Squarks decay into quarks and gluino in the MSSM

The formulae for the decay width and numerical results are obtained. We have calculated the conclusion of the one-loop vertex correction, wave-function correction and renormalization of the bare couplings to the decay width. We revealed that the effect of the complex parameters At and Ab could be quite significant in a large region of the MSSM parameter space.
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Squarks decay into quarks and gluino in the MSSM JOURNAL OF SCIENCE OF HNUE Mathematical and Physical Sci., 2012, Vol. 57, No. 7, pp. 94-99 This paper is available online at http://stdb.hnue.edu.vn SQUARKS DECAY INTO QUARKS AND GLUINO IN THE MSSM Nguyen Chinh Cuong1 and Phung Van Hao2 1 Faculty of Physics, Hanoi National University of Education 2 Son Tay High School, Hanoi Abstract. We present a phenomenological study of the decay of squarks (top and bottom) into quarks (top and bottom) and gluino in the Minimal Supersymmetric Standard Model (MSSM). The formulae for the decay width and numerical results are obtained. We have calculated the conclusion of the one-loop vertex correction, wave-function correction and renormalization of the bare couplings to the decay width. We revealed that the effect of the complex parameters At and Ab could be quite significant in a large region of the MSSM parameter space. Keywords: MSSM, squark, CP violation.1. Introduction The minimal supersymmetric standard model (MSSM) is one of the most promisingextensions of the standard model (SM) [1]. Only three terms in the supersymmetricLagrangian can give rise to CP violating phases. The superpotential contains a complexcoefficient µ in the bilinear term of the Higgs superfield. There are two complex terms inthe soft supersymmetry (SUSY) breaking part: the gaugino mass M f and the left and righthanded squark mixing term Aq [2]. f = |M µ = |µ|eiφµ = |µ|eiφ1 , Aq = |Aq |eiφqe = |Aq |eiφ2 , M f|eiφM f f|eiφ3 . = |M (1.1) In the MSSM, there are two types of scalar quarks (squarks): qeL and qeR ,corresponding to the left and the right helicity states of a quark. The mass matrix on qL , qeR ) is given by [3]the basis (e 2 2 2 mqeL aq mq qe † mqe1 0 Mqe = = R Rqe. (1.2) aq mq m2qeR 0 mq2e2Received April 16, 2012. Accepted October 20, 2012.Physics Subject Classification: 60 44 01.Contact Phung Van Hao, e-mail address: k20ch.phunghao@yahoo.com.vn94 Squarks decay into quarks and gluino in the MSSM According to Eq.(1.2), Mq2e is diagonalized by a unitary matrix Rqe. The weakeigenstates qe1 and qe2 are thus related to their mass eigenstates qeL and qeR by qe1 qe qeL =R , qe2 qeRwhere i ! φ − 2i φqe e cos θqe e 2 qe sin θqe Rqe = − 2i φqe i φqe . (1.3) −e sin θqe e cos θqe 2 As known, CP violation arises naturally in three generations of SM and it can appearonly through the phase in the CKM - matrix. In the MSSM with complex parameters,additional complex couplings can lead to CP violation within one generation at one -loop level [2]. Recently, the gauge boson in the MSSM with explicit CP violation hasbeen studied [4] and CP violation as a probe of flavor origin in supersymmetry has beendiscussed [5]. To discover new particles in the MSSM, some collider problems have beenstudied [6, 7]. The CP violation has been considered and the one-loop correction has beencaculated in these problems. Similarly, some decays of squarks have been studied whencalculating the one-loop correction and evaluating the effects of CP violation on decaywidth. The particular researches are: squark decays into Higgs bosons and squark [8],squark decays into Charginos (or Neutralinos) and quark [9], Squark decays into Gaugebosons and squark [10]. Since the decays of squarks into quarks and gluino have not been calculated indetail, in this ar ...