{"arxiv_id":"hep-ph/0305273","incoming":{"papers":57,"sentences":102,"groups":[{"kind":"extends","label":"Builds on it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2302.08140","title":"Complete One-loop Renormalization-group Equations in the Seesaw Effective Field Theories","url":"/paper/2302.08140","section":"Introduction","sentence":"As a practical application of these one-loop RGEs, we take the type-I SEFT for example and further derive the explicit expressions of the one-loop RGEs for the physical parameters involved in the charged- and neutral-current interactions of leptons, like those done for the type-I SEFT with only the Weinberg operator [ref] .","intent_p":0.96,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":8,"sentences":9,"quotes":[{"arxiv_id":"1912.11517","title":"Breaking of the tetra-maximal neutrino mixing pattern","url":"/paper/1912.11517","section":"Spontaneous Breaking of TMM","sentence":"Considering the leading order approximation, we write down the renormalization group equations for leptonic mixing angles in the MSSM [ref] as","intent_p":0.84,"contests_p":null},{"arxiv_id":"1005.0708","title":"Measurable Neutrino Mass Scale in A4 x SU(5)","url":"/paper/1005.0708","section":"Renormalisation Group Corrections","sentence":"Setting the small Majorana phases to zero and with $δ_MNS ≈90^∘$, we can estimate in leading order [ref] [equation] where $μ$ is the renormalisation scale.","intent_p":0.82,"contests_p":null},{"arxiv_id":"2312.08357","title":"Leptogenesis in the minimal flipped $SU(5)$ unification","url":"/paper/2312.08357","section":"Experimental inputs","sentence":"According to [ref] , the mass effects may be to a good degree approximated by universal multiplicative factors, e.g., [equation] where the hat denotes seesaw-scale quantities, see Section [ref].","intent_p":0.93,"contests_p":null},{"arxiv_id":"0912.3427","title":"Running effects on neutrino parameters and l_i -> l_j gamma predictions in the triplet-extended MSSM","url":"/paper/0912.3427","section":"Running of the neutrino masses and mixing matrix","sentence":"To obtain the RGE for $U$, we adopt the procedure first introduced in Ref. [ref] for the renormalisation of the Cabbibo-Kobayashi-Maskawa mixing matrix, and later used for the neutrino case [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1104.2448","title":"Neutrino mass hierarchy and the origin of leptonic flavor mixing from the right-handed sector","url":"/paper/1104.2448","section":"Numerical analysis","sentence":"For the accepted points, the second step consists of calculating the mixing angles [ref] .","intent_p":0.93,"contests_p":null}]},{"kind":"data_used","label":"Uses its data or values","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2312.08357","title":"Leptogenesis in the minimal flipped $SU(5)$ unification","url":"/paper/2312.08357","section":"The seesaw","sentence":"This evolution effect will be, in the first approximation, accounted for by a simple multiplication of their low-scale values ($m_i$) by a common $r$-factor, i.e., [equation] where $r ∼1.32$ (cf. Ref. [ref] and Appendix [ref]).","intent_p":0.91,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":3,"sentences":3,"quotes":[{"arxiv_id":"0812.2776","title":"Renormalization group evolution of neutrino masses and mixing in the Type-III seesaw mechanism","url":"/paper/0812.2776","section":"Illustrative examples of RG running of masses and mixing","sentence":"As can be observed, the running of masses is quite substantial in Type-III seesaw, as compared to the SM, the MSSM [ref] , or the Type-I seesaw [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"0912.3427","title":"Running effects on neutrino parameters and l_i -> l_j gamma predictions in the triplet-extended MSSM","url":"/paper/0912.3427","section":"RGEs for the neutrino masses, mixing angles and CP-violating phases","sentence":"Not surprisingly, the results for $θ̇_ij^ν$ agree with those obtained for the MSSM in Ref. [ref] .","intent_p":0.97,"contests_p":null},{"arxiv_id":"1912.13508","title":"Majorana phases in high-scale mixings unification hypotheses","url":"/paper/1912.13508","section":"Summary and Outlook","sentence":"We made full parameter scan via the RG evolution of the Majorana neutrinos with non-zero Majorana phases and show the correlations between the Majorana phases and “neutrino less double beta decay mass” $m_e e$ to be different compared