Physics Letters B 692 (2010) 26–31 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb The soft supersymmetry breaking in D = 5 supergravity compactified on S1/Z2 orbifolds ∗ G.A. Diamandis, B.C. Georgalas, P. Kouroumalou, A.B. Lahanas University of Athens, Physics Department, Nuclear and Particle Physics Section, GR-15771 Athens, Greece article info abstract Article history: We study the origin of the supersymmetry breaking induced by the mediation of gravity and the Received 22 February 2010 radion multiplet from the hidden to the visible brane in the context of the N = 2, D = 5supergravity Received in revised form 23 June 2010 compactified on S1/Z2 orbifolds. The soft supersymmetry breaking terms for scalar masses, trilinear Accepted 3 July 2010 scalar couplings and gaugino masses are calculated to leading order in the five-dimensional Newton’s Availableonline13July2010 constant k2 and the gravitino mass m . These are finite and non-vanishing, with the scalar soft Editor: L. Alvarez-Gaumé 5 3/2 masses being non-tachyonic, and are all expressed in terms of the gravitino mass and the length scale Keywords: R of the fifth dimension. The soft supersymmetry breaking parameters are thus correlated and the Supersymmetry phenomenological implications are discussed. Supergravity © 2010 Elsevier B.V. Open access under CC BY license. Supersymmetry breaking CORE Extra dimensions Metadata, citation and similar papers at core.ac.uk Provided by Elsevier - Publisher Connector 1. Introduction the radion multiplet may turn this picture yielding positive masses squared. In Refs. [27,28] these corrections were reconsidered, the soft scalar masses were found to be non-tachyonic [28] and the The idea that our world is a brane embedded in a higher– induced soft scalar trilinear couplings were derived. dimensional space–time has attracted much attention over the last In this Letter, and in order to have a complete picture of the su- decade, mainly because it offers new insights in particle physics persymmetry breaking sector, we study the transmission of the su- beyond the standard model. It has opened new ways to resolve persymmetry breaking in N = 2, D = 5 supergravity [29–31] com- long-standing problems, and has brought new revolutionary con- pactified on an S /Z orbifold, in the on-shell scheme, and com- cepts in cosmology. Brane world models have been invoked for the 1 2 pute, in addition, the induced soft gaugino mass corrections when hierarchy problem [1,2] as an alternative towards explaining the the theory possesses a gauge symmetry with gauge fields confined large hierarchies between the Planck and the electroweak energy on the brane. This Letter is organized as follows: We first dis- scales [3–5]. Models with extra dimensions have their origin in cuss the bulk–brane interactions, that induce soft supersymmetry string theory, where supersymmetry is a basic ingredient [6–9]. breaking terms, and we calculate these to leading approximation The mechanism of the supersymmetry breaking and the deter- in the five-dimensional gravitational coupling and the zero mode mination of the soft-breaking terms of the effective low energy gravitino mass which sets the scale of supersymmetry breaking. four-dimensional theory, is of outmost importance, especially in They depend on the size of the S /Z orbifold and the gravitino view of the LHC operation [10]. These models may be constructed 1 2 mass and are thus correlated. These can be used in the constrained by orbifolding a supersymmetric five-dimensional theory, and the MSSM to derive the mass spectrum which due to these correla- supersymmetry breaking is triggered on the hidden brane which tions has distinct features from the popular MSSM schemes studied through the bulk is communicated to the visible brane [11–22]. in literature. In particular the gaugino masses are negative, the tri- The transmission is done via the exchange of bulk gravitational linear soft scalar couplings are linearly dependent on the gaugino fields, notably the radion multiplet, which are the messengers of masses and the gravitino mass may be substantially larger than the supersymmetry breaking in this scheme. The induced corrections, soft scalar and gaugino masses and therefore the difficulties asso- which are finite, have been calculated [22–26], and the resulting ciated with Big Bang Nucleosynthesis can be, in principle, evaded. soft scalar masses on the visible brane were found to be tachy- onic, although it has been clearly stated that a proper treatment of 2. Brane couplings = * Corresponding author. In the context