Set Flags in MC_SET_MSW.DAT

The easiest way to learn to use the code is to look at the mc_set_msw.dat file. The first line in the user section is a flag to set which solar model (SSM) is to be used. The relevance of this is to set the total flux of $^{8}$B and hep neutrinos. There are fairly significant differences in the event rates for SNO for the different SSMs. SSM=1 is the Bahcall-Ulrich (BU) SSM, the first SSM to specify neutrino energy spectra. This is the one in Bahcall's book "Neutrino Astrophysics". The second SSM (SSM=3) is the Bahcall-Pinsanault (BP) SSM of 1992 with no diffusion. The third (SSM=4) is BP with Helium (He) diffusion. (For information on these models see [22].The fourth (SSM=5) and fifth (SSM=6) are the latest BP SSMs (1995); the fourth with both He and heavy element diffusion and the last with no diffusion. The BP SSM with He and heavy element diffusion is the one that agrees most closely with various astrophysical measurements of related solar parameters such as the surface abundance of Helium and the depth of the convective zone determined from Heliosiesmology. This model gives the largest $^{8}$B rate and the BP95 SSM with no diffusion gives the lowest rate showing how diffusion affects the production of neutrinos. (See [23] for more details). The BP 1998 and 2000 SSM values have been added as of version 4.0182. The BP 1998 is the sixth (SSM=7) choice while BP 2000 is the seventh choice (SSM=8). To learn more about these models see [24,25]. The default choice of SSM in SNOMAN is BP 2000. In addition, starting with version 4.0186, a separate option (SSM=9) has been added for the modified BP 2000 SSM values known as BP2001.

The second item is an energy shift in the spectra (both $^{8}$B and hep). It is what Bahcall calls the bias in the spectrum. The units are in MeV and it can be set positive or negative. This can be used to study energy mis-calibration effects.

The third and fourth items are factors which multiply the $^{8}$B and hep spectra respectively. So they can be used to scale either or both spectra relative to the SSM one is using.

The fifth item that can be set is the core temperature of the Sun in units of the SSM core temperature. This is used in the MSW code to calculate neutrino fluxes.

The sixth item is the neutrino model. One can choose SSM which means no neutrino oscillations, MSW Dirac or Majoranna, or vacuum oscillations. Vacuum oscillations are included automatically if one chooses MSW Dirac or Majoranna. If one wants to use the MSW effect in the earth, there is another flag for that which is described later.

Next is neutrino type. One can choose B8 only, hep only or both.

After that comes the neutrino flavor flag which voids the neutrino flavor flag which is set in en_param(ipart,10) (or anywhere else) in mc_generator.dat. This flag is in a binary format, the first number turns on(=1)/off(=0) electron neutrinos and the second does the same for muon neutrinos (or more precisely, the type of neutrino which the electron neutrino turns into during oscillation. i.e. either $\nu _{\mu}$ or $\nu _{\tau}$ for MSW and vacuum oscillations or sterile $\nu _x$ for sterile oscillations.). Only two flavor mixing is considered in this MSW code. Three flavor mixing is much harder to deal with.

The ninth item is a flag to set normal or sterile neutrino oscillations. The sterile neutrinos will not interact with the SNO detector and so will give a lower NC rate than normal MSW for the same mixing parameters.

The next user set parameter is a flag to set hard-wired or user set mixing parameters. SOL_SLTN=0 automatically sets sin-squared-two-theta (sin$^2(2{\theta})$) and delta-m-squared ($\delta m^2$) to the values which are the most probable values of those parameters according to simultaneous fits to the 4 major solar neutrino experiment's data. (See, for example, the above-mentioned papers by Bludman, Hata et. al.). This is the so-called non-adiabatic MSW (NA) solution to the solar neutrino problem. Other hard-wired solutions are the so-called large- angle MSW (LA) solution and the just-so vacuum oscillations (JS) solution. If one wants to set there own value of sin$^2(2{\theta})$ and ${\delta}_{m^2}$, set the SOL SLTN flag equal to 3 and then set the next two flags. These two flags are only read in if SOL_SLTN is equal to three.

The thirteenth flag is a flag to choose which method is used to calculate the probability of mixing in the sun. There are different approximations for this calculation such as infinite/finite, Pizzacharo, Petcov formula etc. For more information on this see Bahcall, "Neutrino Astrophysics". Set this flag = 2 for starters. This uses the Petcov formula which is for an exponentially changing electron density profile.

Next comes another binary flag for neutrino interactions with SNO. The first bit turns on/off elastic scattering (ES) interactions. One must be careful to choose which region(s) one wants to generate these in. The second and third bits are for charged-current (CC), and neutral-current (NC) interactions respectively. If one wants all three interactions, set this flag to 111. So, all of the interactions can be run at the same time with all of the correct relative rates.

