We tested several models in which the Standard Model (SM) gauge group is
extended by an additional U(1) gauge symmetry, against available electroweak
precision data to impose limits on the mass of the neutral Z' boson, M_Z',
predicted in all such models, and on the Z-Z' mixing angle, theta_ZZ', at 95%
C.L. We found lower limits on M_Z' of order 1 TeV in most cases, while
theta_ZZ' was found to be constrained to very small values.Comment: Format fixed, 5 pages, 2 figures, Talk given at the 17th
  International Conference on Supersymmetry and the Unification of Fundamental
  Interactions (SUSY09), Boston, MA, USA, 5-10 June 2009, to be published in
  the conference proceedings (AIP

Erler, J.

Langacker, P.

Munir, S.

Rojas, E.

English

arXiv

Erler, Jens

Langacker, Paul

Munir, Shoaib

Rojas, Eduardo

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Constraints on the mass and mixing of $Z$ bosons

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Constraints on the mass and mixing of Zʹ bosons

We tested several models in which the Standard Model (SM) gauge group is extended by an additional U (1) gauge symmetry against available electroweak precision data to impose limits

on the mass of the neutral Z ′ boson, M Z ′ , predicted in all such models, and on the Z − Z ′ mixing angle, θ ZZ ′ , at 95% C.L. We found lower limits on M Z ′ of order 1 TeV in most cases, while θ ZZ ′ was found to be constrained to very small values

Universidad de Nariño (UDENAR)

