Pierre Fayet

Supergauge invariant extension of the Higgs mechanism and a model for the electron and its neutrino

Abstract We extend the Higgs mechanism in a supergauge invariant way. Spontaneous symmetry breaking occurs for all allowed values of the parameters of the scalar potential. With SU(2) × U(1) as gauge group and after spontaneous breaking of supergauge invariance, we obtain a model of weak and electromagnetic interactions for the electron and its neutrino, which includes also heavy leptons and scalar particles. The neutrino is the Goldstone fermion, associated with the photon in a massless vector multiplet.

Spontaneously Broken Supergauge Symmetries and Goldstone Spinors

Abstract We present a model with a spontaneously broken supergauge symmetry which results in the appearance of a massless Goldstone spinor. The model combines supergauge invariance with ordinary gauge invariance. After the breaking the gauge boson acquires a mass as a result of the Higgs mechanism.

Supersymmetry and weak, electromagnetic and strong interactions

Abstract We study a possible way to construct supersymmetric theories which could be considered as realistic, excepted that the problem of mass generation for electron, muon and quarks remains. There is a new class of leptons which includes charged ones, and a “photonic neutrino”. Spin 1 2 -gluons and heavy spin 0- quarks are associated with ordinary vector gluons and quarks.

Fermi-Bose Hypersymmetry

Abstract A new algebra, combining supersymmetry and internal symmetry, is presented. A massless vector hypermultiplet contains a vector, an isodoublet of left-handed Dirac spinors, and a complex scalar. These can be used as generalized gauge fields. Abelian as well as non-Abelian gauge theories are studied, and the Higgs mechanism is extended in a hypersymmetric way. We present, also, a (mom-realistic) SU(2)× U(1) model; gauge invariance and hypersymmetry are spontaneously broken; two Goldstone spinors appear. Hypersymmetry allows one to define “electronic” and “muonic” numbers, and suggests that a weakly interacting scalar particle ωγ is associated with the photon and the two neutrinos.

Supersymmetric grand unification in a six-dimensional spacetime

Abstract We formulate N=2 supersymmetric GUTs in a six-dimensional spacetime, studying in particular the spontaneous breaking of gauge invariance and the construction of massive gauge multiplets. In six dimensions the photon and gluons are associated with a Weyl photino and Weyl gluinos; the massive W±, with two Dirac Winos and three spin-0 Higgs bosons; the massive Z, with one Dirac Zino and three neutral Higgs bosons. The X± 4 3 is massless, and the Y± 1 3 has the same mass as the W+-. The grand-unification mass, generated by the breaking of the 6D Poincare invariance, is associated with the large momenta carried by the grand-unification gauge bosons along the new compact dimensions.

Constraining dark matter candidates from structure formation

Abstract We show that collisional damping of adiabatic primordial fluctuations yields constraints on the possible range of mass and interaction rates of dark matter particles. Our analysis relies on a general classification of dark matter candidates, that we establish independently of any specific particle theory or model. It holds for very weakly as well as very strongly interacting particles. From a relation between the collisional damping scale and the dark matter interaction rate, we find that dark matter candidates must have cross-sections at decoupling ≲10 −33 m dm 1 MeV cm 2 with photons and ≲10 −37 m dm 1 MeV cm 2 with neutrinos, to explain the observed primordial structures of 10 9 M ⊙ . When marginally satisfied, these damping constraints provide warm dark matter candidates whose astrophysical relevance is worth to be explored. They also leave open less known regions of parameter space corresponding to particles having much higher interaction rates with other species than neutrinos and photons.

Spontaneous supersymmetry breaking without gauge invariance

Abstract We present a model of interacting scalar multiplets, where supersymmetry is spontaneously broken, generating a Goldstone spinor. Besides ordinary Goldstone bosons there exist scalar particles, massless at zeroth order.

