///// Introduction 
 
Updated 20181119 

Prob3++ is software for computing three flavor neutrino oscillation probabilities based on the work of Barger et al. Phys. Rev. D22(1980) 2718. It has been written by members of the Super-Kamiokande collaboration in C/C++ and is available for public use at the links below. Example programs designed to explain the code usage as well as documentation are included.


As of December 2018 support for Lorentz invariance-violating oscillations has been added to the library. The computation uses the SME framework (A. Kostelecky et al.) and follows the parameterization in Phys. Rev. 91 052003.


The code is liscenced under GNU GPLv3 (see LISCENCE document).


////// Library Version 
   This document is valid for library version
    v3.10  

   The main library libThreeProb.a can be used to externally call the oscillation computations. 


////// main library compilation

Makefile:
    > make


Included in this module are two simple programs to give the user a general feel
for how the library works. 

probLiner.cc:

 Makefile 
 made with -> make probLinear 
 run with -> ./probLinear

 This program will compute neutrino oscillations for neutrinos passing through
a slab of the constant density. The output file, LinearProb.root will contain 
ROOT histograms of these probabilities as a function of density, L/E, and as functions
of L and E separately. The oscillation probabilities are set with the main body of the code.


probRoot.cc:

GNUmakefile (source appropriate env.csh)
 made with -> make probRoot 
 run with -> ./probRoot


  ProbRoot similarly computes oscillations but for neutrinos travelling through a sphere. The defualt 
radial denisty profile is that of the Earth. However a density profile may be loaded from a text file
for a sphere of any denisty profile and radius. More will be discussed below. In this case oscillation
probabiliteies as a funciton of neutrino zenith angle, and energy are computed and dumped into 
a file RawProb.root. The histograms therein can readily be viewed using makeOne.C 
 

    > root -l RawProb.root makeOne.C


probLV.cc:
> make probLV 
> ./probLV 
   
  This module computes Lorentz-violating oscillation probabilities as a function of pathlength and neutrino 
  energy either for neutrinos traversing the earth or through a slice of constant density 
  matter.

  > root -l fullSME_Prob.root drawLV.C

////// including Prob3plusplus in your CMake project

  Expose Prob3plusplusConfig.cmake to your project, either by adding the repo directory to the 
  `CMAKE_MODULE_PATH` or by exporting `Prob3plusplus_ROOT` to your environment pointing to the
  repo root. In both instances you should have already built the `libThreeProb_<version>.a` before
  attempting to link this in.

  Use Prob3plusplus in your CMake project like:

```
  find_package(Prob3plusplus)
```

  if successfully found, `Prob3plusplus_FOUND` will be set to true and the imported target 
  `Prob3plusplus::All` will have been defined. You can then link your target to Prob3plusplus like

```
  target_link_libraries(<target name> Prob3plusplus::All)
```

  This will link in `libThreeProb_<version>.a` and add the neccessary `-I` include flags to all 
  source files associated with the dependent target (and other targets dependent on that target).

///// About Parameter inputs 

   The software has been written assuming neutrino propagation in a normal 
   hierarchy. In this convention the atmospheric delta-m^2 is defined to be 
   a positive number for the normal hierarchy. The fundamental input mass squared 
   difference for atmospheric mixing is m^2_{32} = m^2_3 - m^2_2.

   There are two modes of mixing which can be specified by a call to 
   BargerPropagator::SetOneMassScaleMode( bool ). The default mode 
   corresponds to true (this is also true if no call to this function is made)

   In this mode, BargerPropagator::SetOneMassScaleMode( true )  
   
   * To compute oscillation probabilities assuming an inverted hierarchy 
     use a negative number for the value of delta-m^2. The code will 
     automatically adjust the input value by the solar mass splitting 
     to provide the correct value of m^2_{32} to internal routines. Effectively
     the input mass squared splitting in this case corresponds to m^2_{31}

   Under BargerPropagator::SetOneMassScaleMode( false )  

   * To compute oscillation probabilities assuming an inverted hierarchy 
     again use a negative number for the value of delta-m^2_32, but the 
     difference between normal hierarch and inverted hierarchy values 
     of this parameter must be specified by hand. That is, the correction
     for the finite size of the solar splitting must be performed manually.
     

