Axial Vector Meson Emitting Decays of Bc Dated: 12 JUNE, 2012

VARIOUS QUARK LEVEL PROCESSES THAT CONTIBUTE TO THE NONLEPTONIC DECAYS These Processes are Classified as:

FACTORIZATION SCHEME Factorization is the assumption that the two-body hadronic decays of B mesons can be expressed as the product of two independent hadronic currents. The decay amplitude is given by Three classes of the decays: 1. Class I transition (caused by color favored), 2. Class II transition (caused by color suppressed) and 3. Class III transition (caused by both color favored and color suppressed diagrams).

WEAK HAMILTONIAN WEAK HAMILTONIAN Selection rules

CKM favored decays 1. involving b  c transition 2. involving b  u transition

CKM suppressed decays 1. involving b  c transition 2. involving b  u transition where,

There have been many theoretical efforts to study the bottom meson emitting decays involving s-wave mesons ( B  PP/PV/VV ) i.e. pseudoscalar ( P ) and vector ( V ) mesons using the factorization scheme. However, B mesons being heavy, can also emit p- wave mesons i.e. axial-vector ( A ), tensor ( T ) and scalar ( S ) mesons, which we have studied in the next chapters.

AXIAL-VECTOR MESON SPECTROSCOPY AXIAL-VECTOR MESON SPECTROSCOPY Experimentally, two types of the axial-vector mesons exist i.e. and For Isovector : Isoscalars: where

For Isovector : Isoscalars: where with

MIXING IN STARNGE AND CHARM AXIAL-VECTOR MESONS MIXING IN STARNGE AND CHARM AXIAL-VECTOR MESONS Strange and charm mesons are the mixing of and Mixing of Strange states Mixing of Charmed states Mixing of strange-Charmed states with

DECAY AMPLITUDES AND RATES where The factorization Scheme expresses the decay amplitudes as a product of matrix element of the weak currents The matrix element of current between mesons states are expressed as

Finally the decay amplitude becomes where

ISGW II MODEL

CALCULATION OF THE FORM FACTORS IN ISGW II MODEL CALCULATION OF THE FORM FACTORS IN ISGW II MODEL For transition form factors have the following expressions

where The value of parameter for s-wave and p-wave are and

DECAY CONSTANTS (in GeV) OF THE AXIAL-VECTOR MESONS

COMPARISION WITH THE EXPERIMENTAL DATA

HADRONIC WEAK DECAYS OF Bc MESON: NAKED BOTTOM-CHARM STATE TO A PSEUDOSCALAR AND A P-WAVE MESONS

UNIQUELY OBSERVED BOTTOM CHARM ( Bc ) MESON

In this chapter, we studied the weak hadronic decays of Bc meson emitting pseudoscalar and one p-wave meson in the final state.

Bc MESON EMITTING DECAYS OF PSEUDOSCALAR AND AXIAL-VECTOR MESONS Bc MESON EMITTING DECAYS OF PSEUDOSCALAR AND AXIAL-VECTOR MESONS BOTTOM MESON SPECTROSCOPY

WEAK HAMILTONIAN

CALCULATION OF THE FORM FACTORS IN ISGW II MODEL

So far, theoretical focus has also been on the s -wave mesons i.e., pseudoscalar and vector mesons emitting decays. However, the bottom mesons and uniquely observed bottom-charm mesons, being heavy, can also emit p -wave mesons i.e., axial-vector, tensor and scalar mesons. The hadronic weak currents are expressed in the terms of the form factors which are usually calculated from the phenomenological models, we have employed BSW model to calculate the B  P form factors which match well with the experimental information.

We have also studied the hadronic weak decays of uniquely observed bottom-charm (Bc) meson made up of both heavy quarks For the Bc  A transition form factors appearing in the decay matrix elements, we employ ISGW II model because it provide the more reliable form factors. We obtained the decay amplitude and consequently predicted the branching ratios for Bc  PA decays. In case of Bc meson, one naively expects the bottom conserving modes (c -> u, s transitions) to be kinematically suppressed in comparison to the bottom changing ones. However, the large CKM angle involved in the charm changing modes overcomes the kinematics suppression.Consequently, bottom changing decays get suppressed in comparison to bottom conserving decays. Measurements of their branching ratios provide a useful test of our model.

We look to extend the present approach to calculate Bc  VA decays. Here also, we look forward to calculate to use the ISGW II model form factors to calculate Bc  V transition form factors. It may be pointed out that so for these transition formfactors have not been used by any one.

The matrix element for various Bc  A and Bc  V transition are given by

Since, final states of Bc  VA carry spin degrees of freedom, the decay amplitudes in terms of helicities, like those in the Bc  VV decays, can be generally described by Because, Bc is a pseudoscalar, the two outgoing vector mesons A and V have to carry the same helicity. Consequently, the amplitudes with different helicities can be decomposed as where p is the magnitude of vector momenta of vector mesons.

In addition, we can also write the amplitudes in terms of polarizations as Accordingly, the polarization fractions can be defined to be representing longitudinal, transverse parallel and transverse perpendicular components, respectively. In sum, the decay rate expressed by polarization amplitudes is given by

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