Pak-China Defense Cooperation and Evolving International Relations

This study is about the impact of different global and regional changes resulting from PakistanChina’s defense cooperation and further examines the increasing range of diplomatic cooperation in the social, tactical, and economic realms. The paper focuses on three events: (i) the 1978 transformation of China and its opening-up policies; (ii) disbanding of the U.S.S.R (1991); and (iii) the event of 9/11 in the United States. These events had a significant influence on Pak-China ties. This study is a literature review and contributes to a better understanding of the evolving international systems namely the India-U.S. Tactical relations and strategic cooperation. The paper concludes that China and Pakistan need to preserve amicable, strategic, and diplomatic connections with one another as it is necessary for the peace, security, and economic development of not only China and Pakistan but for the region overall.

Rare Semileptonic B Meson Decays Beyond the Standard Model

In this thesis the exclusive rare semileptonic decays of B-mesons have been studied beyond the Standard ∗ Model. In particular the decays B → K1 (1270, 1400)l+ l− and Bc → Ds l+ l− are considered. These decays are induced by flavor changing neutral current (FCNC) transitions which at quark level arises as b → sl+ l− . In the Standard model these FCNC decays are not allowed at tree level but are allowed at loop level through Glashow-Iliopoulos-Maiani (GIM) mechanism. In addition they are also suppressed in the Standard Model due to their dependence on weak mixing angles of the quark flavor rotation matrix- the Cabibo Kobayashi Maskawa (CKM) matrix. These two circumstances make the FCNC decays relatively rare and hence are important to study physics beyond the Standard Model, commonly known as new physics. The main points of this thesis are: • The implications of the fourth generation quarks in the decay B → K1 (1270, 1400)l+ l− with l = μ, τ are studied, where the mass eigenstates K1 (1270) and K1 (1400) are mixture of 1 P1 and 3 P1 states with the mixing angle θK . In this context, we have studied various observables like branching ratio (BR), forward-backward asymmetry (AF B ) and longitudinal and transverse helicity fractions (fL,T ) of K1 meson in B → K1 l+ l− decays. To study these observables, we have used the Light Cone QCD sum rules form factors and set the mixing angle θK = −34◦ . It is noticed that the BR is suppressed for K1 (1400) as a final state meson compared to that of K1 (1270). Same is the case when the final state leptons are tauons rather than muons. In both the channels all of the above mentioned observables are quite sensitive to the fourth generation effects. Hence the measurements of these observables at LHC, for the above mentioned processes can serve as a good tool to investigate the indirect manifestations of the fourth generation quarks. • The same decay B → K1 (1270, 1400)l+ l− is also studied in the standard model (SM) and in universal extra dimension (UED) model. In this work we first relate the form factors through Ward identities and then express their normalization atq 2 = 0 in terms of a single constant g+ (0) which is extracted from the decays B → K1 (1270, 1400)γ. These form factors are then used to analyze the physical observables such as the branching ratio and the forward-backward asymmetry in the SM. This analysis is then extended to the UED model where the dependency of the above mentioned physical observables on the compactification radius R, the only unknown parameter in the UED model. It is shown that the zero position of the forward-backward asymmetry for the decay B → K1 (1270, 1400)μ+ μ− is sensitive to the UED model, therefore the zero position of the forward-backward asymmetry can serve as a handy tool to establish new physics predicted by the UED model. ∗ • The semileptonic Bc → Ds l+ l− (l = μ, τ ) decays have been studied in the Standard Model (SM) and in the Universal Extra Dimension (UED) model. In addition to the contribution from the Flavor Changing Neutral Current (FCNC) transitions the weak annihilation (WA) contribution is also important for this decay. It is found that the WA gives 6.7 times larger branching ratio ∗ than the penguin contribution for the decay Bc → Ds μ+ μ− . The contribution from the WA and FCNC transitions are parameterized in terms of the form factors. In this work we first relate the form factors through Ward identities and then express them in terms of g+ (0) which is extracted ∗ from the decay Bc → Ds γ through QCD sum rules approach. These form factors are then used to analyze the physical observables like branching ratio and helicity fractions of the final state ∗ Ds meson in the SM. This analysis is then extended to the UED model where the dependency of above mentioned physical observables depend on the compactification radius R. It is shown that ∗ the helicity fractions of Ds are sensitive to the UED model especially when we have muons as the final state lepton. This sensitivity is marked up at low q 2 region, irrespective of the choice of the form factors. It is hoped that in the next couple of years LHC will provide enough data on the ∗ Bc → Ds l+ l− channel, and then , these helicity fractions would serve as a useful tool to establish new physics predicted by the UED model.