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Bc Absorption Cross Sections by Pion in Meson-Exchange Model

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Bc Absorption Cross Sections by Pion in Meson-Exchange Model Hadronic Cross Sections of Bc Mesons A thesis submitted for the fulfillment of Ph.D degree in Physics By Faisal Akram Physics Department University of the Punjab Lahore, Pakistan (2013) i Declaration The results of the cross sections of Bc meson by pions discussed in the chapter 4 of the thesis have appeared in M.Phil thesis of F. Akram and the paper Faisal Akram, Shaheen Irfan, and M.A.K. Lodhi, Hadronic absorption cross sections of Bc, Phys. Rev. C 84, 034901 (2011). The results of the cross sections of Bc meson by rho meson presented in the chapter 4 of the thesis have appeared in the paper Faisal Akram, M.A.K Lodhi, Bc absorption cross sections of rho mesons, Phys. Rev. C 84, 064912 (2011). The results on K mesons are to be published in the paper Faisal Akram, Bc absorption cross sections of K mesons. The results on the cross sections of Bc meson by nucleons presented in the chapter 5 of the thesis have appeared in the paper Faisal Akram, M.A.K Lodhi, Bc absorption cross sections of nucleons, Nucl. Phys. A 877, 95 (2012). The copyrights of the thesis rest with the author. Faisal Akram ii List of Papers Attached: Faisal Akram, M.A.K Lodhi, Bc absorption cross sections of rho mesons, Phys. Rev. C 84, 064912 (2011). Faisal Akram, M.A.K Lodhi, Bc absorption cross sections of nucleons, Nucl. Phys. A 877, 95 (2012). Faisal Akram, et. al., Dynamical Chiral Symmetry Breaking: Phase diagrams of unquenched QED with 4-fermion contact interaction, Phys. Phys. Rev. D 87, 013011 (2013). iii Certificate It is certified that Faisal Akram s/o Muhammad Akram carried out the work contained in this thesis at Physics Department, Punjab University Lahore under my supervision. _______________________________ (Dr. Shaukat Ali) Professor, Physics Department, Punjab University, Lahore. _______________________________ (Dr. Mujahid Kamran) Vice Chancellor, Punjab University, Lahore. Submitted through: _______________________________ Chairperson, DPCC, Punjab University, Lahore. iv Acknowledgements I would like to thank my supervisors Dr. Shaukat Ali and Dr. Mujahid Kamran for their support and my collaborator Dr. M.A.K Lodhi for his valuable contribution in the work. I would also like to thank my wife Nargis for her years of patience and never complaining about anything. Thank you Nargis! v Abstract In this work we calculate Bc absorption cross sections by light mesons and baryons; π, ρ , and K mesons and nucleons. The processes studied are important from the view of relativistic heavy-ion experiments. The formalism used for the calculations is based on an effective hadronic Lagrangian developed by imposing SU(5) symmetry. This approach is similar to other papers in the literature in which absorption cross sections of J= and Υ mesons are calculated using the hadronic Lagrangian based on SU(4)/SU(5) symmetry. The motivation for these calculations comes from the studies of the production of heavy mixed flavor mesons and baryons in quark gluon plasma. It is expected that Bc production could be enhanced in heavy-ion experiments due to formation of QGP. However, it is also expected that the Bc production rate in heavy-ion collisions will be affected by its interaction with comoving hadrons. Thus we require the knowledge of the cross sections of Bc absorption processes to interpret the observed rates in the experiments. We find that calculated values of cross sections highly depend upon the choice of form factors, related cutoff parameters, and coupling constants. The effect of uncertainties in these parameters on the cross sections is also studied. These results could be useful in calculating the production rate of Bc meson in relativistic heavy-ion collisions. Contents 1 Introduction 12 2 The Hadronic Lagrangian 17 2.1 Irreducible tensors . 17 2.2 The Effective Lagrangian . 20 2.2.1 Meson-Meson Interaction . 20 2.2.2 Baryon-Meson Interaction . 24 2.2.3 Anomalous parity interaction . 27 2.3 Vertex factors of interactions . 27 3 Bc Absorption Processes: Born Diagrams and Amplitudes 39 3.1 Bc absorption processes . 39 3.2 Amplitudes of Bc absorpriton by pions: . 41 3.3 Amplitudes of Bc absorpriton by rho mesons: . 43 3.4 Amplitudes of Bc absorpriton by K mesons . 45 3.5 Amplitudes of Bc absorption by nucleons . 48 3.6 Effect of anomalous parity interaction . 50 3.7 Couplings and Form Factors . 52 3.8 Vector-Meson dominance model . 54 4 Bc Absorption Cross Sections by π, ρ, and K Mesons 58 4.1 Spin and Isospin averaged cross sections . 58 4.2 Cross sections of Bc by π .......................... 