improved sensitivity to charged higgs searches in top quark decays t→bh+→b(τ+ντ) at the lhc...

Eur. Phys. J. C (2011) 71:1737DOI 10.1140/epjc/s10052-011-1737-8

Special Article - Tools for Experiment and Theory

Improved sensitivity to charged Higgs searches in top quarkdecays t bH+ b(+ ) at the LHC using polarisationand multivariate techniques

Ahmed Ali1,a, Fernando Barreiro2,b, Javier Llorente2,c1Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany2Facultad de Ciencias C-XI, Departamento de Fisica, Universidad Autonoma de Madrid (UAM), Cantoblanco, Madrid 28049, Spain

Received: 14 March 2011 / Revised: 7 July 2011 / Published online: 8 September 2011 The Author(s) 2011. This article is published with open access at Springerlink.com

Abstract We present an analysis with improved sensitiv-ity to the light charged Higgs (mH+ < mt mb) searchesin the top quark decays t bH+ b(+ ) + c.c. in thet t and single t/t production processes at the LHC. In theMinimal Supersymmetric Standard Model (MSSM), one an-ticipates the branching ratio B(H+ + ) 1 over al-most the entire allowed tan range. Noting that the + aris-ing from the decay H+ + are predominantly right-polarized, as opposed to the + from the dominant back-ground W+ + , which are left-polarized, a number ofH+/W+ + discriminators have been proposed andstudied in the literature. We consider hadronic decays of the, concentrating on the dominant one-prong decay chan-nel . The energy and pT of the charged prongsnormalised to the corresponding quantities of the areconvenient variables which serve as polariser. We usethe distributions in these variables and several other kine-matic quantities to train a boosted decision tree (BDT). Us-ing the BDT classifier, and a variant of it called BDTD,which makes use of decorrelated variables, we have cal-culated the BDT(D)-response functions to estimate the sig-nal efficiency vs. the rejection of the background. We ar-gue that this chain of analysis has a high sensitivity to lightcharged Higgs searches up to a mass of 150 GeV in the de-cays t bH+ (and charge conjugate) at the LHC. For thecase of single top production, we also study the transversemass of the system determined using Lagrange multipliers.

a e-mail: [email protected] e-mail: [email protected] e-mail: [email protected]

1 Introduction

In many extensions of the standard model (SM), the Higgssector of the SM is enlarged by adding an extra doublet ofcomplex Higgs fields. After spontaneous symmetry break-ing, one finds three neutral Higgs bosons (h,H,A) anda pair of charged Higgs bosons, H. These neutral andcharged Higgs bosons have been searched for in high energyexperiments, in particular, at LEP and the Tevatron. None ofthese Higgses have been seen so far, and upper limits existon all of them [1]. We will concentrate here on the chargedHiggs searches, in which the two key phenomenological pa-rameters are the charged Higgs mass, mH , and tan , theratio of the two vacuum expectation values, tan = v2/v1.The searches for the H are model-dependent, and the ex-clusion limits (expressed as a contour in the mHtanplane) have to be taken together with the underlying model.For example, in the so-called two-Higgs-doublet-models(2HDM), a stringent limit exists on mH from the measuredbranching ratio for B Xs and the NNLO estimates ofthe same in the SM, yielding mH > 295(230) GeV at the95% (99%) C.L., for almost the entire tan values of inter-est [2]. This limit can be easily evaded in other models, inparticular, in the minimal supersymmetric model (MSSM).

Direct H-searches are limited by the center-of-massenergy in e+e H+H annihilation processes, wherethey can be produced via s-channel exchange of a photonor a Z boson. These searches assume for the branching ra-tios B(H+ + ) + B(H+ cs) = 1 and hold for allvalues of B(H+ + ). In the 2HDM framework, thecross section in the Born approximation depends only onmH (modulo the known couplings) and the present limitis mH > 79.3 GeV at 95% C.L. obtained at Ecm(e+e) =209 GeV from LEP [1]. The mass range mH+ < mt mbhas been searched in the process pp t tX at the Tevatron,followed by the decay t bH+ (and its charge conjugate).

of 19 Eur. Phys. J. C (2011) 71:1737

For example, Altonen et al. [3] have searched for the decayt bH+, followed by H+ cs in 2.2 fb1 of pp col-lisions at Ecm(pp) = 1.96 TeV, obtaining upper limits onB(t bH+) between 0.08 and 0.32 (95% C.L.), assumingB(H+ cs) = 1. In the MSSM, this probes only a verysmall tan region, namely < 1, which is not favoured bytheoretical considerations [4]. The search for t bH+, fol-lowed by H+ + by Abazov et al. [5] in 0.91 of ppcollisions at the Tevatron yield upper limits on B(t bH+)between 0.19 and 0.25 (95% C.L.) for mH+ = 80155 GeVand B(H+ + ) = 1. This excludes a small region(tan > 35 and mH+ = 100120 GeV) [6]. Thus, it is fairto conclude that the searches of the charged Higgses over agood part of the mHtan plane in the MSSM is a pro-gramme that still has to be carried out and this belongsto the LHC experiments. In anticipation, searches for theH in pp collisions at Ecm = 714 TeV at the LHC havereceived a lot of attention [712]. There are two regions,namely mH+ < mt mb , which will be looked into in boththe t t pair production and in single top (or anti-top) pro-duction in pp collisions, followed by the decays t bH+and H+ + , and for mH above the top quark mass,in which case H production mainly takes place throughthe process gb tH+, followed dominantly by the decayH+ t b. However, despite larger branching fraction, itmay be hard to distinguish the H+ t b mode from thebackground. For large tan , the decay mode H+ +becomes discernible. In this paper, we will concentrate onthe light H-scenario.

