1. 1 Study of physics impacts of putting a far detector in Korea with GLoBES - work in progress - Eun-Ju Jeon Seoul National University Nov. 18, 2005 International Workshop on a Far Detector in Korea for the J-PARC Neutrino Beam (KIAS)

2. 2 Present knowledge and what is next? What is merit of putting a far detector in Korea? Physics impacts with a far detector in Korea Summary

3. 3 Neutrino mixing in three flavor solar + reactor + future solar atmospheric + accelerator future reactor + accelerator  13 = ?  m 13 2 ~  m 23 2 ?  23 = ~ 45 deg.  12 = ~ 34 deg. Maki-Nakagawa-Sakata Matrix (c ij =cos  ij, s ij =sinq ij )

4. 4 Latest constraint on θ 13

5. 5 What is merit of placing far detector in Korea?  The off-axis angle of the neutrino beam from J-PARC on the sea level in Korea, when the beam center is 2. 5deg. off at SK.  the baseline length is about 1000km ~ 1200km.

6. 6  The probability for transitions     e  are written as, P (     e  e  (t)       4c 13 2 s 13 2 s 23 2 sin 2  31  Main + 8c 13 2 s 12 s 13 s 23 (c 12 c 23 cos  - s 12 s 13 s 23 )cos  32 *sin  31 *sin  21 - 8c 13 2 c 12 c 23 s 12 s 13 s 23 sin  sin  32 *sin  31 *sin  21  CP-odd + 4s 12 2 c 13 2 (c 12 2 c 23 2 + s 12 2 s 23 2 s 13 2 - 2c 12 c 23 s 12 s 23 s 13 cos  sin 2  21  Solar - 8c 13 2 s 13 2 s 23 2 (1 - 2s 13 2 ) (aL/4E  cos  32 *sin  31  matter effect a = 2√  G F N e E  = 7. 6 x 10 -5 [eV 2 ]  [g/cm 3 ] E  [GeV]  ij =  m ij 2 L/4 E   m ij 2 [eV 2 ]L[km]/E [GeV]  m ij 2 = m j 2 - m i 2  Since the order of sin   term is too mall to observe clearly at the SK site the linear terms(cos  sin  sin  31 ) in sin   are suppressed.  in Korea, sin   is at least 3. 3 times larger because the baseline from Tokai is as long as (295km->1000km). It allows us to measure both cos  sin  and hence the sign of  m 13 2  can be determined through the sign of sin  31.

7. 7  Probability in vacuum as a function of energy(GeV) :     e appearance sin 2 2  12 = 0. 8  m 12 2 = 7*10 -5 eV 2  =  /2 sin 2 2  23 = 1. 0  m 13 2 = 3*10 -3 eV 2 sin 2 2  13 = 0. 01 Probability(%) Energy (GeV) Baseline=295k m Baseline=1000k m 0.7

8. 8  Probability in vacuum as a function of length(km) : at Energy 0. 7GeV     e Probability      Probability( %) Probability      Length (km)

9. 9 Check of the physics impacts of putting a far detector in Korea with GLoBES  What is GLoBES?  GLoBES : General Long Baseline Experiment Simulator (hep-ph/0407333 and GLoBES manual(2004), http://www.ph.tum.de/~globes)

10. 10 How to calculate the raw event rates in GLoBES (1) (2)  The total number of events is proportional to the product of,  Fid.detector mass[kt] x Running time[yr] x source power[MW] useful muon decays[yr -1 ]

11. 11 Calculating Chi-square in GLoBES  In GLoBES, “pull-method” is used for the analysis of the systematical errors. (G. L. Fogli, et. al., Phys. Rev. D66(2002), 053010, hep-ph/0206162)  k systematical errors are included by introducing k additional variables  k with simple Gaubian statistics :  The treatment of external input is done by the addition of GauBian to chi- square funtion.  the fit manifold is restricted by the knowledge from earlier experiments. ex) matter density scaling factor and the solar parameters,...etc.  n-parameter correlation is treated by the simultaneous local minimization over all free fit parameters using n-dimensional, local minimizer of the projection. Here refers to the oscillation parameters(  12,  23,  13, ,  m 13 2,  m 12 2  including matter density , GauBian distributed systematical error

