Table Of ContentIPMU14-0012
Dark decay of the top quark
Kyoungchul Kong,1 Hye-Sung Lee,2,3 and Myeonghun Park4
1Department of Physics and Astronomy, University of Kansas, Lawrence, Kansas 66045, USA
2Department of Physics, College of William and Mary, Williamsburg, Virginia 23187, USA
3Theory Center, Jefferson Lab, Newport News, Virginia 23606, USA
4Kavli IPMU (WPI), The University of Tokyo, Kashiwa, 277-8583, Japan
(Dated: January,2014)
We suggest top quark decays as a venueto search for light dark force carriers. The top quark is
the heaviest particle in the standard model whose decays are relatively poorly measured, allowing
sufficientroomforexoticdecaymodesfromnewphysics. Averylight(GeVscale)darkgaugeboson
(Z′)isarecentlyhighlightedhypotheticalparticlethatcanaddresssomeastrophysicalanomaliesas
wellasthe3.6σ deviationinthemuong−2measurement. Wepresentandstudyapossiblescenario
4 thattopquarkdecaysast→bW+Z′s. Thisisthesameasthedominanttopquarkdecay(t→bW)
1 accompaniedbyoneormultipledarkforce carriers. TheZ′ canbeeasily boosted,anditcandecay
0
into highly collimated leptons (lepton-jet) with large branching ratio. We discuss the implications
2
for theLarge Hadron Collider experimentsincluding theanalysis based on the lepton-jets.
r
p
A
I. INTRODUCTION b
5
b
With a recent discovery of a new scalar particle [1, 2], t W+
] which is consistent with the standardmodel (SM) Higgs
h t
boson, the understanding of the SM is near completion
p
- except for precision studies. With this, the interest to-
p ward new physics beyond the SM soars. One definite W+ Z′
e
evidence of new physics is the existence of dark sectors
h (a) (b)
[ such as dark energy and dark matter [3].
Dark force was introduced as a newcomer to dark sec-
3
v tor [4]. It is a hypothetical interaction among the dark FIG. 1: (a) Dominant top quark decay mode (t→bW). (b)
0 mattersthatcanaddressvariousastrophysicalanomalies Thetop quarkdecay into dark force carriers (t→bW +Z′s)
2 such as positron excess. Positron excess has been ob- is the same to the dominant top quark plus one or multiple
0 served at numerous experiments including PAMELA [5] Z′s. A very light Z′ can be easily boosted and, it can decay
5 andAMS[6]. Averylight(roughly,GeVscale)darkforce into highly collimated jets or leptons (lepton-jet).
. carrier (which we call Z′) is supposed to couple to dark
1
0 matter strongly, but extremely weakly to the SM parti-
4 cles. It is expected to be light because such a light force cays. We show thatthe topquarkdecays into darkforce
1 carrier can provide the the required enhancement (via carriers are possible and it can be searched for at the
: the so-calledSommerfeldeffect)ofthe presenttime dark Large Hadron Collider (LHC) with excellent discovery
v
i matter annihilation at the Galactic center while satisfy- potential.
X
ingthedarkmatterrelicdensityconstraints[4]. Through
r asimplekinematics,itcanalsonaturallyexplainwhyan-
a tiproton excess has not been observed. In addition, such II. TOP TO Z′ PRODUCTION
a gauge boson with small mass and very weak coupling
can address the 3.6σ deviation in the muon anomalous Thetopquarkistheheaviestelementaryparticleinthe
magneticmoment[3]throughaone-loopcorrectionofZ′ SM, quite possibly heavier than new particles in many
[7, 8]. (For more motivations and details about the light models beyond the SM. (For a short review about the
dark force carriers,see Ref. [9].) topquark,seeareviewarticleinRef.[3].) Becauseofits
With such appealing motivations, there are active largemass,itslifetime(τ 0.5 10−24sec)isveryshort.
t
searchesforlightdarkforcecarriers. Adarkforcecarrier Since it is shorter than th≈e QC×D scale (Λ 10−23
QCD
is roughly of GeV scale, and can be searchedfor both at sec),topquarkdecaysbeforeforminganyhadron∼s,unlike
the low energy and high energy experiments. The major otherquarks[15]. Forthisreason,topquarkdecayshave
searchschemesarebasedonbremsstrahlungatfixedtar- been considered as an ideal probe of new physics even
getexperimentsormesondecays[10]. Collidersignatures before its discovery at Tevatron in 1995 [16, 17].
for certain supersymmetric models [11] and the decay of Although top quark mass is precisely measured(m =
t
the Higgs bosons into the Z′ [12–14] have been studied 173.1 GeV with 0.5% level uncertainty), its decay width
as well. is not [3]:
In this paper, we present a novel channel to produce
and searchfor the dark force carrier using top quark de- Γ =2.0 0.5 GeV. (1)
t
±
2
WhileitisinareasonableagreementwiththeSMpredic- astrophysical anomalies, we need some extended Higgs
tion (ΓSM 1.3 GeV with theoretical error better than sectortogiveamasstotheZ′. (Wedonotconsiderother
t ≃
1% [3]), quite a large uncertainty (25%) indicates a lack possiblewaysto provideamasssuchastheStueckelberg
of precise knowledge about top quark properties. While mechanism [18].)
the exact values are process dependent, typical experi- Z′ is typically taken as a gauge boson of a new gauge
mental errorsrelated to top quark decays are of (10%) symmetry, dark U(1), under which the SM particles do
O
[3],leavingplenty roomfornew decaymodes originating not have charges. Although Z′ does not couple to the
fromnew physics beyondthe SM. (Later,in ourillustra- SM particles directly, it can couple through the mixing
tion, we will take the top quark decay branching ratio oftheZ′ withtheSMgaugebosonsviathegaugekinetic
intolightZ′snotmorethan0.1% 1%althoughitcould mixing parametrized by ε [19]
−
be much greater in principle.) With these observations,
1 1 ε 1
we view the top quark decay as an ideal window to look = B Bµν + B Z′µν Z′ Z′µν.
