Irreducible background and interference effects for Higgs-boson production in association with a top-quark pair

We present an analysis of Higgs-boson production in association with a top-quark pair at the LHC investigating in particular the final state consisting of four b jets, two jets, one identified charged lepton and missing energy. We consider the Standard Model prediction in three scenarios, the resonant Higgs-boson plus top-quark-pair production, the resonant production of a top-quark pair in association with a b-jet pair and the full process including all non-resonant and interference contributions. By comparing these scenarios we examine the irreducible background for the production rate and several kinematical distributions. With standard selection criteria the irreducible background turns out to be three times as large as the signal. For most observables we find a uniform deviation of eight percent between the scenario requiring two resonant top quarks and the full process. In particular phase-space regions the non-resonant contributions cause larger effects, and we observe shape changes for some distributions. Furthermore we investigate interference effects and find that neglecting interference contributions results in an over-estimate of the total cross-section of five percent.


Introduction
The discovery of the long-sought Higgs boson at the LHC in July 2012 [1,2] ushered in a new era of probing the mechanism of spontaneous symmetry breaking and thus mass generation in nature. The determination of the properties of the discovered Higgs boson is a major goal of the LHC. Especially the couplings of the Higgs boson to matter particles are important for the understanding of the origin of mass. The production of a Higgs boson in association with a top-quark pair is of particular interest, since it allows to directly access the topquark Yukawa coupling. Although the production rate is small and the measurement is experimentally challenging, ATLAS [3][4][5] and CMS [6][7][8][9][10] have already performed searches using the data of the LHC runs at 7 and 8 TeV. With the upcoming run 2 of the LHC at 13 TeV the determination of the ttH signal and the potential measurement of the top-quark Yukawa coupling will be pursued.
The production of a Higgs boson in association with a top-antitop pair has been studied theoretically by many authors. Leading-order (LO) predictions for the production of ttH for stable Higgs boson and top quarks have been presented in Refs. [11][12][13][14][15] while the corresponding next-to-leading-order (NLO) corrections have been calculated in Refs. [16][17][18][19][20]. More recently the matching of the NLO corrections to parton showers has been performed [21,22]. Very recently also electroweak corrections to ttH have been elaborated [23,24]. NLO QCD corrections for the most important irreducible background process, ttbb production in LO QCD, have been worked out [25][26][27][28] and matched to parton showers [29][30][31]. A combined analysis of ttH and ttbb production was carried out in Ref. [32]. Further analyses and results can be found in the yellow reports of the LHC Higgs Cross Section Working Group [33][34][35].
In this article we study Higgs-boson production in association with a top-quark pair (ttH) including the subsequent semileptonic decay of the top-quark pair and the decay of the Higgs boson into a bottom-antibottom-quark pair, pp → ttH → ℓ + ν ℓ jjbbbb. (1.1) The final state under consideration consists of six jets, four of which are b jets, one identified charged lepton (electron or muon) and missing energy, and our primary goal is the study of the irreducible background. We consider this process in three different scenarios. In the first scenario we include the complete Standard Model (SM) contributions, comprising all resonant, non-resonant and interference contributions to the 8-particle final state. For the second scenario we require the intermediate resonant production of a top-quark pair in association with a bottom-quark pair. We employ the pole approximation for the top quarks and include the leptonic/hadronic decay of the top/antitop quark. Similar approaches have been used for tt production in association with massless particles at NLO QCD [36,37].
In the third scenario, corresponding to the signal, we require in addition to the resonant top-quark pair an intermediate resonant Higgs boson decaying into a bottom-quark pair and employ the pole approximation for the Higgs boson as well. We use the matrix-element generator RECOLA [38] to compute all matrix elements at leading order in perturbation theory.
Comparing the predictions in the three scenarios allows us to examine the size of the irreducible background for Higgs production in association with a top-antitop-quark pair. Further we determine the quality of the approximations compared to the calculation of the full process and quantify deviations for the total cross section and differential distributions. We investigate the total cross section and differential distributions for the LHC operating at 13 TeV with particular emphasis on distributions that allow to enhance the signal over the irreducible background. We study, in particular, different methods of assigning a b-jet pair to the Higgs boson and compare their performance in reconstructing the Higgs signal. Furthermore, we investigate the size of interference effects between contributions to the matrix elements of different order in the strong and electroweak coupling constants.
The paper is organised as follows. In Section 2 we specify the setup of our calculation and identify the various partonic contributions to the signal process. In Section 3 we present numerical results for the total cross section and kinematical distributions and quantify the size of the irreducible background. Our conclusions are presented in Section 4. In Appendix A we explain in detail the on-shell projections needed for the pole approximations we apply and in Appendix B we present additional results.

Notation and setup
This section provides some technical details about our computation. We consider gluons and light (anti-)quarks (u, d, c, s) to be the only constituents of the proton and disregard contributions from bottom quarks and photons in the parton distribution functions. We neglect flavour mixing as well as finite-mass effects for the light quarks and leptons. The considered matrix elements involve (multiple) resonances of electroweak gauge bosons, top quarks and the Higgs boson. For the consistent description of these resonances we use the complex-mass scheme [39][40][41] where all masses of unstable particles are defined by the poles of the propagators in the complex plane, µ 2 = m 2 − imΓ. In addition, all couplings, and, in particular the weak mixing angle, are consistently derived from the complex masses and thus are complex, too.
We consider three scenarios to calculate the process pp → ℓ + ν ℓ jjbbbb: • In the first scenario, the full process, we include all SM contributions to the process pp → ℓ + ν ℓ jjbbbb. Counting u, d, c, and s quarks separately, we distinguish 48 partonic channels. Eight channels can be constructed from gg → ℓ + ν ℓ q ′q′′ bbbb and 40 from qq → ℓ + ν ℓ q ′q′′ bbbb using crossing symmetries and substituting different quark flavours. Matrix elements involving external gluons receive contributions of O α s α 3 , O α 2 s α 2 and O α 3 s α , whereas amplitudes without external gluons receive an additional O α 4 term of pure electroweak origin. Some sample diagrams are shown in Figures 1a-1c.
• In the second scenario we only take those diagrams into account that contain an intermediate top-antitop-quark pair. The resulting amplitude, labelled ttbb production in the following, corresponds to the production of a bottom-antibottom pair and an intermediate top-antitop pair followed by its semileptonic decay, i.e.  Figure 1: Representative Feynman diagrams for (a)-(c) the full process (top), (d)-(f) ttbb production (middle) and (g)-(i) ttH production (bottom).
pp → ttbb → ℓ + ν ℓ jjbbbb. Some sample diagrams are shown in Figures 1d-1f. Note that we use the pole approximation for the top quarks only, hence we take into account all off-shell effects of the remaining unstable particles. The details of our implementation of the pole approximation are described in Appendix A. This scenario involves 10 partonic channels, comprising 2 gluon-fusion and 8 quark-antiquark-annihilation channels. As a consequence of the required top-antitop-quark pair the amplitudes receive no contribution of O α 3 s α .
• Finally, we consider the signal process pp → ttH → ℓ + ν ℓ jjbbbb and label it ttH production. In addition to the intermediate top-antitop-quark pair we require an intermediate Higgs boson decaying into a bottom-antibottom-quark pair and use the pole approximation for the top-quark pair and the Higgs boson. Here the same 10 partonic channels as in the previous case contribute. The requirement of the Higgs boson eliminates contributions of the O α 2 s α 2 from the amplitude. The implementation of the pole approximation applied to the Higgs boson is explained in Appendix A, and some sample diagrams are shown in Figures 1g-1i.
The full process involves partonic channels with up to 78,000 diagrams. All matrix elements are calculated with RECOLA [38] which provides a fast and numerically stable computation. RECOLA computes the matrix elements using recursive methods, i.e. the complexity does not scale with the number of Feynman diagrams, and allows to specify intermediate particles for a given process. The phase-space integration is performed with an in-house multi-channel Monte-Carlo program. Here the number of diagrams matters for the construction of the integration channels.

Results
We present results for the LHC operating at 13 TeV. For the calculation of the hadronic cross section we employ LHAPDF 6.0.5 with the CT10 LO parton distributions (LHAPDF ID 10800). Following Ref. [17] we use a fixed renormalisation and factorisation scale The corresponding value of the strong coupling constant α s provided by LHAPDF reads All other masses and widths in (3.3) are considered as pole values. The width of the top quark Γ t in (3.3) for unstable W bosons is computed at leading order according to Ref. [43], i.e.
λ(ǫ, y) = 1 + y 2 + ǫ 4 − 2(y + ǫ 2 + yǫ 2 ). (3.6) The masses and widths of all other quarks and leptons are neglected. We derive the electromagnetic coupling α from the Fermi constant in the G µ scheme [44], We impose cuts on the transverse momenta and rapidities of leptons, jets, b jets and missing transverse momentum as well as distance cuts between all jets in the rapidityazimuthal plane, with the distance between two jets i and j defined as where φ i and y i denote the azimuthal angle and rapidity of jet i, respectively. Our selection of cuts represents standard acceptance cuts and is neither deliberately chosen to enhance the contribution of ttH production nor to suppress any background process: (3.9)

Total cross section
In this section we analyse the total hadronic cross section for the three scenarios and cuts defined above. In Table 1 we show the total cross section for ttH production and the corresponding contributions resulting from quark-antiquark annihilation and gluon fusion. In this scenario the total cross section is σ Total ttH = 7.39 fb, and about 70 % of the events originate from the gluon-fusion process. While the bulk of the contributions results from matrix elements of order O α s α 3 , quark-antiquark annihilation receives an additional small contribution from pure electroweak interactions. Note that there are no interferences between diagrams of O α 4 and O α s α 3 in this scenario.
The cross section for ttbb production is presented in Table 2. In column two to four we show the contributions to the cross section resulting from matrix elements of specific orders in α s . The corresponding matrix elements include only Feynman diagrams that originate exclusively from one specific order in the strong and electroweak coupling constant, e.g. results in column three are exclusively build upon Feynman diagrams of O α s α 3 and do not include interferences between diagrams of O α 4 and O α 2 s α 2 . The fifth column, labelled "Sum" represents the sum of the contributions in columns two to four and thus contains no interferences between matrix elements of different orders. The total cross section in the last column is calculated from the complete matrix element for pp → ttbb → ℓ + ν ℓ jjbbbb pp Cross section (fb) (9) 0.014887 (2) 7.377(1) 7.3920(9) Table 1: Composition of the total cross section in fb for ttH production at the LHC at 13 TeV. In the first column the partonic initial states are listed. In the second and third column we list the contributions resulting from the square of matrix elements of specific orders in the strong and electroweak coupling. The last column provides the total cross section.
pp Cross section (fb) (6) 2.4932(9) 0.9199 (2) 3.4312 (9) 3.4366 (6) gg -7.818(4) 16.650 (9) 24.47 (1) 23.010 (7) 0.018134 (6) 10.311 (4) 17.570 (9) 27.90 (1) 26.446(7) Table 2: Composition of the total cross section in fb for ttbb production at the LHC at 13 TeV. In the first column the partonic initial states are listed. In the second, third and fourth column we list the contributions resulting from the square of matrix elements of specific orders in the strong and electroweak coupling. The fifth column shows the sum of the columns two to four, while the last column provides the total cross section incorporating all interference effects.
including all interferences. For the total cross section we find a significant enhancement of the production rate compared to ttH production, σ Total ttbb = 26.45 fb, and thus the irreducible background which exceeds the ttH signal by a factor of 2.6. Note that in this definition of the irreducible background interference effects between signal and background amplitudes are included. The major contribution to the irreducible background (87 %) arises from gluon fusion at O (α 2 s α 2 ) 2 while for quark-antiquark annihilation we find a relative contribution of about 5 % at this order. A comparison of the results at O (α s α 3 ) 2 between Table 1 and Table 2 shows a rise of the cross section of 49 % (16 %) for the gluon-fusion (quarkantiquark-annihilation) process. These enhancements of the O (α s α 3 ) 2 contribution in the ttbb scenario result from Feynman diagrams involving electroweak interactions with Z bosons, W bosons and photons (like in Figure 1e). (1) 3.511 (6) 3.538 (4) gg -8.01 (2) 17.19 (6) 0.00756 (2) 25.21 (6) 23.71 (6) 0.02120 (3) 10.87 (2) 18.69 (6) 0.516 (2) 30.10 (6) 28.60(6) Table 3: Composition of the total cross section in fb for the full process at the LHC at 13 TeV. In the first column the partonic initial states are listed, where qq (′) denotes pairs of quarks and/or antiquarks other than qq. In the columns two to five we list the contributions resulting from the square of matrix elements of specific orders in the strong and electroweak coupling. The sixth column shows the sum of the columns two to five, while the last column provides the total cross section incorporating all interference effects.

pp Cross section (fb)
A comparison between the fifth (Sum) and sixth (Total) column in Table 2 allows a determination of interference contributions between matrix elements of different orders in the coupling constants. Neglecting those interference effects results in an over-estimation of the cross section of about 5 %. The main interference contributions originate from the gluon-fusion channel, where they reduce the cross section by 6 %, while the qq channel is hardly affected. We could trace the dominant contribution to interferences of diagrams of O α s α 3 with W-boson exchange in the t-channel (like in Figure 1e) with diagrams of O α 2 s α 2 that yield the dominant irreducible background (like in Figure 1d). We confirmed the size and sign of these contributions by switching off all other contributions in RECOLA. We note that these kinds of interferences are absent in the qq channel. We also investigated the interference of the signal process, i.e. all diagrams of order O α s α 3 involving s-channel Higgs-exchange diagrams (like in Figures 1g and 1h) with the dominant irreducible background of order O α 2 s α 2 and found it to be below one per cent.
The results for the full process are listed in Table 3. We show contributions resulting from matrix elements of different orders similar as in Table 2. In addition we list the contributions of additional partonic channels separately. Here gq and gq denote channels with gluons and quarks or antiquarks in the initial state and qq (′) all channels involving two quarks and/or antiquarks in the initial state other than qq (including channels with gluons in the final state). We compute the total cross section to σ Total full = 28.60 fb including all interference effects, with the major contribution (about 83 %) arising from the purely gluon-induced process. The consideration of contributions without an intermediate topantitop-quark pair results in an increase of about 3 % for both the gg and qq processes compared to the ttbb scenario. The additional partonic channels contribute about 5 %. For the total cross section we find a relative increase of 8 % while for the irreducible background we note an enhancement of 11 % relative to ttbb production. The signal cross section σ Total ttH amounts to 26 % of the full cross section σ Total full . In the full process sizeable interference effects only appear in the gluon-induced channel and are of the same size, roughly −6 %, as for ttbb production. Since the total cross section of the full process and ttbb production differ by only about 8 % we conclude that the major interference effects are those that we identified in the underlying ttbb production process.

Differential distributions
In this section we present differential distributions for all three scenarios. We compare results for the full process with ttbb production and ttH production to assess the irreducible background to ttH production in distributions. In the upper panels in each plot we show the differential distribution of the full process with a black solid line, ttbb production with a dashed blue line and ttH production with a dotted red line. The lower panels provide the ratio of ttbb production to the full process with a dashed blue line and the ratio of ttH production to the full process with a dotted red line.
We study specifically the distribution in the invariant mass of two b jets selected according to different criteria in view of identifying the b-jet pairs originating from the Higgs-boson decay. In particular, we consider the invariant mass of • the two b jets that form the invariant mass closest to the Higgs-boson mass, M bb,Higgs , • the two b jets that are most likely not originating from the (anti-)top-quark decay, M bb,non-top , • the two b jets that have the smallest ∆R distance as defined in (3.8), M bb,∆R min , • the two b jets that have the highest transverse momenta, M b 1 b 2 . Figure 2 displays the corresponding b-jet pair invariant-mass distributions. In all cases the shape of the full process is well represented by the ttbb approximation including the Higgs-boson and the Z-boson resonance. In the lower panels we observe that the difference between ttbb production and the full process is generally of the same order as for the total cross section of about 8 %. For ttH production the shape and the relative size compared to the full process depends on the observable. In the following we analyse in detail the four invariant-mass distributions.

Invariant mass of b-jet pair closest to the Higgs-boson mass
For this observable we compute the invariant masses of all six b-jet pairs and choose the one that is closest to the Higgs-boson mass used in the Monte Carlo run. Figure 2a displays the resulting invariant-mass distribution. For ttH production it features a very clear peak  The lower panels show the relative size of ttbb and ttH production normalised to the full process.
at the Higgs-boson mass with a strong drop-off according to the Breit-Wigner shape of the Higgs-boson resonance. Thus, the ratio of ttH production and the full process almost vanishes outside the resonant region. The finite off-shell contributions are a result of the pole approximation where the on-shell projected momenta are only applied to the matrix element evaluation, but not to the resonant propagator. The phase-space integration and thus the histogram binning is performed with off-shell momenta. The ttbb and the full process have contributions where the Higgs boson is replaced by a Z boson, visible as a bump around the Z-boson mass in the differential distribution.
This observable is strongly biased, since we always choose the b-jet combination that gives the invariant mass closet to the Higgs-boson mass. This explains the rise of the differential cross section for ttbb production and the full process towards the Higgs resonance outside the peak.

Invariant mass of b-jet pair determined by top-antitop Breit-Wigner maximum likelihood
Motivated by Ref. [3] we determine the two b jets that most likely originate from the decay of the top quark (t → W + b → ℓ + ν ℓ b) and antitop quark (t → W −b →ūdb, with u = u, c, d = d, s) and plot the invariant mass of the remaining b-jet pair. Since in most events the top quark and antitop quark in ttH production are nearly on-shell, the two b jets maximising the corresponding propagator contributions are most likely to originate from the top-quark and antitop-quark decay. To determine the maximising b-jet combination we compute a top-momentum candidate with the charged lepton, neutrino and a b-jet momentum (p b i ), and an analogous antitop-momentum candidate with the two momenta of the non-b jets and a different b-jet momentum (p b j ), As b jets originating from the top-quark and antitop-quark decay we select those that maximise the likelihood function L defined as a product of two Breit-Wigner distributions corresponding to the top-quark and antitop-quark propagators: (3.12) In Figure 2b we present the b-jet-pair invariant mass that has been identified to originate from the Higgs-boson decay by the maximum-likelihood method described above. In the off-shell region the ratio of ttH production to the full process drops considerably below the corresponding ratio for the total cross section of about a fourth. Owing to the absence of the bias, the peak in the resonant region is more pronounced for the full process compared the method based on the b-jet-pair invariant mass closest to the Higgs-boson mass (Figure 2a), yielding a better signal to background ratio. Since this method tags the b jets resulting from the top and antitop quarks, any resonance in the invariant mass of the remaining b-jet pair is resolved, and thus the Z resonance is clearly visible in the plot.

Invariant mass of minimal ∆R-distance b-jet pair
Next we compute for each event the ∆R distance of all six b-jet pairs and plot the invariant mass of the pair with the smallest ∆R distance. Since the Higgs boson, as a scalar particle, decays isotropically, this observable is not sensitive to Higgs-boson production at the ttH threshold but potentially for boosted Higgs bosons. Figure 2c displays the corresponding invariant-mass distribution for all three scenarios. The Higgs-boson peak is clearly visible in all cases. However, it is less pronounced compared to the Breit-Wigner maximum-likelihood method (Figure 2b) and the ratio of peak over background is only weakly enhanced compared to the purely combinatorial effect. Outside the regions of the Higgs and Z-boson resonances the ratio of ttH production vs. the full process equals the average value of about a fourth, which we see in the total cross-section ratio. This indicates that the b-jet pair with minimal ∆R distance is almost evenly distributed among all six possible b-jet pairs, i.e. the method fails to tag the b-jet pair originating from the Higgs-boson decay.
The bump around the Z-boson mass in the differential distributions is weaker as compared to Figure 2b and there appears a ditch in the ttH ratio because the Z-boson resonance is absent in ttH production. The ditch in the ttbb ratio is due to relative differences in contributions from resonant Z bosons in the full process and in ttbb production. Thus, in the considered set-up this method is not suitable to tag the Higgs boson. This might be different if strongly boosted Higgs bosons are required.

Invariant mass of two hardest b jets
For comparison we show the distribution in the invariant mass of the pair of the two hardest b jets in Figure 2d. Also here the Higgs-boson signal is clearly visible for all processes but there is no enhancement above the purely statistical level. The apparently smaller enhancement of the Higgs peak as compared to Figure 2c is basically due to the larger bin width (10 GeV as compared to 1.5 GeV). Furthermore, outside the resonance regions ttH production is about a fourth of the full process, as for the total cross section.

Further differential distributions
In this section we investigate further differential distributions concentrating on observables that show deviations in the shape between the full process and the approximations. Some other distributions which show no significant shape deviations are listed in Appendix B. Figure 3a shows the azimuthal separation of the b-jet pair determined by top-antitop Breit-Wigner maximum likelihood according to Section 3.2.2. While ttbb production and the full process yield a very similar shape, ttH production exhibits clearly a different shape. This behaviour can be explained by the dominant production mechanisms of bottomantibottom pairs. In the signal process these result from the Higgs boson and owing to the finite Higgs-boson mass tend to have a finite opening angle. In the background processes the bottom-antibottom pairs result mainly from gluons and thus tend to be collinear leading to a peak at small φ bb that is cut off by the acceptance function. Thus, this distribution can help to separate bottom-antibottom pairs resulting from Higgs bosons from those of other origin. Figure 3b displays the transverse-momentum distribution of the third-hardest b jet. We find that all three approximations are similar in shape for p T values below 150 GeV. For higher transverse momenta the distribution for ttH production diverges from those of the full process and ttbb production. We do not see this behaviour in the transverse momentum distributions of the two harder b jets (see Figure 5c in Appendix B) but to some extent in the one of the fourth-hardest b jet. This results from the fact that in the  ttH signal all b jets originate from heavy-particle decays, while in the full process some are directly produced yielding more b jets with high transverse momenta. The distributions in the transverse momenta of the two non-b jets are displayed in Figures 3c-3d. For the hardest non-b jet, we find a similar picture as for the 3rd hardest b jet and an enhancement for the full process relative to ttbb production and ttH production for transverse momenta above 150 GeV. The explanation is similar as in the preceding case. While in the ttbb process the jets originate from the top-quark decay, in the full process they can be produced directly leading to more jet activity at high transverse momenta. In the case of the second hardest jet both approximations exhibit a strong drop near p T,j,min = 200 GeV. For higher transverse momenta two jets originating from W-boson decay are too collinear to pass the rapidity-azimuthal-angle-separation cut of ∆R jj > 0.4 such that the corresponding events are eliminated. On the other hand, events with jets pairs with higher invariant masses, which are present in the full process, are not cut.
The sum of all transverse energies (including missing transverse energy) is depicted in Figure 3e. For small H T the different thresholds of the approximations are clearly visible. For H T ∼ 400 GeV-800 GeV the ttbb approximation describes the full process within 10 %.
As it decreases stronger with increasing H T the deviation becomes larger above 800 GeV.
Since H T incorporates all transverse energies of the process it is a measure for the average deviation of the transverse energies between the approximations and the full process.
Finally, Figure 3f presents the invariant mass of the three hardest b jets. Below the threshold M H + p T,b,cut ≈ 150 GeV the signal process is strongly suppressed, above its ratio to the full process rises to 36 % at M b 1 b 2 b 3 ∼ 195 GeV and then drops slowly to 26 % at M b 1 b 2 b 3 ∼ 400 GeV. The ratio of ttbb production and the full process on the other hand is

Interference effects in differential distributions
In this section we study in detail the effects of the interference contributions between matrix elements of different orders in α s . For most distributions we find a uniform shift by roughly the same amount as for the total cross section, i.e. about 5 % for ttbb production and the full process (interference effects are absent in ttH production). For both scenarios we observe a few kinematical distributions that are sensitive to these interference effects. The upper panels of Figure 4 show the results for the full process and the central and lower panels highlight the interference effects. Specifically, the central panels show the relative difference (σ tot − σ sum )/σ tot for ttbb production with a solid blue line and the lower panels the same relative difference for the full process with a dashed line.
In Figures 4a and 4b we see that the effect of the interference for the distributions in the transverse momentum of the third-hardest b jet and for the harder non-b jet, respectively, varies monotonically with increasing p T from −6 % to −2 %. Figure 4c shows the interference effects on the distribution of the invariant mass of the b-jet pair determined by top-antitop Breit-Wigner maximum likelihood. The suppression of interference in the regions of the Higgs-and Z-boson resonances is clearly visible. For invariant masses above the Higgs threshold the interference effect exceeds −10 %. As shown in Figure 4d, the relative interference effects grow with increasing azimuthal-angle separation of the b- . The lower panels show the relative interference effects of ttbb production and the full process, respectively. The upper panel shows the corresponding differential distribution of the full process as reference.
jet pair determined by top-antitop Breit-Wigner maximum likelihood from almost zero at small angles to −25 % for φ bb,non-top = 180 • , while the cross section drops with increasing azimuthal-angle separation. Also in the distributions the dominant interference effects arise from diagrams of order O α s α 3 involving t-channel W-boson exchange interfering with diagrams of order O α 2 s α 2 . Interferences with diagrams for ttH production are by a factor five or more smaller.

Conclusion and outlook
We have presented an analysis of the irreducible background for ttH production at the LHC. Specifically, we have compared the full Standard Model cross section for the production of four b jets, two jets, one identified charged lepton and missing energy with the contributions from the subprocesses ttbb production and ttH production, obtained using the pole approximation. With standard acceptance cuts we find that the total cross section of ttH production and decay is roughly a fourth of the full process, while ttbb production constitutes the major contribution to the full process with about 92 %. For all scenarios the bulk of the cross section originates from gluon-induced processes.
We analysed various b-jet-pair invariant-mass distributions based on different methods to select two of the four b jets to be identified with the decay products of the Higgs boson. We find that assigning two b jets to the top-and antitop-quark decay by maximising a combined Breit-Wigner likelihood function and assigning the remaining two b jets to the potential Higgs boson yields a good unbiased determination of the b-jet pair originating from the Higgs-boson decay.
We investigated the interferences between contributions to the matrix element of different orders in the strong and electroweak couplings constants. We find that interference effects are only sizeable for gluon-induced processes and lower the hadronic cross section by about 5 %. The dominant contributions result from interferences of the QCD ttbb production diagrams of order O α 2 s α 2 with diagrams of order O α s α 3 involving t-channel W-boson exchange. Interferences between the dominant background and the ttH signal on the other hand are below one per cent. In most of the differential distributions the interference effects lead to a constant shift. We found, however, a few distributions where non-uniform shape changes appear.
Our analysis demonstrates the complexity of this process and provides useful information for a future NLO calculation. We found that the ttbb process provides a good approximation to the full process, with a deviation of only about 8 % for the total cross section and a uniform shift for most differential distributions. While the QCD corrections to the leading QCD contributions to ttbb production are already known, a calculation of the NLO corrections to the full ttbb process should be feasible with available tools [38,45].

Acknowledgments
This work was supported by the Bundesministerium für Bildung und Forschung (BMBF) under contract no. 05H12WWE.

A On-shell projection
In this appendix we discuss some details of our implementation of the pole approximation. For ttbb production (ttH production) we compute the matrix element with on-shell momenta for the top quarks (and the Higgs boson) and consider off-shell effects only in the corresponding propagators of the unstable particles. Thus, starting from off-shell momenta we use an on-shell projection to generate the momenta of the resonant particles. Since the procedure of on-shell projection is not uniquely defined we impose suitable requirements. The matrix element is strongly sensible to resonances and hence we project such as to retain sensible invariants as far as possible. As a consequence of the on-shell projection of the top quarks we also need to incorporate proper on-shell projections for their decay products.
Analogously we obtain for the projection of the W − decay products in W − →ūd(cs): Thus, we perform six projections in total for ttH production and five for ttbb production.
Of course, the on-shell projections do not change the momenta, if the resonant particles are already on shell.

B Further differential distributions
In this appendix we present further differential distributions which exhibit only minor shape deviations between the full process and the approximations. As for the total cross section we find for most distributions a constant offset of 8 % between the full process and the ttbb approximation and about a factor four between the full process and the ttH approximation. Only in tails of distributions larger deviations between the full process and the approximations appear.
In Figures 5a-5b we show the transverse momentum and the rapidity distribution of the identified charged lepton, while the transverse momentum and the rapidity distribution of the hardest b jet are depicted in Figures 5c-5d. Finally, the missing transverse momentum and the transverse mass of the charged lepton, the neutrino and the hardest b jet are provided in Figures 5e-5f.