These lectures, presented at the 2006 TASI summer school, give a general introduction to supersymmetry, emphasizing its application to models of elementary particle physics at the 100 GeV energy scale. I discuss the following topics: the construction of supersymmetric Lagrangians with scalars, fermions, and gauge bosons, the structure and mass spectrum of the Minimal Supersymmetric Standard Model (MSSM), the measurement of the parameters of the MSSM at high-energy colliders, and the solutions that the MSSM gives to the problems of electroweak symmetry breaking and dark matter.
We investigate a spectrum of the low-energy composite particles with the quantum numbers $J^p=0^\pm,\frac {1}{2}^\pm$ in a $SU_{F}(3)$ model of hadron supersymmetry. We derive the mass spectrum of two, three and four-quark states and determine all free parameters of a theory, including the masses of quarks and diquarks.
We present a model in which elementary particles and forces are unified in the framework of quantum field theory in higher dimensions. The particles include gauge bosons, quarks and leptons, as well as the Higgs bosons and the forces include strong, weak, hypercharge as well as Yukawa interactions. The model is based on a simple group SO(16) in six dimensions with N=2 supersymmetry. The gauge symmetry, as well as supersymmetry is broken to SU(4) x SU(2)_L x SU(2)_R x U(1)^3 with N=1 supersymmetry upon compactification in four dimension on a T^2/Z_6 orbifold.
These notes are an expanded version of a short course of lectures given for graduate students in particle physics at Oxford. The level was intended to be appropriate for students in both experimental and theoretical particle physics.The purpose is to present an elementary and self-contained introduction to SUSY that follows on, relatively straightforwardly, from graduate-level courses in relativistic quantum mechanics and introductory quantum field theory. The notation adopted, at least initially, is one widely used in RQM courses, rather than the `spinor calculus' (dotted and undotted indices…
We use the idea of partial compositeness in a minimal supersymmetric model to relate the fermion and sfermion masses. By assuming that the Higgs and third-generation matter is (mostly) elementary, while the first- and second-generation matter is (mostly) composite, the Yukawa coupling hierarchy can be explained by a linear mixing between elementary states and composite operators with large anomalous dimensions. If the composite sector also breaks supersymmetry, then composite sfermions such as selectrons are predicted to be much heavier than the lighter elementary stops. This inverted sfermion…
We introduce in an arbitrary supersymmetric version of the standard model without elementary scalars a logarithmic operator which is irrelevant in the limit in which all symmetries are respected. However through a dynamical mechanism of the Nambu Jona Lasinio type this operator may produce two fermion vacuum condensates that may account for electroweak and contribute to supersymmetry breaking. Some of the phenomenological consequences of this set-up are discussed.
We consider a supersymmetric model that uses partial compositeness to explain the fermion mass hierarchy and predict the sfermion mass spectrum. The Higgs and third-generation matter superfields are elementary, while the first two matter generations are composite. Linear mixing between elementary superfields and supersymmetric operators with large anomalous dimensions is responsible for simultaneously generating the fermion and sfermion mass hierarchies. After supersymmetry is broken by the strong dynamics, partial compositeness causes the first- and second-generation sfermions to be split fro…
We discuss the possible applications supersymmetric theories might find in the field of elementary particle physics. The supersymmetric generalization of the $SU(3)\times SU(2)\times U(1)$ standard model is discussed in detail. Special attention has been devoted to the question of gauge coupling constant unification in the framework of supersymmetric grand unified models.
A fairly elementary introduction to supersymmetric field theories in general and the minimal supersymmetric Standard Model (MSSM) in particular is given. Topics covered include the cancellation of quadratic divergencies, the construction of the supersymmetric Lagrangian using superfields, the field content of the MSSM, electroweak symmetry breaking in the MSSM, mixing between different superparticles (current eigenstates) to produce mass eigenstates, and the embedding of the MSSM in so--called minimal supergravity.