to previous analyses [ref] where a few data points at unification scale were used.","intent_p":0.92,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":4,"sentences":5,"quotes":[{"arxiv_id":"2310.04077","title":"Neutrino CP Measurement in the Presence of RG Running with Mismatched Momentum Transfers","url":"/paper/2310.04077","section":"Vacuum Oscillation with RG Running and Zero-Distance Effect","sentence":"However, since the neutrino mass receives negligible RG running effect [ref] , the neutrino mass eigen-fields can be treated universally during the whole process.","intent_p":0.98,"contests_p":null},{"arxiv_id":"1407.2913","title":"Order and Anarchy hand in hand in 5D SO(10)","url":"/paper/1407.2913","section":"Fitting the fermion mass spectrum: a viability test","sentence":"For such a hierarchical neutrino spectrum, the RGE running in the neutrino parameters can be considered negligible to a good approximation [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"1612.09049","title":"Analysis of right-handed Majorana neutrino mass in an $SU(4) \\times SU(2)_{L} \\times SU(2)_{R}$ Pati--Salam model with democratic texture","url":"/paper/1612.09049","section":"Analysis of the right-handed Majorana neutrino mass matrix","sentence":"The renormalization of the neutrino mass can be neglected for the normal hierarchy case [ref] .","intent_p":0.97,"contests_p":null},{"arxiv_id":"1005.1938","title":"Renormalization group evolution of neutrino masses and mixing in seesaw models: A review","url":"/paper/1005.1938","section":"RG evolution of the light neutrino masses","sentence":"Thus in such cases, the running is given by a common scaling of the mass eigenvalues [ref] and can be given by m_i ≈m_i^0 exp[∫_t_0^t α_ν(t^') dt^'] .","intent_p":0.96,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":16,"sentences":19,"quotes":[{"arxiv_id":"2411.18251","title":"Testing the RG Running of the Leptonic Dirac CP Phase with Reactor Neutrinos","url":"/paper/2411.18251","section":"Introduction","sentence":"RG Running and Zero-Distance Effect – In the presence of RG running, the Dirac CP phase $δ_D$ can possess scale dependence parametrized by its $β$ function [ref] , as follows: [equation] where $μ^2$ is the renormalization scale.","intent_p":0.96,"contests_p":null},{"arxiv_id":"0911.3037","title":"Running Effects on Lepton Mixing Angles in Flavour Models with Type I Seesaw","url":"/paper/0911.3037","section":"Flavour symmetries and RGE effects","sentence":"The analysis of how $U_PMNS$ changes with the RG running has already extensively performed [ref] in the context of SM and MSSM.","intent_p":0.96,"contests_p":null},{"arxiv_id":"2512.17235","title":"Running of neutrino mass parameters in the Zee model","url":"/paper/2512.17235","section":"Introduction","sentence":"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] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"1011.5306","title":"Renormalization Group Running of Lepton Mixing Parameters in See-Saw Models with $S_4$ Flavor Symmetry","url":"/paper/1011.5306","section":"RG running effects in $S_4$ flavor models","sentence":"We note that the approximate analytical solutions based on leading log approximation to the RG equations have been derived in Refs. [ref] , which allows one to understand the generic behavior of the renormalization effects.","intent_p":0.85,"contests_p":null},{"arxiv_id":"2005.12277","title":"Probing Lepton Flavor Models at Future Neutrino Experiments","url":"/paper/2005.12277","section":"Lepton Flavor Models","sentence":"In the SM and its minimal supersymmetric extension (MSSM), augmented with either the Weinberg dimension-5 operator or heavy electroweak singlet neutrinos to generate the small neutrino masses, the RG evolution of the leptonic mixing parameters is known [ref] (for a review, see Ref. [ref] ).","intent_p":0.85,"contests_p":null}]}],"unlabelled_sentences":64},"outgoing":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. 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A paper with fewer citing papers gets a line counted by code, which names uses only: a later paper whose only label is a contest is counted as not described.","line":null,"summary":"4 later papers by other authors are listed below: 4 used its method or tool. 1 more paper by the same authors is listed: 1 used its method or tool."},"_links":{"html":"https://pith.science/paper/hep-ph/0305273"}}