Table Of ContentSelected topics from the single top t-channel:
cross section and other properties
Benedikt Maier1
1Karlsruhe Institute of Technology (KIT) – D-76131 Karlsruhe, Germany
on behalf of the ATLAS and CMS collaborations.
Preprint of the proceedings for the contribution to the LHCP2015 conference, St.Petersburg, Russia.
Measurements of the cross section and of the interactions happening at the tWb vertext are
√
performedinthesingletopt-channelatcenter-of-massenergiesof s=7and8TeV.Resultsofboth
ATLAS and CMS collaborations are presented. No indications for new physics and no deviations
from the Standard Model predictions within the experimental and theoretical uncertainties are
found.
6
1
0 I. INTRODUCTION II. CHANNEL TOPOLOGY AND ANALYSIS
2 STRATEGY
n
a
Single top t-channel events have a distinct topology
J The single top t-channel has the largest cross section
explained in the following: most characteristic is the up-
1 of the three modes the electroweak production of a top
per outgoing quark line in Figure 1, representing a light
2 quark at hadron colliders typically is devided into. The
separation into t-, tW- and s-channel makes most sense quark which recoils against the exchanged virtual W bo-
] son. Upon hadronization it results in light jet with sub-
at leading order in the strong coupling constant α . At
x S stantial transverse momentum, which tends to go in a
e next-to-next-to-leadingorderatthelatest,thedefinitions
forward direction. In a typical analysis the resonant top
- are not unambiguous anymore, and t- and s-channels
p quark is required to decay leptonically, rejecting multi-
start to interfere. It therefore makes it an interesting
e jetbackgroundprocessesforwhichitisdifficulttofakea
h place to look for potential new structures in the tWb
prompt lepton. The sign of the lepton will also be used
[ couplingandtomeasurekeyparametersoftheStandard
for distinguishing between t and ¯t production. The top
Model(SM)suchastheCKMmatrixelementV that,in
1 tb decayalsofeaturesabquarkgivingrisetoacentralbjet.
contrast to top quark pair production which is mediated
v Theinitialbquarkisimpliedtostemfromagluonsplit-
2 bythestronginteraction,appearsalreadyintheproduc- ting. Theb¯quarkanditscorrespondingbjethoweverlie
6 tion. The leading order Feynman diagram of Figure 1
out of the tracker acceptance most of the time and thus
6 moreover suggests that the rates for the production of a
5 top quark (t) are different from the anti-top (¯t) quark cannot be tagged. Depending on whether one chooses
0 the 5- or 4-flavor-scheme (5F, 4F) to describe the proton
in proton-proton collisions, because the incoming light
. (in the latter the b quark is not considered a massless
1 quark is more likely to be a quark than its anti-partner.
parton, but must be produced in a gluon splitting), the
0 Inturnthismeansthet-channelcanalsobeusedtocon-
6 strain parton distribution functions (PDFs), which each leading order formulation in terms of Feynman diagrams
1 and calculus is either a 2 → 2 or 2 → 3 process. This
: predict a different R = σt/σ¯t according to the respec- has deep implications for the predictions and the mod-
v tive energy and momenta distributions the partons are
elling of the t-channel: for an all-orders-expansion the
i carrying.
X two schemes must give exactly the same results; in prac-
r tice simulations at next-to-leading order are employed,
a
and this circumstance leads to different predictions for
the 4F and 5F. These can then be compared to experi-
mental data, and conclusions can tried to be drawn on
which model is the better. A detailed theoretical intro-
q q(cid:48) q q(cid:48) duction into this subject is provided in [1].
Thetopologydescribedabovelendsitselftoasocalled
W W+ “2 jets 1 tag” selection (2j1t), which is widely employed
in single top measurements and also consistently applied
b t in every analysis presented here. Besides an isolated,
hard lepton one expects one jet identified as b jet and a
b t g b¯ light, forward jet. In this signal enriched phase space it
istypicallythedisciminatorofaNeuralNetworktrained
FIG. 1. Leading order Feynman diagram of the t-channel in with variables separating between single top production
the 5F (left) and the 4F (right). and the main background processes (t¯t, W + jets and
2
multi-jet production) or the pseudorapidity of the un- · 10·31C03MS, s = 8 TeV, L = 19.7 fb-1, muon, 2-jet 1-tag
tagged jet, |ηj(cid:48)|, that is used to extract the signal. The 0.25 Data
correct modelling of backgrounds is often verified in 2j0t s/ 5 t-channel
ot¯tre3vj2etntcso,nrtersoplercetgiivoenlsy.wThihcihsagrueaernarnitceheesdtihnaWt a+ll ajentaslaynsids Event 4 tWQt,C/ ZtDW+ j,me stu-scl,th idjaeinbt noeslons
Syst. uncertainty
ingredients are validated in phase spaces which are very 3
close yet entirely orthogonal to the signal region.