We introduce the standard model of elementary particles and discuss the reasons why we have to modify it. Emphasis is put on the indications from the neutrinos and on the role of the Higgs particle; some promising theoretical ideas, like quark-lepton symmetry, existence of super-heavy ``right-handed'' neutrinos, grand unification and supersymmetry at the weak scale, are introduced and shortly discussed.
Supersymmetry phenomenology is an important component of particle physics today. I provide a definition of supersymmetry phenomenology, outline the scope of its activity, and argue its legitimacy. This essay derives from a presentation given at the 2000 SLAC Summer Institute.
We investigate the algebraic structure of supersymmetric Ward- and Slavnov-Taylor identities (STI) in field theories with global supersymmetry. We develop diagrammatical methods for STI in supersymmetric gauge theories within a generalized BRST formalism. These identities are used as consistency checks for the implementation of phenomenological supersymmetric models of elementary particle physics in Monte Carlo simulations. We discuss the infrastructure necessary for generalizing the matrix element generator O'Mega to supersymmetric field theories.
Here I briefly discuss why supersymmetry is considered a leading candidate of physics beyond the standard model. I also highlight the salient features of different supersymmetry breaking models. A few other symmetries, broken or intact, asscociated with any realistic supersymmetric model are also identified. This write-up is too simple-minded for an expert on supersymmetry. It is basically intended for those who are busy in other areas of high energy physics.
We discuss the prospect of studying physics at short distances, such as Planck length or GUT scale, using supersymmetry as a probe. Supersymmetry breaking parameters contain information on all physics below the scale where they are induced. We will gain insights into grand unification (or in some cases string theory) and its symmetry breaking pattern combining measurements of gauge coupling constants, gaugino masses and scalar masses. Once the superparticle masses are known, it removes the main uncertainty in the analysis of proton decay, flavor violation and electric dipole moments. We will b…
In this talk, I briefly review a selection of SUSY effects in B physics. First, I consider models with Minimal Flavour Violation. Then I discuss SUSY models with new sources of flavour violation in squark mass matrices, analyzing present constraints and possible developments with forthcoming data on b -> s and b -> d transitions.
An attempt is made to present modern hopes to find manifestation of supersymmetry, a new symmetry that relates bosons and fermions, in particle physics from the point of view of renormalization group flow. The Standard Model of particle interactions is briefly reviewed, the main notions of supersymmetry are introduced. In more detail the RG flow in the Minimal Supersymmetric Standard Model is considered. Predictions of particle spectrum are obtained based on the RG fixed points.
We show a natural form of the interaction between unparticle and supersymmetry. Using the couplings of unparticle to supersymmetry presented, as examples, we calculate the differential decay rates for the processes ${\it {\tilde f}}\to {\it f}+{\cal U}_{3/2}$, ${\it {\tilde χ}}^0\to{\it γ}+{\cal U}_{3/2}$, ${\it {\tilde χ}}^\pm\to W^\pm+{\cal U}_{3/2}$ and ${\it {\tilde χ}}^0\to Z^0+{\cal U}_{3/2}$. Finally, we discuss the phenomenological implication of our results and give some comments.
In this contribution we present a discussion of some aspects of the capabilities of a photon collider to probe physics beyond the standard model. I will take a few examples from Higgs physics, supersymmetry, extra dimensional theories as well as unparticles, pointing out the special rôle that a photon collider can play in each case.
An elementary review of models and phenomenology for physics beyond the Standard Model (excluding supersymmetry). The emphasis is on LHC physics. Based upon a talk given at the Physics at LHC conference, Vienna, 13-17 July 2004.
The experimental potential of e+e- Linear Colliders to explore the properties of supersymmetric particles is reviewed. High precision measurements of masses, spin-parity, gauge quantum numbers, couplings and mixings, production and decay properties will be possible in a clean environment. These achievements will allow the underlying supersymmetry breaking scheme to be revealed, the parameters of the fundamental theory to be determined and to test their unification through extrapolation to very high energie scales.
