A method for identifying H -> tau tau -> e mu pTmiss at the CERN LHC

21 Pages·0.58 MB·English

by  T. Plehn

University of Wisconsin - Madison
MADPH-99-1142
FERMILAB-Pub-99/290-T
hepph/9911385
November 1999
A method for identifying
H ττ e±µ∓p/T
→ →
0 at the CERN LHC
0
0
2

n T. Plehn1, D. Rainwater2 and D. Zeppenfeld1
a
J
1Department of Physics, University of Wisconsin, Madison, WI 53706
1
1 2Fermi National Accelerator Laboratory, Batavia, IL 60510

2
v Abstract datahaveforsometimesuggestedarelativelysmall
5
8 Higgs boson mass, of order 100 GeV [1], which is
3 also the preferred mass range for the lightest Higgs
1 Weak bosonfusion promises to bea copious source
1 boson in the minimal supersymmetric extension of
of intermediate mass Higgs bosons at the LHC.
9 the Standard Model (MSSM).
9 The additional very energetic forward jets in these
For the intermediate mass range, most of the
/
h events provide for powerful background suppres-
literature has focused on Higgs boson production
p sion tools. We analyze the subsequent H
- → via gluon fusion [2] and tt¯H [3] or WH(ZH) [4]
p ττ e±µ∓p/ decay for Higgs boson masses in
e → T associated production. Cross sections for Stan-
the 100-150 GeV range. A parton level analysis of
h dard Model (SM) Higgs boson production at the
: the dominant backgrounds demonstrates that this
v LHC are well-known [2], and while production via
i channel allows the observation of H ττ in a
X → gluon fusion has the largest cross section by al-
low-background environment, yielding a significant
r most one order of magnitude, there are substan-
a Higgsbosonsignalwith anintegratedluminosity of
tial QCD backgrounds. A search for the very
order 60 fb−1 or less, over most of the mass range.
clean four-lepton signature from H ZZ de-
We also restate a No-Lose Theorem for observa- →
cay can find a Higgs boson in the mass region
tion of at least one of the CP-even neutral Higgs
>
M 125 GeV, but due to the small branching
bosons in the MSSM, which requires an integrated H
fracti∼on of this mode very large integrated lumi-
luminosity of only 40 fb−1.
nosities, up to 100 fb −1 or more, are required. For
Higgs boson masses less than about 140 GeV, the
inclusive search for H γγ events is usually con-
→
I. INTRODUCTION sidered the most promising strategy [5], while for
140 < M < 200 GeV the most promising search
H
The search for the Higgs boson and, hence, for is for decay to W pairs [5–8].
the origin of electroweak symmetry breaking and The search for MSSM Higgs bosons must in-
fermion mass generation, remains one of the pre- clude neutral CP even and CP odd mass eigen-
miertasksofpresentandfuturehighenergyphysics states, as well as charged ones. The upper mass
experiments. Fits to precision electroweak (EW) limit of 130 GeV [9,10] on the light scalar makes
∼
1
it look similar to its intermediate-mass Standard ous processes, and important parameters. In Sec-
Model analogue, for large regions of the MSSM pa- tion III we demonstrate how forward jet tagging,
rameter space. While one would expect the most a b veto, and lepton cuts can be combined to yield
promising channel to again be γγ decay [2,5], the an 2/1 to 1/2 signal-to-background (S/B) ratio,
≈
branching ratio for this mode is even smaller than depending on the Higgs mass. The different mini-
in the Standard Model. jet patterns in signal and background processes are
The second largest production cross section is discussed in Section IV. We describe how they can
predicted for weak-boson fusion (WBF), qq be used to achieve additional large suppression of
→
qqVV qqH. These events contain additional the QCD backgrounds relative to the signal. Com-
→
information in their observable quark jets. Tech- bined with the results of Section III this yields pro-
niques like forward jet tagging [11–13] can then be duction cross sections of signal and backgrounds as
exploited to significantly reduce the backgrounds. given in Table IV, which summarizes our results.