59 + ! 4.2.1 Bc π DB ............................. 59 1 + ! ∗ ∗ 4.2.2 Bc π D B ............................ 60 4.3 Cross sections of Bc by ρ .......................... 60 + ! ∗ 4.3.1 Bc ρ D B ............................. 60 + ! ∗ 4.3.2 Bc ρ DB ............................. 61 4.4 Cross sections of Bc by K ......................... 61 + ! + 4.4.1 KBc Ds B ............................ 61 + ! ∗+ ∗ 4.4.2 KBc Ds B ........................... 62 + ! 0 4.4.3 KBc DBs ............................ 62 + ! ∗ ∗0 4.4.4 KBc D Bs ........................... 63 4.5 Numerical values of the couplings and other input parameters . 64 4.6 Results of Bc absorption cross sections by π ............... 65 4.6.1 Results without form factors . 65 4.6.2 Form Factors . 67 4.6.3 Amplitudes of Bc absorption by pions with form factor . 69 4.6.4 Results with form factor . 70 4.7 Results of Bc absorption cross sections by ρ ............... 72 4.7.1 Results without form factors . 72 4.7.2 Amplitudes of Bc absorption by ρ with form factor . 74 4.7.3 Results of Bc absorption by ρ with form factor . 76 4.8 Results of Bc absorption cross sections by K ............... 79 4.8.1 Results without form factors . 79 4.8.2 Amplitudes of Bc absorption by K with form factor . 81 4.8.3 Results of Bc absorption by K with form factor . 85 5 Bc Absorption Cross Sections by Nucleons. 101 5.1 Cross sections of Bc by N ......................... 101 + ! 5.1.1 NBc ΛcB ............................ 101 + ! ∗ 5.1.2 NBc ΛcB ............................ 102 − ! 5.1.3 NBc DΛb ............................ 102 − ! ∗ 5.1.4 NBc D Λb ............................ 102 2 5.2 Numerical values of input parameters . 103 5.3 Results and Discussion . 104 5.4 Effect of anomalous parity interaction . 107 6 Discussion 117 Appendix A Feynman Rules for Vertex 121 Appendix B Kinematics 123 3 List of Figures 2.1 Vertex factors of the coupling given in Eqs. 2.21a and 2.21b. 28 2.2 Vertex factors of the couplings given in Eqs. 2.21c, 2.21d, and 2.21e. 29 2.3 Vertex factors of the couplings given in Eqs. 2.22a, 2.22b, 2.22c, and 2.22d 30 2.4 Vertex factors of the couplings given in Eqs. 2.22e and 2.22f. 31 2.5 Vertex factors of the couplings given in Eqs. 2.23a and 2.23b. 32 2.6 Vertex factors of the couplings given in Eqs. 2.23c and 2.23d. 33 2.7 Vertex factors of the couplings given in Eqs. 2.23e and 2.23f. 34 2.8 Vertex factors of the couplings given in Eqs. 2.23g and 2.23h. 35 2.9 Vertex factors of the couplings given in Eqs. 2.33a and 2.33b. 36 2.10 Vertex factors of the couplings given in Eqs. 2.33c, 2.33d, and 2.33e. 37 2.11 Vertex factors of the couplings given in Eqs. 2.36 . 38 + ! 3.1 Born diagrams of Bc absorption process Bc π DB .......... 42 + ! ∗ ∗ 3.2 Born diagrams of Bc absorption process Bc π D B ......... 43 + ! ∗ 3.3 Born Diagrams of Bc absorption process Bc ρ D B .......... 44 + ! ∗ 3.4 Born Diagrams for Bc absorption process Bc ρ DB ......... 44 + ! + 3.5 Born Diagrams for Bc absorption process KBc Ds B ........ 45 + ! ∗+ ∗ 3.6 Born Diagrams for Bc absorption process KBc Ds B ........ 46 + ! 0 3.7 Born Diagrams for Bc absorption process KBc DBs ......... 47 + ! ∗ ∗0 3.8 Born Diagrams for Bc absorption process KBc D Bs ........ 48 + ! 3.9 Born Diagrams for Bc absorption process NBc ΛcB ......... 49 + ! ∗ 3.10 Born Diagrams for Bc absorption process NBc ΛcB ......... 50 − ! 3.11 Born Diagrams for Bc absorption process NBc DΛb ......... 51 4 − ! ∗ 3.12 Born Diagrams for Bc absorption process NBc D Λb ........ 52 + ! ∗ 3.13 Additional diagrams for Bc absorption processes: (2) NBc ΛcB and − ! ∗ (4) NBc D Λb; due to anomalous parity interaction. 53 3.14 Vector Meson Dominance (VMD) model. 54 + ! 4.1 Bc absorption cross sections for the process Bc π DB without form factor . 67 + ! ∗ ∗ 4.2 Bc absorption cross sections of the process Bc π D B without form ∗ ∗ factor for three different values four-point coupling gπBcB D = 105; 200; 295 for dotted, solid and dashed curves respectively. 68 + ! 4.3 Bc absorption cross sections of the process Bc π DB with form fac- tors. Lower and upper curves are with cutoff parameter Λ = 1 and 2 GeV respectively. 71 + ! 4.4 Comparison of the cross sections of the process Bc π DB with and without form factor. Solid and dashed curves represents cross sections without and with form factor respectively. Lower and upper dashed curves are with cutoff parameter Λ = 1 and 2 GeV respectively. 72 + ! ∗ ∗ 4.5 Bc absorption cross sections for the process Bc π D B with form factors. Lower and upper curves are with cutoff parameter Λ = 1 and 2 GeV respectively. 73 + ! ∗ ∗ 4.6 Comparison of the cross sections of the process Bc π D B with and without form factor.
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