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Search for Resonant and Nonresonant Higgs Boson Pair Production in the b

bτ

−

Decay Channel in pp Collisions at

ﬃﬃ

=13 TeV with the ATLAS Detector

M. Aaboud et al.

(ATLAS Collaboration)

(Received 2 August 2018; published 7 November 2018)

A search for resonant and nonresonant pair production of Higgs bosons in the b

bτ

−

final state is

presented. The search uses 36.1 fb

−1

of pp collision data with

ﬃﬃﬃ

¼ 13 TeV recorded by the ATLAS

experiment at the LHC in 2015 and 2016. Decays of the τ -lepton pairs with at least one τ lepton decaying to

final states with hadrons and a neutrino are considered. No significant excess above the expected

background is observed in the data. The cross-section times branching ratio for nonresonant Higgs boson

pair production is constrained to be less than 30.9 fb, 12.7 times the standard model expectation, at

95% confidence level. The data are also analyzed to probe resonant Higgs boson pair production,

constraining a model with an extended Higgs sector based on two doublets and a Randall-Sundrum bulk

graviton model. Upper limits are placed on the resonant Higgs boson pair production cross-section times

branching ratio, excluding resonances X in the mass range 305 GeV <m

< 402 GeV in the simplified

hMSSM minimal supersymmetric model for tan β ¼ 2 and excluding bulk Randall-Sundrum gravitons

in the mass range 325 GeV <m

< 885 GeV for k=

¼ 1.

DOI: 10.1103/PhysRevLett.121.191801

In 2012, the ATLAS and CMS Collaborations at the

LHC discovered a new particle with a mass of approx-

imately 125 GeV [1–3]. According to all current measure-

ments it is compatible with the standard model (SM) Higgs

boson (H) [4–8]. An important pending test of the Brout-

Englert-Higgs mechanism is the measurement of Higgs

boson pair production. At the LHC, pairs of SM Higgs

bosons can be produced via the Higgs self-interaction

(“triangle diagram”) and the destructively interfering top-

quark loop (“box diagram”) [9,10]. Nonresonant Higgs

boson pair production (NR HH) can be significantly

enhanced relative to the SM prediction by modifications

to the top-quark Yukawa coupling, the trilinear Higgs

boson coupling λ

HHH

, or by introducing production mech-

anisms with new intermediate particles. Many theories

beyond the SM predict heavy resonances that could decay

into a pair of SM Higgs bosons, such as a heavy CP-even

scalar X in two-Higgs-doublet models [11], or spin-2

Kaluza-Klein (KK) excitations of the graviton, G

,in

the bulk Randall-Sundrum (RS) model [12–14].

This Letter describes a search for resonant and nonreso-

nant Higgs boson pair production in a final state with two b

quarks and two τ leptons using 36.1 fb

−1

of pp collision

data recorded with the ATLAS detector [15,16] in 2015 and

2016. The τ

lep

had

and τ

had

decay channels are consid-

ered, where the subscripts (lep ¼ electron or muon,

had ¼ hadrons) indicate the decay mode of the τ lepton.

Previous searches for Higgs boson pair production were

performed at center-of-mass energies

ﬃﬃﬃ

¼ 8 TeV [17–19]

and

ﬃﬃﬃ

¼ 13 TeV [20–22] by the ATLAS and CMS

Collaborations. The ATLAS search in the 4b channel

constitutes the most sensitive result to date and the

observed (expected) limit excludes a cross section greater

than 13.0 (20.7) times the SM prediction at 95% confidence

level (C.L.).

The SM nonresonant HH process was simulated with

RAPH

5_aMC@NLO at next-to-leading order (NLO)

[23–27] using the CT10 parton distribution function

(PDF) set [28]. Parton showers and hadronization were

simulated with H

ERWIG

++ [29] using the UEEE5 set of

tuned parameters (tune) [30]. The events were reweighted

to reproduce the m

spectrum obtained in Refs. [9,31],

which fully accounts for the finite mass of the top quark.

The cross-section times branching ratio to the bbττ final

state, evaluated at next-to-next-to-leading order (NNLO)

and including next-to-next-to-leading logarithm (NNLL)

corrections and NLO top-quark mass effects, is 2.44

þ0.18

−0.22

[32]. Events with a generic narrow-width scalar X or

decaying into HH were produced in M

RAPH

aMC@NLO at leading order (LO) and interfaced to the

YTHIA

8 [33] parton shower model using the A14 tune [34]

together with the NNPDF23LO PDF set [35]. The cross

section and width of the G

were taken from Ref. [36] and

Full author list given at the end of the article.