WBF and gluon fusion nicely complement each In Section V we reanalyze the impact on covering
other: together they allow for a measurement of the MSSM parameter space and discuss the lumi-
the tt¯H/WWH coupling ratio. nosity requirement at the LHC for which the entire
Another feature of the WBF signal is the lack m ,tanβ plane can be covered. A final discussion
A
of color exchange between the initial-state quarks. ofourresultsandconclusionsisgiveninSectionVI.
Color coherence between initial- and final-state
gluon bremsstrahlung leads to suppressed hadron
II. CALCULATIONAL TOOLS
production in the central region, between the two
tagging-jet candidates of the signal [14]. This is in
We simulate pp collisions at the CERN LHC,
contrast to most background processes, which typ-
√s = 14 TeV. All signal and background cross sec-
ically involve color exchange in the t-channel and
tions are determined in terms of full tree-level ma-
thus lead to enhanced hadronic activity between
trix elements for the contributing subprocesses and
the tagging jets. We exploit these features, via a
are discussed in more detail below.
veto of soft jet activity in the central region [15].
For all our numerical results we have chosen
We have previously established the feasibility
1/α = 128.933, M = 91.187 GeV, and G =
of WBF intermediate-mass Higgs production as Z F
1.16639 10−5 GeV−2, which translates into M =
both a discovery channel (via H W(∗)W(∗) · W
→ → 79.963 GeV and sin2θ = 0.2310 when using the
e±µ∓p/ decays [6,7]) and as a means to provide W
T
tree-levelrelationsbetweentheseinputparameters.
the first direct Higgs boson-fermion coupling mea-
This value for M is somewhat lower than the cur-
surement [16,7] (H ττ h±ℓ∓p/ ). The latter W
T
→ → rent world average of 80.39 GeV. However, this dif-
allows one to na¨ıvely extend the Standard Model
ference has negligible effects on all cross sections,
search to the MSSM case: the structure of the
e.g. the qq qqH signal cross section varies by
Higgs sector predicts at least one scalar in the in- →
about0.5%between these two W mass values. The
termediate mass range, rendering the ττ channel a
tree level relations between the input parameters
crucial test of the MSSM [17]. Here, we show how
are kept in order to guarantee electroweak gauge
the additional channel H ττ e±µ∓p/ can be
T
→ → invariance of all amplitudes. For all QCD effects,
isolated, effectively doubling theavailablestatistics
the running of the strong coupling constant is eval-
for a measurement of the Hττ coupling.
uated at one-loop order, with α (M ) = 0.118. We
Our analysis is a parton-level Monte Carlo s Z
employ CTEQ4L parton distribution functions [18]
study, using full tree-level matrix elements for the
throughout. Unless otherwise noted the factoriza-
WBF Higgs signal andthe variousbackgrounds. In
tion scale is chosen as µ = min(p ) of the defined
Section II we describe our calculational tools, the f T
jets.
methods employed in the simulation of the vari-
2
A. The qq qqH(g) signal process (and gq tt¯q, gq¯ tt¯q¯, qq¯ tt¯g, gg tt¯g,
→ → → → →
background)
and the subprocesses for tt¯+jj events can be ob-
The signal can be described, at lowest order, tained similarly. For the case of no additional par-
by two single-Feynman-diagram processes, qq tons, the b’s from the decaying top quarks may be
→
qq(WW,ZZ) qqH, i.e. WW and ZZ fusion identified as the tagging jets. At the same time,
→
wheretheweakbosonsareemittedfromtheincom- we can identify a distinctly different, perturbative
ing quarks [19]. Because of the small Higgs boson region of phase space, where the final-state light
widthinthemassrangeofinterest,theseeventscan quark or gluon gives rise to one tagging jet, and
reliably be simulated in the narrow width approx- one of the two decay b’s is identified as the other
imation. From previous studies of H γγ [20], tagging jet. Finally, there is a third distinct region
→
H ττ [16] and H WW [6] decays in weak of phase space, for the perturbative hard process
bos→on fusion we know→several features of the sig- pp tt¯+ jj, where the final-state light quarks
→
nal, which can be exploited here also: the centrally or gluons are the two tagging jets. The tt¯ and
produced Higgs boson tends to yield central decay tt¯j matrix elements were constructed using mad-
products (in this case τ+τ−), and the two quarks graph [22], while the tt¯jj matrix elements are
enter thedetectoratlargerapiditycomparedtothe from Ref. [23].
