Non-standard top substructure

0.31 MB·

by  Christoph Englert

Non-standard top substructure
Christoph Englert,1,∗ Dorival Gon¸calves,2,† and Michael Spannowsky2,‡
1SUPA, School of Physics and Astronomy,University of Glasgow,
Glasgow, G12 8QQ, United Kingdom
2Institute for Particle Physics Phenomenology, Department of Physics,
Durham University, DH1 3LE, United Kingdom
The top quark,being theheaviest particle of theStandard Model, is aprime candidate of where
physicsbeyondtheSMmightcurrentlyhidebefore oureyes. Therearemanynaturalextensionsof
the SM that rely on top compositeness, and the top quark could follow the paradigm of revealing
asubstructurewhen it isprobed at high enough momentum transfers. Observinghigh pT top final
states naturally drives us towards boosted hadronic analyses that can be tackled efficiently with
jet substructuretechniques. In thispaper weanalyse theprospects of constraining exemplary non-
4
standardQCDtopinteractionsinthiskinematicalregime. WecorrectlyincludeQCDmodifications
1
0 to additional gluon emission off the boosted top quark and keep track of the modified top tagging
2 efficiencies. Weconcludethatnon-standardtopQCDinteractionscanbeformidablyconstrainedat
theLHC14TeV.Experimentalsystematicuncertaintiesareamajorobstacleofthedescribedmea-
n
surement. Unlesssignificantlyimprovedforthe14TeVrun,theywillsaturatethedirectsensitivity
a
tonon-resonant BSM top physics at luminosities of around 100/fb.
J

7

INTRODUCTION resemblance of the Higgs phenomenology with the SM,
]
h whilst the composite effects are hidden in the fermionic
p After the discovery of a SM Higgs boson [1] at the sector. Phenomenologicalsearchesthattargetthepoten-
p- LHC [2, 3] and preliminary measurements of its proper- tial substructure of the top quark are therefore also ex-
e tiesandcouplings[4,5]whichindicatecloseresemblance tremely important in the context of Higgs physics, since
h totheSMhypothesis,hintsforphysicsbeyondtheSMre- bothphenomena,the (100GeV)electroweakscalewith
[ O
mainelusive. ApuzzlethatremainsinthecontextofSM the top quark in the same ball park, might point us to-
1 irrespectiveofaseeminglyunnaturalelectroweakscaleis wards a solution in terms of strong interactions.1
v the mass hierarchy in the fermion sector and the large
2 Of course, the phenomenological implications of com-
mass of the top quark rather close to the Higgs vacuum
0 positeness are not new to particle and, more broadly
expectation value. The restoration of chiral symmetry
5
speaking, to nuclear physics (see Ref. [13] for a review).
1 for vanishing Yukawa interactions guarantees that cor-
The deviation from the anticipated Rutherford scatter-
. rections to elementary fermion masses are proportional
1
ing cross section at large angles observed by Geiger
0 to the fermion mass themselves in the SM. Using the
and Marsden [14] and the later resolution of atomic nu-
4 language of effective field theory, the Yukawa couplings
1 aremarginaloperators,i.e. oncetheirvaluesarefixedby clei[15,16]isawell-knownexampleofsuchaprogramme
: resolvingpoint-like sources by probing the characteristic
v some UV dynamics [6], they remain small at low energy
energyscalewithhighenoughmomentumtransfers. The
i scales. Hence, the large hierarchy among the Yukawa
X non-linear structure of QCD and the mismatch of the
couplings largely determined by the top quark is typi-
r theory’sfundamental degreesof freedomwith the exper-
a cally considereda potentialsourceofphysicsbeyondthe
imental observables, however, introduces another layer
SM.
