1. Properties and Decays of Heavy Flavor S-Wave Hadrons Rohit Dhir Department of Physics, Yonsei University, Seoul 120-749. Dated:11 th June, 2012

2. Matter & Forces Matter Leptons Charged Neutrinos Forces Weak EM Strong Gravity Hadrons Baryons Mesons Quarks Anti-Quarks Quarks Anti-Quarks

3. The Standard Model  Quarks and leptons are the most fundamental particles of nature that we know about.  Up & down quarks and electrons are the constituents of ordinary matter.  The other quarks and leptons can be produced in cosmic ray showers or in high energy particle accelerators.  Each particle has a corresponding antiparticle.

4. Quantum Numbers of quarks Light quarks (u, d, s) Heavy quarks (c, b, t)

5. Quark Interactions

6. Mesons  Mesons are also in the hadron family.  They are formed when a quark and an anti-quark “bind” together. (We’ll talk more later about what we mean by “bind”). u d What’s the charge of this particle? c d Q=+1, and it’s called a  + Q= -1, and this charm meson is called a D - s d What’s the charge of this particle? Q= 0, this strange meson is called a K 0 M~140 [MeV/c 2 ] Lifetime~2.6x10 -8 [s] M~1870 [MeV/c 2 ] Lifetime~1x10 -12 [s] M~500 [MeV/c 2 ] Lifetime~0.8x10 -10 [s]

7. HADRONS/BARYONS The forces which hold the protons and neutrons together in the nucleus are VERY strong. They interact via the STRONG FORCE. Protons and neutrons are among a class of particles called “hadrons” (Greek for strong). Hadrons interact very strongly with other hadrons! Baryons are hadrons which contain 3 quarks (no anti-quarks). Anti-baryons are hadrons which contain 3 anti-quarks (no quarks).

8. Pseudoscaler Mesons Vector Mesons Baryons Low lying (s-wave) Hadrons

9. Introduction to Standard Model Leptonic and semileptonic weak interactions of hadrons are explained accurately to a great precision by Standard Model. However, there exist serious problems in understanding the hadronic weak decays, as the theory deals with leptons and quarks, whereas the experiments are performed at hadronic level. Theoretical description of the exclusive weak hadronic decays based on Standard Model is not yet obtained as these experiences strong interaction interference. Weak currents in the Standard Model generate leptonic, semileptonic and hadronic decays of the heavy flavor hadrons. Since the quarks are confined inside the colorless hadrons, matching between theory and experiment requires an exact knowledge of the low energy strong interactions. The weak decays of heavy quark hadrons provide a unique opportunity to learn more about QCD particularly on the interface between the perturbative and nonperturbative regimes, to determine SM parameters and finally to search for the physics lying beyond the model.

10. In this section, we present the meson spectroscopy and masses of all the mesons, including charm and bottom mesons. Normally, in theoretical predictions, spatial part of the hadronic wavefunction is kept same for all the particles but experimental data require it to be flavour dependent. We study the impact of this variation on the weak semileptonic decays of heavy flavor meson Bc, recently observed unique state made up of two heavy quarks (bottom and charm).

11. Weak decays: Leptonic Decays: e. g. Semileptonic Decays: e. g. Nonleptonic Decays: e. g.

19. Mass Relations and Hyperfine Interaction

22. Semileptonic Weak Decays of Meson B c  P+l+ l B c  V+l+ l. Bottom Changing (  b = 1,  C = 1,  S = 0;  b = 1,  C = 0,  S = -1) B c  D + e+ e, B c  D* +  +  Charm Changing ( (  b = 0,  C = -1,  S = -1 ) B c  B + e+ e, B c  B* +  + 

23. Introduction

24. In the present work, we investigate the effects of flavor dependence of on Bc transition form factors, caused by the variation of average transverse quark momentum  and consequently on decays of Bc meson. Employing BSW frame work we have predicted the branching ratios of semileptonic and nonleptonic decays of Bc mesons. We observe that the branching ratios of all the decays of Bc meson get significantly enhanced due to the flavor dependence effects generated by the variation of meson overlap function.

25. Semileptonic Decays

28. q 2 -dependence

29. BSW Model – An Outline

35. Observations

45. Nonleptonic Weak Decays of B c Meson B c  P 1 P 2 B c  PV B c  V 1 V 2.

46. Weak Hamiltonian

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

54. Observations

68. Rare weak Decays of J/  and  a) Semileptonic Weak Decays. J/   P/V+l+ l and   P/V+l+ l. b) Nonleptonic Weak Decays. J/   P 1 P 2 /PV / V 1 V 2 and   P 1 P 2 /PV / V 1 V 2.

69. Introduction

70. Semileptonic Weak Decays of

82. Semileptonic Weak Decays

92. Nonleptonic Weak Decays

108. Masses and Magnetic Moments of S-Wave Flavor Hadrons

117. Baryon Masses

124. Magnetic moments of heavy baryons in effective quark mass scheme

134. Quark Model

149. Comparison with others

152. Summary

153. The standard model has worked well in explaining leptonic and semileptonic processes, however weak hadronic processes have posed serious problems due to the strong interaction interference. In this thesis, we have investigated the properties and weak decays of heavy flavor hadrons based on the framework of the standard model and have developed a model based on the flavor dependence of as demanded by the experimental meson mass spectra. Presently, almost all the s-wave mesons upto bottom have been observed and their masses are well known. We observe that the present experimental data require to be different for different flavor mesons.

154. Further, we have investigated the effects of flavor dependence of  caused by the observed variation of on the form factors appearing in the meson-meson transitions of Bc, J/  and  mesons made up of heavy flavor (bottom and charm) quarks only. All such form factors get significantly enhanced due to inclusion of the flavor dependent effects, which in turn enhance the branching ratios of all the decay modes of these mesons. 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 kinematic suppression.

155. Further, we find that the form factors involving the bottom changing transitions (b  u, s transitions) are small as compared to those of the bottom conserving transitions, due to the reduced overlap of the initial and the final state wave functions. Consequently, bottom changing decays get suppressed in comparison to bottom conserving decays. Measurements of their branching ratios provide a useful test of our model. In heavy baryon sector, we have extended the effective quark mass scheme, which has worked well in case of the hyperon magnetic moments, to predict the magnetic moments of heavy flavor baryons. We hope these magnetic moments will be measured soon, as some experimental groups are likely to focus on their measurements.

156. THANKYOU FOR YOUR PATIENCE