τ’s and with transverse momenta in the 20 to 100 Decays of the top quarks and W’s are included
GeV range, thus leading to two observable forward in the matrix elements; however, while the W’s are
tagging jets. allowed to be off-shell, the top quarks are required
Forthestudy ofacentral jet veto, weutilize the to be on-shell. This approximation neglects the
results of previous studies where we simulated the contribution from Wt production, which has been
emission ofatleast oneextra parton[7,16,21]. This shown to be comparable to tt¯ rates in studies of
was achieved by calculating the cross sections for the H WW signal [8,5]. We will compensate by
→
theprocessqq qqHg,i.e. weakbosonfusionwith being conservative in assessing minijet veto prob-
→
radiation of an additional gluon, and all crossing abilities for top backgrounds. Note that these ap-
related processes. proximations are not critical because backgrounds
We note that the signal simulations, with de- with real W pairs can be distinguished quite ef-
cays to tau pairs replaced by decays to W pairs, fectively from ττ events and the real top decay
which in turn decay leptonically, will ultimately backgrounds that we consider willbeshown tocon-
also be a source of background for the H ττ stitute a minor fraction of the final backgrounds.
signal under study. → In the calculation of the tt¯background energy loss
from b ℓνX is included to generate more accu-
→
rate p/ distributions. In all cases, the factorization
T
B. The QCD t¯t+jets backgrounds
scale is chosen as µ = min(E ) of the massless
f T
partons/top quarks. As in our earlier work [6], the
Given the H decay signature, the main physics
overall strong coupling constant factors are taken
background to our e±µ∓p/T signal arises from tt¯+ as (α )n = n α (E ), where the product runs
jets production, due to the large top production s i=1 s Ti
over all light quarks, gluons and top quarks.
Q
crosssectionattheLHCandbecausethebranching
ratio B(t Wb) is essentially 100%.
The ba→sic process we consider is pp tt¯, which C. The QCD bb¯ +jj background
→
can be either gg- or qq¯-initiated, with the former
strongly dominating at the LHC. QCD corrections The semileptonic decays of bottom or charm
to this lead to additional real parton emission, i.e. quarks provide another source of leptons and neu-
to tt¯+j events. Relevant subprocesses are trinos which can be misidentified as tau decays.
3
These heavy quark pairs areproduced strongly and by x and y , respectively, the double differential
ν ℓ
a priori one is dealing with a very large potential b-quark decay distribution is given by [24]
background. It can be reduced by several orders of
1 d2Γ 2c
magnitude, however, by requiring the leptons from
= c (1 x ) [c+(3 c) x ]
ν ν
the decay of the heavy quarks to be isolated. Be- Γdxνdyℓ f(r) − −
cause of the softer fragmentation function of a c- (2 c) x +c
ν
+3ry −
quarkascomparedtob-quarks, leptonsfromcharm ℓ
decay are much less likely to be isolated than b- 1−xν −yℓ ! (1)
decay leptons. In the phase space region of interest
assuming an unpolarized initial b-quark. Here
to us, where both heavy quarks must reside in the
r = m2/m2, and the dependence on the final state
central angular region and have substantial trans- c b
charm quark mass, m , is absorbed into the correc-
c
verse momentum, the production cross sections for
tion term
charm and bottom pairs are roughly equal. As a
result we consider only the b-quark background in 1 r xν yℓ r
c = − − − = 1 . (2)
the following. 1 x y − z
ν ℓ c
− −
In addition to the two high transverse momen-
Finally, f(r) is the width suppression factor for the
tum b-quarks, which both must undergo semilep-
b νℓc decay due to the finite charm quark mass,
tonic decay, two forward tagging jets will be re-
→
quired as part of the signal event selection. The
f(r) = (1 r2)(1 8r+r2) 12r2logr .
relevant leading order process therefore is the pro- − − −
(3)
¯
duction of bb pairs in association with two jets,
which includes the subprocesses
Inour numerical simulations we set m = 5.28GeV
b
and m = 1.87 GeV, i.e. we use the lightest meson
¯ ¯ ¯ c
gg bbgg , qg bbqg , q q bbq q .
