Higgs boson as a dilaton
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ELEMENTARY PARTICLES AND FIELDS Theory
Higgs Boson as a Dilaton* M. G. Ryskin and A. G. Shuvaev** Petersburg Nuclear Physics Institute, Russian Academy of Sciences, Gatchina Received December 7, 2009
Abstract—We study possible phenomenological consequences of the recently proposed new approach to the Weinberg–Salam model. The electroweak theory is considered as a gravity and the Higgs particle is interpreted in it as a dilaton, without the usual potential of interaction in the Higgs sector. We have taken as a test the process of photon pair production, e+ + e− → Z + γ + γ. In the framework of new formulation this reaction is mediated in the lowest order by the dilaton. The cross section is found to be rather small. DOI: 10.1134/S1063778810060104
1. INTRODUCTION Recently, a new formulation of the Weinberg– Salam model has been suggested [1–4] (the similar ideas are discussed also in papers [5–9]). A novel feature of this approach is the interpretation of the electroweak theory in terms of a gravity theory with the Higgs field as a dilaton. The bosonic sector of the standard electroweak theory given by the Lagrangian including Yang–Mills triplet Wμa , Abelian vector field Yμ , and complex scalar Higgs dublet Φ = (φ1 , φ2 )1) , 1 1 2 (Y ) LWS = − G2μν (W ) − Fμν 4 4 + |Dμ Φ|2 + μ2 |Φ|2 − λ|Φ|4 ,
(1)
Gμν =
ρ2 ημν , m2
(4)
with flat Minkowski metric ημν = (+ − −−), where ρ is the modulus of the Higgs field, ρ2 = |Φ|2 , and m is the arbitrary parameter having dimension of mass. It provides a scale through which all other mass parameters are expressed, 1 2 2 2 g m = MW , 4
can be equivalently reformulated as an effective gravity2) , √ (2) LWS = −G −(Mp2 R + λ) + LM . Here, R is the scalar curvature, Mp plays the role of a Plank mass, and the second term is the matter Lagrangian, 1 LM = − G μρ G νσ Gμν Gρσ 4 1 1 μρ νσ − G G Fμν Fρσ + MZ2 G μν Zμ Zν 4 2 2 μν + + MW G Wμ Wν−
including massive vector bosons Z and W ± and massless photon Aμ . Lagrangian LM does not contain Higgs boson, which is interpreted in this approach as a dilaton and gives rise to the first, gravity, term. The metric tensor is always taken to be conformally flat,
(3)
1 2 (g + g2 )m2 = MZ2 , 2
Mp2 =
(5) 1 2 m . 6
The kinetic part of the dilaton field, (∂ρ)2 , turns into the scalar curvature in the gravity action3) , 2 m2 √ −GR = − ∂ρ + total derivatives. 6 The vector bosons acquire finite masses for m = 0 in the absence of the usual Higgs mechanism based on a symmetry breaking. There is no strict relation between the value of m and scalar potential parameter λ or Higgs mass μ, the nonzero masses can be generated in this interpretation even for λ = 0.
∗
The text was submitted by the authors in English. E-mail: [email protected] 1) Our notations are a bit different from those used in papers [1–4]. 2) The Higgs mass μ = 0 in LWS , the case μ = 0 is discussed in the next section.
3)
**
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There is a possible ambiguity related to the analytical continuation from Euclidean space, where the theory is originally formulated, to Minkowski
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