Deviations of the lepton mapping matrix from the Harrison-Perkins-Scott form

  • We propose a simple set of hypotheses governing the deviations of the leptonic mapping matrix from the Harrison-Perkins-Scott (HPS) form. These deviations are supposed to arise entirely from a perturbation of the mass matrix in the charged lepton sector. The perturbing matrix is assumed to be purely imaginary (thus maximally T-violating) and to have a strength in energy scale no greater (but perhaps smaller) than the muon mass. As we shall show, it then follows that the absolute value of the mapping matrix elements pertaining to the tau lepton deviate by no more than O((mμ/mτ)2)≈3.5×10-3 from
    their HPS values.

    Assuming that (mμ/mτ)2 can be neglected, we derive two simple constraints on the four parameters θ12, θ23, θ31, and δ of the mapping matrix. These constraints are independent of the details of the imaginary T-violating perturbation of the charged lepton mass matrix. We also show that the e and μ parts of the mapping matrix have a definite form governed by two parameters α and β; any deviation of order mμ/mτ can be accommodated by adjusting these two parameters.

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  • [1] Harrison P F,Perkins D H,Scott W G.Phys.Lett.B,2002,530:167; HE X G,Zee A.Phys.Lett.B,2003,560:87[2] MA E,Rajasekaran G.Phys.Rev.D,2001,64:113012[arXiv:hep-ph/010629]; MA E.Mod.Phys.Lett.A,2002,17:627[arXiv:hep-ph/0203238]; Altarelli G,Ferruglio F.Nucl.Phys.B,2006,741:215[arXiv:hep-ph/0512103][3] XING Z Z.Phys.Lett.B,2002,533:85; Harrison P F,Scott W G.Phys.Lett.B,2002,535:163[4] Friedberg R.,Lee T D.Ann.Phys.,2009,324:2196; Araki T,Geng C Q.Phys.Rev.D,2009,79:077301[arXiv:0901.4820v2][5] Jarlskog C.Phys.Rev.D,1987,35:1685[6] Ashie Yet al(Super Kam collaboration).Phys.Rev.Lett.,2004,93:101801[arXiv:0808.2016]; Hosaka Jet al.Phys.Rev.D,2006,74:032002; Abe K et al.Phys.Rev.Lett.,2006,97:171801[7] Apollonio M et al(Chooz collaboration).Eur.Phys.J.C,2003,27:331[arXiv:hep-ex/0301017][8] Araki T et al(KamLAND collaboration).Phys.Rev.Lett.,2005,94:081801[arXiv:hep-ex/0406035][9] Adamson Pet al(MINOS collaboration).Phys.Rev.Lett.,2009,103:261802[arXiv:0909.4996][10] Fogli G L et al.Phys.Rev.D,2008,78:033010; Schwetz T et al.New J.Phys.,2008,10:113011; XING Z Z.Int.J.Mod.Phys.A,2008,23:4355[11] Abdurashitov J N et al(SAGE collaboration).Phys.Rev.C,2009,80:015907[arXiv:0901.2200][12] Aharmin B et al(SNO collaboration).Phys.Rev.Lett.,2008,101:111501[13] Hosaka J et al(Super Kam collaboration).Phys.Rev.D,2006,73:112001[arXiv:hep-ex/0508053][14] GE S F,HE H J,YIN F R..JCAP 05(2010)017[arXiv:1001.0940][15] Palomares C(Double-Chooz collaboration).[arXiv:0911.3227]; Ardellier F et al.[arXiv:hep-ex/0405032]; Ardellier F et al.[arXiv:hep-ex/0606025][16] Gue X et al(Daya Bay collaboration).[arXiv:hepex/070120]; CHEN S.J.Phys.:Conference Series,2008,120:052024; White C.J.Phys.:Conference Series,2008,136:022012[17] Ichikawa A K(J Parc collaboration).Lect.Notes Phys.,2009,781:17[18] Ayres D S et al(Nova collaboration).[arXiv:hep-ex/0503053]
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Deviations of the lepton mapping matrix from the Harrison-Perkins-Scott form[J]. Chinese Physics C, 2010, 34(10): 1547-1555. doi: 10.1088/1674-1137/34/10/001
Deviations of the lepton mapping matrix from the Harrison-Perkins-Scott form[J]. Chinese Physics C, 2010, 34(10): 1547-1555.  doi: 10.1088/1674-1137/34/10/001 shu
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Received: 2010-08-02
Revised: 2010-08-03
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Deviations of the lepton mapping matrix from the Harrison-Perkins-Scott form

Abstract: 

We propose a simple set of hypotheses governing the deviations of the leptonic mapping matrix from the Harrison-Perkins-Scott (HPS) form. These deviations are supposed to arise entirely from a perturbation of the mass matrix in the charged lepton sector. The perturbing matrix is assumed to be purely imaginary (thus maximally T-violating) and to have a strength in energy scale no greater (but perhaps smaller) than the muon mass. As we shall show, it then follows that the absolute value of the mapping matrix elements pertaining to the tau lepton deviate by no more than O((mμ/mτ)2)≈3.5×10-3 from
their HPS values.

Assuming that (mμ/mτ)2 can be neglected, we derive two simple constraints on the four parameters θ12, θ23, θ31, and δ of the mapping matrix. These constraints are independent of the details of the imaginary T-violating perturbation of the charged lepton mass matrix. We also show that the e and μ parts of the mapping matrix have a definite form governed by two parameters α and β; any deviation of order mμ/mτ can be accommodated by adjusting these two parameters.

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