12. 12  Conditions of experiments (hep-ex/0106019, 2001)  flux file used : T2K off-axis beam for OA2.0degree (taken from hep-ex/0106019)  cross section tables – CC, NC, and QE process : those cross sections are taken from UMI-99023965(for low energies) and hep-ph/0107261(for high energies) SKKorea Beam J-PARC to SK,  (OA2.0deg   J-PARC to SK,  (OA2.0deg   Running time5 yr Power0. 77MW, 4MW Target mass22. 5kt, 1000kt100kt, 500kt, 1000kt Baseline295km1000km Matter density2. 8 g/cm 3 3. 0 g/cm 3 Conditions for the check of physics impacts with a far detectors in Korea

13. 13  Neutrino oscillation channels      e appearance in QE       disppearance in QE      e appearance in CC Three channels are treated in chi-square calculation simultaneously.  Systematic errors considered in chi-square calculation (hep-ex/0106019, 2001)  For signal and background energy, calibration error and overall normalization error are considered as systematic errors in the chi- square calculation.  External input in order to reduce the extension of the fit manifold by the knowledge from earlier experiments.  5% uncertainty for the matter density scaling factor  10% uncertainty for the solar parameters

14. 14  Comparison of   and  e spectra for OA2.0deg. nu-e nu-mu Flux(/50MeV/cm 2 /yr) E(GeV)

15. 15 SK: 0.77MW, 22.5kt Korea: 0.77MW, 100kt Korea: 0.77MW, 500kt  Allowed region in the plane of sin 2 2  13 and  cp sin 2 2  12 = 0. 8  m 12 2 = 7*10 -5 eV 2 sin 2 2  23 = 1. 0  m 13 2 = 3*10 -3 eV 2 > 0  =  /2 sin 2 2  13 = 0. 01 by assuming the constant matter density Korea: 0.77MW, 1000kt sin 2 2  1 3  cp (degree) 100 10 - 3 10 -2

16. 16 SK: 4MW, 22.5kt SK: 4MW, 1000kt Korea: 4MW, 1000kt Korea: 4MW, 100kt Korea: 4MW, 500kt sin 2 2  1 3  cp (degree) 10 0 10 -3 10 -2

17. 17  Calculating chi-square with (systematics + parameter correlations + external input)   12,  23,  m 12 2,  m 13 2 are treated as free in fit analysis  external input: 5% uncertainty for matter density scaling factor and 10% uncertainty for solar parameters  cp (degree) 10 0 10 -3 10 -2 sin 2 2  1 3 10 -3 10 -2  cp (degree) Korea: 4MW, 1000kt with systematics only Korea: 4MW, 1000kt with (systematics+correlations+external input) 10 0

18. 18 Summary  We study the physics impacts with a far detector in different size and power in Korea.  we cite the reference, hep-ex/0106019 for this work.  We use GLoBES software package for the simulation of long baseline neutrino oscillation experiment.  we considered chi-square calculation with systematics only for the allowed region in the plane of  cp and  sin 2 2  13.  we tested chi-square calculation with (systematics + correlations + external input)  To-do list (1) We need more studies with a far detector in Korea.  the mixed  m 13 2 –sign degeneracy : determination of mass hierarchy  matter effect (2) Who is working on it? - Eunju Jeon(SNU), Pyungwon Ko(KIAS), Jeongyeon Lee(Ewha. U)

19. 19 BACK UP

20. 20  The GLoBES standard function to obtain a chisquare value with systematics only or systematics and correlations.

