Explorations of Neutrino Flux from the NuMI Beam at Different Positions From the Beam Axis

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1 Explorations of Neutrino Flux from the NuMI Beam at Different Positions From the Beam Axis Sonya Paola Vidal REU Program, College of William and Mary Dr. M. Kordosky College of William and Mary August 29, 206 Abstract The Neutrinos at the Main Injector (NuMI) beam at Fermilab are used for several particle physics experiments. The three detectors of relevance are the MINERvA, MI- NOS Near, and NOvA Near detectors. These experiments are integral in exploring neutrino-nucleon interactions and neutrino oscillations. Recent data from the NuMI beam reveals a disagreement between the Monte Carlo simulation and the data taken due to the flux. A possible cause of this problem would be a physical error in the position of the detectors themselves. The research presented will look into this cause by changing the positions up to 00cm in both directions of x and y in the beam reference frame. Analysis is done using data files from FermiLab and ROOT in a general kinematics loop across all detectors. Background. NuMI Beam The Neutrinos at the Main Injector (NuMI) beam at Fermilab creates neutrinos that are used for several particle physics experiments. The wide-band NuMI beam is created by first directing a 20 GeV beam from Fermilab s Main Injector onto a graphite carbon target []. The hadrons that are produced are focused by two parabolic magnetic horns that allow more neutrinos to hit the detectors for more data. The magnetic horns allow for sign selection in the hadrons to create a beam of neutrinos or antineutrinos [2]. Later the hadrons go into a 675m long decay pipe [2]. In the decay pipe there are many extraneous interactions that do not lead to neutrinos, but mainly the beam is made up of pions and kaons that decay into muons and neutrinos. At the end of the decay pipe there are hadron monitors and hadron absorbers to measure the quality of the beam. Next the beam passes through muon absorbers and 240m of dolomite rock to attenuate any remaining muons [2]. The rock allows for the neutrinos to pass through and the muon monitors are located in between rock layers to continue measuring the quality of the beam s direction and composition. In Figure a side view of the NuMI beam s journey is shown. Downstream from the rock are where the detectors for the various projects taking place are located. Three of the detectors focused on in this paper are the Main Injector Experiment for v-a (MINERvA), Main

2 Figure : Displays side view of the the NuMI beam as discussed. The two horns are the parabolic magnetic horns and the absorbers are the muon absorbers downstream from the decay pipe [2]. Injector Neutrino Oscillation Search (MINOS), and the NuMI Off-Axis Electron Neutrino Appearance (NOvA). MINERvA is slightly off-axis of the beamline and studies the neutrino reactions in five different nuclei in the -0 GeV energy range [4]. Its measurements provide a better understand of the proton and neutron structures and the characteristics of force between neutrinos and nucleons [4]. MINOS is on-axis of the beamline and observes neutrino oscillations [5]. NOvA is more off-axis than MINERvA and is also a neutrino oscillation experiment concentrating on the disappearance of muon neutrinos and the appearance of electron neutrinos [3]..2 Changing Positions of MINERvA, MINOS Near, and NOVA Near Figure 2: Displays a histogram energy distribution of the MINERvA Data and Monte Carlo and their disagreement [7]. In all three detectors (NOvA, MINERvA, and MINOS) there exists a discrepancy between the data taken and the Monte Carlo simulation. The discrepancy is noted in MINERvA in 2

