Note NA62-14-10 Radiative Pion Decay MC Generators



NA62 checks of MC and Reconstruction (2015)

See Section 8 , Figures 8 for summary of results. (1/6/15)

Section 9 Acceptance for Ke3 decay

Section 10 Acceptance for Kmu3 decay

Section 11 Studies of K+ -> pi+ pi0 , pi+ -> e+ nu .

Section 12 Studies of K+ -> pi+ pi0 , pi+ -> mu+ nu .

Section 13 Reconstruction of the K+ decay (1/5/15)

Section 14 Summary (20/08/2015)

Section 15 MC studies using the NA62 Analysis Framework (21/09/2015)




Two analysis programs have been written to check the output of the NA62 MC and Reconstruction programs,respectively.

The channel generated for this study is

             K+ ->  pi0 + pi+
                     |     |->  mu+ + neutrino
                     |
                     |-> gamma + gamma 

thus the detectable final state is a muon + two gammas


The objective is to compare the reconstructed tracks/clusters with the input lepton and gammas, and to determine the acceptance of the channel(s).




Fig 1 LKr This figure plots the ratio of the sum of cluster candidate energies to the sum of the energies of the two gammas. A ~ 1% systematic error is evident - possibly due to the muon. This Figure shows the energy distribution of clusters in the LKr; a low energy peak due to muons is present.

Fig 1a LKr is a repeat of the above figure but selected to have two gammas well contained with the LKr. The low energy tail is eliminated, but the systematic shift remains.

Fig 1b LKr plots the ratio of the sum of Lkr cluster energies to the gamma energies for cluster energies greater than 2 GeV. This removes, in part, the muon clusters, and reduces the systematic shift and width of the distribution.

Fig 2 Spectrometer This shows the ratio of the momentum measured in the spectrometer to the muon energy. No significant systematic errors are present.

Fig 3a Spectrometer - Lkr correlation The fitted spectrometer track has been extrapolated into the LKr. This plot shows the difference in x between the predicted and measured x for the cluster. To centre the x-distribution, the muon has been extrapolated to z = 240.5 m. The plots have been made for cluster energies less than 2 GeV.

Fig 3b Spectrometer - Lkr correlation The corresponding y difference.

Fig 4 LKr This is the same as Fig 1 except that the sum is over all clusters that are not associated with the muon track. A systematic shift , ~0.4 %, is still present. This Figure shows the energy distribution of clusters in the LKr after clusters linked to muons have been removed.


Fig 5a LKr compares true X cluster position with measured ( muons removed). Note shift.

Fig 5b LKr compares true Y cluster position with measured ( muons removed).

Fig 5c LKr shows ratio of measured cluster energy to true cluster energy ( muons removed). note ~1% shift.


The following plots are for single gammas - to avoid any influence from muons

Fig 6a LKr compares true X cluster position with measured . Note shift.

Fig 6b LKr compares true Y cluster position with measured .

Fig 6c LKr shows ratio of measured cluster energy to true cluster energy .

The above plots confirm that, for photon-clusters, x is shifted by about 1 cm, y is accurate, and the measured cluster energy is high by ~ 1 %.


The following plots are for single muons

Fig 7a LKr compares LKr X cluster position with X of the muon track projected from the end of the spectrometer to z = 240.5 m.

Fig 7a LKr compares LKr X cluster position with X of the muon track projected from the end of the spectrometer to z = 241.8 m. Note the 1 cm shift.

    // center of the LKr detector (Z position)
    fLKrDetectorZPosition = 241807 *mm - 2*mm;

Fig 7b LKr compares LKr Y cluster position with Y of the muon projected from the spectrometer to the LKr.

Fig 7c LKr shows the LKr cluster energy distribution from muons.


Section 8: Single positrons

For the majority of these events the MC Generated events tree does not include a positron with fKineParts.fParentID = 0 . The fKineParts branch contains many soft gammas with fParentID = 0. . The same feature is present for reconstructed events in the mcEvent tree.



Positron decay of Pi+

             K+ ->  pi0 + pi+
                     |     |->  e+ + neutrino
                     |
                     |-> gamma + gamma

thus the detectable final state is a positron  + two gammas

The problem with this channel is that the mcEvent tree frequently does not contain the final state positron, consequently it will be difficult to determine acceptances.

The reconstructed LKr and spectrometer show the same features as the pi+ -> muon channel discussed above, see the following Figures:

Fig 8a LKr compares true X cluster position with measured . Note shift ~ 1 cm.

Fig 8b LKr compares true Y cluster position with measured - agrees.

Fig 8c LKr shows ratio of measured cluster energy to true cluster energy . ~1% discrepancy.

Fig 8d Spectrometer shows ratio of measured momentum to true momentum for the positron - agrees.

See /data/na62_01/skilli/rootreco  gen4e.C -> histo4e.root (using  reconstruction o/p recogge5k.root)  23/7/2015 .

Fig 8e shows the energy in the summed energy in the calorimeters (LKr + LAV + IRC +SAC) compared with the gamma + gamma energy for K+ -> pi0( -> gamma + gamma) + pi+( -> mu + nu). This gives a pictorial indication of the hermiticity of the detector.