The decay channel H + will play the keyrole in the searches of the light H-bosons. The + leptonsarising from the decays W+ + and H+ + arepredominantly left- and right-polarised, respectively. Polar-isation of the influences the energy distributions in thesubsequent decays of the . Strategies to enhance the H-induced effects in the decay t b(W+,H+) b(+ ),based on the polarisation of the + have been discussed atlength, starting from the pioneering work [1316] to theproduction and decays of a t t pair at the hadron collid-ers Tevatron and the LHC [1722]. Also the effects of the(QED and QCD) radiative corrections on such distributionsin the dominant (one-charged prong) decay channels + + , + , a+1 and + have been worked out [23].Following these studies, the construction of the -jet (aswell as b-jet) are of central importance in H-searches. Weuse the dominant single-charged-prong decay as the polariser. As 0 is the dominant decaymode, the energy and transverse momentum of the inthe -jet become quantities of main interest for our study.Likewise, the distribution in the angle , defined as

cos = 2m2b

m2top m2W 1, (1)

plays an important role in our analysis. Since the energy-momentum vectors of the b-jet and the can be measured,this distribution is measurable at the LHC. We also note thatthis distribution is different from the conventional definitionof the angle [24], in which the invariant mass m2b is mea-sured instead of m2b . The other distributions that enter inour analysis are listed in the next section.

Having generated these distributions, characterising thesignal t bH+ b(+ ) b(+ ) and the back-ground t bW+ b(+ ) b(+ ) events, weuse a technique called the Boosted Decision Tree (BDT)a classification model used widely in data mining [25]todevelop an identifier optimised for the t bH+ decays. Inour calculation, we use both BDT and a variant of it calledBDTD (here D stands for decorrelated), where possible cor-relations in the input variables are removed by a proper ro-tation obtained from the decomposition of the square root ofthe covariance matrix, to discriminate the signal events fromthe large backgrounds. We recall that this technique has beensuccessfully used to establish the single top quark produc-tion in pp collisions at the Tevatron [26, 27] (see [28] fordetails). Recently, we have applied this technique to a fea-sibility study of measuring the CKM matrix element |Vts |from the decay t Ws at the LHC@14 TeV, and have es-timated that a benchmark with 10% accuracy for this decaymode with a 103 rejection of the background t Wb can beachieved with an integrated luminosity of 10 (fb)1 [29]. Weshow in this paper that a similar BDTD-based analysis holdsgreat promise in light-H searches at the LHC both in thepp t tX pair production and in the single top (or anti-top)production pp t/tX. Furthermore, we show that using atransverse mass definition, as suggested in [30], the processpp t/tX followed by the decays t bH+, bW+, allowsone to determine rather sharp Jacobian peaks for the trans-verse mass of the H-bosons. The conventional definitionof the transverse mass [31], which was very helpful in thedetermination of the transverse mass of the W bosons, isless suited for constructing the corresponding mass of theH bosons.

We note that an analysis using an iterative discriminantanalysis method similar to the one presented here was car-ried out by Hesselbach et al. [32]. In particular, detailedMonte Carlo comparisons of several variables incorporatingthe spin effects in charged Higgs boson production were pre-sented to separate the tbH+ signal from the standard modelt t background both at the Tevatron (s = 1.96 TeV) andthe LHC (s = 14 TeV). However, there are several signif-icant differences in the two studies, such as the distributionin cos (defined in (1)), which plays an important role inour analysis. In addition, we have studied the case of sin-gle top production at the LHC, pp t/t + X, followed bythe decays t b(H+/W+ + ) + c.c., which was notconsidered in [32].

Eur. Phys. J. C (2011) 71:1737 Page 3 of 19

This paper is organised as follows: In Sect. 2, we anal-yse the process pp t tX at the LHC, followed by thedecay chains t bW+, bH+, and the subsequent decays(H+,W+) + , together with the BDTD-based analy-sis of the signal (t bH+) and the SM decay background(t bW+). The BDTD response functions are then used towork out the signal efficiency vs. the background rejection.In Sect. 3, we repeat this analysis for the single top (or anti-top) production pp t/tX at the LHC. Section 4 containsa brief summary.

2 t t production and the decay chainst bW+/H+ b(+ ) at the LHC

2.1 Production cross sections

Theoretical predictions of the top quark production at theLHC have been obtained by including up to the next-to-next-to-leading order (NNLO) corrections in the strong couplingconstant [3336] using modern parton distribution functions(PDFs) [37, 38]. Typical estimates for (pp t tX) rangefrom 874+1433 pb for mt = 173 GeV and

s = 14 TeV [39]

to 943 4(kinematics)+7749(scale) 12(PDF) pb [35]. Com-pared to the t t production cross section at the Tevatron, thisis larger by two orders of magnitude. The cross sections atthe lower LHC energies, 7 and 10 TeV, have also been cal-culated [35, 39], with (pp t tX) 400 pb at 10 TeVand about half that number at 7 TeV. Thus, for the top quarkphysics, the dividends in going from 7 to 14 TeV are higherby a good factor 4.

2.2 Top quark decays t b(W+,H+) and charged Higgsdecays H+ cs, +

Top-quark decays within the Standard Model are completelydominated by the mode

t b + W+, (2)due to Vtb = 1 to a very high accuracy. In beyond-the-SM theories with an extended Higgs sector, a light chargedHiggs can also be produced via

t b + H+. (3)The relevant part of the interaction Lagrangian is [18, 19]:

LI = g2

2MWVtbH

+ [ut (pt ){A(1 + 5)

+ B (1 5)}ub (pb)

]

+ gC2

2MWH+

[ul (p) (1 5)ul (pl)

], (4)

where A, B and C are model-dependent parameters whichdepend on the fermion masses and tan:

A = mt cot, B = mb tan, C = m tan. (5)

The decay widths of processes (2) and (3) in the Born ap-proximation are [18, 19]:

BorntbW =g2

64M2Wmt

12

(1,

m2bm2t

,M2Wm2t

)

[M2W(m2t + m2b

) + (m2t m2b)2 2M4W

], (6)

BorntbH =g2

64M2Wmt

12

(1,

m2bm2t

,M2Hm2t

)

[(m2t cot2 + m2b tan2 )(

m2t + m2b M2H)

4m2t m2b], (7)

where (x, y, z) = x2 +y2 +z2 2xy2xz2yz is the tri-angle function. The total top quark decay width in the Bornapproximation is obtained by adding the two partial widths

tot, Bornt = BorntbW + BorntbH . (8)

QED corrections in the total decay width of the top quark arenumerically small. The O(s) QCD corrections were calcu-lated in [40, 41] (see, also [42]) and have the form:

tott,RC = Born+QCDtbW + Born+QCDtbH ,

Born+QCDtb(W,H) = tot,Bornt

(1 + fW,H

),

fW,H = s3(

5 42

3

).

