Beautiful mathematics for beauty-full and other multi-heavy hadronic systems

Abstract

In most non-perturbative methods in hadron physics the calculations are started with a correlation function in terms of some interpolating and transition currents in $x$-space. For simplicity, the calculations are then transformed to the momentum space by a Fourier transformation. To suppress the contributions of the higher states and continuum; and enhance the ground state contribution, Borel transformation as well as continuum subtraction are applied by the help of quark-hadron duality assumption. In the present study we work out the mathematics required for these processes in the case of light and multi-heavy hadrons. We address a well-known problem in subtraction of the effects of the higher states and continuum and discuss how we find finite results without any divergence by using an appropriate representation of the modified Bessel functions, appearing in the heavy quark propagator, and successive applications of the Borel transformations, which lead to more suppression of the higher states and continuum contributions. The results obtained can be used in determination of the spectroscopic and decay properties of the multi-heavy standard and non-conventional (exotic) systems in many non-perturbative methods, specially the QCD sum rules.

31 Pages

References in corpus (16)

• Observation of the doubly charmed baryon ${\Xi }_{cc}^{++}$
• Heavy Baryons in a Quark Model
• Spectroscopy and Regge trajectories of heavy baryons in the relativistic quark-diquark picture
• Towards an understanding of heavy baryon spectroscopy
• Weak Decays of Doubly Heavy Baryons: Multi-body Decay Channels
• Interpretation of the new ${\Omega }_c^0$ states via their mass and width
• Properties of triply heavy spin--3/2 baryons
• Strong coupling constants of light pseudoscalar mesons with heavy baryons in QCD
• Magnetic and quadrupole moments of the $Z_c(3900)$
• Strong Decay of $P_c(4380)$ Pentaquark in a Molecular Picture
• Vector meson-baryon strong coupling contants in light cone QCD sum rules
• The structure, mixing angle, mass and couplings of the light scalar $f_0(500)$ and $f_0(980)$ mesons
• Properties of ${\Sigma }_Q^{\ast }$, ${\Xi }_Q^{\ast }$ and ${\Omega }_Q^{\ast }$ heavy baryons in cold nuclear matter
• Analysis of the structure of $\Xi (1690)$ through its decays
• Spectroscopy and decays of the fully-heavy tetraquarks
• Strong Coupling Constants of Decuplet Baryons with Vector Mesons

Cited by in corpus (14)

• Magnetic dipole moments of the $T_{cc}^{+}$ and $Z_V^{++}$ tetraquark states
• Magnetic moments of doubly heavy baryons in light-cone QCD
• Magnetic dipole moment of the $Z_{cs}(3985)$ state: diquark-antidiquark and molecular pictures
• The newly observed $Z_{cs}(3985{)}^{-}$ state: in vacuum and a dense medium
• Magnetic moments of the doubly charged axial-vector $T_{cc}^{++}$ states
• Magnetic dipole moments of the spin-$\frac{3}{2}$ doubly heavy baryons
• Strong Coupling Constants of the Doubly Heavy ${\Xi }_{QQ}$ Baryons with $\pi$ Meson
• Magnetic moment of the $X_1(2900)$ state in the diquark-antidiquark picture
• Strong interaction of doubly heavy spin-3/2 baryons with light vector mesons
• Newly discovered ${\Xi }_c^0$ resonances and their parameters
• Strong vertices of doubly heavy spin-3/2--spin-1/2 baryons with light mesons in light-cone QCD sum rules
• Magnetic moments of the vector hidden-charmed tetraquark states
• Strong Coupling Constants of the Doubly Heavy Spin-1/2 Baryons with Light Pseudoscalar Mesons
• Strong Vertices of Doubly Heavy Spin-3/2 Baryons with Light Pseudoscalar Mesons