Light gluinos and unification of couplings

Abstract

We analyze the implications of the light gluino scenario for the unification of gauge and Yukawa couplings within the minimal supersymmetric standard model. Within this scheme all fermionic supersymmetric particles are naturally light, while the scalar partners of quarks and leptons, together with the heavy Higgs doublet may be heavy. This implies both a bound on tan β < 2.3, in order to fulfill the experimental constraints on the chargino masses, and a strong correlation between sin 2 θ W (M Z ) and α 3 (M Z ), due to the suppression of the supersymmetric threshold corrections to the low energy values of the gauge couplings. Assuming the scalar sparticles to be lighter than 10 TeV, the physical top quark mass is constrained to be 145 GeV < M t < 210 GeV for tan β > 1, while the strong gauge coupling values, 0.122 ≤ α 3 (M Z ) ≤ 0.133, are in good agreement with the measured LEP ones. We also show that a relaxation of some of the conventional assumptions is necessary in order to achieve the radiative breaking of the electroweak symmetry within the grand unification scheme. * On leave from the

Low energy measurements of the strong coupling constant and the question of a light gluino

“…If, as is the case in the minimal supergravity-inspired model, the W-inos, Z-ino, and Higgsinos are also below the Z when the gluino is light, the consistency is destroyed [16] and solutions are only found for 0.122 < a 3 ( M Z ) < 0.132. Although this is not in disagreement with the LEP data of Eq.…”

Grand unification scale effects in supersymmetric unification

“…However there are some problems. First of all radiative breaking in the light gluino scenario requires a much lower physical top quark mass (124 GeV) [5,6] than Eq. (1) found in the numerical solutions.…”

“…Another potential problem in the MSSM may be emerging with regard t o the prediction for a 3 ( M Z ) In the supergravity (SUGRA) inspired MSSM with light gluinos, the solution space is restricted [5] to the narrow region (Lower values can be obtained if one in effect gives up the idea of a universal gaugino mass and puts the charginos and neutralinos other than the photino a t Ms [lo].) This 1 4 % prediction is consistent with measurements a t the Z [11,12] which however have large errors.…”

“…The system of differential equations as given, for example, in [4] then relates the following 10 parameters: (1) the unification scale Mx; (2) the unified gauge coupling a o ( M x ) ; (3) the top Yukawa at the unification scale a t ( M x ) ; (4) the SUSY scale Ms; (5) the ratio tan(,B) of the Higgs vacuum expectation values; (6) the weak angle sin2 (ow); (7) the fine-structure constant at the Z scale a ( M z ) ; (8) the strong-coupling constant at the Z scale a3(Mz); (9) the value of the top quark mass Mt; (10) the value of the b1.r mass ratio a t the b quark scale. In the L L t o p -d o~n "approach that we follow, random values are chosen for the first five parameters, the system is evolved to lower energy and solutions are stored in a file that can be queried for correlations.A "solution" is defined as a set of values for these ten parameters that is consistent with the renormalizationgroup system of differential equations and with the experimental constraintsIn the light gluino variant, the gluino slows the running of the strong-coupling constant between Ms and mb, and if, in addition, the standard supergravity-inspired model is chosen for soft SUSY breaking, the charginos and two of the neutralinos are at the Z scale [5]. In either the light or heavy gluino case, the solution space is a compact region in the ten-dimensional space defined above which can be projected onto any of its 45 planes to explore correlations between the various parameters.…”

“…In the light gluino variant, the gluino slows the running of the strong-coupling constant between Ms and mb, and if, in addition, the standard supergravity-inspired model is chosen for soft SUSY breaking, the charginos and two of the neutralinos are at the Z scale [5]. In either the light or heavy gluino case, the solution space is a compact region in the ten-dimensional space defined above which can be projected onto any of its 45 planes to explore correlations between the various parameters.…”