The BESIII Collaboration has observed a candidate for a $c bar c s bar u$ tetraquark $Z_{cs}$ at $(3982.5^{+1.8}_{-2.6} pm 2.1)$ MeV and width $(12.8^{+5.3}_{-4.4} pm 3.0)$ MeV, while the LHCb Collaboration has observed a $Z_{cs}$ candidate in the $j
psi K^-$ channel with mass of $(4003 pm 6 ^{+4}_{-14})$ MeV and width $(131 pm 15 pm 26)$ MeV. In this note we examine the possibility that these two states are distinct eigenstates of a mixing process similar to that which gives rise to two axial-vector mesons labeled by the Particle Data Group $K_1(1270)$ and $K_1(1400)$. The main point is that on top of a $bar c c$ pair, the $Z_{cs}$ states have the same light quark content as the $K_1$-s. In the compact tetraquark picture this implies several additional states, analogous to members of the $K_1$ nonet. These states have not yet been observed, nor are they required in the molecular approach. Thus experimental discovery or exclusion of these extra states will be a critical test for competing models of exotic mesons with hidden charm.
Structure in the di-$J/psi$ mass spectrum observed by the LHCb experiment around 6.9 and 7.2 GeV is interpreted in terms of $J^{PC}=0^{++}$ and $2^{++}$ resonances between a $cc$ diquark and a $bar c bar c$ antidiquark, using a recently confirmed str
ing-junction picture to calculate tetraquark masses. The main peak around 6.9 GeV is likely dominated by the $0^{++}(2S)$ state, a radial excitation of the $cc$-$bar c bar c$ tetraquark, which we predict at $6.871pm 0.025$ GeV. The dip around 6.75 GeV is ascribed to the opening of the Swave di-$chi_{c0}$ channel, while the dip around 7.2 GeV could be correlated with the opening of the di-$eta_c(2S)$ or $Xi_{cc} bar Xi_{cc}$ channel. The low-mass part of the di-$J/psi$ structure appears to require a broad resonance consistent with a predicted $2^{++}(1S)$ state with invariant mass around $M_{rm inv} = 6400$ MeV. Implications for $bb bar b bar b$ tetraquarks are discussed.
The LHCb Collaboration has reported resonant activity in the channel $D^+ K^-$, identifying two components: $X_0(2900)$ with $J^P = 0^+$ at $2866 {pm} 7$ MeV, $Gamma_0=57{pm} 13$ MeV and $X_1(2900)$ with $J^P = 1^-$ at $2904 {pm} 7$ MeV, $Gamma_1=110
{pm} 12$ MeV. We interpret the $X_0(2900)$ component as a $cs bar ubar d$ isosinglet compact tetraquark, calculating its mass to be $2863 {pm} 12$ MeV. This is the first exotic hadron with open heavy flavor. The analogous $bsbar ubar d$ tetraquark is predicted at $6213 {pm} 12$ MeV. We discuss possible interpretations of the heavier and wider $X_1(2900)$ state and examine potential implications for other systems with two heavy quarks.
Recently LHCb reported the discovery of four extremely narrow excited $Omega_b$ baryons decaying into $Xi_b^0 K^-$. We interpret these baryons as bound states of a $b$-quark and a $P$-wave $ss$-diquark. For such a system there are exactly five possib
le combinations of spin and orbital angular momentum. We predict two of spin 1/2, two of spin 3/2, and one of spin 5/2, all with negative parity. We favor identifying the observed states as those those with spins 1/2 and 3/2, and give a range of predicted masses for the one with spin 5/2. We update earlier predictions for these states based on the five narrow excited $Omega_c$ states reported by LHCb. An alternative picture of the states in which one of $J=1/2$ is extremely wide and hence not seen by LHCb is discussed.