The following plots show the end-points of gammas in the detector:

Fig 8f All detector. Z vs Radius

Fig 8g 235 - 243 m. Z vs Radius . Compare with:

    // center of the LKr detector (Z position)
    fLKrDetectorZPosition = 241807 *mm - 2*mm;

and

Fig 8h LKr region. Z histogram.


Section 9: Ke3 decay - acceptance studies

In view of the difficulties with K+ -> pi+ pi0 decay, followed by the pi+ decaying to e+ nu , discussed above, the K+ decay to pi0 e+ nu channel has been used to check acceptances.

Fig 9a shows the distribution of e+ energies as measured in the spectrometer. All candidates.

Fig 9b shows the distribution of e+ energies from fKineParts_fInitialEnergy.

Fig 9c gives the acceptance defined as 9a/9b as a function of e+ energy.

Fig 9d Acceptance as a function of z-start for electrons measured in the spectrometer. All candidates.

Fig 9e Acceptance as a function of z-start for electrons measured in spectometer for spectrometer momentum agreeing with true value to 2% ( see here for measured momentum/true ) .


Section 10: Kmu3 decay - acceptance studies

Fig 10a shows the distribution of mu+ energies as measured in the spectrometer . All candidates.

Fig 10b shows the distribution of mu+ energies from fKineParts_fInitialEnergy.

Fig 10c gives the acceptance defined as 10a/10b as a function of muon energy.

Fig 10d Acceptance as a function of z-start for muons measured in the spectrometer. All candidates.

Fig 10e Acceptance as a function of z-start for muons measured in spectometer for spectrometer momentum agreeing with true value to 2% ( see here for measured momentum/true ) .



Section 11 Studies of K+ -> pi+ pi0 , pi+ -> e+ nu . (10/8/15)

These studies are based on events generated with Bruno's new generator which forces a pi-decay in the region 104 m < Z < 180 m.


             K+ ->  pi0 + pi+
                     |     |->  e+ + neutrino
                     |
                     |-> gamma + gamma


Measurement accuracy

Fig 11.1 e+ momentum: the Figure shows that there is little systematic mismeasurement in the spectrometer but that the Lkr measures ~1% high.

Fig 11.2 e+ position in LKr: these plots show a comparison of the position of the cluster in the LKr compared with the expected position from (a) the track projected from the spectrometer and (b) the position given in fKineParts. The y-position is correct; the x-position is in error by about 1cm if the nominal Z-position or fKineParts Y-value is used.

Fig 11.3 gamma position and momentum in LKr: the plots show a ~1cm displacement in X, and ~ 1% systematic shift in energy, for the LKr.

Acceptances

Fig 11.4 shows the fraction of energy from the e+ and gammas measured in the LKr as a function of the (true) energy of the e+ and gammas. As would be expected the acceptance reduces rapidly below below 40 GeV.

Fig 11.5 shows the fraction of energy from the e+ and gammas measured in the LKr as a function of the K+ decay position in Z. There is little Z-dependence.

Fig 11.6 shows the acceptance of the e+ in the spectrometer as a function of e+ momentum. The true and measured values are required to match within 5%.

Fig 11.7 shows the acceptance of the e+ in the spectrometer as a function of the Z-value of the start of the electron. The true and measured values are required to match within 5%.

Fig 11.8 shows the acceptance of the e+ in the spectrometer as a function of the Z-value of K-decay. The true and measured values are required to match within 5%.

Fig 11.9 shows the acceptance of the e+ in the spectrometer as a function of the Z-value of K-decay for muon momenta in the range 15-35 GeV. The true and measured values are required to match within 5%




Section 12 Studies of K+ -> pi+ pi0 , pi+ -> mu+ nu . (11/8/15)

These studies are based on events generated with Bruno's new generator which forces a pi-decay in the region 104 m < Z < 180 m.


             K+ ->  pi0 + pi+
                     |     |->  mu+ + neutrino
                     |
                     |-> gamma + gamma


Measurement accuracy

Fig 12.1 mu momentum: the Figure shows that there is little systematic mismeasurement in the spectrometer. The muon is characterised by a low energy deposit in the LKr.

Fig 12.2 mu position in LKr: these plots show a comparison of the position of the cluster in the LKr compared with the expected position from (a) the track projected from the spectrometer and (b) the position given in fKineParts. The y-position is correct; the x-position is in error by about 1cm if the nominal Z-position is used.

Fig 12.3 gamma position and momentum in LKr: the plots show a ~1cm displacement in X, and ~ 1% systematic shift in energy.

Acceptances

Fig 12.4 shows the fraction of energy from the gammas measured in the LKr as a function of the (true) energy of the gammas. As would be expected the acceptance reduces rapidly below below 40 GeV.

Fig 12.5 shows the fraction of energy from the gammas measured in the LKr as a function of the K+ decay position in Z. There is little Z-dependence.

Fig 12.6 shows the acceptance of the mu in the spectrometer as a function of mu momentum. The true and measured values are required to match within 5%.