We make an attempt to describe the spectrum of masses of elementary particles, as it comes out empirically in six distinct scales. We argue for some rather well defined mass scales, like the electron mass: it seems to us that there is a minimum mass associated to any electric charge, so we elaborate on this assumption; indeed, some scales of masses will cover also masses of composite particles or mass differences. We extend some plausibility arguments for other scales, as binding or self-energy effects of the microscopic forces, plus some speculative uses, here and there, of gravitation. We al…
We propose a new framework for the observed flavor hierarchy and mixing based on left-right supersymmetry. The model contains the most minimal Higgs sector consisting only of gauge doublets which forbid the standard model Yukawa couplings. New mediator fields then connect the left- and right-chiral fermion sectors and result in effective tree level Yukawa couplings for the third generation charged fermions. The remaining fermions, including all neutrinos, acquire effective Yukawa couplings sourced by the supersymmetry breaking sector at loop level. We predict new TeV range scalars, as well as …
A global fit to quark flavour-physics data disfavours the Standard Model with 3.6 standard deviations and points towards new CP-violating physics in meson-antimeson mixing amplitudes. Tevatron data call for a new Bs-Bs-bar mixing phase and new physics in Bd-Bd-bar mixing alleviates the tension on the unitarity triangle driven by B(B-> tau nu). In supersymmetric GUT models the large atmospheric neutrino mixing angle can influence b -> s transitions. I present the results of a recent analysis in an SO(10) GUT model which accomodates the large Bs-Bs-bar mixing phase while simultaneously obeying a…
A machine learning method is applied to analyze lepton mass matrices numerically. The matrices were obtained within a framework of high scale SUSY and a flavor symmetry, which are too complicated to be solved analytically. In this numerical calculation, the heuristic method in machine learning is adopted. Neutrino masses, mixings, and CP violation are obtained. It is found that neutrinos are normally ordered and the favorable effective Majorana mass is about $7\times 10^{-3}$ eV.
Many models of electroweak symmetry-breaking with an extended Higgs sector exhibit improved naturalness, wherein the new physics scale, at which quadratic divergences of Higgs mass parameters due to top quark loops are cut off, can be pushed beyond the reach of the Large Hadron Collider without unnatural fine tuning. Such models include examples where the new physics is supersymmetry, implying that supersymmetry may still solve the hierarchy problem, even if it eludes detection at the LHC.
The physics of supersymmetry is reviewed from the perspective of physics at ever increasing energies. Starting from the minimal supersymmetric extension of the Standard Model at the electroweak scale, we proceed to higher energies seeking to understand the origin of the many model parameters. Supersymmetric grand unification, supergravity, and superstrings are introduced sequentially, and their contribution to the sought explanations is discussed. Typical low-energy supersymmetric models are also presented, along with their possible experimental consequences via direct and indirect processes a…
We study flavour physics and CP violation in the context of low energy Supersymmetry with non-universal soft mass terms for sfermions. Large deviations from Standard Model predictions are allowed in B-physics, as shown in two explicit examples. In particular, the consequences of these models for a_(J/ψK) and Delta m_(B_s) are worked out.
In SUSY models, it is still possible to have large signals even if the current data on $K$ and $B$ systems are consistent with the CKM paradigm for flavor mixing and CP violation. I first discuss $b\to d$ and $b\to s$ transitions including time-dependent CP asymmetries in $B_d \to ϕK_s$, and usefulness of $B_s \to μ^+ μ^-$ to distinguish various SUSY breaking mechanisms. Then I will discuss some possible connections between B physics and cosmology: (i) B physics and electroweak baryogenesis within SUSY models, and (ii) the correlation between the neutralino dark matter scattering and $B (B_s \…
Although supersymmetry has not been seen directly by experiment, there are powerful physics reasons to suspect that it should be an ingredient of nature and that superpartner masses should be somewhat near the weak scale. I present an argument that if we dismiss our ordinary intuition of finetuning, and focus entirely on more concrete physics issues, the PeV scale might be the best place for supersymmetry. PeV-scale supersymmetry admits gauge coupling unification, predicts a Higgs mass between 125 GeV and 155 GeV, and generally disallows flavor changing neutral currents and CP violating effect…
Gauge coupling unification and the stability of the Higgs vacuum are among two of the cherished features of low-energy supersymmetric models. Putting aside questions of naturalness, supersymmetry might only be realised in nature at very high energy scales. If this is the case, the preservation of gauge coupling unification and the stability of the Higgs vacuum would certainly require new physics, but it need not necessarily be at weak scale energies. New physics near the unification scale could in principle ensure Grand Unification, while new physics below $μ\sim 10^{10}$ GeV could ensure the …
Ten reasons are given why supersymmetry is the leading candidate for physics beyond the Standard Model. Ultimately, the experimental discovery of supersymmetric particles at future colliders will determine whether supersymmetry is relevant for TeV scale physics. The grand hope of supersymmetry enthusiasts is to connect TeV scale supersymmetry with Planck scale physics. The ten most pressing theoretical problems standing in the way of this goal are briefly described.
