**3.2 Simulations of the** *H*<sup>±</sup> → *τν* **decay mode**

10 Will-be-set-by-IN-TECH

 **/ 10GeV eve N**

*<sup>F</sup>*) <sup>≈</sup> *<sup>α</sup><sup>s</sup>*

*dy*<sup>∗</sup> *<sup>π</sup> s*

*dzPqg*(*z*)

, *<sup>s</sup>* <sup>=</sup> *<sup>τ</sup>s*. *<sup>θ</sup>*

 **(GeV) mT 0 50 100 150 200 250 300 350 400**

> *dz z*

Including kinematic constraints due to finite center of mass energy (CM) and finite *b* quark

*Pqg*(*z*) *g*

)|M2→2|

*<sup>H</sup>*<sup>±</sup> )<sup>2</sup> <sup>−</sup> <sup>4</sup>*m*<sup>2</sup>

*x*1 *z g x*<sup>1</sup> *<sup>z</sup>* , *<sup>μ</sup>*<sup>2</sup> *F* 

 *x z* , *μ*<sup>2</sup> *F* 

<sup>2</sup> *αs*(*μ*<sup>2</sup> *R*) 2*π*

is the polar angle of the *t*-quark in the CM system of the

*<sup>t</sup> <sup>m</sup>*<sup>2</sup>

*<sup>F</sup>*) the gluon density function, *μ<sup>F</sup>* the factorization

*x*2*g*(*x*2, *μ*<sup>2</sup>

*b* → *tH*<sup>±</sup> process, *μ<sup>F</sup>* and *μ<sup>R</sup>* are the factorization

*bH*± process, and the kinematical variables are

Fig. 5. Plots of the transverse mass of the charged Higgs in *H* → *τν* for a luminosity of 300fb−<sup>1</sup> scaled to 30fb−1. The three lines in each plot correspond to positive events (the dotted red lines), negative events (dotted and blue) and matched events (shaded portion and black). The three graphs corresponds to three different values of *R*−<sup>1</sup> as indicated in each

*<sup>F</sup>*) is the leading order *b*-quark density given by [22]:

<sup>2</sup>*<sup>π</sup>* log *<sup>μ</sup>*<sup>2</sup> *F m*2 *b*

scale and *z* the longitudinal gluon momentum fraction taken by the *b*-quark.

 1 −1

 *<sup>Q</sup>*<sup>2</sup> max *Q*2 min

(*<sup>s</sup>* <sup>−</sup> *<sup>m</sup>*<sup>2</sup>

*<sup>t</sup>* <sup>−</sup> *<sup>m</sup>*<sup>2</sup>

incoming *b*-quark and *z* is identified with the ratio of the CM energies of the *gb* system and

Note that since the double-counting contribution should be subtracted from the sum of the positive processes, this weight is negative for double-counting events. This means that if all three processes are run simultaneously in PYTHIA, the total cross-section will be correctly

With use of MATCHIG, issues of double-counting in our event generator are resolved. However, we shall not use the Monte-Carlo event generator, PYTHIA, to calculate the precise normalisation of the cross-sections, for though it gives an accurate description of the simulated data in both the low and high transverse momenta regions (with the inclusion of the external process MATCHIG), we can more accurately determine these by taking the leading order cross-section multiplied by an appropriate *k*-factor. The reason for this is that the matched

mass, the resulting expression for the double-counting term can be written as [24]:

*β*34 <sup>2</sup> *<sup>d</sup>*(cos *<sup>θ</sup>*

*d*(*Q*2) *Q*<sup>2</sup> + *m*<sup>2</sup> *b*  **/ 10 GeV eve N**

**0 2 4 6 8 10 12 14 16 18 tan = 40 = 1.2 -1 R33 mA = 250 GeV**

 **(GeV) mT 0 50 100 150 200 250 300 350 400**

, (23)

*<sup>F</sup>*) + *x*<sup>1</sup> ↔ *x*<sup>2</sup>

*<sup>H</sup>*<sup>±</sup> . *<sup>Q</sup>*<sup>2</sup> is the virtuality of the

. (24)

