Neutrinoless double beta decay induced by light Majorana neutrino exchange
between two decaying nucleons with squark/slepton exchange inside one and W
exchange inside the other nucleon (so-called vector-scalar exchange) gives
stringent limits on R-parity violating interactions. We have extended previous
work by including the tensor contribution to the transition rate. We discuss
the improved limits on trilinear \Rp -MSSM couplings imposed by the current
experimental limit on the $\znbb$ decay half-life of $^{76}$Ge.Comment: replaced by revised version to appear in Phys. Lett. 

Adler

Babu

Baudis

Faessler

H. Päs

H.V. Klapdor-Kleingrothaus

Hirsch

Kalinowski

M. Hirsch

Tomoda

Physics Letters B

English

arXiv

Crossref

Improved bounds on SUSY accompanied neutrinoless double beta decay

Neutrinoless double beta decay (0 nu beta beta) induced by light Majorana neutrino exchange between two decaying nucleons with squark/slepton exchange inside one and W exchange inside the other nucleon (so-called vector-scalar exchange) gives stringent limits on R-parity violating interactions. We have extended previous work by including the tensor contribution to the transition rate. We discuss the improved limits on trilinear R-p-MSSM couplings imposed by the current experimental limit on the 0 nu beta beta decay half-life of Ge-76

Päs, Heinrich

Hirsch, Martin

Klapdor-Kleingrothaus, H.V.