Lgauge −4 µν 2cosθ µν − 4 µν
for a dark force carrier. W
(2)
In the SM, nearly 100% of top quark decay is the on-
The exact coupling, however, depends on the details of
shell t bW decay. Possible scenarios to search for Z′
→ model, especially on how the Z′ gets a mass. For exam-
in connection to the top quark decay include
ple, it depends on whether the extra Higgs is a SU(2)
(i) t bH+ bW +Z′ L
(t→hrough H→±W∓Z′ coupling), singlet or doublet [12].
DependingontheHiggssector,theZ′maycoupleboth
(ii) t bH+ bW +h bW +Z′Z′
(w→ith a lig→ht non-SM→Higgs boson h), to the electromagnetic current (Jem) and the weak neu-
tralcurrent(J ). The interactionLagrangianofthe Z′
(iii) t bW∗ bW +Z′ NC
(th→rough Z→′WW coupling), with the SM fermions is given by
(iv) t bW∗ bW +h bW +Z′Z′ = (εeJµ +ε g Jµ )Z′ (3)
→ → → LdarkZ − em Z Z NC µ
(through hWW coupling). = f¯ g γµ g γµγ5 fZ′ (4)
There can be also Z′ radiation off from top not being a V − A µ
decay product. For a relatively heavy Z′, mZ′ &1 GeV, with (cid:0) (cid:1)
the radiation cross sections are negligibly small though.
1
While the off-shell processes are worth investigating as gV = εeQf εZgZ T3f Qfsin2θW , (5)
− − 2 −
they may prevail in different situations (for example, (cid:18) (cid:19)
when a charged Higgs is absent), we will focus on the 1
g = ε g T , (6)
A Z Z 3f
on-shell decays in this paper. − 2
(cid:18) (cid:19)
Theremay be alsootherwaysthe t candecayinto Z′s
whereQ andT arethe electricchargeandisospin,re-
without producing bW such as t qZ′ (with q = u,c) f 3f
→ spectively. Boundsonthe couplingsofthe Z′ come from
through the W loop. Nevertheless, it is interesting to
various experiments such as the lepton anomalous mag-
observe that there are abundant ways the t can decay
neticmoment,atomicparityviolation,polarizedelectron
into Z′s with bW, the decay products of the dominant
scattering,mesondecays,fixedtargetexperiments,beam
top quark decay. (See Fig. 1.)
dumpexperiments,andHiggsdecays. The exactbounds
Throughoutthis paper,wewillassumemW .mH± . depend on the mZ′ and its decay branching ratio, but
mt, and study the on-shell decays (i) and (ii). Whether typically, it is set as ε . 10−2 and δ . 10−2 (with
(i) or (ii) dominates depends on the masses of the Higgs ε δ mZ′) [12, 20]. | | | |
bosons, especially whether the non-SM Higgs h is light Z ≡ mZ
ForourinterestedZ′ofroughly (GeV),theBR(Z′
enoughsothat the chargedHiggs candecayinto it dom- ℓ+ℓ−) for ℓ = e, µ is expectedOto be large, typical→ly
inantly or not.
0.2 1 depending on mZ′ and other details. Such a
light∼Z′ gauge boson shows many distinguishable prop-
erties from heavy (electroweak or TeV scale) Z′ gauge
III. INGREDIENTS OF DARK FORCE MODELS
bosons in various contexts [21]. (Also see Refs. [22, 23]
for some recent studies on invisible or partly invisible
A. Dark force carrier heavy Z′ gauge bosons.)
Because the Z′ can be easily boosted in the top decay
While the final particles in the aforementioned modes processes we consider, it is expected to appear as highly
arethesameuptothenumberofZ′s,someofthemodes collimated leptons or jets. Depending on its mass and
are model dependent, and it is worth describing some coupling, it could be more identifiable as a lepton-jet or
aspects of the models. a simple pair of isolated leptons. (See the Appendix for
The minimum ingredients of extra particles to extend some detailed discussions.) A lepton-jet is a final state
the SM to the dark sector are, besides the dark matter consisting of collimated electrons or muons. Measuring
itself, theZ′ (darkforcecarrier)andanadditionalHiggs properties of lepton-jets have been studied and experi-
to givea mass to the Z′. As the Z′ should be massivein mental searchesatthe LHC experiments already started
orderto decayinto the leptons so thatit canexplainthe [24, 25].
3
B. New Higgs bosons In both scenarios (i) and (ii), for most of the parame-
ter space, a dominant decay of the charged Higgs is into
ThedarkforcecanbecategorizedintohowtheZ′ gets Z′s. The dominance of the H± decay into the Z′ par-
ticles in both scenarios originates from the enhancement
a mass. We will consider the dark Z model based on
the type-I two Higgs doublet model (2HDM) [12], with of couplings for boosted gauge bosons, formally known
as Goldstone boson equivalence theorem. Detailed dis-
notations taken from Ref. [14], for scenarios (i) and (ii).