Published by the American Physical Society under the terms of

the Creative Commons Attribution 4.0 Internationa l license.

Further distribution of this work must maintain attribution to

the author(s) and the published article’s title, journal citation,

and DOI. Funded by SCO AP

PHYSICAL REVIEW LETTERS 121, 191801 (2018)

depend on k=

, where k corresponds to the curvature of

the warped extra dimension and

¼ 2.4 × 10

GeV is

the effective four-dimensional Planck scale. Events with

¼ 1 and k=

¼ 2 were simulated.

The dominant SM background processes are t

t, QCD

multijet and Z bosons produced in association with jets

originating from heavy-flavor quarks (bb; bc; cc), sub-

sequently referred to as Z þ heavy flavor [37]. SM Higgs

boson production in association with a Z boson, sub-

sequently decaying into a bbττ [38] final state, is an

irreducible background in this analysis. The t

t and single-

top-quark background events were simulated using

OWHEG

-B

[39], with the CT10 PDF set, and

[40]. The parton showers were simulated using

YTHIA

6 [41] and the Perugia 2012 tune [42]. The t

background was scaled to match the NNLO þ NNLL cross

sections [43], while the single-top samples were corrected to

NLO [44,45] (approximate NNLO [46]) predictions for the

t- and s-channel (Wt final state). Events with W or Z bosons

and associated jets were simulated with the S

HERPA

2.2.1

generator [47–51], using the NNPDF30NNLO PDF set [52]

and normalized to the NNLO cross sections [53]. Diboson

and Drell–Yan backgrounds were produced with S

HERPA

2.2.1 [47] using the CT10NLO PDF set and the generator

cross-section predictions. Quark-induced ZH processes

were generated with P

YTHIA

8, using the A14 tune and

the NNPDF23LO PDF set. The samples were normalized to

NNLO cross sections for QCD and NLO for electroweak

processes [54–60]. The gluon-induced ZH process [61] was

generated with P

OWHEG

using the CT10 PDF set and using

YTHIA

8 with the AZNLO tune [62] to simulate parton

showers. Cross sections [63–67] were scaled to NLO þ

NLL in QCD. SM Higgs boson production in association

with a top-quark pair was simulated with M

RAPH

aMC@NLO; P

YTHIA

8 was used to simulate the parton

shower, while the cross section was taken from Ref. [10].

In all signal and background samples, the mass of the H

bosons was set to 125 GeV. The contributions from other SM

Higgs boson processes are negligible. E

v1.2.0 [68]

was used to model the properties of bottom and charm

hadron decays for all processes except those simulated in

HERPA

. The detector response to the generated events was

simulated with G

EANT

4 [69,70]. Simulated events are

reweighted to match the distribution of the number of

inelastic collisions per event (pileup) in data.

Events are required to have at least one collision vertex

reconstructed from at least two charged-particle tracks

with transverse momentum [71] p

track

> 0 .4 GeV. The

primary vertex for each event is selected as the vertex

with the highest

ðp

track

. Jets are formed using the anti-

algorithm [72] with a radius parameter R ¼ 0.4 and

calorimeter energy clusters as inputs [73–75]. These jets are

taken as seeds for the reconstruction of the visible products

of hadronically decaying τ leptons (τ

had-vis

) [76–78], which

are subsequently required to have one or three associated

tracks. In order to distinguish τ

had-vis

from quark- and

gluon-initiated jets, a boosted decision tree (BDT) [79],

trained separately for τ

had-vis

with one and three charged

particles, is employed. Selected τ

had-vis

candidates must

satisfy the “medium” BDT working point [77]. Electron

candidates are identified using a likelihood technique in

combination with additional track-hit requirements [80];

the transition region between the barrel and end cap

calorimeters is excluded. Information from the tracking

and muon systems is used to reconstruct muon candidates

[81]. Only isolated electrons and muons are considered,

where no nearby tracks or calorimeter energy deposits

within a p

-dependent variable-size ΔR cone around the

lepton are allowed. Jets arising from pileup are suppressed

using dedicated track and vertex requirements [82]. The

missing transverse momentum, with magnitude E

miss

,is

defined as the negative vectorial sum of all reconstructed

and fully calibrated objects in the event, along with an

additional track-based soft term [83]. Jets containing b

hadrons are identified using the MV2c10 multivariate

discriminant [84,85] trained against a light-quark-flavor

sample also containing 10% of c hadrons. A working point

with 70% efficiency on simulated t

t events is used. An

overlap-removal procedure is applied to the reconstructed

electrons, muons, τ

had-vis

, and jets to prevent double

counting of energy deposits in the detector as described

in Ref. [86].

