Abstract:
We have analyzed the atmospheric neutrino data to study the octant of $\theta_{23}$ and the precision of the oscillation parameters for a large Iron CALorimeter (ICAL) detector. The ICAL being a tracking detector has the ability to measure the energy and the direction of the muon with high resolution. From bending of the track in magnetic field it can also distinguish its charge. We have generated events by Nuance and then considered only the muons (directly measurable quantities) produced in charge current interactions in our analysis. This encounters the main problem of wide resolutions of energy and baseline. The energy-angle correlated two dimensional resolution functions are used to migrate the energy and the zenith angle of the neutrino to those of the muon. A new type of binning has been introduced to get better reflection of the oscillation pattern in chi-square analysis. Then the marginalization of the $\chi^2$ over all parameters has been carried out for neutrinos and anti-neutrinos separately. We find that the measurement of $\theta_{13}$ is possible at a significant precision with atmospheric neutrinos. The precisions of $\Delta m_{32}^2$ and $\sin^2\theta_{23}$ are found $\sim$ 8% and 38%, respectively, at 90% CL. The discrimination of the octant as well as the deviation from maximal mixing of atmospheric neutrinos are also possible for some combinations of ($\theta_{23}, ~\theta_{13}$). We also discuss the impact of the events at near horizon on the precision studies.

Abstract:
In the atmospheric neutrino experiments the primary problems are the huge uncertainties of flux, very rapid fall of flux with increase of energy, the energy dependent wide resolutions of energy and zenith angle between true neutrinos and reconstructed neutrinos. These all in together make the choice of binning of the data for chi-square analysis complicated. The large iron calorimeter has the ability to measure the energy and the direction of the muon with high resolution. From the bending of the track in the magnetic field it can also distinguish its charge. We have analyzed the atmospheric neutrino oscillation generating events by Nuance and then considering the muons produced in the charge current interactions as the reconstructed neutrinos. This practically takes into account the major problem of wide resolutions. We have binned the data in three ways: i) in the grids of $\log E -\log L$ plane, ii) in the grids of $\log E -\cos\theta_{\rm zenith}$ plane, and iii) in the bins of $\log (L/E)$. We have performed a marginalized $\chi^2$ study over $\Delta m_{32}^2, ~\theta_{13}$ and $\theta_{23}$ for neutrinos and anti-neutrinos separately for each method and finally compared the results.

Abstract:
We have studied the prospects of measuring the CP violating phase with atmospheric neutrinos at a large magnetized iron calorimeter detector considering the muons (directly measurable) of the neutrino events generated by a MonteCarlo event generator Nuance. The effect of $\theta_{13}$ and $\delta_{CP}$ appears dominantly neither in atmospheric neutrino oscillation nor in solar neutrino oscillation, but appears as subleading in both cases. These are observable in range of $E \sim 1$ GeV for atmospheric neutrino, where solar and atmospheric oscillation couple. In this regime, the quasi-elastic events dominate and the energy resolution is very good, but the angular resolution is very poor. Unlike beam experiments this poor angular resolution acts against its measurements. However, we find that one can be able to distinguish $\delta_{CP}\approx 0^\circ$ and $180^\circ$ at 90% confidence level. We find no significant sensitivity for $\delta_{CP}\approx 90^\circ$ or $270^\circ$.

Abstract:
We have studied the mass hierarchy with atmospheric neutrinos considering the muon energy and zenith angle of the event at the magnetized iron calorimeter detector. For $\chi^2$ analysis we have migrated the number of events from neutrino energy and zenith angle bins to muon energy and zenith angle bins using the two-dimensional energy-angle correlated resolution functions. The binning of data is made in two-dimensional grids of $\log_{10} E - L^{0.4}$ plane to get a better reflection of the oscillation pattern in the $\chi^2$ analysis. Then the $\chi^2$ is marginalized considering all possible systematic uncertainties of the atmospheric neutrino flux and cross section. The effects of the ranges of oscillation parameters on the marginalization are also studied. The lower limit of the range of $\theta_{13}$ for marginalization is found to be very crucial in determining the sensitivity of hierarchy for a given $\theta_{13}$. Finally, we show that one can discriminate atmospheric neutrino mass hierarchy at $>$90% C.L. if the lower limit of $\theta_{13} \ge 5^\circ$.

Abstract:
In the atmospheric neutrino experiments the primary problems are the huge uncertainties of flux, very rapid fall of flux with increase of energy, the energy dependent wide resolutions of energy and zenith angle between true neutrinos and reconstructed neutrinos. These all in together make the choice of binning of the data for chi-square analysis complicated. The large iron calorimeter has the ability to measure the energy and the direction of the muon with high resolution. From the bending of the track in the magnetic field it can also distinguish its charge. We have analyzed the atmospheric neutrino oscillation generating events by Nuance and then considering the muons produced in the charge current interactions as the reconstructed neutrinos. This practically takes into account the major problem of wide resolutions. We have binned the data in three ways: i) in the grids of $\log E -\log L$ plane, ii) in the grids of $\log E -\cos\theta_{\rm zenith}$ plane, and iii) in the bins of $\log (L/E)$. We have performed a marginalized $\chi^2$ study over $\Delta m_{32}^2, ~\theta_{13}$ and $\theta_{23}$ for neutrinos and anti-neutrinos separately for each method and finally compared the results.

