One-loop radiative corrections to the production cross section of a pair of
light charginos in e+e- colliders are calculated within the MSSM. Top and
bottom quarks and squarks are considered in the loops, and they are
renormalized using the MS-bar scheme. If the center of mass energy is equal to
192 GeV, positive corrections typically of 10% to 15% are found when the squark
mass parameters are equal to 1 TeV.Comment: 6 pages, including 5 figures. Latex. Talk given by M.A.D. at the
  International Workshop "Beyond the Standard Model: From Theory to
  Experiment", 13--17 October 1997, Valencia, Spai

Diaz, Marco A.

King, Steve F.

Ross, Douglas A.

English

arXiv

One-loop radiative corrections to the production cross section of a pair of light charginos in e+e- colliders are calculated within the MSSM. Top and bottom quarks and squarks are considered in the loops, and they are renormalized using the MS-bar scheme. If the center of mass energy is equal to 192 GeV, positive corrections typically of 10% to 15% are found when the squark mass parameters are equal to 1 TeV.One-loop radiative corrections to the production cross section of a pair of light charginos in e+e- colliders are calculated within the MSSM. Top and bottom quarks and squarks are considered in the loops, and they are renormalized using the MS-bar scheme. If the center of mass energy is equal to 192 GeV, positive corrections typically of 10% to 15% are found when the squark mass parameters are equal to 1 TeV

