Supersymmetry Parameter Analysis: SPA Convention andProject Page: 3 of 19
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J.A. Aguilar-Saavedra et al.
At future colliders, experiments can be performed in
the supersymmetric particle sector [1 4], if realized in
Nature, with very high precision. While the Large Ha-
dron Collider LHC can provide us with a set of well-
determined observables [5,6], in particular masses of
colored particles and precise mass differences of var-
ious particle combinations, experiments at the Inter-
national e+e Linear Collider ILC [7 9] offer high-
precision determination of the non-colored supersym-
metry sector. Combining the information from LHC on
the generally heavy colored particles with the informa-
tion from ILC on the generally lighter non-colored par-
ticle sector (and later from the Compact Linear Col-
lider CLIC  on heavier states) will generate a com-
prehensive high-precision picture of supersymmetry at
the TeV scale . Such an analysis can be performed
independently of specific model assumptions and for
any supersymmetric scenario that can be tested in lab-
oratory experiments. It may subsequently serve as a
solid base for the reconstruction of the fundamental su-
persymmetric theory at a high scale, potentially close
to the Planck scale, and for the analysis of the micro-
scopic mechanism of supersymmetry breaking [12,13].
The analyses will be based on experimental accura-
cies expected at the percent down to the per-mil level
[9,14]. These experimental accuracies must be matched
on the theoretical side. This demands a well-defined
framework for the calculational schemes in perturba-
tion theory as well as for the input parameters. The
proposed Supersymmetry Parameter Analysis Conven-
tion (SPA) [Sect.2] provides a clear base for calculating
masses, mixings, decay widths and production cross
sections. They will serve to extract the fundamental
supersymmetric Lagrangian parameters and the super-
symmetry-breaking parameters from future data. In
addition, the renormalization group techniques must
be developed for all the scenarios to determine the
high-scale parameters of the supersymmetric theory
and its microscopic breaking mechanism.
By constructing such a coherent and unified basis,
the comparison between results from different calcula-
tions can be streamlined, eliminating ambiguous pro-
cedures and reducing confusion to a minimum when
A program repository [Sect.3] has therefore been
built in which a series of programs has been collected
that will be expanded continuously in the future. The
programs relate parameters defined in different schemes
with each other, e.g. pole masses with DR masses, and
they calculate decay widths and cross sections from the
basic Lagrangian parameters. An additional set of pro-
grams predicts the values of high-precision low-energy
observables of Standard Model (SM) particles in su-
persymmetric theories. The program repository also
includes global fit programs by which the entire set
of Lagrangian parameters, incorporating higher-order
corrections, can be extracted from the experimental
observables. In addition, the solutions of the renormal-
ization group equations are included by which extrapo-
lations from the laboratory energies to the Grand Uni-
fication (GUT) and Planck scales can be performed
and vice versa. Another category contains programs
which relate the supersymmetry (SUSY) parameters
with the predictions of cold dark matter in the uni-
verse and the corresponding cross sections for search
experiments of cold dark matter (CDM) particles.
It is strongly recommended that the programs avail-
able in the repository adopt the structure of Ref. 
for the Lagrangian, including flavor mixing and CP
phases, and follow the generally accepted Supersym-
metry Les Houches Accord, SLHA, for communication
between different programs . For definiteness, we
reproduce from  the superpotential (omitting R-
parity violating terms), in terms of superfields,
W =ab (YE)ujHi j + (YD)ijH Q j
+ (YU)2jfIQ"Uj - Hp tf]
where the chiral superfields of the Minimal Supersym-
metric Standard Model (MSSM) have the following
SU(3)c & SU(2)L & U(1)y quantum numbers
L : (1, 2, -), E : (1, 1, 1), Q : (3, 2, ), U : (3, 1, -3)
D) : (3, 1, 1), Hd : (1, 2, - ), Hw : (1, 2, z).
The indices of the SU(2)L fundamental representation
are denoted by a, b 1, 2 and the generation indices by
i, j 1, 2, 3. Color indices are everywhere suppressed,
since only trivial contractions are involved. Eab is the
totally antisymmetric tensor, with E12 12 1.
The soft SUSY breaking part is written as
-Lsoft Eab (TE)ijHd47LxE + (TD)1jHaSbtdjR
+(TU)2jHtQ"U R] + h.c.
+fmlaHj~aH + mI H* Hf- (min3abH HnH +h.c.)
+ Qra(n )jQjL + L4*L(T)jiL7
+ ,2R (mnJ1/iJ> + d1R (mitnk d> + CI(Tn-)
+ - M1bb + M2zbAzbA + M3jxI + h.c.,
where the H2 are the scalar Higgs fields, the fields with
a tilde are the scalar components of the superfield with
the identical capital letter; the bino is denoted as b,
the unbroken SU(2)L gauginos as mA= 1,2,3, and the
gluinos as Xl .8, in 2-component notation. The T
matrices will be decomposed as T2p A2jY4, where Y
are the Yukawa matrices and A the soft supersymmetry
breaking trilinear couplings.
Much work on both the theoretical and the exper-
imental side is still needed before data could be eval-
uated in the future at the desired level of accuracy.
These tasks of the SPA Project will be defined in de-
tail in Sect.4.
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Aguilar-Saavedra, J.A.; Ali, A.; Allanach, B.C.; Arnowitt, R.; Baer, H.A.; Bagger, J.A. et al. Supersymmetry Parameter Analysis: SPA Convention andProject, article, December 2, 2005; [Menlo Park, California]. (https://digital.library.unt.edu/ark:/67531/metadc876418/m1/3/: accessed March 25, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.