Abstract
Using the Regge-like formula (M-m_Q)^2=pi sigma L between hadron mass M and angular momentum L with a heavy quark mass m_Q and a string tension sigma , we analyze all the heavy–light systems, i.e., D/D_s/B/B_s mesons and charmed and bottom baryons. Numerical plots are obtained for all the heavy–light mesons of experimental data whose slope becomes nearly equal to 1/2 of that for light hadrons. Assuming that charmed and bottom baryons consist of one heavy quark and one light cluster of two light quarks (diquark), we apply the formula to all the heavy–light baryons including the recently discovered Omega _c and find that these baryons experimentally measured satisfy the above formula. We predict the average mass values of B, B_s, Lambda _b, Sigma _c, Xi _c, and Omega _c with L=2 to be 6.01, 6.13, 6.15, 3.05, 3.07, and 3.34 GeV, respectively. Our results on baryons suggest that these baryons can be safely regarded as heavy quark–light cluster configuration. We also find a universal description for all the heavy–light mesons as well as baryons, i.e., one unique line is enough to describe both of charmed and bottom heavy–light systems. Our results suggest that instead of mass itself, gluon flux energy is essential to obtain a linear trajectory. Our method gives a straight line for B_c although the curved parent Regge trajectory was suggested before.
Highlights
Nature has chosen the quantum number 2S+1 L J to classify light and heavy hadrons including light u/d/s and heavy c/b quarks, respectively. This is true for light hadrons which can be treated nonrelativistically but this holds for heavy– light mesons, as analytically derived in Ref. [1] using our semi-relativistic potential model [2,3]
According to Eq (7), we plot the figures for heavy–light mesons, D/B/Ds/Bs, as well as charmed and bottom baryons, Q/ Q/ Q/ Q/ Q with Q = c, b, for the experimental data listed in PDG [16] and some theoretical models Refs. [17,18,19,20,21]
U, d, and s, form the so-called chiral particles, e.g., π, K, etc. These quarks have the current quark masses, i.e., very tiny masses. When these quarks are dressed with gluon clouds, they become constituent quarks
Summary
Nature has chosen the quantum number 2S+1 L J to classify light and heavy hadrons including light u/d/s and heavy c/b quarks, respectively This is true for light hadrons which can be treated nonrelativistically but this holds for heavy– light mesons, as analytically derived in Ref. We have observed that mass differences within a heavy quark spin doublet and between doublets with the same L are very small compared with a mass gap between different multiplets with different L, which is nearly equal to the value of QCD ∼ 300 MeV This fact is analytically explained by our semi-relativistic potential model [2] which is proposed to describe heavy– light mesons, spectra and wave functions. In Refs. [7,8], the authors noticed that suppression of L S coupling should occur
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