The o ine signal selections are listed in Table 3.1. No high level reconstructed observables were used or are available in ALICE beyond |η| < 0.9, which would naturally be the optimal case with hypothetical large forward acceptance tracking and calorimetry.
Detector Signal Cut ADC ∆t ∈ [63, 69]ns V0C ∆t ∈ [0, 6] ns SPDC F ≥ 2 SPDA F ≥ 2
V0A ∆t ∈ [7, 14] ns ADA ∆t ∈ [54, 60]ns
Table 3.1: O ine signal selection quality cuts in terms of the signal arrival time ∆t and the number of red chips F .
After the low-level signal decision criteria, the data was corrected for the irre-ducible residual beam gas, satellite collisions and noisy events. That is, diractive events, especially single diractive, are experimentally very similar to a xed target like beam gas collisions passing through the time window and charge threshold cuts.
To correct this, we used beam-beam, beam-empty, empty-beam and empty-empty trigger masks which were based utilizing the normal and special LHC bunch bucket sequences. The data was corrected with
Nj ← Nj(B)− α(A)Nj(A)− α(C)Nj(C)+ 2α(E)Nj(E), (3.4) where Nj(k)represent the number of events in the j-th combination with the k running over the aforementioned special bunch trigger collected event statistics. The last factor with a positive sign and a factor of two takes into account the double counting.
The correction scale factors α(k) taking into account the dierent bunch sequence luminosity dierences and the deterministic and random trigger downscaling were obtained from the trigger statistics with
α(k)=
LMb(B) LMb(k)
L0a(B)/L0b(B) L0a(k)/L0b(k)
, (3.5)
where k = A is a beam from the A-side and nothing from the C-side, k = C is a beam from the C-side and nothing from the A-side and k = E is nothing from both
63
Figure 3.2: ALICE simulation at √
s = 13 TeV: The 6-dimensional detector folding matrix constructed with Pythia 6 MC + GEANT. The matrix elements are proba-bilities (%) with each column normalized to unity. Elements < 1% are not shown.
sides. The k = E case is negligible whenever detectors are operating with low noise levels. The trigger statistics are given in TablesA.3,A.4andA.5. The detector level marginal distributions of each detector are given in Figures A.1to A.13.
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Figure 3.3: ALICE simulation at √
s = 13 TeV: The 6-dimensional detector folding matrix constructed with Phojet MC + GEANT, otherwise the same as Figure3.2.
0.05 0.1 0.15 0.2 0.25 0.3 0.35 2.3
2.35 2.4 2.45 2.5 2.55
Figure 3.4: ALICE data at √
s = 13 TeV: The unfolded data Shannon entropy (vertical) versus relative entropy of raw data vs the unfolded (horizontal). The evolution is shown using two MC models used in the detector response simulation.
A suitable number of unfolding algorithm iterations (1 . . . 25) is near the maximum curvature.
Now speaking of 6-dimensional unfolding of data, we used the standard iterative Bayes method (D'Agostini) of the RooUnfold package [46]. However, we compared the implementation against our own implementation of the same algorithm and also Tikhonov regularized matrix inversion. To be precise, this iterative Bayes unfolding is a frequentist maximum likelihood method using the Expectation Maximization algorithm, which uses the Bayes formula, but is not a Bayesian method. The only Bayesian part is actually the number of iterations, which is an implicit regulator or prior. The unfolding here inverts the ine ciencies and the smearing ow of event topologies from one combinatorial category to another one, thus formally easily de-scribed by a folding matrix in the same way as any single dimensional histogram unfolded measurement. These combinatorial folding matrices are shown in Figures 3.2and 3.3, which demonstrate the major role of detector material rescattering and e ciency corrections.
In the forward domain, even half of the accumulated charge seen by the detector
is from particles propagating from the material interactions, such as γ → e+e− conversions. This is demonstrated in Figure A.17. Fiducial (generator) level event topologies are easily transformed into another topology at the detector level. The simplest acceptance characterizations, here for the visualization purposes, are the diractive mass e ciency × acceptances shown in Figure A.16 and A.15, where we see that for the SPD the pure ducial acceptance and the e ciency × acceptance are very close. However, for the AD we see a large dierence between these two. This is due to the material distributions which actually yield larger eective acceptance than what is geometrically expected. The dierence between Pythia 6 and Phojet is due to dierences in the fragmentation of the diractive systems. Phojet has a hard (perturbative) pt-tail, Pythia 6 generates diractive events only with soft pt. Also, the multiplicity distributions are dierent, as is visible in Figure A.14 where the detector level MC/Data ratios are shown. For a generator level comparisons together with Pythia 8, see the work in [47].
Figure3.4demonstrates the unfolding regularization parameter (number of itera-tions) abstract behavior in terms of Shannon entropy and relative entropy (Kullback-Leibler divergence) between the raw with no unfolding and the unfolded measure-ment. Interestingly, the two dierent MC models have approximately the same `sweet spot' but opposite trajectories in this abstract entropy space. We found out that this technique gives a purely data driven handle to control the regularization strength.
The point where the regularization should be optimal is the point of maximum cur-vature, by highly often used L-curve heuristics in inverse problems [48]. Or it could be also the point where trajectories between dierent models cross. Zero iterations gives no unfolding, whereas too many iterations will push the results towards Monte Carlo estimates, speaking in general. Based on this and simulations, we chose the point of 4 ± 2 iterations in the unfolding algorithm. Accidentally, the default values of the LHC unfolding package parameters are usually around 4 iterations. We should study this interesting topic further in the future, because it has been basically ne-glected in all existing rapidity gap based measurements, even unfolded ones, because they integrate out the multidimensional information.
We found out that the unfolding has here the largest experimental systematic uncertainty besides the forward detector geometry and material budget simulation, the SPD chip noise and the V0 and AD signal response modeling uncertainties.
Understanding these systematic uncertainties in extreme detail would be required for higher precision measurement. Also the beam-gas correction can be in some runs very large, but our combinatorics has a self-consistent way to correct it. Still, run-by-run dierences remain much larger than statistical uncertainties in some combinations. A forward tracking and calorimetry with very low material budget would be bene cial.