→ → 1 2 → 1 2 massesinordertoapproximatelyobtainthecorrect
kinematics for the heavy quark decays. In Ref. [25]
The exact matrix elements for the (α4) pro-
O s a factor 100 reduction of the b¯b background was
cesses are evaluated, including all the crossing re-
found as a result of lepton isolation for a single
lated subprocesses, and retaining a finite b-quark
b νℓc decay, requiring E < 5 GeV in a cone
mass [23]. The Pauli interference terms between T
→
identical quark flavors in the process q q b¯bq q of radius 0.6 around the charged lepton of pTℓ >
1 2 1 2
→ 20 GeV. In our simulation, after energy smearing
are neglected, with little effect in the overall cross
of the charm quark jet (see below), we reproduce
section, duetothelargedifference intherapidityof
this reduction factor. The suppression from lepton
the final state light quarks. The factorization and
isolation is smaller for lower p cuts. We model
renormalization scales are chosen as in the analo- Tℓ
gous tt¯jj case. these effects by using Eq. (1).
Since our suppression of b νℓc decays from
The semileptonic decay b νℓc of both of the
→
→ ¯ lepton isolation strongly depends on the energy
b-quarks is simulated by multiplying the bbjj cross
resolution assumed for the very soft charm quark
section by a branching ratio factor of 0.0218 (cor-
jet, the determination of heavy quark backgrounds
responding to an e+µ− or µ+e− final state) and
should eventually be repeated with a full detector
by implementing the V A decay distributions of
− simulation. We will show, however, that the b¯bjj
the b-quarks in the collinear limit. The collinear
background is truly negligible after all the selec-
approximation for the b νℓc decay is appropri-
→ tion cuts to be described in this paper. Therefore,
ate here because the lepton transverse momentum
the approximate treatment of these backgrounds is
andp/ cutsto beimposedbelow forcetheparent b-
T
sufficient for our purposes.
quarks to move relativistically in the lab. Denoting
the neutrino and charged lepton energy fractions
4
D. The QCD and EW τ+τ− +jj qg qgW+W−, qq′ qq′W+W−,
→ →
backgrounds
which are dominated by t-channel gluon exchange,
The next obvious backgrounds arise from Z and all crossing related processes, such as
decays to real τ’s which then decay leptonically.
qq¯ ggW+W−, gg qq¯W+W−.
Thus, we need to study real-emission QCD cor-
→ →
rections to the Drell-Yan process qq¯ (Z,γ)
→ → We call these processes collectively the “QCD
τ+τ−. For τ+τ−jj events these background pro-
WWjj” background. To estimate the minijet ac-
cesses include [26]
tivity in these events we use the results for QCD
qg qgτ+τ−, qq′ qq′τ+τ−, Z + jets processes, which are kinematically simi-
→ →
lar [6,7].
which are dominated by t-channel gluon exchange,
Note that we neglect W τν ℓνν decays
and all crossing-related processes, such as → →
in our simulation of WWjj backgrounds. This
qq¯ ggτ+τ−, gg qq¯τ+τ−. is justified by the suppressed leptonic branching
→ → ratio of the τ decays. We show below that the
All interference effects between virtual photon and WW eµνν backgrounds are already negligible
→
Z-exchange are included. We call these processes and, therefore, the extra W τν decays do not
→
collectively the “QCD ττjj” background. Similar need to be analyzed in detail.
to the treatment of the signal processes, we use
a parton-level Monte-Carlo program based on the
F. The EW WW+jj background
work of Ref. [27] to model the QCD ττjj back-
ground.
These backgrounds, analogous to QCD WWjj
From our study of H ττ in weak boson fu-
→ production, arise from W+W− bremsstrahlung in
sion [16], we know that the EW (t-channel weak
quark-(anti)quark scattering via t-channel elec-
boson exchange) cross section for Zjj production
troweak boson exchange, with subsequent decay
will be comparable to the QCD cross section in the
W+W− ℓ+ℓ−p/ :
phase space region of interest. We use the results → T
of Ref. [28] for modeling the EW ττjj background.
qq′ qq′W+W−
The dual leptonic decays of the τ’s are sim- →
ulated by multiplying the τ+τ−jj cross section
Na¨ıvely, this EW background may be thought of as
by a branching ratio factor of (0.3518)2/2 and by
suppressed compared to the analogous QCD pro-
implementing the lepton energy distributions for
cess above. However, it includes electroweak boson
collinear tau decays, with helicity correlations in- fusion, VV W+W− via s- or t-channel γ/Z-
cluded as in our previous analysis of H ττ [16]. →
exchange or via VVVV 4-point vertices, which has
→
a momentum and color structure identical to the
signal. Thus, it cannot easily be suppressed via
E. The QCD WW+jj background
cuts.
