Radiation Uncertainty

Model uncertainties caused by a different amount of initial and final state radiation are determined with two dedicated PO W H E G+PY T H I Asamples producing more or less radiation due to modified underlying parameter settings. These modifications include alternative values of the factorisation and normalisation scale, µ_F and µ_R, which are varied by factor 0.5 to 2. Theh_damp parameter is correlated with these scales and, thus, depending on the scale values,h_damp is set to eitherm_t or 2m_t. In addition, the coupling parameter αs affecting initial and final state radiation is also changed in the alternative MC samples; it depends onµRbut is also varied in different generator tunes. The alternative tunes are calledPerugia2012 radHi(referred to as P2012 radHi) and Perugia2012 radLo(P2012 radLo in the following)[261], the nominal tune is P2011C.

Thus, the two alternative MC samples rely on the following parameters: One sample has the values

µR=µF=2 andh_damp=m_t combined with the P2012 radLo tune, the other sample has values of µ_R=µ_F =0.5 andh_damp=2m_t combined with the P2012 radHi tune. These two configurations were chosen based on unfolded data distributions. The variations constitute an envelope of all individual modifications in the resulting distributions.

The nominalt¯tsignal sample withµR=µF =1 andh_damp=m_tis compared to these two variation samples again according to the standard procedure using pseudo-experiments. The largest of the resulting differences in the mean values is symmetrised and considered as the systematic uncertainty from ISR and FSR.

Depending on the chosen observables for theΓ_tmeasurement, the radiation systematic uncertainty reached the order of several GeV, as revealed by comparison studies in Ch. 9. This uncertainty is thus the dominant source of systematic effects for some of the tested observables. Its impact was investigated in more detail.

Three different parameter settings differ from each other between the ISR/FSR samples. But the scales and parameters µF, µR andh_damp as well as the associated PY T H I A tune change only simultaneously. For the detailed study, MC samples containing truth parton and particle level information were generated in which these parameters and tunes are varied independently, also comprising a comparison of the nominal tune P2011C, as the actually used tune, with the tune P2012, which is combined with the “radHi” and “radLo” contributions in the variation samples.

Such a setup allows to check whether a certain scale or tune variation is responsible for the large discrepancies and whether the effects observed for the observable distributions at the reconstruction level are also present at parton or particle level.

The two nominal tunes P2012 and P2011C are expected to yield similar observable distributions.

Fig. 8.2a and Fig. 8.2b show a comparison between these two tunes for the hadronically decaying top quark mass and the corresponding hadronically decayingW boson mass. The observablem^had_t as reconstructed from three jets is very sensitive to the radiation uncertainty. The massm^had_W as the related two-jet mass shows a very similar behaviour asm^had_t . Only slight differences between the tunes occur.

An independent variation ofh_damp and the scalesµ=µF =µR revealed that the differences with respect to the nominal setup are relatively small for changes in the scales and larger for theh_damp variation, shown in Figs. 8.2c-8.2f. A value ofh_damp=0.5m_tis actually not used in the two official samples but applied here in order to allow for a comparison with two alternativeh_dampvalues. The two nominal Perugia tunes lead to widely consistent results.

A comparison of the two PY T H I A radiation tunes, as the third source of difference between the alternative radiation MC samples unveils significantly larger differences in the obtainedm^had_t distri-butions at truth level compared to discrepancies caused by varying the scale orh_dampparameters, visualised in Fig. 8.3a and Fig. 8.3b.

In particular, the shape differences between the alternative tunes with regard to the nominal tunes are very distinct. This applies to both nominal tunes P2011C and P2012. Such shape differences are not only present for masses of compound particles such as the three-jet massm^had_t of the top

8 . 4 U N C E RTA I N T I E S I N S I G N A L M O D E L L I N G

(a) (b)

(c) (d)

(e) (f)

Figure 8.2: (a,b) Particle level mass distributions showing the difference between the two nominal Perugia tunes P2011C and P2012 for the masses m^had_t and m^had_W . The ratios at the bottom are given with respect to the P2012 tune. (c-f) Parton level mass distributions showing the difference between two differenth_dampparameter values and between two different values of the renormalisation and factorisation scaleµfor the massesm^had_t andm^had_W with details given in the legends. According to the labels, either the tune P2012 or P2011C is used as reference.

The ratios in the lower panels are given with respect to these nominal tunes. The hatched bands in all plots represent the statistical uncertainty of these samples.

(a) (b)

(c) (d)

(e) (f)

Figure 8.3:Particle level mass distributions showing the difference between the two different radiation tunes P2012 radHi and radLo for (a,b) the massm^had_t as a compound particle as well as (c,d) the masses of thebjet of the hadronically decaying top quark and (e,f) the masses of the light jets of the hadronically decaying top quark. Either the tune P2012 (a,c,e) or the tune P2011C (b,d,f) is used as reference. The ratios in the lower panels are given with respect to these two nominal tunes, the hatched bands represent the statistical uncertainty of these samples.

8 . 4 U N C E RTA I N T I E S I N S I G N A L M O D E L L I N G

quark or the two-jet mass m^had_W of the W boson but also for masses associated with the jets of the hadronically decaying top quark. The corresponding jet mass distributions at particle level are illustrated in Figs. 8.3c-8.3f for the two nominal tunes used as reference. This demonstrates once more that these shape effects are directly related to the underlying PY T H I A radiation tunes and neither caused by the creation of compound two- or three-jet particles, by the usage of other nominal tunes nor by a certain requirement applied in the event selection or event reconstruction.

This large effect on the mass shapes at truth level is propagated directly to reconstruction level and thus also occurs in the observable distributions used in the fit. The differences between the templates translate into the considerable shifts in the mean values from the pseudo-experiments.

Consequently, a lot of effort was spent on designing an analysis configuration where radiation effects do not dominate the total systematic uncertainty to such an extent, shown in Ch. 9.

Since the effect is mainly driven by the radiation tunes, a more careful evaluation of the variation samples based on more precise and better measurements is required in the future, especially for analyses at a centre-of-mass energy of 13 TeV. Besides, the large impact of the radiation also points to the relatively simple description of the top quark decay which is utilised in the three MC t¯t samples available for the comparison in this section. This description relies on LO matrix elements and involves an approximate implementation of interference and finite width effects. The radiation uncertainty is assumed to be reduced further with an adequately tuned setup that considers NLO effects, which is covered more thoroughly in Sec. 8.5.