2
1
III. CROSS SECTIONS 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
|h |
j'
A. Inclusive CMS, s = 8 TeV, L = 19.7 fb-1
√ CMS
TheCMScrosssectionmeasurementat s=8TeV[2] 1.95 – 0.10 (stat.) – 0.19 (syst.)
ABM11
is designed as a template analysis in |η |, the pseudo-
j(cid:48)
rapidity of the light recoil jet. It selects events with ex- CT10
actly one muon (electron) with p > 26GeV (30GeV) CT10w
T
and | η | < 2.1 (2.5). Events with additional lepton HERAPDF
candidates with looser selection criteria are rejected.
MSTW2008
For the muon channel a cut on the transverse mass
NNPDF 2.3
of the reconstructed W boson m > 50GeV is im-
T
p(cid:113)osed. The definition for the transverse mass is mT = 1 1.2 1.4 1.6 1.8Rt-ch. = s t2-ch.(t)/s t-ch.(2t).2
(pµ +Emiss)2−(pµ+pmiss)2−(pµ+pmiss)2. It relies
T T x x y y
FIG. 2. 2j1t distribution of the pseudorapidity of the un-
on the missing transverse energy components to bal-
taggedjet(top);RvaluepredictionsfordifferentPDFs(bot-
ance the sum of all observed momenta. In the electron
tom), which are all in agreement with the measured value
channel it is a cut on the missing transverse energey
within the uncertainties. Taken from the CMS cross section
of ETmiss > 45GeV that helps reject the QCD multi-jet measurement at √s=8TeV [2].
background. By means of a range for the reconstructed
topquarkmass,whichis130<m <220GeV,asignal
(cid:96)νb
(inside) and sideband (outside) region is defined.
by nuisance parameters in the maximum-likelihood fit;
Theanalysisexploitsa3j2tcontrolregiontodetermine the signal normalization is left free to float. The left dis-
the t¯t contribution in a semi-data driven way by looking tribution of Figure 2 shows the post-fit distribution in
at the |η| templates of the untagged jet. Contributions themuonchannel. Averygoodagreementbetweendata
for all other SM processes except for t¯t are subtracted andpredictionsisobserved. Theresultingcrosssectionis
from the data template, and bin-by-bin correction fac- σ =83.6±2.3(stat.)±7.4(syst.)pb. Thedominatingsys-
tors are derived by dividing the observed yields by the tematicsarerelatedtothemodellingofthesignalprocess
t¯tpredictionastakenfromsimulation. Thissetofcorrec- and the jet energy scale. Separating the events by the
tion factors is then applied to the t¯t template in the 2j1t lepton charge and fitting the top and anti-top templates
region, both in the signal and sideband regions. Since independently gives σ = 53.8±1.5(stat.)±4.4(syst.)
t
events in the 2j0t sample are predominantly stemming and σ¯t = 27.6±1.3(stat.)±3.7(syst.). Their ratio is
by W + jets production and hence these events have R = σt/σ¯t = 1.95 ± 0.10(stat.) ± 0.19(syst.). This
jets mostly coming from light quarks, this region is only pseudo-observable is sensitive to which PDF has been
used to perform a general validation of W + jets shapes usedinthecalculationofthehardinteraction. Theright
and it is instead preferred to derive bin-by-bin correc- figure of Figure 2 contrasts the measurement with differ-
tion factors for this background from the sidebands in ent PDFs. The data does not really disfavor one of the
2j1t region. Predicted yields from all other processes are sets within the uncertainties, but most of them predict a
subtracted from the data |ηj(cid:48)| template and scale factors smaller R value than the one observed.
with respect to the W + jets simulation are obtained.