 **(GeV) mT 0 50 100 150 200 250 300 350 400**

> *b*� (*x*, *μ*<sup>2</sup>

with *Pqg* the *<sup>g</sup>* <sup>→</sup> *qq*¯ splitting function, *<sup>g</sup>*(*x*, *<sup>μ</sup>*<sup>2</sup>

 <sup>−</sup> <sup>1</sup> <sup>2</sup> log *τ*

> 1 <sup>2</sup> log *τ*

Here <sup>M</sup>2→<sup>2</sup> is the matrix element for the *<sup>g</sup>*¯

*<sup>b</sup>* <sup>→</sup> *tH*<sup>±</sup> scattering, and *<sup>β</sup>*<sup>34</sup> <sup>=</sup> *<sup>s</sup>*−<sup>1</sup>

and renormalization scales as in the *gg* <sup>→</sup> *<sup>t</sup>*¯

 *<sup>z</sup>*max *x*1

 **/ 10 GeV eve N**

plot.

where *b*�

*σ*DC =

the *gg* system.

matched.

*g*¯

 1 *τ*min

*<sup>τ</sup>* <sup>=</sup> *<sup>x</sup>*1*x*2, *<sup>x</sup>*1,2 <sup>=</sup> <sup>√</sup>*τe*±*y*<sup>∗</sup>

*dτ τ*

×

(*x*, *μ*<sup>2</sup>

**0 2 4 6 8 10 12 14 <sup>16</sup> tan = 40 = 0.8 -1 R33 mA = 250 GeV**

> As has already been mentioned, the *τν* decay channel offers a high transverse momenta, *pT*, of the *τ* and a large missing energy signature that can be discovered at the LHC over a vast region of the parameter space, where constraints have already been determined [17, 18]. To simulate this the events were generated in PYTHIA using the *gb* → *tH*<sup>±</sup> process, explicitly using the mechanism *pp* → *t*(*b*)*H*<sup>±</sup> → *jjb*(*b*)*τν*. That is, the associated top quark is required to decay hadronically, *t* → *jjb*. The charged Higgs decays into a *τ* lepton, *H*<sup>±</sup> → *τ*±*ντ*, and the hadronic decays of the *τ* are considered. The backgrounds considered are QCD, *W*+ jets, single top production *Wt*, and *<sup>t</sup>*¯*t*, with one *<sup>W</sup>* <sup>→</sup> *jj* and the other *<sup>W</sup>*<sup>±</sup> <sup>→</sup> *<sup>τ</sup>*±*ντ*.

The width of the process *H*<sup>±</sup> → *τ*±*ντ* is:

$$
\Gamma(H^- \to \tau^- \nu\_\tau) \simeq \frac{m\_{H^\pm}}{8\pi\nu^2} \left[ m\_\tau^2 \tan^2 \beta \left( 1 - \frac{m\_\tau^2}{m\_{H^\pm}^2} \right) \right] \left( 1 - \frac{m\_\tau^2}{m\_{H^\pm}^2} \right) \tag{25}
$$

If the decay *H*<sup>±</sup> → *tb* is kinematically allowed, comparing its width with Eq.(25) can give a rough estimate of the *H*<sup>±</sup> → *τ*±*ντ* branching ratio:

$$\begin{split} \operatorname{Br}(H^{\pm} \to \tau^{\pm} \nu\_{\tau}) &\simeq \frac{\Gamma(H^{\pm} \to \tau^{\pm} \nu\_{\tau})}{\Gamma(H^{\pm} \to tb) + \Gamma(H^{\pm} \to \tau^{\pm} \nu\_{\tau})} \\ &= \frac{m\_{\tau}^{2} \tan^{2} \beta}{\Im(R\_{t}^{-1})^{2} (m\_{t}^{2} \cot^{2} \beta + m\_{b}^{2} \tan^{2} \beta) + m\_{\tau}^{2} \tan^{2} \beta} . \end{split} \tag{26}$$

Note that a measurement of the signal rate in *H*<sup>±</sup> → *τ*±*ντ* can allow a determination of tan *β*.