(9)

Thus, in the branching ratio B(t bH+), also this QCDcorrection drops out. However, radiative corrections comingfrom the supersymmetric sector to B(t bH+) are ratherimportant. They have been calculated in great detail in theliterature, in particular for the MSSM scenario in [4345],and can be effectively incorporated by replacing the b-quarkmass mb in the Lagrangian for the decay t bH+ by theSUSY-corrected mass mcorrectedb = mb/[1 + b]. The cor-rection b is a function of the supersymmetric parametersand, for given MSSM scenarios, this can be calculated us-ing the FeynHiggs programme [46]. In particular, for largevalues of tan (say, tan > 20), the MSSM corrections in-crease the branching ratio for t bH+ significantly. This,for example, can be seen in a particular MSSM scenario ina recent update [47], from where we show B(t bH+) asa function of tan , calculated for mt = 175 GeV and vari-ous assumed values of the charged Higgs mass, indicated inFig. 1.

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Fig. 1 Branching ratio B(t H+b) in MSSM as a function of tanfor the charged Higgs masses as indicated. (Figure taken from [47])

Since we are treating the case of the light charged Higgs,there are essentially only two decay modes which are im-portant: H+ + and H+ cs. The branching ratio ofinterest to us B(H+ + ) is given by [18, 19]:

B(H+ +) = H

H + Hcs,

H =g2MH

32M2Wm2 tan

2 ,

Hcs = 3g2MH

32M2W

(m2c cot

2 + m2s tan2 ).

(10)

For the numerical values of tan that we entertain in thispaper, the branching ratio B(H+ + ) = 1, to a veryhigh accuracy.

2.3 Event generation, trigger

We consider in this section the process pp t tX, with boththe t and t decaying into Wb. Our trigger is the leptonic de-cay W ee or W . The other W+ decaysvia W+ + . This makes up our main background. Thesignal events are generated in which one of the t or t decaysvia W+ bH+ (or its charge conjugate W bH),see Fig. 2. The other t or t then decays leptonically, as inour trigger. In the Minimal Supersymmetric Standard Model(MSSM), for large tan and mH+ < mt , the branching ra-tio for the decay H+ cs is small and one anticipates thebranching ratio B(H+ + ) 1. This is the parame-ter space in which the analysis reported here is valid. Notingthat the + arising from the decay H+ + are predom-inantly right-polarized, as opposed to the + from the dom-inant background W+ + , which are left-polarized,a number of H+/W+ + discriminators have beenproposed and studied in the literature. We have used thedominant single-charged-prong decay + + as the

Fig. 2 Feynman diagram for gg t t , followed by the decayt b(H+ + ) and t b(W ee)

+ polariser. Having set these branchings, we have gener-ated 50K events for the process pp t t bW+(bW),with all of them decaying according to the chain describedearlier, i.e., W ee and W+ + , with all the sforced to decay into + (here and below, charge conju-gates are implied). In calculating the required luminosity, wetake into account the corresponding branching ratios, whichare as follows [1]

B(W+ e+e) = (10.75 0.13)%,

B(W+ +) = (11.25 0.20)%,

B(H+ +) = 1.0,

B(+ +) = (25.5 0.10)%.

(11)

We also generate the same number (50K) signal events,for each of the following charged Higgs masses: mH+ =90,110,130,150 GeV. As for the background process, weforce the + to decay into + 100% of the time. Theseevents are generated using PYTHIA 6.4 [48] and for the de-cays of the , we use the programme called TAUOLA [49]to incorporate the polarization information on the decaydistributions.

We impose the following acceptance and trigger cuts:

|| < 2.5, with = e, |b,b| < 2.5 PTe > 20 GeV PT > 10 GeV PTb,b > 20 GeV

In order to discriminate the signal and background, wehave studied a number of distributions, summarized below.


Fig. 3 (Color online) The distribution dN/d cos for the t t produc-tion as measured in the decay chain t bW b( ) b( ) )(right-hand frame), and in t bH b( ) b( ) ) for four

different charged Higgs masses, as indicated on the figure (left-hand frame)

Distribution in the angle , defined in (1). This is de-fined for both the decay chains: t bW b( ) b( ) and t bH b( ) b( ) . Since theenergy-momentum vectors of the b-jet and the canbe measured, this distribution is measurable at the LHC.We also note that this distribution is different from theconventional definition of the angle [24], in which theinvariant mass m2b is measured instead of m

2b .

Energy and pT of the b-jets from the decays t bW+and t bH+.

Energy and pT of the + jets from the decays W+ + and H+ + , concentrating on the single-charged-prong decays + + .

The ratio of the energy and pT of the + jets and theiraccompanying b-jet.

As a measure of the polarisation, we consider the frac-tional energy and transverse momentum of the single-charged prong (+ in +-jet).

For the case of single top production, we also study thetransverse mass of the system determined using Lagrangemultipliers [30].

These distributions are used to train a boosted decisiontree (BDT). Using the BDT classifier, and a variant of itcalled BDTD, which makes use of decorrelated variables,we have calculated the BDT(D)-response functions to es-timate the signal efficiency vs. the rejection of the back-ground.