The simulation is also used to derive additional correc-
tions by extrapolating from the sideband into the signal
region. QCD contributions are derived in a purely data B. Fiducial
driven manner from a region with inverted criteria on
lepton isolation, but turn out to be very small. Compared to fully inclusive results, fiducial cross sec-
The templates in the 2j1t region are simultaneously tions have the advantage that their dependence on the
fit to data in |η | in both the electron and muon chan- event generation (knobs to turn are e.g. matrix ele-
j(cid:48)
nel. The (semi-)data driven background estimations ex- mentgenerators,scalechoices,hadronizationmodelsand
plained above come with uncertainties that are reflected PDFs) is reduced. Therefore differences related to the
3
×103 invariant mass of the jet pair. The shape of the dis-
05 400 ATLAS Preliminary ∫ L dt = 20.3 fb-1 s=8 TeV criminator is validated in a t¯t enriched 2j2t region and
0. SR data a 2j1t region with relaxed b tagging requirement, which
ents / 300 tWt-tc,W+hjaet,ntssn-cehlannel mforaktehseiQtCbeDinmgudlotim-jientapteroddbuyctWion,+wjheitcsheivseensttsi.maEtxecdepint
Ev 200 Z+jets, diboson a data driven technique, shapes of all backgrounds are
Multijet
t-ch.gen⊕ η-inter. takenfromsimulation,andthetemplatesarenormalized
100 tothemostpreciseavailable(N)NLOtheorypredictions.
In Figure 3 a good agreement between data and simula-
tion is found after a maximum-likelihood fit has been
0
d. 0.2 performed in the Neural Network discriminator. The fit
Data-PrePred. -0.200 0.2 0.4 0.6 NN0. 8output1 rσefisdu.l=ts3t.r3a7n±sla0t.0e5i(nsttoata.)±m0e.a4s7u(rseydstfi.)d±uc0i.a0l9c(rluosmsi.s)e.cFtiiogn-
NN output ure 3 also shows a comparison of the result with predic-
tionsofvariouseventgenerationsetups,owingtothefact
ATLAS Preliminary ∫ L dt = 20.3 fb-1 s=8 TeV that,asmentionedintheintroduction,thet-channelisa
ATLAS result good place to constrain modelling aspects in the Monte-
stat. ⊕ sys. stat.
Carlosimulation. ExceptfortheAcerMCsetup,whichis
Predicted fiducial cross-section:
aaMMCC@@NNLLOO((22→→33))++HHeerrwwiigg acalculationbasedonmatching4Fand5Feventsatlead-
PPoowwhheegg((22→→33))++PPyytthhiiaa66 ingorderinα basedofthep oftheadditionalbquark,
PPoowwhheegg((22→→33))++PPyytthhiiaa88 S T
PPoowwhheegg((22→→22))++PPyytthhiiaa66 all setups give predictions that are well compatible with
AAcceerrMMCC++PPyytthhiiaa66 µµ==117722..55 GGeeVV data. The inclusive cross section can easily be obtained
AAcceerrMMCC++PPyytthhiiaa66 µµ==6600 GGeeVV –atthecostoflargeruncertaintiesduetotheextrapola-
1.5 2 2.5 3 3.5 4 tion – by dividing the fiducial cross section by the selec-
σftid [pb] tion effiency of the fiducial selection (σ = (1/(cid:15)fid)·σfid.)
and turns out to be σ =82.6±1.2(stat.)±11.4(syst.)±
FIG. 3. Results from the ATLAS fiducial cross section mea- 3.1(PDF)+2.3(lumi.). This information can be used to
√
surement at s=8TeV [3]: post-fit NN output distribution measure the CKM matrix element V , which is (cid:39) 1 for
tb
in the 2j1t region (top). Fiducial cuts have been imposed on theSMbutwhosevaluecouldbealteredbynewphysics.
the simulations. The bottom figure compares the measured Assuming |V | (cid:29)|V |,|V | and B(t → bW) = 1, it
tb ts td
fiducial cross section with the predictions of various gener- (cid:112)
is simply given by |V | = σ/σ and numerically
ation setups, disfavoring only the matched 2 → 2/2 → 3 tb theor.
for this analysis |V | = 0.97+0.09(exp.+theor.), i.e. it
calculations. tb −0.10
is compatible with the SM prediction. More details are
given in [3].