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CERN-TH/98-26SHEP{98/02FTUV/98{7IFIC/98{7hep-ph/9801373Radiatively Corrected Chargino Pair Production at LEP2yMarco A. Daz1, Steve F. King2, and Douglas A. Ross31 Departamento de Fsica Teorica, IFIC{CSIC, Universidad de ValenciaBurjassot, Valencia 46100, Spain2 CERN, Theory Division, CH{1211 Geneva, Switzerland3 Department of Physics and Astronomy, University of SouthamptonSouthampton, SO17 1BJ, U.K.AbstractOne{loop radiative corrections to the production cross section of a pair of lightcharginos in e+e− colliders are calculated within the MSSM. Top and bottom quarksand squarks are considered in the loops, and they are renormalized using the MSscheme. If the center of mass energy is equal to 192 GeV, positive corrections typi-cally of 10% to 15% are found when the squark mass parameters are equal to 1 TeV.CERN-TH/98-26January 1998yTalk given by M.A.D. at the International Workshop \Beyond the Standard Model:From Theory to Experiment", 13{17 October 1997, Valencia, Spain. On leave of absence from 3.; Z~+b~+a=; Z~+b~+a(a) (b)(c) (d)(e) (f)+; Z ; Z~+b~+aiGab;Z+; Z Z; ~+b~+a+; Z~+b~+a+; Z~+a~+b+1.P.I.; Z~+b~+ai ab;ZFigure 1: One{loop renormalized γ+b −a and Z+b −a vertex functions.In the Minimal Supersymmetric Standard Model (MSSM), the supersymmetricpartners of the charged Higgs and the W gauge bosons mix to form a set of twocharged fermions called charginos. Experimental searches for charginos at LEP2 havebeen negative so far, and lower bounds on the lightest chargino mass have been set.The bound depends mainly on the sneutrino mass and the mass dierence betweenthe chargino and the LSP m = m1 − m01 . ALEPH has found that m1 > 85GeV for m~e > 200 GeV [1]. DELPHI’s bound corresponds to m1 > 84:3 GeV form~e > 300 GeV and m > 10 GeV [2]. A lower bound of m1 > 85:5 GeV was foundby L3 for m~e > 300 GeV [3]. Finally, OPAL has found that if m > 10 GeV thenm1 > 84:5 GeV if m0 > 1 TeV and m1 > 65:7 GeV for the smallest m0 compatiblewith current limits on sneutrino and slepton masses [4].In the Born approximation, chargino masses and mixing angles in the MSSMdepend only on the SU(2) gaugino mass M , the ratio between Higgs vacuum expec-tation values tan, and the supersymmetric Higgs mass parameter . Much can belearned about these parameters from an accurate measurement of the total charginoproduction cross section and masses in e+e− colliders, and also about the rest of thesupersymmetric particles in the case of MSSM{SUGRA [5]. Nevertheless, for thisto work, accurate experimental measurements must be accompanied by precise the-oretical calculations. In this talk we report on a recent calculation of the one{loopcorrections to the total production cross section of a pair of charginos in e+e− colliders[6].Charginos are produced in the s{channel with intermediate Z bosons and photons,1; Z=q; Z+~q; Z+~q; ZFigure 2: Top and bottom quark and squark contributions to the unrenormalized Zand γ self-energies and to the Z − γ mixing.~+c~+b=t~bi~+c~+b+b~ti~+c~+bFigure 3: Feynman diagrams contributing to the unrenormalized chargino two{pointfunctions (self{energies and mixing).and in the t{channel with intermediate electron sneutrino. In our approximation onlyZ ~+ ~−, γ ~+ ~−, e+~e ~−, and e−~e ~+ vertices are renormalized. We denote these one{loop renormalized total vertex functions iGabZ, iGabγ, iG+b~ee, and iG−a~ee respectively.The rst two total vertex functions are given in Fig. 1, where we have the followingcontributions: (a) tree level, (b) gauge boson self energies, (c) Z − γ mixing, (d){(e) chargino self energy and chargino mixing, and (f) the 1PI triangular diagrams.The two total vertex functions involving sneutrinos are simpler because they receivecontributions only from the tree level vertex and chargino self energy and mixing,and we do not display them.One-loop diagrams contributing to the gauge boson self energies and Z−γ mixingcan be seen in Fig. 2. The rst diagram corresponds to quarks and the secondtwo diagrams correspond to squarks. Similarly, in Fig. 3 we display the diagramscontributing to chargino self energies and mixing. They involve top{sbottom andbottom{stop loops. Finally, 1PI triangular diagrams are shown in Fig. 4. All diagramsin Figs. 2 to 4 have been calculated [6] in terms of Passarino{Veltman’s functions [7].We have used the DR scheme, which in our approximation is completely equivalentto the MS, and taken Q = mZ as the subtraction point.21.P.I.; Z~+b~+a=; Z~bi~bj~+b~+at(T1)+; Ztt~+b~+a~bi(T2)i ab;Z+; Z~ti~tj~+b~+ab(T3)+; Zbb~+b~+a~ti(T4)Figure 4: Unrenormalized one{particle irreducible triangular diagrams contributingto renormalization of the Z ~+ ~− and γ ~+ ~− vertices.In Fig. 5 we have plot the tree{level and renormalized one{loop total productioncross section of a pair of light charginos as a function of the gaugino mass M , whilekeeping constant the chargino mass m1 = 90 GeV, the sneutrino mass m~e = 100GeV, and tan = 10. We consider the case  < 0 and a center of mass energyps = 192 GeV, relevant for LEP2. The tree level cross section decreases from 1.6 pb.when M = 500 GeV to a minimum of 0.22 pb. at around M = 105 GeV, and growsagain up to 0.34 pb. at M = 90 GeV. Below this value of the gaugino mass M thereis no solution for  < 0 which gives m1 = 90 GeV. Radiative corrections to thiscross section are parametrized by the squark soft masses which we take degenerateMQ = MU = MD, and by the trilinear soft mass parameters A  AU = AD, alsotaken degenerate. This choice is done at the weak scale and it is made for simplicity.Three radiatively corrected curves are presented given by MQ = A = 200 GeV (dots),MQ = A = 600 GeV (dashes), and MQ = A = 1 TeV (dotdashes).We observe from Fig. 5 that radiative corrections are positive and grow with thesquark mass parameters. For M close to 90 GeV the corrections are only of a fewpercent, but they grow fast until a maximum of 21% at M = 140 GeV. For largervalues of the gaugino mass, the corrections slowly decrease until they reach the value6% at M = 500 GeV. A logarithmic growth of quantum corrections with the squarkmass parameters is observed, as it should be. It is worth pointing out that the valueof  is not constant along the curves because it is xed by the constant value of thechargino mass m~1 .3Figure 5: One{loop and tree level chargino production cross section as a function ofthe SU(2) gaugino mass M , for 192 GeV center of mass energy.In summary, if charginos are discovered much information can be learned fromthe measurements of the total production cross section and masses. Neverthelessit is essential to have a precise theoretical calculation of these observables. In thissense, one{loop radiative corrections must be included. We have found that for LEP2energies they are typically 10% to 15% and can reach up to 30% if the squark massesare equal to 1 TeV.AcknowledgmentsThe authors are grateful to PPARC for partial support under contract no. GR/K55738.M.A.D. was also supported by a postdoctoral grant from Ministerio de Educacion yCiencias, by DGICYT grant PB95-1077 and by the EEC under the TMR contractERBFMRX-CT96-0090.References[1] ALEPH Collaboration (R. Barate et al.), Report No. CERN{PPE{97{128 (hep{ex/9710012), Sep. 1997, submitted to Z. Phys. C.[2] DELPHI Collaboration (P. Abreu et al.), Eur. Phys. J. C1, 1 (1998).4[3] L3 Collaboration (M. Acciarri et al.), Report No. CERN{PPE{97{130, Sep.1997, submitted to Phys. Lett. B.[4] OPAL Collaboration (K. Ackersta et al.), Report No. CERN{PPE{97{083,(hep{ex/9708018), submitted to Z. Phys. C.[5] M.A. Daz and S.F.King, Phys. Lett. B 349, 105 (1995); J. Feng and M. Strassler,Phys. Rev. D 51, 4661 (1995); M.A. Daz and S.F.King, Phys. Lett. B 373, 100(1996); J.L. Feng and M.J. Strassler, Phys. Rev. D 55, 1326 (1997); M.A. Daz,Mod. Phys. Lett. A12, 307 (1997); A.S. Belyaev and A.V. Gladyshev, ReportNo. JINR-E2-97-76, Mar 1997, (hep-ph/9703251).[6] M.A. Daz, S.F. King, and D.A. Ross, Report No. CERN-TH/97-313, hep-ph/9711307, Nov. 1997.[7] G. Passarino and M. Veltman, Nucl. Phys. B 160, 151 (1979).5

Radiatively Corrected Chargino Pair Production at LEP2

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Radiatively Corrected Chargino Pair Production at LEP2

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