of complexity when we deal with non-standard interac-
Indeed, the top typically plays a central role in most
tionsofacolour-chargedobject. We usuallyparametrize
modelsthattrytoexplaintheelectroweakscaleatamore
the deviations from the SM via introducing higher di-
fundamental level. Supersymmetric constructions [7],
mensional operators in an effective field theory descrip-
fixed-point gravity scenarios [8], and strong interac-
tion that is guided by the low-energy gauge symmetry
tions [9] are just three well-known and well-established
requirements. Since we can expect a separationbetween
examples. In the latter case, the large mass of the top
the new physics and the electroweak scale, it is custom-
canbe understoodasa (linear)mixing effectoflightele-
ary to limit analyses to dimension six operator exten-
mentarystates with composite fermions ofa stronglyin-
sions to the SM [17–19]. However, since we cannot sep-
teractingsector[10,11]thatalsoprovidesasetofNambu
arate different partonic initial and final states and due
Goldstone bosons forming the Higgs doublet. The mix-
ing effects together with fermion and gauge boson loops
induce a Coleman-Weinberg Higgs potential that trig-
gers breaking of electroweak symmetry at a scale much
1It should be noted that such interactions typically also alter low
smallerthanthestronginteractionscale. Insuchpseudo-
energy observables (see, e.g.,Ref. [12]), but we remindthe reader
Nambu Goldstone Higgs scenarios, we can have a large thatwefocusontheprospectsofdirectmeasurementsinthiswork.
2
t
t
t g
g
g
t
g t
t
g t
g
g
FIG.1: Feynmandiagramscontributingtoanomalousp(g)p(g) tt¯productionatleadingorder,arisingfrom theoperatorsof
→
Eq. (1).
to the gauge structure, all operatorsthat introduce non- A PHENOMENOLOGICAL APPROACH TO
standardQCDpropertieswillcontributesimultaneously. ANOMALOUS QCD TOP INTERACTIONS
Their different kinematical dependencies can be used to
disentangle them [20–23], but modifications due to new To get a quantitative estimate of the leading effects of
interactionswillalsochangetheresponseofthemeasure- non-standard top interactions at the LHC we focus on
ment strategy. new physics contributions to tt¯production arising from
The top quark production cross section will receive modified QCD interactions. Non-standard electroweak
modifications for energetic events if new physics in properties do impact the top decay t Wb [30], but
→
the top sector is present. This immediately motivates can be studied separately in single top-production and
boostedtopsearches[24]asasensitiveprobeofmodified interlaced with our findings.
QCD interactions on which we focus our analysis in the Since the current LHC searches imply strong bounds
following. Frompreviousanalyses[23]itisexpectedthat on the masses of potential new degrees of freedom, it is
upon correlating inclusive and boosted measurements of expected to have a mass gap between the SM and the
pp tt¯+X we will be able to tightly constrain such BSM fields (which, e.g., lift the top mass via mixing ef-
→
non-standard interactions. However, there is a caveat: fects [31]). In this case, the new physics effects can be
top quarks when produced at high p are very likely to parametrized via higher dimension operators involving
T
emithardgluonsbeforetheydecay[25,26]. InRef.[23]it only the SM particles and there is a number of new con-
wasshownthatsuchaninteractionhasadecreasedsensi- tact operators which impact tt¯+jets production [18, 20].
