DOCSLIB.ORG

The Soft Supersymmetry Breaking in D=5 Supergravity Compactified On

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Soft Supersymmetry Breaking in D=5 Supergravity Compactified On 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 ).
Load more

Recommended publications
  • Report of the Supersymmetry Theory Subgroup
    Report of the Supersymmetry Theory Subgroup J. Amundson (Wisconsin), G. Anderson (FNAL), H. Baer (FSU), J. Bagger (Johns Hopkins), R.M. Barnett (LBNL), C.H. Chen (UC Davis), G. Cleaver (OSU), B. Dobrescu (BU), M. Drees (Wisconsin), J.F. Gunion (UC Davis), G.L. Kane (Michigan), B. Kayser (NSF), C. Kolda (IAS), J. Lykken (FNAL), S.P. Martin (Michigan), T. Moroi (LBNL), S. Mrenna (Argonne), M. Nojiri (KEK), D. Pierce (SLAC), X. Tata (Hawaii), S. Thomas (SLAC), J.D. Wells (SLAC), B. Wright (North Carolina), Y. Yamada (Wisconsin) ABSTRACT Spacetime supersymmetry appears to be a fundamental in- gredient of superstring theory. We provide a mini-guide to some of the possible manifesta- tions of weak-scale supersymmetry. For each of six scenarios These motivations say nothing about the scale at which nature we provide might be supersymmetric. Indeed, there are additional motiva- tions for weak-scale supersymmetry. a brief description of the theoretical underpinnings, Incorporation of supersymmetry into the SM leads to a so- the adjustable parameters, lution of the gauge hierarchy problem. Namely, quadratic divergences in loop corrections to the Higgs boson mass a qualitative description of the associated phenomenology at future colliders, will cancel between fermionic and bosonic loops. This mechanism works only if the superpartner particle masses comments on how to simulate each scenario with existing are roughly of order or less than the weak scale. event generators. There exists an experimental hint: the three gauge cou- plings can unify at the Grand Uni®cation scale if there ex- I. INTRODUCTION ist weak-scale supersymmetric particles, with a desert be- The Standard Model (SM) is a theory of spin- 1 matter tween the weak scale and the GUT scale.
    [Show full text]
  • Supersymmetry Breaking and Inflation from Higher Curvature
    Prepared for submission to JHEP Supersymmetry Breaking and Inflation from Higher Curvature Supergravity I. Dalianisa, F. Farakosb, A. Kehagiasa;c, A. Riottoc and R. von Ungeb aPhysics Division, National Technical University of Athens, 15780 Zografou Campus, Athens, Greece bInstitute for Theoretical Physics, Masaryk University, 611 37 Brno, Czech Republic cDepartment of Theoretical Physics and Center for Astroparticle Physics (CAP) 24 quai E. Ansermet, CH-1211 Geneva 4, Switzerland E-mail: [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: The generic embedding of the R + R2 higher curvature theory into old- minimal supergravity leads to models with rich vacuum structure in addition to its well-known inflationary properties. When the model enjoys an exact R-symmetry, there is an inflationary phase with a single supersymmetric Minkowski vacuum. This appears to be a special case of a more generic set-up, which in principle may include R- symmetry violating terms which are still of pure supergravity origin. By including the latter terms, we find new supersymmetry breaking vacua compatible with single-field inflationary trajectories. We discuss explicitly two such models and we illustrate how arXiv:1409.8299v2 [hep-th] 22 Jan 2015 the inflaton is driven towards the supersymmetry breaking vacuum after the inflationary phase. In these models the gravitino mass is of the same order as the inflaton mass. Therefore, pure higher curvature supergravity may not only accommodate the proper inflaton field, but it may also provide the appropriate hidden sector for supersymmetry breaking after inflation has ended.
