About R-parity and the Supersymmetric Standard Model

We recall the obstacles which seemed, long ago, to prevent one from viewing supersymmetry as a possible fundamental symmetry of Nature. Is spontaneous supersymmetry breaking possible ? Where is the spin-1/2 Goldstone fermion of supersymmetry, if not a neutrino ? Which bosons and fermions could be related ? Can one define conserved baryon and lepton numbers in such theories, although they systematically involve self-conjugate Majorana fermions ? If we have to postulate the existence of new bosons carrying B and L (the new spin-0 squarks and sleptons), can we prevent them from mediating new unwanted interactions ? We then recall how we obtained the three basic ingredients of the Supersymmetric Standard Model: 1) the SU(3) x SU(2) x U(1) gauge superfields; 2) the chiral quark and lepton superfields; 3) the two doublet Higgs superfields responsible for the electroweak breaking, and the generation of quark and lepton masses. The original continuous ``R-invariance'' of this model was soon abandoned in favor of its discrete version, R-parity, so that the gravitino, and gluinos, can acquire masses - gluinos getting their masses from supergravity, or radiative corrections. R-parity forbids unwanted squark and slepton exchanges, and guarantees the stability of the ``lightest supersymmetric particle''. It is present only since we restricted the initial superpotential to be an even function of quark and lepton superfields (so as to allow for B and L conservation laws), as made apparent by the formula re-expressing R-parity as (-1)^2S (-1)^(3B+L). Whether it turns out to be absolutely conserved, or not, R-parity plays an essential role in the phenomenology of supersymmetric theories, and the experimental searches for the new sparticles.Comment: 23 pages, Latex, no figures. To be published as a contribution to the Yuri Gol'fand Memorial Volume, M.Shifman ed., World Scientifi

Invisible Upsilon decays into Light Dark Matter

Invisible psi and Upsilon decays into light neutralinos, within the MSSM or N(n)MSSM, are smaller than for nu nubar production, even if light spin-0 particles are coupled to quarks and neutralinos. In a more general way, light dark matter particles are normally forbidden, unless they can annihilate sufficiently through a new interaction stronger than weak interactions (at lower energies), as induced by a light spin-1 U boson, or heavy-fermion exchanges in the case of scalar dark matter. We discuss the possible contributions of U-boson, heavy-fermion, or spin-0 exchanges to invisible psi and Upsilon decays. U-exchanges could lead, but not necessarily, to significant branching fractions for invisible decays into light dark matter. We show how one can get the correct relic density together with sufficiently small invisible branching fractions, and the resulting constraints on the U couplings to ordinary particles and dark matter, in particular |c_chi.f_bV| < 5 10^-3 from Upsilon decays, for 2 m_chi smaller than a few GeV. We also explain why there is no model-independent way to predict psi and Upsilon branching fractions into light dark matter, from dark matter annihilation cross sections at freeze-out time.Comment: 10 pages, 9 figures, to appear in Phys. Rev.

Equivalence Principle tests, Equivalence theorems and New long-range forces

We discuss the possible existence of new long-range forces mediated by spin-1 or spin-0 particles. By adding their effects to those of gravity, they could lead to apparent violations of the Equivalence Principle. While the vector part in the couplings of a new spin-1 U boson involves, in general, a combination of the B and L currents, there may also be, in addition, an axial part as well. If the new force has a finite range \lambda, its intensity is proportional to 1/(\lambda^2 F^2), F being the extra U(1) symmetry-breaking scale. Quite surprisingly, particle physics experiments can provide constraints on such a new force, even if it is extremely weak, the corresponding gauge coupling being extremely small (<< 10^-19 !). An ``equivalence theorem'' shows that a very light spin-1 U boson does not in general decouple even when its gauge coupling vanishes, but behaves as a quasimassless spin-0 particle, having pseudoscalar couplings proportional to 1/F. Similarly, in supersymmetric theories, a very light spin-3/2 gravitino might be detectable as a quasi massless spin-1/2 goldstino, despite the extreme smallness of Newton's gravitational constant G_N, provided the supersymmetry-breaking scale is not too large. Searches for such U bosons in \psi and \Upsilon decays restrict F to be larger than the electroweak scale (the U actually becoming, as an axion, quasi ``invisible'' in particle physics for sufficiently large F). This provides strong constraints on the corresponding new force and its associated EP violations. We also discuss briefly new spin-dependent forces.Comment: 19 page

Constraints on Light Dark Matter and U bosons, from psi, Upsilon, K+, pi0, eta and eta' decays

Following searches for photinos and very light gravitinos in invisible decays of psi and Upsilon, we discuss new limits on Light Dark Matter and U bosons, from psi and Upsilon decays, as well as rare decays of K+ and invisible decays of pi0, eta and eta' ... . The new limits involving the vector couplings of the U to quarks turn out, not surprisingly, to be much less restrictive than existing ones on axial couplings, from an axionlike behavior of a light U boson, tested in psi --> gamma U, Upsilon --> gamma U and K+ --> pi+ U decays (or as compared to the limit from parity-violation in atomic physics, in the presence of an axial coupling to the electron). Altogether the hypothesis of light U bosons, and light dark matter particles, remains compatible with particle physics constraints, while allowing for the appropriate annihilation cross sections required, both at freeze-out (for the relic abundance) and nowadays (if e+ from LDM annihilations are at the origin of the 511 keV line from the galactic bulge).Comment: 8 page