tivitytoanomalousQCDtopinteractions. Itistherefore Here we focus on some operators that allow an interpre-
crucial to include the anomalous top interactions to the tationinterms of composite structuressuchas radiiand
proper modelling of the exclusive final state to correctly anomalous magnetic dipole moments as a proof of prin-
evaluatetheprospectsofthedescribedmeasurement. By ciple. These non-standard properties can be introduced
analyzingthefullyhadronizedfinalstateinsuchasetup, in a gauge-covariant way through the following effective
we are also guaranteed to correctly reflect the different dimension six interaction terms [17, 21–23]
selectionefficienciesfortheboostedsubjectanalysisthat
emerge from the BSM-induced modifications of the top = g Rt2t¯γµG Dνt+h.c., (1a)
R s µν
spectrum. Moreprecisely: weinvestigatethe constraints L − 6
thatwe canexpectfromadaptedsearchesforanomalous =g 1 t¯σµν(k +ik γ5)G t, (1b)
k s V A µν
top interactions in the busy QCD-dominated LHC en- L 4mt
vironment using realistic simulation, analysis and limit
where G is the gluon field, G = D G D G its
setting techniques. µ µν ν µ − µ ν
fieldstrengthandDµ =∂µ+ig Gµ thecovariantderiva-
s
Especially experimental systematics are known to be
tive. The convention of Eq. (1) follows Ref. [29]; the top
largeinthetailsoftopdistributionswherethedeviations
quarkradiusR andtheanomalouschromomagneticand
t
from the SM will be most pronounced. Unless these un-
chromoelectric dipole k ,k moments are related to the
V A
certainties are properly included in the formulation of
new physics scale Λ in the “traditional” dimension six
the BSMlimits we cannottrust the analysis. We discuss
extension approach by
thepresentsystematicsandincludethemtoourCLs[27]
projection for the 14 TeV LHC run in the most conser- √6 m2
vativeway. Tokeepouranalysistransparentwefocuson Rt = Λ , kV(A) =ρV(A)Λ2t, (2)
two representative anomalous top-QCD operators that
arecharacteristicforcompositefermionicstructuresfrom where ρ is a (1) parameter.
V(A)
O
a QCD point of view, namely colour charge radius and Tohaveaconsistenttreatmentofthedimensionsixop-
anomalousmagneticmoment[28](seeRef.[29]forsimilar eratorexpansionthe new physicscontributions areman-
work on composite leptons). The generalisationto other ifest only through the interference of these new physics
non-standardtop-related interactions is straightforward. operators’ contribution with the SM amplitude, i.e. we
3
✶ ✶
▲✏✑✒✓✔✕✖ ▲✏✑✒✓✔✕✖
✗❘❂✗❋❂✘✙✙ ✚❘❂✚❋❂✛✜✜
✵☎✝ ✵☎✝
P❚✗❃✒✘✘✙✕✖
❣❣➤✎✎
✞✟✍ ✵☎✆ ✞✟✍ ✵☎✆ ❣❣➤✎✎❣
✴s ✌ ✴s ✌
☛☞ ☛☞
✡ ✡
✠ ✠
✞✟ ✵☎✹ ✞✟ ✵☎✹
s s
qq➤✎✎ ❣q➤✎✎q
✵☎✷ ✵☎✷ qq➤✎✎❣
✵ ✵
✵ ✶✵✵✵ ✷✵✵✵ ✸✵✵✵ ✹✵✵✵ ✵ ✶✵✵✵ ✷✵✵✵ ✸✵✵✵ ✹✵✵✵
♠ ❬(cid:0)✁✂✄ ♠ ❬(cid:0)✁✂✄
tt tt
1
LHC 14 TeV
µ =µ =m
R F T
0.8 P >100GeV
Tj
m
σsu0.6 gg→ttg
/oc
pr
σsub0.4 qq→ttg
gq→ttq
0.2
0
0 500 1000 1500 2000
P [GeV]
Tt
FIG.2: Fractional contribution ofeach partonicchanneltothehadroniccrosssection forσtt¯(left) andσtt¯j (right)production
as a function of thecut on thereconstructed top pair mass mtt¯(top) and thetransverse momentum of thetop pT,t (bottom).
