]>NUPHB13088S05503213(14)00165510.1016/j.nuclphysb.2014.05.023The AuthorsHigh Energy Physics – PhenomenologyFig. 1Scatter plot showing Δm232 at low energy versus initial value of m1 at high energy for inverted hierarchy while keeping all other neutrino parameters at low energy within 3σ range.Fig. 2Scatter plot showing Δm232 at low energy versus initial value of m2 at high energy for inverted hierarchy while keeping all other neutrino parameters at low energy within 3σ range.Fig. 3Scatter plot showing Δm232 at low energy versus initial value of m3 at high energy for inverted hierarchy while keeping all other neutrino parameters at low energy within 3σ range.Fig. 4Scatter plot showing Δm312 at low energy versus initial value of m1 at high energy for normal hierarchy while keeping all other neutrino parameters at low energy within 3σ range.Fig. 5Scatter plot showing Δm312 at low energy versus initial value of m2 at high energy for normal hierarchy while keeping all other neutrino parameters at low energy within 3σ range.Fig. 6Scatter plot showing Δm312 at low energy versus initial value of m3 at high energy for normal hierarchy while keeping all other neutrino parameters at low energy within 3σ range.Fig. 7Radiative generation of sin2θ13 for tanβ=15, 25, 40, 45, 50, 55 for inverted hierarchy using input values given in Table 2.Fig. 8Evolution of sin2θ12 for tanβ=15, 25, 40, 45, 50, 55 for inverted hierarchy using input values given in Table 2.Fig. 9Evolution of sin2θ23 for tanβ=15, 25, 40, 45, 50, 55 for inverted hierarchy using input values given in Table 2.Fig. 10Evolution of Δm212 for tanβ=15, 25, 40, 45, 50, 55 for inverted hierarchy using input values given in Table 2.Fig. 11Evolution of Δm232 for tanβ=15, 25, 40, 45, 50, 55 for inverted hierarchy using input values given in Table 2.Fig. 12Evolution of ∑imi for tanβ=15, 25, 40, 45, 50, 55 for inverted hierarchy using input values given in Table 2.Fig. 13Evolution of mee for tanβ=15, 25, 40, 45, 50, 55 for inverted hierarchy using input values given in Table 2.Fig. 14Radiative generation of sin2θ13 for tanβ=15, 25, 40, 45, 50, 55 for normal hierarchy using input values given in Table 3.Fig. 15Evolution of sin2θ12 for tanβ=15, 25, 40, 45, 50, 55 for normal hierarchy using input values given in Table 3.Fig. 16Evolution of sin2θ23 for tanβ=15, 25, 40, 45, 50, 55 for normal hierarchy using input values given in Table 3.Fig. 17Evolution of Δm212 for tanβ=15, 25, 40, 45, 50, 55 for normal hierarchy using input values given in Table 3.Fig. 18Evolution of Δm312 for tanβ=15, 25, 40, 45, 50, 55 for normal hierarchy using input values given in Table 3.Fig. 19Evolution of ∑imi for tanβ=15, 25, 40, 45, 50, 55 for normal hierarchy using input values given in Table 3.Fig. 20Evolution of mee for tanβ=15, 25, 40, 45, 50, 55 for normal hierarchy using input values given in Table 3.Table 1Character table of A4.Classχ(1)χ(2)χ(3)χ(4)
C11113

C21ωω20
C31ω2ω0
C4111−1
Table 2Input and output values with different tanβ values for Inverted Hierarchy.Input valuesOutput values for different tanβ
tanβ=15tanβ=25tanβ=40tanβ=45tanβ=50tanβ=55
m1 (eV)0.09246190.09246190.09253750.09334330.09453430.09781260.1086331
m2 (eV)−0.0938539−0.0938539−0.0939295−0.0947101−0.0958434−0.0989746−0.1089959
m3 (eV)0.08535990.08535990.08541020.08609020.08707230.08974170.0979824
sinθ230.7071070.70709990.70669700.70305230.69757240.68316600.6398494
sinθ130.000.00006550.00062870.00810880.01882130.04673520.1265871
sinθ120.577350.577350.577350.577350.57745920.57799580.5820936
Table 3Input and output values with different tanβ values for Normal Hierarchy.Input valuesOutput values for different tanβ
tanβ=15tanβ=25tanβ=40tanβ=45tanβ=50tanβ=55
m1 (eV)0.09925960.09925960.09933520.10019140.10147570.10494220.1159424
m2 (eV)−0.1000997−0.1000996−0.1001752−0.1010062−0.1022256−0.1055608−0.1162467
m3 (eV)0.10859960.10859960.10867510.10953130.11079050.11423190.1253917
sinθ230.7071070.70709990.70730140.71072630.71590940.73059020.7876961
sinθ130.000.00005820.00056040.00736470.01761990.04749220.1684841
sinθ120.577350.577350.577350.577350.57744100.57801040.5857702
