4.7 Thin target inelastic and absorption cross- cross-section datasetscross-section datasets
4.7.4 Technical implementation of the absorption and in- in-elastic cross-sectionin-elastic cross-section
The correction is implemented as follows:
1. pC inelastic and absorption cross-sections:
• For the inelastic cross-sections (needed in cases when we use Equation 4.9), we implement the value given by NA49 data with its associated uncertainty (226 mb± 2.5%). For the absorption cross-section (needed for the proton at-tenuation correction in the target), we add the implemented inelastic cross-section and the quasi-elastic component, which has 40% uncertainty as de-scribed in Section 4.6.1.
(GeV/c)
40 Cronin et al.
Denisov et al.
C absorption cross-section data-MC comparison π±
60 Cronin et al.
Denisov et al.
Al absorption cross-section data-MC comparison π±
(b) πAl
FIG. 4.42: π Data - MC absorption cross-section data - MC comparisons.
(GeV/c)
Al absorption cross-sections C and K+
450 Abrams et. al.
Denisov et. al.
Al absorption cross-sections C and K
-K
-(b) K−C and K−Al
FIG. 4.43: Charged kaon on C and Al data and MC absorption cross-section. Error bars on many of the points are too small to be seen.
(GeV/c)
70 Abrams et. al.
Denisov et. al.
Carroll et al.
C absorption cross-section data-MC comparison K+
60 Abrams et. al.
Denisov et. al.
Carroll et al.
Al absorption cross-section data-MC comparison K+
(b) K+Al.
FIG. 4.44: K+data - MC absorption cross-section data - MC comparisons.
(GeV/c)
100 Abrams et. al.
Denisov et. al.
Allaby et. al.
Carroll et al.
C absorption cross-section data-MC comparison K
60 Abrams et. al.
Denisov et. al.
Allaby et. al.
Carroll et al.
Al absorption cross-section data-MC comparison K
-(b) K− Al.
FIG. 4.45: K− data - MC absorption cross-section data - MC comparisons.
• The MC, the calculated inelastic cross-section for the incident proton energy shown in Figure 4.40 is implemented and a linear interpolation is made for intermediate incident proton energies.
• We should note that this correction has a central value different than 1.
2. π± and K± absorption cross-section:
• The central value for this correction is equal 1.
• For π±, we noted that almost all of the differences between the datasets and the MC are less than±5% of the MC value. Based on this, the uncertainty associated to π±C and π±Al are 10 mb and 23.8 mb, respectively.
• For K±, the data and MC discrepancies are larger than π±, especially for low momentum (< 2 GeV/c), and these discrepancies are different for K+ and K−. Based on this, we implement uncertainties that cover almost all of the dataset - MC differences in Figures 4.44 and 4.45. Table 4.3 lists these values.
3. Details about attenuation correction:
• This correction is applied to all hadron neutrino parents, grandparents, and, when they exist, great-grandparents.
• For the target, the amount of carbon traversed longitudinally by the particles interacting or leaving the target is tabulated precisely. We add the material traversed only in the fins.
• The correction is also applied to others NuMI components: the horn inner conductor (Al), the decay volume (He) and decay pipe walls (Fe).
• For nucleons, and in general any other particles, we assign the biggest un-certainty (K+ on aluminum).
data ∆σ (mb)
π on carbon 10
π on aluminum 23.8
K+ on carbon (P < 2 GeV/c) 68 K− on carbon (P < 2 GeV/c) 80 K+ on aluminum (P < 2 GeV/c) 83 K− on aluminum (P < 2 GeV/c) 49 K+ on carbon (P > 2 GeV/c) 13 K− on carbon (P > 2 GeV/c) 20 K± on aluminum (P > 2GeV /c) 30.5
TABLE 4.3: Summary of the meson absorption cross-section uncertainty implemented in our hadron production procedure.
A summary of the uncertainty per particle and material is listed in Table 4.3.
4.8 PPFX
Note: This is a technical section which may not interest some readers.
PPFX is the package we wrote to implement the hadron production corrections and propagate uncertainties described in the previous section. PPFX stands for Package to Predict the FluX and is an experiment-independent neutrino flux de-termination package for the NuMI beam that provides a correction for hadron pro-duction mismodeling 8 using almost all relevant data. Currently, PPFX corrects the beamline simulated with g4numi using geant4 2.p03 and the FTFP BERT hadronic model 9. The inputs are dk2nu and dkmeta objects [82] for each neutrino event, and it returns a set of correction values to be used as weights to calculate the right
8The uncertainties associated with the focusing process have not been implemented yet and are currently handled inside the MINERvA framework.
9The prescription followed for the current model can be applied directly to extend to other hadronic models.
neutrino yield. Internally, PPFX:
• Accounts for the attenuation of all particles passing through the relevant NuMI materials: the target and Budal monitors, the magnetic horn inner conductors, the decay pipe volume and the decay pipe walls.
• Implements energy-scaled thin-target data for incident particles in the energy range 12-120 GeV. All data is carefully interpolated to smooth transition between bins.
• Implements MIPP NuMI target data for pions and high energy kaons.
• When there are no data, PPFX attempts first to use theoretically guided extensions and when it is not possible, uses a data-driven best guess.
• Handles correlated and uncorrelated uncertainties using the multi-universe tech-nique for uncertainty propagation.
Figure 4.46 shows a schematic view of how the main classes of PPFX work. They are described below:
4.8.1 MakeReweight
MakeReweight is a singleton class that controls the process. It has to be in-stantiated and initialized by the user selecting options that are entered in an xml file through the class member SetOptions. Three options are currently settable:
• The process mode. Two modes are implemented: MIPPNuMIOn and MIPPNuMIOff.
When MIPPNuMIOn is selected, the code tries to use thick target data as a pri-mary correction and thin target data for any interaction not yet covered. When MIPPNuMIOff is selected, the code does not use thick target at all and instead
FIG. 4.46: PPFX flowchart.
applies a correction based on thin-target data for all interactions. This switch-ing mechanism will be use for Gen2-thin and Gen2-thick flux versions as will be described in Section 5.3.
• The number of universes to be used in the process.
• The MIPP NuMI hadron production bin to bin correlation for systematic uncer-tainties. The default value is +75%.
MakeReweight is also in charge of initializing:
• The CentralValueAndUncertainties class that creates tables of central values and deviates per universe (it is called ParameterTable). This is done by reading the input data from an xml file (parameter file).
• The binning convention of the data input matching the parameter file convention.
• A vector of ReweighterDriver�s (where every entry corresponds to one universe and becomes its identification, ID) and a ReweighterDriver for the central value (which has an ID of -1).
Its member CalculateWeights constructs an InteractionChainData object using the dk2nu and dkmeta inputs, and passes them to every ReweighterDriver to make the calculations, and provide the user a vector of universe weights by calling the member GetWeights() and a central value weight by GetCVWeight().