Theborn cross sections are generated for theLHCat √s=14 TeV with thescales set at thereconstructed top pair mass mtt¯
(top) and at the transverse mass mT (bottom).
do not include terms to the hadronic cross section other
than the ones that formally scale as (1/Λ2). Splitting
∆σ s 6k
the amplitude that results from Eqs.O(1) into a SM and (qq¯ tt¯)= R2+ V , (5a)
σ → 3 t 3 β2
B
BSM piece −
∆σ
(gg tt¯)
= + (Λ−2), (3) σ →
SM BSM B
M M M
k (36β 64tanh−1β)
we have for the (partonic) cross section = V − ,
β(59 31β2) 2(33 18β2+β4)tanh−1β
σ ∼|MSM|2+2ℜ{MSMM∗BSM(Λ−2)}+O(Λ−4). (4) − − − (5b)
Theexpansionofthecrosssectionto (1/Λ2)removes where s is the squared partonic center of mass energy
O
the chromoelectric operator from the tt¯sample [21] and and β = 1 4m2/s. Notice that for qq¯ initial states
the sensitivity to kA arises from the less dominant tt¯j both newpphy−sics ctontributions Rt and kV are present,
contribution. The squared BSM matrix elements has a whereasforgg-inducedproduction(themainproduction
dependence on kA [21]. At (1/Λ4), however, when kA mode for inclusive tt¯ production at the LHC) there is
O
becomesresolvable,wecanalsoexpectadditionaldimen- only sensitivity to the anomalous chromomagnetic mo-
sion eight operators to enter the stage via interference ment k . This is due gauge invariance of the dimension
V
with the SM amplitude. In such a case it is not clear six operator, i.e., there is a Ward identity that guaran-
how to interpret a limit obtained on kA. Expanding of teesthecancellationoftheRt dependence2 inthesumof
thecrosssectionto (1/Λ2)willthereforeonlyyieldmild
O
constraints on k .
A
Thedeviations∆σ fromthe SMBorn-levelpartonictt¯
crosssectionsσB sketchedinEq.(4)factorize[20,21,23]: 2Anidentical cancellation isrequiredtoensureamasslessgluonin
4
0.8
µ 5
(1) F (2) µ =5µ0 (3) µ =0.2µ0 (4) µ =0.2µ0 (5) µ =5µ0
0.7 R F R F
1
pb] 0.6 4 2 PTt > 600 GeV
_→tt) [ 0.5 3 µR NLO
p
p 0.4
σ ( LO
0.3
0.2
1 1 1 1 1
µ /µ0 µ /µ0 µ /µ0 µ /µ0 µ /µ0
R,F F R F R
FIG.3: Renormalizationandfactorizationscaledependenciesfortoppairproductionintheboostedtopregime,pT,t >600GeV.
The plot traces the contour in the µF µR plane with µ = (0.2 5)µ0 as shown in the first panel, with µ0 defined as the
event’stransverse mass. The results are−generated with aMC@NL−Ofor theLHC at √s=14 TeV.
Fig. 1. It can be shown that for the tt¯j sample the same and qg initial states. Therefore, to constrain this opera-
conclusionholds, i.e., the gg sub-channelstill has no de- tor it is necessary to suppress the dominant sub-channel
pendence onthe R parameterwhichoriginatesfromthe at the LHC, namely the gg initial state. The boosted
t
qq¯and gq induced subprocesses [23]. high p selection serves two purposes in this sense: it
T
We can enhance the fraction of the qq¯ initial state removesthe lesssensitiveinitialstatesandfocusesonre-
and still probe R at the LHC by requiring boosted top gions where deviations from the SM are large, Eq. (5).4.
t
events.3 This is because energetic events probe the in- Ourimplementationstartsbyincluding the new inter-
coming partons at high momentum fractions where the actions presented in Eqs. (1) through FeynRules [38],
proton’s valence quarks’ parton densities peak. We il- which outputs a Ufo model file [39] that is further
lustrate this in Fig. 2, where we present the fractional used into MadGraph5 [40]. MadGraph performs
contributionof eachpartonic subprocess to the hadronic the event generation that is subsequently showered with
SM tt¯(j) cross section as a function of the reconstructed Pythia6 [41] where we take into account the initial and
tt¯mass and the top transverse momentum pT,t. We can finalstateradiation,hadronizationandunderlyingevent.