21. 21  The most important components of AEDL: Channels, rules, and experiments How to simulate/analyze long baseline neutrino oscillation experiment with GLoBES channel(#nu_mu_disappearance_CC)< @channel = #JHFplus: +: m: m: #CC: #ERES > /* '+/-' : determine whether neutrinos or antineutrinos are taken from the flus file */ /* 'm: m:' : nu_mu -> nu_mu process */ /* 앞에서 정의된 'CC' 의 cross section 과 energy resolution(ERES) 및 JHFplus.dat 의 flux 파일을 이용하여 nu_mu -> nu_mu process 에서의 events rates 을 계산한다 */ rule(#rule1)< @signal = 0.9@#nu_mu_disappearance_QE @signalerror = 0.025 : 0.0001 @background = 0.0056373@#nu_mu_disappearance_NC : 0.0056373@#nu_e_appearance_NC : 0.0056373@#nu_tau_appearance_NC @backgrounderror = 0.2 : 0.0001 @backgroundcenter = 1.0 : 0.0 @errordim_sys_on = 0 @errordim_sys_off = 2 @energy_window = 0.4 : 1.2

22. 22 /* Initialize experiment JHFSKnew.glb */ glbInitExperiment("JHFSKnew.glb",&glb_experiment_list[0],&glb_ num_of_exps); ……. /* The simulated data are computed */ glbSetOscillationParameters(true_values); glbSetRates(); /* Iteration over all values to be computed */ double thetheta13,x,y,res; for(x=-4.0;x<-1.0+0.01;x=x+2.0/50) for(y=0.0;y<200.0+0.01;y=y+200.0/50) { /* Set vector of test values */ thetheta13=asin(sqrt(pow(10,x)))/2; glbSetOscParams(test_values,thetheta13,GLB_THETA_13); glbSetOscParams(test_values,y*M_PI/180.0,GLB_DELTA_CP); /* Compute Chi^2 for all loaded experiments and all rules */ res=glbChiSys(test_values,GLB_ALL,GLB_ALL); AddToOutput(x,y,res); } /* Define standard oscillation parameters */ double theta12 = asin(sqrt(0.8))/2; double theta13 = asin(sqrt(0.01))/2; double theta23 = M_PI/4; double deltacp = M_PI/2; double sdm = 7e-5; double ldm = 3e-3; Chi square calculation with the treatment of systematics parameters is performed by “pull method” AEDL file

23. 23 Possible physics with neutrino oscillation experiments  Three Neutrino Model has 9 physical parameters:  3 neutrino masses, 3 mixing angles and 3 CP violating phases.  neutrino oscillation experiment can probe 6 parameters  2 mass squared differences, 3 mixing angles, and 1 CP phase  so far, determined (1) the magnitude of two of the mass squared differences, (2) the sign of the smaller mass squared difference, (3) the magnitudes of two of the three mixing angles, (4) the upper bound on the third mixing angle.  in the future oscillation experiments, (5) the sign of the larger mass squared difference, (6) the magnitude of the third mixing angle, (7) the CP violating phase.,which will be determined.

24. 24  Neutrino oscillation process :      e appearance in QE with backgrounds of (nu_mu_disappearance_CC + nu_mu_disappearance_NC + nu_e_beam + nu_e_bar_beam + nu_e_appearance_NC + nu_tau_appearance_NC)       disppearance in QE with backgrounds of (nu_mu_disappearance_NC + nu_e_appearance_NC + nu_tau_appearance_NC)      e appearance in CC with backgrounds of (nu_mu_disappearance_CC + nu_e_appearance_NC + nu_e_beam + nu_e_bar_beam + nu_e_appearance_NC + nu_tau_appearance_NC)  Systemaic errors considered in Chi-square calcuation (hep-ex/0106019, 2001) energy calibration error and overall normalization error      e appearance in QE  10% and 0.01% for signal, 5% and 0,01% for background       disppearance in QE  2.5% and 0.01% for signal, 20% and 0.01% for backgound       disppearance in QE  0.01% and 0.01% for signal, 5% and 0.01% for backgound  External input in order to reduce the extension of the fit manifold by the knowledge from earlier experiments.  5% uncertainty for the matter density scaling factor  10% uncertainty for the solar parameters

25. 25  Test result : nu_mu  nu_mu disappearance in QE (Signal) Reconstructed Energy(GeV) # of events(/0. 04GeV) Total no. of evts = 1635. 5 (W/O Oscillation) Total no. of evts = 197. 732 (W/ Oscillation)