Fig 12.7 shows the acceptance of the mu in the spectrometer as a function of the Z-value of the start of the muon. The true and measured values are required to match within 5%

Fig 12.8 shows the acceptance of the mu in the spectrometer as a function of the Z-value of K-decay. The true and measured values are required to match within 5%

Fig 12.9 shows the acceptance of the mu in the spectrometer as a function of the Z-value of K-decay for muon momenta in the range 15-35 GeV. The true and measured values are required to match within 5%

Comment the lower efficiency for electron versus muon measurement in the spectometer is evident from a comparison of Figs. 11.9 and 12.9.



Section 13 Reconstruction of the K+ decay (1/5/15)

This is a first examination of the accuracy of reconstruction of the K+ and pi+ decay vertices. For this it was assumed that that K+ x, y cordinates were known and that the K+ was parallel to the z-axis. The two gammas from the pi0 decay were smeared in x, y and energy according to the expressions in Bruno's thesis. The K+ decay z-coordinate was determined to give the correct pi0 mass. Energy- momentum conservation then gives the pi+ direction and energy. Assuming the lepton is accurately measured in the spectrometer allows in turn the intersection of the lepton and pi+ to be calculated and hence the Pi+ decay length. Fig 13.1 shows three plots that indicate the accuracy of these measurements. These calculations will be repeated with the full simulation in due course.



Section 14 Summary (20/08/15)


IRC, SAC:        No data

LAV:             Energy not calibrated.  

LKr              Energy    1% systematic error
                 x-coord   1 cm  systematic error.  
                 y-coord   accurate

Spectrometer:    accurate
                 Efficiency:      ~ 100% for muons  Fig 12.9      see   Section 12 
                                  ~ 90%  for electrons Fig 11.9   see   Section 11  

GigaTracker:     cannot read fCandidates.fPosition  using MakeClass
                 Pz fixed at 74.9999
                 possible problem with z-values in 2nd module.




Section 15 Study of MC using the standard NA62 Analysis Framework

Electron plots




             K+ ->  pi0 + pi+
                     |     |->  e+   + neutrino
                     |
                     |-> gamma + gamma


Fig 15.1 shows that the positron deposits its energy in the LKr at 241.3 m on average.

Fig 15.2 compares Lkr gamma cluster x and y positions with the matched end-values. There is a 1cm shift in x; y is, on average, correct. The measured energy of the cluster is ~ 1% higher than the true value.

Fig 15.3 compares Lkr gamma cluster x and y positions with the position of the positron projected from the spectrometer to the LKr. A 1 cm shift in x is again apparent. The y position is correct. The momentum measured by the spectrometer shows no significant systematic error.

Fig 15.4 These plots show the K+ decay position in Z determined from the two gammas (h7) and the pi+ decay point in Z from the intersection of the calculated pi+ and the positron measured in the spectometer (h9). The measured and true(red) distributions are also shown. The accuracy of the K+ and pi+ vertex determinations are ~2m and ~5m , respectively.

Fig 15.5 Acceptances in the spectrometer for, (a) all events, (b) events with lepton momentum 15-35 GeV, as a function of the Z-position of the K-decay.

Fig 15.6 Two-gamma acceptances in the LKr for, (a) all events, (b) eventa with lepton momentum 15-35 GeV, as a function of the Z-position of the K-decay.


Muon plots




             K+ ->  pi0 + pi+
                     |     |->  mu+   + neutrino
                     |
                     |-> gamma + gamma


Fig 15.2a compares Lkr gamma cluster x and y positions with the matched end-values. There is a 1cm shift in x; y is, on average, correct. The measured energy of the cluster is ~ 1% higher than the true value.

Fig 15.3a compares Lkr gamma cluster x and y positions with the position of the muon projected from the spectrometer to the LKr. A 1 cm shift in x is again apparent. The mean y position is correct. The momentum measured by the spectrometer shows no significant systematic error.

Fig 15.4a These plots show the K+ decay position in Z determined from the two gammas (h7) and the pi+ decay point in Z from the intersection of the calculated pi+ and the muon measured in the spectometer (h9). The measured and true(red) distributions are also shown. The accuracy of the K+ and pi+ vertex determinations are ~2m and ~5m , respectively. A nomininal K+ direction along the z-axis has been used.

Fig 15.5a Acceptances in the spectrometer for, (a) all events, (b) events with lepton momentum 15-35 GeV, as a function of the Z-position of the K-decay.

Fig 15.6a Two-gamma acceptances in the LKr for, (a) all events, (b) events with lepton momentum 15-35 GeV, as a function of the Z-position of the K-decay.

Fig 15.7a RICH (muons), (a) Comparison of ring center measured - expected; note shift in x. ('Expected' from focal length * slope at exit of spectrometer). (b) Comparison of measured and expected ring radii. Agree to rms ~ 1.5 mm. (Expected ring radius from true lepton momentum).

Fig 15.8a RICH (muons), (a) Hits: distribution in x,y. (b) Hits: measured - expected radius. Measured -expected X; Measured - expected Y.