CMS探索7 TeV和8 TeV下MSSM中性希格斯粒子μ+μ-衰变的无显著信号

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CMS Collaboration / Physics Letters B 752 (2016) 221–246 225

Fig. 4. The dimuon invariant mass distribution for events that belong to C1 (upper left) and C2 category (upper right), for data and simulated events at

√

s = 7TeV. The

corresponding quantities are shown for

√

s = 8 TeV (lower left and lower right). The expected contributions to signal assuming the m

mod+

scenario for m

= 150 GeV and

tan β =30 are displayed for comparison.

5. Signal selection eﬃciency

While the calculations for the MSSM cross sections performed

in the narrow-width approximation refer to the on-shell Higgs bo-

son

production, at large values of m

and tan β the convolution

of the larger intrinsic signal widths with the parton distribution

functions (PDF) results in a non-negligible fraction of signal events

produced signiﬁcantly off-shell. Events with invariant mass signiﬁ-

cantly

smaller than its nominal value have a lower reconstruction

eﬃciency than those produced near the mass peak. For consis-

tency,

we deﬁne signal eﬃciency as the probability for a signal

event with the generated invariant mass close to its nominal value

to be reconstructed and pass all selection requirements of this

analysis. The closeness is deﬁned using a window of size equal to

3 times the intrinsic signal width (an uncertainty associated with

this deﬁnition is evaluated using a window of 5 times its width,

as discussed in Section 7). With this deﬁnition, the product of the

MSSM Higgs boson production cross section, luminosity and signal

eﬃciency provides the normalization for the Higgs boson produced

near on-shell. The full predicted rate of signal events also con-

tains

an additional off-shell contribution, which varies with m

and tan β and is less than 5% for m

< 250 GeV and tan β<15,

and can be as large as 15% for m

= 300 GeV and tan β = 30.

Additional

corrections are applied to the signal eﬃciency to

take into account differences between data and simulation in the

muon trigger, reconstruction, and isolation eﬃciencies. A correc-

tion

is also applied to account for known data-simulation discrep-

ancies

in the b tagging eﬃciency and mistagging probability. The

corrections are summarized by a weight factor, which is assigned

to each signal event. The average of the weight factors computed

over all the events is very close to one, reﬂecting the fact that the

simulation describes the data with good accuracy.

Fig. 5 shows the signal eﬃciency at

√

s = 8TeVfor AP (top)

and GF (bottom) process after combining the two event categories

C1 and C2. The eﬃciencies at

√

s = 7TeVare similar. The band in

the ﬁgure represents the variation of the eﬃciency due to the lim-

ited

statistics of the samples used. The relative amount of AP and

GF events in the two event categories varies with m

and tan β,

since the production cross sections of the two processes depend

on these parameters. For example, in the case m

= 150 GeV and

tan β = 30, more than 90% of the signal events in C1 would be

from AP production, and about 60% in C2. For m

= 150 GeV and

tan β = 5, where the GF contribution becomes more relevant, the

content of AP events would be 60% in C1 and only 15% in C2.

6. Fit procedure

The procedure described below is applied separately to C1 and

C2 events. The event selection criteria are applied to the simu-

lated

samples listed in Table 1. For each sample, and for each of

the three φ bosons, the invariant mass distribution of the events

that pass the event selection is approximated with a Breit–Wigner

226 CMS Collaboration / Physics Letters B 752 (2016) 221–246

Fig. 5. Signal eﬃciency for the AP process at

√

s = 8TeV, shown separately for the three φ boson types, (upper left) h, (upper centre) H, and (upper right) A, as a function

of m

. The corresponding eﬃciency for the GF production process is shown in the lower row. The contributions from the two event categories C1 and C2 are combined.

The results are integrated over tan β, since the eﬃciency does not strongly depend on this quantity. The band shows the change in eﬃciency due to the limited number of

simulated events.

function convolved with a Gaussian, that accounts for detector res-

olution.

This analytical expression provides a good description of

the signal shape for all the m

and tan β values. The three func-

tions

are denoted F

, F

, and F

, and contain the mass and width

of the Breit–Wigner and the width of the Gaussian as free param-

eters.

The function F

sig

represents the expected signal yield, and it

is a linear combination of the three functions described above:

sig

= w

+ w

, (2)

where w

, w

, and w

, are the number of events containing h, H,

and A bosons, respectively, calculated according to their expected

production cross sections. An example of this procedure is shown

in Fig. 6 (top) for m

= 150 GeV and tan β =30. The highest peak

represents the superposition of the contributions from H and A

bosons, that in this case are almost degenerate in mass.

Since

the Drell–Yan muon pair production is the dominant

background process, it is modeled by a Breit–Wigner function plus

a photon-exchange term, which is proportional to 1/m

−

. Deﬁn-

ing

m = m

−

, the function F

bkg

becomes:

bkg

= e

λm

⎡

⎣

norm

(m −m

)



(

1 − f

)

norm

⎤

⎦

(3)

where e

λm

describes the effects of the PDF, and the N

norm

terms

correspond to the integral of the corresponding functions in the

chosen mass range. The quantity f

represents the contribution of

the Breit–Wigner term relative to the photon-exchange term. The

quantities λ and f

are free parameters of the ﬁt. The parameters



and m

are determined separately for the C1 and the C2 events

from a ﬁt to the m

−

distribution in the mass range of the Z

boson

between 80 and 120 GeV. The ﬁt provides the effective val-

ues

of such quantities, that include detector and resolution effects

for each set of data. Their values are used in F

bkg

and are kept

constant in the ﬁt.

linear combination of the two functions for the expected sig-

nal

and background is then used in an unbinned likelihood ﬁt to

the data:

ﬁt

= (1 − f

bkg

) F

sig

+ f

bkg

. (4)

The parameters that describe the signal are determined in the

ﬁt of the simulated signal to Eq. (2), for each pair of m

and tan β

values. Subsequently, they are ﬁxed in F

ﬁt

, where the free parame-

ters

are the quantities λ, f

, and f

bkg

. The fraction of signal events

is deﬁned as f

sig

= (1 − f

bkg

). The data are ﬁtted to F

ﬁt

in the

mass range from 115 to 300 GeV for each point in the m

and

tan β parameter space. As an example, the ﬁt to the data of C2 at

√

s = 8TeVis illustrated in Fig. 6, (bottom), assuming a signal with

= 150 GeV and tan β = 30.

7. Systematic uncertainties

The following sources of systematic uncertainties are taken into

account, and the impact of one standard deviation change is re-

ported

in terms of a variation in the nominal signal eﬃciency

deﬁned in Section 5.

The

limited number of simulated events introduces an un-

certainty

in the signal selection eﬃciency that is at most 2.0%.

The muon trigger, reconstruction, identiﬁcation, and isolation ef-

ﬁciencies

are determined from data using a tag-and-probe tech-

nique [38].

The uncertainty in the trigger eﬃciency correction is

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