Eur. Phys. J. C (2016) 76:514 DOI 10.1140/epjc/s10052-016-4362-8 Regular Article - Theoretical Physics On the exotic Higgs decays in effective field theory Hermès Bélusca-Maïtoa, Adam Falkowskib Laboratoire de Physique Théorique, Université Paris-Sud, Bat. 210, 91405 Orsay, France Received: 22 April 2016 / Accepted: 9 September 2016 / Published online: 22 September 2016 © The Author(s) 2016. This article is published with open access at Springerlink.com Abstract We discuss exotic Higgs decays in an effec- in powers of 1/. The leading effects are expected from tive field theory where the Standard Model is extended by operators of dimension 6, as their coefficients are suppressed dimension-6 operators. We review and update the status of by 1/2. The first classification of dimension-6 operators two-body lepton- and quark-flavor-violating decays involv- was performed in Ref. [1]. For one generation of fermions, ing the Higgs boson. We also comment on the possibility of a complete non-redundant set (henceforth referred to as a observing three-body flavor-violating Higgs decays in this basis) was identified and explicitly written down in Ref. [2]. context. Reference [3] extended this to three generations of fermions, in which case a basis is characterized by 2499 independent parameters. Contents In this paper we are interested in the subset of these operators that lead to exotic decays of the 125 GeV Higgs 1 Introduction ..................... 1 boson. By “exotic” we mean decays that are forbidden in 2 Exotic Higgs couplings from dimension-6 Lagrangian 2 the SM or predicted to occur with an extremely suppressed 3 Two-body Higgs decays ............... 3 branching fraction. More specifically, we are interested in 3.1 Lepton-flavor-violating decays ......... 3 decays that violate the lepton flavor or quark flavor. Lepton- 3.2 Flavor-changing top quark decays ....... 5 flavor-violating (LFV) processes are completely forbidden 4 Three-body decays .................. 6 in the SM in the limit of zero neutrino masses. Quark-flavor- 4.1 h → Wbq .................... 6 violating (QFV) Higgs decays as a flavor-changing neutral 4.2 h → 12γ ................... 6 current process are forbidden in the SM at tree level. The- 4.3 h → 12 Z ................... 7 oretical studies of exotic Higgs decays have a long history; 4.4 t → hqV .................... 8 see e.g. Refs. [4–11] and [12] for a review. Most of these 5 Conclusions ..................... 9 papers assume new light degrees of freedom, in which case References ........................ 9 the EFT approach described here is not adequate. On the other hand, Refs. [13,14] recently studied the possibility of LFV and QFV two-body decays of the 125 GeV Higgs within 1 Introduction the EFT framework. Such decays can arise in the presence of Yukawa-type dimension-6 operators [15]. These papers If new particles beyond the standard model (SM) are much demonstrated that LFV Higgs decays to τ ±μ∓ and τ ±e∓ heavier than 100 GeV, physics at the weak scale can be with the branching fraction as large as 10 % are allowed by described by an effective field theory (EFT) with the SM current indirect constraints. At the same time, the LHC is Lagrangian perturbed by higher-dimensional operators. The currently sensitive to branching fractions of order 1 % [16]. latter encode, in a model-independent way, possible effects This corresponds to probing the scale suppressing the corre- of new heavy particles at energies well below the new physics sponding dimension-6 operators at the level of ∼ 10 TeV. scale . The EFT framework allows for a systematic expan- The goal for this paper is to extend this study to a full set of sion of these effects in operator dimensions or, equivalently, dimension-6 operators. Apart from the Yukawa-type opera- tors, exotic Higgs decays can arise in the presence of vertex- † ¯ μ ¯ μν a e-mail: [email protected] type ∼ H Dμ Hψγ ψ and dipole-type ∼ Hψσ ψ Fμν b e-mail: [email protected] operators. We systematically discuss these operators and the 123 514 Page 2 of 10 Eur. Phys. J. C (2016) 76 :514 new Higgs decay channels that they imply. The structure of The gauge couplings of SU(3) × SU(2) × U(1) are denoted the dimension-6 Lagrangian then implies certain relations by gS, gL , gY , respectively; we also define the electromag- between these Higgs couplings, as well as relations between = / 2 + 2 netic coupling e gL gY gL gY , and the weak angle single-Higgs