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					Controlling Systematics in a Future
     Reactor q13 Experiment

              Jonathan Link
           Columbia University
  Workshop on Future Low-Energy Neutrino
               Experiments
          April 30 − May 2, 2003
   A Simple Counting Experiment Study
Look for disappearance in the ratio R, defined as
                                 N far L2far
                            R            2
                                                 ε
                                 N      L
                                     near near
Where:
• The N’s are the number of observed events
• The L’s are the baselines and
• e is the relative efficiency of the near and far detectors.
Disappearance is measured as a deviation of R from 1 and the
sensitivity to sin2q13 at 90% CL is just
                                       1.64   R
                  
            S m13 
                2
                                                          L far
                         ( E ) ( E ) sin(1.27m
                                                     2
                                                     13           )dE
                       E
                                                          E
                        Counting vs. Shape
• Huber, Lindner, Schwetz and Winter have shown that a pure shape analysis
works well with large statistics.
• A combined shape and rate analysis improves sensitivity over a pure rate
analysis only slightly at the scale of current proposals.
                              50 tons, 6 GW, 3 years and 1200 meters

        Counting Experiment                                            Shape & Rate




• Therefore, the counting experiment is sufficient to study/compare these
scenarios.
    Significant Contributions to the Error
1. Statistics in the far detector
                                       N far  N bg
                            stat 
                                          N far
2. Uncertainty in the relative efficiency of the near and far
   detector
                                   2
                        e               (with movable detectors)
                                N near f

          where f is the fraction of run time used for cross calibration

3. Uncertainty in the background rate in the far detector
                              bg rate  N bg
                       bg 
                                  N far
                  Kr2Det Proposal
• This elegant proposal can be simply stated as 2
detectors and one reactor
• Identical near and far detectors target the dominate
source of error in CHOOZ and Palo Verde − flux
uncertainty
• It explicitly address the background error by doubling
the depth compared to CHOOZ and has 65 reactor off
days a year
• The reactor power (~2 GW) is low by modern
standards
• The 1000 metes far baseline may not be ideal
            Few Words on Methodology
This analysis starts with the assumptions in the Kr2Det
proposal (Mikaelyan et al.):

• Two identical, 46 ton (fiducial) detectors at 115 and 1000 meters
• 55 events/day in far detector, 4200 near
• Reactor is on for 300 days in a year
• Relative efficiency of near and far detectors know to 0.8%
• 600 mwe shielding  Background of 0.1 events/ton/day
• The background rate is measured during reactor off days
                                        Spreadsheet Study
Allowing the variation of:
     • reactor power                      • near and far baselines • number of far detectors
     • run time                           • background rate        • fraction time for cross calibration
     • detector size                      • background sensitivity • one or two reactor scenarios
     • reactor capacity factor
 den               0.85   g/cm^3      L near               150   m            coverage      0.2                   depth                  300   mwe
 flux         2.00E+20    nu/s/GWth   L far               1200   m            diam_pmt        8 in                veto_ineff            0.05
 power_th           6.1   GWth        near flux     4.315E+11    /cm^2/s      area_pmt 0.032429 m^2               eff depth             6000   mwe
 flux0        1.22E+21    nu/s        far flux      6.742E+09    /cm^2/s                                          near_bg               0.01   /ton/day
 years                3               Hden           7.85E+22    H/cm^3                                           far_bg                0.01   /ton/day
 upfrac            0.89               xsec*eff        5.59E-44   cm^2                                             near_bg_err             50   %
 uptime       3.25E+02    day/year                                                                                far_bg_err              25   %

 tons/unit fid far units active frac near bg sub far bg sub near events near error far tot/unit far err/unit far total          eff error      R error
           50            1          1      547.5       547.5   7977144 2837.72 124642 353.82128                    124642            0.008        0.0086
           50            1        0.9     492.75      492.75   7179429 2690.84 112178 335.66464                    112178       0.001669        0.003621
           25            2        0.9   246.375      246.375   3589714 1898.72          56089 237.35074            112178         0.00236        0.00364
        16.6             3        0.9   163.593      163.593   2383570    1546.1        37243 193.40784            111729       0.002897        0.003666
           10            5       0.85     93.075      93.075   1356114 1165.49          21189 145.88377            105946       0.003136        0.003662
             5          10        0.9     49.275      49.275    717942 847.702          11217 106.14271            112178       0.005278         0.00379


 far units = The number of identical detectors at the far location (n).
 active frac = The fraction of time that each far unit spends at the far location (time spent at the near location is 1-active frac).
 bg sub = The total number of background events subtracted from each unit.
 near events = The number of signal events (after BG subtraction) seen by the near detector during the active fraction (N_n).
 far events = The number of signal events seen by each far detector during the active fraction (N_f).
 eff error = The error on the reletive efficiency (eff) of a far detector wrt the near detector as measured side-by-side.
 R = far^2/near^2 * 1/n * sum(N_f*eff)/N_n
 R error = The error on R.
    Ways of Improving the Statistics
          at the Far Detector
There are three ways…