The fifteenth flag sets which set of CC, NC total cross sections will be used, Kubodera, Haxton, improved Kubodera, Butler, Bahcall and Kubodera 2002. The improved Kubodera cross sections are the default choice in snoman, there is fairly good agreement with the old Kubodera cross sections, but both sets of Kubodera cross sections are about 5$\%$ higher along most of the solar neutrino energy range than the Haxton cross sections, and so will give slightly larger interaction rates. The Bahcall cross sections are only calculated for CC interactions and these are between 5 and 10% lower than the Kubodera values. The Butler total cross sections agree very well with Kubodera when the choice of L1A, the effective field theory floating variable is set to 5.6 fm$^3$, this is the default value in snoman and can be changed using the twenty-third flag. The double differential cross sections are in table form for both Kubodera options. If you choose the Haxton option, the Kubodera double differential cross sections are scaled by neutrino energy (comparing the Kubodera and Haxton total cross sections) to give the Haxton double differential cross sections. For both Butler and Bahcall, the double differential cross sections are calculated analytically. The Kubodera 2002 total cross sections are within 1% of the previous improved Kubodera cross sections. The main differences in the 2002 version involve updated constants and some improvements in their models to include some of the radiative corrections, although not all radiative corrections are taken into account. (The total cross sections are used by the MSW code to calculate the daily rates of each of the interactions. The differential cross sections are used later in the code when the actual Monte Carlo is run. We do not yet have the differential cross sections from Haxton and so all of the Monte Carlos use the Kubodera differential cross sections as of SNOMAN 2_08. When the Haxton differential cross sections are obtained they will be installed for consistency.)

The sixteenth flag controls the use of duration instead of particle number to determine the length of time for data. The one following it is the duration in days for data. If these are set to 1 and the number of days of data desired respectively, the code will calculate how many particles one should get in that time and override MGEN set in job_control.dat. If the flag is set to 2 the code will generate events until the required duration is reached. The difference between 1 and 2 is that the former specifies the number of events the produce the average number expected in the specified duration while the later allows for statistical fluctuations in the number of events generated. This feature makes it easy to generate, say, 100 days of data, with all of the correct partial rates for CC, ES, NC, $\nu_e$ , $\nu _{\mu}$ etc.

The eighteenth flag turns on/off the correction of the neutrino flux due to the earth's orbital eccentricity. It is useful for studying seasonal effects. This flag nullifies the same flag which is set in mc_generator.dat.

The next set of 3 flags relates to the earth MSW effect. One must have the neutrino model flag non-zero for this flag to work. The earth effect survival probability can be averaged over a year (both day and night or night only) or it can be calculated for a specific time and date. One can study the so-called Day-Night effect using these flags. If averaging is desired, set the last two flags for the number of points to average over for a year and night respectively. If specific time/date is chosen this taken, as for all other types of generation (including CC, NC events without the MSW effect) from the JOB bank. Note: before version 3.00, MSW, CC and NC events took their start time from the time parameters of the MCPI bank.

Another feature of the nineteenth flag for Earth effect is that one can turn off MSW in the sun by using a minus sign in front of the flag. For instance, if one wanted MSW in the earth (and not the sun) averaged over day and night then one would set this flag to -1. For specific date and time MSW in the earth (and not the sun) set this to -3, etc. This allows study of the earth effect independent of the solar MSW effect.

The twenty second flag is set to the choice of B-8 spectrum. There are 9 choices. The first is the spectrum by Bahcall et al. (PR C54, 411 (1996)). This is the default choice and is the spectrum that has traditionally been implemented in SNOMAN prior to version 4.084. Choice 2 is this Bahcall spectrum but with each bin increased by the 1-sigma uncertainty estimate given by the authors. Choice 3 is the Bahcall spectrum decreased by 1 sigma. Choice 4 is the spectrum by Ortiz et al. (nucl-ex/0003006). Choices 5 and 6 are the plus and minus 1 sigma versions of the Ortiz work respectively. Choice 7 is the Freedman et. al spectra (nucl-ex/0406019). Choices 8 and 9 are the plus and minus 1 sigma versions of the Freedman work respectively.

The twenty third flag is set to the choice of the L1A parameter. The default choice is 5.6 fm$^3$, which will allow the total cross sections of Butler to match Kubodera. (To learn more about the effective field theory method of calculating total cross sections see nucl-th/0008032).

The twenty fourth flag activates the radiative corrections model on the charged and neutral current cross-section on an event-by-event basis. The number chooses which radiative model will be used. At the present time, only the KMV model ($N = \pm 1$) is active (A. Kurylov, M. J. Ramsey-Musolf, and P. Vogel,nucl-th/0110051 (2001)). Note that N can be both positive and negative. If N is positive, only the energy correction is applied. If N is negative, then a brem photon is also created. The effect of the brem photon is well below the 0.1% level. One must take special care in using brem photons, since SNOMAN creates two particles for a given event. Because SNOMAN counts neutrino and brem photon events separately, there are issues with double counting/under counting when using the bem photon option. It is advised that the brem photon option only be invoked for spectrum studies. There are no counting issues associated with using $N \ge 1$.

The twenty fifth flag activates the anti-CC, NC or ES cross sections, if the appropriate flag is set above. The cross sections should be run as separate jobs, since the anti-CC reaction has three visible output particles while the anti-NC or ES have only 1 visible output particle. The anti-cross sections exist for only the original Kubodera (KN) and the Kubodera 2002 (NETAL) options. Although the two calculations agree for the most part within 1%

The twenty sixth flag activates the radiative correction on ES when it is 1. The reference is Bahcall et al, PRD 51, 6146-6158 (1995). This radiative correction code is consistent with QPhyics. The pre-calculated tables from QPhysics are used.