jan Kalinowski Instytut Fizyki Teoretycznej, Ho_za 69, 00681 Warszawa, Poland E-mail: [email protected] Abstract: A procedure to determine the chargino mixing angles and, subsequently, the fundamental SUSY parameters M2,µand tan β by measurements of the total cross section and the spin correlations + − + − in e e annihilation toχ ˜1 χ˜1 chargino pairs is discussed. 1. Introduction role in the first direct experimental evidence for supersymmetry. Despite the lack of direct experimental evidence The doubling of the spectrum of states in for supersymmetry (SUSY), the concept of sym- the MSSM together with our ignorance on the metry between bosons and fermions [1] has so dynamics of the supersymmetry breaking mech- many attractive features that the supersymmet- anisms gives rise to a large number of unknown ric extension of the Standard Model is widely parameters. Even with the R-parity conserving considered as a most natural scenario. SUSY en- and CP-invariant SUSY sector, which we will as- sures the cancellation of quadratically divergent sume in what follows, in total more than 100 new corrections from scalar and fermion loops and parameters are introduced. This number of pa- thus stabilizes the Higgs boson mass in the de- rameters can be reduced by additional physical 2 sired range of order 10 GeV, predicts the renor- assumptions. In the literature several theoreti- 2 θ malized electroweak mixing angle sin W in strik- cally motivated scenarios have been considered. ing agreement with the measured value, and pro- The most radical reduction is achieved by embed- vides the opportunity to generate the electroweak ding the low–energy supersymmetric theory into symmetry breaking radiatively. a grand unified (SUSY-GUT) framework called Supersymmetry predicts the quarks and lep- mSUGRA. The mSUGRA is fully specified at tons to have scalar partners, called squarks and the GUT scale by a common gaugino mass m1=2, sleptons, the gauge bosons to have fermionic part- a common scalar mass m0, a common trilinear ners, called gauginos. In the Minimal Supersym- scalar coupling AG, the ratio tan β = v2/v1 of metric Standard Model (MSSM) [2] two Higgs the vev’s of the two neutral Higgs fields, and the doublets with opposite hypercharges, and with sign of the Higgs mass parameter µ.Allthecou- their superpartners: higgsinos, are required to plings, masses and mixings at the electroweak give masses to the up and down type fermions scale are then determined by the RGEs [3]. It and to ensure anomaly cancellation. The hig- turns out, however, that the interpretation of ex- gsinos and electroweak gauginos mix; the mass perimental data and derived limits on sparticle eigenstates are called charginosχ ˜1;2 and neutrali- masses and their couplings strongly depends on 0 nosχ ˜1;2;3;4 for electrically charged and neutral the adopted scenario. Therefore it is important states, respectively. Actually in many supersym- to develop strategies to measure all low-energy metric models the lighter chargino statesχ ˜1 are SUSY parameters independently of any theoret- expected to be the lightest observable supersym- ical assumptions. The experimental program to metric particles and they may play an important search for and explore SUSY at present and fu- Corfu Summer Institute on Elementary Particle Physics, 1998 Jan Kalinowski ture colliders should thus include the following 2. Chargino masses and couplings points: The superpartners of the W boson and charged (a) discover supersymmetric particles and mea- Higgs boson, W˜ and H˜ , necessarily mix since sure their quantum numbers to prove that the mass matrix (in the {W˜ −, H˜ −} basis) [2] they are superpartners of standard parti- √ M2 2mW cβ cles, MC = √ (2.1) 2mW sβ µ (b) determine the low-energy Lagrangian pa- is nondiagonal (cβ =cosβ,sβ =sinβ). It is ex- rameters, pressed in terms of the fundamental supersym- (c) verify the relations among them in order to metric parameters: the gaugino mass M2,the distinguish between various SUSY models. Higgs mass parameter µ,andtanβ. Two dif- ferent matrices acting on the left– and right– If SUSY is realized in Nature, it will be a matter chiral (W,˜ H˜) states are needed to diagonalize + − of days for the future e e linear colliders (LC) the asymmetric mass matrix (2.1). The (posi- to discover the kinematically accessible super- tive) eigenvalues are given by symmetric particles. Once they are discovered, m2 1 M 2 µ2 m2 ∓ χ~ = 2 2 + +2 W ∆ (2.2) the priority will be to measure the low-energy 1;2 SUSY parameters independently of theoretical prejudices and then check