Our approach for this process is as follows:


Note that we were required to impose additional cuts, namely:

*R*−<sup>1</sup>

*σ* (fb) 204 249 273 Pre-selection <sup>48</sup> <sup>×</sup>10−<sup>3</sup> <sup>48</sup> <sup>×</sup>10−<sup>3</sup> <sup>48</sup> <sup>×</sup>10−<sup>3</sup> <sup>N</sup><sup>1</sup> 12.8 <sup>×</sup> <sup>10</sup>−<sup>3</sup> <sup>13</sup> <sup>×</sup> <sup>10</sup>−<sup>3</sup> <sup>13</sup> <sup>×</sup> <sup>10</sup>−<sup>3</sup> <sup>N</sup><sup>2</sup> <sup>61</sup> <sup>×</sup> <sup>10</sup>−<sup>4</sup> <sup>67</sup> <sup>×</sup> <sup>10</sup>−<sup>4</sup> <sup>66</sup> <sup>×</sup> <sup>10</sup>−<sup>4</sup> <sup>N</sup><sup>3</sup> <sup>47</sup> <sup>×</sup> <sup>10</sup>−<sup>4</sup> <sup>53</sup> <sup>×</sup> <sup>10</sup>−<sup>4</sup> <sup>52</sup> <sup>×</sup> <sup>10</sup>−<sup>4</sup>

� (*<sup>σ</sup>* <sup>×</sup> BR) / (*<sup>σ</sup>* <sup>×</sup> BR) (<sup>L</sup> <sup>=</sup> <sup>100</sup> *f b*−1) 10.6 % 9.5 % 8.6 % � (*<sup>σ</sup>* <sup>×</sup> BR) / (*<sup>σ</sup>* <sup>×</sup> BR) (<sup>L</sup> <sup>=</sup> <sup>300</sup> *f b*−1) 6.2 % 5.5 % 5 % Table 1. Cumulative efficiencies of cuts and estimated errors for measurements of a signal cross-section for the process *pp* <sup>→</sup> *<sup>t</sup>*(*b*)*H*(<sup>→</sup> *<sup>τ</sup>hadν*). For these numbers we have fixed

Constraining the Couplings of a Charged Higgs to Heavy Quarks 41

error in the measurement of the cross-section in this channel to be 10% for a luminosity of 100 fb−<sup>1</sup> and 7.5% for a luminosity of 300 fb−1. At this point we would like to note that for our results we have used fast detector simulator ATLFAST [28] and have followed the methodology

Finally, for the decay chain *H*<sup>±</sup> → *tb*, recall that the interaction term of the charged Higgs

For the hadroproduction process *gb* → *tH*<sup>±</sup> (see Fig.3) with the decay mechanism *H*<sup>±</sup> → *tb*,

<sup>33</sup> )−<sup>2</sup> *m*2

*<sup>t</sup>* cot2 *<sup>β</sup>* + *<sup>m</sup>*<sup>2</sup>

<sup>2</sup> 1/2

where the factor 3 takes into account the number of colours. The final state of the hadroproduction process contains two top quarks, one of which we required to decay semi-leptonically to provide the trigger, *t* → *νb* ( = *e*, *μ*), and the other hadronically, ¯*<sup>t</sup>* <sup>→</sup> *jjb*. The main background comes from *<sup>t</sup>*¯*tb* and *<sup>t</sup>*¯*tq* production with *<sup>t</sup>*¯*<sup>t</sup>* <sup>→</sup> *WbWb* <sup>→</sup> *<sup>ν</sup>bjjb*. As such, we have used the production channel *pp* → *tH*<sup>±</sup> for this decay, and have tried to

with the *t* and *b* quarks in the 2HDM of type II, as given by Ref.[10], is:

*<sup>σ</sup>*(*gb* <sup>→</sup> *tH*±) <sup>∝</sup> (*R*−<sup>1</sup>

<sup>33</sup> )−<sup>2</sup>

The procedure we have used in reconstructing the masses is:

*<sup>m</sup>*<sup>2</sup>

 *mt* + *mb mH*<sup>±</sup>

reconstruct the charged Higgs mass. That is, we have the following decay chain:

*mH*<sup>±</sup> = 300 GeV.

as given in Ref.[10].