Radiative generation of nonzero θ13 in MSSM with broken A4 flavor symmetryManikantaBorahmani@tezu.ernet.inDebasishBorah⁎dborah@tezu.ernet.inMrinal KumarDasmkdas@tezu.ernet.inDepartment of Physics, Tezpur University, Tezpur 784028, IndiaDepartment of PhysicsTezpur UniversityTezpur784028India⁎Corresponding author.Editor: Tommy OhlssonAbstractWe study the renormalization group effects on neutrino masses and mixing in Minimal Supersymmetric Standard Model (MSSM) by considering a μ–τ symmetric mass matrix at high energy scale giving rise to TriBiMaximal (TBM) type mixing. We outline a flavor symmetry model based on A4 symmetry giving rise to the desired neutrino mass matrix at high energy scale. We take the three neutrino mass eigenvalues at high energy scale as input parameters and compute the neutrino parameters at low energy by taking into account of renormalization group effects. We observe that the correct output values of neutrino parameters at low energy are obtained only when the input mass eigenvalues are large m1,2,3=0.08–0.12 eV with a very mild hierarchy of either inverted or normal type. A large inverted or normal hierarchical pattern of neutrino masses is disfavored within our framework. We also find a preference towards higher values of tanβ, the ratio of vacuum expectation values (vev) of two Higgs doublets in MSSM in order to arrive at the correct low energy output. Such a model predicting large neutrino mass eigenvalues with very mild hierarchy and large tanβ could have tantalizing signatures at oscillation, neutrinoless double beta decay as well as collider experiments.1IntroductionExploration of the origin of neutrino masses and mixing has been one of the major goals of particle physics community for the last few decades. The results of recent neutrino oscillation experiments have provided a clear evidence favoring the existence of tiny but nonzero neutrino masses [1]. Recent neutrino oscillation experiments like T2K [2], Double ChooZ [3], DayaBay [4] and RENO [5] have not only confirmed the earlier predictions for neutrino parameters, but also provided strong evidence for a nonzero value of the reactor mixing angle θ13. The latest global fit values for 3σ range of neutrino oscillation parameters [6] are as follows:(1)Δm212=(7.00–8.09)×10−5 eV2Δm312(NH)=(2.27–2.69)×10−3 eV2Δm232(IH)=(2.24–2.65)×10−3 eV2sin2θ12=0.27–0.34sin2θ23=0.34–0.67sin2θ13=0.016–0.030 where NH and IH refer to normal and inverted hierarchy respectively. Another global fit study [7] reports the 3σ values as(2)Δm212=(6.99–8.18)×10−5 eV2Δm312(NH)=(2.19–2.62)×10−3 eV2Δm232(IH)=(2.17–2.61)×10−3 eV2sin2θ12=0.259–0.359sin2θ23=0.331–0.637sin2θ13=0.017–0.031The observation of nonzero θ13 which is evident from the above global fit data can have nontrivial impact on neutrino mass hierarchy as studied in recent papers [8]. Nonzero θ13 can also shed light on the Dirac CP violating phase in the leptonic sector which would have remained unknown if θ13 were exactly zero. The detailed analysis of this nonzero θ13 have been demonstrated both from theoretical [9], as well as phenomenological [10] point of view, prior to and after the confirmation of this important result announced in 2012. It should be noted that prior to the discovery of nonzero θ13, the neutrino oscillation data were compatible with the so called TBM form of the neutrino mixing matrix [11] given by(3)UTBM=(23130−16131216−1312), which predicts sin2θ12=13, sin2θ23=12 and sin2θ13=0. However, since the latest data have ruled out sin2θ13=0, there arises the need to go beyond the TBM framework. In view of the importance of the nonzero reactor mixing and hence, CP violation in neutrino sector, the present work demonstrates how a specific μ–τ symmetric mass matrix (giving rise to TBM type mixing) at high energy scale can produce nonzero θ13 along with the desired values of other neutrino parameters Δm212, Δm232, θ23, θ12 at low energy scale through renormalization group evolution (RGE). We also outline how the μ–τ symmetric neutrino mass matrix with TBM type mixing can be realized at