THE UNIVERSITY OF ALABAMA University Libraries R Mediation of Dynamical Supersymmetry Breaking N. Kitazawa – Tokyo Metropolitan University N. Maru – University of Tokyo N. Okada – Theory Group, KEK Deposited 05/22/2019 Citation of published version: Kitazawa, N., Maru, N., Okada, N. (2000): R Mediation of Dynamical Supersymmetry Breaking. Physical Review D, 63(1). DOI: https://doi.org/10.1103/PhysRevD.63.015005 ©2000 American Physical Society PHYSICAL REVIEW D, VOLUME 63, 015005 R mediation of dynamical supersymmetry breaking Noriaki Kitazawa* Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan Nobuhito Maru† Department of Physics, University of Tokyo, Tokyo 113-0033, Japan Nobuchika Okada‡ Theory Group, KEK, Tsukuba, Ibaraki 305-0801, Japan ͑Received 24 July 2000; published 30 November 2000͒ We propose a simple scenario of dynamical supersymmetry breaking in four-dimensional supergravity theories. The supersymmetry breaking sector is assumed to be completely separated as a sequestered sector from the visible sector, except for communication by gravity and U(1)R gauge interactions, and supersymme- try breaking is mediated by the superconformal anomaly and U(1)R gauge interaction. Supersymmetry is dynamically broken by the interplay between the nonperturbative effect of the gauge interaction and the Fayet-Iliopoulos D term of U(1)R which necessarily exists in supergravity theories with gauged U(1)R sym- metry. We construct an explicit model which gives a phenomenologically acceptable mass spectrum of super- partners with a vanishing ͑or very small͒ cosmological constant. DOI: 10.1103/PhysRevD.63.015005 PACS number͑s͒: 12.60.Jv, 11.30.Na I. INTRODUCTION in the different branes separated in the direction of extra dimensions ͑now the hidden sector should be called the se- Low energy supersymmetry may play an important role in questered sector ͓2͔͒. In this case supersymmetry breaking at solving many problems of particle physics. If this is the case, the sequestered sector is transmitted to the visible sector only supersymmetry must be spontaneously broken, and all super- through the superconformal anomaly ͓2–4͔. In this anomaly partners must have appropriate masses, since their effect has mediation the masses of squarks are highly degenerate at low not been observed yet. Therefore, finding a simple mecha- energies and there is no supersymmetric flavor problem, but 2 Ͻ nism of supersymmetry breaking and its mediation without sleptons have negative masses (mslepton 0). There have any phenomenological problems is an important task. If we been many attempts to solve this problem ͓2,5–7͔, and we believe low energy supersymmetry, it is natural to consider usually need some additional fields which bring contact be- the supergravity framework. tween two sectors. In this paper we introduce this additional The simplest scenario of supersymmetry breaking and its communication by gauging U(1)R symmetry in four- mediation in supergravity theories is gravity mediation with dimensional supergravity theories ͓8–10͔. Since the charge ͓ ͔ a Polonyi potential in the hidden sector 1 , but supersym- of U(1)R symmetry does not commute with supercharges, it metry is not dynamically broken in this scenario. Moreover, is natural to consider that the U(1)R gauge boson propagates it is well known that gravity mediation has a phenomenologi- in whole space-time including extra dimensions, and brings cal problem: the degeneracy of squark masses at the Planck contact between two sectors. scale is distorted by the quantum effect at low energies, It is also interesting to note that the Fayet-Iliopoulos term which causes the supersymmetric flavor problem. There is for U(1)R must exist due to the symmetry of supergravity, another conceptual problem with gravity mediation as and this term can play an important role in supersymmetry pointed out in Ref. ͓2͔: it is not the mediation by gravity, but breaking. In fact it has been shown that supersymmetry can the mediation by higher dimensional contact interactions in- be dynamically broken by the interplay between this Fayet- troduced by hand. Although it is possible that the superspace Iliopoulos term and the nonperturbative effect of a gauge ͓ ͔ density, which defines the supergravity Lagrangian, contains interaction 11 . Since the auxiliary field of the U(1)R gauge an infinite number of higher dimensional contact interactions multiplet has vacuum