**3.3 Simulations of the** *H*<sup>±</sup> → *tb* **decay mode**

<sup>33</sup> )−<sup>1</sup>

the cross section for *gb* → *tH*<sup>±</sup> can be written as:

Therefore, the decay width of *<sup>H</sup>*<sup>−</sup> <sup>→</sup> ¯*tb* is given by:

8 *πv*<sup>2</sup>

× 1 −

<sup>L</sup> <sup>=</sup> *<sup>g</sup>*(*R*−<sup>1</sup>

<sup>Γ</sup>(*H*<sup>−</sup> <sup>→</sup> ¯*tb*) � <sup>3</sup> *mH*<sup>±</sup> (*R*−<sup>1</sup>

2 <sup>√</sup><sup>2</sup> *mW* <sup>33</sup> = 0.7 *<sup>R</sup>*−<sup>1</sup>

*VtbH*<sup>+</sup> ¯*t*(*mt* cot *<sup>β</sup>*(<sup>1</sup> <sup>−</sup> *<sup>γ</sup>*5) + *mb* tan *<sup>β</sup>*(<sup>1</sup> <sup>+</sup> *<sup>γ</sup>*5)) *<sup>b</sup>* <sup>+</sup> *<sup>h</sup>*.*c*. . (27)

*<sup>b</sup>* tan2 *<sup>β</sup>* 

<sup>1</sup> <sup>−</sup> *<sup>m</sup>*<sup>2</sup> *t m*2 *H*±

> <sup>2</sup> 1/2

<sup>−</sup> *<sup>m</sup>*<sup>2</sup> *b m*2 *H*±

. (28)

<sup>−</sup> <sup>4</sup>*m*<sup>2</sup> *<sup>t</sup> <sup>m</sup>*<sup>2</sup> *b m*2 *H*±

, (29)

*<sup>t</sup>* cot<sup>2</sup> *<sup>β</sup>* + *<sup>m</sup>*<sup>2</sup>

*pp* → *tH*<sup>±</sup> → *t*(*tb*) → (*νb*)(*jjb*)*b* → *jjbbbν* . (30)

 *mt* <sup>−</sup> *mb mH*<sup>±</sup>

*<sup>b</sup>* tan2 *<sup>β</sup>*

1 −

<sup>33</sup> = 1 *<sup>R</sup>*−<sup>1</sup>

<sup>33</sup> = 1.3


Note also, that in order to add a greater degree of realism to our analysis we have also required that the:


which is somewhat more optimistic than current ATLAS results [17].

In Fig.5 we have plotted the transverse mass of the charged Higgs in the *H* → *τν* decay for a luminosity of 300 *f b*−1, scaled to 30 *f b*−1. In the plot the three lines correspond to positive events (where all three subprocesses are considered together), negative events (the amount to be subtracted to avoid double-counting) and the final matched events. The three panels correspond to different values of *R*−1, as indicated. From this it can be observed that the resonance just below 250GeV is not particularly sensitive to the value of *R*−1, the height of peak is slightly larger for higher values of *R*−1. To further demonstrate the value of this process, we present in table 1 a comparison of the number of signal to background events, where the uncertainty in cross-section measurements is estimated as [10]:

$$\frac{\triangle(\sigma \times BR)}{(\sigma \times BR)} = \sqrt{\frac{S+B}{S^2}}\ \ .$$

where *S* and *B* are signal and background events respectively.