Repositori d'Objectes Digitals per a l'Ensenyament la Recerca i la Cultura

arXiv:hep-ph/9810382v2  14 Jul 1999Improved bounds on SUSY accompaniedneutrinoless double beta decayH. Pa¨s 1, M. Hirsch 2, H.V. Klapdor–Kleingrothaus 3Max–Planck–Institut fu¨r Kernphysik,P.O.Box 10 39 80, D–69029 Heidelberg, GermanyAbstractNeutrinoless double beta decay (0νββ) induced by light Majorana neutrino ex-change between two decaying nucleons with squark/slepton exchange inside oneand W exchange inside the other nucleon (so–called vector–scalar exchange) givesstringent limits on R–parity violating interactions. We have extended previous workby including the tensor contribution to the transition rate. We discuss the improvedlimits on trilinear Rp/ -MSSM couplings imposed by the current experimental limiton the 0νββ decay half–life of 76Ge.PACS 13.15;23.40;21.60J;14.80Key words: Supersymmetry; R–parity violation; Double beta decay; Neutrino;QRPAIn supersymmetric models, the new SUSY partners differ from the SM fieldcontent in a discrete multiplicative quantum number R–parity defined asRp = (−1)3B+L+2S . (1)Here B denotes the baryon number, L the lepton number and S the spin of aparticle leading to Rp = +1 for SM particles and Rp = −1 for superpartners.Thus in Rp conserving models superpartners can only be produced in pairs andthe LSP is stable, leading to a natural WIMP dark matter candidate. While inthe minimal supersymmetric extension (MSSM) of the standard model (SM)R–parity is assumed to be conserved, there are no theoretical reasons for Rpconservation and several GUT [1] and Superstring [2] models require R–parityviolation in the low energy regime. Also the reports concerning an anomaly1 E-mail: Heinrich.Paes@mpi-hd.mpg.de2 Present Address: Inst. de Fisica Corpuscular - C.S.I.C. - Dept. de Fisica Teorica,Univ. de Valencia, 46100 Burjassot, Valencia, Spain,E-mail: mahirsch@flamenco.ific.uv.es3 E-mail: klapdor@mickey.mpi-hd.mpg.dePreprint submitted to Elsevier Preprint 13 January 2014at HERA in the inelastic e+p scattering at high Q2 and x [3] have renewedthe interest in RP/ –SUSY (see for example [4,5]). Generally, one can add thefollowing trilinear R–parity violating terms to the superpotential [1]WRP/ = λijkLiLjEk + λ′ijkLiQjDk + λ′′ijkU iDjDk, (2)where i, j, k denote generation indices, L,Q denote lepton and quark doubletsuperfields and E,U,D lepton, up– and down quark singlet superfields. Termsproportional to λ, λ′violate lepton number, those proportional λ′′violatebaryon number. While simultaneous presence of both kinds of terms wouldlead to too fast proton decay and thus is forbidden, assuming the λ′′terms tobe zero no constraints on λ and λ′terms can be derived from proton decay.The search for neutrinoless double beta decay, converting a nucleus (Z,A) intoa nucleus (Z + 2, A) under emission of two electrons, has been proven to be-long to the most powerful tools to search for lepton number violating physicsbeyond the SM (for a review see [6,7]). Contributions occuring through Feyn-man graphs involving the exchange of superpartners as well as RP/ –couplingsλ′have been discussed in [8–12] and yield the most stringent bound on λ′111.Taking into account the fact that the SUSY partners of the left and right–handed quark states can mix with each other, also diagrams appear in whichthe neutrino–mediated double beta decay is accompanied by SUSY exchangein the vertices (see fig. 1). These contributions allow to constrain also combi-nations of couplings of higher generations λ′11jλ′1j1. They have been discussedin [13] and more extensively in [11], where however only scalar-pseudoscalarcurrents have been taken into account, whereas the tensor contribution to thedecay rate has been neglected. On the other hand, in a recent work [14] thedominance of the tensor contribution in a general framework for neutrino me-diated