Decoupling of supersymmetric particles

The possibility of a heavy supersymmetric spectrum at the Minimal Supersymmetric Standard Model is considered and the decoupling from the low energy electroweak scale is analyzed in detail. The formal proof of decoupling of supersymmetric particles from low energy physics is stated in terms of the effective action for the particles of the Standard Model that results by integrating out all the sparticles in the limit where their masses are larger than the electroweak scale. The computation of the effective action for the standard electroweak gauge bosons , Z and is performed by integrating out all the squarks, sleptons, charginos and neutralinos to one-loop. The Higgs sector is not considered in this paper. The large sparticle masses limit is also analyzed in detail. Explicit analytical formulae for the two-point functions of the electroweak gauge bosons to be valid in that limit are presented. Finally, the decoupling of sparticles in the S, T and U parameters is studied analitically. A discussion on how the decoupling takes place in terms of both the physical sparticle masses and the non-physical mass parameters as the -parameter and the soft-breaking parameters is included. Received: 27 March 1998 / Published online: 5 October 1998     

Relativistic quantum mechanics of supersymmetric particles

The quantum mechanics of an electron in an external field is developed by Hamiltonian path integral methods. The electron is described classically by an action which is invariant under gauge supersymmetry transformations as well as worldline reparametrizations. The simpler case of a spinless particle is first reviewed and it is pointed out that a strictly canonical approach does not exist. This follows formally from the gauge invariance properties of the action and physically it corresponds to the fact that particles can travel backwards as well as forward in coordinate time. However, appropriate application of path integral techniques yields directly the proper time representation of the Feynman propagator. Next we extend the formalism to systems described by anticommuting variables. This problem presents some difficulty when the dimension of the phase space is odd, because the holomorphic representation does not exist. It is shown, however, that the usual connection between the evolution operator and the path integral still holds provided one indludes in the action the boundary term that makes the classical variational principle well defined. The path integral for the relativistic spinning particle is then evaluated and it is shown to lead directly to a representation for the Feynman propagator in terms of two proper times, one commuting, the other anticommuting, which appear in a symmetric manner. This representation is used to derive scattering amplitudes in an external field. In this step the anticommuting proper time is integrated away and the analysis is carried in terms of one (commuting) proper time only, just as in the spinless case. Finally, some properties of the quantum mechanics of the ghost particles that appear in the path integral for constrained systems are developed in an appendix.     

Electroproduction of supersymmetric particles and gauge bosons

The electroproduction of scalar leptons and gauginos at HERA and at supercollider energies is studied. In particular, the channel $\text{ep}\text{→}\text{e}\text{(→}\text{e}\text{+}\text{γ}\text{)}\text{γ}\text{X}$ is analyzed in full detail. The exa analytic expressions for the cross section and the spectrum of the final electron are derived and evaluated for $\text{√s ? 0.15?3}\text{TeV}$ and different values of the scalar electron and photino masses. Since the exact formulae are relatively complicated, simplified expressions in the Weizsäcker-Williams approximation are also given and their accuracy is discussed by comparison with the exact formulae. The standard processes $\text{ep}\text{→}\text{Z}\text{(→ v}\text{v}\text{)}\text{eX and ep}\text{→}\text{W}\text{(→}\text{e}\text{v}\text{)v}\text{X}$ which also lead to one final electron and two invisible particles are considered in parallel. The corresponding cross sections and distributions are discussed in comparison with the supersymmetric signal. The Z⁰ cross section is found to be quite smaller than was reported previously. To clarify this point the Z⁰ production at the leptonic vertex was computed both exactly and in the Weizsäcker-Williams approximation with quite consistent results.     

Z decay constraints on supersymmetric particles revisited

The allowed regions in the chargino-gluino mass plane are mapped out using the latestZ decay data from experiments. The determination of these masses in future experiments will uniquely fix the neutralino mass spectrum for a fixedv ₁/v ₂. Since the usual two-fold ambiguity is removed by LEP data for gluino masses upto 200 GeV. Constraints have also been placed on neutralino masses.     