whether the correla- where tions among parameters, if any, support a given 2 2 2 2 ∆= [(M2 +µ +2mW) theoretical framework [4], like SUSY-GUT rela- − M µ − m2 β 2 1=2 tions. Particularly in this respect the e+e− lin- 4( 2 W sin 2 ) ] (2.3) ear colliders are indispensable tools, as has been The left– and right–chiral components of the cor- demonstrated in a number of dedicated work- − responding chargino mass eigenstateχ ˜1 are re- shops [5]. In my talk I will concentrate on the lated to the wino and higgsino components in the i.e. first phase of LC, when only a limited number following way of supersymmetric particles can kinematically be − − − produced. In contrast to earlier analyses [6, 7], I χ˜1L = W˜ L cos φL + H˜1L sin φL will not elaborate on global chargino/neutralino − − − χ˜1R = W˜ R cos φR + H˜2R sin φR (2.4) fits but rather attempt to explore the event char- acteristics to isolate the chargino sector. The with the rotation angles given by analysis will be based strictly on low–energy su- φ − M 2 − µ2 − m2 β / persymmetry. We will see that even if the light- cos 2 L = ( 2 2 W cos 2 ) ∆ 2 2 2 est chargino statesχ ˜1 are, before the collider cos 2φR = −(M2 − µ +2mW cos 2β)/∆ (2.5) energy upgrade, the only supersymmetric states β M that can be explored experimentally in detail, As usual, we take tan positive, 2 positive and µ some of the fundamental SUSY parameters can of either sign. φ φ χχZ be reconstructed from the measurement of char- The angles L and R determine the ˜˜ and theχ ˜νe˜ couplings: gino mass m , the total production cross sec- χ~1 tion and the chargino polarization in the final − − e 2 hχ˜1L|Z|χ˜1Li = − (4sW − 3 − cos 2φL) state. Beam polarization is helpful but not nec- 4sW cW e essarily required. hχ− |Z|χ− i − s2 − − φ ˜1R ˜1R = s c (4 W 3 cos 2 R) The results presented here have been obtained 4 W W − − e in collaboration with S.Y. Choi, A. Djouadi, H. hχ˜1R|ν˜|eL i = − cos φR (2.6) sW Dreiner and P. Zerwas [8]. For an alternative way 2 2 2 of determining the SUSY parameters from the where sW =1−cW ≡sin θW . The coupling measurement of (some) chargino and neutralino to the higgsino component, being proportional masses, see [9]. to the electron mass, has been neglected in the 2 Corfu Summer Institute on Elementary Particle Physics, 1998 Jan Kalinowski sneutrino vertex. The photon–chargino vertex After a Fierz transformation of theν ˜–exchange is diagonal, i.e. it is independent of the mixing term, the amplitude angles: 2 e + − T = Qαβ[¯v(e )γµPαu(e )] − − s hχ˜1L;R|γ|χ˜1L;Ri = e (2.7) − µ + ×[¯u(˜χ1 )γ Pβv(˜χ1 )] (3.2) The chargino couplings, and therefore mixing an- gles, are physical observables and they can be can be expressed in terms of four bilinear charges, measured. Their knowledge together with the classified according to the chiralities of the asso- measurement of the chargino masses is sufficient ciated lepton (α = L, R) and chargino (β = L, R) to determine the fundamental supersymmetric currents M2 µ β parameters , and tan . DZ 2 2 QLβ =1+ 2 2(2sW − 1)(4sW − 3 − cos 2φβ) 8sWcW 3. Chargino production and decay Dν~ + δβ,R 2 (1 + cos 2φR) 4sW + − Charginos are produced in e e collisions, either DZ 2 QRβ =1+ 2(4sW − 3 − cos 2φβ) (3.3) in diagonal or in mixed pairs. Here we will con- 4cW sider the diagonal pair production of the lightest + − Theν ˜ exchange affects only the LR charge while charginoχ ˜1 in e e collisions, all other charges are built up by γ and Z ex- + − + − D e e → χ˜1 χ˜1 (3.1) changes. ν~ denotes the sneutrino propagator 2 Dν~ = s/(t − mν~), and DZ the Z propagator 2 assuming the second charginoχ ˜2 too heavy to DZ = s/(s − mZ + imZΓZ). Above the Z pole be produced in the first phase of e+e− linear col- the non–zero width can be neglected so that the liders. If the chargino production angle could be charges are real. − + measured unambiguously on an event-by-event Theχ ˜1 andχ ˜1 helicities are in general not basis, the chargino couplings could be extracted correlated due to the non–zero masses of the par- χ directly from the angular dependence of the cross ticles; amplitudes√ with equal ˜1 helicities vanish section. However, charginos are not stable. We only ∝ mχ~ / s for asymptotic energies. De- 1 will assume that they decay into the lightest neu- noting the electron helicity by the first index 0 − + tralinoχ ˜1, which is taken to be stable, and a pair σ and theχ ˜1 andχ ˜1 helicities by the remain- of quarks and antiquarks or charged leptons and ing two indices λ and λ¯, the helicity amplitudes 0 neutrinos.
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