high energy scale within the framework of MSSM with an additional A4 flavor symmetry at high energy scale. After taking the RGE effects into account, we observe that the output at TeV scale is very much sensitive to the choice of neutrino mass ordering at high scale as well as the value of tanβ=vuvd, the ratio of vev's of two MSSM Higgs doublets Hu,d. We point out that this model allows only a very mild hierarchy of both inverted and normal type at high energy scale. We scan the neutrino mass eigenvalues at high energy and constrain them to be large m1,2,3=0.08–0.12 eV in order to produce correct neutrino parameters at low energy. We consider two such input values for mass eigenvalues, one with inverted hierarchy and the other with normal hierarchy and show the predictions for neutrino parameters at low energy scale. We also show the evolution of effective neutrino mass mee=∑iUei2mi (where U is the neutrino mixing matrix) that could be interesting from neutrinoless double beta decay point of view. Finally we consider the cosmological upper bound on the sum of absolute neutrino masses (∑imi<0.23 eV) reported by the Planck collaboration [12] to check if the output at low energy satisfy this or not.This article is organized as follows. In Section 2, we discuss briefly the A4 model at high energy scale. In Section 3 we outline the RGE's of mass eigenvalues and mixing parameters. In Section 4 we discuss our numerical results, and finally conclude in Section 5.2A4 model for neutrino massType I seesaw framework is the simplest mechanism for generating tiny neutrino masses and mixing. In this seesaw mechanism neutrino mass matrix can be written as(4)mLL=−mLRMR−1mLRT. Within this framework of seesaw mechanism neutrino mass has been extensively studied by discrete flavor groups by many authors [13] available in the literature. Among the different discrete groups the model by the finite group of even permutation, A4 also can explain the μ–τ symmetric mass matrix obtained from this type I seesaw mechanism. This group has 12 elements having 4 irreducible representations, with dimensions ni, such that ∑ini2=12. The characters of 4 representations are shown in Table 1. The complex number ω is the cube root of unity. In the present work we outline a neutrino mass model with A4 symmetry given in Ref. [14]. This flavor symmetry is also accompanied by an additional Z3 symmetry in order to achieve the desired leptonic mixing. In this model, the three families of lefthanded lepton doublets l=(le,lμ,lτ) transform as triplets, while the electroweak singlets ec, μc, τc and the electroweak Higgs doublets Hu,d transform as singlets under the A4 symmetry. In order to break the flavor symmetry spontaneously, two A4 triplet scalars ϕl=(ϕl1,ϕl2,ϕl3), ϕν=(ϕν1,ϕν2,ϕnu3) and three scalars ζ1, ζ2, ζ3 transforming as 1, 1′, 1″ under A4 are introduced. The Z3 charges for l, Hu,d, ϕl, ϕν, ζ1,2,3 are ω, 1, 1, ω, ω respectively.Under the electroweak gauge symmetry as well as the flavor symmetry mentioned above, the superpotential for the neutrino sector can be written as(5)Wν=(yνϕϕν+yνζ1ζ1+yνζ2ζ2+yνζ3ζ3)llHuHuΛ2 where Λ is the cutoff scale and y's are dimensionless couplings. Decomposing the first term (which is in a 3×3×3 form of A4) into A4 singlets, we getllϕν=(2lele−lμlτ−lτlμ)ϕν1+(2lμlμ−lelτ−lτle)ϕν2+(2lτlτ−lelμ−lμle)ϕν3 Similarly, the decomposition of the last three terms into A4 singlet givesllζ1=(lele+lμlτ+lτlμ)ζ1llζ2=(lμlμ+lelτ+lτle)ζ2llζ3=(lτlτ+lelμ+lμle)ζ3 Assuming the vacuum alignments of the scalars as 〈ϕν〉=ανΛ(1,1,1), 〈ζ1〉=αζΛ, 〈ζ2,3〉=0, the neutrino mass matrix can be written as(6)mLL=vu2Λ(a+2d/3−d/3−d/3−d/32d/3a−d/3−d/3a−d/32d/3), where d=yνϕαν, a=yνζ1αζ and vu is the vev of Hu. The above mass matrix has eigenvalues m1=vu2Λ(a+d), m2=vu2Λa and m3=vu2Λ(−a+d). Without adopting any unnatural fine tuning condition to relate the mass eigenvalues further, we wish to keep all the three neutrino mass eigenvalues as free parameters in the A4 symmetric theory at high energy and determine the most general parameter space at high energy scale which can reproduce