of five-dimensional N 2 supergavity orbifolds E-mail address: [email protected] (A.B. Lahanas). we addressed the problem of the coupling of N = 1multiplets, 0370-2693 © 2010 Elsevier B.V. Open access under CC BY license. doi:10.1016/j.physletb.2010.07.005 G.A. Diamandis et al. / Physics Letters B 692 (2010) 26–31 27 which live on the boundary branes, and we derived the interac- W (φ) for the calculation of the soft trilinear scalar couplings. The tions of the brane fields with the bulk gravitational fields [27,28]. relevant terms to that purpose are given by We found that the N = 1 supersymmetric couplings of the brane chiral multiplets with the bulk fields are determined by a Kähler (4) F/2 ∗ μν i 2 μ ¯ 2 L =−e (5) e W ψμσ ψν + K ψ˙ σ Dμψ˙ + h.c. function reminiscent of the no-scale model [32,33]. The Lagrangian 2 5 5 derived in this way describes the full brane–radion coupling at 2 (3) least to order k5, which is adequate for the derivation of the soft supersymmetry breaking terms to leading order, induced by the The last term in this equation yields the coupling of the radion mediation of the radion multiplet. For the derivation we worked 2 ∗ = ∗ +··· multiplet fermion ψ5 to φ φ when K is expanded as K φ φ in the on-shell scheme, avoiding the numerous auxiliary fields of in order to yield canonical kinetic terms for the brane fields. In the the off-shell formulation. Besides in the on-shell scheme all pos- above formulae we have written the Lagrangian for a chiral multi- sible gaugings have been classified which is essential for a unified plet located on the brane at x5 = 0 but similar expressions hold for description in which the standard model may be embedded [30]. the hidden brane located at x5 = π R as well.√ In this case we have The radion multiplet propagates in the bulk but it also consists F = 5 − 2 ∗ just to add a hidden part H δ(x π R) T +T ∗ K H (ϕH , ϕH ) to the of even fields able to couple to the brane fields and therefore it Kähler function F of Eq. (1), which depends only on the hidden can communicate supersymmetry breaking from one brane to the brane fields, and a corresponding hidden superpotential W H . other. The scalar and the fermion fields of the radion multiplet are For the gauge multiplets confined on the visible brane, there are 1 ˙ i 4-fermion interaction terms coupling gauginos to gravitinos. By a ≡ √ 5 − √ 0 (T ) ≡− 2 T e5 A5, χ ψ5 Fierz rearrangement these that give rise to non-vanishing gaugino 2 3 masses at one loop can be brought to the form 0 where Aμ is the graviphoton field, and the couplings of the brane 1 (4) 5 ¯ α ¯ β μ fields are those of the N = 1, D = 4 supergravity derived from the − e δ x Re fαβ λ λ ψμψ + h.c. (4) 4 following generalized Kähler function √ In this ,β are gauge group indices and f (φ) is the gauge ∗ α αβ T + T 2 F =− √ + 5 ∗ kinetic function which is a holomorphic function of the brane 3ln δ x ∗ K ϕ, ϕ , (1) ¯ α ¯ β 2 T + T fields φ. Other 4-fermion terms, coupling ψμψν to λ λ ,existbut do not induce through loops gaugino masses. in the basis where the restriction of the Einstein–Hilbert part of the action on the brane is in its canonical form, for details see [27, ∗ 3. Transmission of the supersymmetry breaking 28].InEq.(1) the function K (ϕ, ϕ ) depends on the scalar fields of the chiral multiplets living on the visible brane at x5 = 0.1 For the study of the transmission of supersymmetry breaking Introducing a superpotential W (ϕ), involving brane fields, gives we consider a constant superpotential on the hidden brane. Other rise to the following Yukawa and potential terms [27], less trivial options lead to the same results concerning the forms i of the induced soft SUSY breaking parameters, whose calculation is L + L =− (4) F/2 ∗ μν + √ i μ ¯ Y P e (5)e W ψμσ ψν Di W χ σ ψμ our main goal. The corresponding Lagrangian on the hidden brane 2 canbereadfromthefirsttermofEq.(3) translated for the hidden 1 2 i j brane. Mass terms for the gravitino ψμ and the spinor field ψ˙ + Di D j W χ χ + h.c. 5 2 of the radion multiplet arise only on the hidden brane while non- ∗ (4) 2 F ij ∗ 2 minimal radion kinetic terms appear on the visible brane, as well, − e ((5)) e F Di WDj∗ W − 3|W | . (2) as can be seen from Eq. (3). We shall follow a procedure in which 1 In this, and in what follows, ψμ stands for ψμ, the even gravitino the bulk kinetic terms of the gravitinos are disentangled from their field, which lives on the visible brane, and the bulk as well, and fifth components and mass terms are treated as vertex insertions 5 5 the function (5) is defined as (5) ≡ e ˙ δ(x ).