The strategy adopted by us to search for the decays t bH+ is somewhat different from the traditional cut-basedanalysis, as, for example, reported in [8]. There the idea isto suppress the SM-background as much as possible, makinguse of additional variables, such as the missing ET , satisfy-ing EmissT > 50 GeV. Our idea is, instead, to train a boosteddecision tree classifier for both the signal and backgroundevents. Eventually, for a realistic analysis of the LHC data,

we may have to reintroduce some of the cuts to suppressother non-t t background, such as coming from the processpp W + jets, which may also fake our signal.

2.4 Details of the analysis

In Fig. 3 (right-hand frame), we show the cos distributionsfor the standard model (SM) process p + p t t + X, fol-lowed by the decay chain t bW b( ) b( ) .In the left-hand frame, we show the same distribution whenone of the t or t decays via the chain t bH b( ) b( ) , for four different charged Higgs masses, as al-ready stated in the previous section. For lower values ofmH+ , the cos distribution falls less steeply than the SMbackground. As mH+ increases, the cos distributions be-come steeper and are essentially confined to the negativevalues of cos . This distribution then provides one of thediscriminators to be fed to the BDTD analysis.

In Fig. 4 (right-hand frames), we show the distributionsin the energy of the b-jet, E(b), and the transverse momen-tum of the b-jet, pT (b) from the SM process pp t tX,followed by the decay chain discussed above. In the left-hand frames, the corresponding distributions are shown forthe charged Higgs case. We remark that for the chargedHiggs case these distributions are softer than those fromthe SM due to the different helicity structure of the decays.This effect becomes stronger as mH+ increases due to phasespace. As a result, these distributions add to the discrimina-tion power of the BDTD analysis. Note that these distribu-tions reflect the event characteristics at the generation level.Obviously, due to the semileptonic decays of the b-quark,and other detector effects, they will be modified. However,we expect that the dilutions due to these effects are sub-dominant.

In Fig. 5 (right-hand frames), we show the distributionsin the energy of the -jet, E( -jet), and in the transverse

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Fig. 4 (Color online) Distributions in the Energy of the b-jet, E(b),and transverse momentum of the b-jet, pT (b) from the processpp t tX, followed by the decay t W+b (right-hand frames),

and the same distributions for the decay chain t H+b with the fourindicated charged Higgs masses (left-hand frame)

Fig. 5 (Color online) Distributions in the Energy of the -jet, E( -jet),and transverse momentum of the -jet, pT ( -jet) from the processpp t tX, followed by the decay t W+b (right-hand frames), and

the same distributions for the decay chain t H+b with the fourindicated charged Higgs masses (left-hand frame)


Fig. 6 (Color online) Distributions in the ratio E( -jet)/E(b) and pT ( -jet)/pT (b) from the process pp t tX, followed by the decay t W+b(right-hand frames), and the same distributions for the decay chain t H+b with the four indicated charged Higgs masses (left-hand frame)

momentum of the -jet, pT ( -jet) from the SM process,followed by the decay chain discussed above. In the left-hand frames, the corresponding distributions are shown forthe charged Higgs case. In these distributions, the energyand pT -spectra of the -jet coming from the charged Higgsdecays are harder than those coming from the SM process,and this difference becomes more marked as mH+ increases.This complementary behaviour is expected for the same rea-son as discussed earlier for Fig. 4, again reflecting the dif-ferences in helicity and phase space. It goes without sayingthat these distributions increase the discrimination power ofthe BDTD analysis.

To make this effect more marked, we show the ratioof the energy and pT -spectra involving the - and b-jetsin Fig. 6. The SM distributions are shown in the right-hand frames, and those from the charged Higgs in the left-hand frames. These distributions show clearly the differ-ent shapes of the distributions SM vs. Higgs. For exam-ple, putting a lower cut on the ratios E( -jet)/E(b) > 1 orpT ( -jet)/pT (b) > 1, most of the SM background is elimi-nated, whereas the charged Higgs-induced distributions sur-viving this cut are considerably larger, with the discrimina-tion becoming stronger as mH+ increases.

In Fig. 7, we show the distributions in the fractional en-ergy of the single-charged prong (+ in +-jet), E()/E( -jet), and in the transverse momentum of the single-charged prong, pT ()/pT ( -jet) from the SM process

(right-hand frames) and those coming from the chargedHiggs-induced process (left-hand frames) for mH+ = 90GeV. As remarked earlier, we are using the dominant single-charged-prong decay + + as the + polariser. Asalready noted in [14], the fractional energy distributionsin z = EA/E , from the -decay products A+ miss-ing energy, the effect of the polarization is most markedfor the decays + + and + + . This has beenworked out in the collinear limit, i.e., for E/m 1. Ourvariables differ from the one used in [14], in that we nor-malize to the visible -energy and the visible pT ( -jet),and not to the total -energy. With our normalization, the+-energy measured in the decays + + will be adelta function, peaked at 1 in the variables shown in Fig. 7,and hence we concentrate on the decay chain + + .These distributions also provide strong discriminants for theBDTD analysis.

Briefly, the generated input is used for the purpose oftraining and testing the samples. We provide the inputin terms of the variables discussed earlier for the signal(t bH+) and the background (t bW+), obtained withthe help of a Monte Carlo generator. This information isused to develop the splitting criteria to determine the bestpartitions of the data into signal and background to build upa decision tree (DT). The separation algorithm used in split-ting the group of events in building up DT plays an impor-

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Fig. 7 (Color online) Distributions in the fractional energy of thesingle-charged prong (+ in +-jet), E()/E( -jet), and in the trans-verse momentum of the single-charged prong, pT ()/pT ( -jet) from

the pp t tX, followed by the decay t W+b (right-hand frames),and the same distributions for the decay chain t H+b with the fourindicated charged Higgs masses (left-hand frame)

tant role in the performance. The software called the Toolkitfor Multivariate Data Analysis in ROOT (TMVA) [50] isused for the BDT(D) responses in our analysis. The re-sponse functions for pp t tX at a center-of-mass-energy

s = 14 TeV at the LHC, followed by the background pro-cess t bW+ (in shaded blue) and the signal t bH+ (inshaded red) are shown in Fig. 8. The four frames shown inthis figure correspond to the charged Higgs masses mH+ =90,110,130 and 150 GeV. As can be seen that the separationbetween the signal and the background increases as mH+increases. This improved separation as a function of mH+will, however, be compensated to some extent by the de-creasing branching ratio for the decay t bH+, as shownin Fig. 1 [47], obtained by using FeynHiggs [51].