the correct neutrino oscillation data at low energy through renormalization group evolution (RGE).Such a parameterization of the neutrino mass matrix however, does not disturb the generic features of the model for example, the μ–τ symmetric nature of mLL, TBM type mixing as well the diagonal nature of the charged lepton mass matrix, which at leading order (LO) is given by [14,15](7)ml=vdαl(ye000yμ000yτ)Here vd is the vev of Hd; ye, yμ, yτ and αl are dimensionless couplings. These matrices in the leptonic sector given by (6) and (7) are used in the next section for numerical analysis.3RGE for neutrino masses and mixingThe lefthanded Majorana neutrino mass matrix mLL which is generally obtained from seesaw mechanism at high scale MR, is usually expressed in terms of K(t), the coefficient of the dimension five neutrino mass operator [16,17] in a scaledependent manner [18],(8)mLL(t)=vu2K(t), where t=ln(μ/1 GeV) and the vev is vu=v0sinβ with v0=174 GeV in MSSM. The neutrino mass eigenvalues mi and the Pontecorvo–Maki–Nakagawa–Sakata (PMNS) mixing matrix UPMNS [19] are then extracted through the diagonalization of mLL(t) at every point in the energy scale t using Eqs. (8),(9)mLLdiag=diag(m1,m2,m3)=VνLTmLLVνL, and UPMNS=VνL in the basis where the charged lepton mass matrix is diagonal. The PMNS mixing matrix,(10)UPMNS=(Ue1Ue2Ue3Uμ1Uμ2Uμ3Uτ1Uτ2Uτ3), is usually parameterized in terms of the product of three rotations R(θ23), R(θ13) and R(θ12), (neglecting CP violating phases) by(11)UPMNS=Ul†Uν=(c13c12c13s12s13−c23s12−c12s13s23c12c23−s12s13s23c13s23s12s23−c12s13c23−c12s23−c23s13s12c13c23), where Ul is unity in the basis where charge lepton mass matrix is diagonal, sij=sinθij and cij=cosθij respectively.The RGE's for vu and the eigenvalues of coefficient K(t) in Eq. (8), defined in the basis where the charged lepton mass matrix is diagonal, can be expressed as [20,22](12)ddtlnvu=116π2[320g12+34g22−3ht2](13)ddtlnK=−116π2[65g12+6g22−6ht2−δi3hτ2−δ3jhτ2] Neglecting hμ2 and he2 compared to hτ2, and taking scaleindependent vev as in Eq. (8), we have the complete RGE's for three neutrino mass eigenvalues,(14)ddtmi=116π2[(−65g12−6g22+6ht2)+2hτ2Uτi2]mi. The above equations together with the evolution equations for mixing angles (23)–(24), are used for the numerical analysis in our work.The approximate analytical solution of Eq. (14) can be obtained by taking static mixing angle Uτi2 in the integration range as [21](15)mi(t0)=mi(tR)exp(65Ig1+6Ig2−6It)exp(−2Uτi2Iτ) The integrals in the above expression are usually defined as [18,21](16)Igi(t0)=116π2∫t0tRgi2(t)dt and(17)If(t0)=116π2∫t0tRhf2(t)dt where i=1,2,3 and f=t,b,τ respectively. For a twofold degenerate neutrino masses that is, mLLdiag=diag(m,m,m′)=UPMNSTmLLUPMNS, Eq. (15) is further simplified to the following expressions(18)m1(t0)≈m(tR)(1+2δτ(c12s13c23−s12s23)2)+O(δτ2)(19)m2(t0)≈m(tR)(1+2δτ(c23s13s12+c12s23)2)+O(δτ2)(20)m3(t0)≈m′(tR)(1+2δτ(c13c23)2)+O(δτ2). While deriving the above expressions, the following approximations are usedexp(−2Uτi2Iτ)≃1−2Uτi2Iτ=1+2Uτi2δτ−δτ=Iτ≃1cos2β(mτ/4πv)2ln(MR/mt)The sign of the quantity δτ in MSSM depends on the neutrino mixing matrix parameters and the approximation on δτ taken here is valid only if t0 is associated with the top quark mass. From Eqs. (18) and (19), the low energy solar neutrino mass scale is then obtained as(21)△m212(t0)=m22−m12≈4δτm2(cos2θ12(s232−s132c232)+s13sin2θ12sin2θ23)+O(δτ2)3.1Evolution equations for mixing anglesThe corresponding evolution equations for the PMNS matrix elements Ufi are given by [20](22)dUfidt=−116π2∑k≠imk+mimk−miUfk(UTHe2U)ki, where f=e,μ,τ and i,k=1,2,3 respectively. Here He is the Yukawa coupling matrices of the charged leptons in the diagonal basis and(UTHe2U)ki=hτ2(UkτTUτi)+hμ2(UkμTUμi)+he2(UkeTUei) Neglecting hμ2 and he2 as before and denoting Aki=mk+mimk−mi, Eq. (22) simplifies to [20](23)ds12dt=116π2hτ2c12[c23s13s12Uτ1A31−c23s13c12Uτ2A32+Uτ1Uτ2A21],(24)ds13dt=116π2hτ2c23c132[c12Uτ1A31+s12Uτ2A32],(25)ds23dt=116π2hτ2c232[−s12Uτ1A31+c12Uτ2A32]. These equations are valid for a generic MSSM with the minimal field