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毕业于985学校的汽车工程专业，毕业后一直从事汽车工程技术研究

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    188宝金博页面版: Neutrino mass operator renormalization revisited(中微子质量算子重归一化)

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    内容提示： 1 November 2001Physics Letters B 519 (2001) 238–242www.elsevier.com/locate/npeNeutrino mass operator renormalization revisitedStefan Antusch, Manuel Drees, J?rn Kersten, Manfred Lindner, Michael RatzPhysik-Department T30, Technische Universit?t München, James-Franck-Stra?e, 85748 Garching, GermanyReceived 2 August 2001; accepted 15 September 2001Editor: P.V. LandshoffAbstractWe re-derive the renormalization group equation for the effective coupling of the dimension f i ve operator which correspondsto ...

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    1 November 2001Physics Letters B 519 (2001) 238–242www.elsevier.com/locate/npeNeutrino mass operator renormalization revisitedStefan Antusch, Manuel Drees, Jörn Kersten, Manfred Lindner, Michael RatzPhysik-Department T30, Technische Universität München, James-Franck-Straße, 85748 Garching, GermanyReceived 2 August 2001; accepted 15 September 2001Editor: P.V. LandshoffAbstractWe re-derive the renormalization group equation for the effective coupling of the dimension f i ve operator which correspondsto a Majorana mass matrix for the Standard Model neutrinos. We f i nd a result which differs somewhat from earlier calculations,leading to modif i cations in the evolution of leptonic mixing angles and CP phases. We also present a general method forcalculating β-functions from counterterms in MS-like renormalization schemes, which works for tensorial quantities.PACS: 11.10.Gh; 11.10.Hi; 14.60.PqKeywords: Renormalization group equation; Beta-function; Neutrino mass1. IntroductionThe Standard Model (SM) is most likely an effec-tive theory up to some scale Λ, above which newphysics has to be taken into account. The discoveryof neutrino masses requires an extension of the SM,which may involve right-handed neutrinos or othernew f i elds. Introducing right-handed neutrinos allowsDirac masses m D via Yukawa couplings analogous tothe quark sector. In general, lepton number need notbe conserved, so that Majorana masses are possible.For left-handed neutrinos this can, for example, beachieved with Higgs triplets. Right-handed neutrinoscan have explicit Majorana masses M R of order Λ,since they are gauge singlets and since there are noprotective symmetries. This leads to a picture withzero or tiny left-handed Majorana masses M L , withE-mail addresses: santusch@ph.tum.de (S. Antusch),drees@ph.tum.de (M. Drees), jkersten@ph.tum.de (J. Kersten),lindner@ph.tum.de (M. Lindner), mratz@ph.tum.de (M. Ratz).m D similar to the charged lepton masses, and with ahuge M R . Diagonalizationof the neutrinomass matrixresults in Majorana fermions and eigenvalues ? M Rand M L − m 2D /M R . For M L= 0 the neutrino massesare thus given by the see-saw relation m 2D /M R[1],whichprovidesaconvincingexplanationforthesmall-ness of neutrino masses.Another, less model dependent approach is to studythe effective f i eld theory with higher-dimensionaloperators of SM f i elds. If lepton number is notconserved, some of these generate Majorana neutrinomasses. The lowest-dimensional operator of this kindhasdimension5andcouplestwoleptonandtwoHiggsdoublets.It appears,e.g.,inthe see-saw mechanismbyintegrating out the heavy right-handed neutrinos.As quarks have only small mixings, it is somewhatsurprising that neutrinos most likely have two largemixing angles [2–4]. It is interesting to investigatemechanisms which can produce such large or max-imal mixings. These mechanisms operate, however,typically at the embedding scale Λ. For a compari-PII: S0370-2693(01)01127-3? 2001 Elsevier Science B.V. Open access under CC BY license.? 2001 Elsevier Science B.V. Open access under CC BY license. 0370-2693/01/

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