The discovery of a light Higgs boson at the LHC opens a broad program of studies and measurements to understand the role of this particle in connection with New Physics and Cosmology. Supersymmetry is the best motivated and most thoroughly formulated and investigated model of New Physics which predicts a light Higgs boson and can explain dark matter. This paper discusses how the study of the Higgs boson connects with the search for supersymmetry and for dark matter at the LHC and at a future $e^+e^-$ collider and with dedicated underground dark matter experiments.
To embed the seesaw mechanism in the MSSM, two or three right-handed neutrino supermultiplets, $N_i$, have to be added to the model. In this framework, the supersymmetry breaking potential will include a new term called neutrino $B$-term: $MB_ν\tilde{N} \tilde{N}/2$. In this talk, we present a toy model that generates a large neutrino $B$-term keeping other supersymmetry breaking parameters small. We then review the consequences of having a large neutrino $B$-term on the electroweak symmetry breaking parameters and electric dipole moments (EDMs) of elementary particles.
In this talk, I first discuss $b\to d$, $b\to s$ and $s\to d$ transitions including time-dependent CP asymmetries in $B_d \to ϕK_s$ and Re ($ε^{'}/ε_K$). Then I show that the decay $B_s \to μ^+ μ^-$ is useful to distinguish various SUSY breaking mechanisms. I will also describe some possible connections between B physics and cosmology: (i) B physics and electroweak baryogenesis within SUSY models, and (ii) the correlation between the neutralino dark matter scattering and $B (B_s \to μ^+ μ^-)$. In particular, we point out that the current upper bound on $B (B_s \to μ^+ μ^-)$ form CDF and D0 col…
Supersymmetry, a new symmetry that relates bosons and fermions in particle physics, still escapes observation. Search for SUSY is one of the main aims of the recently launched Large Hadron Collider. The other possible manifestation of SUSY is the Dark Matter in the Universe. The present lectures contain a brief introduction to supersymmetry in particle physics. The main notions of supersymmetry are introduced. The supersymmetric extension of the Standard Model - the Minimal Supersymmetric Standard Model - is considered in more detail. Phenomenological features of the MSSM as well as possible e…
This collection of studies on new physics at the LHC constitutes the report of the supersymmetry working group at the Workshop `Physics at TeV Colliders', Les Houches, France, 2007. They cover the wide spectrum of phenomenology in the LHC era, from alternative models and signatures to the extraction of relevant observables, the study of the MSSM parameter space and finally to the interplay of LHC observations with additional data expected on a similar time scale. The special feature of this collection is that while not each of the studies is explicitely performed together by theoretical and ex…
This Fifth International WEIN Symposium is devoted to physics beyond the standard model. This talk is about tau lepton physics, but I begin with the question: do we know how to find new physics in the world of elementary particles? This question is interwoven with the various tau physics topics. These topics are: searching for unexpected tau decay modes; searching for additional tau decay mechanisms; radiative tau decays; tau decay modes of the W, B, and D; decay of the Z^0 to tau pairs; searching for CP violation in tau decay; the tau neutrino, dreams and odd ideas in tau physics; and tau res…
The determination of supersymmetric parameters at the LHC in favorable as well as difficult scenarios is presented. If discovered and measured at the LHC and the ILC, supersymmetry may provide a link between collider physics and cosmology.