double beta decay has been proven. In the present letter we reanalyzeSUSY–accompanied double beta decay and discuss the relative importance ofthe different nuclear matrix elements involved.The mixing between scalar superpartners f˜L,R of the left and right-handedfermions fL,R occurs due to non-diagonality of the mass matrix which can bewritten asM2f˜=m2f˜L+m2f − 0.42DZ −mf (Af + µ tanβ)−mf (Af + µ tanβ) m2f˜R +m2f − 0.08DZ. (3)Here, f = d, s, b, e, µ, τ and f˜ are their superpartners. DZ = M2Z cos2β withtanβ = 〈H02 〉/〈H01〉 being the ratio of vacuum expectation values of the twoHiggs doublets, mf˜L,R are soft sfermion masses, Af are soft SUSY breakingparameters describing the strength of trilinear scalar interactions, and µ is thesupersymmetric Higgs(ino) mass parameter. Once sfermion mixing is included,the current eigenstates f˜L, f˜R become superpositions of the mass eigenstatesf˜i with the masses mf˜i and the corresponding mixing angle θf is defined assin2θf =2m2(f)LRm2f˜1−m2f˜2,2m2f˜1,2=12(m2LL +m2RR ∓√(m2LL −m2RR)2 + 4m4LR)(4)where m2LR, m2LL, m2RR denote the (1, 2), (1, 1), (2, 2) entries of the mass matrix((3)).Now it is straightforward to find the effective 4-fermion ν − u− d − e vertexinduced by the sfermion exchange in the diagrams presented in fig. 1. Thecorresponding effective Lagrangian, after a Fiertz rearrangement, takes theformLeffSUSY (x) =GF√2[14(ηnj(q)LR − 4ηnj(l)LR)· U∗ni ·(ν¯i(1 + γ5)ecj)(u¯(1 + γ5)d)−− 2ηnj(l)LL · Uni ·(ν¯i(1− γ5)ecj)(u¯(1 + γ5)d) + (5)+12ηnj(q)RR · Uni(ν¯i γµ(1 + γ5)ecj)(u¯ γµ(1− γ5)d) ++18ηnj(q)LR · U∗ni ·(ν¯i σµν(1 + γ5)ecj)(u¯ σµν(1 + γ5)d)].The Rp/ MSSM parameters η and neutrino mixing matrix Uij are defined asfollowsηnj(q)LR =∑kλ′j1kλ′nk12√2GFsin 2θd(k) 1m2d˜1(k)− 1m2d˜2(k) , (6)ηnj(q)RR =∑kλ′j1kλ′n1k2√2GFsin2 θd(k)m2d˜1(k)+cos2 θd(k)m2d˜2(k) , (7)ηnj(l)LR =∑kλ′k11λnjk2√2GFsin 2θe(k) 1m2e˜1(k)− 1m2e˜2(k) , (8)ηnj(l)LL =∑kλ′k11λnkj2√2GFcos2 θe(k)m2e˜1(k)+sin2 θe(k)m2e˜2(k) , (9)ν0i =∑jUijνj. (10)Here η(f)LR denotes the contribution vanishing in the absence of f˜L− f˜R - mix-ing while η(f)LL and η(f)RR in this limit correspond to the f˜L and f˜R exchangecontribution in fig. 1. We use the notations d(k) = d, s, b and e(k) = e, µ, τ .Due to the antisymmetry of the Yukawa coupling λnjk in nj it follows thatηnn(l)LR = 0. This is an essential difference between the slepton l˜L − l˜R andthe squark q˜L − q˜R contributions. The latter is not imposed to vanish at anycombination of indexes. Since the ηnj(l)LL and ηnj(q)RR contributions to the di-agram fig. 1 are helicity suppressed ∝ 〈mν〉 ≃ O(0.5)eV, we can restrictourselves to the consideration of ηnj(q)LR and ηnj(l)LR, which contributions aremomentum enhanced ∝ q ≃ pF ≃ 100 MeV, where pF denotes the Fermimomentum. Here 〈mν〉 and q denote the effective neutrino mass and momen-tum entering the neutrino propagator. The first line in eq. (5) corresponds tothe scalar-pseudoscalar (S +P ) contribution, the last line in (5) to the tensorcontribution.3In the light neutrino case the 0νββ decay rate is given byT−11/2(0νββ) = G01{4η¯(l)MS+P +(−η¯(q) + η(q))(MS+P +MT )}2. (11)Here G01 denotes the phase space factor defined in [15], η(q) = η11(q)LR andeffective parameters are introduced asη¯(l,q) =∑n∆nηn1(l,q)LR. (12)For the η¯(l) summation starts from n = 2 and ∆n denotes the combination ofmixing matrices corresponding to heavy or sterile neutrinos∆i =′′∑jU∗ijUei + U∗isUei, (13)where the sum extends over heavy mass eigenstatesmνi > 10 GeV (see [11]). Ins-wave approximation for the outgoing electrons and under some assumptionsaccording to [16,11] (the s-wave approximation is expected to affect the resultless than 10 % [14]) the matrix element isMS+P = F(3)P (0)4RmeGA(MT ′ +13MGT ′), (14)MT = α1(23MGT ′ −MT ′), (15)with (summation over nucleons a, b is suppressed)MGT ′ = 〈0+f |hR( ~σa ~σb)τ+a τ+b |0+i 〉 (16)MT ′ = 〈0+f |hT ′{( ~σa~ˆrab)(~σb~ˆrab)−13(~σa~σb)}τ+a τ+b |0+i 〉, (17)α1 =T(3)1 (0)GV (1− 2mP (GW/GV ))2G2ARme. (18)hR and hT ′ are neutrino potentials defined ashR =2πR2mP∞∫0dqq4j0(qrab)f2(q2)ω(ω + E), (19)hT ′ =2πR2mP∞∫0dqq2f 2(q2)ω(ω + E){q2j0(qrab)− 3 qrabj1(qrab)}. (20)Here R denotes the nuclear radius, mP the proton mass.Further ω =√q2 +m2ν , q = |~q|, rˆ = ~r/r and jk(qr) are spherical Besselfunctions. (ω + E)−1 is the energy denominator of the perturbation theory.The form factors F ai (0) = Fai (q2)/f(q2) and T(3)1 (0) = T(3)1 (q2)/f(q2) withf(q2) = (1 + q2/m2A)−2 (m2A = 0.85 GeV) have been calculated in the MITbag model in [17], GA ≃ 1.26, GV ≃ 1 and the strength of the induced weakmagnetism (GW/GV ) =µP−µn2mP≃ −3.72mPis obtained by the CVC hypothesis.For comparison and to correct some details in [11] we first concentrate on theS+P part, , i.e.MT = 0 in eq. 11. Inserting the numerical value of the matrixelements MGT ′ = 2.95 and MT ′ = 0.224 [11] for the special case of 76Ge andthe half life limit obtained from the Heidelberg–Moscow experiment, T 0νββ1/2 >1.2 · 1025y, [18,7] one derives ηq ≤ 4.5 · 10−8, η¯(l) ≤ 1.1 · 10−8, corresponding to4limits ofλ′112λ′121 ≤ 5.0 · 10−6( ΛSUSY100GeV)3λ′113λ′131 ≤ 1.6 · 10−7( ΛSUSY100GeV)3∆nλ′311λn13 ≤ 9.9 · 10−8( ΛSUSY100GeV)3. (21)Here in the last equation only the term corresponding to τ˜ exchange has beenkept. These limits differ from the ones given in [11] due to an erroneous factorof 2 in the definition of MS+P in that reference as well as the improvementin the experimental bound.Keeping the tensor part in eq. 11 the half life limit of the Heidelberg–MoscowExperiment implies:λ′112λ′121 ≤ 1.1 · 10−6( ΛSUSY100GeV)3,λ′113λ′131 ≤ 3.8 · 10−8( ΛSUSY100GeV)3(22)for supersymmetric mass parameters of order 100 GeV. For ΛSUSY ∼ 1 TeV,motivated by SUSY naturalness arguments, one obtains λ′112λ′121 ≤ 1.1 · 10−3,λ′113λ′131 ≤ 3.8 · 10−5. These are by more than a factor of four more stringentthan the limits obtained from the scalar pseudoscalar part considered in [11].The uncertainty of the nuclear matrix elements involved can be estimated tobe less than a factor of two. This is motivated by the fact that the 2νββhalflife of 76Ge has been predicted correctly within a factor of 2 (the 2νββmatrix element within a factor of√2) [19]. Since the uncertainty in bothparts (S + P and tensor) is expected to be about the same, the improvementcan still be considered as substantial.The obtained bound should be compared with the limits obtained from treelevel K0−K¯0 and B0−B¯0 mixing, which yield λ′i12λ′i21 < 1·10−9 and λ′i13λ′i31 <8 · 10−8 respectively, for me˜ = 100 GeV [20]. While the second generationis bounded by about three orders of magnitude more stringent from the Ksystem, for the third generation the double beta bound is most stringent.Moreover, since the masses of different exchanged particles (selectrons andsquarks) enter, the limits are complementary in some sense.In conclusion, we have performed a reanalysis of the SUSY–accompanied neu-trino exchange mode of neutrinoless double beta decay. Contrary to the pre-vious ansatz we included the tensor contribution to the decay rate, which hasbeen shown to be the dominant contribution. This improves the limits onλ′11jλ′1j1 derived without the tensor contribution by a factor of four and thusprovides the most stringent bound on λ′113λ′131.AcknowledgementM.H. would like to acknowledge support by the European Union’s TMR pro-gram under grant ERBFMBICT983000.5References[1] L. Hall, M. Suzuki, Nucl. Phys. B 231 (1984) 419; D. Brahm, L. Hall, Phys. RevD 40 (1989) 2449; K. Tamvakis Phys. Lett. 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Improved bounds on SUSY accompanied neutrinoless double beta decay

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Repositori d'Objectes Digitals per a l'Ensenyament la Recerca i la Cultura