The selected final state is characterized by one electron

or muon and one τ

had-vis

of opposite charge, or two τ

had-vis

of opposite charge, plus two b-tagged jets and E

miss

. In all

cases, events with additional electrons or muons above

7 GeV or τ

had-vis

above 20 GeV are rejected. The off-line

selection criteria for the electron, muon, and τ

had-vis

depend

on the triggers used. In the τ

lep

had

channel events are

selected with a single-lepton trigger (SLT) and a lepton

plus τ

had

trigger (LTT), which are analyzed separately

and combined with the τ

had

channel in the final fit.

Depending on the data period, the electron or muon that

passes the SLT trigger is required to have p

25–27 GeV. Events which fail this requirement are con-

sidered for the LTT category if the electron (muon) has

> 18 GeV (15 GeV). In all cases, these p

require-

ments are 1 GeV higher than the trigger thresholds to

ensure a nearly constant trigger efficiency relative to the

off-line selection. The τ

lep

had

events are required to have

one τ

had-vis

candidate with jηj < 2.3 and p

> 20 GeV for

SLT events, raised to 30 GeV for LTT events due to τ

had-vis

requirements applied in this category of triggers. In the

had

channel a logical OR of single τ

had

triggers (STT)

and di-τ

had

triggers (DTT) is used. The leading τ

had-vis

candidate is required to have a minimum p

of 40 GeV for

DTT and between 100 and 180 GeV for STT events,

depending on the data-taking period. The subleading τ

had-vis

is required to have a minimum p

of 20 (30) GeV for

STT (DTT) events. The leading jet is required to have

PHYSICAL REVIEW LETTERS 121, 191801 (2018)

191801-2

> 45 GeV, except in the LTT and DTT channels where

this is raised to 80 GeV due to a requirement on the

presence of a jet at the Level 1 trigger to reduce the rate

(during 2016 data taking only for the DTT). In all cases the

subleading jet must have p

> 20 GeV. The invariant mass

of the di-τ system, m

MMC

ττ

, is calculated using the Missing

Mass Calculator [87] and is required to be greater than

60 GeV. Signal region (SR) events are defined as those

meeting the criteria above, and in addition containing two

b-tagged jets; they are further separated into τ

lep

had

SLT,

lep

had

LTT and τ

had

categories.

BDTs are used in the analysis to improve the separation

of signal from background. Their distributions in the three

signal regions, along with control region yields to constrain

the normalization of the dominant backgrounds, form the

inputs to the final fit. The BDTs for the τ

had

channel are

trained against the main backgrounds, t

t, Z → ττ, and

multijet events; in the τ

lep

had

channel they are trained

solely against the dominant t

t background. For the BDT

trainings, the t

t and Z → ττ backgrounds are taken purely

from simulation, while the multi-jet events are estimated

using the data-driven approach described below. Variables

which provide good discrimination and are minimally

correlated are used as inputs to the BDTs, as summarized

in Table I. The variables selected in each channel differ,

reflecting the different background compositions. In the

resonant search, BDTs are trained separately for each signal

mass considered, from 260 to 1000 GeV (800 GeV for

LTT), where the signal model combines the target reso-

nance mass and its two neighboring mass points, to be

sensitive to masses between the simulated points. For NR

HH production, the BDTs are trained on a signal sample

with the SM admixture of the contributions from the box

diagram and triangle diagram. The BDTs are more sensitive

to the box diagram where the two Higgs bosons are

produced at higher p

and the selection efficiency is

greater.

In both channels, simulated events are used to model

background processes containing reconstructed τ

had-vis

that

are matched to generated τ

had

within ΔR ¼ 0.2 (sub-

sequently referred to as true τ

had

) and other minor back-

ground contributions. The rate of events with at least one

true τ

had

and a jet reconstructed as an electron or muon is

found to be negligible. For t

t background events containing

one or more true τ

had

the normalization is obtained in the

final fit, constrained mainly by the low τ

lep

had

BDT score

regions, resulting in a normalization factor of 1.06  0.13.