The matrix elements for these processes were
We must further consider any other significant
constructed using madgraph [22]. We include
source of one electron, one muon and significant p/
T
charged-current (CC) and neutral-current (NC)
to make a realistic analysis of the backgrounds. An
processes, but discard s-channel EW boson and t-
obvious candidate arises from real-emission QCD
corrections toW+W− production, withsubsequent channel quark exchange processes as their contri-
bution was found to be only 1%, while adding
decay of the two W‘s to electrons or muons. For
≈
W+W−jj events these background processes in- significantly to the CPU time needed for the cal-
culation. In general, for the regions of phase space
clude [29]
5
containing far-forward and -backward tagging jets, hard jets. An ATLAS analysis [25] showed that
s-channel processes are severely suppressed. We these effects are well parameterized by a Gaussian
refer collectively to these processes as the “EW distribution of the components of the fake missing
WWjj” background. Both W’s are allowed to transverse momentum vector, ~p/ , with resolution
T
be off-shell, and all off-resonance graphs are in-
cluded. In addition, the Higgs boson graphs must
σ(p/ ,p/ ) = 0.46 E , (6)
x y T,had
be included to make the calculation well-behaved ·
r
X
at large W-pair invariant masses. However, it is
for each component. In our calculations, these fake
convenient to separate continuum W-pair produc-
missing transverse momentum vectors are added
tion from the very narrow H W+W− resonance.
linearly to the neutrino momenta.
→
We do this by setting M to 60 GeV in the EW
H
WWjj background which effectively removes the
s-channel Higgs contribution. The H W+W− III. HIGGS SIGNAL AND
→
background is then calculated separately for ‘ each BACKGROUNDS
Higgs boson mass under consideration. A clean
separation of the Higgs boson signal and the EW The qq qqH, H ττ e±µ∓νν¯ double
→ → →
WWjj background is possible because interference leptonic decay signal is characterized by two for-
effects between the two are negligible for the Higgs ward jets and the τ decay leptons (e,µ). Before
boson mass range of interest. discussing background levels and further details
The effects of additional gluon radiation are es- like minijet radiation patterns, we need to iden-
timated by using the results of Refs. [6,7] for EW tify the search region for these hard Hjj events.
ττjj events, which are directly applied here. The The task is identical to the Higgs searches in qq
→
EW ττjj and EW WWjj backgrounds are quite qqH, H γγ,ττ,WW whichwereconsideredpre-
→
similar kinematically, which justifies the use of the viously [6,7,16,20]. We can thus adopt the strategy
same veto probabilities for central jets. of these earlier analyses and start out by discussing
a basic level of cuts on the qq qqH, H ττ
→ →
signal. Throughout this section we assume a Higgs
G. Detector resolution
mass of M = 120 GeV for illustration purposes,
H
but we do not optimize cuts for this mass.
The QCD processes discussed above lead to
The minimum acceptance requirements ensure
steeply falling jet transverse momentum distribu-
that the two jets and two charged leptons are ob-
tions. As a result, finite detector resolution can
served inside the detector (within the hadronic and
have a sizable effect on cross sections. These reso-
electromagnetic calorimeters, respectively), and
lution effects are taken into account via Gaussian
are well-separated from each other:
smearing oftheenergiesofjets/b’sandchargedlep-
tons. We use
p 20 GeV, η 5.0, R 0.7,
Tj ≥ | j| ≤ △ jj ≥
E 3.3 0.6
p 10 GeV, η 2.5, R 0.7. (7)
△ = 0.03 , (4) Tℓ ≥ | ℓ| ≤ △ jℓ ≥
E E ⊕ √E ⊕
Thechargedleptonsmust beisolatedinordertore-
for central jets (with individual terms added in
duce backgrounds from heavy quark decays. Thus
quadrature), based on ATLAS expectations [5].
