Towards a Two-Loop Matching of Gauge Couplings in Grand Unified Theories

Waldemar Martens

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Towards a Two-Loop Matching of Gauge Couplings in Grand Unified Theories

Waldemar Martens

High Energy Physics - Phenomenology · Submitted 12 Nov 2010

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The numerical effects in this theory are found to be larger than the current experimental uncertainty on $alpha_s$.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.78 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.16 · compares with prior results 0.27 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We calculate the two-loop matching corrections for the gauge couplings at the Grand Unification scale in a general framework that aims at making as few assumptions on the underlying Grand Unified Theory (GUT) as possible. In this paper we present an intermediate result that is general enough to be applied to the Georgi-Glashow SU(5) as a "toy model". The numerical effects in this theory are found to be larger than the current experimental uncertainty on $alpha_s$. Furthermore, we give many technical details regarding renormalization procedure, tadpole terms, gauge fixing and the treatment of group theory factors, which is useful preparative work for the extension of the calculation to supersymmetric GUTs.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We calculate the two-loop matching corrections for the gauge couplings at the Grand Unification scale in a general framework that aims at making as few assumptions on the underlying Grand Unified Theory (GUT) as possible.	contribution 0.99	0.97	0.18	asserted 1.00
s1	In this paper we present an intermediate result that is general enough to be applied to the Georgi-Glashow SU(5) as a "toy model".	contribution 0.76	0.81	0.05	asserted 0.98
s2	The numerical effects in this theory are found to be larger than the current experimental uncertainty on $alpha_s$.	result 0.91	0.94	0.34	asserted 1.00
s3	Furthermore, we give many technical details regarding renormalization procedure, tadpole terms, gauge fixing and the treatment of group theory factors, which is useful preparative work for the extension of the calculation to supersymmetric GUTs.	contribution 0.46	0.90	0.04	asserted 0.98

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.81.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We calculate the two-loop matching corrections for the gauge couplings at the Grand Unification scale in a general framework that aims at making as few assumptions on the underlying Grand Unified Theory (GUT) as possible. In this paper we present an intermediate result that is general enough to be applied to the Georgi-Glashow SU(5) as a "toy model". The numerical effects in this theory are found to be larger than the current experimental uncertainty on $alpha_s$. Furthermore, we give many technical details regarding renormalization procedure, tadpole terms, gauge fixing and the treatment of group theory factors, which is useful preparative work for the extension of the calculation to supersymmetric GUTs.

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2 arXiv papers cite this in 4 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 3 sentences without a confident label

Cites it as background 1 paper

However, at the two-loop level there are only the attempts of Refs. [ref] towards a general derivation.

Selected topics on multi-loop calculations to Higgs boson properties and renormalization group functions · Decoupling at the GUT scale · 0.91

What it cites · 19 sentences without a confident label

Uses the method or tool of 8 papers

The RGE running in the SM was implemented at two loops [ref] for the electroweak sector and at three loops [ref] for QCD.

The Standard Model Effective Potential at Two Loops · Numerical study for the Georgi-Glashow model · 0.99
The RGE running in the SM was implemented at two loops [ref] for the electroweak sector and at three loops [ref] for QCD.

The three-loop QCD $\beta$-function and anomalous dimensions · Numerical study for the Georgi-Glashow model · 0.99
These parameters are converted to six-flavor theory using RunDec [ref] and then used to compute the starting values for $y_t, y_b$ and $y_τ$ at the electroweak scale.

RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses · Numerical study for the Georgi-Glashow model · 1.00

Uses data or values from 4 papers

They are obtained from the effective weak mixing angle in the $MS$ scheme [ref] , the QED coupling constant at zero momentum transfer and its hadronic [ref] contribution in order to obtain its counterpart at the $Z$-boson scale, and the strong coupling constant [ref] .[We adopt the central value from ref.

The 2009 World Average of $\alpha_s$ · Numerical study for the Georgi-Glashow model · 1.00
They are obtained from the effective weak mixing angle in the $MS$ scheme [ref] , the QED coupling constant at zero momentum transfer and its hadronic [ref] contribution in order to obtain its counterpart at the $Z$-boson scale, and the strong coupling constant [ref] .[We adopt the central value from ref.

Update of g-2 of the muon and Delta alpha · Numerical study for the Georgi-Glashow model · 1.00
For the convenience of the reader we also specify their numerical values [ref] : [equation] The corresponding uncertainties are not important for our analysis.

Charm and Bottom Quark Masses: an Update · Numerical study for the Georgi-Glashow model · 1.00

Compares with 1 paper

We did the calculation in our framework and found agreement with the known result in the literature [ref] .

Three loop gauge beta-function for the most general single gauge-coupling theory · Renormalization · 0.98

Cites as support 1 paper

Furthermore, in GUT models that contain large representations, as for example the so-called Missing Doublet Model [ref] , the decoupling scale dependence at the GUT scale can exceed the experimental uncertainty by an order of magnitude [ref] .

Minimal Supersymmetric SU(5) and Gauge Coupling Unification at Three Loops · Introduction · 0.96

Cites as background 9 papers

Up to date most Renormalization Group (RG) analyses that study gauge coupling unification use two-loop Renormalization Group Equations (RGEs) and one-loop matching at the SUSY and GUT scales [ref] .

Not Even Decoupling Can Save Minimal Supersymmetric SU(5) · Introduction · 0.90
Up to date most Renormalization Group (RG) analyses that study gauge coupling unification use two-loop Renormalization Group Equations (RGEs) and one-loop matching at the SUSY and GUT scales [ref] .

On Unification and Nucleon Decay in Supersymmetric Grand Unified Theories Based on SU(5) · Introduction · 0.90
Up to date most Renormalization Group (RG) analyses that study gauge coupling unification use two-loop Renormalization Group Equations (RGEs) and one-loop matching at the SUSY and GUT scales [ref] .

Nucleon Decay in the Minimal Supersymmetric $SU(5)$ Grand Unification · Introduction · 0.90

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