invokecutsoneitherobservabletosuppressthegginitial The hardmatrix elements havebeen adapted to only in-
statealthoughpT,t ismoreeffectiveandthemorecrucial clude the interference of the new physics amplitude with
observable in the context of top tagging [32, 33]. the SM counterpart; this way we guarantee a consistent
expansionofthe crosssectionupto (Λ−2)asdiscussed
O
earlier when QCD emission is hard and sensitive to the
BSM effects. We have validated our parton level matrix
DETAILS, ANALYSIS AND RESULTS
element implementation against existing analytic calcu-
lationsaswellasanindependentMonteCarloimplemen-
Inouranalysiswefocustt¯productionwithonetopde-
tation [20, 21, 23].
caying semi-leptonically and the other hadronically. As
Thejetmergingissubsequentlyperformedbyemploy-
this process involves the production of heavy coloured
ing the MLM scheme [42] as implemented in the Mad-
particles and we are selecting the boosted kinematical
Graph package. Throughout the analysis we consider
regime, we can expect an important contribution from
the LHC running at √s = 14 TeV and the SM tt¯cross
initial and final-state jet radiation [34, 35]. To take this
section normalization is re-scaled to the NNLO value,
sufficiently into account we include the BSM-mediated
σ = 918 pb [43]. We find that for our boosted se-
hard radiation effects via jet merging, keeping the full NNLO
lection that the background is completely dominated by
BSMdependence onthe non-standardparametersofthe
respectivesamplesto (Λ−2). Asalreadymentioned,the SM tt¯production. All other background contributions
O are negligible and well below the SM tt¯uncertainty.
dependencies onthe topradiusariseentirelyfromthe qq¯
Weincludethe expecteddominantNLOshapemodifi-
cationsviaaMC@NLO[44]: weconstructare-weighting
function with respect to the R ,k ,k = 0 sample (the
t V A
the extended theory: by closing the top-loop we have a contri-
bution to the gluon two-point function from the two diagrams on
the right hand side of Fig. 1 which do not vanish in dimensional
regularization.
3Asimilarstrategyhasbeendiscussedinthecontextofthecentral- 4Itisworthnoticingthatforboostedfinalstateswedonotneedto
forwardtopasymmetry[32]. worryabouttriggerissues[36,37].
5
0.7 0.2
SMuncertainty SMuncertainty
0.6 SMcentral 0.175 SMcentral
V] Rt=1/TeV 0.15 Rt=1/GeV
Ge 0.5 5]
2
0 0. 0.125
8 0.4 /
/ b
b a 0.1
m[f¯tt 0.3 dy[ℓ 0.075
/
σ/d 0.2 dσ 0.05
d
0.1
0.025
0 0
0.5 1 1.5 2 2.5 3 -3 -2 -1 0 1 2 3
mtt¯[TeV] yℓ
FIG. 4: Central value and uncertainty distributions of mtt¯ and yℓ. We also include an exemplary value of Rt = 1/TeV for
comparisons.
SM) to account for differential QCD corrections in the selected with properties p > 30 GeV and η < 4.
T,j j
| |
BSM histograms. This is a necessary procedure to have We also require an isolated lepton in the final state with
a well-defined limit R ,k ,k 0. Throughout, we p >20 GeV and η <2.5 where the lepton is defined
t V A T,ℓ ℓ
→ | |
choosetherenormalizationandfactorizationscalesasthe isolated if the transverse energy deposit E inside a
T,had
transversemasssincethischoicesyieldaratherflatscale cone around the lepton of size R = 0.2 is less than 20%
dependence of the NLO matched tt¯cross section, Fig. 3. of its transverse energy E .
