Capítulo V. Resultados
5.5 Percepciones y apreciaciones del PRONI como guía del trabajo
As a final step to estim ate the to ta l num ber of electrons from photon conversions, we have to ascertain an overall, “global” efficiency. This is a M onte Carlo based procedure and we have to somehow estim ate from all th e tru e conversions, how m any are found from our previous two steps. W ithin the ZEUS detector, there are a large num ber of photon conversions which could never enter into our sample of candidate tracks and can therefore be neglected. If we were not to remove them and simply count all th e photon conversions as produced by G EA N T, then our efficiency would be less th a n 1%. However, knowing exactly which tru e photon conversions to remove is non-trivial. Photons which convert a t th e edge of th e CTD could have the electron passing through the CTD and into th e calorim eter, th e positron not entering the C TD . This may or may not then enter our sample b u t knowing which of these kind of tru e events to remove is impossible. We
Extraction of Semi-leptonic Decays to Electrons C hapter 7
therefore choose not to define th e undefinable tru e sample and seek another m ethod.
T he m ethod used is in a sense analysis specific, being only relevant to the analysis requirem ents as detailed and cannot therefore be used in any other context although should be com parable for a sim ilar kinem atic region. By requiring
no final state electrons and perform ing th e analysis on these events, we find an effective to ta l num ber of conversions. A pplying th e conversion finder and applying the asym m etric efficiency, we have th e num ber of conversions our m ethod so far finds. T he ratio of th e two therefore provides us w ith our global efficiency. This was found to be 90%, which upon application to the num ber so far ascertained in the analysis yields a to ta l of 830 ± 36 electrons coming from photon conversions. The num ber of electrons estim ated as arising from photon conversions represents ab o ut one-third of our to ta l electron signal sample, reducing it to, 1646 ± 82 electrons. The identification of the num ber of electrons from photon conversions is sum m arised in Table 7.1.
No. conversions No. electrons
Initial - 2476 ± 74
After C 0N V E R T 2 599 ± 26 1877 ± 79 Tsai weighting 748 ± 33 1728 ± 81 Global weighting 830 d= 36
1646
±82
Table 7.1:
Table showing the number of electrons from conversions and the subsequent number of electrons in the final sample.We have now fully estim ated th e background in our signal sample, the rem aining electrons entering into our cross-section calculations.
7.6
E x tr a c tio n o f
a n d p ^ ‘ D is tr ib u tio n s
Using the electrons now found, we can use them to calculate physics distributions, and being the interesting ones in this analysis, where defined in C h ap ter 2 and in C hapter 3. T he basic m ethod to extract them is th e same in each case so we will initially concentrate on th e d istribution by way of an example.
Each tim e we tag a track as being an electron or hadron enriched candidate we calculate th e event property where the hadron enriched sample is
Chapter 7 7.6 Extraction of and Distributions
appropriately weighted from the normalisation factors. The result of this can be seen in Figure 7.22 (Top), where the distribution is shown for the events containing the two classes of track-island m atched quantities. The electron enriched is displayed as the open squares and the hadron enriched as the histogram. The first and most obvious point of the graph is th a t there is a peak at high for the electron enriched sample consistent with direct photon events which is not as pronounced in the hadron enriched sample. The distribution for the hadron enriched sample is reasonably flat in indicating th a t the presence of the electron and hence heavy quarks enhances the direct peak. The same conclusion was drawn in the analysis of D* mesons in which the signal region was peaked at high and the wrong-charge background estim ator was flatter in x°^^. 1000 S 750 0) 500 250 C 0 5 600
I
<D 400 0> 200 0 400 0) 300 □ Electron enriched Hadron enriched A Subtracted electrons S Conversion electrons • data; 1996+97 o HERWIG MG; direct+resolved OID HERWIG MG; direct (57%) ^ HERWIG MG; resolved (43%)A
Figure 7.22; Distribution in fo r the electron (squares) and hadron (histogram) enriched samples (top) after all cuts. Also shown (centre) are the two subtracted (triangles) compared to the conversion electrons (histogram). The final electron signal (solid circles) is then compared to Monte Carlo (open circles) predictions (bottom) with direct and resolved also shown separately.
