Former measurements of the structure function xF3 have been performed by the CCFR [96]
and IHEP-JINR [97] collaborations in neutrino-proton scattering. However, these measurements were limited inQ2to a few 10 GeV2. Together with similar results from H1 [98] the measurements presented in this thesis are the first extractions ofxF3 at highQ2 in lepton-proton scattering.
The parity violating nature of the weak force leads, depending on the charge of the incoming lepton, to different signs in parts of the interference and the Z-only contributions to the NC DIS cross section in (2.19). The size of these parity-violating contributions is predicted by the SM electroweak theory and hence the latter can be tested by extracting the structure function xF3 from the data. In principle, this could already be performed with either e+p ore−p data.
However, in this case one would have to calculate theF2contribution11to the cross section from theory, where both electromagnetic and weak forces are involved as can be seen from (2.22), or, to put it in a different way, the electroweak theory would be used to test itself. In order to avoid this, bothe−p ande+pdata have to be available12 as then the double-differential cross sections can be subtracted leading to:
xF3NC= xQ4 2πα2 · 1
2Y− .
σ−−σ+
(7.18) with
σ±= d2σNC(e±p)
dx dQ2 (7.19)
from (2.19). Note that this formula only holds if both data sets were recorded at the same center-of-mass energy, whereas for different ones (300 GeV and 318 GeV in the case of HERA) (7.18) transforms into:
xF3 = xQ4 2πα2 ·
Y−300
Y+300 +Y−318 Y+318
−1
· 1
Y+318 ·σ−− 1 Y+300 ·σ+
+ ∆FL , (7.20) where Y±300,318 denote Y± calculated for center-of-mass energies of 300 GeV and 318 GeV, re-spectively. The term ∆FL is a remnant of the difference between they2FLNC terms for e−p and e+p in (2.19) which do not exactly cancel due to the y2 factor and the different center-of-mass energies. The contribution of ∆FL(calculated from QCD) toxF3 in (7.20) is of the order of 7%
at Q2 = 1500 GeV2 and x = 0.04 and decreases rapidly with increasing Q2 and x. For x0.1 it is always below 1%.
In addition to thee−pcross sections measured in this thesis, those from the publishede+pdata set [7] taken during the 1996/97 run period at a center-off-mass energy of 300 GeV are used to extract xF313. The latter are based on a data set corresponding to an integrated luminosity of 30 pb−1.
7.6.1 Binning
The double-differential binning (Fig. 7.11) cannot be adopted unmodified for the extraction of xF3 as statistics is very low in the high Q2 region. This in combination with the subtraction
11The longitudinal structure functionFLis neglected here due to its small contribution at highQ2.
12This not only holds for the extraction ofxF3 but also for that ofF2 in the high Q2 regime MZ2. Here, thexF3 contribution to the cross section is no longer negligible and the extraction ofF2 relies heavily on the correct prediction of the size ofxF3. This difficulty can be solved by adding the measured double-differential cross sections fore−pande+p. However, as the statistical errors are very small, systematic uncertainties play a significant role and have to be investigated very carefully, which is a major task when combining two different data sets.
13The 1999/2000e+pcross sections, recorded at√
s= 318 GeV, have not been published yet.
104 105
10-2 10-1 x
Q2 [GeV2 ]
801 1112
● 523
897
● 347
579
● 69
127
●
433 600
●
210 279
●
56 62
●
162
162
●
23
36
●
24
13
●
y = 1
# of evts e−p
e+p
Figure 7.23: xF3 binning in the x-Q2 plane. Bins with a thick frame are xF3 bins, whereas the original double-differential bins are marked with dashed lines. The numbers in thexF3 bins denote the number of events for e−pand e+pin that bin. The full circles indicate the quoted points for the measurement.
of the two cross sections leads to huge statistical errors. Therefore, several bins are merged yielding the binning displayed in Fig. 7.23. The “old” double-differential binning is also shown for reference. The points in the kinematic plane where the xF3 will be quoted are marked with a full circle.
7.6.2 Systematic checks
Systematic investigations are of major importance when combining two data sets as the experi-mental conditions like detector setup or beam conditions can be quite different over the years.