modelling are reduced to residual differences within the
fiducial volume entirely covered by the experimental ac-
ceptance. Uncertainties stemming from the extrapola-
tion from a visible into the inclusive phase space do not
applytosuchameasurement; moreoveritiseasiertore-
interprettheresultsoncebetterMCgeneratorsareavail-
C. Differential
able at some later point. Practically this is achieved my
mimickingtheselectionimposedonreconstructedobjects
on behalf of cuts on stable particles at generator level. Both ATLAS and CMS have also measured a cross
Consequently the following cuts are applied, defining a section differential in the p of the top quark [4, 5]. The
T
2j1t signal region: exactly one lepton (muon or electron) analysis designs are similar: a Neural Network is trained
with pT > 25GeV and |η| < 2.5. Jets are reconstructed in the 2j1t region for a better separation between the t-
within |η| < 4.5 and must have pT > 30GeV (or even channel and background processes, and its discriminator
pT >35GeVif2.75<|η| <3.5). Exactlytwojetsneedto iscutoninordertoobtainahigh-puritysampleofsingle
be present, one of which must be identified as a b jet, ei- top events. After the background contributions are sub-
therbydeployingamultivariatealgorithmforidentifying tracted, the distributions are unfolded to parton level,
secondaryverticesonreconstructionlevelorbymatching where the kinematics of the top quark are understood
stableBhadronstogeneratedjets. Theleptonmusthave to reflect the resonance before its decay and after radia-
(cid:112)
a distance in the φ-η-plane of ∆R= ∆φ2+∆η2 >0.4 tion effects. The normalized p distributions are shown
√ T
toanyjet. QCDmulti-jeteventsarerejectedbyrequiring in Figure 4 for s = 7 and 8TeV, respectively, and dis-
Emiss >30GeV and m >50GeV. play good agreement between data and simulation. The
T T
A Neural Network is trained with 14 variables, the (dis)agreement in the tail of the 8TeV distribution sug-
three most relevant being the pseudorapidity of the un- gests that the 4F is able to model high p objects better
T
tagged jet, the reconstructed top quark mass and the than the 5F.
4
CMS 19.7 fb-1 (8 TeV)
1
σd1 )t(pd GeVT10-2 ATLAS ∫ L dt = 4.DsNs5tt9aLaa tOttaf bu⊕ (n-M 1sc yS.sTs uW=n72c 0.T0e8V) Events / 0.23500000 Dttt t((ato-ttachhear)n.) WOQSttC+ahDtjee. rtussnc.m +jets
1⋅ σ 10-3 PDF ⊕ scale unc. 2000
1500
10-4
O 1000
L 1.5
N
ata / 0.51 500
D
0 100 200 300 400 500
p (t) [GeV] 0
-1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1
T cos(q *)
CMS Preliminary 19.7 fb-1 (8 TeV) CMS 19.7 fb-1 (8 TeVℓ)
dpT Data 1
s/d0.5 POWHEG (5FS) + Pythia6
aMC@NLO (4FS) + Pythia8
·
s1/0.4 CompHEP + Pythia6
0.5
0.3
)
R
0.2 e(g 0
R
0.1
0
-0.5 @ 68% CL Best fit
mulationData1.51 @ 95% CL SM pred.
Si 0.50 20 40 60 80 100120140160180200220240
top p [GeV] -0.4 -0.2 0 0.2 0.4
T Re(g)
L
FIG. 4. Normalized distributions of the top quark p have
√ T
been measured by ATLAS (top) at s = 7 [4] and by CMS FIG. 5. Distribution of cosθ(cid:96)∗ (top) and limits on real tensor
(bottom) at 8TeV [5]. components in the tWb coupling (bottom), taken from the
8TeV CMS analysis [6].
IV. W BOSON HELICITY
In terms of the event selection, it is closely following
The helicity of the W boson is usually subject to what has been done for the t-channel inclusive cross sec-
t¯t analyses and is measured with a single top selection tion measurement presented earlier. Since a boost in
for the first time in the analysis presented here [6]. The the top quark rest frame is required, a top quark can-
helicityangleθ∗isdefinedastheanglebetweenthedirec- didate must be reconstructed. Two solutions for the
(cid:96)
tion of the reconstructed W boson in the top quark rest z-component of the escaping neutrino arise when solv-
frame and the direction of the lepton in the W boson ing a quadratic equation for p . Events which only
z,ν
rest frame. Its probability function (which is the same have two imaginary solutions are discarded, otherwise
for t¯t and single top events) is proportional to each he- the one with the smallest absolute value is picked. Fig-
licity component (F : left-handed, F : longitudinal, F : ure 5 shows the simulated cosθ∗ templates compared to
L 0 R (cid:96)
right-handed) of the W boson, data in the 2j1t muon channel. All single top events
(t, s, tW) and t¯t events contribute to the signal sam-
ple, since one can reconstruct a tWb vertices in all of
Γ1 dcdoΓsθ∗ = 38(1−cosθ(cid:96)∗)2FL+ t+hejmet.s,Tishetaskheanpefrionmcossimθ(cid:96)∗uloaftitohne, mwahiinlebtahcekgnroorumnadl,izWa-
(cid:96)
3 3 tion is introduced as an unconstrained parameter and is
sin2θ∗F + (1+cosθ∗)2F ,
4 (cid:96) 0 8 (cid:96) R fit simultaneously together with two of the three helic-
ity fractions, F and F . The third component is ob-
L 0
where Γ is the total width of the top quark decay. SM tainedfromtheconstraintΣ F =1. Normalizationesti-
i i
predictions are F = 0.311±0.005, F = 0.687±0.005 mates from [2] are used for all other backgrounds, whose
L 0
and F = 0.0017±0.0001 [7]. In the analysis they are shapes are either taken from simulation or taken from a
R
extracted from a maximum-likelihood fit in cosθ∗. control region in the case of multi-jet production. The
(cid:96)
5
V. TOP POLARIZATION
800 dsiagtnaal (t-channel) CMS preliminary s = 8 TeV, L = 20 fb-1
stW-channel Muon channel, 2J1T BDT > 0.06 In the Standard Model the top quark is highly polar-
tt
600 DY ized along the direction of the light recoil quark, and its
W
diboson decay products bear information on the spin of the res-
QCD
stat. + syst. onance. This can be used to construct an observable,
400
cosθ∗, which is sensitive to the top quark polarization.