content and are independent of the flavor symmetry structure at high energy scale.4Numerical analysis and resultsFor the analysis of the RGE's, Eqs. (14), (23)–(25) for neutrino masses and mixing angles, here we follow two consecutive steps (i) bottomup running [21] in the first place, and then (ii) topdown running [18] in the next. In the first step (i), the running of the RGE's for the third family Yukawa couplings (ht,hb,hτ) and three gauge couplings (g1,g2,g3) in MSSM, are carried out from topquark mass scale (t0=lnmt) at low energy end to high energy scale MR [21,22]. In the present analysis we consider the high scale value as the unification scale MR=1.6×1016 GeV, with different tanβ input values to check the stability of the model at low energy scale. For simplicity of the calculation, the SUSY breaking scale is taken at the topquark mass scale t0=lnmt [18,21]. We adopt the standard procedure to get the values of gauge couplings at topquark mass scale from the experimental CERNLEP measurements at MZ, using oneloop RGE's, assuming the existence of a onelight Higgs doublet and five quark flavors below mt scale [21,22]. Using CERNLEP data, MZ=91.187 GeV, αs(MZ)=0.118±0.004, α1−1(MZ)=127.9±0.1, sin2θW(MZ)=0.2316±0.0003, and SM relations,(26)1α1(MZ)=35(1−sin2θW(MZ))α(MZ),1α2(MZ)=sin2θW(MZ)α(MZ),gi2=4παi, we calculate the gauge couplings at MZ scale, α1(MZ)=0.0169586, α2(MZ)=0.0337591, α3(MZ)=0.118. As already mentioned, we consider the existence of one light Higgs doublet (nH=1) and five quark flavors (nF=5) in the scale MZ−mt. Using oneloop RGE's of gauge couplings, we get g1(mt)=0.463751, g2(mt)=0.6513289 and g3(mt)=1.1891996. Similarly, the Yukawa couplings are also evaluated at topquark mass scale for input values of mt(mt)=174 GeV, mb(mb)=4.25 GeV, mτ(mτ)=1.785 GeV and the QEDQCD rescaling factors ηb=1.55, ητ=1.015 in the standard fashion [22],(27)ht(mt)=mt(mt)1+tan2β174tanβ,hb(mt)=mb(mt)1+tan2β174,hτ(mt)=mτ(mt)1+tan2β174, where mb(mt)=mb(mb)ηb, mτ(mt)=mτ(mτ)ητ. The oneloop RGE's for top quark, bottom quark and τlepton Yukawa couplings in the MSSM in the range of mass scales mt≤μ≤MR are given by(28)ddtht=ht16π2(6ht2+hb2−∑i=13cigi2),(29)ddthb=hb16π2(6hb2+hτ2−∑i=13ci′gi2),(30)ddthτ=hτ16π2(4hτ2+3hb2−∑i=13ci″gi2), where(31)ci=(13153163),ci′=(7153163),ci″=(9530). The twoloop RGE's for the gauge couplings are similarly expressed in the range of mass scales mt≤μ≤MR as(32)ddtgi=gi16π2[bigi2+116π2(∑j=13bijgi2gj2−∑j=t,b,τ3aijgi2hj2)], where(33)bi=(6.61−3),bij=(7.95.4171.825242.2914),aij=(5.22.83.6662440). Values of ht, hb, hτ, g1, g2, g3 evaluated at high scale MR=1.6×1016 from Eqs. (28)–(30) and (32) areht(MR)=0.142685458,hb(MR)=0.378832042,hτ(MR)=0.380135357,g1(MR)=0.381783873,g2(MR)=0.377376229,g3(MR)=0.374307543. In the second step (ii), the running of three neutrino masses (m1,m2,m3) and mixing angles (s12,s23,s13) are carried out together with the running of Yukawa and gauge couplings, from high scale tR(=lnMR) to low scale to. In this case, we use the input values of Yukawa and gauge couplings evaluated earlier at scale tR from the first stage running of RGE's in case (i). In principle, one can evaluate neutrino masses and mixing angles at every point of the energy scale. It can be noted that in the present problem, the running of other SUSY parameters such as M0, M1/2, μ, are not required and hence, it is not necessary to supply their input values.We are now interested in studying radiative generation θ13 for the case when m1,2,3≠0 and s13=0 at high energy scale. Such studies can give the possible origin of the reactor angle in a broken A4 model. During the running of mass eigenvalues and mixing angles from high to low scale, the nonzero input value of mass eigenvalues m1,2,3 will induce radiatively a nonzero values of s13. Similar approach was followed in [23] considering m3=0. The authors in [23] used inverted hierarchy neutrino mass pattern (m,−m,0) at high scale. Such a specific structure of mass eigenvalues however, require fine tuning conditions in the flavor symmetry model at high energy. Instead of assuming a specific