In this kind of dark force model, tanβ v /v & 1 is cussionsandillustrationsaregivenintheaforementioned
2 1
≡ references [14, 28, 29]. We will use a parameter for the
required, where Φ couples to the SM fermions and Φ
2 1
does not. (For a heavy Z′ model in 2HDM frames, for charged Higgs to Z′s decay branching ratio
example, see Ref. [26].)
A new neutral Higgs boson that can mix with the SM Y BR(H± W +Z′s), (10)
≡ →
Higgs doublet is generically expected, and if an extra
Higgs is a doublet, there are charged Higgs bosons too. which corresponds to Y = BR(H± WZ′) with one
TheHiggspropertiesofsuchscenarioshavebeenstudied Z′ [for scenario (i)], and Y = BR(H±→ Wh)BR(h
inmanyliteratures[12,14,27]. AnewneutralHiggscan Z′Z′) with two Z′s [for scenario (ii)]. I→n a large area→of
be very light and it can dominantly decay as h Z′Z′. the parameter space, Y 1 is obtained. In our analysis,
A charged Higgs can be also much lighter than→typical insteadofusinganexact≃valuewhichdependsonvarious
experimental bounds as its dominant decay may be into model parameters, we will take a range of Y = 0.5 1
rather elusive light Z′s [14]. (the branching ratio of 50% or greater). −
For the mH± . mt, the major decay modes of H+
in the typical 2HDM are into ντ+ and cs¯. Their decay
widths are
IV. PRODUCTION AND DECAYS OF TOP
Γ(H+ ντ+) mH± m2τ , (7) QUARK AT THE LHC
→ ≃ 8πv2 tan2β
A. Top pair production
andsimilarlyforcs¯withacolorfactor. Despitethecolor
factor, because of the small mass of charm quark (c) at
the electroweak scale, the cs¯ mode is subdominant to TopquarkscanbeproducedinpairbydominantQCD
the τν mode. With a recently discovered 125 GeV SM- process (qq¯′, gg) or singly by electroweak process with a
like Higgs (H ), the off-shell decay H± W∗H W bosonattheTevatronandtheLHC.Atthe LHC,the
SM SM
ff¯′H canbealsoquitesizable,evenlarg→erthanH+ → tt¯canbeproducedabundantlyviadominantgluon-gluon
SM
ντ+ for certain parameter space. → fusion. Thegluonfusionmakesup90%ofthetotaltt¯for
The scenario (i) is based on the assumption that the center-of-mass energy √s = 14 TeV (about 80% for
the SM-like Higgs is the lighter Higgs doublet. The √s=7 TeV).
H±W∓Z′ couplingisverysmall,butitsdecaybranching The total tt¯pair production cross section at the LHC
ratiocouldbesizable[28,29]. Thetree-leveldecaywidth (at next-to-next-to-leading order QCD corrections) is
is given by predicted to be σtt¯ ≃ 167 pb (for 7 TeV), 239 pb (for
8 TeV), and 933 pb (for 14 TeV) [30]. Currently, at the
m3 m2 3 LHC,integratedluminosity(L)isabout5fb−1for7TeV,
Γ(H± →WZ′)≃ 16πHv±2 (sinβcosβd)2 1− m2W and about 20 fb−1 for 8 TeV [31]. The 14 TeV LHC is
(cid:18) H±(cid:19)
(8) scheduled to operate soon, and is expected to reach the
where β is a parameterrelated to the dark sector Higgs luminosity of several hundreds of fb−1.
d
singlet, introduced in Ref. [12].
Scenario (ii) is based on the assumption that there is
a light Higgs h that a chargedHiggs can decay into. For
B. Top decay into dark gauge bosons through H±
definiteness,letustaketheHiggsmixingangleα π/2
≃±
limit, which is a decoupling limits of doublets where a
heavier Higgs doublet is the SM-like Higgs (125 GeV) A top quark can decay into a charged Higgs through
and a lighter one is the other doublet. The decay width t bH+ for a relatively light H±. While there are
→
[14] is searchesforlightchargedHiggsint bH+ bντ+ and
t bH+ bcs¯ based on typical→2HDMs,→the results
sin2β 1 ar→e negativ→e [32]. These searches, however, would have
Γ(H± Wh) λ3/2(m2 ,m2 ,m2) (9)
→ ≃ 16πv2m3 H± W h missed the light charged Higgs of t bH+ bW +
H± Z′s that would dominate in our scena→rio. As d→escribed
with λ(x,y,z) x2 + y2 + z2 2xy 2yz 2zx. In earlier,the H± candecayinto the Z′s dominantlyinthe
this limit, we al≡so get BR(h Z−′Z′) −1 as −h does not presence of the dark force.
→ ≃
couple to the SM fermions. Neglecting m /m and higher order corrections, the
b t
4
0.12 the LHC to produce Z′ is given by
0.10 σ(pp bW¯bW +Z′s) σtt¯2X (15)
→ ≃
0.08 using BR(t bW) 1 and a new parameter X for the
+LbH tanΒ=2 top to Z′ de→cay bran≃ching ratio
® 0.06
HRt X BR(t bW +Z′s), (16)
B 0.04 ≡ →
whose detail depends on the specific scenario.