String theory avoids the ultraviolet infinities that arise in trying to quantize gravity. It is also more predictive than conventional quantum field theory, one aspect of this being the way that it contributed to the emergence of the concept of ``supersymmetry'' of particle interactions. There are hints from the successes of supersymmetric unified theories of particle interactions that supersymmetry is relevant to elementary particles at energies close to current accelerator energies; if this is so, it will be confirmed experimentally and supersymmetry is then also likely to be important in co…
We present a simple scheme for constructing models that achieve successful gauge mediation of supersymmetry breaking. In addition to our previous work [1] that proposed drastically simplified models using metastable vacua of supersymmetry breaking in vector-like theories, we show there are many other successful models using various types of supersymmetry breaking mechanisms that rely on enhanced low-energy U(1)_R symmetries. In models where supersymmetry is broken by elementary singlets, one needs to assume U(1)_R violating effects are accidentally small, while in models where composite fields…
With the aim of linking natural supersymmetry to flavour physics, a model is proposed based on a family symmetry G \times U(1), where G is a discrete nonabelian subgroup of SU(2), with both F-term and (abelian) D-term supersymmetry breaking. A good fit to the fermion masses and mixing is obtained with the same U(1) charges for the left- and right- handed quarks of the first two families and the right-handed bottom quark, and with zero charge for the left-handed top-bottom doublet and the the right handed top. The model shows an interesting indirect correlation between the correct prediction fo…
In recent years, significant experimental indications that point towards Lepton Flavour Universality violating effects in B-decays, involving $b \to c τν$ and $b \to s \ell^+ \ell^-$ have been accumulated. A possible New Physics explanation can be sought within the framework of R-parity violating Supersymmetry, which contains the necessary ingredients to explain the anomalies via both leptoquark, tree-level exchange and one-loop diagrams involving purely leptonic interactions. In addition, an approximate $U(2)^2$ flavour symmetry, that respects gauge coupling unification, successfully controls…
The European School of High-Energy Physics is intended to give young physicists an introduction to the the- oretical aspects of recent advances in elementary particle physics. These proceedings contain lecture notes on the theory of quantum chromodynamics, Higgs physics, Flavour physics and CP violation, and Supersymmetry.
The direct detection rate for supersymmetric cold dark matter (CDM) particles is calculated for a number of suitable nuclear targets. Both the coherent and spin contributions are considered. By considering representative phenomenologically acceptable input in the restricted SUSY parameter space, detectable rates are predicted for some choices of the parameters. The modulation effect, due to the Earth's annual motion, has also been considered and found to be $\le 4%$. Its precise value depends on the mass of CDM particles (LSP) and the structure of the target.
Supersymmetry, a new symmetry that relates bosons and fermions in particle physics, still escapes observation. Search for supersymmetry is one of the main aims of the Large Hadron Collider. The other possible manifestation of supersymmetry is the Dark Matter in the Universe. The present lectures contain a brief introduction to supersymmetry in particle physics. The main notions of supersymmetry are introduced. The supersymmetric extension of the Standard Model -- the Minimal Supersymmetric Standard Model -- is considered in more detail. Phenomenological features of the Minimal Supersymmetric S…
Various aspects of physics at LEP 2 are reviewed from a phenomenological point of view. We first discuss the search for Higgs bosons, which might be relatively light if indications from the precision electroweak data and supersymmetry are correct. Then WW physics is discussed, with particular emphasis on the problems in measuring mW by the kinematic reconstruction of events with purely hadronic final states. Finally, possible manifestations of supersymmetry are reviewed, comparing different scenarios for the lightest supersymmetric particle, which may or may not be stable. Possible scenarios f…
After promoting the phases of the soft masses to dynamical fields corresponding to Goldstone bosons of spontaneously broken global symmetries in the supersymmetry breaking sector, the next-to-minimal supersymmetric model is found to solve the $μ$ problem and the strong CP problem simultaneously with an invisible axion. The domain wall problem persists in the form of axionic domain formation. Relaxation dynamics of the physical CP-violating phases is determined only by the short-distance physics and their relaxation values are not necessarily close to the CP-conserving points. Having observable…
These lectures survey the present situation and future prospects in selected areas of particle physics phenomenology: (1) the top quark, (2) the Higgs boson in the Standard Model, (3) strong $WW$ scattering, (4) supersymmetry, (5) the Higgs sector in minimal supersymmetry, and (6) low-energy constraints on supersymmetry.