a minimum angular distance must be imposed on
For charged leptons we use
theelectronandthemuonsignaling thetaudecays:
E
△ = 2% . (5)
E Reµ 0.4. (8)
△ ≥
In addition, finite detector resolution leads to
Thishas negligibleeffect ontheHiggsbosonsignal.
fake missing-transverse-momentum in events with
6
A feature of the QCD Zjj and WWjj back- region where we search for the W decay leptons.
grounds is the generally higher rapidity of the Z or Vetoing events with these additional b jets pro-
W’s as compared to the Higgs signal: weak boson vides a powerful suppression tool to control the
bremsstrahlung occurs at small angles with respect top background [6]. Note that this does not re-
totheparentquarks, producingaZ orW’sforward quire a b-tag, merely rejection of any events that
of the jets. Thus, we also require both ℓ’s to lie be- have an additional jet, which in this case would be
tween the jets with a separation in pseudorapidity from a b-quark and its decay products. (It is quite
η > 0.7, and the jets to occupy opposite hemi- possible that b-tagging could improve this simple
j,ℓ
△
spheres: rejection criterion, especially in the p < 20 GeV
T
¯
region.) We discard all events where a b or b with
η +0.7 < η < η 0.7,
j,min ℓ1,2 j,max − pT > 20 GeV is located in the gap region between
ηj1 ·ηj2 < 0 (9) the tagging jets,
Finally, to reach the starting point for our consid- p > 20 GeV, η < η < η .
Tb j,min b j,max
eration of the signal and various backgrounds, a (11)
wide separation in pseudorapidity is required be-
This leads to a reduction of tt¯j events by a fac-
tween the two forward tagging jets,
tor 7 while tt¯jj events are suppressed by a factor
η = η η 4.4, (10) 100, resulting in cross sections of 50 and 8.7 fb, re-
△ tags | j1 − j2| ≥
spectively, at the level of the forward tagging cuts
leaving a gap of at least 3 units of pseudorapidity
of Eqs. (7)-(10), which are now comparable to the
in which the charged leptons can be observed. For-
irreducible backgrounds, realtausfromZjj events.
ward jet tagging has been discussed as an effective
(SeethesecondlineofTableI.) Notethatthemuch
technique to separate weak boson scattering from higher b veto probability for tt¯jj events results in a
various backgrounds in the past [11–16,6,7,20,21], lower cross section than that for tt¯j events, an or-
in particular for heavy Higgs boson searches. Line
dering which will remain even after final cuts have
1 of Table I shows the effect of the above cuts on
been imposed (see below).
the signal and backgrounds for a SM Higgs boson ¯
The large bbjj background is most effectively
of mass M = 120 GeV. Overall, about 13% of all
H reduced by requiring a significant level of missing
H ττ e±µ∓νν¯ events generated in weak bo-
transverse momentum in the event. The p/ distri-
→ → T
son fusion are accepted by the cuts of Eqs. (7)-(10)
butions for the signal and the various backgrounds
(for M = 120 GeV).
H areshowninFig.1. Theextremelysoftp/ distribu-
T
As is readily seen from the first line of Ta- ¯
tionfor bb events is mostly due to the stringent lep-
ble I, the dominant backgrounds are e,µ pairs from
ton isolation requirements. A low transverse mo-
heavy quark decays. Of the tt¯(+jets) events 14 fb
mentum of the charm quark in the b cℓν decay
are from tt¯, 360 fb are from tt¯j, and the remain- →
requires a fairly soft parent b-quark, which in turn
ing 860 fb arise from tt¯jj production. The addi-
doesnotpermitalargep/ tobecarriedawaybythe
T
tional jets (corresponding to massless partons) are
escaping neutrino. This effect is amplified by the
required to beidentified asfar forwardtaggingjets. ¯
QCD nature of the bbjj background which favors
The tt¯jj cross section is largest because the tt¯pair
the production of low p b-quarks in the first place.
