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New Charged Particles from Higgs Couplings

The recently reported observation of a new particle with mass about 125 GeV and couplings generally resembling those of the Standard Model Higgs boson provides a potential probe of the physics of electroweak symmetry breaking. Although the current data only provides hints, we suggest a particular combination of Higgs couplings as an assay for new charged particles connected with electroweak symmetry breaking, and construct a simple model with charge 5/3 quarks as a demonstration of its use.


I. INTRODUCTION AND CONCLUSIONS
The CMS and ATLAS collaborations have recently reported [1] the near-discovery of a new particle whose properties are generally consistent with those of the Standard Model (SM) Higgs boson. Such a discovery would herald the start of a new era in our quest to understand the physics of electroweak (EW) symmetry breaking. While experimenters continue to refine their measurements of the mass and couplings of this new state, theorists have already begun the daunting task of interpreting these results in the context of existing ideas for the origin of electroweak symmetry breaking and beyond the SM physics [2][3][4][5][6][7][8][9][10][11][12][13][14][15].
What observations indicate that a new particle h is directly connected with the physics of electroweak symmetry breaking? Broadly speaking the particle should have interactions reflective of the electroweak symmetry breaking masses of the SM fermions and gauge bosons.
But somewhat paradoxically some of the best information on the nature of electroweak symmetry breaking is likely to come from the couplings to the gauge bosons that do not acquire electroweak breaking masses, the gluons and the photon. The couplings of a Higgslike state to gluons and photons probe the quantum corrections coming from the SM fermions and gauge bosons as well as those from any new states that carry charge or color and couple, directly or indirectly, to the physics of electroweak symmetry breaking. Therefore the quantum-induced couplings hGG and hF F are a useful discriminant for models of EW symmetry breaking, can help test naturalness of this symmetry breaking, and may be one of the earliest indicators of the existence of charged particles beyond those of the SM.
Consider the addition to the standard model of a new fermion ψ in a color representation R carrying electric charge Q. If this new fermion couples to the physics of electroweak symmetry breaking we expect its mass to vary with the electroweak-breaking vev v ∼ 246 GeV.
But generally not all of the fermion's mass will arise from electroweak breaking and the mass parameter is a function of v: m ψ (v). Then the (non-derivative) coupling to the Higgs 1 h is dm ψ /dv. Our convention is m ψ ≥ 0 so a positive value for dm ψ /dv increases the fermion mass in the presence of electroweak breaking while a negative value decreases it.
The contributions of the new fermion ψ to the hGG and hF F couplings at one loop are easily calculated [16]. We can parameterize the new contributions to h couplings to gluons 1 We simplify the discussion by restricting to a SM Higgs doublet. Our discussion is easily generalized to more complex Higgs sectors. and photons as in [2]: With this parameterization the top quark loop contributes (in the limit 2m t m h ) δc g = 1 and δc γ = (2/3) 2 /2 = 2/9. For a general fermion the results are where I(R) and D(R) are the index and the dimension of the color representation R respec- is very close to unity for fermion masses larger than the h mass.
The relations eq. (2) already provide a useful result: the ratio of the deviation in the couplings of the h to photons and gluons is independent of the mass and (non-zero) coupling of the new fermion and is a measure of the fermion charge: The last equality follows from the relation between the index of a representation and its quadratic Casimir, C 2 (R)D(R) = I(R)D(G) with D(G) = 8 for SU (3). A measurement of δc γ /δc g is a measurement of Q 2 /C 2 (R) for the heavy fermion, solely from Higgs physics.
Several comments are in order: 1. Increasing the mass of the heavy fermion relative to its EW symmetry breaking mass contribution decreases δc g and δc γ in magnitude. Therefore this method of determining the charge of a very heavy fermion requires precise measurements of the Higgs couplings.
2. When more than one fermion contributes to eqs. (2) interpretation of the ratio in eq. (3) is not as straightforward. In the special case that all heavy fermions whose masses receive significant contributions from EW symmetry breaking have identical color and electric charges, the charges in eq. (2) factor out and eq. (3) still holds.
3. We may define For a single color-triplet fermion this is just the square of the electric charge of the fermion. More generally this is an "average" of the squared charges of multiple fermions weighted by d ln m/d ln v. The quantity q 2 provides a useful discriminant among and building guide for models of new physics.
