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Elena Guardincerri, 04/04/2012 01:58 PM

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

## 1-1) Significance of MH determination as a function of exposure inkt.yrs with a LAr detector from 30kt.yr. to 300 kt.yrs. 2 plots, onefor NH and one for IH. On each plot the significance is plotted fordcp = -pi/2, 0, +pi/2. Use the standard set of assumptions withtheta13 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 {{latex($\delta_{CP}=-\pi/2,0,\pi/2$)}}. Correlations among the parameters are considered (including {{latex($\theta_{13}$)}} 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%)EGI 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.

## 1-3) Significance at which we determine dcp!=0 or pi as a function ofexposure. 2 plots, one for NH and one for IH. On each plot there are 3curves: a) CP frac at 25% b) CP frac at 50 % c) CP frac at75%. 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.

## 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.