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Robert Harlander:
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Brookhaven
Supersymmetry at higher orders
↳Supersymmetry (SUSY) is one of the prime
candidates for the theory beyond the ↳Standard
Model. It solves some of the most severe problems of the Standard
Model, above all the socalled
↳finetuning problem.
Higgs mass in Supersymmetry The ↳Minimal Supersymmetric
extension of the Standard Model (MSSM) contains five physical ↳Higgs bosons whose masses are determined by
only two SUSY parameters at lowest order in ↳perturbation theory. Radiative
corrections soften this constraint and lead to relations among the Higgs
boson masses and other SUSY parameters. Therefore, a precise measurement of
one or more of these masses allows for stringent tests of the MSSM. We have
calculated the lightest Higgs boson mass at threeloop level as a function
of the other SUSY parameters [5], [7]. To our knowledge, this is the
first observable which is known to this order in SUSY.
Matching conditions for the strong coupling constant SUSY exhibits
the remarkable feature of socalled ↳gauge coupling unification.
This means that the three (energy dependent) gauge couplings of the strong,
the weak, and the electromagnetic interaction are equal at one particular
energy value M_{GUT}. However, this value is about a trillion
times larger than what will be achieved at the ↳Large Hadron Collider.
Nevertheless, assuming that the SUSY parameters are known, one can predict
the value of this unification energy very precisely. On the other hand, the
requirement of unification allows one to restrict the parameter space of
supersymmetry. The energydependence of the coupling constants is
determined by ↳renormalization
group equations and threshold matching conditions. In Ref. [1], we evaluated the matching
conditions for the strong coupling at twoloop level, while the threeloop
beta function was calculated in 6 (see also [ref]).
This provides the most precise prediction of M_{GUT}.
Similar relations hold for the quark masses. In Ref. [4], we evaluated the energy
dependence of the strong coupling and the bottom quark mass in the MSSM at
threeloop level.
Dimensional Reduction As is the case for any field theory in
general, quantum effects in SUSY lead to divergences which need to be
regularized. In a nonsupersymmetric theory, this can be done most
efficiently by working in a Ddimensional spacetime at intermediate
steps of the calculation, and letting D→4 at the end. This
procedure is called ↳Dimensional Regularization (DREG). However, since
altering the number of spacetime dimensions from 4 to D leads to a
mismatch between the fermionic and the bosonic degrees of freedom, DREG
breaks supersymmetry explicitely. For this reason, an alternative method
to DREG has been suggested long ago, so called Dimensional Reduction
(DRED) [ref].
Conversion formulas between the DRED and the DREG scheme have been evaluated
at twoloop order in Ref. [2],
and at threeloop order in Ref. [3].
Journal articles:
[7] 
P. Kant, R.V. Harlander, L. Mihaila, M. Steinhauser 
 Light MSSM Higgs boson mass to threeloop accuracy


JHEP 08 (2010) 104 [arXiv:1005.5709] 

additional material available at this URL 

[6] 
R.V. Harlander, L. Mihaila, M. Steinhauser 
 The SUSYQCD beta function to three loops


Eur. Phys. J. C 63 (2009) 383 [arXiv:0905.4807] 

additional material available at this URL 

[5] 
R.V. Harlander, P. Kant, L. Mihaila, M. Steinhauser 
 Higgs boson mass in supersymmetry to three loops


Phys. Rev. Lett. 100 (2008) 191602 [arXiv:0803.0672] 

erratum: ibid. 101 (2008) 039901 

[4] 
R. Harlander, L. Mihaila, M. Steinhauser 
 Running of alpha_s and m_b in the MSSM


Phys. Rev. D 76 (2007) 055002 [arXiv:0706.2953] 



[3] 
R.V. Harlander, D.R.T. Jones, P. Kant, L. Mihaila,
M. Steinhauser 
 Fourloop beta function and mass anomalous dimension
in Dimensional Reduction 

JHEP 12 (2006) 024 [hepph/0610206]




[2] 
R. Harlander, P. Kant, L. Mihaila, M. Steinhauser 
 Dimensional reduction applied to QCD at three loops 

JHEP 09 (2006) 053 [hepph/0607240]




[1] 
R. Harlander, L. Mihaila and M. Steinhauser 
 Twoloop matching coefficients for the strong coupling in the MSSM 

Phys. Rev. D 72 (2005) 095009 [hepph/0509048]




Proceedings contributions:
