Improved sensitivity to charged Higgs searches in Top quark decays $t \to bH^+ \to b (\tau^+\nu_\tau)$ at the LHC using $\tau$ polarisation and multivariate tecnniques

We present an analysis with improved sensitivity to the light charged Higgs ($m_{H^+}<m_t-m_b$) searches in the top quark decays $t \to b H^+ \to b (\tau^+\nu_\tau) + ~{\rm c.c.}$ in the $t\bar{t}$ and single $t/\bar{t}$ production processes at the LHC. In the Minimal Supersymmetric Standard Model (MSSM), one anticipates the branching ratio ${\cal B} (H^+ \to \tau^+\nu_\tau)\simeq 1$ over almost the entire allowed $\tan \beta $ range. Noting that the $\tau^+$ arising from the decay $H^+ \to \tau^+\nu_\tau$ are predominantly right-polarized, as opposed to the $\tau^+$ from the dominant background $W^+ \to \tau^+\nu_\tau$, which are left-polarized, a number of $H^+/W^+ \to \tau^+\nu_\tau$ discriminators have been proposed and studied in the literature. We consider hadronic decays of the $\tau^\pm$, concentrating on the dominant one-prong decay channel $\tau^\pm \to \rho^\pm \nu_\tau$. The energy and $p_T$ of the charged prongs normalised to the corresponding quantities of the $\rho^\pm$ are convenient variables which serve as $\tau^\pm$ polariser. We use the distributions in these variables and several other kinematic quantities to train a boosted decision tree (BDT). Using the BDT classifier, and a variant of it called BDTD, which makes use of decorrelated variables, we have calculated the BDT(D)-response functions to estimate the signal efficiency vs. the rejection of the background. We argue that this chain of analysis has a high sensitivity to light charged Higgs searches up to a mass of 150 GeV in the decays $t \to b H^+$ (and charge conjugate) at the LHC. For the case of single top production, we also study the transverse mass of the system determined using Lagrange multipliers.


I. INTRODUCTION
m H + = 80 − 155 GeV and B(H + → τ + ν τ ) = 1. This excludes a small region (tan β > 35 and m H + = 100 − 120 GeV) [6]. Thus, it is fair to conclude that the searches of the charged Higgses over a good part of the m H ± -tan β plane in the MSSM is a programme that still has to be carried out and this belongs to the LHC experiments. In anticipation, searches for the H ± in pp collisions at E cm = 7 − 14 TeV at the LHC have received a lot of attention [7][8][9][10][11][12].
There are two regions, namely m H + < m t − m b , which will be looked into in both the tt pair production and in single top (or anti-top) production in pp collisions, followed by the decays t → bH + and H + → τ + ν τ , and for m H ± above the top quark mass, in which case H ± production mainly takes place through the process gb → tH + , followed dominantly by the decay H + → tb. However, despite larger branching fraction, it may be hard to distinguish the H + → tb mode from the bckground. For large tan β, the decay mode H + → τ + ν τ becomes discernible. In this paper, we will concentrate on the light H ± -scenario.
The decay channel H ± → τ ± + ν τ will play the key role in the searches of the light H ± -bosons. The τ + leptons arising from the decays W + → τ + ν τ and H + → τ + ν τ are predominantly left-and right-polarised, respectively. Polarisation of the τ ± influences the energy distributions in the subsequent decays of the τ ± . Strategies to enhance the H ±induced effects in the decay t → b(W + , H + ) → b(τ + ν τ ), based on the polarisation of the τ + have been discussed at length, starting from the pioneering work [13][14][15][16] to the production and decays of a tt pair at the hadron colliders Tevatron and the LHC [17][18][19][20][21]. Also the effects of the (QED and QCD) radiative corrections on such distributions in the dominant (one-charged prong) decay channels τ + → π + ν τ , ρ + ν τ , a + 1 ν τ and +ν ν τ have been worked out [22]. Following these studies, the construction of the τ ± -jet (as well as b-jet) are of central importance in H ± -searches. We use the dominant single-charged-prong decay τ ± → ρ ± ν τ as the τ ± polariser. As ρ ± → π ± π 0 is the dominant decay mode, the energy and transverse momentum of the π ± in the τ ± -jet become quantities of main interest for our study. Likewise, the distribution in the angle ψ, defined as plays an important role in our analysis. Since the energy-momentum vectors of the b-jet and the ρ ± can be measured, this distribution is measurable at the LHC. We also note that this distribution is different from the conventional definition of the angle ψ [23], in which the invariant mass m 2 b is measured instead of m 2 ρb . The other distributions that enter in our analysis are listed in the next section.
Having generated these distributions, characterising the signal t → bH + → b(τ + ν τ ) → b(ρ +ν τ )ν τ ) and the background t → bW + → b(τ + ν τ ) → b(ρ +ν τ )ν τ ) events, we use a technique called the Boosted Decision Tree (BDT) -a classification model used widely in data mining [24] -to develop an identifier optimised for the t → bH + decays. In our calculation, we use both BDT and a variant of it called BDTD (here D stands for decorrelated), where possible correlations in the input variables are removed by a proper rotation obtained from the decomposition of the square root of the covariance matrix, to discriminate the signal events from the large backgrounds. We recall that this technique has been successfully used to establish the single top quark production in pp collisions at the Tevatron [25,26] (see [27] for details). Recently, we have applied this technique to a feasibility study of measuring the CKM matrix element |V ts | from the decay t → W s at the LHC@14 TeV, and have estimated that a benchmark with 10% accuracy for this decay mode with a 10 3 rejection of the background t → W b can be achieved with an integrated luminosity of 10 (fb) −1 [28].
We show in this paper that a similar BDTD-based analysis holds great promise in light-H ± searches at the LHC both in the pp → ttX pair production and in the single top (or antitop) production pp → t/tX. Furthermore, we show that using a transverse mass definition, as suggested in [29], the process pp → t/tX followed by the decays t → bH + , bW + , allows one to determine rather sharp Jacobian peaks for the transverse mass of the H ± -bosons.
The conventional definition of the transverse mass [30], which was very helpful in the determination of the transverse mass of the W ± bosons, is less suited for constructing the corresponding mass of the H ± bosons.
We note that an analysis using an iterative discriminat analysis method similar to the one presented here was carried out by Hesselbach et al. [31]. In particular, detailed Monte Carlo comparisons of several variables incorporating the spin effects in charged Higgs boson production were presented to separate the tbH + signal from the standard model tt background both at the Tevatron ( √ s = 1.96 TeV) and the LHC ( √ s = 14 TeV). However, there are several significant differences in the two studies, such as the distribution in cos ψ (defined in eq. (1)), which plays an important role in our analysis. In addition, we have studied the case of single top production at the LHC, pp → t/t + X, followed by the decays , which was not considered in Ref. [31].
This paper is organised as follows: In section 2, we analyse the process pp → ttX at the LHC, followed by the decay chains t → bW + , bH + , and the subsequent decays (H + , W + ) → τ + ν τ , together with the BDTD-based analysis of the signal (t → bH + ) and the SM decay background (t → bW + ). The BDTD response functions are then used to work out the signal efficiency vs. the background rejection. In section 3, we repeat this analysis for the single top (or anti-top) production pp → t/tX at the LHC. Section 4 contains a brief summary.  [34]. Compared to the tt production cross section at the Tevatron, this is larger by two orders of magnitude. The cross sections at the lower LHC energies, 7 and 10 TeV, have also been calculated [34,38], with σ(pp → ttX) 400 pb at 10 TeV and about half that number at 7 TeV. Thus, for the top quark physics, the dividends in going from 7 to 14 TeV are higher by a good factor 4.
B. Top quark decays t → b(W + , H + ) and charged Higgs decays H + → cs, τ + ν τ Top-quark decays within the Standard Model are completely dominated by the mode due to V tb = 1 to a very high accuracy. In beyond-the-SM theories with an extended Higgs sector, a light charged Higgs can also be produced via The relevant part of the interaction Lagrangian is [18]: where A, B and C are model-dependent parameters which depend on the fermion masses and tan β: (7) where λ (x, y, z) = x 2 + y 2 + z 2 − 2xy − 2xz − 2yz is the triangle function. The total top quark decay width in the Born approximation is obtained by adding the two partial widths Γ tot, Born QED corrections in the total decay width of the top quark are numerically small. The O(α s ) QCD corrections were calculated in [39,40] (see, also Ref. [41]) and have the form: Thus, in the branching ratio B(t → bH + ), also this QCD correction drops out. However, radiative corrections coming from the supersymmetric sector to B(t → bH + ) are rather important. They have been calculated in great detail in the literature, in particular for the MSSM scenario in [42][43][44], and can be effectively incorporated by replacing the b-quark mass m b in the Lagrangian for the decay t → bH + by the SUSY-corrected mass m corrected The correction ∆ b is a function of the supersymmetric parameters and, for given MSSM scenarios, this can be calculated using the FeynHiggs programme [45]. In particular, for large values of tan β (say, tan β > 20)), the MSSM corrections increase the branching ratio for t → bH + significantly. This, for example, can be seen in a particular MSSM scenario in a recent update [46], from where we show B(t → bH + ) as a function of tan β, calculated for m t = 175 GeV and various assumed values of the charged Higgs mass, indicated in Fig. 1.
Since we are treating the case of the light charged Higgs, there are essentially only two decay modes which are important: H + → τ + ν τ and H + → cs. The branching ratio of interest to us B(H + → τ + ν τ ) is given by [18]: For the numerical values of tan β that we entertain in this paper, the branching ratio B(H + → τ + ν τ ) = 1, to a very high accuracy.

C. Event generation, trigger
We consider in this section the process pp → ttX, with both the t andt decaying into W b.
Our trigger is the leptonic decay W − → e −ν e or W − → µ −ν µ . The other W + decays via W + → τ + ν τ . This makes up our main background. The signal events are generated in which one of the t ort decays via W + → bH + (or its charge conjugate W − → bH − ), see Fig. 2.
The othert or t then decays leptonically, as in our trigger. In the Minimal Supersymmetric Standard Model (MSSM), for large tan β and m H + < m t , the branching ratio for the decay H + → cs is small and one anticipates the branching ratio B(H + → τ + ν τ ) 1. This is the parameter space in which the analysis reported here is valid. Noting that the τ + arising from the decay H + → τ + ν τ are predominantly right-polarized, as opposed to the τ + from the dominant background W + → τ + ν τ , which are left-polarized, a number of H + /W + → τ + ν τ discriminators have been proposed and studied in the literature. We have used the dominant single-charged-prong decay τ + → ρ + ν τ as the τ + polariser. Having set these branchings, we have generated 50K events for the process pp → tt → bW + (bW − ), with all of them decaying according to the chain described earlier, i.e., W − → e − ν e and W + → τ + ν τ , with all the τ 's forced to decay into ρ + ν τ (here and below, charge conjugates are implied). In calculating the required luminosity, we take into account the corresponding branching ratios, which are as follows [1] B(W + → e + ν e ) = (10.75 ± 0.13)% , We also generate the same number (50K) signal events, for each of the following charged Higgs masses: m H + = 90, 110, 130, 150 GeV. As for the background process, we force the τ + to decay into ρ + ν τ 100% of the time. These events are generated using PYTHIA 6.4 [47] and for the decays of the τ ± , we use the programme called TAUOLA [48] to incorporate the τ ± polarization information on the decay distributions.
We impose the following acceptance and trigger cuts: • |η | < 2.5, with = e, τ • |η b,b | < 2.5 • P Te > 20 GeV • P Tρ > 10 GeV In order to discriminate the signal and background, we have studied a number of distributions, summarized below.
• Distribution in the angle ψ, defined in eq. 1. This is defined for both the decay Since the energy-momentum vectors of the b-jet and the ρ ± can be measured, this distribution is measurable at the LHC. We also note that this distribution is different from the conventional definition of the angle ψ [23], in which the invariant mass m 2 b is measured instead of m 2 ρb .
• Energy and p T of the b-jets from the decays t → bW + and t → bH + .
• The ratio of the energy and p T of the τ + jets and their accompanying b-jet.
• As a measure of the τ polarisation, we consider the fractional energy and transverse momentum of the single-charged prong (π + in τ + -jet).
• For the case of single top production, we also study the transverse mass of the system determined using Lagrange multipliers [29].
• These distributions are used to train a boosted decision tree (BDT). Using the BDT classifier, and a variant of it called BDTD, which makes use of decorrelated variables, we have calculated the BDT(D)-response functions to estimate the signal efficiency vs. the rejection of the background.
The strategy adopted by us to search for the decays t → bH + is somewhat different from the traditional cut-based analysis, as, for example, reported in [8]. There the idea is to suppress the SM-background as much as possible, making use of additional variables, such as the missing E T , satisfying E miss T > 50 GeV. Our idea is, instead, to train a boosted decision tree classifier for both the signal and background events. Eventually, for a realistic analysis of the LHC data, we may have to reintroduce some of the cuts to suppress other non-tt background, such as coming from the process pp → W ± + jets, which may also fake our signal.

D. Details of the Analysis
In Fig. 3 (right-hand frame), we show the cos ψ distributions for the standard model (SM) In the left-hand frame, we show the same distribution when one of the t ort decays via the chain   In Fig. 4 (right-hand frames), we show the distributions in the energy of the b-jet, E(b), and the transverse momentum of the b-jet, p T (b) from the SM process process pp → ttX, followed by the decay chain discussed above. In the left-hand frames, the corresponding distributions are shown for the charged Higgs case. We remark that for the charged Higgs case these distributions are softer than those from the SM due to the different helicity structure of the decays. This effect becomes stronger as m H + increases due to phase space. As a result, these distributions add to the discrimination power of the BDTD analysis. Note that these distributions 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 distributions in the energy of the τ -jet, E(τ − jet), and in the transverse momentum of the τ -jet, p T (τ − jet) from the SM process, followed by the decay chain discussed above. In the left-hand frames, the corresponding distributions are shown for the charged Higgs case. In these distributions, the energy and p T -spectra of the τ -jet coming from the charged Higgs decays are harder than those coming from the SM process, and this difference becomes more marked as m H + increases. This complementary behaviour is expected for the same reason as discussed earlier for Fig. 4, again reflecting the differences in helicity and phase space. It goes without saying that these distributions increase the discrimination power of the BDTD analysis. To make this effect more marked, we show the ratio of the energy and p T -spectra involving the τ -and b-jets in 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 different shapes of the distributions SM vs. Higgs. For example, putting a lower cut on the whereas the charged Higgs-induced distributions surviving this cut are considerably larger, with the discrimination becoming stronger as m H + increases.
In Fig. 7, we show the distributions in the fractional energy of the single-charged prong (π + in τ + -jet), E(π)/E(τ − jet), and in the transverse momentum of the single-charged prong, p T (π)/p T (τ −jet) from the SM process (right-hand frames) and those coming from the charged Higgs-induced process (left-hand frames) for m H + = 90 GeV. As remarked earlier. we are using the dominant single-charged-prong decay τ + → ρ +ν τ as the τ + polariser. As already noted in [14], the fractional energy distributions in z = E A /E τ , from the τ -decay products τ → A+ missing energy, the effect of the τ ± polarization is most marked for the decays τ + → π +ν τ and τ + → ρ +ν τ . This has been worked out in the collinear limit, i.e., for E τ /m τ 1. Our variables differ from the one used in [14], in that we normalize to the visible τ -energy and the visible p T (τ − jet), and not to the total τ -energy. With our normalization, the π + -energy measured in the decays τ + → π +ν τ will be a delta function, peaked at 1 in the variables shown in Fig. 7, and hence we concentrate on the decay chain τ + → ρ +ν τ . These distributions also provide strong discriminants for the BDTD analysis. Briefly, the generated input is used for the purpose of training and testing the samples.
We provide the input in terms of the variables discussed earlier for the signal (t → bH + ) and the background (t → bW + ), obtained with the help of a Monte Carlo generator. This information is used to develop the splitting criteria to determine the best partitions of the data into signal and background to build up a decision tree (DT). The separation algorithm m H + will, however, be compensated to some extent by the decreasing branching ratio for the decay t → bH + , as shown in Fig. 1 [46], obtained by using FeynHiggs [50].
The corresponding background rejection vs. signal efficiency curves from the process for the four charged Higgs masses, as indicated on the frames. For a signal efficiency value of 90%, the background rejection varies between 50% and 90% as we move from m H + = 90 GeV to m H + = 150 GeV.
In order to calculate the significance of our signal, we do the following simplified calculation. We consider the less preferred case for tan β = 10, for which the branching ratio Fig. 1). For the process pp → ttX, the trigger is based on the decay t → bW + → b + ν , with + = e + , µ + , which has a summed branching ratio of about 0.2. Since, in the large-tan β limit we are working, B(H + → τ + ν τ ) 1, and the τ + -decay mode we are concentrating on is τ + → ρ +ν τ , which has a branching ratio of 0.25, the product branching ratio t → bH + → b(τ + ν τ ) → b(ρ +ν τ )ν τ = 5 × 10 −3 , which taking into account the trigger is reduced to 1.0 × 10 −3 . For an integrated luminosity of 10 (fb) −1 at √ s = 14 TeV, and summing over the charge conjugated modes yielding a factor 2, this yields 2 × 10 4 signal events. For the background events, resulting from the production and the SM decays from the process pp → ttX, the corresponding product branching ratio is 2.5%, which together with the trigger branching gives 5 × 10 −3 , resulting in 10 5 background events, where we have again taken into account the factor 2 from the sum of the charge conjugated states. Using the BDTD analysis, we get for a 50% signal efficiency, a background rejection of 90%. Thus, our estimated significance will be S = N signal events N background events = 10 4 √ 10 4 100 .
A more realistic calculation should consider a factor of 2 reduction due to the acceptance cuts, discussed in section A, as well as the efficiency to tag two b-jets which is another factor of 2, and the efficiency of reconstructing a τ − jet, estimated as 0.3 [7]. This amounts to a factor of about 10 reduction in both the number of signal and background events, resulting in a significance of about 30. This is high enough to take another factor 2 reduction due to various other cuts, which will be inevitable in a detector-based analysis taking into account non-tt backgrounds, not estimated here. Of course, this significance goes down as m H + increases, keeping tan β fixed. Thus, for example, for tan β = 10 and m H + = 150 GeV, the reduction in the number of events will be approximately 5 (a factor 10 decrease in B(t → H + b), compensated by a factor 2 increase in the signal efficiency calculated from the BDTD response). This would yield S 6, which is just above the discovery limit for a charged Higgs below the top quark mass.
A number of checks has been performed in order to test the robustness of the results. For instance, the cut on the minimum transverse momentum of the τ -jet has been raised from 10 GeV to 20 GeV. The corresponding figure displaying the background rejection vs. the charged Higgs signal efficiency is shown in Fig. 10. A comparison with Fig. 8, obtained with a 10 GeV cut on the minimum transverse momentum of the τ -jet, shows that the two figures are very similar. The price to pay for the acceptance is, relatively speaking, minor, going down from 0.6 to 0.5. We had conservatively 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 data currently. As of preparing this report, the integrated luminosity of the LHC is above 1 inverse femtobarn, and the projection for end 2012 is of order 10 inverse femtobarns. We have generated events at √ s = 7 TeV, and have calculated all the distributions presented earlier for 14 TeV. The shapes of these distributions are essentially similar. This is reflected in the BDTD response functions for the SM background and the charged Higgs signal, presented in Fig. 11, and in the SM background rejection vs. the charged Higgs signal efficiency, shown in Fig. 12.
However, the cross sections for pp → ttX at 7 TeV is approximately a factor 4 smaller than at 14 TeV [34,38]. This implies that our calculations for the significance obtained at √ s = 14 TeV have to be divided by a factor 2 to get the corresponding significance at √ s = 7 TeV. This will reduce the sensitivity of the charged Higgs in tan β-m H + plane.
For example, for m H + close to the kinematic limit m t − m b , a signal is expected only for tan β > 20. charged-prong hadronic decays of the τ ± are essentially made up of the decays τ ± → π ± +ν τ (with a branching ratio of 10.9%), τ ± → ρ ± (→ π ± π 0 ) + ν τ decays (with a branching ratio of 25.5%) and τ ± → a ± 1 (→ π ± π 0 π 0 ) + ν τ decays (with a branching ratio of 9.3%). Separating the π ± ν τ mode from the ρ ± ν τ mode should, in principle, be possible due to the lack of deposited energy in the π 0 or electromagnetic cluster accompanying the π ± in the former, but separating the ρ ± ν τ mode from the a ± 1 ν τ mode will not be easy. Fortunately, the branching ratio of the latter is only 40% of the former. So, the number of π 0 clusters (0, 1 and 2) will have to be included in the analysis as a new variable. The τ ± → ρ ± ν τ decays dominate the one charged track (π ± , K ± ) and one electromagnetic or π 0 cluster. However, we stress that the BDT can be trained to reduce the dilution.
In a realistic analysis, a further source of reduction in our estimates of the significance would come from the wrong assignment of the b-jet charges, though this effect is minor compared to the ones discussed above. The b-jet charge identification efficiency is estimated at present to be around 65% [7], using standard techniques based on a weighted average of the charges of the particles in the jet, with the weights being proportional to their momenta.
