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A new mechanism of Higgs-radion mixing

A new mechanism of Higgs-radion mixing. Igor Volobuev (SINP MSU). QFTHEP'2011 Sochi, 29 September 2011. Introduction It is a common knowledge in QFT that fields with the same quantum numbers can mix, if there is an interaction between them.

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A new mechanism of Higgs-radion mixing

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  1. A new mechanism of Higgs-radion mixing Igor Volobuev (SINP MSU)

  2. QFTHEP'2011 Sochi, 29 September 2011 Introduction It is a common knowledge in QFT that fields with the same quantum numbers can mix, if there is an interaction between them. A canonical example is the mixing of the weak hyper-charge U(1) gauge filed and of the neutral component of the SU(2) gauge field, which gives rise to the electromag- netic field and the field of the Z boson. In extensions of the SM additional fields can mix with the fields of the SM, if they have the same quantum numbers.

  3. QFTHEP'2011 Sochi, 29 September 2011 1 The Randall-Sundrum model L. Randall and R. Sundrum, “A large mass hierarchy from a small extra dimension”, Phys. Rev. Lett. 83 (1999) 3370 Two branes with tension at the fixed points of the orbifoldS1/Z2:

  4. QFTHEP'2011 Sochi, 29 September 2011 The solution for the background metric: The parameters k, Λ иλ1,2 satisfy the fine tuning conditions: The linearized gravity is obtained by the substitution

  5. QFTHEP'2011 Sochi, 29 September 2011 It is a gauge theory with the gauge transformations The functions ξM(x,y) satisfy the orbifold symmetry conditions The field hMN can be transformed to the gauge

  6. QFTHEP'2011 Sochi, 29 September 2011 The distance between the branes along the geodesic x = const The equations for the fields hμν(x,y) и Φ(x) can be decoupled by the substitution

  7. QFTHEP'2011 Sochi, 29 September 2011

  8. QFTHEP'2011 Sochi, 29 September 2011 The hiearrchy problem is solved, if M ~ k~ 1 TeV и kL~ 35. There appears a tower of tensor fields on the brane with the lowest mass of the order of M and the coupling to the SM fields of the order of 1/M. The branes in the Randall-Sundrum model can oscillate with respect to each other, which manifests itself as a massless four-dimensional scalar field, -- the radion field. The coupling of the radion to matter on the brane at y=L is too strong and contradicts the experimental constraints even at the level of classical gravity!

  9. QFTHEP'2011 Sochi, 29 September 2011 The radion field can mix with the Higgs field, if they are coupled. Such a coupling was put forward in paper G.F. Giudice, R. Rattazzi and J.D. Wells, “Graviscalars from higher-dimensional metrics and curvature-Higgs mixing”, Nucl. Phys. B 595 (2001) 250 [arXiv:hep-ph/0002178] and it looks like

  10. QFTHEP'2011 Sochi, 29 September 2011 2 Stabilized Randall-Sundrum model • Stabilization mechanisms: W.D.Goldberger and M.B.Wise, “Modulus stabilization with bulk fields”, Phys.Rev. Lett. 83 (1999) 4922 O.DeWolfe, D.Z.Freedman, S.S.Gubser and A.Karch, “Modeling the fifth dimension with scalars and gravity”, Phys.Rev. D 62 (2000) 046008

  11. QFTHEP'2011 Sochi, 29 September 2011 The second model is more consistent. Its action is taken to be If the potential V is of the form one can find exact solutions for this model.

  12. QFTHEP'2011 Sochi, 29 September 2011 For and the finetuned brane potentials the solution for the scalar field and the metric looks like For uL<<1 we have

  13. QFTHEP'2011 Sochi, 29 September 2011 The physical degrees of freedom of the model in the linear approximation were isolated in the paper E.E.Boos, Y.S.Mikhailov, M.N.Smolyakov and I.P.Volobuev, “Physical degrees of freedom in stabilized brane worldmodels”, Mod. Phys.Lett. A 21 (2006) 1431 They are: • tensor fields bμνn(x), n=0,1, …with masses mn (m_0 = 0) and wave functions in the space of extra dimension ψn(y), • scalar fields φn(x), n=1,2, …with masses μnand wave functions in the space of extra dimension gn(y).

  14. QFTHEP'2011 Sochi, 29 September 2011 The Higgs-radion mixing due to the curvature term in this model was discussed in paper C. Csaki, M.L. Graesser and G.D. Kribs, “Radion dynamics and electroweak physics”, Phys. Rev. D 63 (2001) 065002 [arXiv:hep-th/0008151] but only the lowest mode φ0(x) of the scalar KK tower was taken into account. It turns out that the cumulative effect of the higher scalar modes can be comparable with that of the first mode and in this case should be taken into account!

  15. QFTHEP'2011 Sochi, 29 September 2011 3New mechanism of Higgs-radion mixing We modify the action of the brane at y=L as follows: Then the equations of motion give We pass to the linearised theory by the substitution

  16. QFTHEP'2011 Sochi, 29 September 2011 The terms responsible for the Higgs-radion mixing are Expanding the field f in terms of four-dimensional modes, we get One can put here

  17. QFTHEP'2011 Sochi, 29 September 2011 Thus, we get the interaction Lagrangian Next we denote and observe that for M ~ 2TeV and μ1 ~ 200 Gev

  18. QFTHEP'2011 Sochi, 29 September 2011 Thus, we get a mass matrix

  19. QFTHEP'2011 Sochi, 29 September 2011 It is not difficult to find that One can approximately find the eigenvalues of this matrix. We introduce the following notations:

  20. QFTHEP'2011 Sochi, 29 September 2011 Then for the Higgs and the radion masses we obtain We also introduce normalization constants:

  21. QFTHEP'2011 Sochi, 29 September 2011 The mass eigenstate fields are

  22. QFTHEP'2011 Sochi, 29 September 2011 And their couplings to fermions and to the trace of the energy-momentum tensor look like

  23. QFTHEP'2011 Sochi, 29 September 2011 where the constants are given by

  24. QFTHEP'2011 Sochi, 29 September 2011 Thus we see that though the interaction of the individual excited scalar states with the Higgs field may be weak, there cumulative effect on the Higgs-radion mixing may be observable due to sizable values of the parameters Δ and ρ. A similar contribution of the directly unobservable KK modes to scattering processes was discussed in E.E. Boos, V.E. Bunichev, M.N. Smolyakov and I.P. Volobuev, “Testing extra dimensions below the production threshold of Kaluza-Kleinexcitations” Phys.Rev.D79:104013,2009 arXiv:0710.3100v4 [hep-ph].

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