0.02 5 In scenarios(i) and(ii), using the on-shell H± decays,
10 we have
0.00 20
80 100 120 140 160
X =BR(t bH+)Y (17)
mH±@GeVD →
with BR(t bH+) given in Fig. 2. In the numerical
→
analysis of this paper, we consider only the scenario (i).
FIG. 2: BR(t → bH+) for tanβ = 2 (black), 5 (blue), 10
(red), 20 (green). The t decay into H+ is larger for smaller [The application for the scenario (ii) would be straight-
forward.] This process is
mH± and smaller tanβ.
top pair: pp tt¯ bW¯bH± bW¯bW +Z′, (18)
• → → →
relevant top decay widths are
which is similar to the dominant tt¯process except that
√2G V 2 m2 2 2m2 Z′ is accompanied in the decay products. We consider
Γt→bW = 1F6π| tb| m3t 1− mW2 1+ m2W , only mW . mH± . mt to avoid additional constraints
(cid:18) t (cid:19) (cid:18) t (cid:19) from W bH± decays, etc.
(11) Figure→3 shows the productioncross sections of the Z′
Γt→bH+ = √2G1F6π|Vtb|2m3t 1− mm2H2± 2 tan12β (12) watitthhem(Ha±) 8inTtehVeLtt¯HcChaannndel(b()pp14→Tett¯V→LHbCW,¯buWsin+g Zth′e)
(cid:18) t (cid:19) highordercalculationofσ(pp tt¯). The bandindicates
withtanβ &1inthedarkforcemodelweconsider. (The Y =BR(H± WZ′)=0.5 →1 range.
→ −
t bW decay itself shows the enhancement from the We will take a rather conservative value of X =0.001
→
Goldstone boson equivalence theorem with a boosted W and assume BR(Z′ ℓ+ℓ−) = 0.2, for our illustration,
→
boson[33].) Asbothdecayshavethesamedependenceon meaning0.02%oftopquarkdecayisintotheleptonpairs.
theCabibbo-Kobayashi-Maskawa(CKM)matrixelement [Only the product XBR(Z′ ℓ+ℓ−) has the realmean-
Vtb 2, even quite sizable Γ(t bH+) may not alter an ing for the final lepton pair p→roduction rate.]
| | →
effective value of Vtb significantly when it is measured The value X = 0.001 can be obtained, for example,
from the top quark decays. for mH± = 100 GeV (with tanβ ≃ 20, Y ≃ 0.8),
topIndoecuarystaunddy,cownesidsteirlltt→akebHt →+ absWtheasimthpeordtaonmtinsuanbt- mmHH±± ==161040GeGVeV(w(itwhitthantaβn≃β5≃, Y1≃0,1Y). ≃ 0.9), and
dominant one. Then the branching ratio of the on-shell We use a rather intuitive parameter X for our presen-
t bH+ decay, which is dependent on unknown mH± tation instead of model-specific parameters. The exact
→
and tanβ, is value of Y, for example, can be more constrained for a
BR(t bH+) Γt→bH+ (13) srpameceifitecrsmsHu±ch, taasnBβR, (mZZ′′. Tℓh+eℓr−e)araendmaonthyeurndkanrokwsnecptoar-
→ ≃ Γt→bW +Γt→bH+ related parameters anyw→ay, and our treatment using X
m2t −m2H± 2 1/tan2β , (14) (with a rather conservative values) allows us more con-
≈ m2 m2 1+2m2 /m2 trollable analysis.
(cid:18) t − W (cid:19) W t
which is plotted in Fig. 2. We can see that a few %
level of the top decay can be easily accommodated for VI. COMPARISON TO THE CHARGED HIGGS
mH± <mt. For mH± =140 GeV, for instance, we have PAIR PRODUCTION
BR(t bH+) 0.03 0.0003, with the tanβ = 2 20
→ ≃ − −
range (higher BR corresponds to lower tanβ).
The chargedHiggsbosoncanbe typicallyproducedin
the Drell-Yan process. Charged Higgs pair production
throughDrell-Yan(γ∗, Z∗) is model independent except
V. SETUP FOR NUMERICAL ANLAYSIS
for the mass.