T,ℓ
Ontheonehand,thesmalltheoreticaluncertaintieson
Instead of proceeding as in a “traditional” semi-
leptonictt¯analysiswetakeadvantageofthe efficienttop the tt¯invariantmass motivates this observable as a suit-
able choice to examine our BSM hypotheses [25]. From
tagging for high p fat jets. This is facilitated by defin-
T
Eq. (5) it becomes clear that dominant BSM corrections
ing a fat jet with a large cone size R = 1.5 using the
Cambridge/Aachen algorithm as implemented in Fast- aredirectlyreflectedinthemtt¯distributions(itisalsothe
jet[45]. We requireatleastoneoftheseobjectsto have variable which typically enters as the only kinematical
parameterintotalcrosssectionandre-summationcalcu-
a transverse momentum larger than p >600 GeV.
T,fatjet
lations, see [25, 43]). On the other hand, the transverse
We choose this exemplary value due to a large top tag-
fat jet momentum and lepton pseudorapidity y deter-
gingefficiency 30%andsmallfakerate 3%. Forthis ℓ
threshold the t∼t¯ cross section is also stil∼l large enough minethett¯+jetskinematicstoalargeextentforboosted
final states. From a boosted top reconstruction point of
(pb) to perform measurements with small statistical
O view, p is the crucial observable as the threshold
uncertainties; the eventual value of pT,fatjet by the ex- T,fatjet
largely determines the working point. Since we choose a
periments willoptimise the systematic uncertainty. This
fat jet is then further processed by the HEPTopTag- specific value for pT,fatjet in our analysis, we turn to mtt¯
ger[33]. InitiallytheHEPTopTaggerwasdesignedto and yℓ in the following.
Missing energy of the final state from the leptonic top
reconstruct only mildly boosted top quarks (p m )
T,t t
≃ decayisnotadrawback: thefinalstateneutrinomomen-
using a very large fat jet cone size. However,in searches
tum can be reconstructed by requiring transverse mo-
for heavy resonances [46] it was shown that due to its
mentumconservationandbyimposingthattheinvariant
flexible reconstruction algorithm and jet grooming pro-
cedures the HEPTopTagger is an effective tool to re- mass ℓ±–neutrino is equal to mW. These conditions de-
finerespectivelytheneutrinotransverseandlongitudinal
constructhighly boostedtopquarkswhile maintaining a
momentum components. To suppress the combinatorics
small backgroundfake rate. Other top taggers,designed
in the tt¯mass reconstruction we need to identify which
to tag highly-boosted top quarks, can be similarly effec-
jet is the most likely to be the b-jet, despite of not using
tive [26, 47]. Top tagging is sensitive to the top’s p
T
b-tagging in this analysis. This can be efficiently done
BSM spectrum modification and modified hard shower
profile that results from including tt¯j at (Λ−2) preci- by identifying the b-jet as the closest jet to the lepton
O with an invariant bottom-lepton mass that satisfies the
sion. Hence, the top tag efficiency itself is a function of
top decay kinematics [48]
the anomalous parameters.
Afterasuccessfultag,thecorrespondingjetisremoved
m < m2 m2 154.6 GeV. (6)
from the event and we proceed by re-clustering the re- bℓ q t − W ≃
maining hadronic activity as usual, i.e. by applying the After these steps we end up with distributions as de-
Cambridge/Aachen algorithm with R = 0.5. Jets are picted in Fig. 4; the BSM-induced shape modification
6
±2σ ±2σ
±1σ ±1σ
exp. 95%CL exp. 95%CL
0.1 0.1
Ls 95%exclusion Ls 95%exclusion
C C
☛ ✟ ☛ ✟
0.01 Rt=0.25/TeV 0.01 kV =0.05
kV,kA=0 Rt,kA=0
✡ ✠ ✡ ✠
50 100 150 200 250 300 50 100 150 200 250 300
luminosityL[fb] luminosityL[1/fb]
(a) (b)
FIG.5: ConfidencelevelcontoursfortheoperatorEq.(1)inaboostedanalysisofpp tt¯+jetsfor14TeVcollisionsasdescribed
→
inthetext. WepickvaluesofRt,kV thatcanbeconstrainedatluminositiesofaround100/fbclosetothesystematics’threshold.
includes a lot of information that we would like to ex- of [36]. We map the integrated mtt¯uncertainty to a flat
ploit in a binned hypothesis test based on sampling the y uncertainty;forcentraltopsattransversemomentaof
ℓ
log-likelihood the orderof600GeVthis isareasonableapproximation.