The corresponding background rejection vs. signal effi-ciency curves from the process pp t tX calculated fromthe previous BDTD response at

s = 14 TeV are shown in

Fig. 9 for the four charged Higgs masses, as indicated onthe frames. For a signal efficiency value of 90%, the back-ground rejection varies between 50% and 90% as we movefrom mH+ = 90 GeV to mH+ = 150 GeV.

In order to calculate the significance of our signal, wedo the following simplified calculation. We consider theless preferred case for tan = 10, for which the branch-ing ratio B(t H+b) in the MSSM shows a dip, with

B(t H+b) 0.02 for mH+ = 90 GeV (see, Fig. 1). Forthe process pp t tX, the trigger is based on the decay t bW+ b+, with + = e+,+, which has a summedbranching ratio of about 0.2. Since, in the large-tan limitwe are working, B(H+ + ) 1, and the +-decaymode we are concentrating on is + + , which hasa branching ratio of 0.25, the product branching ratio t bH+ b(+ ) b(+ ) = 5 103, which takinginto account the trigger is reduced to 1.0 103. For an in-tegrated luminosity of 10 (fb)1 at s = 14 TeV, and sum-ming over the charge conjugated modes yielding a factor 2,this yields 2104 signal events. For the background events,resulting from the production and the SM decays from theprocess pp t tX, the corresponding product branching ra-tio is 2.5%, which together with the trigger branching gives5 103, resulting in 105 background events, where wehave again taken into account the factor 2 from the sum ofthe charge conjugated states. Using the BDTD analysis, weget for a 50% signal efficiency, a background rejection of90%. Thus, our estimated significance will be

S = Nsignal eventsNbackground events

= 104

104

100. (12)

A more realistic calculation should consider a factor of 2 re-duction due to the acceptance cuts, discussed in Sect. 2.3,


Fig. 8 (Color online) BDTD response functions for pp t tX, with s = 14 TeV, followed by the decay t W+b (SM) and the decay chaint H+b, with the SM background (in shaded blue) and the charged Higgs signal process (in shaded red) for four different charged Higgs masses

Fig. 9 (Color online) SM background rejection vs. charged Higgs signal efficiency for the four charged Higgs masses indicated on the figure fromthe process pp t tX, with s = 14 TeV

of 19 Eur. Phys. J. C (2011) 71:1737

Fig. 10 (Color online) SM background rejection vs. charged Higgssignal efficiency for the four charged Higgs masses indicated on thefigure from the process pp t tX. This figure differs from the one

shown in Fig. 9 in the minimum transverse momentum of the -jet,which is set to 20 GeV as opposed to 10 GeV used in the earlier figure

as well as the efficiency to tag two b-jets which is anotherfactor of 2, and the efficiency of reconstructing a -jet, es-timated as 0.3 [7]. This amounts to a factor of about 10 re-duction in both the number of signal and background events,resulting in a significance of about 30. This is high enoughto take another factor 2 reduction due to various other cuts,which will be inevitable in a detector-based analysis tak-ing into account non-t t backgrounds, not estimated here.Of course, this significance goes down as mH+ increases,keeping tan fixed. Thus, for example, for tan = 10 andmH+ = 150 GeV, the reduction in the number of events willbe approximately 5 (a factor 10 decrease in B(t H+b),compensated by a factor 2 increase in the signal efficiencycalculated from the BDTD response). This would yieldS 6, which is just above the discovery limit for a chargedHiggs below the top quark mass.

A number of checks has been performed in order to testthe robustness of the results. For instance, the cut on theminimum transverse momentum of the -jet has been raisedfrom 10 GeV to 20 GeV. The corresponding figure display-ing the background rejection vs. the charged Higgs signalefficiency is shown in Fig. 10. A comparison with Fig. 8,obtained with a 10 GeV cut on the minimum transverse mo-mentum of the -jet, shows that the two figures are very sim-ilar. The price to pay for the acceptance is, relatively speak-

ing, minor, going down from 0.6 to 0.5. We had conserva-tively taken this to be 0.5 in our numerical calculations.

The above analysis presented for the LHC energy

s =14 TeV has been repeated for a center of mass energy

s = 7 TeV, at which energy the LHC is collecting datacurrently. As of preparing this report, the integrated lumi-nosity of the LHC is above 1 inverse femtobarn, and theprojection for end 2012 is of order 10 inverse femtobarns.We have generated events at

s = 7 TeV, and have calcu-

lated all the distributions presented earlier for 14 TeV. Theshapes of these distributions are essentially similar. This isreflected in the BDTD response functions for the SM back-ground and the charged Higgs signal, presented in Fig. 11,and in the SM background rejection vs. the charged Higgssignal efficiency, shown in Fig. 12. However, the cross sec-tions for pp t tX at 7 TeV is approximately a factor 4smaller than at 14 TeV [35, 39]. This implies that our cal-culations for the significance obtained at

s = 14 TeV have

to be divided by a factor 2 to get the corresponding signifi-cance at

s = 7 TeV. This will reduce the sensitivity of the

charged Higgs in tanmH+ plane. For example, for mH+close to the kinematic limit mt mb , a signal is expectedonly for tan > 20.

