1. Non-standard physics and user- defined priors in GLoBES Workshop on physics and applications of the GLoBES software Workshop on physics and applications of the GLoBES software Max-Planck-Institut für Kernphysik January 24, 2007 Walter Winter Universität Würzburg TexPoint fonts used in EMF: AAAA A

2. January 24, 2007GLoBES Workshop - Walter Winter2 Outline Introduction: Different levels in GLoBES Introduction: Different levels in GLoBES Probability level and the simulation of non-standard physics Probability level and the simulation of non-standard physics Systematics level Systematics level Physics level and user-defined priors Physics level and user-defined priors Summary Summary

3. January 24, 2007GLoBES Workshop - Walter Winter3 Different levels in GLoBES Probability level Systematics level Correlation and degeneracy level Additional “nuisance“ parameters. Example : (Fogli et al, 2002) Projection onto sub-space/marginalization: Channel Rule Experi- ment(s) AEDL:

4. January 24, 2007GLoBES Workshop - Walter Winter4 “Evolution“ operator in one layer, being diagonalized: Probability level Hamiltonian in constant matter density layer: Probability calculation:

5. January 24, 2007GLoBES Workshop - Walter Winter5 Non-standard physics in GLoBES 1. Modify the Hamiltonian, probability calculation, etc. Example: Non-standard matter effect in e-  -sector: 2. GLoBES now carries k more oscillation parameters, which need to be maintained:

6. January 24, 2007GLoBES Workshop - Walter Winter6 Example: Decoherence at reactor exp. Oscillation probabilities with damping effects: Oscillation probabilities with damping effects: Damping factors for (wave packet) decoherence: Damping factors for (wave packet) decoherence:  E : Intrinsic wave packet width Can be implemented analytically in quasi-vacuum (short L) (Blennow, Ohlsson, Winter, hep-ph/0502147) (J. Kopp for GLoBES 3.0)

7. January 24, 2007GLoBES Workshop - Walter Winter7 Modification of the access functions const int GLB_SIGMA_E = 6; double th12, th13,th23,deltacp,sdm,ldm,sigma_E; int my_set_oscillation_parameters(glb_params p, void *user_data) { th12 = glbGetOscParams(p, GLB_THETA_12); th13 = glbGetOscParams(p, GLB_THETA_13); th23 = glbGetOscParams(p, GLB_THETA_23); deltacp = glbGetOscParams(p, GLB_DELTA_CP); sdm = glbGetOscParams(p, GLB_DM_21) * 1.0e-18; ldm = glbGetOscParams(p, GLB_DM_31) * 1.0e-18; sigma_E = glbGetOscParams(p, GLB_SIGMA_E); return 0; } int my_get_oscillation_parameters(glb_params p, void *user_data) { glbSetOscParams(p, th12, GLB_THETA_12); glbSetOscParams(p, th13, GLB_THETA_13); glbSetOscParams(p, th23, GLB_THETA_23); glbSetOscParams(p, deltacp, GLB_DELTA_CP); glbSetOscParams(p, sdm*1.0e18, GLB_DM_21); glbSetOscParams(p, ldm*1.0e18, GLB_DM_31); glbSetOscParams(p, sigma_E, GLB_SIGMA_E); return 0; } Define access functions for the oscillation parameters: Define access functions for the oscillation parameters: Set oscillation parameters from internal structure Get oscillation parameters from internal structure

