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Two-loop parameter relations between dimensional regularization and dimensional reduction applied to SUSY-QCD
High Energy Physics - Phenomenology · Submitted 24 Aug 2009
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This result confirms the equivalence of the two schemes through three-loops, if applied to SUSY-QCD.
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The abstract, sentence by sentence
The two-loop relations between the running gluino-quark-squark coupling, the gluino and the quark mass defined in dimensional regularization (DREG) and dimensional reduction (DRED) in the framework of SUSY-QCD are presented. Furthermore, we verify with the help of these relations that the three-loop beta-functions derived in the minimal subtraction scheme combined with DREG or DRED transform into each other. This result confirms the equivalence of the two schemes through three-loops, if applied to SUSY-QCD.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The two-loop relations between the running gluino-quark-squark coupling, the gluino and the quark mass defined in dimensional regularization (DREG) and dimensional reduction (DRED) in the framework of SUSY-QCD are presented. | contribution 0.65 | 0.90 | 0.21 | asserted 1.00 |
| s1 | Furthermore, we verify with the help of these relations that the three-loop beta-functions derived in the minimal subtraction scheme combined with DREG or DRED transform into each other. | result 0.76 | 0.90 | 0.12 | asserted 0.99 |
| s2 | This result confirms the equivalence of the two schemes through three-loops, if applied to SUSY-QCD. | interpretation 0.98 | 0.74 | 0.80 | asserted 0.95 |
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The paper
Original abstract
The two-loop relations between the running gluino-quark-squark coupling, the gluino and the quark mass defined in dimensional regularization (DREG) and dimensional reduction (DRED) in the framework of SUSY-QCD are presented. Furthermore, we verify with the help of these relations that the three-loop beta-functions derived in the minimal subtraction scheme combined with DREG or DRED transform into each other. This result confirms the equivalence of the two schemes through three-loops, if applied to SUSY-QCD.
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How the literature uses it
8 arXiv papers cite this in 10 sentences
Papers citing it · 8 sentences without a confident label
Uses its method or tool 2 papers
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We employed the one-loop conversion relations [ref] for all parameters except $α_3$ and $m_b$ where two-loop relations [ref] have been used in order to be consistent with the decoupling at the SUSY scale.
Minimal Supersymmetric SU(5) and Gauge Coupling Unification at Three Loops · Running and decoupling · 0.95
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To establish the conversion relations between the running parameters in the two schemes, one can use the method discussed in section [ref], where such relations have been derived in the context of non-supersymmetric theories.[For more details see Ref. [ref] .] The conversion relations that are of interest for the numerical analysis discussed in this section are those involving the gauge couplings and the quark masses of the third generation, as only their Yukawa couplings give sizable effects.
Precision Calculations in Supersymmetric Theories · Gauge coupling unification in the minimal SUSY SU(5) model · 0.88
What it cites · 33 sentences without a confident label
Uses the method or tool of 5 papers
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We adopted here the prescription introduced in Ref [ref] .
The SUSY-QCD beta function to three loops · Three-loop renormalization group functions in DREG · 1.00
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For the computation of the translation relations between the and schemes we employed a simpler computation method [ref] .
Dimensional Reduction applied to QCD at three loops · Running coupling constants · 0.99
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We did the calculation for vanishing external momenta and regularized the infrared divergences giving a common mass to all particles [ref] .
Beta functions and anomalous dimensions up to three loops · Three-loop renormalization group functions in DREG · 0.97
Compares with 3 papers
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As a by-product result we reconfirm the two-loop conversion relation derived in [ref] .
Two-loop matching coefficients for the strong coupling in the MSSM · Introduction · 0.83
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For the gluino mass anomalous dimension we obtain [equation] It is an easy exercise to verify that the three-loop mass anomalous dimensions given above differ from the ones computed in scheme [ref] only by the finite shifts for coupling constants and masses discussed in Section [ref].
The SUSY-QCD beta function to three loops · Three-loop fermion mass anomalous dimensions in · 1.00
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For the gluino mass anomalous dimension we obtain [equation] It is an easy exercise to verify that the three-loop mass anomalous dimensions given above differ from the ones computed in scheme [ref] only by the finite shifts for coupling constants and masses discussed in Section [ref].
$N=1$ supersymmetry and the three loop anomalous dimension for the chiral superfield · Three-loop fermion mass anomalous dimensions in · 1.00
Cites as support 1 paper
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This can be understood from the fact that they are proportional to the corresponding one-loop effective charges, which have been shown to be equal [ref] , and the proportionality factors are universal quantities equal for gluon and gluinos in a supersymmetric theory.
SUSY-QCD Decays of Squarks and Gluinos · Running coupling constants · 0.97
Cites as background 8 papers
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In the framework of QCD, the translation rules for the change from to is known up to three loops for the strong coupling constant and the quark masses [ref] .
Four-loop beta function and mass anomalous dimension in Dimensional Reduction · Introduction · 0.84
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In the framework of QCD, the translation rules for the change from to is known up to three loops for the strong coupling constant and the quark masses [ref] .
Dimensional Reduction applied to QCD at three loops · Introduction · 0.84
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In the scheme, the anomalous dimensions of all SM parameters are known up to two-loop level [ref] , while for QCD even the four-loop order results are available [ref] .
Quark Mass Anomalous Dimension to alpha_s**4 · Three-loop renormalization group functions in DREG · 0.84
Discussion
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