The numerical results of our analysis are therefore summarized in table 1. The table shows that for a reasonable range of input parameters the cross-sections at the LHC can be measured with a 10% accuracy for a luminosity of <sup>L</sup> = 100 fb−1, whereas the measurement can be improved substantially for higher luminosities. Note that the error in the measurement of tan *β* is consistent with the observations made in Ref.[10]. For our analysis we have taken the 12 Will-be-set-by-IN-TECH

• N1: On the transverse momenta, *pT >* 100GeV. A hard cut that allows events for a more massive charged Higgs bosons to pass through. This cut is satisfied by the events that originate from *W* with large *pT*. This cut is severe for relatively light charged Higgs bosons (up to 200GeV) as it removes a large number of events, but is a very good cut for a relatively

removes any possible QCD backgrounds, as typically QCD events have no hard leptons. Again this cut is problematic for relatively light Higgs masses, as it removes a large number

the events coming from *W* with large *pT*. The decay product of such high *pT W*-bosons will

*W*-bosons gives a large boost to the final products, and hence forces a rather small opening in the angle between the *τ* and *ν*. In the case of the charged Higgs (whose mass is much greater than the *W*'s) the boost is relatively smaller, and this gives a relatively large angle between the *τ* and *ν*. As such we cut the azimuthal angle for *δφ >* 1 rad. This cut becomes much more effective as we move to larger Higgs masses, as the Lorentz boost for larger masses is much less, and hence there shall be larger angles between the final products. Note also, that in order to add a greater degree of realism to our analysis we have also required

In Fig.5 we have plotted the transverse mass of the charged Higgs in the *H* → *τν* decay for a luminosity of 300 *f b*−1, scaled to 30 *f b*−1. In the plot the three lines correspond to positive events (where all three subprocesses are considered together), negative events (the amount to be subtracted to avoid double-counting) and the final matched events. The three panels correspond to different values of *R*−1, as indicated. From this it can be observed that the resonance just below 250GeV is not particularly sensitive to the value of *R*−1, the height of peak is slightly larger for higher values of *R*−1. To further demonstrate the value of this process, we present in table 1 a comparison of the number of signal to background events,

The numerical results of our analysis are therefore summarized in table 1. The table shows that for a reasonable range of input parameters the cross-sections at the LHC can be measured with a 10% accuracy for a luminosity of <sup>L</sup> = 100 fb−1, whereas the measurement can be improved substantially for higher luminosities. Note that the error in the measurement of tan *β* is consistent with the observations made in Ref.[10]. For our analysis we have taken the

*S* + *B <sup>S</sup>*<sup>2</sup> ,

*<sup>T</sup> >* 100GeV. Another hard cut which

*<sup>T</sup>* as defined above. Such events originating from large *pT*

*<sup>T</sup>* was made. This cut removes

heavy Higgs.

of events.

that the:

satisfy the cuts on *p<sup>τ</sup>*

• *B*-tagging efficiency be 60%.

• *τ* jet tagging efficiency be 70%,

• *c*-jets being misidentified as *b*-jets at 10%. • light jets be misidentified as *b*-jets at 3%.

• <sup>N</sup>2: On the missing transverse momenta, *<sup>p</sup>miss*

• <sup>N</sup>3: Finally, a cut on the azimuthal angle between *pT* and *<sup>p</sup>miss*

which is somewhat more optimistic than current ATLAS results [17].

where the uncertainty in cross-section measurements is estimated as [10]:

where *S* and *B* are signal and background events respectively.

�(*σ* × *BR*) (*<sup>σ</sup>* <sup>×</sup> *BR*) <sup>=</sup>

*<sup>T</sup>* and *<sup>p</sup>miss*


Table 1. Cumulative efficiencies of cuts and estimated errors for measurements of a signal cross-section for the process *pp* <sup>→</sup> *<sup>t</sup>*(*b*)*H*(<sup>→</sup> *<sup>τ</sup>hadν*). For these numbers we have fixed *mH*<sup>±</sup> = 300 GeV.

error in the measurement of the cross-section in this channel to be 10% for a luminosity of 100 fb−<sup>1</sup> and 7.5% for a luminosity of 300 fb−1. At this point we would like to note that for our results we have used fast detector simulator ATLFAST [28] and have followed the methodology as given in Ref.[10].