Higgs model and supersymmetry

SummaryThe Higgs model can be made supersymmetric, provided a Dirac spinor is added, and the quartic interaction term in the Lagrangian density is —(e2/2)(ϕ†φ)2, wheree is the gauge coupling constant. The model describes a vector, a Dirac spinor and a real scalar; it depends only on two arbitrary parameters,m ande. As a gauge-invariant model, it can be studied in a Wess-Zumino gauge, or in a supersymmetric gauge. It can also be obtained as a theory of a self-interacting vector multiplet. Finally, it is suggested that a scalar particle may be associated with the photon and the two neutrinos in the theory of weak and electromagnetic interactions.RiassuntoIl modello di Higgs può essere reso supersimmetrico purché si aggiunga uno spinore di Dirac, ed il termine quartico d’interazione nella densità lagrangiana sia —(e2/2)(ϕ†ϕ)2, in cuie è la costante di accoppiamento di gauge. Il modello descrive un vettore, uno spinore di Dirac ed uno scalare reale; esso dipende solo da due parametri arbitrari,m ede. Come modello invariante di gauge esso può essere studiato in una gauge di Wess-Zumino od in una gauge supersimmetrica. Esso può anche essere ottenuto come una teoria di un multipletto vettoriale autointeragente. Infine si suggerisce che una particella scalare può essere associata al fotone ed ai due neutrini nella teoria delle interazioni deboli ed elettromagnetiche.РеэюмеМодель Хиггса может быть сделана суперсимметричной, при условии, что добавляется спинор Дирака и квадратичный член вэаимодействия в плотности Лагранжиана имеет вид — (e2/2)(ϕ†ϕ)2, где е есть калибровочная константа свяэи. Эта модель описывает вектор, спинор Дирака и вешественный скаляр. Эта модель эависит только от двух проиэвольных параметров т и е. Предложенная модель может быть исследована в калибровке ВессаДэумино или в суперсимметричной калибровке, так как она является калибровочно инвариантной моделью. Эта модель может быть также получена, как теория самовэаимодейству юшего векторного мультиплета. В эаключение предполагается, что скалярная частица может быть ассоциирована с фотоном и двумя нейтрино в теории слабых и злектромагнитных вэаимодействий.

Extra U(1)'s and new forces

We discuss possible extra U(1) gauge symmetries for extensions of the standard model, in connection with their Higgs boson sectors. The more electroweak Higgs doublets, the larger the number of extra U(1) symmetries which may be gauged. For small numbers of Higgs doublets such extra U(1) symmetries usually appear as blind to quark flavor, while this is not necessary for leptons. With only one Higgs doublet any extra U(1) generator must act on quarks and leptons as a linear combination of the baryonic and leptonic numbers B and Li with the weak hypercharge Y. Withtwo or more Higgs doublets they may act as linear combinations of B, Li and Y with axial baryonic and/or leptonic symmetry generators. We also discuss extra U(1) groups in left-right symmetric and grand-unified theories. The corresponding neutral gauge bosons, U, in general mix with the Z bosons, and may be heavy, light, or even remain massless. The strength of the resulting interaction, of unknown range λU = ħ/mUc, is proportional to 1/λU2, and also depends on the extra U(1) symmetry-breaking scale. For very light U bosons this interaction may appear as a deviation from the laws of gravitation (or electromagnetism). After mixing with the Z current the new current is then purely vectorial, in the case of a single Higgs doublet; or it also includes an axial part, which could be responsible for the direct production of U bosons in particle physics experiments, as well as for a new spin-spin force. The vector part of the current is associated with the fifth force charge Q5 = xB + yiLi + zQ, or, in the framework of grand-unified theories: Q5 = x(B − L) + zQ. We discuss, finally, some of the main physical implications of this analysis.

Spontaneously Broken Supersymmetric {GUTs} With Gauge Boson / Higgs Boson Unification

We construct an anomaly-free, spontaneously broken, supersymmetric grand-unified theory with no hierarchy problem. It is an SU(5) × U(1) [or, more generally, G × U(1) vectorlike extension of a previous SU(3) × SU(2) × U(1) × U(1) supersymmetric model, which includes mirror fermions and extends the idea of gauge boson/Higgs boson unification. Before the introduction of leptons and quarks and the spontaneous breaking of the supersymmetry, the theory has an N = 2 extended supersymmetry and depends on four parameters only, e, mW, mX, and mU. The photon and gluons are associated with a Dirac photino and Dirac gluinos. Each of the gauge bosons W±, Z, Y±13 and U(respectively X±43) is associated with four (two) spin-12 inos and five (one) spin-0 Higgs bosons. Alternately, one may disregard the extra U(1) in favor of gravity-induced supersymmetry breaking.