# 1) Sensitivity vs exposure plots at 1300km, LAr, s22theta13=0.1:

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## 1-1) Significance of MH determination as a function of exposure in

kt.yrs with a LAr detector from 30kt.yr. to 300 kt.yrs. 2 plots, one

for NH and one for IH. On each plot the significance is plotted for

dcp = -pi/2, 0, +pi/2. Use the standard set of assumptions with

theta13 floating.¶

**EG**

I am using globes-discovery to get chi2 values for delta_cp = 0, pi/2, -pi/2 using increasing values for the exposure.

I then extract the sentitivity for MH determination and plot it aganist the exposure.

Theta13 is free to vary during the fit.

**MIB**

I am using a custom tool (senseVlum, again). It's very similar to what is done with globes-discovery for mass hierarchy because it uses the same eightfold degeneracy finder. For each exposure I use eightfold to find each mass hierarchy degeneracy and take the minimum among all of them. I repeat this for . Correlations among the parameters are considered (including unless specified otherwise).

## 1-2) Significance of MH determination vs exposure plot for NH, dcp = +pi/2

(worst case) with the following curves

a) no theta13 constraint, assume NDC constraints on bkgd (1% signal

and 5% bkgd normalization uncertainties)

b) Add theta13 constraint, assume NDC constraints on bkgd

c) theta13 constraint, no NDC (Signal normalization = 5%

background normalization uncertainties = 15%)¶

**EG**

I am generating the plot as in 1-1. "No ND" means Signal normalization uncertainty = 5%

background normalization uncertainty = 15%

**MIB**

See my comments in 1-1 and 1-4. Note that in the inverted hierarchy dcp=-pi/2 is the worst case.

In order to test that the theta13 prior is working as expected I had my code output the value of theta13 (from the minimization) associated with the significance value. Results are below. The value of theta13 is constrained to be closer to the input value (0.154).

## 1-3) Significance at which we determine dcp!=0 or pi as a function of

exposure. 2 plots, one for NH and one for IH. On each plot there are 3

curves: a) CP frac at 25% b) CP frac at 50 % c) CP frac at

75%. Standard setup.¶

**MIB**:

I use a custom tool (senseVlum, in SVN soon) for this. For each exposure I compute chi-squared at each dcp value using glbChiDelta and take the minimum between dcp_true=0 and dcp_true=pi. Each value is stored in an array which gets sorted. I then find the significance(=sqrt(chisquared)) at the 25th, 50th, and 75th percentile in this list. So the output file contains an entry for exposure (kt*years), 25% dcp coverage, 50% dcp coverage, and 75% dcp coverage.

Example of CPV significance vs exposure. This example is for the v3 LAr configuration without(left) and with(right) correlations. The hierarchy is assumed to be normal in these.

**LW**

I used globes-discovery data to find the significance at which we have 25%, 50%, 75% CP coverage for each exposure. This includes the theta13 constraint.

## 1-4) Significance at which we determine dcp!=0 or pi for CP frac = 50% with

a) no theta13 constraint, with NDC

b) theta13 constraint with NDC

c) theta13 constraint and no NDC¶

**MIB**:

Same tool as in 1-3.

"no theta13 constraint, with NDC" is a run where the oscillation parameter errors for theta13 are set to zero which allows it to float without penalty in the glbChiDelta minimization.

"theta13 constraint with NDC" is just the same as the 50% curve in 1-3.

"theta13 constraint and no NDC" is with the constraint turned back on and with 5% for the signal normalization error and 15% for the background normalization error.

Example of CPV significance vs exposure. This example is for the v3 LAr configuration without (left) correlations (which causes the theta13 constraint to be meaningless) and with correlations (right). The hierarchy is assumed to be normal in these.

## 1-5) dcp resolution vs exposure plots for dcp = 0 and dcp = +pi/2, NH with

a) no theta13 constraint, with NDC

b) theta13 constraint with NDC

c) theta13 constraint and no NDC¶

**ETW**:

I am using globes-accuracy to get chi2 values for a range of delta_cp values. I then fit the chi2 maps to get the 1-sigma resolution on delta_cp. This plot is delta_cp vs exposure for normal (known) hierarchy for delta_cp = 0,90,-90 for cases a,b,c.

**LW**

Using globes-accuracy. Cases a,b,c for delta=0 and delta=90 (separate plots)

**MIB**

I use a custom tool (senseVlum). For each exposure I calculate the glbchiDelta difference between the true dcp(e.g. 0) and each point in dcp. This outputs an array of exposure, deltacp, deltachi^2 values that I can contour plot. This process is a bit different than what is done in globes-accuracy, but the results are similar and we can see the differences between positive and negative dcp values. This plot is for

I also plot 3 and 5 sigma contours. This plot is for . It's a mess but still partially decipherable.