    [Show full text]
  • TASI 2008 Lectures: Introduction to Supersymmetry And
    TASI 2008 Lectures: Introduction to Supersymmetry and Supersymmetry Breaking Yuri Shirman Department of Physics and Astronomy University of California, Irvine, CA 92697. [email protected] Abstract These lectures, presented at TASI 08 school, provide an introduction to supersymmetry and supersymmetry breaking. We present basic formalism of supersymmetry, super- symmetric non-renormalization theorems, and summarize non-perturbative dynamics of supersymmetric QCD. We then turn to discussion of tree level, non-perturbative, and metastable supersymmetry breaking. We introduce Minimal Supersymmetric Standard Model and discuss soft parameters in the Lagrangian. Finally we discuss several mech- anisms for communicating the supersymmetry breaking between the hidden and visible sectors. arXiv:0907.0039v1 [hep-ph] 1 Jul 2009 Contents 1 Introduction 2 1.1 Motivation..................................... 2 1.2 Weylfermions................................... 4 1.3 Afirstlookatsupersymmetry . .. 5 2 Constructing supersymmetric Lagrangians 6 2.1 Wess-ZuminoModel ............................... 6 2.2 Superfieldformalism .............................. 8 2.3 VectorSuperfield ................................. 12 2.4 Supersymmetric U(1)gaugetheory ....................... 13 2.5 Non-abeliangaugetheory . .. 15 3 Non-renormalization theorems 16 3.1 R-symmetry.................................... 17 3.2 Superpotentialterms . .. .. .. 17 3.3 Gaugecouplingrenormalization . ..... 19 3.4 D-termrenormalization. ... 20 4 Non-perturbative dynamics in SUSY QCD 20 4.1 Affleck-Dine-Seiberg
    [Show full text]
  • CP Violation Beyond the Standard Model*
    INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS G: NUCLEAR AND PARTICLE PHYSICS J. Phys. G: Nucl. Part. Phys. 28 (2002) 345–358 PII: S0954-3899(02)30104-X CP violation beyond the standard model* GLKane1 and D D Doyle2 1 Randall Physics Laboratory, University of Michigan, Ann Arbor, MI 48109, USA 2 CPES, University of Sussex, Falmer, Brighton BN1 9QJ, UK E-mail: [email protected] Received 25 October 2001 Published 21 January 2002 Online at stacks.iop.org/JPhysG/28/345 Abstract In this paper a number of broad issues are raised about the origins of CP violation and how to test the ideas. 1. Introduction The fundamental sources of CP violation in theories of physics beyond the standard model is an important issue which has not been sufficiently studied. In this paper, we begin by discussing the possible origins of CP violation in string theory and the potential influence of its phenomenology on string theory. This naturally develops into a consideration of supersymmetry breaking, specifically the soft-breaking supersymmetric Lagrangian, Lsoft. There exist two extreme scenarios which may realistically accommodate CP violation; the first involves small soft phases and a large CKM phase, δCKM, whereas the second contains large soft phases and small δCKM. We argue that there is reasonable motivation for δCKM to be almost zero and that the latter scenario should be taken seriously. Consequently, it is appropriate to consider what CP violating mechanisms could allow for large soft phases, and hence measurements of these soft phases (which can be deduced from collider results, mixings and decays, experiments exploring the Higgs sector or from electric dipole moment values) provide some interesting phenomenological implications for physics beyond the standard model.
    [Show full text]
  • Atomic Electric Dipole Moments and Cp Violation
    261 ATOMIC ELECTRIC DIPOLE MOMENTS AND CP VIOLATION S.M.Barr Bartol Research Institute University of Delaware Newark, DE 19716 USA Abstract The subject of atomic electric dipole moments, the rapid recent progress in searching for them, and their significance for fundamental issues in particle theory is surveyed. particular it is shown how the edms of different kinds of atoms and molecules, as well Inas of the neutron, give vital information on the nature and origin of CP violation. Special stress is laid on supersymmetric theories and their consequences. 262 I. INTRODUCTION In this talk I am going to discuss atomic and molecular electric dipole moments (edms) from a particle theorist's point of view. The first and fundamental point is that permanent electric dipole moments violate both P and T. If we assume, as we are entitled to do, that OPT is conserved then we may speak equivalently of T-violation and OP-violation. I will mostly use the latter designation. That a permanent edm violates T is easily shown. Consider a proton. It has a magnetic dipole moment oriented along its spin axis. Suppose it also has an electric edm oriented, say, parallel to the magnetic dipole. Under T the electric dipole is not changed, as the spatial charge distribution is unaffected. But the magnetic dipole changes sign because current flows are reversed by T. Thus T takes a proton with parallel electric and magnetic dipoles into one with antiparallel moments. Now, if T is assumed to be an exact symmetry these two experimentally distinguishable kinds of proton will have the same mass.
