We study the process $e^-e^+to gamma H$, where $H$ represents $H_{SM}$, $h^0$ or $H^0$, which occurs at the one loop level in the standard model (SM) or in the minimal supersymmetric standard model (MSSM). We establish supersimple (sim) high energy e
xpressions for all helicity amplitudes of this process, and we identify their level of accuracy for describing the various polarized and unpolarized observables, and for distinguishing SM from MSSM or another beyond the standard model (BSM). We pay a special attention to transverse electron-positron polarizations and azimuthal dependencies induced by the imaginary parts of the amplitudes, which are relatively important in this process.
We study the process $e^-e^+to ZH$ where $H$ represents the standard model (SM) Higgs particle $H_{SM}$, or the MSSM ones $h^0$ and $H^0$. In each case, we compute the one-loop effects and establish very simple expressions, called supersimple (sim),
for the helicity conserving (dominant) and the helicity violating (suppressed) amplitudes. Such expressions, are then used to construct various cross sections and asymmetries, involving polarized or unpolarized beams and Z-polarization measurements. We examine the adequacy of such expressions to distinguish SM or MSSM effects, from other types of BSM (beyond the standard model) contributions.
In previous work, we have established that for any 2-to-2 process in MSSM, only the helicity conserving (HC) amplitudes survive asymptotically. Studying a large number of such processes, at the 1loop Electroweak (EW) order, it is now found that their
high energy HC amplitudes are determined by just three forms: a log-squared function of the ratio of two of the (s,t,u) variables, to which a pi^2 is added; and two Sudakov-like ln- and ln^2-terms accompanied by respective mass-dependent constants. Apart from an additional residual constant, all high energy HC amplitudes, may be expressed as linear combinations of the above three forms, with coefficients being rational functions of the $(s,t,u)$ variables. We call this fact supersimplicity. Applying to the $ugto dW$ amplitudes, for which the complete 1loop expressions are available, we find that supersimplicity may be a very good approximation at LHC energies, provided the SUSY scale is not too high. SM processes are also discussed, and their differences are explored.
According to the helicity conservation (HCns) theorem, the sum of the helicities should be conserved, in any 2-to-2 processes in MSSM with R-parity conservation, at high energies; i.e. all amplitudes violating this rule, must vanish asymptotically. T
he realization of HCns in gluon-fusion to charginos or neutralinos is studied, at the one loop electroweak order (EW), and simple high energy expressions are derived for the non-vanishing helicity conserving (HC) amplitudes. These are very similar to the corresponding expressions for $gg to W^+W^-, ZZ, gamma Z, gammagamma $ derived before. Asymptotic relations among observable unpolarized cross sections for many such processes are then obtained, some of which may hold at LHC-type energies.
We study how the property of asymptotic helicity conservation (HCns), expected for any 2-to-2 process in the minimal supersymmetric model (MSSM), is realized in the processes $gg to gammagamma,gamma Z,ZZ,W^+W^-$, at the 1loop electroweak order and ve
ry high energies. The violation of this property for the same process in the standard model (SM), is also shown. This strengthens the claim that HCns is specific to the renormalizable SUSY model, and not generally valid in SM. HCns strongly reduces the number of non-vanishing 2-to-2 amplitudes at asymptotic energies in MSSM. Consequences at LHC and higher energy colliders are identified.
We summarize the extensive work started in ref.1, according to which total helicity is conserved for any two-to-two process, at sqrt{s} larger than M_{SUSY} and fixed angles, in any SUSY extension of SM. Asymptotically the theorem is exact. But it ma
y also have important implications at lower energies sqrt{s} close to M_{SUSY}. Up to now, these have been investigated to 1loop electroweak (EW) order for the processes ug to d W+, sd_L chi+; as well as the 17 gg to HH, and the 9 gg to VH processes, where H,H denote Higgs or Goldstone bosons, and V=Z, W.
Within the MSSM and SM frameworks, we analyze the 1loop electroweak (EW) predictions for the helicity amplitudes describing the 17 processes $ggto HH$, and the 9 processes $ggto VH$; where $H,H$ denote Higgs or Goldstone bosons, while $V= Z, ~W^pm$.
Concentrating on MSSM, we then investigate how the asymptotic helicity conservation (HCns) property of SUSY, affects the amplitudes at the LHC energy range; and what is the corresponding situation in SM, where no HCns theorem exists. HCns is subsequently used to construct many relations among the cross sections of the above MSSM processes, depending only on the angles $alpha$ and $beta$. These relations should be asymptotically exact, but with mass-depending deviations appearing, as the energy decreases towards the LHC range. Provided the SUSY scale is not too high, they may remain roughly correct, even at the LHC energy range.
We write explicit and self-contained asymptotic expressions for the tensorial B, C and D Passarino-Veltman functions. These include quadratic and linear logarithmic terms, as well as subleading constant terms. Only mass-suppressed O(m^2/s) contributi
ons are neglected. We discuss the usefulness of such expressions, particularly for studying one-loop effects in 2-to-2 body processes at high energy.
We analyze the quark-gluon induced process $u gto tilde dtchi_i^+$, including the one loop electroweak (EW) effects in the minimal supersymmetric model (MSSM). This process is determined by four helicity amplitudes, three of which are violating helic
ity conservation, and another one which respects it and is logarithmically enhanced at high energy. Combining this $u gto tilde dtchi_i^+$ analysis with a corresponding one for $u g to d W^+$, we obtain simple approximate relations between the two processes, testing the MSSM structure at the amplitude and the cross section levels. These relations become exact at asymptotic energies and, provided the SUSY scale is not too heavy, they may be approximately correct at LHC energies also. In addition to these, we study the 1loop EW corrections to the inclusive $tilde dtchi_i^+$ production at LHC, presenting as examples, the $p_T$ and angular distributions. Comparing these to the corresponding predictions for $W$+jet production derived earlier, provides an accurate test of the supersymmetric assignments.
We present a complete 1-loop study of the electroweak corrections to the process $ugto dW^+$ in MSSM and SM. The occurrence of a number of remarkable properties in the behavior of the helicity amplitudes at high energies is stressed, and the crucia
l role of the virtual SUSY contributions in establishing them, is emphasized. The approach to asymptopia of these amplitudes is discussed, comparing the effects of the logarithmic and constant contributions to the mass suppressed ones, which are relevant at lower energies. Applying crossing to $ugto d W^+$, we obtain all subprocesses needed for the 1-loop electroweak corrections to $W^pm$-production at LHC. The SUSY model dependence of such a production is then studied, and illustrations are given for the transverse $W^{pm}$ momentum distribution, as well as the angular distribution in the subprocess center of mass.
