Horn Focusing Errors in the (Ideal) World of DUNE-Prism ( with - - PowerPoint PPT Presentation

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Horn Focusing Errors in the (Ideal) World of DUNE-Prism ( with - - PowerPoint PPT Presentation

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Horn Focusing Errors in the (Ideal) World of DUNE-Prism ( with ideal systematics ) University of Rochester Tejin Cai Introduction The aim of this study is to constrain beam focusing systematics due to mis-modelling by measuring flux from

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Horn Focusing Errors in the (Ideal) World of DUNE-Prism ( with ideal systematics )

University of Rochester Tejin Cai

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Introduction

  • The aim of this study is to constrain beam focusing systematics due to

mis-modelling by measuring flux from different angles

  • The horns could be mis-modelled, i.e. shifts in horn positions, shifts in horn

current

  • The DUNE PRISM design allows ND to move off-axis by 50 mrad
  • Measuring the relative difference in flux between “real” setup and ideal setup

would allow us to constrain the modelling errors and make better flux prediction

  • This talk uses νμ flux, in real world νe might be a better candidate
  • Most of the talk consists of flipping books

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Shifts in Horn Position

We expect a shift in horn position will also shift the beam to the same direction, while also creating an asymmetric conical cross section. An increase in horn current will focus π of higher energy and vice versa.

π+ of E ν flux

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Horn offset, flux tilt

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Horns

We expect a shift in horn position will also shift the beam to the same direction, while also creating an asymmetric conical cross section. An increase in horn current will focus π of higher energy and vice versa.

π+ of E ν flux

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Ideal horn

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Changes in Horn Position

We expect a shift in horn position will also shift the beam to the same direction, while also creating an asymmetric conical cross section. An increase in horn current will focus π of higher energy and vice versa.

π+ of E ν flux Higher horn current

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Higher horn current, flux peaks at higher energy

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Beam Setups

  • We generated flux using the near detector task force macro

○ 3 Horns at 547 m ○ 1.2 MW beam ○ Horn current 296.2 kA

  • Modelling errors covered in this talk

○ Changes in horn positions ○ Shifts: entire horn moves in particular direction ○ Tilt: the ends of the horn moves in opposite direction ○ Changes in horn current

  • Changes in horn positions:
  • Each horn is shifted or tilted in X, Y or Z axis by 3 mm
  • The horn current varies between -5 kA to 5 kA
  • 2.5E8 POT was produced for each configuration

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Flux Reweighting

The off axis angles are obtained through reweighting

  • We assume a 2x2 m surface area for the detector
  • The detector is 574 m from source and
  • The detector could move laterally for ~ 30 m ~ 50 mrad
  • The flux will strike the detector area at random, therefore causing fluxes at left

and right angles to be asymmetric

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Ideal Flux - 1D Plots

As we increases off axis angle, the flux becomes narrower and peaks at lower energy as expected

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In the rest of the talk, each energy bin is .5 GeV and

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Ideal flux -2D

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Asymmetry Due to Reweighting, Ideal flux

The flux to the left and right from the same beam file is not symmetric due to the

  • reweighting. The plot shows relative difference between flux at θ and -θ

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Statistical uncertainties on asymmetry plot

The sizes of the statistical uncertainties on par with the asymmetries. The asymmetry is probably statistical.

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Asymmetry: SNR

The sizes of the statistical uncertainties on par with the asymmetries. The asymmetry is probably statistical.

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Asymmetry Signal to Noise Ratio

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Horn Uncertainties Plots Overviews

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Horn1 Shifts 3.0mm, relative to ideal, color in [-1,1]

angle 50

  • 50

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Region with high SNR Large asymmetric shifts in the X axis Symmetric shift in Y, almost no shift in Z

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Horn1 Shifts 3.0mm, relative to ideal, stats error

angle 50

  • 50

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Large asymmetric shifts in the X axis Symmetric shift in Y, almost no shift in Z

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Horn1 Shifts 3.0mm, relative to ideal, SNR

angle 50

  • 50

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Very small SNR in Z

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Horn2 Shifts 3.0mm, relative to ideal, color in [-1,1]

angle 50

  • 50

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More “washed” than Horn 1 across board, X is more symmetric than in Horn 1, because horn 1 and horn 3 will correct the beam?