Search for supersymmetry is carried out in the framework of the Minimal Supersymmetric Standard Model (MSSM). Using the software programs SOFTSUSY and PROSPINO, the mass spectrum and the production cross-sections of superpartners are calculated. The results obtained are of importance for searching the new physics at the LHC.
This Resource Book reviews the physics opportunities of a next-generation e+e- linear collider and discusses options for the experimental program. Part 2 reviews the possible experiments on Higgs bosons and supersymmetric particles that can be done at a linear collider.
The realization in the early 1980s that weak scale supersymmetry stabilizes the Higgs sector of the spectacularly successful Standard Model led several authors to explore whether low energy supersymmetry could play a role in particle physics. Among these were Richard Arnowitt, Ali Chamseddine and Pran Nath who constructed a viable {\em locally} supersymmetric Grand Unified Theory (GUT), laying down the foundation for supergravity GUT models of particle physics. Supergravity models continue to be explored as one of the most promising extensions of the Standard Model. After a quick overview of s…
We discuss how to extract non-Standard Model effects from B-factory phenomenology. We then analyze the prospects for uncovering evidence for Effective Supersymmetry, a class of supersymmetric models which naturally suppress flavor changing neutral currents and electric dipole moments without squark universality or small CP violating phases, in experiments at BaBar, BELLE, HERA-B, CDF/D0 and LHC-B.
Discovery of the Higgs boson and lack of discovery of superpartners in the first run at LHC are both predictions of split supersymmetry with thermal dark matter. We discuss what it would take to find gluinos at hadron supercolliders, including the LHC at 14 TeV center of mass energy, and future pp colliders at 100 TeV and 200 TeV. We generalize the discussion by re-expressing the search capacity in terms of gluino to lightest superpartner mass ratio, and apply results to other scenarios, such as gauge mediation and mirage mediation.
Theories with elementary scalar degrees of freedom seem nowadays required for simple descriptions of the Standard Model and of the Early Universe. It is then natural to embed theories of inflation in supergravity, also in view of their possible ultraviolet completion in String Theory. After some general remarks on inflation in supergravity, we describe examples of minimal inflaton dynamics which are compatible with recent observations, including higher-curvature ones inspired by the Starobinsky model. We also discuss different scenarios for supersymmetry breaking during and after inflation, wh…
We propose a framework for natural breaking of electroweak symmetry in supersymmetric models, where elementary Higgs fields are semi-perturbatively coupled to a strong superconformal sector. The Higgs VEVs break conformal symmetry in the strong sector at the TeV scale, and the strong sector in turn gives important contributions to the Higgs potential, giving rise to a kind of Higgs bootstrap. A Higgs with mass $125\GeV$ can be accommodated without any fine tuning. A Higgsino mass of order the Higgs mass is also dynamically generated in these models. The masses in the strong sector generically …
The purpose of these lectures is to describe the state of affairs in modern particle physics to young physicists who do not specialize in this subject.
A brief overview of Higgs physics and of supersymmetry is given. The central theme of the overview is to explore the implications of the recent discovery of a Higgs like particle regarding the prospects for the discovery of supersymmetry assuming that it is indeed the spin 0 CP even boson that enters in the spontaneous breaking of the electroweak symmetry. The high mass of the Higgs like boson at $\sim 125$ GeV points to the weak scale of supersymmetry that enters in the loop correction to the Higgs boson mass, to be relatively high, i.e., in the TeV region. However, since more than one indepe…