The Drell-Yan productionof H± pair,for scenario(i),
We will consider the tt¯production followed by one of
is
the top quark pair decaying into Z′s. We will also con-
sider only the Z′ ℓ+ℓ− channel. The cross section at Drell-Yan: pp H+H− WW +Z′Z′. (19)
→ • → →
5
100 8 TeV LHC with 20 fb-1
LHC 8TeV 140
@Dpb 10 tanΒ=2 V signal
n e120
Z'productioncrosssectio 00.0.111 tttaaDannnrΒΒeΒ==l=l-12500YanHH+H-L er of events / 0.3 G146800000 background
b
0.001 m
80 100 120 140 160 u20
n
mH±@GeVD 0
(a) 0.5 1 1.5 2 2.5 3 3.5 4 4.5
m [GeV]
LJ
100 (a)
tanΒ=2
LHC 14TeV
Db 14 TeV LHC with 10 fb-1
@p 10 tanΒ=5
n 140
o
cti tanΒ=10 V signal
se 1 e120
ductioncross 0.1 taDnrΒe=ll-20YanHH+H-L nts / 0.3 G18000 background
pro 0.01 ve
Z' of e60
0.001 r 40
80 100 120 140 160 e
b
mH±@GeVD um20
(b) n
0
0.5 1 1.5 2 2.5 3 3.5 4 4.5
m [GeV]
LJ
FIG.3: Production cross sections oftheZ′ with mH± in the (b)
tt¯channel(pp→tt¯→bW¯bW+Z′)atthe(a)8TeVLHCand
(b)14TeVLHC.Crosssectionatthe14TeVisabout4times
largerthanthatatthe8TeV.InthemW .mH± .mtrange, FIG.4: Distributionsoflepton-jet mass (m ) in thett¯+LJ
LJ
theresultsfortanβ =2(black),5(blue),10(red),20(green) mode at the LHC for (a) 8 TeV LHC with L = 20 fb−1
areshown. Drell-Yanchannel(pp→H+H− →WW+Z′Z′) and (b) 14 TeV LHC with L = 10 fb−1. mH± = 140 GeV,
(BDRa(sHhe±d)→isWalZso′)s=ho0w.5n−fo1r rcaonmgpe.arison. The band indicates mZ′ =2GeV with X =0.001 and BR(Z′ →ℓ+ℓ−)=0.2 are
used.
VII. DISCOVERY POTENTIAL AT THE LHC
In Fig. 3, we can see the difference of the production
crosssectionsofthe Z′ throughthett¯channelandDrell-
Yan channel. In both cases, the cross section decreases
We discuss the discovery potential of the Z′ from
with mH± because of the phase space. We use the on- the tt¯process at the LHC. For definiteness, we assume
shell decays only using branching ratio of Fig. 2.
BR(Z′ ℓ+ℓ−) = 0.2. For the background events, we
takeonl→ytheirreducibleprocessestt¯+ℓ+ℓ− fromtheoff-
The Drell-Yan and the tt¯ processes have a few dif- shell photon and Z boson, although there may be more
ferences. First, the tt¯production cross section is much sources of backgrounds such as tt¯ + jets with the jets
larger than the Drell-Yan case, except for the very large faking leptons. In this section, we require two b-tagged
tanβ (tanβ & 20) or large mH±. Second, tt¯produces jetsto limitbackgroundstott¯events. TheAppendix de-
only one charged Higgs while the Drell-Yan produces a scribes more details of our Monte Carlo study including
pair of charged Higgs. Third, tagging is different (bW the tagging efficiencies. The efficiency depends on mH±
pair for tt¯, W pair for Drell-Yan). With different tag- and mZ′ as well as the LHC energy. We assume a K-
gingandasmallproductioncrosssection,weneglectthe factor for the background events K 2 and apply it
bkg
≃
Drell-Yan process in our study. to our background events generated by tree-level Monte
6
mZ′ mH± mZ′ mH±
[GeV] 100 GeV 140 GeV 160 GeV BKG [GeV] 100 GeV 140 GeV 160 GeV
1 40.0 86.2 58.1 69.6 1 7.8fb−1 1.9fb−1 3.4fb−1
2 8.2 59.9 47.8 5.0 2 14.5fb−1 0.7fb−1 1.0fb−1
5 0.1 5.0 9.1 0.3 5 - 7.3fb−1 3.5fb−1
TABLE I: Expected number of events in each lepton-jet bin TABLE II: Required luminosity for 14 TeV LHC to see the
(20% window of the Z′ mass) with two b-tagging in 8 TeV likelihood ratioS =5(correspondingto5σ discovery). Ba-
cL
LHC 20 fb−1. We set X = 0.001 and BR(Z′ → ℓ+ℓ−) = sically thesame method as Table I is used.
0.2. Signaleventswereobtainedwithhighorderσtt¯withthe
branching ratio, and the background events were obtained
with tree-level simulation with Kbkg =2. Thus, re-analysis of existing 8 TeV data with tt¯ +
lepton-jet can potentially bring a discovery of the light
Z′.
Carlo simulation.1
witFhirisntt,ewgeractoendsliudmerinthoesi√tyso=fa8bToueVtLca=se2(0σftbt¯−∼1.2T39abplbe)I, theForreqtuhiere√dslum=in1o4siTtyeVforcaSsceL(=σt5t¯ (∼co9r3re3sppobn)d,iwngetsoho5wσ
discovery) in TableII. Basically the same method as the
showsthenumberofsignaleventsandbackgroundevents
8 TeV case (Table I) is used. It shows the dark force
for various choices of mH± and mZ′, with X = 0.001 searchatthe veryearlystageof the 14TeV LHC will be
and BR(Z′ ℓ+ℓ−) = 0.2. The numbers are for each
→ a very interesting program. Both Table I and Table II,
lepton-jet bin (20% window of a given mZ′) with two for given X and BR(Z′ ℓ+ℓ−), can be obtained from
b-tagging. (See the Appendix for details including the →
Table III in the Appendix up to the precision.
tagging efficiencies for signal and backgroundevents.)
