The rest of the paper is organized as follows. In section 2 we describe the parametriza-
tion of the effective interaction Lagrangian relevant for our study, the CP-odd observable
defined in terms of the ρ
±
decay planes, and the details of our MC simulation of the signal
and background processes. The kinematic selection criteria used to achieve an optimum
signal to background ratio is described in the first part of section 3, along with the signal
and background rates for 14 TeV LHC. We then go on to discuss the CP-odd correlations,
the impact of detector resolution uncertainties on them, the signal and background distri-
butions after all cuts, and finally the projected measurement reach of the CP-mixing angle
at the HL-LHC. We summarize our findings in section 4. The validation of our simulation
framework against the ATLAS 8 TeV analysis of h → τ
+
τ
−
in the VBF category is briefly
discussed in the appendix.
2 Analysis setup
2.1 Effective interaction Lagrangian
We parametrize the effective hτ
+
τ
−
interaction after electroweak symmetry breaking as
follows:
L
hτ τ
= −
y
τ
√
2
h¯τ(cos ∆ + iγ
5
sin ∆)τ. (2.1)
Here, h is the observed 125 GeV scalar mass eigenstate, y
τ
is the Yukawa coupling of the
tau lepton in the SM, y
τ
=
√
2m
τ
/v, with m
τ
being the τ mass and v ' 246 GeV. With this
parametrization, the branching fraction (BR) of h → τ
+
τ
−
is fixed at its SM prediction,
whose central value is 6.32% for a 125 GeV SM Higgs [51].
1
Such an effective vertex can
arise, for example, in a general two-Higgs doublet model, where the CP-even and CP-odd
scalars can mix after electroweak symmetry breaking, thereby breaking CP symmetry. We
shall refer to the angle ∆ as the CP-mixing angle, which, in our convention, takes values
in the range
− π/2 < ∆ ≤ π/2, (2.2)
with ∆ = 0 and ∆ = π/2 corresponding to pure CP-even and pure CP-odd couplings re-
spectively. While discussing our results in later sections, in addition to ∆ = 0 and ∆ = π/2,
we shall also use ∆ = π/4 as a benchmark, which corresponds to a maximal mixing.
Although there are no direct constraints on ∆ from any measurement so far, there can
be indirect constraints from the upper bound on the electric dipole moment of electrons
and neutrons. Such constraints on the CP-odd component of the hτ
+
τ
−
coupling is rather
weak at present due the smallness of the τ Yukawa coupling, and in fact they do not restrict
the coupling range [52] considered in this study. Furthermore, the electric dipole moment
constraints hold only under the further assumption that the first generation Yukawa cou-
plings are the same as in the SM, making the direct collider measurement an important
complementary probe.
As discussed earlier, for studying the CP property of the hτ
+
τ
−
coupling, we shall focus
on the one prong tau decay mode, τ
∓
→ ρ
∓
(−)
ν
τ
, which has the highest branching fraction of
1
In a more general parametrization of the hτ
+
τ
−
effective interaction, the h → τ
+
τ
−
partial decay
width can also be modified from its SM prediction.
– 3 –