8. January 24, 2007GLoBES Workshop - Walter Winter8 Definition of a probability engine int my_probability_matrix(double P[3][3], int cp_sign, double E, int psteps, const double *length, const double *density, double filter_sigma, void *user_data) { int i, j; double L, Delta21, Delta31, Delta32, D21, D31, D32, s13, c13, s12, c12, t; /* Set all probabilities to zero initially */ for (i=0; i < 3; i++) for (j=0; j < 3; j++) P[i][j] = 0.0; /* Calculate total baseline from the input lists*/ L = 0.0; for (i=0; i < psteps; i++) L += length[i]; L = GLB_KM_TO_EV(L) * 1.0e9; /* Convert to GeV^{-1} */ /* Compute P_ee analytically with a piece of code*/ s12 = sin(th12);c12 = cos(th12);s13 = sin(th13);c13 = cos(th13); t = L / (4.0 * E); Delta21 = sdm * t;Delta31 = ldm * t;Delta32 = Delta31 - Delta21; t = M_SQRT2 * sigma_E / E; D21 = exp(-square( Delta21 * t )); D31 = exp(-square( Delta31 * t )); D32 = exp(-square( Delta32 * t )); P[0][0] = square(square(c13)) * ( 1 - 2.0*square(s12*c12)* (1–D21* cos(2.0*Delta21))) + 2.0*square(s13*c13) * ( D31*square(c12) * cos(2.0*Delta31) + D32*square(s12) * cos(2.0*Delta32) ) + square(square(s13)); return 0; } (GLoBES 3.0, example6.c )

9. January 24, 2007GLoBES Workshop - Walter Winter9 Using the new probability engine Register the new probability engine and access functions Register the new probability engine and access functions glbRegisterProbabilityEngine(7, // Number of params &my_probability_matrix, &my_set_oscillation_parameters, &my_get_oscillation_parameters, NULL); Maintain the new oscillation parameter(s): Maintain the new oscillation parameter(s): –Use glbSetOscParams and glbGetOscParams to access the non-standard parameter(s) –Always use glbChiNP (instead of glbChiTheta13 etc.) to define how the non-standard degrees of freedom behave –Define your non-standard behavior in the projection with glbSetProjectionFlag

10. January 24, 2007GLoBES Workshop - Walter Winter10 Results for our example glbDefineProjection(myproj, GLB_FREE, GLB_FIXED, GLB_FIXED, GLB_FIXED, GLB_FREE, GLB_FREE); glbSetDensityProjectionFlag(myproj, GLB_FIXED, GLB_ALL); glbSetProjectionFlag(myproj,GLB_FIXED,GLB_SIGMA_E); glbSetProjection(myproj); for(x=0; x < 0.05+0.001; x+=0.005) /* th13 */ for(y=0.0; y < 0.010+0.001; y+=0.001) /* sigma_E */ { /* Set vector of test=fit values */ thetheta13=asin(sqrt(x))/2.0; glbSetOscParams(test_values,thetheta13, GLB_THETA_13); glbSetOscParams(test_values,y,GLB_SIGMA_E); /* Compute Chi^2 with correlations */ res=glbChiNP(test_values,NULL,GLB_ALL); AddToOutput(x,y,res); } glbDefineProjection(myproj, GLB_FREE, GLB_FIXED, GLB_FIXED, GLB_FIXED, GLB_FREE, GLB_FREE); glbSetDensityProjectionFlag(myproj, GLB_FIXED, GLB_ALL); glbSetProjectionFlag(myproj,GLB_FIXED,GLB_SIGMA_E); glbSetProjection(myproj); for(x=0; x < 0.05+0.001; x+=0.005) /* th13 */ for(y=0.0; y < 0.010+0.001; y+=0.001) /* sigma_E */ { /* Set vector of test=fit values */ thetheta13=asin(sqrt(x))/2.0; glbSetOscParams(test_values,thetheta13, GLB_THETA_13); glbSetOscParams(test_values,y,GLB_SIGMA_E); /* Compute Chi^2 with correlations */ res=glbChiNP(test_values,NULL,GLB_ALL); AddToOutput(x,y,res); } True values:  13 =  e =0 (Original figure from hep-ph/0502147) Correlations

11. January 24, 2007GLoBES Workshop - Walter Winter11 More physics examples computed with GLoBES Simulation of Hamiltonian-level effects Simulation of Hamiltonian-level effects (Blennow, Ohlsson, Winter, hep-ph/0508175; hep-ph/0508175; also: Kopp, Lindner, Ota, in prep.) Mass-varying neutrinos: Environment-dependence of neutrino mass (Schwetz, Winter, hep-ph/0511177)

12. January 24, 2007GLoBES Workshop - Walter Winter12 Systematics level Discussed in Joachim Kopp´s talk … Discussed in Joachim Kopp´s talk … User-defined?