Extraction of Semi-leptonic Decays to Electrons C hapter 7
U pon subtraction of th e two distributions, we have th e distrib u tio n shown as the open triangles in Figure 7.22 (Centre), which represents the distribution for 2476 electrons in th e signal region. Also shown is the distrib u tio n for those electrons identified as conversions appropriately weighted for the tw o-step efficiency procedure. T he distribution for conversion electrons is also peaked at high b u t not as rem arkably as for the to ta l electron signal. S ubtraction of th e two yields th e distrib u tio n shown as solid points in Figure 7.22 (B ottom ), which represents our uncorrected distribution.
The uncorrected d istrib u tio n is compared to M onte Carlo predictions from HERW IG (open circles). The proportion of direct and resolved from a fit to the d a ta are also separately shown. T he fit reveals a value of 43±4% for resolved photon processes, th e combined sample in good agreem ent w ith the m easured d ata. The proportion of LG resolved photon M onte Carlo required is also vindication of th e results for th e analysis w ith D* mesons (which is consistent w ith the predicted value) even though the kinem atic range and the am ount of charm events is different.
We can also follow the same process for a m easurem ent of and it is shown in Figure 7.23. The same d istributions are displayed as for th e m easurem ent of The distributions have variable bin widths, due to a sm all am ount of statistics in th e higher bins, which th en makes the perform ing of M onte Carlo fits to the d a ta more reliable.
The com parison of th e electron and hadron enriched samples Figure 7.23 (Top) reveals nothing of rem ark, b o th being of sim ilar shape. T he same applies to th e com parison of th e su b tracted electrons and conversion electrons in Figure 7.23 (Centre), although the subtracted electrons are slightly harder in
pl^K However, on com parison w ith HERW IG M onte Carlo predictions the d a ta shows an interesting tren d Figure 7.23 (B ottom ). The M onte Carlo has been area normalised to the d ata, and th e proportion of direct and resolved from th e fit to used. No further fits for proportions of direct and resolved or quark content were made. From th e Figure, we see th a t there is a tendency for th e d a ta to be harder th an the M onte Carlo prediction. In th e first two bins, th e d a ta lies below th a t of the M onte Carlo, this then inverts itself, w ith th e d a ta lying above th e Monte Carlo in the last two bins. If we fit the am ount of beauty and charm-f-other to the d a ta we obtain a value for beauty of 42±6% . Is th is an indication of th e Monte Carlo predicting too much or too little of certain processes? We will first
Chapter 7 7.7 Other Sources of Background?
correct the data, reassess the comparison w ith Monte Carlo and then try and draw some conclusions.
;g 10
(/)
c
o
k. o 0) <D 1 0 ^c
1
1
0) <D □ Electron enriched Hadron enriched _i I I I I I I I I I l_ A Subtracted electrons Conversion electrons d a ta :1996+97 HERWIG MG; direct+resolved HERWIG MG; direct (57%) HERWIG MG; resolved (43%) 3 3.5Pjre\ (GeV/c)
Figure 7.23: Distribution in p ^ ^ fo r the electron (squares) and hadron (histogram) enriched samples (top) after all cuts. Also shown (centre) are the two subtracted (triangles) compared to the conversion electrons (histogram) in the data. The final electron signal (solid circles) is then compared to Monte Carlo (open circles) predictions (bottom) with direct and resolved also shown separately.
7 .7
O th er S ou rces o f B ackground?
Having now achieved our uncorrected distribution in we briefly return to the question of backgrounds apart from electrons from photon conversions. As was stated previously, there are no other backgrounds to subtract. The decays from light quarks remain as well as those from heavy quarks as only model dependent methods exist for their subtraction.