Itbecomes immediately clearthatthe shape uncertainty
= 2 npseudolog 1+ nBiSM const (7) will be the limiting factor of this analysis, especially if
Q − i (cid:18) nSM (cid:19) − we want push limits R ,k ,k 0.
i∈Xbins i t V A →
The standard way of including such an uncertainty
withMonteCarlopseudo-data npseudo ,giventheinput is via nuisance parameters of the null hypothesis (SM
{ i }
of the (B)SM histograms n(B)SM [27, 49]. tt¯+jets productionin our case)[27, 49, 50]. When com-
There is a caveat. Th{eiuncer}tainties, especially in puting the confidence level, these nuisance parameters
the mtt¯ tails of the distributions can be large, and are are marginalized or profiled. However, it can happen
currently driven by experimental systematics [36] rather that the process of marginalization can stealth the sys-
than theoretical limitations (for a recent high precision tematic uncertainty entirely. By, e.g., including a shape
calculationsee[25]). Togetafeelingofthesizeofthesys- uncertainty to only the null hypothesis and not to the
tematics we include the relative systematic uncertainty alternativehypothesis,marginalizationwillshiftthe me-
from [36] for √s = 7 TeV to Fig. 4; the theoretical un- dianofthetoy-sampledlog-likelihooddistributionforthe
certaintyof[25]isnegligiblecomparedtothesystematics nullhypothesisawayfromthealternativehypothesis’me-
dian. Theexclusioninthiscaseappearstobelargerthan
itshouldbe,especiallywhentheuncertaintybandsover-
±2σ lap with the difference of null- and alternative hypoth-
±1σ esis. To avoid issues of this type we include only bins
expected 95%CL
which exceed the SM uncertainty to the log-likelihood;
0.1
i.e. our null hypothesis is the one sigma upwards fluctu-
ated SM hypothesis. This way we reflect the systematic
Ls 95%exclusion
C uncertainty in an extremely conservative way; profiling
or marginalization will correctly reduce the uncertainty
☛ ✟
0.01 Rt=1/TeV when correlations with other signal regions (e.g. total
✡kV,kA=0 ✠ crosssectionsandsubsidiarytopmeasurementsusingthe
ABCD method) aretakeninto account. This is informa-
tion which requires access to the LHC data samples is
50 100 150 200 250 300
not available to us and also somewhat beyond the scope
luminosityL[fb]
ofthis work. We remind the readerto keepin mind that
theoutlinedanalysiswhenperformedbytheexperiments
FIG. 6: Confidence level contours for the operator Eq. (1a)
in a boosted analysis of pp tt¯+jets for 14 TeV collisions is likely to yield improved constraints eventually.