The relation between motion in $-1/r$ and $r^{2}$ potentials, known since Newton, can be demonstrated by the substitution $rrightarrow r^{2}$ in the classical/quantum radial equations of the Kepler/Hydrogen problems versus the harmonic oscillator. Th
is suggests a duality-type relationship between these systems. However, when both radial and angular components of these systems are included the possibility of a true duality seems to be remote. Indeed, investigations that explored and generalized Newtons radial relation, including algebraic approaches based on noncompact groups such as SO(4,2), have never exhibited a full duality consistent with Newtons. On the other hand, 2T-physics predicts a host of dualities between pairs of a huge set of systems that includes Newtons two systems. These dualities take the form of rather complicated canonical transformations that relate the full phase spaces of these respective systems in all directions. In this paper we focus on Newtons case by imposing his radial relation to find an appropriate basis for 2T-physics dualities, and then construct the full duality. Using the techniques of 2T-physics, we discuss the hidden symmetry of the actions (beyond the symmetry of Hamiltonians) for the Hydrogen atom in $D$-dimensions and the harmonic oscillator in $bar{D}$ dimensions. The symmetries lead us to find the one-to-one relation between the quantum states, including angular degrees of freedom, for specific values of $left( D,bar{D}right) $, and construct the explicit quantum canonical transformation in those special cases. We find that the canonical transformation has itself a hidden gauge symmetry that is crucial for the respective phase spaces to be dual even when $D eqbar{D}$. In this way we display the surprising beautiful symmetry of the full duality that generalizes Newtons radial duality.
Baryons with one or more heavy quarks have been shown, in the context of a nonrelativistic description, to exhibit mass inequalities under permutations of their quarks, when spin averages are taken. These inequalities sometimes are invalidated when s
pin-dependent forces are taken into account. A notable instance is the inequality $2E(Mmm) > E(MMm) + E(mmm)$, where $m = m_u = m_d$, satisfied for $M = m_b$ or $M = m_c$ but not for $M = m_s$, unless care is taken to remove effects of spin-spin interactions. Thus in the quark-level analog of nuclear fusion, the reactions $Lambda_b Lambda_b to Xi_{bb}N$ and $Lambda_c Lambda_c to Xi_{cc}^{++}n$ are exothermic, releasing respectively 138 and 12 MeV, while $Lambda Lambda to Xi N$ is endothermic, requiring an input of between 23 and 29 MeV. Here we explore such mass inequalities in the context of an approach, previously shown to predict masses successfully, in which contributions consist of additive constituent-quark masses, spin-spin interactions, and additional binding terms for pairs each member of which is at least as heavy as a strange quark.
An earlier analysis of observed and anticipated $Lambda_c$ decays [M. Gronau and J. L. Rosner, Phys. Rev. D {bf 97}, 116015 (2018)] is provided with a table of inputs and a figure denoting branching fractions. This addendum is based on the 2018 Parti
cle Data Group compilation and employs a statistical isospin model to estimate branching fractions for as-yet-unseen decay modes.
The decays of the ground-state charmed baryon $Lambda_c$ are now close to being completely mapped out. In this paper we discuss some remaining open questions, whose answers can help shed light on weak processes contributing to those decays, on calcul
ations of such quantities as transition form factors in lattice QCD, and on missing decay modes such as $Lambda_c to Lambda^* ell^+ u_ell$, where $Lambda^*$ is an excited resonance. The discussion is in part a counterpart to a previous analysis of inclusive $D_s$ decays.
Why do we see certain types of strongly interacting elementary particles and not others? This question was posed over 50 years ago in the context of the quark model. M. Gell-Mann and G. Zweig proposed that the known mesons were $q bar q$ and baryons
$qqq$, with quarks known at the time $u$ (up), $d$ (down), and $s$ (strange) having charges (2/3,-1/3,-1/3). Mesons and baryons would then have integral charges. Mesons such as $qq bar q bar q$ and baryons such as $qqqq bar q$ would also have integral charges. Why werent they seen? They have now been seen, but only with additional heavy quarks and under conditions which tell us a lot about the strong interactions and how they manifest themselves. The present article describes recent progress in our understanding of such exotic mesons and baryons.
It has been pointed out that the currently most precise determination of the weak phase $phi_2 = alpha$ of the Cabibbo-Kobayashi-Maskawa (CKM) matrix achieved in $B to rhorho$ decays is susceptible to a small correction at a level of $(Gamma_rho/m_rh
o)^2$ due to an $I=1$ amplitude caused by the $rho$ width. Using Breit-Wigner distributions for the two pairs of pions forming $rho$ mesons, we study the $I=1$ contribution to $Bto rhorho$ decay rates as function of the width and location of the $rho$ band. We find that in the absence of a particular enhancement of the $I=1$ amplitude reducing a single band to a width $Gamma_rho$ at SuperKEKB leads to results which are completely insensitive to the $rho$ width. If the $I=1$ amplitude is dynamically enhanced relative to the $I=0,2$ amplitude one could subject its contribution to a magnifying glass measurement using two separated $rho$ bands of width $Gamma_rho$. Subtraction of the $I=1$ contribution from the measured decay rate would lead to a very precise determination of the $I=0,2$ amplitude needed for performing the isospin analysis.
