156
5 Direct Searches for New Physics
A matrix-element method [886] is used to separate signal from background events,
and the analysis uses the logarithm of the signal likelihood distribution as final discriminating variable. The multijet background is estimated from sideband regions,
obtained from a loosely tagged boson selection and large p
miss
T . The expected mass
limits obtained by this analysis are 970 GeV for B(B → Hb) = 1 and 1010 GeV for
B(T → Ht) = 1, which constitute the strongest channels of this analysis. The sensitivity of the analysis degrades for high m VLQ , because the matrix-element method
uses VLQ signals with a mass set to 900 GeV, leading to a decreasing separation
power of the signal likelihood distribution with increasing m VLQ . In the CMS analysis [887] a similar strategy is employed, where events with exactly four large-R
jets are categorised based on the labels from the BEST algorithm [229]. The BEST
algorithm runs on large-R jets, and boosts the jet constituents into four different
rest frames under the assumption that the jet originates from a W , Z , H or t. The
boost vector is formed by using the jet four-vector with the mass altered to be that of
the particle under consideration, while keeping the jet momentum constant. In each
rest frame, the jet constituents are used to calculate kinematic quantities including
Fox-Wolfram moments [202, 203], aplanarity, sphericity, and isotropy, based on the
eigenvalues of the sphericity tensor [43], and the jet thrust [44–46]. In addition, the
soft drop jet mass, jet charge, τ 32 , τ 21 , and the CSVv2 [504] discriminator values
calculated for the soft drop subjets in the original jet reference frame are used. In
total, 59 quantities are used as inputs to a DNN, which labels jets as W , Z , H , t, b or
light. All possible combinations of these labels, given to four jets, result in 126 independent signal regions with varying signal and background contributions. Regions
with high multiplicities of W , Z , H and t have the best sensitivity to VLQ pair production. An advantage of the BEST algorithm is that it naturally includes subjet b
tagging, making a matching between small-R and large-R jets unnecessary. In all signal regions with sufficient simulated events to model the dominant and sub-dominant
background processes, the H T distribution is used as discriminating variable between
signal and backgrounds. The H T is calculated from the scalar p T -sum of the large-R
jets. The multijet background in the signal regions is estimated by measuring the jet
classification probability for each BEST label in a sample with exactly three large-R
jets, which is dominated by multijet production with negligible signal contamination.
These probabilities are used to calculate event weights in an untagged selection with
exactly four large-R jets, considering every possible permutation of jets to arrive
at a given event category. In the final result, uncertainties in the signal efficiency
originating from the BEST classification are included through 11 independent nuisance parameters, one each for the classification and misclassification efficiencies
for the five BEST labels, and a final one for the QCD categorisation efficiency. These
nuisance parameters are allowed to float during the signal extraction, such that the
signal efficiencies are determined in-situ in this measurement, with their prior values
set to the expectations from simulation. The expected mass limits obtained by this
analysis are 1170 GeV for B(T → Ht) = 1, 1100 GeV for B(T → Zt) = 1 and
950 GeV for B(B → W t) = 1, which are the strongest channels of this analysis.
The weakest sensitivity is observed for final states with two b jets, as obtained from
B(T → W b) = 1 and B(B → Zb) = 1, where the backgrounds from multijet pro-
5 Direct Searches for New Physics
A matrix-element method [886] is used to separate signal from background events,
and the analysis uses the logarithm of the signal likelihood distribution as final discriminating variable. The multijet background is estimated from sideband regions,
obtained from a loosely tagged boson selection and large p
miss
T . The expected mass
limits obtained by this analysis are 970 GeV for B(B → Hb) = 1 and 1010 GeV for
B(T → Ht) = 1, which constitute the strongest channels of this analysis. The sensitivity of the analysis degrades for high m VLQ , because the matrix-element method
uses VLQ signals with a mass set to 900 GeV, leading to a decreasing separation
power of the signal likelihood distribution with increasing m VLQ . In the CMS analysis [887] a similar strategy is employed, where events with exactly four large-R
jets are categorised based on the labels from the BEST algorithm [229]. The BEST
algorithm runs on large-R jets, and boosts the jet constituents into four different
rest frames under the assumption that the jet originates from a W , Z , H or t. The
boost vector is formed by using the jet four-vector with the mass altered to be that of
the particle under consideration, while keeping the jet momentum constant. In each
rest frame, the jet constituents are used to calculate kinematic quantities including
Fox-Wolfram moments [202, 203], aplanarity, sphericity, and isotropy, based on the
eigenvalues of the sphericity tensor [43], and the jet thrust [44–46]. In addition, the
soft drop jet mass, jet charge, τ 32 , τ 21 , and the CSVv2 [504] discriminator values
calculated for the soft drop subjets in the original jet reference frame are used. In
total, 59 quantities are used as inputs to a DNN, which labels jets as W , Z , H , t, b or
light. All possible combinations of these labels, given to four jets, result in 126 independent signal regions with varying signal and background contributions. Regions
with high multiplicities of W , Z , H and t have the best sensitivity to VLQ pair production. An advantage of the BEST algorithm is that it naturally includes subjet b
tagging, making a matching between small-R and large-R jets unnecessary. In all signal regions with sufficient simulated events to model the dominant and sub-dominant
background processes, the H T distribution is used as discriminating variable between
signal and backgrounds. The H T is calculated from the scalar p T -sum of the large-R
jets. The multijet background in the signal regions is estimated by measuring the jet
classification probability for each BEST label in a sample with exactly three large-R
jets, which is dominated by multijet production with negligible signal contamination.
These probabilities are used to calculate event weights in an untagged selection with
exactly four large-R jets, considering every possible permutation of jets to arrive
at a given event category. In the final result, uncertainties in the signal efficiency
originating from the BEST classification are included through 11 independent nuisance parameters, one each for the classification and misclassification efficiencies
for the five BEST labels, and a final one for the QCD categorisation efficiency. These
nuisance parameters are allowed to float during the signal extraction, such that the
signal efficiencies are determined in-situ in this measurement, with their prior values
set to the expectations from simulation. The expected mass limits obtained by this
analysis are 1170 GeV for B(T → Ht) = 1, 1100 GeV for B(T → Zt) = 1 and
950 GeV for B(B → W t) = 1, which are the strongest channels of this analysis.
The weakest sensitivity is observed for final states with two b jets, as obtained from
B(T → W b) = 1 and B(B → Zb) = 1, where the backgrounds from multijet pro-