A potential dilution of the polarization information hasto be kept in mind. The single charged-prong hadronic


Fig. 11 (Color online) BDTD response functions for pp t tX, with s = 7 TeV, followed by the decay t W+b (SM) and the decay chaint H+b, with the SM background (in shaded blue) and the charged Higgs signal process (in shaded red) for four different charged Higgs masses

Fig. 12 (Color online) SM background rejection vs. charged Higgs signal efficiency for the four charged Higgs masses indicated on the figurefrom the process pp t tX with s = 7 TeV

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decays of the are essentially made up of the decays + (with a branching ratio of 10.9%), ( 0)+ decays (with a branching ratio of 25.5%)and a1 ( 00) + decays (with a branchingratio of 9.3%). Separating the mode from the mode should, in principle, be possible due to the lack ofdeposited energy in the 0 or electromagnetic cluster ac-companying the in the former, but separating the mode from the a1 mode will not be easy. Fortunately, thebranching ratio of the latter is only 40% of the former. So,the number of 0 clusters (0, 1 and 2) will have to be in-cluded in the analysis as a new variable. The decays dominate the one charged track (,K) and oneelectromagnetic or 0 cluster. However, we stress that theBDT can be trained to reduce the dilution.

In a realistic analysis, a further source of reduction in ourestimates of the significance would come from the wrongassignment of the b-jet charges, though this effect is mi-nor compared to the ones discussed above. The b-jet chargeidentification efficiency is estimated at present to be around65% [7], using standard techniques based on a weightedaverage of the charges of the particles in the jet, with theweights being proportional to their momenta. However, asimple algorithm can be designed, which takes into accountin addition the angular correlations between the trigger lep-ton, the tau-jet and the charges, reducing the b-jet mis-assignment to about 20% for the charged Higgs masses closeto the W mass. For higher charged Higgs masses, this canbe further brought down by simply taking the b-jet with thesmaller (larger) transverse momentum to be that associatedwith the charged Higgs (resp. W) boson.

We also mention that we have not considered the back-ground from the process pp t t (b)(bjj). However,it has been shown in [7] that this background can be wellseparated in a standard cut analysis from the pp t t (b)(b ) process. With our TMVA approach, this back-ground will be tamed though we will have to introduce alsothe missing ET as a variable in the BDT training. We areaware of the non-t t background, which are dominated bythe Z + jets and W + jets. These have been studied in greatdetail in [8], with the conclusion that they can be broughtbelow the signal by the additional use of the EmissT -cut. Wehave not used the EmissT -cut, as we have concentrated onlyon the SM t tX background, but will do so in a more realis-tic detector-based analysis in the future.

3 Single t/t production and the decay chainst bW+/H+ b(+ ) at the LHC

3.1 Cross sections at the LHC

The single top (or anti-top) cross sections in hadron col-lisions have been calculated in the NLO approximation

Fig. 13 Feynman diagram for qb q t , followed by the decayt b(H+ + )

[5256]. Recalling that there are three basic processes at theleading order which contribute to (pp t/tX), namelythe t-channel: qb q t , the s-channel: qq bt ; and theassociated tW production bg tW, the cross section es-timated at the Tevatron is [57]: (pp tX) = (pp tX) 1.8 pb for both the top and anti-top production. Atthe LHC@14 TeV, one estimates (pp tX) 200 pband about half this number for (pp tX), yielding thesummed single top and anti-top cross sections at about300 pb, also approximately two orders of magnitude largerthan those at the Tevatron. With a luminosity of 10 fb1, oneanticipates O(3 106) single top (or anti-top) events.

As mentioned in the introduction, there are three differentmechanisms of producing a single top (or anti-top) quark inhadronic collisions, the s-channel, the t-channel, and the as-sociated production tW -channel. The Feynman diagram forthe dominant t-channel partonic process qb q t , followedby the decay t b(H+ + ) is shown in Fig. 13.The partonic cross section is then convoluted with the par-ton distribution functions to calculate the cross sections inpp t +X and pp t +X. Since, we are using PYTHIA6.4 [48] to do the simulation of the single top (or anti-top)production, not all channels are encoded there yet. However,as we use the generator to calculate the acceptance only, butthe total cross sections are normalized to the theoretical cal-culations, the estimates presented here should hold approx-imately. Since most of the distributions calculated by us forthe processes pp t tx and pp t/tX are in the samevariables, we comment only briefly on the distributions forthe signal t bH+ b+ and the background processt bW+ b+ .

In Fig. 14, we show the distribution dN/d cos forthe pp t/t + X production as measured in the decaychain for the SM background process t bW b( ) b( ) (right-hand frame), and for the signal t bH b( ) b( ) (left-hand frame) for four differentcharged Higgs masses, as indicated on the figure. The SMbackground in the process pp t/t +X falls more steeplyas a function of cos than is the case for the t t production


Fig. 14 (Color online) The distribution dN/d cos for the pp t/t + X production as measured in the decay chain t bW b( ) b( ) (right-hand frame), and in t bH b( )

b( ) for four different charged Higgs masses, as indicated on thefigure (left-hand frame)

Fig. 15 (Color online) Distributions in the energy of the b-jet, E(b),and transverse momentum of the b-jet, pT (b) from the processpp t/tX, followed by the decay t W+b (right-hand frames),

and the same distributions for the decay chain t H+b with the fourindicated charged Higgs masses (left-hand frame)

pp t t + X, due to the acceptance cuts. The trend is simi-lar in the signal process. However, also in the single top (oranti-top) production, this distribution provides a good dis-criminant as input to the BDTD analysis.

The distributions in the energy of the b-jet, E(b), andtransverse momentum of the b-jet, pT (b) from the processpp t/tX, followed by the SM decay t W+b are shownin Fig. 15 (right-hand frames), and the same distributions for

the decay chain t H+b with the four indicated chargedHiggs masses are also shown in this figure (left-hand frame).These distribution are very similar to the ones shown for thepp t tX processes, as they essentially reflect the kinemat-ics of the decays t W+b and t H+b.