Abstract:
We have analyzed the atmospheric neutrino data to study the octant of $\theta_{23}$ and the precision of the oscillation parameters for a large Iron CALorimeter (ICAL) detector. The ICAL being a tracking detector has the ability to measure the energy and the direction of the muon with high resolution. From bending of the track in magnetic field it can also distinguish its charge. We have generated events by Nuance and then considered only the muons (directly measurable quantities) produced in charge current interactions in our analysis. This encounters the main problem of wide resolutions of energy and baseline. The energy-angle correlated two dimensional resolution functions are used to migrate the energy and the zenith angle of the neutrino to those of the muon. A new type of binning has been introduced to get better reflection of the oscillation pattern in chi-square analysis. Then the marginalization of the $\chi^2$ over all parameters has been carried out for neutrinos and anti-neutrinos separately. We find that the measurement of $\theta_{13}$ is possible at a significant precision with atmospheric neutrinos. The precisions of $\Delta m_{32}^2$ and $\sin^2\theta_{23}$ are found $\sim$ 8% and 38%, respectively, at 90% CL. The discrimination of the octant as well as the deviation from maximal mixing of atmospheric neutrinos are also possible for some combinations of ($\theta_{23}, ~\theta_{13}$). We also discuss the impact of the events at near horizon on the precision studies.

Abstract:
We have studied $CPT$ violation in neutrino oscillation considering three flavor framework with matter effect. We have constructed a new way to find the oscillation probability incorporating $CPT$ violating terms without any approximation. Then $CPT$ violation with atmospheric neutrinos for a magnetized iron calorimeter detector considering the muons (directly measurable with high resolution) of the charge current events has been studied for zero and nonzero $\theta_{13}$ values. It is found that a potential bound of $\delta b_{32} \lapp 6\times 10^{-24}$ GeV at 99% CL can be obtained with 1 Mton.year exposure of this detector; and unlike neutrino beam experiments, there is no possibility to generate `fake' $CPT$ violation due to matter effect with atmospheric neutrinos. The advantages of atmospheric neutrinos to discriminate $CPT$ violation from CP violation and nonstandard interactions are also discussed.

Abstract:
We study the effects of SO(10) D-terms on the allowed parameter space (APS) in models with $t - b - \tau$ and $b - \tau$ Yukawa unifiction. The former is allowed only for moderate values of the D-term, if very precise ($\le$ 5%) unification is required. Next we constrain the parameter space by looking for different dangerous directions where the scalar potential may be unbounded from below (UFB1 and UFB3). The common trilinear coupling $A_0$ plays a significant role in constraing the APS. For very precise $t - b - \tau$ Yukawa unification, $-m_{16} < or \approx A_0 < or \approx m_{16}$ can be probed at the LHC, where $m_{16}$ is the common soft breaking mass for the sfermions. Moreover, an interesting mass hierarchy with very heavy sfermions but light gauginos, which is strongly disfavoured in models without D-terms, becomes fairly common in the presence of the D-terms. The APS exhibits interesting characteristics if $m_{16}$ is not the same as the soft breaking mass $m_{10}$ for the Higgs sector. In $b - \tau$ unification models with D-terms, the APS consistent with Yukawa unification and radiative electroweak symmetry breaking, increases as the UFB1 constraint becomes weaker. However for $A_0 \leq 0$, a stronger UFB3 condition still puts, for a given $m_{16}$, a stringent upper bound on the common gaugino mass ($m_{1/2}$) and a lower bound on $m_{16}$ for a given $m_{1/2}$. The effects of sign of $\mu$ on Yukawa unification and UFB constraints are also discussed.

Abstract:
The light slepton-sneutrino scenario with non-universal scalar masses at the GUT scale is preferred by the electroweak precision data. Though a universal soft breaking mass at or below the Plank scale can produce the required non-universality at the GUT scale through running, such models are in conflict with the stability of the electroweak symmetry breaking vacuum. If the supergravity motivated idea of a common scalar mass at some high scale along with light sleptons is supported by future experiments that may indicate that we are living in a false vacuum. In contrast SO(10) D-terms, which may arise if this GUT group breaks down directly to the Standard Model, can lead to this spectrum with many striking phenomenological predictions, without jeopardizing vacuum stability.

Abstract:
It is widely believed that charm meson production and decay may play an important role in high energy astrophysical sources of neutrinos, especially those that are baryon-rich, providing an environment conducive to pp interactions. Using slow-jet supernovae (SJS) as an example of such a source, we study the detectability of high-energy neutrinos, paying particular attention to those produced from charmed-mesons. We highlight important distinguishing features in the ultra-high energy neutrino flux which would act as markers for the role of charm in the source. In particular, charm leads to significant event rates at higher energies, after the conventional (pi, K) neutrino fluxes fall off. We calculate event rates both for a nearby single source and for diffuse SJS fluxes for an IceCube-like detector. By comparing muon event rates for the conventional and prompt fluxes in different energy bins, we demonstrate the striking energy dependence in the rates induced by the presence of charm. We also show that it leads to an energy dependant flux ratio of shower to muon events, providing an additional important diagnostic tool for the presence of prompt neutrinos. Motivated by the infusion of high energy anti-electron neutrinos into the flux by charm decay, we also study the detectability of the Glashow resonance due to these sources.