Figure 4 shows the signals and backgrounds for the
anFdomrZa′s=pe2ciGfiecVe.xaWmepelxep,ewcettchoennsiudmerbemrHof±si=gna1l4e0vGenetVs aXbo=ve 0sa.0m01p)lewpiothintB(Rm(ZH±′ = 1ℓ4+0ℓ−G)eV=, m0.2Z.′ =Fo2r GcuetVs,,
(after the tagging efficiency), for L=20fb−1, →
we require the CMS-like analysis cuts[Sec. A2] with
Nsig =σtt¯2XBR(Z′ →ℓ+ℓ−)ǫsigL≈60, (20) t0w.2oGb-etVag.gFedorjebtasckagnrdouconndsst,rtuhcet lleeapdtoinng-jeotrsdewritchromssLsJec>-
and the SM background events tionis3.73pbat8TeVand15.33pbat14TeVLHCwith
partonlevelcuts for the rapidity ofquarkandleptons as
N =σ ǫ L 5, (21)
bkg bkg bkg ≈ ηq < 5, ηℓ < 3 and a dilepton invariant mass cut for
| | | |
which would give a very large number of signal events thesameflavor,anopposite-signleptonpairgreaterthan
compared to the backgrounds (resulting the likelihood 0.2GeV. Corresponding efficiencies are about 1.4% for
ratio ScL 14.6). The likelihood ratio, which is defined both collision energies. We take Kbkg = 2 for the K-
as ≃ factor of the background. We can see that the signal
shows up as a clear spike over the SM background.
S = 2N log(1+N /N ) 2N (22) The t bW +Z′ decay (via H±) can be compared
cL obs sig bkg sig
− →
to the dominant top decay mode t bW. The top
q
with Nobs = Nsig +Nbkg, is a good method even when decay into the charged Higgs might lo→ok similar to the
there are relatively small backgroundevents. dominant top decay accompanied by a Z′ that can de-
Even this kind of large signal can be still missed in cay into a pair of collimated leptons or others that are
conventionalanalysis. Forexample,inthe CMStt¯dilep- hard to identify. It has important implication as the
tonanalysis(see the Appendix) with 5.3fb−1 luminosity current experimental measurements might have counted
at 8TeV LHC [34], signals can be lost by invariantmass the t bW +Z′ as t bW depending on the analysis
requirements for the lepton pair (mℓℓ > 20 GeV). The metho→ds. Z′ mayalsoh→avesizabledecaybranchingratio
contributionofsignalsto dileptons inthe tt¯channelsare into neutrinos or invisible particles. As mentioned ear-
verysmallwithCMSanalysiscuts(oneb-taggedjet). For lier, since both decays have the same dependence on the
the above sample point, we estimate the expected num- CKM matrix element V 2, [Eqs. (11) and (12)], even
tb
berofsignal,Nsig 4(ǫsig 0.71%)canbeburiedunder quite sizable Γ(t bH| +)| may not alter the effective
the uncertainties o≃f tt¯dilep≃ton events (Expected uncer- value of V signifi→cantly when it is measured from the
tb
taintyintt¯dileptonsamples,∆Nbkg 591withobserved top quark decays.
data N 1.7 104 ), resulting in≃only S 0.03.
bkg cL
≃ × ≃
VIII. SUMMARY
1 TheassumedKbkg≃2canbecomparedtoKfactorsforsignals We discussed the production of light Z′ gauge boson
Ksig = 1.74 (1.84) for 8TeV(14TeV) LHC, obtained from the through a top quark at the LHC. A light Z′ of roughly
estimation with our leading order Monte Carlo simulation and
Ref.[30]. (1) GeV with small coupling is a very well motivated
O
7
new physics candidate as it can address some astrophys- as
icalanomalies as wellas the muong 2 anomaly. While
− m2 = 2P P (cosh∆η 1) (A1)
its search is very active at the low energy experimental ℓ+ℓ− T1 T2 −
facilities, its search at the LHC is relatively limited so ≃ 2PT1PT2(cosh∆R−1), (A2)
far.
with observation ∆R ∆η since ∆φ distribution is
The LHC can produce the top quark pair abundantly ≃
peaked at 0. For a moderate lepton tagging efficiency,
through the gluon fusion. We considered the scenario most analyses require Pmin as a P cut of leptons
the top quark decaysthrougha chargedHiggs t bH+, T(ℓ) T
→
where the chargedHiggs can decay into one Z′ or multi- Pmin =10 GeV, Pmin =5 GeV. (A3)
ple Z′s dominantly. The top decay into the dark gauge T(e) T(µ)
boson is very close to its dominant decay mode accom- Nowwithanisolationrequirementof∆R>0.3,the cor-
panied by one or two illusive Z′s (t bW +Z′s). Even responding minimum invariant mass of an electron pair
a small BR(t bH+) can be enoug→h to produce the Z′ and muon pair from Z′ would be
at the observa→ble level at the LHC experiments. The Z′
production through a top can be larger than the typical mee > 2PTm(ien)PTm(ien)(cosh(0.3)−1)≃3 GeV, (A4)
Drell-Yanmechanismtoproduce apairofchargedHiggs q
and produce one Z′ when the Drell-Yan produces a pair mµµ > 2PTm(iµn)PTm(iµn)(cosh(0.3)−1)≃1.5 GeV.(A5)
of Z′. q
We considered the process pp tt¯ bW¯bW + Z′ Therefore conventional analyses would miss Z′ lighter
with Z′ decayinginto alepton pair→. Beca→useoflightness than 3 (1.5) GeV in the dielectron (dimuon) channel.