  1. More target volume at the far detector site

  2. More reactor power

  3. More running time

  Twice Volume = Twice Power = Twice Run Time
              (Statistical errors only)
More Target Volume at the Far Detector Site
       Small near detector and bigger far detector:
          Important errors may not cancel if the detectors
          are not identical


       Bigger detectors near and far:
           Error cancellation intact
           Possible attenuation problems in large Gd loaded
           detectors
           Detectors are impossible to move
       More same size far detectors:
          The errors scale like one big detector
          Could phase in the experiment or improve
          sensitivity by adding more detectors
          $$$$
             Add More Reactor Rower

See earlier talk:

We can get ~9 GW with French reactor sites

            ~8 GW in Germany,

            ~7 GW in the U.S. and

            Less elsewhere.

I’ll show later in this talk that no reactor off running is
                       not needed.
                 More Running Time
I think that it is a bad idea to plan on an extra long run
(more than 3 years)

   • More time for efficiency to drift (i.e. degradation of
   Gd loaded scintillator)

   • Hard on young scientists

   • Could get beat by off-axis

Extra running time could be useful if we get to the end
of our run and we have a marginal (≤3) effect, but we
must not be systematics limited.
Controlling the Relative Efficiency Systematic
 • Bugey (the only near/far reactor exp.) had e = 2%

 • 1.8% if you ignore the solid angle error

 • Kr2Det assumes 0.8%


            What value should we be using?

          How will we determine/measure e?

        One possibility is movable detectors
                    Movable Detectors
This idea originated with Giorgio Gratta and Stan Wojcicki
  • Our idea is to have a far detector(s) that can be moved to sit at
  the same baseline as the near detector
  • The two detectors record events in the same flux at the same time
  (head-to-head calibration)
  • Relative efficiency error:              2
                                 e 
                                         N near f
  • Near running fraction of 10 to 15% optimizes the total error
  • A movable detector experiment is best achieved by connecting
  the two detector sites by a tunnel
  • Such a tunnel might cost $10 to $20 million depending on the site
  geology, topology and hydrology.
                                                    Sensitivity of Kr2Det
  Kr2Det is ultimately limited by the 0.8% error on the relative
  efficiency of their two detectors.
                                     Physics Reach of Kr2Det Proposal
                        0.045

                                                             Kr2Det Proposal
Sensitivity at 90% CL




                         0.04
                                                             Systematics Limit

                        0.035


                         0.03


                        0.025


                         0.02
                                0         5          10           15             20
                                                     Years

  The limit in sensitivity imposed by the 0.8%
  error. It is possible to overcome this limit
  with a shape analysis and high statistics (à la
  Huber, et al.) but only after about 65 years of
  running (~6000 GW ton yrs)!

                                    One can do better with a movable far detector…
                        Sensitivity of Kr2Det with Movable Detectors
                         10% of the running time is spent
                         doing the cross calibration.
                                   Physics Reach of Kr2Det with Movable Detector
                        0.04

                                                                 Modified Kr2Det
Sensitivity at 90% CL




                        0.03


                        0.02


                        0.01


                          0
                               0            5          10          15              20
                                                       Years
                                                                                        12 years
                        With this modification you get to a
                        sensitivity of 0.01 at m2 of 2.5×10-3 eV2
                        by adding fiducial mass (138 tons) or time
                        (12 years).