Extraction of Semi-leptonic Decays to Electrons C hapter 7 0 2000
01500
1 1.5 2dE/dx (mips)
.51800
f 1600
C l 400 O >1200 1000 800 600 400 200 0, l-iH I I I I I I I I I I I 0.2 0.4 0.6 0.8 X^obsFigure
7.24: Distributions in d E /d x for subtracted positron signal (Left) andsubsequent distribution (Right).
If we were considering positrons as well as electrons, then we would have to th in k more carefully ab o u t backgrounds. In Figure 7.24 we see the distrib u tio n if we tag positrons ra th e r th an electrons w ith all other analysis criteria rem aining the same. From the distribution in dE/dx^ we can see th a t the result of statistical subtraction is poor. This has been influenced by the large am ount of ex tra positrons (com pared to electrons) observed, which shifts th e peak value and affects the norm alisation of the background. T he m ethod we have adopted is reliant upon the num ber of electrons being small particularly a t high m om entum . At high m om entum the separation in d E/ d x of electrons and hadrons becomes worse; consequently one has to s ta rt norm alising th e hadron enriched signal to the electron enriched signal in th e region of th e electron signal itself. As m any of the ex tra positrons here observed are a t higher m om entum , the problem therefore arises. One has to th en ask th e question, w hat are these ex tra positrons? T he first and obvious tho u g h t would be th a t they are scattered DIS positrons, which from the shape of Figure 7.24 (Right) is given some credance. T he d istrib u tio n shows a sim ilar shape to th a t for electrons (see Figure 7.22) except for th e last bin which is high being indicative of DIS processes.
As we are specifically rejecting DIS and tagging photoproduction events, we should have no DIS scattered positrons, although there is always contam ination in one from th e other. However, this then p uts into question th e results using electrons and begs the question, how much DIS contam ination do we have?
C hapter 7 7.8 Comparison of Data and Monte Carlo
Obviously th e num ber of ex tra positrons cannot be exactly stated as th e m ethod needs to be changed to perform the analysis, b u t it seems to be of th e order of a few thousand. This may seem like a large num ber, bu t as the analysis is to specifically ta g positrons, we find a large num ber of them . It also has to be taken into context of how many electron enriched tracks we have; 100000, which implies th a t th e scattered positrons are a few percent of those tracks, indicating th a t th e DIS contam ination is not large.
The above explains why positrons have no t been used. For them to be used, the m ethod needs to be adapted w ith th e following being im p o rtan t points which need to be addressed:
• C an we more efficiently elim inate scattered positrons? • If not, can we estim ate the num ber?
• C an we improve th e resolution of th e CTD ?
• If we do have scattered positrons, th en an upper lim it on th e m om entum of th e track will reject many.
The inclusion of the positron d a ta obviously needs more study and will not be possible w ithout solving th e above problems. This is not covered fu rth er in this thesis and we will concentrate solely on th e electron sample.
7.8
C o m p a riso n o f D a ta an d M o n te C arlo
Before correcting our d a ta to a cross-section, we would like to com pare event properties and look a t resolutions in the M onte Carlo.
We first consider the resolutions in pseudorapidity and transverse m om entum of tracks which are our candidate tracks. The resolution distributions are shown in Figure 7.25 for all tracks. B oth th e d istributions in pseudorapidity (Left) and transverse m om entum (Right) show no average shift and b o th have good resolutions. O f particular interest is the resolution of the transverse m om entum which is,
^
= 0 .011,Extraction of Semi-leptonic Decays to Electrons C hapter 7
This represents an upper lim it as we have assumed p r = 1 6 G eV /c, which is the lower cut-off value. The p t resolution of the C TD as stated in C hapter 1 is not in good agreem ent w ith th is figure; again w ith p t = 1.6 C eV /c, the resolution is predicted to be;
P
t0.005
pt
0 0.016 = 0.018,
which in this case represents a lower limit.F urther research has been done [91] and found th a t th e above form of the resolution is not a good estim ator particularly for low transverse m om entum tracks and as high as ~ 3 — 4 C eV /c. An improved form was postulated such th a t,