interactions and Lagrangian terms without a sθ = g / g2 + g2 . The Higgs doublet H acquires the Higgs that affect precision observables. We give the limits Y L Y√ on each of the couplings from precision tests of the SM. That VEV H=(0,v/ 2), where v ≈ 246.2GeV.Wealso ˜ = ∗ information can be explored to place limits on the allowed define Hi ijH j . After electroweak symmetry break- ± magnitude of the Higgs couplings. We will discuss the maxi- ing, the gauge√ mass eigenstates are defined as W = mum exotic Higgs branching fraction that these limits permit. (W 1 ∓ iW2)/ 2, Z = cθ W 3 −sθ B, A = sθ W 3 + cθ B, The paper is organized as follows. In Sect. 2 we define where cθ = 1 − s2 = g / g2 + g2 . The fermions our notation and introduce the dimension-6 Lagrangian with θ L L Y = ( , † ) = (ν , ) LFV and QFV interactions in the Higgs basis. In Sect. 3 we qL uL VCKMdL and L L eL are doublets of review and update the results of Refs. [13,14] concerning the SU(2) gauge group. All fermions are three-component two-body exotic Higgs decays. In Sect. 4 we study the possi- vectors in the generation space. We work in the basis where u,d, bility of LFV and QFV Higgs decays mediated by vertex- and the fermions are mass eigenstates, thus Y are 3×3 diago- f √v nal matrices such that [Y ]ij = m f δij. The Higgs boson dipole-type operators, respectively. Obviously, studying the 2 i full parameter space of the dimension-6 Lagrangian would interactions following from Eq. (2), be an extremely difficult task. To deal with the degeneracies 2 SM h h 2 + − μ 2 μ among the parameters, one simplifying assumption we make L = + 2m W W + m Zμ Z h v v2 W μ Z throughout this paper is that the flavor-diagonal Higgs cou- 2 2 2 plings are not significantly affected by higher-dimensional h ¯ mh 3 mh 4 − m f ff− h − h , (3) operators. Furthermore, we will assume that there are no large v 2v 8v2 f fine-tuned cancellations between different parameters so as to satisfy constraints from precision experiments. In such a do not contain any LFV nor QFV couplings. constrained framework, we discuss the limits on the LFV and We move to describe the effect of dimension-6 opera- QFV Higgs couplings from various precision measurements. tors. In Eq. (1) we choose to normalize them by the elec- Given these constraints, we discuss the implications for the troweak scale v, while the new physics scale is absorbed 2 2 rate of exotic Higgs decays at the LHC. into the coefficients ci ∼ v / of these operators in the Lagrangian. A complete non-redundant LD=6 for three gen- erations of fermions was explicitly written down in Ref. [3]. Here we work at the level of Higgs boson couplings with 2 Exotic Higgs couplings from dimension-6 Lagrangian other SM mass eigenstates, as in [17,18]. In this language, the Lagrangian is defined by a set of couplings [δy ], [δgVf], and We consider an effective theory where the SM is extended f [d ], which are in general 3×3 matrices with non-diagonal by dimension-6 operators: Vf elements for all fermion species f . A subset of these inter- actions violates lepton flavor and introduces tree-level flavor 1 = L = LSM + LD 6. (1) changing neutral currents for quark-flavor violation. eff v2 The first group is related to corrections to the SM Higgs Yukawa couplings in Eq. (3): We assume the SM electroweak symmetry is linearly real- L ized. This implies eff contains local operators invariant D=6 h ¯ under the SU(3) × SU(2) × U(1) symmetry; in particu- L =− m m [δy ] f , f , + h.c. hff v fi f j f ij R i L j lar, the Higgs boson h enters the Lagrangian only through f ∈u,d,e i = j gauge invariant interactions of the Higgs doublet H. The SM (4) Lagrangian in our notation takes the form These couplings arise from dimension-6√ operators of the LSM =−1 a a μν − 1 i i μν − 1 μν form c |H|2 fHf¯ , with [c ] ∼ m m [δy ] . 4 Gμν G 4 Wμν W 4 Bμν B f f ij fi f j f ij μ The second group is related to the contact interactions +D H † Dμ H + μ2 H † H − λ(H † H)2 H between the Higgs boson, fermions, and the massive SU(2) + ¯ γ μ + ¯ γ μ i fL Dμ fL i f R Dμ f R vector bosons: f ∈q, f ∈u,d,e − ˜ † ¯ u + † ¯ d + † ¯ + . 2 H u RY qL H dRY VCKMqL H eRY L h c D=6 gL h + μ Wq L = √ + W u¯ , γ [δg ] d , hV f f 1 v μ L i L ij L j (2) 2 i = j 123 Eur. Phys. J. C (2016) 76 :514 Page 3 of 10 514 +¯ γ μ[δ Wq] +¯ν γ μ[δ W] + . u R,i gR ijdR, j L,i gL ijeL, j h c ing these parameters in the low-energy EFT is expected to ⎡ exhibit some sort of chiral suppression.