In addition to heavy fermions we may also entertain the possibility of heavy scalars and vectors whose masses arise in part from EW symmetry breaking. Similarly to the fermion case, a scalar with mass-squared m 2 S (v) and a vector with mass-squared m 2 V (v) contribute R S and Q S are the color representation and charge of the scalar and are the corresponding quantities for the vector. A S and A V both approach one for small arguments. Again for a single particle (scalar, fermion or vector) the discriminant q 2 is simply (4/3)(Q 2 /C 2 (R)). In the more general case of several particles the contribution of scalars to δc is a factor of 4 smaller than that of fermions of the same charges, while the contribution from vectors is more than 5 times larger. However, most models of EW symmetry breaking do not contain new colored vectors with EW symmetry breaking masses so that I(R V ) = 0, and electrically charged vectors are strongly constrained from precision EW measurements, usually requiring masses in the multi-TeV range.
As an example we consider a simple model in which the dominant contributions to δc g and δc γ stem from a vector-like colored heavy fermion. We determine the desired charges of this new fermion by consulting fits of δc g and δc γ to LHC data. Such fits have been performed by a number of groups [2][3][4][5][6] with generally consistent results. For example, [2] fit δc g and δc γ to the combined LHC and Tevatron cross section data assuming that the tree level couplings of the Higgs to SM particles maintain their SM values. The fit in Figure   1 of their paper indicates that current data somewhat prefer negative values for δc γ and δc g , indicating that the heavy fermion mass should receive negative contributions from EW symmetry breaking. Furthermore, the fit shows a correlation between δc γ and δc g . Although the current data is not highly constraining, it does hint at a ratio For our example of a single fermion dominating the ratio this implies the electric charge of the fermion should satisfy The quadratic Casimir for SU (3) representations is bounded below by C 2 (R) ≥ 4/3 (with equality for a color triplet), and eq. (7) then forces the colored fermion to have charge > ∼ √ 2.
In the interest of keeping the electric charges as small as possible we choose the color-triplet representation: our new fermion is a "quark" with an exotic charge. The null results from experimental searches for fractionally charged heavy baryons or mesons suggest that the charges of any color triplet quarks should be quantized as The smallest charge greater than √ 2 consistent with eq. (8) The gauge invariant mass terms and Higgs couplings of these new fields are then Bear in mind that bars on the fields are part of the field names (they do not correspond to complex conjugation) and the coupling constant λ is unrelated to λ.
The mass matrix and Higgs couplings follow from the substitution H = (v + h, 0)/ √ 2.
Notice that the charge 2/3 quark does not couple to the Higgs field h and therefore does not contribute to δc g and δc γ . There are two Dirac charge 5/3 quarks which mix after electroweak symmetry breaking. Since they have the same color and electric charges eq. (3) applies and we confirm the prediction 2 δc γ δc g = 2 2 3 gluon couplings. The contributions to δc γ allow us to further fix the fraction of the fermion masses arising from EW symmetry breaking. Only the charge 5/3 quarks contribute and from eq. (2) we see that we need to compute The charge 5/3 mass matrix is   We will briefly focus on modest couplings 10 −6 < ∼ λ decay < ∼ 10 −1 with the lightest new quark decay being prompt yet still much slower than the decays of the heavier quarks.
Then the heavier new quarks always decay down to the lightest new quark, which in turn decays via W + t → W + W + b. Thus pair production of any of the heavy quarks leads to clear signatures with 4 to 8 W s and 2 b jets, an example of which is shown in fig. 2.
Precision EW constraints on this model are not expected to be very severe. Contributions of the new fermions to precision observables arise at loop level and scale like δ P EW ∼ λ 2 /(16π 2 )(v 2 /M 2 ) which we expect to be sufficiently small for most of parameter space. Also note that the contributions to the S and T parameters, which usually place the strongest constraints on new physics coupling to weak gauge bosons, are not enhanced by the square of the large charges of the new quarks.
The strongest lower bounds on the masses of the heavy quarks come from ATLAS and CMS searches for fourth family B quarks which are assumed to decay as B → W − t → W W b, and therefore BB production leads to the same final state as pair production of the lighter charge 5/3 quark. ATLAS searches require the B mass heavier than about 480 GeV [17], while CMS searches require a mass greater than 611 GeV [18].