expectation value, both squarks and so that the Ka¨hler potential has a simple canonical form, the sleptons can have positive masses of the order of the grav- origin of these interactions is mysterious. itino mass in an appropriate R-charge assignment, and the There is another possibility, that the visible sector and problem of the anomaly mediation can be avoided. hidden sector are completely separated, namely, no contact This paper is organized as follows. In the next section we interaction among them in the superspace density. This situ- give a general argument on the supergravity Lagrangian with ation would be naturally realized if two sectors are confined U(1)R gauge symmetry. We give a general formula for the chirality-conserving scalar mass in the presence of U(1)R gauge symmetry, which is an extension of the formula given *Email address: [email protected] in Ref. ͓12͔. An explicit model is constructed in Sec. III, and †Email address: [email protected] the analysis of the dynamics and mass spectrum is given in ‡ Email address: [email protected] Sec. IV. Section V contains our conclusions. 0556-2821/2000/63͑1͒/015005͑6͒/$15.0063 015005-1 ©2000 The American Physical Society NORIAKI KITAZAWA, NOBUHITO MARU, AND NOBUCHIKA OKADA PHYSICAL REVIEW D 63 015005 II. SUPERGRAVITY WITH U„1…R GAUGE SYMMETRY The Lagrangian becomes In the superconformal framework ͓13–15͔ the general su- 1 pergravity Lagrangian with U(1) gauge symmetry is given LϭϪ ͓¯ ⌽˜ ͑ ¯ I 2QIgRVR 2gGVG͔͒ ϩ͓ 3͔ R S0S0 SI ,S e e D S0 F by 2 1 1 1 1 Ϫ Ϫ ͓W W ͔ Ϫ ͓W W ͔ Ϫ ͓W W ͔ , LϭϪ ͓⌺¯ e 2gRVR⌺ ⌽͑S ,¯SIe2QIgRVRe2gGVG͔͒ 4 R R F 4 Gv Gv F 4 Gh Gh F 2 c c I D ͑7͒ 1 ϩ͓W͑S ͒⌺3͔ Ϫ ͓ f ͑S ͒W W ͔ I c F 4 R I R R F where 1 a b ⌽˜ ͑ ¯ I 2QIgRVR 2gGVG͒ Ϫ ͓ f ͑S ͒W W ͔ , ͑1͒ SI ,S e e 4 ab I G G F ⌽͑S ,¯SIe2QIgRVRe2gGVG͒ ͓ ͔ ϵ I ͑ ͒ where we use the notation in Ref. 14 . Here, SI are matter . 8 ¯ ¯ I 2QIgRVR 2gGVG͒ ͒ 1/3 ͓W͑S e e W͑SI ͔ chiral multiplets with flavor index I and U(1)R charge QI , ͑ ͒ and VR and VG (WR and WG) are vector chiral multiplets The compensating multiplet S0 is U(1)R singlet now. It was corresponding to the gauge group of U(1)R and G, respec- ⌺ shown in Ref. ͓14͔ that the gauge fixing conditions of tively. The multiplet c is the compensating multiplet, whose component should be appropriately fixed to obtain ϭͱ ⌽˜ Ϫ1/2͑ ͒ ␹ ϭϪ ⌽˜ Ϫ1⌽˜ J␹ ϭ Poincare´ supergravity. The functions ⌽ and W are su- z0 3 zI ,zI* , R0 z0 RJ , b␮ 0 perspace densities in which interactions are described by the ͑9͒ products of multiplets. Following the arguments in the pre- vious section, we assume that there is no interaction between directly give the standard form of the supergravity Lagrang- ͑ ian given in Ref. ͓16͔, where z and ␹ are scalar and the visible sector fields Si and VGv and the hidden seques- 0 R0 ͒ ⌽˜ J tered sector fields S␣ and VGh in these superspace densities, spinor components of the compensating multiplet S0 , ץ ⌽˜ Iץnamely, ϵ (zI ,z* )/ zJ , and zJ is the scalar components of SJ . After all, the resultant Lagrangian in component fields has ⌽͑ ¯ 2QIgRVR 2gGVG͒ϭ⌽ ͑ ¯ i 2QigRVR 2gGvVGv͒ SI ,SIe e v Si ,S e e the standard form of Ref. ͓16͔ including covariant deriva- ␣ 2Q␣g V 2g V tives for U(1)R gauge symmetry. The Lagrangian is deter- ϩ⌽ ͑S␣ ,¯S e R Re Gh Gh͒, h mined by a function ͑2͒ G͑z ,z*I͒ϵϪ3ln⌽˜ ͑z ,z*I͒ϭϪ3ln⌽͑z ,z*I͒ ͑ ͒ϭ ͑ ͒ϩ ͑ ͒ ͑ ͒ I I I W SI Wv Si Wh S␣ , 3 ϩ ͉ ͉͒2 ͑ ͒ ln W͑zI , 10 where the indices i and ␣ denote the flavors in the visible and hidden sectors, respectively, and Gv and Gh are gauge where ⌽ and W satisfy the conditions of Eqs. ͑2͒ and ͑3͒. groups in each sector. The gauge kinetic function f ab(SI) The difference of R charges in covariant derivatives for each should also be restricted as follows: component field in a multiplet automatically appears due to the fact that W has nontrivial R charge ͑see Ref. ͓8͔͒. ͓ ͑ ͒ a b ͔ !͓ Gv͑ ͒ a b ͔ f ab SI WGWG F f ab Si WGvWGv F The potential for scalar fields is given as follows: Gh a b ϩ͓ f ͑S␣͒W W ͔ . ͑4͒ ϭ ϩ ͑ ͒ ab Gh Gh F V VF VD , 11 ϭ Gvϭ Ghϭ␦ In the following we assume f R(SI) 1 and f ab f ab ab , where the F-term contribution is for simplicity. ⌺ Ϫ Note that the compensating multiplet c must have R V ϭeG͓G ͑G 1͒I GJϪ3͔ ͑12͒ charge, since the superpotential W has R charge. Therefore, F I J the usual gauge choice to give Poincare´ supergravity, and the U(1)R D-term contribution is ϭͱ ␹ ϭ ϭ ͑ ͒ zc 3, Rc 0, b␮ 0, 5 2 gR V ϭ ͑GIQ z ͒2.