arXiv:0910.0269v2  [hep-ph]  7 Oct 2009PITHA 09/26September 6, 2018Constraints on the mass and mixing of Z′bosonsJ. Erlera,b1, P. Langackerc2, S. Munira3, E. Rojasa4a Departamento de F́ısica Teórica, Instituto de F́ısica, Universidad NacionalAutónoma de México, 04510 México D.F., Méxicob Institut für Theoretische Physik E, RWTH Aachen, 52056 Aachen, Germanyc School of Natural Sciences, Institute for Advanced Study, Einstein Drive,Princeton, NJ 08540, USAAbstractWe tested several models in which the Standard Model (SM) gauge group is extended by anadditional U(1) gauge symmetry against available electroweak precision data to impose limitson the mass of the neutral Z ′ boson, MZ′ , predicted in all such models, and on the Z − Z ′mixing angle, θZZ′ , at 95% C.L. We found lower limits on MZ′ of order 1 TeV in most cases,while θZZ′ was found to be constrained to very small values.Keywords: Beyond Standard Model, Extended Gauge Sectors, Electroweak DataPACS: 2.60.Cn Extensions of electroweak gauge sector, 14.70.Pw Other gauge bosons1 IntroductionOne of the best motivated extensions of the SM is a neutral gauge sector with an extraU(1) symmetry in addition to the SM hypercharge U(1)Y and an associated Z′ gauge boson,predicted in most Grand Unified Theories (GUTs) such as SO(10) or E6 [1]. There is anextensive range of models with such an additional U(1) symmetry (for reviews, see [2, 3,4] and references therein). Among these, models based on the E6 GUT group and left-right symmetry groups have been extensively pursued in the literature and are particularlysignificant from the point of view of LHC phenomenology. Here we summarize the analysisdone in [5] of various Z ′ models, which include E6 based Zχ, Zψ, Zη [6, 7, 8, 9], ZN [10, 11]and ZR [12] bosons, a ZLR boson appearing in models with left-right symmetry (reviewed inRef. [13]), a sequential ZSM boson and a family non-universal Zstring boson [14].1erler@fisica.unam.mx2pgl@ias.edu3smunir@fisica.unam.mx4eduardor@fisica.unam.mx12 Mixing and ParametersThe mixing between the mass eigenstates of Z ′ and the Z is given by,tan2 θZZ′ =M20−M2ZM2Z′ −M20, (1)where M0 is the mass of Z boson in the absence of Z − Z ′ mixing and is given asM0 =MW√ρ0 cos θW; ρ0 ≡∑i(t2i − t23i + ti)|〈φi〉|2∑i 2t23i|〈φi〉|2. (2)We set ρ0 = 1 here, which corresponds to a Higgs sector with only SU(2) doublets andsinglets. Furthermore, if the U(1)′ charge assignments of the Higgs fields, Q′i, are known ina specific model, then there exists an additional constraint [15],θZZ′ = Cg2g1M2ZM2Z′, (3)where g1 = gL/ cos θW and where g2 =√5/3 g1 sin θW√λ is the U(1)′ gauge coupling. Thelatter is given in terms of λ whose value is conventionally set to 1 here. C is a function ofvacuum expectation values (VEVs) of the Higgs fields and the Q′i,C = −∑i t3iQ′i|〈φi〉|2∑i t23i|〈φi〉|2. (4)For E6 based models one may restrict oneself to the case where the Higgs fields arise froma 27 representation. The U(1)′ quantum numbers are then predicted and eq. 4 receivescontributions from the VEVs of three Higgs doublets, x ≡ 〈φν〉, v ≡ 〈φN〉 and v̄ ≡ 〈φN̄〉,respectively, in correspondence with the standard lepton doublet, as well as the two dou-blets contained in the 10 of SO(10) ⊂ E6. They satisfy the sum rule, |v|2 + |v̄|2 + |x|2 =(√2 GF )−1 = (246.22 GeV)2, and we introduce the ratios,τ =|v̄|2|v|2 + |v̄|2 + |x|2 , ω =|x|2|v|2 + |v̄|2 + |x|2 ; (0 ≤ τ, ω ≤ 1), (5)resulting in different expressions and ranges for C in different models [5].3 ResultsWe used the special purpose FORTRAN package GAPP [16] dedicated to the Global Analysisof Particle Properties, wherein the effects of the Z ′ bosons are taken into account as firstorder perturbations to the SM expressions. The most stringent indirect constraints on MZ′come from low-energy weak neutral current (WNC) experiments, while the size of the mixingangle θZZ′ is strongly constrained by the very high precision Z-pole experiments at LEP andSLC. For details on the data, input parameters and analysis, see [5].2Z ′ MZ′ [GeV] sin θZZ′ χ2minEW (this work) CDF DØ LEP 2 sin θZZ′ sin θminZZ′ sin θmaxZZ′Zχ 1,141 892 640 673 −0.0004 −0.0016 0.0006 47.3Zψ 147 878 650 481 −0.0005 −0.0018 0.0009 46.5Zη 427 982 680 434 −0.0015 −0.0047 0.0021 47.7ZN 623 861 −0.0004 −0.0015 0.0007 47.4ZR 442 −0.0003 −0.0015 0.0009 46.1ZLR 998 630 804 −0.0004 −0.0013 0.0006 47.3ZSM 1,403 1,030 780 1,787 −0.0008 −0.0026 0.0006 47.2Zstring 1,362 0.0002 −0.0005 0.0009 47.7SM ∞ 0 48.5Table 1: 95% C.L. lower mass limits on extra Z ′ bosons for various models from EW precisiondata and constraints on sin θZZ′. For comparison, we show also (where applicable) the limitsobtained by CDF, DØ and LEP 2.In Table 1 we present our limits on the Z ′ parameters for the models listed in the in-troduction. Also shown in Table 1 are the current limits on various Z ′ boson masses fromthe Tevatron and LEP 2. The mass limits at the Tevatron assume that no decay channelsinto exotic fermions or superpartners are open to the Z ′; otherwise the limits would bemoderately weaker. The Table shows that the mass limits from the EW precision data aregenerally competitive with and in many cases stronger than those from colliders.Figures 1 and 2 show 90% C.L. exclusion contours for all models. The solid lines specifyuse of the constraint ρ0 = 1 while the dashed lines are for ρ0 free. We also show the extraconstraints for the specific Higgs sectors discussed above. These are represented by thedotted and long-dashed lines. The numbers in the plots refer to the values of τ or ω, fromranges given in eq. 5. The best fit locations are indicated by an "x". The lower limitsfrom CDF (dot-dashed), DØ (double-dot-dashed) and LEP 2 (dot-double-dashed) given inTable 1 are also shown.AcknowledgmentsThe work at IF-UNAM is supported by CONACyT project 82291–F. The work of P.L. issupported by the IBM Einstein Fellowship and by NSF grant PHY–0503584.References[1] H. Georgi and S. L. Glashow, Phys. Rev. Lett. 32, 438–441 (1974).[2] P. Langacker, arXiv:0801.1345 [hep-ph].[3] T. G. Rizzo, arXiv:hep-ph/0610104; in the proceedings of Exploring New FrontiersUsing Colliders and Neutrinos (TASI 2006), Boulder, CO, June 4–30, 2006.3Figure 1: 90% C.L. contours in MZ′ vs. sin θZZ′ for various models. See the text for details.[4] A. Leike, Phys. Rept. 317, 143 (1999).[5] J. Erler, P. Langacker, S. Munir and E. Rojas, JHEP 0908:017 (2009).[6] R. W. Robinett and J. L. Rosner, Phys. Rev. D 26, 2396 (1982).[7] P. Langacker, R. W. Robinett and J. L. Rosner, Phys. Rev. D 30, 1470 (1984).[8] J. L. Hewett and T. G. Rizzo, Phys. Rept. 183, 193 (1989).[9] P. Candelas, G. T. Horowitz, A. Strominger and E. Witten, Nucl. Phys. B 258, 46(1985).[10] E. Ma, Phys. Lett. B 380, 286 (1996).4Figure 2: 90% C.L. contours in MZ′ vs. sin θZZ′ for various models. See the text for details.[11] J. Kang, P. Langacker and T. Li, Phys. Rev. D 71, 015012 (2005).[12] J. Erler and P. Langacker, Phys. Rev. Lett. 84, 212 (2000).[13] R. N. Mohapatra, Unification And Supersymmetry, Springer–Verlag, Berlin, 1986.[14] S. Chaudhuri, S. W. Chung, G. Hockney and J. D. Lykken, Nucl. Phys. B 456, 89(1995).[15] P. Langacker and M. Luo, Phys. Rev. D 45, 278 (1992).[16] J. Erler, arXiv:hep-ph/0005084; in the proceedings of Physics at RUN II: QCD andWeak Boson Physics Workshop: 2nd General Meeting, Batavia, IL, June 3–4, 1999.5

Constraints on the mass and mixing of Z-prime bosons

Constraints on the mass and mixing of Z' bosons

Constraints on the mass and mixing of Z' bosons

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