The normalization of the Z → ee=ττ þ heavy-flavor back-

ground is determined using Z → μμ þ heavy-flavor events.

Their selection closely follows the event selection used for

signal events. Instead of two τ-lepton candidates, two

muons with p

> 27 GeV and dimuon invariant mass

between 81 and 101 GeV are selected. To remove the

contribution from SM ZH ðH → bbÞ production, m

required to be lower than 80 GeV or greater than 140 GeV.

The normalization is determined by including the Z →

μμ þ heavy-flavor control region yield in the final fit,

resulting in a normalization factor of 1.34  0.16.

Normalization factors are not applied to the Z þ

light-flavor contributions. The modeling of the BDT score

TABLE I. Variables used as inputs to the BDTs for the different channels and signal mo dels. Here, m

reconstructed from the ττ and bb systems using a 125 GeV Higgs mass constraint; m

MMC

ττ

is the invariant mass of

the di-τ system, calculated using the Missing Mass Calculator [87]; m

is the invariant bb-mass; ΔRðτ; τÞ is

evaluated between the electron or muon and τ

had-vis

(two τ

had-vis

) in the case of the τ

lep

had

(τ

had

) channel; E

miss

centrality qua ntifies the relative angular position of the E

miss

relative to the visible τ decay products in the transverse

plane [88] and is defined as ðA þBÞ=ð

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

þB

Þ, where A ¼sinðϕ

miss

− ϕ

Þ=sinðϕ

− ϕ

Þ, B ¼ sinðϕ

− ϕ

miss

Þ=

sinðϕ

− ϕ

Þ, and τ

and τ

stand for electron or muon and τ

had-vis

(two τ

had-vis

) in the case of the τ

lep

had

(τ

had

)

channel; m

is the transverse mass of the lepton and the E

miss

; ΔϕðH; HÞ is the azimuthal angle between the two

Higgs boson candidates; Δp

ðlep; τ

had-vis

Þ is the difference in p

between the electron or muon and τ

had-vis

Variable

lep

had

channel

(SLT resonant)

lep

had

channel

(SLT nonresonant & LTT)

had

channel

✓✓✓

MMC

ττ

✓✓✓

ΔRðτ; τÞ ✓✓✓

ΔRðb; bÞ ✓✓✓

miss

✓

miss

ϕ centrality

✓✓

ΔϕðH; HÞ ✓

Δp

ðlep; τ

had-vis

Þ ✓

Subleading b-jet p

✓

PHYSICAL REVIEW LETTERS 121, 191801 (2018)

191801-3

distributions is validated in the 0-b-tag and 1-b-tag regions

as well as in dedicated t

t and Z þ heavy-flavor validation

regions.

Contributions from processes in which a quark- or

gluon-initiated jet is misidentified as a τ

had-vis

candidate

(fake-τ

had

) are estimated using data-driven methods for

major backgrounds. A fake-τ

had

enriched sample is defined

by requiring that a τ

had-vis

fails the “medium” BDT

identification but satisfies a very loose requirement on

the BDT score. This selection maintains a composition of

quark- and gluon-initiated jets similar to those mimicking

had-vis

in the SR. In the case where the event contains more

than one such fake τ

had

, one is chosen randomly. The SR

selection, except for the τ

had-vis

identification, is applied to

the fake-τ

had

enriched sample to extract template distribu-

tions for the fake-τ

had

background after the true-τ

had

contamination is subtracted using simulation. The tem-

plates are scaled with fake factors (FF) defined as the ratio

of the number of fake τ

had

that pass the τ

had-vis

identification

to the number that fail, calculated in dedicated control

regions (CR) and parametrized in p

ðτ

had-vis

Þ and the

number of associated tracks.

For the τ

lep

had

final state, fake-τ

had

background con-

tributions from t

t, W þ jets and multijet processes are

estimated using a combined fake-factor method similar to

that described in Refs. [86,89]. In order to account for the

different sources of fake τ

had

, the FFs are derived separately

for each background contribution. The CR for multijet

events is defined by inverting the isolation requirement

applied to the electron or muon for events with 0 or 1

b-tagged jets. The t

t (W þ jets) control region is defined

by requiring two (zero) b-tagged jets and m

> 40 GeV,

where m

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

lep

miss

ð1− cosΔϕ

lep;E

miss

, and Δϕ

lep;E

miss

is the azimuthal angle between the electron or muon and the

miss

. Fake factors for t

t and W þ jets are found to be

consistent for both processes. The individual fake factors

are then combined as FFðcombÞ¼FFðQCDÞ × r

QCD

FFðt

t=W þ jetsÞ × ð1 − r

QCD

Þ, where r

QCD

is defined as

the fraction of fake τ

had

from (predominantly multijet)