13. January 24, 2007GLoBES Workshop - Walter Winter13 Correlation and degeneracy level … and the inclusion of external input Projection onto sub-space/marginalization: Standard GLoBES: Include of external input by Gaussian priors, e.g., for  12 with an error   12 User-defined priors:

14. January 24, 2007GLoBES Workshop - Walter Winter14 How to define user-defined priors double my_prior(const glb_params in, void* user_data) { glb_params central_values = glbAllocParams(); glb_params input_errors = glbAllocParams(); glb_projection p = glbAllocProjection(); glbGetCentralValues(central_values); glbGetInputErrors(input_errors); glbGetProjection(p); int i; double pv = 0.0; double fitvalue,centralvalue,inputerror; /* Add oscillation parameter priors */ for(i=0;i 1e-12) { if(i==GLB_THETA_12) pv+=square(( square(startvalue-sin(fitvalue)))/inputerror); else pv+=square((startvalue-fitvalue)/inputerror); } } /* Add matter parameter priors */ for(i=0;i 1e-12) pv+=square((fitvalue-1.0)/inputerror); } glbFreeParams(central_values); glbFreeParams(input_errors); glbFreeProjection(p); /* Add matter parameter priors */ for(i=0;i 1e-12) pv+=square((fitvalue-1.0)/inputerror); } glbFreeParams(central_values); glbFreeParams(input_errors); glbFreeProjection(p); /* Add any input from other experiments: */ /* pv+=... */ return pv; } In main(): /* Add any input from other experiments: */ /* pv+=... */ return pv; } In main(): glbInit(argv[0]); glbRegisterPriorFunction(my_prior, NULL,NULL,NULL); Define a prior function and register it. Example: Gaussian error in sin 2  12 (instead of  12 )

15. January 24, 2007GLoBES Workshop - Walter Winter15 Example: Astrophysical sources … for neutrino oscillations? Astrophysical neutrino sources produce certain flavor ratios of neutrinos ( e :  :  ): Neutron decays: (1:0:0) Muon damped sources: (0:1:0) Pion decays: (1:2:0) Astrophysical neutrino sources produce certain flavor ratios of neutrinos ( e :  :  ): Neutron decays: (1:0:0) Muon damped sources: (0:1:0) Pion decays: (1:2:0) These ratios are changed through averaged neutrino oscillations: Only CP-conserving effects remaining ~ cos  CP These ratios are changed through averaged neutrino oscillations: Only CP-conserving effects remaining ~ cos  CP Measure muon track to shower ratio at neutrino telescope: R =   /(  e   ) (conservative, since in future also flavors!?) Measure muon track to shower ratio at neutrino telescope: R =   /(  e   ) (conservative, since in future also flavors!?)

16. January 24, 2007GLoBES Workshop - Walter Winter16 Complementarity to beams Use R to obtain information on osc. parameters? Difficult, since Use R to obtain information on osc. parameters? Difficult, since –Low statistics –No spectral info (Serpico, Kachelriess, 2005; Serpico, 2005) But: Complementary dependence on  CP Here: Constant-rates/ constant-R curves But: Complementary dependence on  CP Here: Constant-rates/ constant-R curves Combine the information from two “low-statistics” sources? Combine the information from two “low-statistics” sources? (Winter, hep-ph/0604191) Best-fit