    [Show full text]
  • A Supersymmetry Primer
    hep-ph/9709356 version 7, January 2016 A Supersymmetry Primer Stephen P. Martin Department of Physics, Northern Illinois University, DeKalb IL 60115 I provide a pedagogical introduction to supersymmetry. The level of discussion is aimed at readers who are familiar with the Standard Model and quantum field theory, but who have had little or no prior exposure to supersymmetry. Topics covered include: motiva- tions for supersymmetry, the construction of supersymmetric Lagrangians, superspace and superfields, soft supersymmetry-breaking interactions, the Minimal Supersymmetric Standard Model (MSSM), R-parity and its consequences, the origins of supersymmetry breaking, the mass spectrum of the MSSM, decays of supersymmetric particles, experi- mental signals for supersymmetry, and some extensions of the minimal framework. Contents 1 Introduction 3 2 Interlude: Notations and Conventions 13 3 Supersymmetric Lagrangians 17 3.1 The simplest supersymmetric model: a free chiral supermultiplet ............. 18 3.2 Interactions of chiral supermultiplets . ................ 22 3.3 Lagrangians for gauge supermultiplets . .............. 25 3.4 Supersymmetric gauge interactions . ............. 26 3.5 Summary: How to build a supersymmetricmodel . ............ 28 4 Superspace and superfields 30 4.1 Supercoordinates, general superfields, and superspace differentiation and integration . 31 4.2 Supersymmetry transformations the superspace way . ................ 33 4.3 Chiral covariant derivatives . ............ 35 4.4 Chiralsuperfields................................ ........ 37 arXiv:hep-ph/9709356v7 27 Jan 2016 4.5 Vectorsuperfields................................ ........ 38 4.6 How to make a Lagrangian in superspace . .......... 40 4.7 Superspace Lagrangians for chiral supermultiplets . ................... 41 4.8 Superspace Lagrangians for Abelian gauge theory . ................ 43 4.9 Superspace Lagrangians for general gauge theories . ................. 46 4.10 Non-renormalizable supersymmetric Lagrangians . .................. 49 4.11 R symmetries........................................
    [Show full text]
  • Supersymmetric Dark Matter Candidates in Light of Constraints from Collider and Astroparticle Observables
    THESE` Pour obtenir le grade de DOCTEUR DE L’UNIVERSITE´ DE GRENOBLE Specialit´ e´ : Physique Theorique´ Arretˆ e´ ministeriel´ : 7 aoutˆ 2006 Present´ ee´ par Jonathan DA SILVA These` dirigee´ par Genevieve` BELANGER´ prepar´ ee´ au sein du Laboratoire d’Annecy-le-Vieux de Physique Theorique´ (LAPTh) et de l’Ecole´ Doctorale de Physique de Grenoble Supersymmetric Dark Matter candidates in light of constraints from collider and astroparticle observables These` soutenue publiquement le 3 juillet 2013, devant le jury compose´ de : arXiv:1312.0257v1 [hep-ph] 1 Dec 2013 Dr. Rohini GODBOLE Professeur, CHEP Bangalore, Inde, Presidente´ Dr. Farvah Nazila MAHMOUDI Maˆıtre de Conferences,´ LPC Clermont, Rapporteur Dr. Ulrich ELLWANGER Professeur, LPT Orsay, Rapporteur Dr. Celine´ BŒHM Charge´ de recherche, Durham University, Royaume-Uni, Examinatrice Dr. Anupam MAZUMDAR Professeur, Lancaster University, Royaume-Uni, Examinateur Dr. Genevieve` BELANGER´ Directeur de Recherche, LAPTh, Directeur de these` A meus av´os. Contents Acknowledgements - Remerciements vii List of Figures xi List of Tables xvii List of Abbreviations xix List of Publications xxiii Introduction1 I Status of particle physics and cosmology ... and beyond5 1 From the infinitely small : the Standard Model of particle physics ...7 1.1 Building of the model : gauge sector . .8 1.2 Matter sector . 10 1.2.1 Leptons . 10 1.2.2 Quarks . 12 1.3 The Higgs mechanism . 13 1.4 Full standard picture . 16 1.5 Successes of the SM . 18 1.6 SM issues . 19 1.6.1 Theoretical problems . 19 1.6.2 Experimental discrepancies . 20 1.6.3 Cosmological connexion . 22 2 ... To the infinitely large : the Lambda Cold Dark Matter model 23 2.1 Theoretical framework .