Structure functions of nucleons with excited supersymmetric particles

We calculate the QCD evolution equations for structure functions with supersymmetric particles excited for the following models: light gluinos, g? and heavy squarks q? with $\text{m}{}_{\mathrm{<mtext>g</mtext><mtext>?</mtext>}}\text{? Q}{}^2\text{? m}{}_{\mathrm{<mtext>q</mtext><mtext>?</mtext>}}{}^2$; light squarks, and heavy gluinos with $\text{m}{}_{\mathrm{<mtext>g</mtext><mtext>?</mtext>}}\text{? Q}{}^2\text{? m}{}_{\mathrm{<mtext>g</mtext><mtext>?</mtext>}}{}^2\text{;}\text{and}\text{m}{}_{\mathrm{<mtext>g</mtext><mtext>?</mtext>}}{}^2\text{, m}{}_{\mathrm{<mtext>g</mtext><mtext>?</mtext>}}{}^2\text{? Q}{}^2$. The momentum sum rules and the behaviour of structure functions as x → 1 are particularly discussed.     

Spin structure of hadrons in supersymmetric quantum chromodynamics at short distances

We study the short-distance spin structure of nucleons in supersymmetric QCD. We calculate the Altarelli-Parisi spin transition coefficients ΔP _ba and corresponding anomalous Δ γ _ab ⁿ fora, b=quarks, gluons, gluinos and squarks and present the supersymmetric relations between them. Further analysis is divided into two parts: the parity conserving case and parity violating case, both following from the mass mixing in the squark sector. Solving theQ ²-evolution equations we determine the quark, gluon, gluino and squark spin distribution at variousQ ² above the threshold for production of supersymmetric partners. We also show the analytic solutions for the first moments in the nonsinglet and singlet sector. In particular the spin carried by the valence quarks turn out to vanish asymptotically except of one particular case of squark mixing.     

Renormalization of the electroweak ϱ-parameter from supersymmetric particles

We compute the renormalization of the neutral-to-charged current Fermi constant ratio, arising from the new particles required in supersymmetric scheme?.We find that ? is insensitive to the scale of the supersymmetry mass-splitting. For a t-quark mass m_t greater than this scale, the scalar-t and scalar-b contribution increases proportionally to m_t² and it is essentially equal, in sign and magnitude, to the t-, b-quark contribution.Contributions from the gaugino-higgsino-Higgs boson sector are generally of the order of a few parts in 10^?3.For a class of models under consideration these results can be traced back to an approximate SU(2) symmetry which is also useful in the classification of the new particle spectrum.     

Spin chains viewed as the fermionic parts of supersymmetric quantum mechanical models

This paper shows that (anisotropic) spin chains of XY type arise by matrix representation of the fermionic terms of hamiltonians of quantum systems whose supersymmetry involves in general no more than a single hermitian supercharge. It provides some background relevant to this type of supersymmetry and makes applications to such chains including those which admit quantum groups as invariance algebras.     

\bar v_e e^ - -Annihilation and supersymmetric particles

In the framework of a minimal supersymmetric (s) extension of the standard Glashow-Weinberg-Salam theory, creation of s-partners of known leptons and gauge bosons in the -annihilation is studied. The angle distributions and total cross sections of s-particle creation are investigated in detail. The comparison with similar processes with the participation of known particles is performed. The possibility of an experimental identification of s-particles in the -annihilation is analyzed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 68–74, October, 1989.The authors thank I. M. Zheleznykh for useful discussions.     

Gauge-invariant effective lagrangians for goldstone-like particles of supersymmetric technicolor models

We point out that generally the low-energy spectrum in supersymmetric technicolor models contains quasi-Goldstone fermions and quasi-Goldstone bosons in addition to the usual (pseudo)- Goldstone bosons. Using the language of Kähler geometry, we present a step-by-step procedure for constructing gauge-invariant non-linear lagrangians involving the fermionic and bosonic Goldstone particles in situations in which supersymmetry is preserved. Both the cases of fully gauged and partially gauged global symmetries are considered. We discuss the dynamical version of the super-Higgs mechanism, and we illustrate it with the supersymmetric Susskind-Weinberg technicolor model.     

