Strong Phase Transition within the U(1)-extended MSSM Amine Ahriche Laboratory of Theoretical Physics, Department of Physics, University of Jijel, PB 98 Ouled Aissa, DZ-18000 Jijel, Algeria. Abstract. In this work, the electroweak phase transition (EWPT) strength has been investigated within the U(1) extended Minimal Supersymmetric Standard Model (UMSSM) without introducing any exotic fields. We found that the EWPT could be strongly first order for reasonable values of the lightest Higgs and neutralino masses. Keywords: electroweak phase transition, extra gauge boson, extra singlet PACS: 11.25.Hf, 123.1K INTRODUCTION The origin of matter-antimatter asymmetry is one of the main problems of both particle physics and cosmology. The explanation of this asymmetry n b /n γ ∼ 10 −10 [1], requires three conditions, known as Sakharov criteria [2], which can be summarized in the existence of such interactions in the early universe that violate the baryon number B, the symmetries C and CP and occur out of equilibrium. It appears that the Standard Model (SM) fulfills all these criteria; the baryon number is not conserved at quantum level due to the B + L anomaly [3], a CP violation source does exist in CKM matrix, and a departure from thermal equilibrium could be reached through a strong first order phase transition [4], but its realization was not possible numerically due to smallness of CP violation effect and the weakness of the electroweak phase transition (EWPT) [5]. In the SM, the EWPT is so weak [6] unless the Higgs mass is less than 45 GeV [7], which is in conflict with present data [8]. But a departure from thermal equilibrium without being in conflict with this severe bound on the Higgs mass, is possible when extending the SM, for e.g. with additional gauge singlets [9, 10], or in some supersymmetric SM extensions. In spite of its success and popularity, the MSSM with R-parity still has two major problems: the μ -problem [11] and the potential proton decay problem due to dimension 5 operators [12]. A natural solution to these problems would probably require that the MSSM be extended by a new mechanism or a new symmetry. The U(1) ′ -extended MSSM (UMSSM) [13] is a straightforward extension of the MSSM with a non-anomalous TeV scale Abelian gauge symmetry. It can solve the μ -problem and the dimension 5 operator problem very naturally with an appropriate charge assignment. In the minimal supersymmetric standard model (MSSM), the EWPT could be strongly first order if the light stop is lighter than the top quark [14]. In the singlet extended MSSM [15], such as the NMSSM [16], the EWPT get stronger easily for a large range of parameters [17]. In gauge extensions of the MSSM, such as UMSSM, the EWPT is also strongly first order but with the price of introducing 3 new extra singlet scalars [18], or by adding new extra heavy singlet fermions [19]. The main difference between the NMSSM and the UMSSM, that makes the EWPT easily strong in the NMSSM, is that the UMSSM is more constrained than the NMSSM. Such constrains that are coming from the extra U(1) ′ gauge interactions, like the mixing between the neutral gauge boson Z and the new one Z ′ (7) [20], and the bound on the heavy Z ′ mass (8) [21], which implies serious constrains on the vacuum expectation value (vev) of the singlet and the new U(1) ′ gauge coupling g ′ . However, both models have similar form for the scalar potential at tree-level, where the singlet can play the same role during the EWPT dynamics. In this type of models, the singlet vev within the wrong vacuum could be nonzero, i.e. 〈S〉 = x 0 = 0, and therefore, is temperature dependant during the EWPT dynamics; this feature could delay the EWPT, i.e. lowers the critical temperature, and enhances the parameter that define the strong first order phase transition criterion [22]: υ (T c ) /T c > 1, (1) where T c is the critical temperature and υ (T ) is the temperature dependent of the scalar vev. 191 Downloaded 15 Nov 2011 to 193.194.69.162. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/about/rights_permissions CP1295, The Third Algerian Workshop on Astronomy and Astrophysics, edited by N. Mebarki and J. Mimouni ©2010 American Institute of Physics 978-0-7354-0852-4/10/$30.00