relation between mass eigenvalues at high energy scale, here we attempt to find out the most general mass eigenvalues at high energy which can give rise to the correct neutrino data at low energy scale. The only assumption in our work is the opposite CP phases i.e. (m1,−m2,m3). In another work [24], authors have shown the radiative generation of △m212 considering the nonzero θ13 at high scale and tanβ values lower than 50. They have also shown that Δm212 can run from zero at high energy to the observed value at the low energy scale, only if θ13 is relatively large and the Dirac CPviolating phase is close to π. The running effects can be observed only when θ13 is nonzero at highenergy scale as per their analysis. In the present work, θ13 is assumed to be zero at high scale consistent with a TBM type mixing within A4 symmetric model. We also examine the running behavior of neutrino parameters in a neutrino mass model obeying special kind of μ–τ symmetry at high scale, which was not studied in the earlier work mentioned above.For a complete numerical analysis, first we parameterize the neutrino mass matrix to have a TBM type structure with eigenvalues in the form (m1,−m2,m3). Since the mixing angles at high energy scale are fixed (TBM type), we only need to provide three input values namely, m1, m2, m3. Using these values at the high energy scale, neutrino parameters are computed at low energy scale by simultaneously solving the RGE's discussed above. We first allow moderate as well as large hierarchies between the lightest and the heaviest mass eigenvalues (with the lighter being at least two orders of magnitudes smaller) of both normal and inverted type and find that the output values of θ13 do not lie in the experimentally allowed range for all values of tanβ=15,25,40,45,50,55 used in our analysis.We then consider very mild hierarchical pattern of mass eigenvalues keeping them in the same order of magnitude range. We vary the neutrino mass eigenvalues at high energy scale in the range 0.01–0.12 eV and generate the neutrino parameters at low energy. We restrict the neutrino parameters θ13, θ12, θ23 and Δm212 at low energy to be within the allowed 3σ range and show the variation of Δm232(IH), Δm312(NH) at low energy with respect to the input mass eigenvalues at high energy. We show the results in Figs. 1–6 for a specific value of tanβ=55. It can be seen from these figures that the correct value of neutrino parameters at low energy can be obtained only for large values of mass eigenvalues at high energy scale m1,2,3=0.08–0.12 eV. We then choose two specific sets of mass eigenvalues at high energy scale corresponding to inverted hierarchy and normal hierarchy respectively and show the evolution of several neutrino observables including oscillation parameters, effective neutrino mass mee=∑iUei2mi, sum of absolute neutrino masses ∑imi in Figs. 7–20. It can be seen from Figs. 7 and 14 that the correct value of θ13 can be obtained at low energy only for very high values of tanβ=55. The other neutrino parameters also show a preference for higher tanβ values. The output values of neutrino parameters at low energy are given in Tables 2 and 3 for both sets of input parameters. The large deviation of θ13 at low energy from its value at high energy (θ13=0 for TBM at high energy) whereas smaller deviation of other two mixing angles can be understood from the RGE equations for mixing angles (23), (24), (25). Using the input values given in Tables 2 and 3, the slope of sinθ13 can be calculated to be hτ216π2(−5.88) and hτ216π2(5.23) for inverted and normal hierarchies respectively. On the other hand, the slope of sinθ23 at high energy scale is found to be hτ216π2(2.95) and hτ216π2(−2.63) for inverted and normal hierarchies respectively. Thus, the lower value of slope for sinθ23 results in smaller deviation from TBM values compared to that of sinθ13. We also note from Figs. 12, 19 that the sum of the absolute neutrino masses at low energy is 0.315 eV and 0.3555 eV for inverted and normal hierarchy respectively. This lies outside the limit set