Search for supersymmetric particles in photon-electron interactions at high energy

We discuss the production of gauge fermions and scalar electrons in high energy scattering of real photons off electrons. We propose to perform scattering experiments with polarized photons to discriminate between left and right partners of electrons and thus test more stringently the supersymmetry character of these particles.     

Quantum-chromodynamic investigation of polarization effects in inclusive photoproduction of supersymmetric particles

A quantum-chromodynamic study of polarization effects in inclusive photoproduction of supersymmetric particles is reported. The two-spin asymmetries are investigated in detail as functions of transverse momentum P_T, effective scalar-pair mass Q², and scattering angle. It is shown that study of spin asymmetry can yield information on the masses of scalar quarks.M. É. Rasulzade Baku State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 120–124, June, 1995.     

Renormalization-group analysis of supersymmetric mass hierarchies

A renormalization-group analysis is performed for supersymmetric models of the O'Raifeartaigh type coupled to a Yang-Mills supermultiplet. For an appropriate range of coupling constants, we find that large mass ratios can be naturally generated by one-loop corrections to the effective potential. The results confirm Witten's recent observation that these models provide a potential solution to the gauge hierarchy problem. The general renormalization-group analysis of symmetry breaking developed in this paper is applicable in contexts other than supersymmetry. We also give a simple argument that the canonical form of the supersymmetric Ward identities can be maintained in the presence of quantum effects.     

Search for supersymmetric particles in light gravitino scenarios and sleptons NLSP

A search for sleptons, neutralinos, charginos, sgoldstinos and heavy stable charged sleptons in the context of scenarios where the lightest supersymmetric particle is the gravitino, is presented. Data collected during 2000 with the DELPHI detector at centre-of-mass energies from 204 to 208 GeV were analysed and combined with all the data collected from 1995 to 1999 at lower energies. No evidence for the production of sleptons, neutralinos and charginos has been found, therefore new limits on the mass of these supersymmetric particles and on the model parameter space are set. The search for heavy stable charged sleptons also updates the stable sleptons mass limit. The absence of evidence for sgoldstino production allows limits to be set on its mass and on the scale of supersymmetry breaking. Received: 6 November 2002 / Published online: 14 February 2003     

Photoformation of supersymmetric particles in deep inelastic scattering of photons by protons

The standard model and the E₆ model have been used to examine inclusive scalar quark photogeneration. Expressions are derived for the differential cross sections. These are related to the transverse momentum and the invariant masses of the scalar pairs.Rasulzade Baku State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 66–70, July, 1995.     

All possible lightest supersymmetric particles in R-parity violating minimal supergravity models

We investigate, which lightest supersymmetric particles can be obtained via a non-vanishing lepton- or baryon-number violating operator at the grand unification scale within the R-parity violating minimal supergravity model. We employ the full one-loop renormalization group equations. We take into account restrictions from the anomalous magnetic moment of the muon and b→sγ$b\to s\gamma$, as well as collider constraints from LEP and the Tevatron. We also consider simple deformations of minimal supergravity models.     

Light singlet particles and their cosmological consequences in witten-type supersymmetric models

In a class of supersymmetric gauge models which generate a large mass scale from a supersymmetry breaking mass scale M through loop corrections, there exists generally a very light scalar particle which transforms like a singlet under SU(3)_c × SU(2)_L with no U(1) charge. Cosmological constraints on such a particle are so severe that an upper bound is set on possible values of supersymmetry breaking scale in this class of models as M ? 500 TeV provided that the large mass scale is 10¹⁵ GeV and the mass of the light scalar particle is generated in one-loop order. This bound holds even if the goldstino is not absorbed into the gravitino.     

Spin particles at stratified media: operator approach

The operator formalism of quantum mechanics is applied to the problem of reflection and transmission of non-relativistic spin particles at stratified media. Two basic numerical methods in optics of stratified media, the matrix method of Abeles and the formalism of Airy, have been thus generalized for non-relativistic spin particles. Such an approach provides numerical solution of the problem of interaction of a spin particle in an arbitrary state with a spin-dependent one-dimensional potential. Application of the generalized Airy's formalism to neutrons in magnetically non-collinear stratified media has been considered as an example.