    [Show full text]
  • Abdus Salam United Nations Educational, Scientific XA0053499 and Cultural International Organization Centre
    the abdus salam united nations educational, scientific XA0053499 and cultural international organization centre international atomic energy agency for theoretical physics CP VIOLATION AS A PROBE OF FLAVOR ORIGIN IN SUPERSYMMETRY D.A. Demir A. Masiero and 4 O. Vives 3 1-02 Available at: http://www.ictp.trieste.it/~pub_off IC/99/165 SISSA/134/99/EP United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS CP VIOLATION AS A PROBE OF FLAVOR ORIGIN IN SUPERSYMMETRY D.A. Demir The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, A. Masiero and O. Vivcs International School for Advanced Studies, via Beirut 4, 1-34013, Trieste, Italy and INFN, Sezione di Trieste, Trieste, Italy. Abstract We address the question of the relation between supersymmetry breaking and the origin of flavor in the context of CP violating phenomena. We prove that, in the absence of the Cabibbo-Kobayashi-Maskawa phase, a general Minimal Supersymmetric Standard Model with all possible phases in the soft-breaking terms, but no new flavor structure beyond the usual Yukawa matrices, can never give a sizeable contribution to ex, Z'/Z or hadronic B° CP asymmetries. Observation of supersymmetric contributions to CP asymmetries in B decays would hint at a non-flavor blind mechanism of supersymmetry breaking. MIRAMARE - TRIESTE November 1999 In the near future, new experimental information on CP violation will be available. Not only the new B factories will start measuring CP violation effects in D° CP asymmetries, but also the experimental sensitivity to the electric dipole moment (EDM) of the neutron and the electron will be substantially improved.
    [Show full text]
  • An Introduction to Dynamical Supersymmetry Breaking
    An Introduction to Dynamical Supersymmetry Breaking Thomas Walshe September 28, 2009 Submitted in partial fulfillment of the requirements for the degree of Master of Science of Imperial College London Abstract We present an introduction to dynamical supersymmetry breaking, highlighting its phenomenological significance in the context of 4D field theories. Observations concerning the conditions for supersymmetry breaking are studied. Holomorphy and duality are shown to be key ideas behind dynamical mechanisms for supersymmetry breaking, with attention paid to supersymmetric QCD. Towards the end we discuss models incorporating DSB which aid the search for a complete theory of nature. 1 Contents 1 Introduction 4 2 General Arguments 8 2.1 Supersymmetry Algebra . 8 2.2 Superfield formalism . 10 2.3 Flat Directions . 12 2.4 Global Symmetries . 15 2.5 The Goldstino . 17 2.6 The Witten Index . 19 3 Tree Level Supersymmetry Breaking 20 3.1 O'Raifeartaigh Models . 20 3.2 Fayet-Iliopoulos Mechanism . 22 3.3 Holomorphicity and non-renormalistation theorems . 23 4 Non-perturbative Gauge Dynamics 25 4.1 Supersymmetric QCD . 26 4.2 ADS superpotential . 26 4.3 Theories with F ≥ N ................................. 28 5 Models of Dynamical Supersymmetry Breaking 33 5.1 3-2 model . 34 5.2 SU(5) theory . 36 5.3 SU(7) with confinement . 37 5.4 Generalisation of these models . 38 5.5 Non-chiral model with classical flat directions . 40 2 5.6 Meta-Stable Vacua . 41 6 Gauge Mediated Supersymmetry Breaking 42 7 Conclusion 45 8 Acknowledgments 46 9 References 46 3 1 Introduction The success of the Standard Model (SM) is well documented yet it is not without its flaws.
