1 / 21

Non-standard physics and user-defined priors in GLoBES

Non-standard physics and user-defined priors in GLoBES. 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: A A A A A. Outline.

milica
Télécharger la présentation

Non-standard physics and user-defined priors in GLoBES

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Non-standard physics and user-defined priors in GLoBES 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: AAAAA

  2. Outline • Introduction:Different levels in GLoBES • Probability level and the simulation of non-standard physics • Systematics level • Physics level and user-defined priors • Summary GLoBES Workshop - Walter Winter

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

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

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

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

  7. Modification of the access functions • Define access functions for the oscillation parameters: 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;} Set oscillationparametersfrom internalstructure Get oscillationparametersfrom internalstructure GLoBES Workshop - Walter Winter

  8. 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) GLoBES Workshop - Walter Winter

  9. Using the new probability engine • 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): • 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 GLoBES Workshop - Walter Winter

  10. 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); } Correlations True values: q13=se=0(Original figure from hep-ph/0502147) GLoBES Workshop - Walter Winter

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

  12. Systematics level • Discussed in Joachim Kopp´s talk … User-defined? GLoBES Workshop - Walter Winter

  13. 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 q12 with an error sq12 • User-defined priors: GLoBES Workshop - Walter Winter

  14. How to define user-defined priors • Define a prior function and register it.Example: Gaussian error in sin2q12 (instead of q12) 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<glbGetNumOfOscParams();i++) if(glbGetProjectionFlag(p,i)==GLB_FREE) { fitvalue=glbGetOscParams(in,i); centralvalue=glbGetOscParams(central_values,i); inputerror=glbGetOscParams(input_errors,i); if(inputerror>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<glb_num_of_exps;i++) if(glbGetDensityProjectionFlag(p,i)==GLB_FREE) { fitvalue=glbGetDensityParams(in,i); inputerror=glbGetDensityParams(input_errors,i); if(inputerror>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(): glbInit(argv[0]); glbRegisterPriorFunction(my_prior, NULL,NULL,NULL); GLoBES Workshop - Walter Winter

  15. Example: Astrophysical sources … for neutrino oscillations? • Astrophysical neutrino sources producecertain flavor ratios of neutrinos (ne:nm:nt):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 dCP • Measure muon track to shower ratio at neutrino telescope: R = fm/(fe+ft)(conservative, since in future also flavors!?) GLoBES Workshop - Walter Winter

  16. Complementarity to beams • Use R to obtaininformation onosc. parameters?Difficult, since • Low statistics • No spectral info (Serpico, Kachelriess, 2005;Serpico, 2005) • But: Complementarydependence on dCPHere: Constant-rates/ constant-R curves • Combine the information from two “low-statistics”sources? Best-fit (Winter, hep-ph/0604191) GLoBES Workshop - Walter Winter

  17. 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,RNeutronanalytically: Add as externalGaussianmeasurement Always together! GLoBES Workshop - Walter Winter

  18. Reactor experiment+astrophysical source (Winter, hep-ph/0604191) • Double Choozcould be thefirst experiment toobserve dCP (1s, 90% CL; 1 d.o.f.) GLoBES Workshop - Walter Winter

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

  20. 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) • Penalties for degeneracy localization:E.g. add penalty if in wrong octant(Schwetz priors) • Tutorial „Finding parameter degeneracies“tomorrow! GLoBES Workshop - Walter Winter

  21. Summary: GLoBES 3.0 Probability level User-definedprobabilities MaximumflexibilityinGLoBES Systematics level User-definedsystematics (Joachim’s talk) Correlation anddegeneracy level (Huber, Kopp, Lindner, Rolinec, Winter, hep ph/0701187) http://www.mpi-hd.mpg.de/lin/globes/ User-definedpriors GLoBES Workshop - Walter Winter

More Related