   The MNS matrix is defined not only by the mixing parameters but 
   also by the expected type of progation, neutrino or antineutrino. 
   This produces an extra argument in the call to SetMNS (see below)

   * To compute oscillation probabilities for antineutrinos 
     - Change the sign of the input neutrino flavor ( see below )


   -- As of v2.00 it is no longer necessary to change the sign of dcp 
      during antineutrino propagation. 



///// About propagators 

  There are a few "propagators" included in this module, all of which derive from the
  NeutrinoPropagator class. The most commonly used one is the BargerPropagator, 
  which describes standard PMNS oscillations.

  The neutrino oscillation probabilities are stored as doubles.
  Its use is as follows:

      // create a pointer to a new BargerPropagator Object
      BargerPropagator * bNu  = new BargerPropagator(  ); 

                    OR to use a user-defined density profile

      BargerPropagator * bNu  = new BargerPropagator( some-file-name ); 
 
      // specify the neutrino oscillation parameters
      // the form of the variables is interpreted by the last boolean, kSquared
      // when true, it means that mixing angles, theta23, etc. are of the form sin^2(  theta23 )
      // when false, the mixing angles,                        are of the form sin^2(2 theta23 )
      // Delta cp should be entered in radians
      // The last parameter is +: neutrinos -:anti-neutrinos , defaults to neutrino
      bNu->SetMNS( theta12,  Theta13, Theta23, dm12, DM23, delta_cp , Energy, kSquared, KNuType ); 

      *****
        N.B.  This routine reverses the sign of delta_cp for antineutrino propagation
        to perform the complex conjugation of the MNS matrix internally. 
        Please note this behavior is different than earlier versions of the library ( <= v1.00 )
        and the user is no longer responsible for changing the sign of delta_cp by hand.

        If the neutrino type is not the same as that in the call to propagate (see below)
        program execution stops.
        This error can be suppressed with a call to
           BargerPropagator::SetWarningSuppression()
         For expert use only
      ***** 
        

      

  After the propagator has been created there is a choice of propagation modes

      // to progagate through linear matter of constant density
      // type is an integer,  +: neutrino propagaton  -: anti-neutrino propagation
      //   it should be the same as in the call to SetMNS (see above)
      // PathLength is the pathlength through the matter in [km]
      // Density is the matter's density in [g/cm^3]
      bNu->propagateLinear( type, PathLength , Density );

                    OR 

      // to propagate through matter in a sphere:
      // cosineZ is the neutrino zenith angle  -1: upward going, 0: horizontal +1:downward going
      // prod_height is the production height in the atmosphere [km]
      // type is an integer,  +: neutrino propagaton  -: anti-neutrino propagation
      bNu->DefinePath( cosineZ, prod_height );
      bNu->propagate( type );


   At this point the computed oscillation probabilities can be obtained with a call to:
      // the neutrino types are:
      // 1:e 2:mu 3:tau   -1: e_bar -2: mu_bar -3: tau_bar
      prob = bNu->GetProb( nu_in, nu_out );
     
                    OR
  
   For Vacuum oscillation probabilities the situation is more straightforward
      // Energy is [GeV]
      // Path is [km] 
      prob = bNu->GetVacuumProb( nu_in, nu_out , Energy,  Path );

   Everytime a the energy or desired oscillation probabilities change one must call 
   the SetMNS() routine before calling one of the above three propagation routines.
   If for instance these parameters are not changed, subsequent calls to the 
   propagation routines may be made _without_ another call to SetMNS().