by the Planck experiment ∑mi<0.23 eV [12]. However, there still remains a little room for the sum of absolute mass to lie beyond this limit depending on the cosmological model, as suggested by several recent studies [25]. Ongoing as well as future cosmology experiments should be able to rule out or confirm such a scenario.It is interesting to note that, our analysis shows a preference for very mild hierarchy of either inverted or normal type at high energy scale which also produces a very mild hierarchy at low energy. This can have interesting consequences in the ongoing neutrino oscillation as well as neutrinoless double beta decay experiments. Also, the large tanβ region of MSSM (which gives better results in our model) will undergo serious scrutiny at the collider experiments making our model falsifiable both from neutrino as well as collider experiments. We note that the present analysis will be more accurate if the two loop contributions [26] RGE's are taken into account.5ConclusionWe have studied the effect of RGE's on neutrino masses and mixing in MSSM with μ–τ symmetric neutrino mass model giving TBM type mixing at high energy scale. We incorporate an additional flavor symmetry A4 at high scale to achieve the desired structure of the neutrino mass matrix. The RGE equations for different neutrino parameters are numerically solved simultaneously for different values of tanβ ranging from 15 to 55. We take the three neutrino mass eigenvalues at high energy scale as free parameters and determine the parameter space that can give rise to correct values of neutrino oscillation parameters at low energy. We make the following observations•Moderate or large hierarchy (both normal and inverted) of neutrino masses at high energy scale does not give rise to correct output at low energy scale.•Very mild hierarchy (with all neutrino mass eigenvalues having same order of magnitude values and m1,2,3=0.08–0.12 eV) give correct results at low energy provided the tanβ values are kept high, close to 55. Such a preference towards large mass eigenvalues with all eigenvalues having same order of magnitude values can have tantalizing signatures at oscillation as well as neutrinoless double beta decay experiments.•No significant changes in running of sin2θ23, sin2θ12 with tanβ are observed.•Sum of absolute neutrino masses at low energy lie above the Planck upper bound ∑mi<0.23 eV [12] hinting towards nonstandard cosmology to accommodate a larger ∑mi or more relativistic degrees of freedom [25].•The preference for high tanβ regions of MSSM could go through serious tests at collider experiments pushing the model towards verification or falsification.Although we have arrived at some allowed parameter space in our model giving rise to correct phenomenology at low energy with the additional possibility that many or all of these parameter space might get ruled out in near future, we also note that it would have been more interesting if the running of the Dirac and Majorana CP violating phases [27] were taken into account. We also have not included the seesaw threshold effects and considered all the right handed neutrinos to decouple at the same high energy scale. Such threshold effects could be important for large values of tanβ as discussed in [28]. We leave such a detailed study for future investigations.AcknowledgementThe work of MKD is partially supported by the grant no. 42790/2013(SR) from UGC, Govt. of India.References[1]S.FukudaSuperKamiokandePhys. Rev. Lett.8620015656arXiv:hepex/0103033Q.R.AhmadSNOPhys. Rev. Lett.892002011301arXiv:nuclex/0204008Q.R.AhmadSNOPhys. Rev. Lett.892002011302arXiv:nuclex/0204009J.N.BahcallC.PenaGarayNew J. Phys.6200463arXiv:hepph/0404061K.NakamuraJ. Phys. G372010075021[2]K.AbeT2K CollaborationPhys. Rev. Lett.1072011041801arXiv:1106.2822 [hepex][3]Y.AbePhys. Rev. Lett.1082012131801arXiv:1112.6353 [hepex][4]F.P.AnDAYABAY CollaborationPhys. Rev. Lett.1082012171803arXiv:1203.1669 [hepex][5]J.K.AhnRENO CollaborationPhys. Rev. Lett.1082012191802arXiv:1204.0626 [hepex][6]M.C.GonzalezGarciaM.MaltoniJ.SalvadoT.SchwetzJ. High