Velocity of light in water Simple Method MC Data

Method (Led run)

Method From Led run (time and position for each OM) Time = Peak (highest bin, bin size=0.5 ns) Position = nominal OM position Eliminate not significant peak (Noise>Peak-5*sqrt(peak)) Time versus distance Fit y=ax+b

Plot MC Take time from bin with maximal hits = Timepeak Timepeak versus distance n=v_vacuum/v_measured

MC (Led) Run Absorption Scattering Fit range n delta n 5 60 55 0-240 1.382 0.001 0-120 1.381 0.003 120-240 1.380 0.004 10 60 Inf 0-310 1.382 0.001 0-155 1.389 0.003 155-310 1.379 0.002 9 60 30 0-210 1.383 0.001 0-105 1.373 0.004 105-210 1.388 0.005 12 120 55 0-310 1.383 0.001 0-155 1.381 0.002 155-310 1.382 0.002 11 30 55 0-170 1.384 0.002 0-85 1.372 0.006 85-170 1.388 0.006

MC (Laser) Led and Laser runs slightly dependent from fit range Run Absorption Scattering Fit range n delta n 15 28.3 60 160-330 1.372 0.002 160-245 1.371 0.006 245-330 1.368 0.006 Led and Laser runs slightly dependent from fit range Fit over full range no dependence of absorption and scattering Led run n = 1.383 +- 0.001 Laser run n = 1.372 +- 0.002 Ciro put in the MC: Led run n = 1.3786 Laser run n = 1.3681 Ciro can you please generate MC with n=1.3 and n=1.5 ???

MC (different Lines)

Thinking about errors Laser (full width 0.8 ns) Led (full width 4 ns) => early photon effect maximum 4 ns Walk effect (is smaller than 4ns) Binning in histogram 0.5ns Positioning (possible 20 cm = 1ns) We measure times of 1000 ns => accuracy of the measurement around 0.5%

Data (Do we crosscheck Pacos timing calibration?)

Data (different fit range) Error in t=2 ns, error in position x=1m Run fit rang[m] n delta n chi/ndf 33987 0-220 1.394 0.004 17.8/38 0-110 1.401 0.01 12.8/19 110-220 1.393 0.013 4.5/17

Data (Different Lines) We crosscheck Pacos timing calibration)

Data (different Lines) Run Line n delta n chi/ndf 33987 2 1.394 0.004 17.8/38 1 1.381 0.004 8.9/49 3 1.391 0.004 136.1/47 6 1.386 0.005 7.3/39

Data (different runs) Run Line n delta n chi/ndf 33983 2 1.392 0.004 19.1/38 33984 2 1.400 0.004 27.1/38 33991 2 1.400 0.004 18.2/36 33995 2 1.397 0.004 16.6/38 33999 2 1.395 0.004 15.4/35 36035 4 1.391 0.004 20.5/43 36041 4 1.395 0.004 19.1/41 36043 4 1.396 0.004 24.2/39 36064 8 1.396 0.004 18.9/42 36063UV 12 1.405 0.005 6.7/30

Is this useful? Only cross check of Pacos work? Improvement:Take real OM positions Define fit range (systematic bias) Method ok? Have a look to Laser runs

Early photon effect (MC) Introduce cut to minimize early photon effect: Ciros cut: charge per hit < 1.5p.e. => minimal distance 100m

Early photon effect (MC and Data)

Method From Led run (time and position for each OM) Time = Peak (highest bin, bin size=0.5 ns) Position = nominal OM position Eliminate not significant peak (Noise>Peak-5*sqrt(peak))=>defines max. fit value Charge per hit < 1.5 p.e=>defines min. fit value Time versus distance Fit y=ax+b

MC Measured refraction index MC Input n=1.3786 (at 470nm) Run Absorption Scattering Fit range n delta n 5 60 55 1.382 0.001 2 60 55 1.380 0.001 10 60 Inf 1.379 0.001 9 60 30 1.386 0.002 18 60 30 1.384 0.002 12 120 55 1.382 0.001 11 30 55 1.386 0.002 Conclusion: Small model dependence about 0.5% Laser MC run: MC Input n=1.3681 (at 532nm) MC measured n=1.370+-0.003

Stability against cuts (Noise>Peak-5*sqrt(peak))=>defines max. fit value Charge per hit < 1.5 p.e=>defines min. fit value Change charge per hit to 5.0 => 0.2% Change charge per hit to 1.2 => 0.2% Change Peak-10*sqrt(peak) => 0.5% Conclusion: Small cut dependence about 0.5%

Data at 470 nm N=1.390+-0.007 (+-0.5%)

Conclusion Method stable against cuts +-0.5% Method stable against different assumption for absorption and scattering +-0.5% Measurement at lambda=470 nm (Led) n=1.390+- 0.5%(stat.)+-0.5%(exp.)+-0.5%(theo.) =>n=1.390+-0.012