   ////  
   //
   //  Lorentz Invariance Violation with the Full SME 
   //
   //
   //  ** 20181819 
   A propagator for the computation of Lorentz invariance-violation oscillations 
   is provided via the FullSME propagator. It assumes propagation through 
   constant density matter and calculates a fully three-flavor oscillation 
   probability using a non-perturbative method from the Standard Model Extension 
   framework. See PRD91 052003. 
 
   In addition to setting the MNS mixing matrix the user must also specify 
   the LV potentials (the "A" and "C" matrices) via the "Set*Matrix*" routines.

   Ie to set the e-tau coefficients of the "C" matrix (only):

   for ( i = 0 ; i < 3 ; i ++ )
     for ( j = 0 ; j < 3 ; j ++ )
     {
       SMEnu->SetLVMatrixEntry( "A" , i, j, 0.0, 0.0 );
       SMEnu->SetLVMatrixEntry( "C" , i, j, 0.0, 0.0 );
     }
   // index 0 is for nue 
   // index 1 is for numu 
   // index 2 is for nutau 
   SMEnu->SetLVMatrixEntry( "C" , 0, 2, 7.5e-23, 0.0    );
   SMEnu->SetLVMatrixEntry( "C" , 2, 0, 7.5e-23, 0.0    );

   This must be done before a call to SetHamiltonian. 

    SMEnu->SetMNS( Theta12,  Theta13, Theta23, dm2, DM2, delta , energy, kSquared, kNuBar ); 
    // For propagation in the Earth
    SMEnu->DefinePathFromLength( PathLength, 25.00  );

    // For propagation in constant density matter, here 22 g/cm^3
    //SMEnu->DefineLinearPath( PathLength, 22.0 );

    SMEnu->SetHamiltonian( energy );
    
    No you can propagate! 
    SMEnu->propagate( kNuBar );

    Probabilities are returned using the same GetProb() routine 
    from BargerPropagator

   


/////// about input density profiles

  User-specified density profiles must contain at least two columns of floating point
  numbers, the first is the radial distance [km] from the sphere center, the second
  is the density [g/cm^3] for 
  0.      x_0
  r_1     x_1
  ..      ..
  r_n     x_n
  the last entry should contain the radius of the sphere.
  each x_i represents the density up to and including r_i
  the entry for zero radial density must be included. 


  so in PREM.dat, the lines
  1220    13.0
  3480    11.3

  indicate that the density of the earth from 1220 to 3480 radial km 
  is 11.3 g/cm^3. ( Below 1220 km, is 13.0 g/cm^3 )

 :: As of 20210425 input files containing the chemical composition factor
  Yp = n_e / (np+nn) , where ne is number of electrons and 
  np and nn are the number of protons, is also included.

  Files of the sort 
  0.      x_0   yp_0
  r_1     x_1   yp_1
  ..      ..    ...
  r_n     x_n   yp_n 

  If Yp is not specified the default is 0.468 for core layers 
  and 0.497 otherwise. 
  (For propagateLinear the default is 0.5 )

//////////


//////////////////
 Python Wrapper 

 - A simple python wrapper for just the BargerPropagator class is provided 
in the py_wrapper.c. It has been written under ctypes, instead of something 
more fancy, because cytpes is bundled (and should therefore be present) in 
all pthon distributions. 

 To use the shared library must be used:

 >make shared 

 Be sure that the Prob3++ directory is included in your LD_LIBRARY_PATH, or install 
the shared library into some directory that is. 


 To run the test script, you may have to change the path to the python executable
at the top of the file: simpleLinear.py . This script requires pyroot.
 


///////////// About

  This code has been written by members of the Super-Kamiokande collaboration
and is presented here in a purified form. Though not the sole author,
Roger Wendell (-rvw) is presently maintaining the software. Comments and suggestions
are welcome at:

   [email protected]
   [email protected]

   Other types of oscillation modules may be provided in the future.  Thanks kindly, 
and please enjoy your personal search for cp and or Lorentz invariance violation!