processes contributing to the data in the fake τ

had

enriched

template region that are not accounted for by simulated

background processes, and is less than 5% in the 2-b-tag

region. Because of the different origin of fake τ

had

, the FFs

for t

t=W þ jets can be up to 30% larger than those for

multijet processes. Events with two b-tagged jets but a

same-sign charge (SS) electron or muon and τ

had-vis

are

used for validating the fake-τ

had

background, showing all

distributions are well modeled. Given this, and the small

size of the contribution, no transfer factor is applied to

correct the multijet estimation from the 1-b-tag region to

the 2-b-tag region.

In the τ

had

final state, only the multijet background is

estimated from data using the FF method. The differential

FFs are derived in a 1-b-tag SS control region, while the

overall normalization is taken from the 2 -b-tag SS control

region. The t

t background is estimated from simulation,

where the fake-τ

had

t contribution is corrected in bins of

ηðτ

had-vis

Þ using the probability for a jet from a hadronic

W-boson decay to mimic a τ

had-vis

candidate (fake rate), as

measured with data in the τ

lep

had

t control region [86].

Contributions from true τ

had

are subtracted using simulation.

The uncertainty in the integrated luminosity of the

combined 2015 þ 2016 data set is 2.1% [90] and is applied

to the signal and background components whose normal-

izations are derived from simulation. An uncertainty related

to the pileup reweighting procedure is also applied [91].

Experimental uncertainties in the identification and

reconstruction of the electron [92], muon [93], τ

had-vis

[76], and jets [74,94] are accounted for and propagated

through the analysis to determine their effect on the final

results. These affect the trigger requirements, the identi-

fication and reconstruction efficiencies, the isolation,

and the reconstructed energies and their resolutions. The

uncertainties are propagated to the calculation of the

miss

[83], which has an additional uncertainty from

the soft term. The uncertainties with the largest impact

on the result are those related to the τ

had-vis

identification

efficiency, which correspond to an uncertainty of 16% on

the NR signal strength, i.e., the simulated NR HH yield

assuming a cross-section times branching fraction equal to

the expected limit and normalized to the SM expectation

(σ

exp

=σ

). Uncertainties in flavor tagging [95,96] also

have a significant impact, inducing an uncertainty in the

NR signal strength of 8.3%, dominated by those associated

with the b-tagging efficiency.

Theory uncertainties in the modeling of the t

t background

containing one or more true τ

had

are assessed by varying

the matrix element generator (using aMC@NLO instead

of P

OWHEG

-B

) and the parton shower model (using

ERWIG

++ instead of P

YTHIA

6), and by adjusting the

factorization and renormalization scales along with the

amount of additional radiation. The resulting variations in

the BDT distributions are included as shape uncertainties in

the final fit. In order to account for potential acceptance

differences between control and signal regions, the normali-

zation of the t

t background containing true τ

had

, determined

predominantly from the τ

lep

had

SR in the final fit, is allowed

to vary within a range determined by the acceptance

variations associated with the t

t modeling uncertainties.

This amounts to þ30%= − 32% for the τ

had

SR and

þ8.1%= − 9.3% for the Z → μμ þ heavy-flavor control

region. This is the dominant uncertainty in the t

t modeling.

For the Z þ jets background, the theory uncertainties

in the modeling of the BDT shapes are derived by

comparing the nominal S

HERPA

sample with an alternative

RAPH

5_aMC@NLO + P

YTHIA

8 sample and by

varying the choice of renormalization and factorization

scales, along with the PDF prescription [97]. The normali-

zation of the Z → ττ þ heavy-flavor background in the

PHYSICAL REVIEW LETTERS 121, 191801 (2018)

191801-4

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使用ATLAS探测器在s = 13 TeV的pp碰撞中搜索衰减至τν的高质量共振

使用ATLAS探测器在s = 13 $$ \ sqrt {s} = 13 $$ TeV的pp碰撞中搜索重狄氏子共振

用ATLAS探测器在s = 13 TeV的pp碰撞中搜索与Z玻色子相关的无形衰变的希格斯玻色子或暗物质候选物

度量标准中的企鹅和介子异常-

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