                               The effect is even more dramatic when considering reactor sites
                               with higher power, where the systematic limit is reached sooner.
         Moving Detectors at a 6 GW Site
Consider 50 ton target detectors at 150                                 0.03
                                                                                   6 GW Reactor, 1200 meter Baseline


meters and 1200 meters and a 3 year run.                               0.025
                                                                                                             Fixed Detectors
                                                                                                             Movable Detectors




                                               Sensitivity at 90% CL
                                                                        0.02
The far detector spends 10% of the run
                                                                       0.015
time at the near site for cross calibration.
                                                                        0.01


Or the relative efficiency is measure to                               0.005


0.8% with fixed detectors                                                 0
                                                                               0      5          10          15            20
                                                                                                 Years
Controlling Uncertainty in the Background Rate
  1. Measure background with reactor off time

  2. Put detectors very far underground so that the
    background is insignificant (The KamLAND
    solution)

  3. Create a large effective depth with an external
    veto/shielding system (The KARMEN solution)

  4. Measure the heck out of it

          Combining 3 and 4 seems to work well
Measure Background with Reactor Off Time
This works best at single reactor sites
     • Commercial reactors can have as little as 3 weeks of down time every 18
     months.
     • For 3 GW, 300 mwe, 1200 BL  bg ≈ 2×far
     • Need 2 months a year to bg ≈ far

CHOOZ ran the detector before their reactors were
                                                         Extrapolation to zero
commissioned                                             power from CHOOZ
Over time the Gd loading degraded their attenuation
length. When they were forced to lower their trigger
threshold their background rate changed

When extrapolating to zero power at two reactor
sites the error scale as N f far   half
so there is no advantage to greater depth.

      This is not a reliable plan for future experiments.
              The KamLAND Solution
• KamLAND is so far underground that they estimate
only one background event in their entire dataset.
• Neglecting this event does not significantly affect their
result.


• Finding a site with an acceptable reactor and the ability
to get far underground at the optimal baseline would be
very hard.
           Perhaps Dave Reyna has a solution?
                The KARMEN Solution
KARMEN was a surface level
neutrino detector that achieved an
effective depth of about 3000 mwe
by using an active veto shield.



                     Saw background
                     reduction of 97%

                     3 meter thick steel shield with embedded
                     muon detectors at 2 meters.
                     • Spallation neutrons created outside the
                     veto are stopped
                     • Muons penetrating the veto are detected.
     The KARMEN Solution (Continued)
   For a reactor experiment it might look something like this:




                                               In my studies I assumed
                                               a 95% efficient veto.
                                               Then 0.2 bg/ton/day at
                                               300 mwe becomes 0.01
                                               bg/ton/day.




The difference between 150 mwe and 300 mwe becomes less
important. So we might save money with a shallower site.
             Measure the Heck Out of It

Even with a 95% efficient veto we still need to estimate
the surviving background to within about 25% to make
this error significantly smaller than the statistical error.


We can achieve this precision by using vetoed events to
study distributions of various parameters and use them to
extrapolate into the signal region for non-veto events.
     Measure the Heck Out of It (Continued)
                              Various Distributions from CHOOZ
Distributions of
   • Positron energy
   • Neutron capture energy
   • Spatial separation
   • Temporal separation
as determined from vetoed
events, could be used to
estimate correlated
backgrounds.

                              These distributions also contain uncorrelated
                              background events.
    Measure the Heck Out of It (Continued)
Matching these vetoed distributions outside the signal range to the
data could easily result in a background uncertainty in the signal
region of ≥ 25%.

         interactions

                   Proton recoils

                                                     Neutron transport
                                                        simulation
                                                   Detector resolution not
                                                          included
       ?
                     From CHOOZ




Can we expect distributions from vetoed events and events that
evade the veto to be the same? Detailed simulations will tell.
                           Conclusions
By controlling the dominant sources of systematic error and
maximizing reactor power a next generation reactor experiment
can be sensitive to sin2q13 down to 0.01 at 90% CL in 3 years or
less.

The dominate sources of systematic                        9 GW, 50 tons,
error                                                     1200 m, 3 years
                                                          15% cross calib.
   • Relative efficiency                                  & 95% eff. veto

   • Background Rate
can be controlled by designing an
experiment with movable detectors
and an active external veto shield.
Systematics are tied to measurements,
they go down as stats go up
                                     Optimal Baseline
                                         6 GW and 3 Years
                            0.05
                                                                   dm^2=5.0e-3
                            0.04                                   dm^2=2.5e-3
       Sensitivity 90% CL




                                                                   dm^2=1.0e-3
                            0.03


                            0.02


                            0.01


                              0
                               500      1000                1500             2000
                                               Baseline (meters)

With m2 = 2.5×10-3 the optimal region is quite wide. In a
configuration with tunnel connecting the two detector sites, choose
a far baseline that gives you the shortest tunnel.

				
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posted:12/24/2012
language:English
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