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Renormalization of the Neutrino Mass Operator
High Energy Physics - Phenomenology · Submitted 3 Sep 1993
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Renormalization from the scale of lepton number violation (e.g., the Planck scale or a GUT scale) to the weak scale decreases the strength of this operator by an order of magnitude or more if the top quark and Higgs boson masses are large.
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The abstract, sentence by sentence
A small neutrino Majorana mass can arise in the Standard Model as an effective dimension 5 operator. We calculate the renormalization of this operator in the minimal Standard Model and in its two-Higgs-doublet and supersymmetric extensions. Renormalization from the scale of lepton number violation (e.g., the Planck scale or a GUT scale) to the weak scale decreases the strength of this operator by an order of magnitude or more if the top quark and Higgs boson masses are large. Neutrino mixing angles also run with momentum. We show instances where small mixing at a high scale becomes large at the weak scale, and vice versa.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A small neutrino Majorana mass can arise in the Standard Model as an effective dimension 5 operator. | background 1.00 | 0.07 | 0.06 | hedged possibility 0.69 |
| s1 | We calculate the renormalization of this operator in the minimal Standard Model and in its two-Higgs-doublet and supersymmetric extensions. | contribution 0.90 | 0.95 | 0.06 | asserted 0.98 |
| s2 | Renormalization from the scale of lepton number violation (e.g., the Planck scale or a GUT scale) to the weak scale decreases the strength of this operator by an order of magnitude or more if the top quark and Higgs boson masses are large. | result 1.00 | 0.86 | 0.57 | asserted 0.87 |
| s3 | Neutrino mixing angles also run with momentum. | result 0.97 | 0.59 | 0.07 | asserted 1.00 |
| s4 | We show instances where small mixing at a high scale becomes large at the weak scale, and vice versa. | result 0.96 | 0.93 | 0.17 | asserted 1.00 |
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The paper
Original abstract
A small neutrino Majorana mass can arise in the Standard Model as an effective dimension 5 operator. We calculate the renormalization of this operator in the minimal Standard Model and in its two-Higgs-doublet and supersymmetric extensions. Renormalization from the scale of lepton number violation (e.g., the Planck scale or a GUT scale) to the weak scale decreases the strength of this operator by an order of magnitude or more if the top quark and Higgs boson masses are large. Neutrino mixing angles also run with momentum. We show instances where small mixing at a high scale becomes large at the weak scale, and vice versa.
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References
How the literature uses it
59 arXiv papers cite this in 86 sentences
Papers citing it · 47 sentences without a confident label
Uses its method or tool 7 papers
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The seesaw model matched onto $c_α β^(5)(μ^2 = M^2)$ is compared to the values of masses and mixing angles extracted at $μ= m̂_Z$ after running the seesaw parameters with one loop RGE evolution of the Weinberg operator.[Here a hat superscript indicates a experimentally measured quantity.] The RGEs of the $c_5$ coefficient are extracted from Refs. [ref] .
Examining the neutrino option · Neutrino parameter running · 0.96
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$2(ℓ_ ϵH_1^*) (ℓ^c_ϵH_2^*)$ $+(ℓ_ϵℓ^c_) (H_1^* ϵH_2^*)$ using the identity ([ref]), as done in the first reference of [ref] . .
Majorana Neutrino Masses in the RGEs for Lepton Flavour Violation · In the case of the 2HDM · 0.91
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Taking this new found liberative message at face value, and the difficulties of the NMSGUT with $d,s$ quark masses as a signal from the model of its character and inner necessity, we have used the diagonal threshold correction formulae to match the down and charged fermion masses to the rather low values found by our ”downhill simplex” based search and fitting program (after running them down from $M_X$ using the full two loop equations of [ref] to $M_S$); we also include running of the Weinberg operator [ref] .
The New Minimal Supersymmetric GUT : Spectra, RG analysis and Fermion Fits · Introduction · 0.91
Uses its data or values 1 paper
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The coefficients $C_e$ are $C_e=-3/2$ in the SM [ref] and two-Higgs models [ref] , and $C_e=1$ in the MSSM [ref] .
Modular invariant holomorphic observables · Renormalization-group invariant expressions · 0.98
Compares with it 1 paper
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Finally, from the 1/$ε$ terms in $δC^(1)_5$ and $δC^(2)_5$, and using Eq. [ref], we obtain the one- and two-loop contributions to the RGE of $C^_5$: [equation] Our one-loop result is consistent with Refs. [ref] including the correction pointed out in Ref. [ref] .
Complete Two-loop Renormalization Group Equation of the Weinberg Operator · Complete Two-loop RGE of the Weinberg Operator · 1.00
Cites it as support 2 papers
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The mixing of neutrinos is also negligibly affected by RG running since the neutrino masses at the $T^'$ scale are not sufficiently degenerate to enhance mixing [ref] .
A Viable Randall-Sundrum Model for Quarks and Leptons with T' Family Symmetry · Results · 0.96
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Further, we disregard the RGE effects in the running of neutrino parameters as they are known to yield insignificant deviations [ref] .
Unravelling the Scalar Sector of Grand Unification: Phenomenology & Implications · Full Three Generations Analysis · 0.97
Cites it as background 25 papers
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The renormalisation group running of the dimension-five operators has been extensively studied in the literature [ref] , and the mixing of the dimension-six operators among themselves have been evaluated at one-loop [ref] in the “Warsaw”-basis [ref] of SMEFT operators.
Majorana Neutrino Masses in the RGEs for Lepton Flavour Violation · Introduction · 0.85
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The matching and running of physical parameters in the type-I seesaw model have been extensively studied in the literature [ref]
The Smallest Neutrino Mass Revisited · One-loop Matching · 0.97
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The RG equations (RGEs) for the Weinberg operator [ref] , which describes Majorana neutrino masses in SM effective field theory (SMEFT), have been calculated at 1-loop order in [ref] and recently at 2-loop order in [ref] ; phenomenological implications have been studied in [ref] .
Running of neutrino mass parameters in the Zee model · Introduction · 0.98
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