T
is not forced to have as large an invariant mass as
All other backgrounds involve the decay of one or
in the first two cases, where one or both b’s from
more massive objects (a Z, Ws, or top quarks) into
the decay of the top quarks must pass the tagging
leptons and neutrinos and thus result in a much
jet cuts.
harder p/ distribution. The distributions of Fig. 1
T
For the events where only one or none of the
motivate a cut
b’s are identified as a forward jet, the b’s will most
frequently lie between the two tagging jets, in the p/ > 30 GeV , (12)
T
7
FIG. 2. Normalized invariant mass distribution
ofthetwotaggingjetsforthesignalandthevarious
backgrounds as in Fig. 1. The cuts of Eqs. (7)-(11)
are imposed. (The distributions are essentially
unchanged after imposing the additional cut of
Eq. 12.)
the transverse momentum of the Higgs boson can-
didate, defined as the recoil needed to balance the
transverse momentum of the observed hadrons in
theevent. These “Higgsboson”transverse momen-
tum distributions are also plotted in Fig. 1. They
FIG. 1. Upper: Normalized p/ distribution for are qualitatively similar to p/ for all processes, but
T T
the signal (red) and various backgrounds: tt¯+jets the peak is shifted to lower values than that of the
¯
(solidblue), bbjj (dashedblue),QCDWWjj (solid real Higgs boson signal for all backgrounds. While
green), EW WWjj (dashed green), QCD ττjj we do not use this distribution here, we point out
(solid magenta) and EW ττjj (dashed magenta). that it may be useful once a multivariate analysis
The cuts of Eqs. (7)-(11) are imposed. Lower: is performed at the detector level.
The same for the normalized p distribution of QCD processes at hadron colliders typically oc-
T
the reconstructed Higgs boson, except that QCD cur at smaller invariant masses than EW processes,
and EW WWjj contributions have been combined due to the dominance of gluons at small Feynman
(solid green). x in the incoming protons. We observe this behav-
ior here, as shown in Fig. 2. The three tt¯+ jets
¯ backgrounds have been combined for clarity, even
which brings the bbjj background to a manageable
though their individual distributions are slightly
level. Thecross sections afterthisp/ cut areshown
T
different. One can significantly reduce the QCD
in the third line of Table I.
¯ backgrounds by imposing a lower bound on the in-
A similar reduction of the bbjj background can
variant mass of the two tagging jets:
be achieved by a harder lepton transverse momen-
tum requirement than the 10 GeV cut of Eq. (7).
M > 800 GeV . (13)
However, thesignaldistribution isquite softaswell jj
and a harder p -cut would lead to an undesirable
Tℓ Resultingcrosssectionsareshowninthefourthline
loss of signal rate. Another optionis to make use of
of Table I.
8
For significant further reduction of the various
backgrounds, reconstruction of the tau-pair invari-
ant mass [30] is necessary. Due to the large mass
of the decaying Higgs boson and also because of its
large transverse momentum (see Fig. 1) the pro-
duced taus are moving relativistically in the labo-
ratory frame. As a result the tau direction closely
follows the direction of the corresponding observed
decay lepton. Since the transverse momentum of
the Higgs boson is known (it is given by the vecto-
rial sum of charged lepton p ’s and missing trans-
T
verse momentum) the momentum parallelogram in
the transverse plane allows one to extract the frac-
tions of the two tau momenta which are carried
by the two charged leptons. We denote these mo-
mentum fractions by x ,x in the following. This
τ1 τ2
reconstruction works only if the taus are not emit- FIG. 3. Scatter plots of x v. x with the
τ1 τ2
ted back-to-back in the transverse plane and we cuts of Eqs.(7)-(14), for the 120 GeV Hjj signal,
therefore impose the technical cut b¯bjj, WWjj and tt¯+jets reducible backgrounds.
The number of points in each plot is arbitrary and
cosφ > 0.9 . (14)
eµ − corresponds to significantly higher integrated lumi-
Theresulting x ,x distributions areshown inthe nosities than expected for the LHC. The solid lines
τ1 τ2
formofascatterplotofunweightedeventsinFig.3. indicate the cuts of Eq. (15).