We adopt an analysis method with lepton-jet proposed
of the Z′, the lepton pairs are highly collimated forming
inRef.[11]. AvariationoftheLJdefinitioncanbefound
lepton-jets. For some parameter space, eventhe existing
in Ref. [24]. Since tt¯+ℓ+ℓ− is a major background in
8TeVLHCdatamaygiveenoughsignalsforadiscovery.
our study, we follow the LJ definition in Ref. [35] with a
It also guarantees a huge discoverypotential even at the
modification to the muon P requirement.
very early stage of the 14 TeV LHC experiments. T
As the top quark decaying into the dark sector mode 1. AtleasttwosameflavorleptonswithPT >10GeV
can be easily mistaken with its dominant bW mode, a (electron), 5 GeV (muon) and in a cone of ∆R <
reanalysisofthetopdataatthehadroncollidercanpos- 0.1.
sibly reveal an interesting hint of the Z′ even if the Z′
2. Isolation: Hadronic and leptonic isolation of
is very elusive or decays invisibly. It calls for attention
P <3 GeV in 0.1<∆R<0.4.
in both the experimentalandtheoreticalsides ofthe top T
quark study. InaddPition, to reduce the backgroundevents,we require
Note: Around the time this work was submitted, 20% window of the expected Z′ mass for an invariant
Ref. [29] preprint (version 2), which overlaps with some mass of lepton-jet.
aspect of this paper, appeared. 3. Invariantmasscutonthelepton-jet: mLJ mZ′ <
| − |
0.2 mZ′.
×
For a Monte Carlo simulation, we add Z′ and H±
Acknowledgments to the SM using FeynRules v2[36] and simulate events
with Madgraph v5.14[37], Pythia 6[38] and Delphes
3.0.11[39]. Wemodifyb-jettagging/mistaggingefficiency
K.K. is supported by the U.S. DOE under Grant
(tagging efficiency is around 60% 75% depending on
No.DE-FG02-12ER41809,theUniversityofKansasGen- −
P and η) according to CMS CSVM tagging [40, 41].
eralResearchFundallocation2301566. H.L.issupported T
We make a change in the Delphes module for a smear-
byU.S.DOEunderGrantNo.DE-AC05-06OR23177,the
ing muon P to reflect the nonzero muon mass in the
NSF under Grant No. PHY-1068008. M.P. is supported T
muon’s four vector. For the lepton-jet analysis, we add
bytheWorldPremierInternationalResearchCenterIni-
the lepton-jet class to the Delphes detector simulation.
tiative (WPI Initiative), MEXT, Japan.
2. Signal boxes
Appendix A: Some details on numerical analysis
Toconsideralltt¯decaymodes,weconsiderthreesignal
boxeswithaslightmodificationofCMSanalysesaccord-
1. Lepton pair from Z′ decay
ing to the number of triggered leptons. Jets are recon-
structed with an anti-k algorithm with ∆R < 0.5. We
T
LightZ′cannotbereconstructedwiththeusuallepton require one b-tagged jet (or two b-tagged jets) and the
tagging because of the following simple kinematical rea- aforementionedlepton-jet mass window. Other eventse-
son. Theinvariantmassofaleptonpaircanbeexpressed lection criteria will depend on signal boxes as following.
8
∆R distribution of a lepton pair from Z’ P distribution of a lepton pair from Z’
2.2 T2
2 lep∆toRn<-0je.1t mmHH±±==110000,, mmZZ’’==15 1.4 mmHH±±==110000,, mmZZ’’==15 PT(Pµ)T (>e )5 > G 1e0V GeV
1.8 mH±=140, mZ’=1 1.2 mH±=140, mZ’=1
zed11..46 lepton misH∆o±=Rla1>t4i0o0.3n, mZ’=5 zed 1 mH±=140, mZ’=5
mali1.2 mali0.8
or 1 or
n n
nit 0.8 nit 0.6
u u
0.6 0.4
0.4
0.2
0.2
0 0
10-2 10-1 1 10-2 10-1 1 10 102 103
∆ Rl+l- PT2
(a) (b)
FIG.5: Weshow(a) ∆Rand(b)PT2 =min[PT(ℓ),PT(ℓ¯)]ofaleptonpairfrom theZ′ decayatthepartonlevelforthe14TeV
LHC, which are useful to understand lepton-jet tagging efficiency.
a. Dilepton box conditionsonlytojets. Sincewetagalepton-jet,werelax
the P conditions of jets compared to the CMS analysis
T
For event selections, we require the following criteria [43]. We require at least six jets with PTj > 30 GeV
[34]. with η <2.4. The CMS requires PT1, PT2, PT3, PT4 >
| |
60 GeV, P > 50 GeV, P > 30GeV, and additional
T5 T4
1. ElectronswithP >20GeV, η <2.5,muonswith
T | | constraints for the distance between two b-tagged jets
PT >20 GeV,|η|<2.1 are taken. and a kinematic fit for the mass reconstruction of t, t¯,
2. For the same flavor opposite-sign leptons, we veto and W.
events with the following invariant mass window:
mℓ+ℓ− <20 GeV and |mZ −mℓ+ℓ−|<15 GeV.
3. Forthesameflavorleptonpairing,werequireE/T > d. Backgrounds
40 GeV.
4. We require at least two jets with P > 30 GeV, We consider only the irreducible background of (tt¯+
T
η <2.5. ℓ+ℓ−) from the virtual photon and virtual Z boson ra-
| |
diations and we do not consider possible reducible back-
groundsfromthemistaggedlepton-jet. Forexample,jets
b. Semilepton box can be misidentified as electrons and overlapped leptons
as discussed in Ref. [25].
