The ATLAS Collaboration / Physics Letters B 784 (2018) 345–366 349
Fig. 1. (a) Invariant mass distribution for the data (points with error bars) shown together with the simultaneous fit result to H → ZZ
∗
→ 4 candidates (continuous line).
The background component of the fit is also shown (filled area). The signal probability density function is evaluated per-event and averaged over the observed data. (b) Value
of −2 ln as a function of m
H
for the combined fit to all H → ZZ
∗
→ 4 categories. The intersection of the −2 ln curve with the horizontal lines labelled 1σ and 2σ
provide the 68.3% and 95.5% confidence intervals.
sample equal in size to the experimental data set is, on average, 3%
smaller
than the statistical uncertainty obtained with the template
method. Both methods are found to be unbiased within the statis-
tical
uncertainty of the simulated samples used of about 8MeVon
m
H
.
7.3. Results
The estimate of m
H
for the per-event and template methods
is extracted with a simultaneous profile likelihood fit to the six-
teen
categories. The free parameters of the fit are m
H
, the nor-
malisation
modifiers of each BDT category, and the nuisance pa-
rameters
associated with systematic uncertainties. The measured
value of m
H
from the per-event method is found to be m
ZZ
∗
H
=
124.79 ± 0.36 (stat) ±0.05 (syst) GeV = 124.79 ±0.37 GeV.
The
total uncertainty is in agreement with the expectation
and is dominated by the statistical component. The root-mean-
square
of the expected uncertainty due to statistical fluctuations
in the event yields of each category was estimated to be 40 MeV.
The p-value of the uncertainty being as high or higher than the
observed value, estimated with pseudo-experiments, is found to
be 0.47. The total systematic uncertainty is 50 MeV, the lead-
ing
sources being the muon momentum scale (40 MeV) and the
electron energy scale (26 MeV), with other sources (background
modelling and simulation statistics) being smaller than 10 MeV.
For
the template method, the total uncertainty is found to be
+0.41
−0.39
GeV, larger by 35 MeV than for the per-event method. The
observed difference for the m
H
estimates of the two methods is
found to be 0.16 GeV, which is compatible with the expected vari-
ance
estimated with pseudo-experiments and corresponds to a one
sided p-value of 0.19. Fig. 1(a) shows the m
4
distribution of the
data together with the result of the fit to the H → ZZ
∗
→ 4
candidates when using the per-event method. The fit is also per-
formed
independently for each decay channel, fitting all BDT cate-
gories
simultaneously; the resulting likelihood profile is compared
with the combined fit in Fig. 1(b). The combined measured value
of m
H
is found to be compatible with the value measured inde-
pendently
for each channel, with the largest deviation being 1.4σ
for the 2μ2e channel and the others being within 1σ .
The
Higgs boson mass in the four-lepton channel is also mea-
sured
by using a profile likelihood ratio to combine the informa-
tion
from the Run 1 analysis [6], where m
H
= 124.51 ± 0.52 GeV,
and the Run 2 analysis, keeping each individual signal normalisa-
tion
parameter independent. The systematic uncertainties taken to
be correlated between the two runs are the muon momentum and
electron energy scales, while all other systematic uncertainties are
considered uncorrelated. The combined Run 1 and Run 2 result is
m
ZZ
∗
H
=124.71 ±0.30 (stat) ±0.05 (syst) GeV = 124.71 ±0.30 GeV.
The difference between the measured values of m
H
in the four-
lepton
channel in the two runs is m
ZZ
∗
H
= 0.28 ± 0.63 GeV, with
the two results being compatible, with a p-value of 0.84.
8. Mass measurement in the H → γγ channel
In the diphoton channel, the Higgs boson mass is measured
from the position of the narrow resonant peak in the m
γγ
distri-
bution
due to the Higgs boson decay to two photons. Such a peak
is observed over a large, monotonically decreasing, m
γγ
distribu-
tion
from continuum background events. The diphoton invariant
mass is computed from the measured photon energies and from
their directions relative to the diphoton production vertex, cho-
sen
among all reconstructed primary vertex candidates using a
neural-network algorithm based on track and primary vertex in-
formation,
as well as the directions of the two photons measured
in the calorimeter and inner detector [49].
Events
are selected and divided into categories with differ-
ent
mass resolutions and signal-to-background ratios, optimised
for the measurement of simplified template cross-sections [30,50]
and
of production mode signal strengths of the Higgs boson in
the diphoton decay channel. The event selection and classifica-
tion
are described in Ref. [24]. A potential reduction of the total
expected uncertainty by 4% could have been obtained using the
same event categories chosen for the mass measurement with the
Run 1 data [7]. Given the small expected improvement, a choice
was made to use the same categorisation for the measurement of
the mass and of the production mode signal strengths.
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