3 Figure 3: Displays a ratio histogram of the data over Monte Carlo for MINERvA. The area of focus is around 5 GeV and 8 GeV [7]. Figure 2 and the energy distributions of MINOS and NOvA in Figures 4 and 5, respectively. The difference between the simulation and data may be due to a number of factors, however the problem most likely lies in the flux. Generally, a cross section is calculated by the quotient of number of events and flux. Theoretical models of cross section do not exhibit any wiggle in the ratio plots, so according to the current understanding of cross sections the discrepancy is not due to that. There is a possibility that the graphite target downstream from the proton beam could be moved to fix the problem, but because of where the data is disagreeing the cause of the discrepancy is attributed to the flux. In order to explore this problem the positions of the MINERvA, MINOS, and NOvA will be moved in a ROOT loop called ReDecay 00cm in the negative y, negative x, positive y, and positive x directions in the beam reference frame. The goal would be to bring all detectors to a Monte Carlo/Data ratio of. There must be one common length to change across all detectors because their relative distance must stay equal in order to track neutrinos. Before any change in position can be concluded, one must explore the ratio plots for MINERvA, MINOS, and NOvA to determine how much percentage each detector must be changed for optimal results. According to Figure 3 MINERvA must be moved a total of approximately 22% at 5 GeV and 8% at 8 GeV to have a ratio of. This proposed change in position focuses solely on the 5 GeV and 8 GeV areas and does not take into account the more than 30% difference prior to 5 GeV. Figure 4 is an example of the energy distribution and data discrepancy of MINOS and its related ratio histogram. The histogram of relevance for the research is the data using neutrinos and horns on. The other histograms will be referenced later. Looking at ratio histogram of the data divided by the tuned Monte Carlo it seems to be over by 5% at 5 GeV and under by 9% at 8 GeV, approximately. The large discrepancy between the data and simulation around -2 GeV is most likely due to statistical error and not thought to be attributed to the change in position. NOvA observes lower energy than MINERvA and MINOS because its main goal is to look for neutrino oscillations. Because of this, the energy range focused on for change is GeV and 3 GeV. In reference to Figure 5, the Monte Carlo looked at is the new one in blue 3

4 Figure 4: Displays a ratio histogram of the data over Monte Carlo for MINOS. The top two histograms are with magnetic focusing horns on and the bottom two are horns off. The left two histograms are neutrino data and the right to histograms are antineutrino data. For the research in this presented in this paper, only neutrinos with horns on (top left) is of relevance [8]. 4

5 Figure 5: Displays a the energy distribution and data of the NOvA detector. The Monte Carlo of relevance is the blue dashed line in the energy distribution and blue squares in the ratio histogram of data over Monte Carlo ratio plot [9]. on both histograms. The data is normalized based on protons on target (POT) of the NuMI beam. According to that Monte Carlo, NOvA should change position such that it attenuates the discrepancy of 25% at GeV and 20% at 3 GeV and bring the ratio to. The change in position used in ROOT aims to find a solution that would bring all detectors close to a ratio of with their Monte Carlo..3 ReDecay Function The ROOT loop used is general for all three detectors where each original position was inputed, changed, then recalculated in the loop to create new energy distributions. The loop is called ReDecay and assumes all positions are in centimeters in the beam reference frame where z points in the direction of the beam and x goes to the left. A section of the loop is shown in Appendix A. The loop processes a two body decay of a pion into a neutrino and muon. It initially computes the kinematics of the pion, the parent particle. Momentum, energy in the lab s frame, gamma, and beta of the pion are calculated. Later the points of the decay vector will be calculated according to where the neutrino needs to be aimed at. Weights are computed and the boost the code refers to is calculated through a Lorentz transformation similar to that of the MINOS Monte Carlo [6]. The objective of the boost is to move reference frames from the lab to the beam s. From there the energy and weight of the neutrino is outputted. The positions (x,y,z) can be changed easily corresponding to the positions of the detectors without damaging the validity of the new energy and weight results similar to the N-Tuple explanation in [6]. New histograms were made with each detector at varying positions and ratio plots of the new positions to the original ones were created for analysis. 5