In Fig. 16, we show the corresponding distributions forthe -jet, E( -jet), and for the transverse momentum of the -jet, pT ( -jet) from the process pp t/tX, followed by

of 19 Eur. Phys. J. C (2011) 71:1737

Fig. 16 (Color online) Distributions in the energy of the -jet,E( -jet), and transverse momentum of the -jet, pT ( -jet) from theprocess pp t/tX, followed by the SM decay t W+b (right-hand

frames), and the same distributions for the decay chain t H+b withthe four indicated charged Higgs masses (left-hand frame)

the SM decay t W+b (right-hand frames), and the samedistributions for the decay chain t H+b with the four in-dicated charged Higgs masses (left-hand frame). These dis-tributions, likewise, are very similar to the ones shown forthe t t production case, shown in the previous section.

The distributions in the ratio E( -jet)/E(b) andpT ( -jet)/pT (b) from the process pp t/tX, followedby the SM decay t W+b are shown in Fig. 17 (right-hand frames), and the same distributions for the decay chaint H+b are also shown in this figure with the four in-dicated charged Higgs masses (left-hand frame). As antic-ipated, these distributions are also similar in the single top(anti-top) production and in the t t production.

The effects of different chiralities in the SM decay chaint bW+ b(+ ) followed by the + decay + + , and in the signal process t bH+ b(+ ) fol-lowed by the + decay + + are shown in Fig. 18.Once again, these distributions in the fractional energy of thesingle-charged prong (+ in +-jet), E()/E( -jet), andin the transverse momentum of the single-charged prong,pT ()/pT ( -jet) are very similar in the processes pp t/tX and pp t tX, as expected.

One important difference between the analysis of the sin-gle top (or anti-top) production compared to the t t produc-tion process lies in the fact that the missing transverse en-

ergy and momentum can be ascribed in the former to the -neutrino, . This is different in the case of the t t production,as one of the t-or t-quarks decays via t bW+ b+,which is used as a trigger. Thus, the missing transverse en-ergy or momentum can not be traced to the decay of the -lepton alone in the case of t t production. As already statedin [30] the missing transverse energy and momentum profilein the case of the single top (or anti-top) process pp t/tXfollowed by t bH+ b+ can be used to constrainthe mass of the charged Higgs. We pursue this idea, by us-ing two different definitions of the transverse mass. In thefirst case, called m(1)T , this is defined as in [31]:

m2T = 2pT pT (1 cos), (13)where pT , p

T , and are the momenta and angle be-

tween the leptons in the plane perpendicular to the pp col-lision axis. This definition was proposed to determine thetransverse mass of the W boson in pp collisions usingthe decay modes W ee and W . In ourcase, where the charged Higgs decays via H+ + , thecharged lepton is the +, which is not measured experimen-tally. Since, we use the decay + + , we replace thepT by the pT of the +. The resulting m

(1)T -distributions

are shown in the upper two frames in Fig. 19 for the SMbackground (right-hand frame) and the charged Higgs case


Fig. 17 (Color online) Distributions in the ratio E( -jet)/E(b) andpT ( -jet)/pT (b) from the process pp t/tX, followed by the SMdecay t W+b (right-hand frames), and the same distributions for

the decay chain t H+b with the four indicated charged Higgsmasses (left-hand frame)

Fig. 18 (Color online) Distributions in the fractional energy of thesingle-charged prong (+ in +-jet), E()/E( -jet), and in the trans-verse momentum of the single-charged prong, pT ()/pT ( -jet) from

the pp t/tX, followed by the SM decay t W+b (right-handframes), and the same distributions for the decay chain t H+b withthe four indicated charged Higgs masses (left-hand frame)

of 19 Eur. Phys. J. C (2011) 71:1737

Fig. 19 (Color online) Transverse mass distributions for the W in theprocess pp t/t + X followed by the decay t bW+ (right-handframes) and for the H transverse mass for the decay chain t H+b

with the four indicated charged Higgs masses (left-hand frame). Thedefinitions used for defining the transverse masses m(1)T and m

(2)T are

given in the text

(left-hand frame). As seen from the distributions shown inthe left-hand frame, this definition is not useful to see theJacobian peak in the transverse mass of the H. This isanticipated since there are two undetected neutrinos fromthe H vertex. The distributions in m(1)T for the SM (W)-background and the H-signal are different, and they do addto the discriminating power in the BDTD analysis.

For the processes pp(p) t tX and pp(p) t bX, withthe subsequent decay of t b(W+,H+), if one of the twob jets could be associated with the semileptonic decay ofthe top quark, then the on-shell constraint for the top quarkcould be used in the form (pmiss + p + pb)2 = m2t . In thiscase, a transverse Higgs mass can be defined by maximiz-ing the invariant mass, (mHT )

2 = max[(p + pmiss)2], sinceit is bounded from above by the top quark mass, with thecharged Higgs transverse mass satisfying mH+ mHT mt,where mH+ is the true charged Higgs mass. This leads to thefollowing transverse mass definition for mHT [30], which wecall m(2)T ,

(mHT

)2 =(

m2t +( pT + pbT + pmissT

)2 pbT)2

( pT + pmissT)2

. (14)

This expression holds by neglecting the b-quark mass. Wehave calculated the m(2)T distributions, by replacing the pT(which is pT for our case) by pT . These distributions areshown in the lower two frames of Fig. 19, with the SM back-ground (yielding the Jacobian peak of the W) shown on theright-hand frame, and the corresponding Jacobian peaks forthe charged Higgs case, shown in the left-hand frame. Forall the four charged Higgs masses shown in this frame, theJacobian in m(2)T has a sharp peak. Measuring these distribu-tions provides, in principle, an estimate of H. We will usethese distributions in m(2)T to train our BDTD sample.

The distributions generated and discussed have been usedto train the BDTD algorithms and the resulting responsefunctions are shown in Fig. 20. The separation between thesignal and the background improves as mH+ increases, atrend which was also observed in the pp t tX productionprocess.