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Horn2 Shifts 3.0mm, relative to ideal

angle 50

  • 50

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Horn2 Shifts 3.0mm, relative to ideal, SNR

angle 50

  • 50

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Similar story

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Horn3 Shifts 3.0mm, relative to ideal, color in [-1,1]

angle 50

  • 50

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Horn3XTilt is almost gone.. The focused beam will pass from center in a tilt and experience little B-field

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Horn3 Shifts 3.0mm, relative to ideal

angle 50

  • 50

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Horn3 Shifts 3.0mm, relative to ideal, SNR

angle 50

  • 50

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Horn Current

angle 50

  • 50

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Horn Current - uncertainties

angle 50

  • 50

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Horn Currents - SNR

angle 50

  • 50

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Flux Uncertainties Plots Scanning angles in Horn 1 Shifts

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Plotting fractional change in flux at fixed energy

Energy Bin (2.5, 3.0) GeV

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We could fit the angles, -5 to 5 mrad seems sufficient

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Plotting fractional change in flux at fixed energy

Energy Bin (3.0, 3.5) GeV

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We could fit the angles, -5 to 5 mrad seems sufficient

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Plotting fractional change in flux at fixed energy

Energy Bin (3.5,4.0) GeV

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We could fit the angles, -5 to 5 mrad seems sufficient

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Plotting fractional change in flux at fixed energy

Energy Bin (4.0,4.5) GeV

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We could fit the angles, -5 to 5 mrad seems sufficient

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Flux Uncertainties Plots Scanning angles in Horn 2 Shifts

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Plotting fractional change in flux at fixed energy

Energy Bin (2.5, 3.0) GeV

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We could fit the angles, -20 to 20 mrad might be needed

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Plotting fractional change in flux at fixed energy

Energy Bin (3.0, 3.5) GeV

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Horn 1 We could fit the angles, -20 to 20 mrad might be needed

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Plotting fractional change in flux at fixed energy

Energy Bin (3.5,4.0) GeV

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Horn 1 We could fit the angles, -20 to 20 mrad might be needed

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Plotting fractional change in flux at fixed energy

Energy Bin (4.0,4.5) GeV

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We could fit the angles, -20 to 20 mrad might be needed

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Flux Uncertainties Plots Scanning angles in Horn 3 Shifts

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Plotting fractional change in flux at fixed energy

Energy Bin (1.0, 1.5) GeV

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Large separation at high angles and lower energy

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Plotting fractional change in flux at fixed energy

Energy Bin (1.5, 2.0) GeV

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Going once

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Plotting fractional change in flux at fixed energy

Energy Bin (2.0, 2.5) GeV

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Going twice

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Plotting fractional change in flux at fixed energy

Energy Bin (2.5, 3.0) GeV

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Going trice…. Now gone

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Flux Uncertainties Plots Scanning angles in Horn Current

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Plotting fractional change in flux at fixed energy

Energy Bin (2.5, 3.0) GeV

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Plotting fractional change in flux at fixed energy

Energy Bin (3.0, 3.5) GeV +5 kA

  • 5 kA

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Plotting fractional change in flux at fixed energy

Energy Bin (3.5,4.0) GeV +5 kA

  • 5 kA

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Plotting fractional change in flux at fixed energy

Energy Bin (4.0,4.5) GeV +5 kA

  • 5 kA

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Plotting fractional change in flux at fixed energy

Energy Bin (4.5, 5.0) GeV +5 kA

  • 5 kA

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Summaries Horn shift uncertainties

By far Horn 1 presents the largest shifts, with succeeding horns increasingly statistics dominated It could be that the beam in later horns are already better focused and small shifts in horn positions don’t affect the beam as much Each horn offsets in X have different pattern of high SNRs. It could provides a fit to the horn errors Shifts in Y and Z axis are not so apparent, the fractional changes are dominated by statistical fluctuations

Horn current uncertainties

Horn current changes relative flux similar to horns shifting in Y direction, making it harder to discern the effect. We could, however, adjust horn current and constrain the effect independently

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Conclusion

At a shifting of 3.0 mm, a DUNE PRISM setup will be sensitive to shifts in Horn 1 in X and Y, but not Z. There is almost ~8% shifts in Horn1XOffset3.0mm There is little sensitivity to Horn 2 and Horn 3 shifts in Y and Z. Horn current effects could be ~5% at ΔA = 5 kA. Shifts in horn current could mask movement of horns in Y axis. We could to some extent constrain the systematics at 0.0 mrad. But going off axis would allow for linearly independent combinations that solve and further constrain the systematics especially in Horn 1. A movement between -5 to 5 mrad is sufficient for Horn 1, Horn 2 and 3 requires going to larger angles.

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Future studies

Get covariance matrix for additional systematics

  • Water layer was determined to be a significant source of systematics
  • Target positions, beam sigma can also be tuned

To study the methods of constraining systematics

  • Fitting the angles could work
  • Needs to assess how independent are the systematics

○ Will need to generate flux with 2 or more known systematics and solve for coefficients ○ I.e for shifting matrix S1, S2, S(1+2) = aT1 S1 + b T2 S2, and hopefully T1=T2=I

  • Needs to get the rate of change of shifts as well.

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Backup Slides

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ΔS/ΔA in Relative Shifts

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ΔS/ΔA in Horn current

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ΔS/ΔA in Horn current

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ΔS/ΔA in Horn current

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