6 2 Results The three detectors were looked at individually to determine what change in position would be best for agreement with its respective Monte Carlo. Looking at the legend in Figure 9, each of the histograms in Figures 6, 7, and 8 correspond to a change in position on the referenced axis away from the original position in 0cm increments up to 00cm. In the ReDecay function one can input new point positions for the detector and recalculate new energies and weights at those points. Instead of using the center points of the detectors, an area of 00cm square was used by looking a the data of a simulated neutrino at random point in the square. An area was used because the detectors observe neutrinos over all of their area instead of just at their center point. Note that only x and y coordinates were changed for all three detectors. This displays a more general result than if the z axis was altered, especially for the NOvA detector because it is angled slightly in the z direction. 2. MINERvA MINERvA histograms in Figure 6 shows that there is subtle change when moving the detector in the positive direction. This small change is because MINERvA is slightly off-axis to the right in the beam reference frame, so moving it in the positive direction would move it more on-axis. The change needed for MINERvA was listed above and is seen in Figure 3 on the ratio plot. In order for MINERvA to have a ratio of it must exhibit at 50cm shift in either the negative x or the negative y direction. A 50cm change in the negative x direction would attenuate 6% at 5 GeV and 6% at 8 GeV and in the negative y direction it would attenuate 6% at 5 GeV and 8% at 8 GeV. 2.2 MINOS MINOS histograms in Figure 7 show that any directional change would be a significant and similar to the others. This is because MINOS is on axis in the x and y direction to the NuMI beam. Note that if one detector is moved, all must be by equal directions and amounts. Since MINERvA would not benefit from positive position movements, only the negative direction will be considered for MINOS. Displayed in Figure 4 and stated above are the amounts in which MINOS must change percentage to achieve a ratio plot of. According to Figure 7 MINOS would have to exhibit an 80cm change in the negative y direction to attenuate 4% at 5 GeV and 7% at 8 GeV. In the negative x direction moving MINOS 70cm would attenuate 4% at 5 GeV and 6% at 8 GeV. 2.3 NOVA NOvA histograms in Figure 8 display an area of focus around GeV and 3 GeV. Again, only the negative direction will be considered because of the limitations seen above by MINERvA. NOvA is more off-axis than MINERvA, and because of this a change in the negative x direction would worsen the data-simulation ratio more. Therefore, the only option for NOvA would be moving it in the negative y direction 00cm to attenuate 3% at GeV and 6% at 3 GeV. 6

7 2.4 Conclusions As stated, all detectors must move equal amounts to maintain their relative distances. Even though all detectors have their respective solution that would fix each ratio problem, this cannot be done individually. Because of this a conclusion of 50cm in the negative y direction is proposed to help all three detectors the most possible. Results of this 50cm shift are plotted for all three detectors in Figure 0. MINERvA will be brought up to a near ratio with an attenuation of 6% at 5 GeV and 8% at 8 GeV. MINOS will become a near ratio with a change of 3% at 5 GeV and 3% at 8 Gev. NOvA will reduce both problems at GeV and 3 GeV by 2% and 8% respectively. This conclusion was reached because MINERvA could be brought up to a ratio of almost completely. MINOS exhibited major change in all directions and the solution chosen would greatly reduce its percentages at both areas of focus. However, NOvA would still see a major discrepancy at GeV and more than 0% at 3 GeV. Speculation suggests that NOvA most likely is seeing a problem that cannot be fixed by changing the position, especially around GeV. The cause of NOvA s disagreement to its Monte Carlo is still under investigation but it is known that merely changing the position would not be fix all its problems. Therefore when determining a conclusion the best solution for NOvA would be one that still attenuated the ratio percentages but did not majorly affect it at the cost of the other two detectors. Negative X Minerva Neutrino Energy Distribution Positive X Minerva Neutrino Energy Distribution Negative Y Minerva Neutrino Energy Distribution Positive Y Minerva Neutrino Energy Distribution Figure 6: Displays the histogram ratios of MINERvA for the new position over the original position changed up to 00cm from the original in the negative x, negative y, positive x, and positive y directions. 7