17. January 24, 2007GLoBES Workshop - Walter Winter17 Implementation in GLoBES double R_neutron_true; /* Simulated/true R */ double relerror = 0.2; /* Relative error */ double R_neutron(const glb_params in) { double theta12 = glbGetOscParams(in,GLB_THETA_12);double theta13 = glbGetOscParams(in,GLB_THETA_13); double theta23 = glbGetOscParams(in,GLB_THETA_23);double deltacp = glbGetOscParams(in,GLB_DELTA_CP); double sdm = glbGetOscParams(in,GLB_DM_21);double ldm = glbGetOscParams(in,GLB_DM_31); double R= (pow(cos(theta13),2.0)*(8.0*pow(cos(theta12),2.0)* pow(cos(theta23),2.0)* pow(sin(theta12),2.0) + sin(theta13)*((7.0 + cos(4.0*theta12))*sin(theta13)* pow(sin(theta23),2.0) + cos(deltacp)*sin(4.0*theta12)*sin(2.0*theta23))))/ (4.0 + 2.0*pow(cos(theta13),2.0)*(2.0*pow(cos(theta12),4.0)*cos(2.0*theta23)* pow(sin(theta13),2.0) + pow(cos(theta12),2.0)*(-2.0*(cos(2.0*theta13) + cos(2.0*theta23))*pow(sin(theta12),2.0) + (-3.0 + cos(2.0*theta12))* pow(sin(theta13),2.0)) + 4.0*cos(deltacp)*cos(theta12)*cos(theta23)* pow(sin(theta12),3.0)*sin(theta13)*sin(theta23) -4.0*pow(sin(theta12),2.0)* pow(sin(theta13),2.0)*pow(sin(theta23),2.0) – 2.0*cos(deltacp)*pow(cos(theta12),3.0)* sin(theta12)*sin(theta13)*sin(2.0*theta23))); return R; } double my_prior(const glb_params in, void* user_data) { [...] /* Standard GLoBES prior */ /* Astrophysical information */ pv+=square((R_neutron(in)-R_neutron_true)/(R_neutron_true*relerror); return pv; } glbSetRates(true_values);R_neutron_true = R_neutron(true_values); Global variables Calculate, for example, R Neutron analytically: Add as external Gaussian measurement Always together!

18. January 24, 2007GLoBES Workshop - Walter Winter18 Reactor experiment+astrophysical source Double Chooz could be the first experiment to observe  CP Double Chooz could be the first experiment to observe  CP (Winter, hep-ph/0604191) (1 , 90% CL; 1 d.o.f.)

19. January 24, 2007GLoBES Workshop - Walter Winter19 Mass hierarchy Astrophysical source may help mass hierarchy measurement at superbeam: 20% prec. good Astrophysical source may help mass hierarchy measurement at superbeam: 20% prec. good (Winter, hep-ph/0604191) No ext. info 20% 5% 10%

20. January 24, 2007GLoBES Workshop - Walter Winter20 Further physics applications Combination with other external measurements, such as atmospheric neutrinos (Huber, Maltoni, Schwetz, hep-ph/0501037; Campagne, Maltoni, Mezzetto, Schwetz, hep-ph/0603172) Combination with other external measurements, such as atmospheric neutrinos (Huber, Maltoni, Schwetz, hep-ph/0501037; Campagne, Maltoni, Mezzetto, Schwetz, hep-ph/0603172) Penalties for degeneracy localization: E.g. add penalty if in wrong octant (Schwetz priors) Penalties for degeneracy localization: E.g. add penalty if in wrong octant (Schwetz priors)  Tutorial „Finding parameter degeneracies“ tomorrow!

21. January 24, 2007GLoBES Workshop - Walter Winter21 Summary: GLoBES 3.0 Probability level Systematics level Correlation and degeneracy level User-defined probabilities User-defined systematics User-defined priors (Joachim’s talk) Maximum flexibility in GLoBES (Huber, Kopp, Lindner, Rolinec, Winter, hep ph/0701187) http://www.mpi- hd.mpg.de/lin/globes/