However, a simple algorithm can be designed, which takes into account in addition the angular correlations between the trigger lepton, the tau-jet and the charges, reducing the b-jet mis-assignment to about 20% for the charged Higgs masses close to the W ± mass. For higher charged Higgs masses, this can be further brought down by simply taking the b-jet with the smaller (larger) transverse momentum to be that associated with the charged Higgs (resp. W ± ) boson.
We also mention that we have not considered the background from the process pp → tt → (b ν )(bjj). However, it has been shown in [7] that this background can be well separated in a standard cut analysis from the pp → tt → (b ν )(bτ ν τ ) process. With our TMVA approach, this background will be tamed though we will have to introduce also the missing E T as a variable in the BDT training. We are aware of the non-tt background, which are dominated by the Z + jets and W + jets. These have been studied in great detail in [8], with the conclusion that they can be brought below the signal by the additional use of the E miss T -cut. We have not used the E miss T -cut, as we have concentrated only on the SM ttX background, but will do so in a more realistic detector-based analysis in the future.

III. SINGLE t/t PRODUCTION AND THE DECAY CHAINS
A. Cross sections at the LHC The single top (or anti-top) cross sections in hadron hadron collisions have been calculated in the NLO approximation [51][52][53][54][55]. Recalling that there are three basic processes at the leading order which contribute to σ(pp → t/tX), namely the t-channel: qb → q t, the schannel: qq →bt; and the associated tW production bg → tW − , the cross section estimated at the Tevatron is [56]: σ(pp → tX) = σ(pp →tX) 1.8 pb for both the top and anti-top production. At the LHC@14 TeV, one estimates σ(pp → tX) 200 pb and about half this number for σ(pp →tX), yielding the summed single top and anti-top cross sections at about 300 pb, also approximately two orders of magnitude larger than those at the Tevatron. With a luminosity of 10 fb −1 , one anticipates O(3 × 10 6 ) single top (or anti-top) events.
As mentioned in the introduction, there are three different mechanisms of producing a single top (or anti-top) quark in hadronic collisions, the s-channel, the t-channel, and the associated production tW -channel. The Feynman diagram for the dominant t-channel partonic process qb → q t, followed by the decay t → b(H + → τ + ν τ ) is shown in Fig. 13.
The partonic cross section is then convoluted with the parton distribution functions to calculate the cross sections in pp → t + X and pp →t + X. Since, we are using PYTHIA 6.4 [47] 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, but the total cross sections are normalized to the theoretical calculations, the estimates presented here should hold approximately. Since most of the distributions calculated by us for the processes pp → ttx and pp → t/tX are in the same variables, we comment only briefly on the distributions for the signal t → bH + → bτ + ν τ and the background process 13: Feynman diagram for qb → q t, followed by the decay t → b(H + → τ + ν τ ).
In Fig. 14, we show the distribution dN/d cos ψ for the pp → t/t + X production as measured in the decay chain for the SM background process t → bW → b(τ ν τ ) → b(ρν τ )ν τ ) (right-hand frame), and for the signal t → bH → b(τ ν τ ) → b(ρν τ )ν τ ) (left-hand frame) for four different charged Higgs masses, as indicated on the figure. The SM background in the process pp → t/t + X falls more steeply as a function of cos ψ than is the case for the tt production pp → tt + X, due to the acceptance cuts. The trend is similar in the signal process. However, also in the single top (or anti-top) production, this distribution provides a good discriminant as input to the BDTD analysis.
The distributions in the energy of the b-jet, E(b), and transverse momentum of the bjet, p T (b) from the process pp → t/tX, followed by the SM decay t → W + b are shown in The distribution dN/d cos ψ for the pp → t/t + X production as measured in the decay four different charged Higgs masses, as indicated on the figure (left-hand frame).
essentially reflect the kinematics of the decays t → W + b and t → H + b.
One important difference between the analysis of the single top (or anti-top) production compared to the tt production process lies in the fact that the missing transverse energy and momentum can be ascribed in the former to the τ -neutrino, ν τ . This is different in the case of the tt production, as one of the t-ort-quarks decays via t → bW + → b + ν , which is used as a trigger. Thus, the missing transverse energy or momentum can not be traced to the decay of the τ -lepton alone in the case of tt production. As already stated in [29] the missing transverse energy and momentum profile in the case of the single top (or anti-top) process pp → t/tX followed by t → bH + → bτ + ν τ can be used to constrain the mass of the charged Higgs. We pursue this idea, by using two different definitions of the transverse mass. In the first case, called m (1) T , this is defined as in [30]: where p T , p ν T , and φ ν are the momenta and angle between the leptons in the plane perpendicular to the pp collision axis. This definition was proposed to determine the transverse mass of the W ± boson in pp collisions using the decay modes W ± → e ± ν e and W ± → µ ± ν µ .