→
as described in the text for a value of Rt = 1/TeV based From Eq. (7) it is clear that the binned log-likelihood
on yℓ. Choosing mtt¯ as discriminant results in a factor ∼ 4 approach will pick up sensitivity from regions in the
improvement of the limit setting, Fig. 5. single-valued discriminant where nBSM/nSM is large but
i i
7
0.06
evenwhenthe systematicuncertainty is larger. Working
in a consistent expansion to Λ−2, we can only obtain
0.05 ∼
unrealistically large values on k 1 that feed into our
A
≫
0.04 results through higher jet multiplicities exclusively.5
V 0.03 expected95%CL
k
CONCLUSIONS AND OUTLOOK
0.02
0.01 After the discoveryofa Higgsbosonthatseems to fol-
low the SM-paradigm and the lack of any hints towards
0 natural physics completions at the TeV scale prompts
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
us study the heavy degrees of freedom of the SM more
Rt [1/TeV]
carefully. Topquarkphysics,typically consideredanim-
pediment for new physics searches by providing a major
FIG. 7: Confidence level contour for operator Eq. (1) in a
boosted analysis of pp tt¯+jets for 14 TeV collisions as a background contribution, is a well-motivated candidate
→
function of Rt,kV,kA=0. forsuchanalyses. Ontheonehand,thepropertiesofthe
topquarkarestilllargelyunknown,evenafteritwasdis-
coverednearly twentyyearsago. On the other hand, the
still resolvable according to our definition. Hence, the abundantproductionoftoppairsattheLHCallowsusto
sensitivity is dominated by the p threshold behavior of tightly constrain smallest resolvable deviations from the
T
the tt¯sample and jet radiation. There the uncertainty SM-predictedcouplingpatternthatisexpectedtobeob-
is comparably low 20% and the absolute cross sec- servedifthetopquarkarises(partially)asaboundstate
tion modification la∼rge (keep in mind that the tails of of a strongly interacting sector. This option is widely
the parton-level distribution grow according to Eq. (5), discussed in the literature and investigating anomalous
whichdoesnotincludethepdfsuppression,whichquickly QCD interactions in the top sector provides a path to
limits the considered analysis statistically). either observe our strongly constrain such a scenario.
Resolving a potential composite structure with large
We show the expected 95% exclusion as a function of
momentum transfers in the top sector naturally moti-
the integrated luminosity in Fig. 5 for three differ-
L vates boosted top analyses as highly sensitive channels.
ent samples that can be excluded with a data sample of
Reconstruction techniques are under good theoretical
100/fbata14TeVLHC.Thewidthofthe1and2sigma
controlandhavesuccessfullybeenappliedintt¯resonance
bands being rather largeindicates that we arevery close
searches [36]. Such resonances are expected in strongly
to the border of the discriminable parameter region (in
interacting theories, too, but typical composite interac-
terms of our definition laid out in the previous section).
tions can be expected to predominantly manifest them-
Indeed, for smaller individual values R ,k we cannot
t V selves in a large deviation of the tt¯spectrum’s tail and
formulateconstraintsas the BSM distributionis entirely
experimentalandtheoreticaluncertaintiesbecomemajor
covered by the SM uncertainty band. We therefore con-
limitations of such searches.
clude thatanimprovementbeyondthe shownparameter
choices depends crucially on the reduction of the experi- Inthispaperwehavecomputedtheexpected95%con-
fidence level constraints on a set of non-SM effective top
mental systematics (which should be well-possible when
QCD interactions resulting from an exemplary boosted
larger data samples are available). As expected the ex-
pectedconstraintsfromusingmtt¯asasinglediscriminant top analyses and a representative set of operators. We
haveincludedthedominantfirsthardgluonradiationef-
are superior to integrated sensitivity observables such as
fects in a matched approach. Systematic differential un-
y , Fig. 6.
ℓ
certainties are taken into account in the most conserva-
Comparing to the preliminary investigations of
tive way,andarebasedoncurrent7 TeVmeasurements.
Ref. [23], we find that applying statistical algorithms as
We therefore expect our constraints to be on the con-
applied by the experiments and realistic simulation and
servative end and believe that the actual analysis when
analysis approaches, we find constraints in roughly the
performedbytheexperimentscanindeedimproveonour
same parameter region: R . 0.25/TeV and k . 0.05
t V results.
at 95% CL. And extrapolation into the (R ,k ,k = 0)
t V A
Our hadron-level analysis correctly captures the top
plane is shown in Fig. 7. Since we include a differen-
tial shape information of the top spectrum and a lower
p threshold that guarantees a quick saturation of the
T
statistical uncertainty at comparably small luminosities
5Goingbeyond the∼Λ−2 approximationwillbeunavoidable ifan
we obtain more stringentexpected constraintsthan sim-
excess inthe tailwillbeobserved withthe describedlimit-setting
ple correlationsofinclusiveandexclusivemeasurements, analysisthatimplementsapractitioners’approach.
8
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