SuperPINGU for measuring CP violation
Abstract
We propose to measure leptonic CP phase, after neutrino mass hierarchy is established, with an upgrade of the PINGU detector and using atmospheric neutrino flux. The upgrade, called superPINGU, will require a few megaton effective volume at 0.51 GeV range to distinguish in the range  from 0 after 4 years of operation. The distinguishability (similar to significance) of measuring depends crucially on various flux, crosssection, event reconstruction (energy and angle) and flavor identification uncertainties. We explore effects of these uncertainties on the distinguishability of measuring CP phase and suggest possible ways to minimize their impact.
keywords:
Neutrino oscillation, CP violation, atmospheric neutrino00 \journalnameNuclear Physics B Proceedings Supplement \runauth \jidnuphbp \jnltitlelogoNuclear Physics B Proceedings Supplement
1 Introduction
Establishing CP violation in the leptonic sector is an outstanding problem in particle physics. Atmospheric neutrino flux measurements in large water/ice detectors can be used to determine the Dirac CP phase . Information on different values is encoded in the neutrino oscillation probabilities after propagation inside the earth (matter effect). A systematic shift of the probabilities with increasing in a wide, –2 GeV, energy range is key to measure with atmospheric neutrino flux (1).
It has been found recently that the PINGU and ORCA detector with GeV threshold will have good sensitivity to determining the neutrino mass hierarchy (2); (3); (4); (5). However, measurement of would require a detector with larger effective volume and improved characteristics in the GeV range and in this context a future upgrade of PINGU (and also of ORCA), called SuperPINGU, was proposed in Ref. (1) with detailed estimate of sensitivity. Here we present highlights from that work.
2 Methodology and Results
To measure CP phase with atmospheric neutrinos, we calculate neutrino events in SuperPINGU by varying and compare with , keeping all other oscillation parameters fixed. We use an effective mass (both for and ) parameterized as
(1) 
which can be realized for a total of 126 strings and 60 DOMs per string. This gives an effective mass of Mt at 2 GeV, which is 4 times larger than PINGU. The number of neutrino events for a particular flavor with energies and zenith angles in small bins and marked by subscript can be calculated as
(3)  
Here is the exposure time, is the Avogadro’s number. The density of events of type , (the number of events per unit time per target nucleon), is given by in terms of fluxes at the detector, and with corresponding oscillation probabilities and . The original muon and electron neutrino fluxes at the production are and .
We have computed the distributions of and events for and and take difference between the distributions in the – plane to study their properties. Since there are errors associated with reconstructing the true neutrino energy and directions, we smear the ideal distributions with the energy and angular resolution functions of the detector to mimic the real situation. To estimate the sensitivity of measuring a CP phase different from zero we employ a distinguishability parameter defined as
(4) 
where and are the reconstructed number of events in the th bin in the – plane for and , respectively, and is the total error in the th bin. Parameter is a measure of uncorrelated systematic errors (2) and we take . The total distinguishability
(5) 
is a quick measure of significance.
Figure 1 shows the distinguishability for events with for different values and using 1year of SuperPINGU data. Normal mass hierarchy is assumed. The shape of the distributions, specially their domain structures, is largely explained as due to grids of solar, atmospheric and interference magic lines in the – plane. The oscillation probabilities are independent of along these lines, thus separating regions of same sign distinguishability. Figure 2 shows distributions for events.
The uncertainties associated with atmospheric neutrino flux, cross section, effective volume, etc. affect neutrino event distributions across bins in the – plane. We include effects of these correlated uncertainties in our calculation with analogy to the pull method in analysis. In particular we minimize the following distinguishability parameter
(7)  
where are the pull variables and are their standard values. The event distributions with varying are calculated as
(9)  
where is the overall normalization factor with the error , is the flux (flavor) ratio uncertainty ( for events), with the error ; is the energy tilt parameter with ; is the zenith angle tilt with . Figure 3 shows the minimized over for different correlated uncertainties as well as for no correlated uncertainties. A threshold energy of 0.5 GeV has been assumed. Note that the contributions of and channels to are comparable.
3 Discussion
We estimate that after 4 years of operation and systematics, SuperPINGU with 0.5 GeV threshold will be able to distinguish from zero with , , , . The ranges depend on effects of different correlated systematics. These values are a factor 4–6 improvement over the sensitivity of PINGU to with 3 GeV threshold.
The sensitivity of SuperPINGU to can be further improved with following possibilities:

Decrease of energy threshold to 0.2 GeV from 0.5 GeV with a denser array. This may increase sensitivity by .

Stringent kinematical cut can be used to create a highquality event sample with better reconstruction of the neutrino energy, direction and flavor.

An increased exposure time will also increase the sensitivity to CP by a factor .

Improved flavor identification at low energies.

Increase the density of DOMs or photocathode coverage.

Statistical separation between the neutrino and antineutrino events.
Our results show that SuperPINGU can be competitive to other proposals for measuring the leptonic CP phase associated with long baseline (LBL) accelerator experiments.
References
Footnotes
 volume:
References
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