In our case, where the charged Higgs decays via H + → τ + ν τ , the charged lepton is the τ + , which is not measured experimentally. Since, we use the decay τ + → ρ +ν τ , we replace the p T by the p T of the ρ + . The resulting m (1) T -distributions are shown in the upper two frames in Fig. 19 for the SM background (right-hand frame) and the charged Higgs case (left-hand frame). As seen from the distributions shown in the left-hand frame, this definition is not useful to see the Jacobian peak in the transverse mass of the H ± . This is anticipated since there are are two undetected neutrinos from the H ± vertex. The distributions in m this frame, the Jacobian in m T has a sharp peak. Measuring these distributions provides, in principle, an estimate of H ± . We will use these distributions in m (2) T to train our BDTD sample.
The distributions generated and discussed have been used to train the BDTD algorithms and the resulting response functions are shown in Fig. 20. The separation between the signal and the background improves as m H + increases, a trend which was also observed in the pp → ttX production process.
The corresponding background rejection vs. signal efficiency curves from the processes pp → t/tX calculated from the previous BDTD response at √ s = 14 TeV are shown in A more realistic calculation should consider a factor of 2 reduction due to the acceptance cuts, discussed in section A, as well as the efficiency to tag the b-jet, estimated as 70%, and the efficiency of reconstructing a τ − jet, estimated as 0.3. This amounts to a factor of about 10 reduction in both the number of signal and background events, resulting in a significance of about 25. Of course, this significance goes down as m H + increases, keeping tan β fixed. Thus, for example, for tan β = 10 and m H + = 150 GeV, the reduction in the number of events will be approximately 5 (a factor 10 decrease in B(t → H + b), compensated by a factor 2 increase in the signal efficiency calculated from the BDTD response). Since the background rejection goes up to 99%, this would yield S 25, allowing to search for a charged Higgs in the decay t → bH + , essentially up to a charged Higgs mass close to the kinematic limit. We would like to stress that our philosophy in this paper is 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 to backgrounds [7] which we have not considsered here. The most relevant of these backgrounds is the W bb production. Needless to say that the cos ψ, the polarisation information on the τ ± from the decay τ ± → ρ ± ν τ , and the transverse mass distribution will retain their discriminant power to suppress them, albeit at the cost of a small loss in the significance of the signal. We plan to take this into account together with a complete treatment of the detector effects in a forthcoming more realistic analysis, which is required to assign an error on the charged Higgs mass due to such effects.

IV. SUMMARY AND OUTLOOK
We have reported here an analysis with improved sensitivity to charged Higgs searches in top quark decays t → bH + → bτ + ν τ at the LHC. We concentrate on hadronic τ ± decays, in particular, the decay mode τ ± → ρ ± ν τ , and take into account the polarisation information of the τ ± passed on to ρ ± . The observables which play a dominant role in our analysis are the energy and p T of the b-jets from the decays t → bW + and t → bH + , energy and p T of the τ ± -jets from the two decay chains, and the energy and p T of the single-charged prong (π ± coming from the decay chain τ ± → ρ ± ν τ → π ± ν τ ). Distributions in these variables are studied together with angular distribution in cos ψ defined in eq. 1. This information is fed to a multivariate analysis using the BDTD techniques. The BDTD response shows that a clear separation between the t → bW + and t → bH + decays can be achieved in both the ttX pair production and the t/tX single top production at the LHC. We have also shown that using a transverse mass definition, as suggested in [29], the process pp → t/tX allows one to determine sharp Jacobian peaks for the mass of the H ± -bosons. With the benchmark integrated luminosity of 10 fb −1 at 14 TeV, the light charged Higgs (m H + < m t − m b ) can be discovered for all values of tan β, where the decay mode H ± → τ ± ν τ is dominant.
In estimating the quoted significances, we have assumed that the decay t → bW + makes up the dominant background. This should be refined by taking into account non-tbackgrounds, such as coming from (Z, W ) + jets.