Properties of $$\boldsymbol{B}_{\boldsymbol{c}}$$ Mesons and Variational Constraints on Their Masses
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ELEMENTARY PARTICLES AND FIELDS Theory
Properties of B c Mesons and Variational Constraints on Their Masses Nosheen Akbar∗ Department of Physics, COMSATS University Islamabad, Lahore Campus, Defence Road, Lahore 54000, Pakistan Received November 11, 2019; revised December 25, 2019; accepted December 25, 2019
Abstract—Spectrum, radii, radial wave functions at origin, decay constants, and momentum widths for radial and orbital excited Bc mesons are derived within non-relativistic quark model framework through ¨ finding numerical solution of the Schrodinger equation by shooting method. Masses of orbitally excited states are derived with a much simpler method that is developed by combining the uncertainty and variational principles. Masses of Bc mesons are also calculated by using Momentum widths. Besides calculations, theoretical results are compared with the experimental observations which have implications for scalar form factors and leptonic decays of Bc mesons. DOI: 10.1134/S1063778820040031
¨ this paper, Schrodinger equation with non-relativistic potential model is solved numerically for Bc meson Bc meson, with beauty (b) and charm (c) quarks, using Born Openheimer formalism and adiabatic apis the most important meson for understanding of proximation for ground, radially and orbitally excited Quantum Chromodynamics (QCD) due to its differ- states of Bc meson. This numerical solution is used ent flavored heavy quark–antiquark pair. Its mass lies to find mass, radial wave function at origin, decay in between charmonium and bottomonium mesons. constants of pseudoscalar and vector meson, rrms and The ground state of Bc meson is discovered in 1998 at momentum width. Fermilab in Collider Detector [1] with mass 6.2749 ± In [25], variational principle is combined with un0.0008 GeV. After decades of Bc (1S) discovery, certainty principle to derive the constraints to the ATLAS Collaboration observed a mass of 6.842 ± mass of cc meson with same flavor of quark and anti0.009 GeV for excited state of Bc meson [2], but this quark. In this paper, work is extended for B mesons c result is not confirmed by LHCb Collaboration [3]. with different flavor of quark and antiquark. Recently, CMS Collaboration [4] observed two peaks Potential model used for conventional mesons is for the excited states of Bc meson, Bc+ (21 S0 ) and discussed in the Section 2 of this paper which was Bc+∗ (23 S1 ). The mass of Bc+ (2S) is measured to further used to calculate radial wave functions for be 6.871 ± 0.0012 ± 0.0008 ± 0.0080 GeV [4]. A the ground and radially excited state Bc mesons by mass difference of 0.0291 ± 0.0015 ± 0.0007 GeV is solving the Schrodinger ¨ equation numerically. The measured between two states [4]. However exact expressions used to find masses, radial wave function mass of Bc+∗ (2S) is unknown. The reason of the at origin, decay constant, root mean square radii and difference between ATLAS and CMS measurements momentum width of Bc mesons are also written in could be that the peak observed by ATLAS was the Section 2. In Section 3, a m
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