It is defined as the angle between the lepton of the top
200
quark decay and the light recoil jet, as seen from the top
quark rest frame. Its differential distribution follows
-1 -0.5 0 0.5 1
cos q *
meas.)/meas. 0.501 where P(cid:96) dΓ1ednocdtoeΓssθ∗th=e t12o(p1q+uPartkα(cid:96)pcoolsaθri∗z)a,tion is α(5(cid:96).1is)
(exp.--0.-51-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 twhiethdreegsrpeeecotftocotrhreelatotiponquoafrkthsepainng(tuhlaisradnisatlryisbisutaisosnumofe(cid:96)s
α = 1). The measured quantity finally is the asymme-
(cid:96)
try A = (N(cosθ∗ > 0)−N(cosθ∗ < 0))/(N(cosθ∗ >
FIG.6. TheCMSanalyis[8]measuresthecosθ∗ distribution (cid:96)
√ 0)+N(cosθ∗ < 0)), which is determined separately in
at s=8TeV in the muon channel after a cut on the BDT
both the electron and muon channel. A more detailed
output.
description of the applied cuts that enhance signal over
background contributions is provided in [8], but it em-
ploys a 2j1t selection similar to [2]. The multi-jet back-
fit results are F = 0.298±0.028(stat.)±0.032(syst.),
L ground is derived from data in a control region enriched
F = 0.720 ± 0.039(stat.) ± 0.037(syst.) and F =
0 R inQCDeventsthatisobtainedbyinvertingleptonisola-
−0.018±0.019(stat.)±0.011(syst.), which is consistent
tion criteria. The default simulation setup for W + jets
with the SM predictions.
suffers from a bad description of cosθ∗ close to −1; an-
Theabove resultscanbere-interpreted inordertoex-
other generator (Sherpa) which performs better in this
clude potential tensor terms appearing in the tWb cou-
region of phase space is used to correct the main Mad-
plings, whose real parts are given by the parameters gL Graph simulation. The shapes of t¯t templates are vali-
and g in the extended Lagrangian
R datedina3j1tand3j2tcontrolregion. Finallyaboosted
decision tree (BDT) is trained in order to further sepa-
rate single top production from the backgrounds. Af-
g
LatWnobm. =−√ b¯γµ(VLPL+VRPR)tW−µ− ter a maximum-likelihood fit to its shape, in which the
2
signal and background normalizations are determined, a
g iσµνq
√ b¯ ν(g P +g P )tW−+h.c., cut on the BDT output is imposed to obtain a signal-
2 mW L L R R µ enriched sample (see Figure 6). The background contri-
butionsaresubtractedfromdata, andthedistributionis
assumingapurelyleft-handedinteractionofthevector unfolded to correct for detector effects. The asymmetry
part, i.e. V = 1, V = 0. The reader is deferred to the A is calculated from the unfolded templates separately
L R (cid:96)
publicationforfurtherinformationandmoredetails. The for the electron and the muon channel. Their combina-
bestfitvaluesareg =−0.017andg =−0.008. Ascan tion gives A = 0.41±0.06(stat.)±0.07(syst.), where
L R (cid:96)
be seen in Figure 5, this is consistent with the leading the jet energy scale is the dominant source of systematic
order SM prediction of 0. The signal modelling is the uncertainty. This results in a top quark polarization of
main source of systematic uncertainty. P =0.82±0.12(stat.)±0.32(syst.).
t
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