The distribution for real tau pairs is shown only for
theHiggsbosonsignalbecause theplotforγ∗/Z The reconstructed tau-pair invariant mass distri-
→
ττ looks virtually identical. butions for the combined W+W− and tt¯ back-
For real τ decays, the p/T vector must lie be- grounds, for b¯bjj events and for the QCD and EW
tween the two leptons, and apart from finite de- Zjj events are shown in Fig. 4, after the back-
tector resolution the reconstruction must yield 0 < to-back cut of Eq. (14). The b¯bjj background is
xτ1,2 < 1. For the WW and tt¯backgrounds, how- almost completely concentrated in the small Mττ
ever, the collinear approximation is not valid be- region and γ∗/Z + jj events are strongly peaked
cause the W’s and top quarks receive only mod- at M = M . When searching for a Higgs bo-
ττ Z
est boosts in the lab. In this case, the p/T vec- son mass peak well above MZ, both backgrounds
tor will rarely lie between the two leptons, and are drastically reduced. As is indicated by the
an attempt to reconstruct a τ pair will result in width of the Z peak in Fig. 4, a resolution of
xτ1 < 0 or xτ2 < 0 for a significant fraction of the about 10% is possible for the reconstructed tau-
events [6]. Many others end up in the unphysical pair invariant mass, which agrees well with ear-
region xτ > 1. The scatter plot of Fig. 3 suggests lier results obtained with full detector simulations
the real τ-reconstruction cuts for A ττ by ATLAS [25]. Here we are inter-
→
ested in SM Higgs bosons with a mass in the range
x , x > 0 , x2 +x2 < 1 . (15)
τ1 τ2 τ1 τ2 100 GeV < M < 150 GeV. As a result we need to
H
Once the momentum fractions carried by the consider only backgrounds which lead to a recon-
e,µ-pair are known, the invariant mass of the tau- structed M in the range
ττ
pair is given by
90 GeV < M < 160 GeV. (17)
ττ
M = m /√x x . (16)
ττ eµ τ1 τ2
9
FIG. 4. Reconstructed tau-pair mass distribution for WWjj and tt¯+jets events (solid blue), b¯bjj
events(dashedblue)andQCD+EWZjj events(magenta). Thecombinedcurvesarealsoshown(black).
The cuts of Eqs. (7)-(14) are imposed.
¯
The reduced background level due to this tau-pair Fig. 5). For the bbjj background, for example, a
mass cut is shown in the last line of Table I. large rapidity separation is induced by the conflict-
Clearly, Higgs mass reconstruction is a very ing requirements of a large tau-pair invariant mass
powerful background suppression tool, in particu- and the low lepton transverse momenta surviving
¯
lar for bbjj events which mostly populate the low the lepton isolation cuts. The lepton correlations
M region. This means that the background cross can be exploited by imposing a lepton pair angular
ττ
sections in Table I exaggerate the background level cut:
and one should rather consider the expected rates
R < 2.6. (18)
inthevicinity oftheHiggsbosonmasspeak. Given eµ
△
the expected mass resolution, we only need to con-
This cut acts primarily against the tt¯+ jets and
sider background events within 10 GeV of the
¯
± bbjj backgrounds, which are already at a quite low
peak. In Table II we have summarized these cross
level. We select the value 2.6 conservatively to re-
sections at the various cut levels for the example
tain more signal rate, in particular for large Higgs
of a Higgs boson at M = 120 GeV. Within the
H boson masses, close to M = 150 GeV.
H
cuts of Eqs. (7)-(15) we have achieved a signal to
At this level of cuts we consider one final back-
background (S/B) ratio of 1/1.
ground, an additional source of e + µ + p/ from
T
Yet another significant difference between sig-
Higgs production itself, via H WW decay. Real
nal and some backgrounds is the angular distri- →
or slightly virtual W’s are produced as opposed to
bution of the charged decay leptons, e± and µ∓,
realτ’s,sothesearchforrealτ’soutlinedabovewill
relative to each other. In the case of the Higgs sig-
restrict the contribution from this decay channel.
nal, the high p of the Higgs boson results in a tau
T However, most of the other cuts we have described
pair, and therefore charged decay leptons, which
isolate Higgs production only, and even the lepton
are emitted fairly close together in the lab frame.
angular cut will select H WW events due to
In the case of the heavy quark backgrounds, this →
the strong anti-correlation of the W spins, which
correlation is not reproduced, in particular when
leads to the e,µ pair being emitted preferentially
viewed as lepton separation in the lego plot (see
together in the rest frame of the Higgs boson [8];
10