Energy Phys.122012123arXiv:1209.3023 [hepph][7]G.L.FogliE.LisiA.MarroneD.MontaninoA.PalazzoA.M.RotunnoPhys. Rev. D862012013012arXiv:1205.5254 [hepph][8]D.BorahM.K.DasNucl. Phys. B8702013461arXiv:1303.1758M.K.DasD.BorahR.MishraPhys. Rev. D862012095006[9]Y.BenTovX.G.HeA.ZeeJ. High Energy Phys.122012093arXiv:1208.1062G.AltarelliF.FeruglioL.MerloE.StamouJ. High Energy Phys.12082012021G.AltarelliF.FeruglioPhys. Rep.3201999295Y.ShimizuM.TanimotoA.WatanabeProg. Theor. Phys.126201181AseshKrishnaDattaLisaEverettPierreRamondPhys. Lett. B620200542[10]S.F.KingPhys. Lett.71812012136C.DuarahA.DasN.N.SinghPhys. Lett. B7182012147N.K.FrancisN.N.SinghNucl. Phys. B863201219B.BrahmachariA.RaychaudhuriPhys. Rev. D862012051302S.GoswamiS.T.PetcovS.RayW.RodejohannPhys. Rev. D802009053013Y.LinL.MerloA.ParisNucl. Phys. B8352010238arXiv:0911.3037 [hepph][11]P.F.HarrisonD.H.PerkinsW.G.ScottPhys. Lett. B5302002167P.F.HarrisonW.G.ScottPhys. Lett. B5352002163Z.z.XingPhys. Lett. B533200285P.F.HarrisonW.G.ScottPhys. Lett. B5472002219P.F.HarrisonW.G.ScottPhys. Lett. B557200376P.F.HarrisonW.G.ScottPhys. Lett. B5942004324[12]P.A.R.AdePlanck CollaborationarXiv:1303.5076 [astroph.CO][13]H.IshimoriT.KobayashiH.OhkiY.ShimizuH.OkadaM.TanimotoProg. Theor. Phys. Suppl.18320101W.GrimusP.O.LudlJ. Phys. A452012233001S.F.KingC.LuhnRept. Prog. Phys.762013056201G.AltarelliF.FeruglioNucl. Phys. B7412006215arXiv:hepph/0512103E.MaD.WegmanPhys. Rev. Lett.1072011061803arXiv:1106.4269 [hepph]S.GuptaA.S.JoshipuraK.M.PatelPhys. Rev. D852012031903arXiv:1112.6113 [hepph]S.DevR.R.GautamL.SinghPhys. Lett. B7082012284arXiv:1201.3755 [hepph]PeiHongGuHongJianHeJ. Cosmol. Astropart. Phys.06122006010PeiHongGuHongJianHePhys. Rev. D862012111301G.C.BrancoR.Gonzalez FelipeF.R.JoaquimH.SerodioPhys. Rev. D862012076008arXiv:1203.2646 [hepph]E.MaPhys. Lett. B6602008505arXiv:0709.0507 [hepph]F.PlentingerG.SeidlW.WinterJ. High Energy Phys.08042008077arXiv:0802.1718 [hepph]N.HabaR.TakahashiM.TanimotoK.YoshiokaPhys. Rev. D782008113002arXiv:0804.4055 [hepph]S.F.GeD.A.DicusW.W.RepkoPhys. Rev. Lett.1082012041801arXiv:1108.0964 [hepph]E.MaR.RajasekaranPhys. Rev. D642001113012E. Ma, Talk at VISilafac, Puerto Vallarta, November 2006, arXiv:0612013.E.MaPhys. Rev. D702004031901T.ArakiY.F.LiPhys. Rev. D852012065016arXiv:1112.5819 [hepph]Z.z.XingChin. Phys. C362012281arXiv:1203.1672 [hepph]Phys. Lett. B6962011232arXiv:1011.2954 [hepph]P.S.Bhupal DevB.DuttaR.N.MohapatraM.SeversonPhys. Rev. D862012035002B.AdhikaryB.BrahmachariA.GhosalE.MaM.K.ParidaPhys. Lett. B6382006345arXiv:hepph/0603059G.AltarelliF.FeruglioRev. Mod. Phys.8220102701arXiv:1002.0211K.M.ParattuA.WingerterPhys. Rev. D842011013011arXiv:1012.2842R.Gonzalez FelipeH.SerodioJoao P.SilvaPhys. Rev. D882013015015[14]G.AltarelliF.FeruglioNucl. Phys. B720200564G.AltarelliD.MeloniJ. Phys. G362009085005[15]G.AltarelliF.FeruglioL.MerloE.StamouJ. High Energy Phys.082012021arXiv:1208.1062 [hepph][16]P.ChankowskiZ.PluciennikPhys. Lett. B3161993312K.S.BabuC.N.LungJ.PantaleonePhys. Lett. B3191993191[17]S.AntuschM.DreesJ.KerstenM.LindnerM.RatzNucl. Phys. B5192001238S.AntuschM.DreesJ.KerstenM.LindnerM.RatzPhys. Lett. B5252002130[18]S.F.KingN.Nimai SinghNucl. Phys. B59120003S.F.KingN.Nimai SinghNucl. Phys. B596200181[19]B.PontecorvoSov. Phys. JETP71958172Z.MakiM.NakagawaS.SakataProg. Theor. Phys.281972870[20]P.H.ChankowskiW.KrolikowskiS.PokorskiPhys. Lett. B4732000109[21]M.K.ParidaN.Nimai SinghPhys. Rev. D591998032001[22]N.N.SinghEur. Phys. J. C192001137[23]A.JoshipuraPhys. Lett. B5432002276A.JoshipuraS.RindaniPhys. Rev. D672003073009[24]S.AntuschJ.KerstenM.LinderM.RatzNucl. Phys. B6742003401[25]E.GiusarmaR.de PutterS.HoO.MenaPhys. Rev. D882013063515JianWeiHuRongGenCaiZongKuanGuoB.HuarXiv:1401.0717E.GiusarmaE.Di ValentinoM.LattanziA.MelchiorriO.MenaarXiv:1403.4852[26]M.BasteroGilB.BrahmachariNucl. Phys. B482199639P.KielanowskiS.R.Juarez WJ.G.Mora HPhys. Lett. B4792000181S.RayW.RodejohannM.A.SchmidtPhys. Rev. D832011033002arXiv:1010.1206[27]S.LuoZ.z.XingPhys. Rev. D862012073003arXiv:1203.3118[28]S.AntuschJ.KerstenM.LindnerM.RatzM.A.SchmidtJ. High Energy Phys.05032005024