The corresponding background rejection vs. signal ef-ficiency curves from the processes pp t/tX calculatedfrom the previous BDTD response at

s = 14 TeV are

shown in Fig. 21 for the four charged Higgs masses, as in-dicated on the frames. For a signal efficiency value of 90%,the background rejection varies between 40% and 99% aswe move from mH+ = 90 GeV to mH+ = 150 GeV.


Fig. 20 (Color online) BDTD response functions for pp t/tX, followed by the decay t W+b (SM) and the decay chain t H+b, with theSM background (in shaded blue) and the charged Higgs signal process (in shaded red) for four different charged Higgs masses

Fig. 21 (Color online) SM background rejection vs. charged Higgs signal efficiency for the four charged Higgs masses indicated on the figurefrom the process pp t/tX

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In order to calculate the significance of our signal, wedo the following simplified calculation. We consider againthe less preferred case for tan = 10, with B(t H+b) 0.02 for mH+ = 90 GeV. For the process pp t/tX,our trigger is based on the -jet, coming from the decaysW/H . Since, in the large-tan limit we areworking, B(H+ + ) 1, and the +-decay mode weare concentrating on is + + , which has a branch-ing ratio of 0.25, the product branching ratio t bH+ b(+ ) b(+ ) = 5 103, which is the same as inthe case of top-quark pair production process pp t tX.For an integrated luminosity of 10 (fb)1, and inclusivesingle top cross section (pp t/tX = 300 pb at s =14 TeV, this yields 1.5 104 signal events. For the back-ground events, resulting from the production and the SM de-cays from the process pp t/tX, the corresponding prod-uct branching ratio is 2.5%, again the same as in the caseof top-quark pair production process pp t tX yielding7.5 104 background events. Using the BDTD analysis, weget for a 50% signal efficiency, a background rejection of90%. Thus, our estimated significance will be

S = Nsignal eventsNbackground events

= 7.5 103

7.5 103 85. (15)

A more realistic calculation should consider a factor of 2reduction due to the acceptance cuts, similar to those dis-cussed in Sect. 2.3, as well as the efficiency to tag the b-jet, estimated as 70%, and the efficiency of reconstructinga -jet, estimated as 0.3. This amounts to a factor of about10 reduction in both the number of signal and backgroundevents, resulting in a significance of about 25. Of course,this significance goes down as mH+ increases, keeping tanfixed. Thus, for example, for tan = 10 and mH+ = 150GeV, the reduction in the number of events will be approx-imately 5 (a factor 10 decrease in B(t H+b), compen-sated by a factor 2 increase in the signal efficiency calculatedfrom the BDTD response). Since the background rejectiongoes up to 99%, this would yield S 25, allowing to searchfor a charged Higgs in the decay t bH+, essentially upto a charged Higgs mass close to the kinematic limit.

We would like to stress that our philosophy in this paperis to show how to disentangle the process pp t + X H+b + X from pp t + X W+b + X. In particular,single top production in hadron colliders is subject itself tobackgrounds [7] which we have not considered here. Themost relevant of these backgrounds is the Wbb production.Needless to say that the cos , the polarisation informationon the from the decay , and the transversemass distribution will retain their discriminant power to sup-press them, albeit at the cost of a small loss in the signif-icance of the signal. We plan to take this into account to-gether with a complete treatment of the detector effects in aforthcoming more realistic analysis, which is required to as-sign an error on the charged Higgs mass due to such effects.

4 Summary and outlook

We have reported here an analysis with improved sensitivityto charged Higgs searches in top quark decays t bH+ b+ at the LHC. We concentrate on hadronic decays,in particular, the decay mode , and take intoaccount the polarisation information of the passed onto . The observables which play a dominant role in ouranalysis are the energy and pT of the b-jets from the de-cays t bW+ and t bH+, energy and pT of the -jets from the two decay chains, and the energy and pT ofthe single-charged prong ( coming from the decay chain ). Distributions in these variables arestudied together with angular distribution in cos definedin (1). This information is fed to a multivariate analysis us-ing the BDTD techniques. The BDTD response shows thata clear separation between the t bW+ and t bH+ de-cays can be achieved in both the t tX pair production and thet/tX single top production at the LHC. We have also shownthat using a transverse mass definition, as suggested in [30],the process pp t/tX allows one to determine sharp Jaco-bian peaks for the mass of the H-bosons. With the bench-mark integrated luminosity of 10 fb1 at 14 TeV, the lightcharged Higgs (mH+ < mt mb) can be discovered for allvalues of tan , where the decay mode H is dom-inant.

In estimating the quoted significances, we have assumedthat the decay t bW+ makes up the dominant back-ground. This should be refined by taking into account non-t-backgrounds, such as coming from (Z,W) + jets.Acknowledgements We thank Merlin Kole, Theodota Lagouri andTorbjorn Sjostrand for helpful discussions. This research was partiallysupported by MICINN (Spain) under contract FPA2008-00601.

Open Access This article is distributed under the terms of the Cre-ative Commons Attribution Noncommercial License which permitsany noncommercial use, distribution, and reproduction in any medium,provided the original author(s) and source are credited.

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[hep-ph]

Improved sensitivity to charged Higgs searches in top quark decays t ->b H+ ->b (tau+ nutau) at the LHC using tau polarisation and multivariate techniquesIntroductiontt production and the decay chains t ->b W+/H+ ->b (tau+ nutau) at the LHC Production cross sectionsTop quark decays t ->b (W+, H+) and charged Higgs decays H+ ->cs, tau+nutauEvent generation, triggerDetails of the analysis

Single t/t production and the decay chains t ->b W+/H+ ->b (tau+ nutau) at the LHCCross sections at the LHC

Summary and outlookAcknowledgementsOpen AccessReferences

improved sensitivity to charged higgs searches in top quark decays t→bh+→b(τ+ντ) at the lhc...

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