If events can not be put in the dilepton box, we pass
them to the semilepton box with the following triggers.
We collect leptons of P > 17 GeV if the lepton is a
T
3. Simple explanation of a lepton-jet tagging
muonandofP >25GeVforelectronsasaleptonpool,
T efficiency for signal events
then we require events to have exactly one lepton with
the following selection criteria [42].
With a goodapproximation,most tt¯pairs will be pro-
muon: PT >26 GeV, |η|<2.1, duced near the energy threshold. At the t(t¯) rest frame,
electron: PT >30 GeV, η <2.5. (A6) the energydistributionofaleptonfromZ′ willdroplog-
| |
arithmically (from flat distribution) [44] after
For jets, we require at least four jets with P , P >
T1 T2
45 GeV and P , P >35 GeV.
T3 T4 E(cusp) mZ′e|ηZ′−ηH±|, (A7)
ℓ ≡ 2
c. Hadronic top box
until
boIxfeesv,ewnetspaasrseenvoetnitnsctloudaehdaidnrothneicdtioleppbtoonxworhseermewileepgtiovne Eℓ(max) = m2Z′e(ηZ′+ηH±), (A8)
9
LHC mZ′ ǫLJ(ǫ(LJ+CMS)) [%] for signal Mass range of σbLkOg ǫLJ(ǫ(LJ+CMS)) [%]
[TeV] [GeV] mH± =100 GeV mH± =140 GeV mH± =160 GeV mℓ+ℓ−[GeV] [pb] for background
1 16.37 (4.18/2.07) 46.77 (10.96/4.51) 52.04 (9.40/3.04) 0.5−1.5 0.617 2.05 (0.61/0.28)
8 2 3.07 (0.92/0.43) 31.01 (7.64/3.13) 40.74 (7.57/2.50) 1.0−3.0 0.157 0.53 (0.19/0.08)
5 0.02 (0.00/0.00) 2.24 (0.64/0.26) 5.55 (1.25/0.48) 3.0−5.0 0.0175 0.32 (0.10/0.04)
1 16.38 (4.28/2.02) 44.28 (10.73/4.37) 50.54 (9.44/3.13) 0.5−1.5 2.536 2.18 (0.60/0.30)
14 2 3.33 (1.11/0.49) 29.73 (7.52/3.13) 39.31 (7.64/2.51) 1.0−3.0 0.640 0.57 (0.23/0.11)
5 0.03 (0.01/0.00) 2.57 (0.76/0.28) 5.90 (1.40/0.47) 3.0−5.0 0.0706 0.34 (0.15/0.08)
TABLEIII:Lepton-jet tagging efficiency ǫLJ (%) in pp→bW¯bW +ℓ+ℓ− for signal (for given mH± and mZ′) and background
(fromvirtualphotonandvirtualZ boson)atthe8and14TeVLHC.Thenumbersinparentheses(ǫ /ǫ )
(LJ+CMS[1b]) (LJ+CMS[2b])
are the efficiencies when we require additional selection cuts, requiring one b-tagged or two b-tagged jets as described in
Appendix A2. Coupling structure of Z′ to the lepton does not give a significant effect on the tagging efficiency. In the above
table, we take axial coupling as an example. For backgrounds, we set the trigger of a mℓ+ℓ− mass window as in the table to
enlarge statistics.
with boost factors (rapidity) of H± and Z′ as second hardest lepton (P ) does not change much from
T2
mZ′ =1to5GeV(Fig.5). Thiscanbeunderstoodsince
ηH± = cosh−1(cid:18)m2t +2mmtm2H±H±−m2b(cid:19), (A9) PwTiptehakEdqo.e(sA7n)o.t cBhauntgethmeuccohrrfersopmon1d8in.9g6∆toR(1p8e.a9k5)GweiVll
m2 +m2 m2 changesignificantlytothepointtochangelepton-jettag-
ηZ′ = cosh−1 H± Z′ − W . (A10) ging efficiency from ∆R(peak) 0.05 to 0.26 estimated
(cid:18) 2mZ′mH± (cid:19) by Eq. (A11). The observed p∼eak is similar to this es-
Thus if we assume that a distribution of the geomet- timation as in Fig. 5. (For mH± = 100GeV, estimated
ric average of leptons’ P is localized around Ppeak ∆R(peak) is over estimated by a factor of 2 since the ac-
1E(cusp), we can estimateTthe peak of ∆R(= ∆RT(peak≡)) tual PT of leptons is not very well localized.) Thus, for
b2etℓween two leptons from Z′ decays with Eq. (A2) by a large mZ′, lepton-jet tagging efficiency is low due to
large ∆R between leptons from Z′.
∆R(peak) cosh−1 2m2Z′ +1 . (A11) Now we consider the effect from the mass of charged
∼ (Eℓ(cusp))2 ! Higgs. The PT of leptons increases with mH±. At the
same time, due to the dilepton mass relation, Eq.(A2),
With this simple kinematical study, we can explain ∆R decreaseswith mH±. This effect from∆R is greater
why ∆R will be the major criteria for a lepton-jet tag- than the effect from P , and the lepton-jet tagging effi-
T
ging. For example, with mH± = 140GeV, PT of the ciency increases with mH±.
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