In the special case of subtracting two cross sections the uncertainty of the integrated luminosity plays also a significant role. The major problem in the present case is that not all systematic checks are made in the same way and that some checks are completely missing for one of the two measured cross sections. Thus, for these calculations the systematic uncertainties for e−p and e+pare assumed to be uncorrelated. Later it will become clear that the systematic uncertainties are much smaller than the statistical errors and hence small inaccuracies in the treatment of the systematic uncertainties do not affect much the total error of the measuredxF3 values.
Fore−pthe systematic uncertainties incorporated into the extraction ofxF3 have been discussed in Chaps. 6.2 – 6.3 and Chap. 7.4.3, whereas for e+p a detailed description can be found in [9]. The error on the measured structure-function values due to the 1.5% uncertainty on the normalization of both data sets is not contained in the total systematic error but is calculated separately. As the correlation between the normalization errors is unknown for now a worst-case scenario is assumed, i.e. that the normalization uncertainties are negatively correlated.
7.6.3 xF3 results
Using (7.20) with the measured e−p (16 pb−1) ande+p (30 pb−1) cross sections yields the xF3 values depicted in Figs. 7.24 a,b (the corresponding table can be found in Appendix D.5). Note
-0.5 0
xF30.5
Q2 = 1800 GeV2 Q2 = 3500 GeV2
0 0.2 0.4
10-1 Q2 = 9000 GeV2
10-1 x
Q2 = 30000 GeV2
e−p DATA (ZEUS analysis AK 2001) normalization uncertainty
PDF uncertainty
CTEQ5D NLO ZEUS NLO MRST (99)
a)
-0.5 0
xF30.5
x = 0.037 x = 0.1
-0.5 0 0.5
103 104
x = 0.23
103 104
Q2 [GeV2] x = 0.43
b)
Figure 7.24: Extracted structure function xF3 as (a) a function of x in bins of Q2 and (b) a function of Q2 in bins of x. In addition calculations based on CTEQ5D, ZEUS NLO and MRST(99) PDFs are shown together with a light shaded band (hardly visible) representing the uncertainty on the ZEUS NLO calculations. The dark shaded band indicates the uncertainty on the measured structure functions due to the limited precision of the normalization of both data sets of1.5%, where a worst-case scenario, i.e.
negatively correlated errors, is assumed.
10-1 1 10 102 103 104 105
10-6 10-5 10-4 10-3 10-2 10-1 1 x Q2 [GeV2 ]
kinematic limit y=1
y=0.005
ZEUS 1998+99 e–p ZEUS 1999+00 e+p ZEUS 1996+97 e+p ZEUS SVX 1995 e+p ZEUS SVX + ISR 1994 e+p ZEUS BPT 1997 e+p Fixed-target experiments
Figure 7.25. Kinematic x-Q2 plane with areas covered by ZEUS analyses and fixed target-experiments. The area labeled “ZEUS 1998+99e−p” is the sub-ject of this analysis.
that the contribution of ∆FL to xF3 has been neglected in these plots due to its smallness compared to the errors. In addition, theoretical calculations based on CTEQ5D, ZEUS NLO and MRST(99) PDF parameterizations are shown together with the uncertainty on the ZEUS NLO fit as a light shaded band (hardly visible). The dark shaded band marks the normalization uncertainty. In Figs. 7.24 b the rise ofxF3 with increasingQ2, already observed in the difference between thee−pande+pcross sections (Figs. 7.9 and 7.19) forQ2 MZ2, is apparent. It should be noted that the fall-off ofxF3 towards low xis not caused by the actual structure functionF3
but solely by thex factor.
A comparison between the calculations and the measured values yields good agreement. The largest deviation for a single point occurs at Q2 = 1800 GeV2 and x = 0.037 and amounts to 2.2σ. The errors are too large to allow discriminating the different PDFs. The error on the measured structure function points is completely dominated by the statistical errors, even if the worst-case normalization uncertainty is considered.
The e−p data set with its much lower luminosity contributes by far the most to the statistical error. Consequently, gathering more e+p data does not further reduce the error on xF3 but high-luminosity data sets of similar size are needed for improved precision.