    [Show full text]
  • Statistical Analysis of the Supersymmetry Breaking Scale
    Statistical analysis of the supersymmetry breaking scale Michael R. Douglas1,&,2 1 NHETC and Department of Physics and Astronomy Rutgers University, Piscataway, NJ 08855-0849, USA & I.H.E.S., Le Bois-Marie, Bures-sur-Yvette, 91440 France 3 Caltech 452-48, Pasadena, CA 91125, USA [email protected] Abstract We discuss the question of what type and scale of supersymmetry breaking might be statistically favored among vacua of string/M theory, building on comments in Denef and Douglas, hep-th/0404116. arXiv:hep-th/0405279v4 29 Jun 2004 1 Introduction Over the last few years, a point of view towards the phenomenology of string and M theory has evolved [9, 6, 14, 3, 10, 11, 17, 20, 12, 2, 4, 7, 16, 8, 21], which develops and tries to work with the following hypotheses: • String/M theory has many consistent vacuum states which at least roughly match the Standard Model, and might be candidates to describe our world. • The number of vacua is so large that the problems of reproducing the Stan- dard Model in detail, and the classic problems of “beyond the Standard Model physics” such as the hierarchy problem and cosmological constant problem, might admit statistical solutions. The basic example is that in an ensemble of N vacua which differ only in a parameter Λ (say the c.c. as in [6]), and in which Λ is uniformly distributed, it is likely that a quan- tity which appears fine tuned by an amount ǫ> 1/N (for the c.c., 10−120 in a generic nonsupersymmetric theory) will be realized by at least one vacuum, just on statistical grounds.
    [Show full text]
  • Multiple Solutions in Supersymmetry and the Higgs
    Multiple solutions in supersymmetry and the Higgs 1 B. C. Allanach 1DAMTP, CMS, Wilberforce Road, University of rspa.royalsocietypublishing.org Cambridge, Cambridge, CB3 0WA, United Kingdom Weak-scale supersymmetry is a well motivated, if Research speculative, theory beyond the Standard Model of particle physics. It solves the thorny issue of the Higgs mass, namely: how can it be stable to quantum 15 corrections, when they are expected to be 10 Article submitted to journal times bigger than its mass? The experimental signal of the theory is the production and measurement of supersymmetric particles in the Large Hadron Subject Areas: Collider experiments. No such particles have been Physics, Particle Physics, seen to date, but hopes are high for the impending Mathematics run in 2015. Searches for supersymmetric particles can be difficult to interpret. Here, we shall discuss Keywords: the fact that, even given a well defined model of MSSM, technical hierarchy problem, supersymmetry breaking with few parameters, there can be multiple solutions. These multiple solutions constrained minimal supersymmetric are physically different, and could potentially mean standard model that points in parameter space have been ruled out by interpretations of LHC data when they shouldn’t Author for correspondence: have been. We shall review the multiple solutions B. C. Allanach and illustrate their existence in a universal model of e-mail: supersymmetry breaking. [email protected] 1. Introduction to Supersymmetry The recent discovery of the Higgs boson of mass 125- 126 GeV at the Large Hadron Collider experiments [1, 2] introduces a new problem: the technical hierarchy problem.
    [Show full text]
  • Supersymmetry
    Supersymmetry Physics Colloquium University of Virginia January 28, 2011 Stephen P. Martin Northern Illinois University 1 The Standard Model of particle physics • The “Hierarchy Problem”: why is the Higgs mass so • small? Supersymmetry as a solution • New particles predicted by supersymmetry • Supersymmetry is spontaneously broken • How to find supersymmetry • 2 The Standard Model of Particle Physics Quarks (spin=1/2): Name: down up strange charm bottom top − 1 2 − 1 2 − 1 2 Charge: 3 3 3 3 3 3 Mass: 0.005 0.002 0.1 1.5 5 173.1 Leptons (spin=1/2): − − − Name: e νe µ νµ τ ντ Charge: −1 0 −1 0 −1 0 Mass: 0.000511 ∼ 0 0.106 ∼ 0 1.777 ∼ 0 Gauge bosons (spin=1): ± 0 Name: photon (γ) W Z gluon (g) Charge: 0 ±1 0 0 Mass: 0 80.4 91.2 0 All masses in GeV. (Proton mass = 0.938 GeV.) Not shown: antiparticles of quarks, leptons. 3 There is a last remaining undiscovered fundamental particle in the Standard Model: the Higgs boson. What we know about it: Charge: 0 Spin: 0 Mass: Greaterthan 114 GeV, and not between 158 and 175 GeV ( in most simple versions) Less than about 215 GeV ( indirect, very fuzzy, simplest model only) Fine print: There might be more than one Higgs boson. Or, it might be a composite particle, made of other more basic objects. Or, it might be an “effective” phenomenon, described more fundamentally by other unknown physics. But it must exist in some form, because... 4 The Higgs boson is the source of all mass.
    [Show full text]