8 Negative X MINOS Neutrino Energy Distribution Positive X MINOS Neutrino Energy Distribution Negative Y MINOS Neutrino Energy Distribution Positive Y MINOS Neutrino Energy Distribution Figure 7: Displays the histogram ratios of MINOS for the new position over the original position changed up to 00cm from the original in the negative x, negative y, positive x, and positive y directions. Negative X Nova Neutrino Energy Distribution Positive X Nova Neutrino Energy Distribution Negative Y Nova Neutrino Energy Distribution Positive Y Nova Neutrino Energy Distribution Figure 8: Displays the histogram ratios of NOvA for the new position over the original position changed up to 00cm from the original in the negative x, negative y, positive x, and positive y directions. 8

9 Histogram Legend 0cm Shift 20cm Shift 30cm Shift 40cm Shift 50cm Shift 60cm Shift 70cm Shift 80cm Shift 90cm Shift 00cm Shift Figure 9: A legend corresponding all colors in Figures 6, 7, and 8 to a length of the change of position. Negative Y Minerva Neutrino Energy Distribution Negative Y MINOS Neutrino Energy Distribution Negative Y Nova Neutrino Energy Distribution Figure 0: Histograms that show the ratio new position over old position result of changing each detector 50cm in the negative y direction. Displayed are MINERvA, MINOS, and NOvA from left to right. 3 Future Work Future research would look into analysis of positions with horns off to verify results, altering the code to account for the z-axis and shape of the detector, changing the reference frame, and more accurate approximations. N-Tuples in ROOT for horns off need to be written for MINERvA like they are for MINOS in Figure 4 [8]. In Figure 4 for the antineutrino plots there is little difference between the data and simulation. This is because the magnetic horns were sign selecting to focus on neutrinos and the antineutrinos plotted in the top right of Figure 4 are residual ones that reached MINOS. Also in the horns off neutrino plot there is little discrepancy between the Monte Carlo and data. In order to verify that changing the position would benefit all three detectors a loop with the code that had horns off would verify the position change in question for all detectors. If the result is that the the discrepancy between the data and simulation decreases, then changing positions of the detectors should be investigated further and more in-depth as a possible solution. The code used for results 9

10 concluded does not alter the z-axis coordinates and assumes a square shaped detector. In reality, NOvA is as a slight angle in the z-direction that would need to be accounted for if future work is to be done. Also the detectors are more circular and the code would need to be edited for a more accurate representation of the shape of the detectors. All coordinates are in the beam reference frame where the beam points 3 degrees downward compared to the earth s ground [2]. The better frame to use would be one where x is parallel to the beam s path. Changing in the y direction in the beam frame would consequently be changing in the x and y direction in the Earth s frame. In future work a Lorentz mapping should be included in the code to change the reference frame for better comparison with other results. Finally, all percentages of attenuation above are approximations based on the histograms analyzed. These are not computed through a code to know the exact measurement of disagreement between each Monte Carlo and data. Thus for more accurate results a code can be written to calculate the exact discrepancy in each detector and an exact position needed for better results instead of a 0cm increment approximation. Acknowledgements This work was supported in part by the National Science Foundation under Grant No. PHY , and by the Babcock Summer Research Fellowship of the College of William and Mary. 0

11 Appendices A Appendix A The following code is that of the ReDecay function used to find the neutrino weights and energies in creating energy distributions at new positions for each detector. It is not listed in full and has been modified to display only the relevant sections that pertain to a two body decay of a pion. It is a general loop that works for the NuMI beam at any coordinate, thus it works for all detectors looked at in this paper.

12 References [] Aliaga, L. and others. Neutrino Flux Predictions for the NuMI Beam. (206), [hep-ex] [2] Adamson, P. and others. The NuMI Neutrino Beam (205), [3] NOvA Neutrino Experiment. [4] MINERvA: Bringing neutrinos into sharp focus. [5] The MINOS Experiment and NuMI Beamline. [6] R. H. Milburn Neutrino Beam Simulation using PAW with Weighted Monte Carlos. Tufts University (995). [7] Courtesy of M. Kordosky and the MINERvA Collaboration. [8] Courtesy of tm. Kordosky and the MINOS Collaboration. [9] Courtesy of M. Kordosky and the NOvA Collaboration. 2