Resummation of large logarithms in exclusive quarkonium + γ production processes
Resummation of large logarithms in exclusive quarkonium + γ production processes
- 주제(키워드) resummation , large logarithm , Abel summation , Padé approximant , ERBL equation , Higgs , J/psi , exclusive decay , NRQCD , light-cone factorization , light-cone distribution amplidue , LCDA , Abel-Padé method , Gegenbauer polynomial , evolution equation
- 발행기관 고려대학교 대학원
- 지도교수 이정일
- 발행년도 2019
- 학위수여년월 2019. 8
- 유형 Text
- 학위구분 박사
- 학과 대학원 물리학과
- 원문페이지 73 p
- 실제URI http://www.dcollection.net/handler/korea/000000084360
- UCI I804:11009-000000084360
- DOI 10.23186/korea.000000084360.11009.0000940
- 본문언어 영어
- 제출원본 000045999256
초록/요약
We consider the resummation of large logarithms of $Q^2/m_Q^2$ in exclusive quarkonium production processes associated with a photon. Here, $Q^2$ is the large momentum transfer of the process and $m_Q$ is the mass of a heavy quark $Q$. For the resummation of the large logarithms, we adopt light-cone factorization where the amplitude of the exclusive process is given as a convolution of the perturbative hard-scattering part and the light-cone distribution amplitude (LCDA) which is universal and contains non-perturbative contributions. In light-cone factorization, the resummation of large logarithms can be readily achieved in terms of the eigensolutions to Efremov-Radyushkin-Brodsky-Lepage (ERBL) equation. We find that the LCDA for heavy quarkonia can be further factorized using nonrelativistic QCD (NRQCD) which is the effective theory describing heavy quarks ($c$ or $b$ quarks). In NRQCD, the LCDA is written as a linear combination of the products of the NRQCD long-distance matrix elements of energy scale $m_Qv$ or lower, and the corresponding short distance coefficients of energy scale $m_Q$ or higher. Here, $v$ is the relative velocity of quark or antiquark in a quarkonium rest frame. We find that the relativistic corrections to LCDA for heavy quarkonia contains nonconvergent eigenfunction series that has been an obstacle to achieve a desirable numerical accuracy. By applying Abel-Pad\'e method, we reorganize the series in which the convergence is significantly improved and we carry out the resummation through next-to-leading-logarithmic accuracy. Our systematic approach for resumming the nonconvergent eigenfunction series is applied to provide the most accurate predictions for Higgs and $Z$ boson decay widths into $J/\psi+\gamma$ up to the present.
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Contents
Abstract
Contents
List of Figures
List of Tables
1. Introduction
2. Vector meson Light-Cone Distribution Amplitudes
2.1 Definition of LCDA
2.2 LL resummations of LCDA
2.3 NLL resummations of LCDA
2.4 Light-cone approach
2.5 NRQCD refactorization of the LCDA
3. Abel-Padé Method
3.1 The problem of nonconvergence
3.2 Solution of the problem and Padé-approximant method
4. H → V + γ
4.1 Introduction
4.2 Light-cone amplitude for the direct process
4.3 The indirect amplitude
4.4. Numerical inputs
4.5 Sources of uncertainties
4.5.1 Direct amplitude
4.5.2 Indirect amplitude
4.5.3 Method for computing uncertainties in the decay rates
4.6 Results
5. Z → V + γ
5.1 Introduction
5.2 Light-cone amplitude for the direct process
5.3 Amplitude for the indirect process
5.4 Decay rate
5.5 Results
5.5.1 Numerical inputs
5.5.2 Sources of uncertainties
5.5.3 Numerical results
6. Conclusion
A. Gegenbauer polynomials
B. Evolution of the LCDA
Bibliography
Acknowledgement
