arXiv subjects

Richard F. Lebed

Publications and source records attributed to Richard F. Lebed.

At least 37 records · Page 2Linked to original sources

arXiv2020

The Dynamical Diquark Model: Fine Structure and Isospin

We incorporate fine-structure corrections into the dynamical diquark model of multiquark exotic hadrons. These improvements include effects due to finite diquark size, spin-spin couplings within the diquarks, and most significantly, isospin-dependent couplings in the form of pionlike exchanges assumed to occur between the light quarks within the diquarks. Using a simplified two-parameter interaction Hamiltonian, we obtain fits in which the isoscalar $J^{PC} = 1^{++}$ state---identified as the $X(3872)$---appears naturally as the lightest exotic (including all states that are predicted by the model but have not yet been observed), while the $Z_c(3900)$ and $Z_c(4020)$ decay predominantly to $J/ψ$ and $η_c$, respectively, in accord with experiment. We explore implications of this model for the excited tetraquark multiplets and the pentaquarks.

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arXiv2019

Precision Model-Independent Bounds from Global Analysis of $b \to c \ell ν$ Form Factors

We present a model-independent global analysis of hadronic form factors for the semileptonic decays $b\rightarrow c\ellν$ that exploits lattice-QCD data, dispersion relations, and heavy-quark symmetries. The analysis yields predictions for the relevant form factors, within quantifiable bounds. These form factors are used to compute the semileptonic ratios $R(H_c)$ and various decay-product polarizations. In particular, we find $R(D_s^*)=0.20(3)$ and $R(J/ψ)=0.25(3)$, predictions that can be compared to results of upcoming LHCb measurements. In developing this treatment, we obtain leading-order NRQCD results for the nonzero-recoil relations between the $B_c^+ \rightarrow \{J/ψ, η_c \}$ form factors.

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arXiv2019

The Dynamical Diquark Model: First Numerical Results

We produce the first numerical predictions of the dynamical diquark model of multiquark exotic hadrons. Using Born-Oppenheimer potentials calculated numerically on the lattice, we solve coupled and uncoupled systems of Schroedinger equations to obtain mass eigenvalues for multiplets of states that are, at this stage, degenerate in spin and isospin. Assuming reasonable values for these fine-structure splittings, we obtain a series of bands of exotic states with a common parity eigenvalue that agree well with the experimentally observed charmoniumlike states, and we predict a number of other unobserved states. In particular, the most suitable fit to known pentaquark states predicts states below the charmonium-plus-nucleon threshold. Finally, we examine the strictest form of Born-Oppenheimer decay selection rules for exotics and, finding them to fail badly, we propose a resolution by relaxing the constraint that exotics must occur as heavy-quark spin-symmetry eigenstates.

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arXiv2018

Model-Independent Bounds on $R(J/ψ)$

We present a model-independent bound on $R(J/ψ) \! \equiv \! \mathcal{BR} (B_c^+ \rightarrow J/ψ\, τ^+ν_τ)/ \mathcal{BR} (B_c^+ \rightarrow J/ψ\, μ^+ν_μ)$. This bound is constructed by constraining the form factors through a combination of dispersive relations, heavy-quark relations at zero-recoil, and the limited existing determinations from lattice QCD. The resulting 95\% confidence-level bound, $0.20\leq R(J/ψ)\leq0.39$, agrees with the recent LHCb result at $1.3 \, σ$, and rules out some previously suggested model form factors.

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arXiv2018

Tests of the Standard Model in $B \to D\ell ν_\ell$, $B \to D^* \ell ν_\ell$ and $B_c \to J/ψ\, \ell ν_\ell$

A number of recent experimental measurements suggest the possibility of a breakdown of lepton ($\ell$) universality in exclusive $b \to c \ell ν_\ell$ semileptonic meson decays. We analyze the full differential decay rates for several such processes, and show how to extract combinations of the underlying helicity amplitudes that are completely independent of $m_\ell$. Ratios of these combinations for different $\ell$ (as well as some combinations for a single value of $\ell$) therefore equal unity in the Standard Model and provide stringent tests of lepton universality. Furthermore, the extractions assume the form of weighted integrals over the differential decay rates and therefore are useful even in situations where data in some regions of allowed phase space may be sparse.

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arXiv2018

Constituent Counting Rules and Exotic Hadrons

The constituent counting rules, i.e., the scaling behavior of amplitudes (in terms of the number of fundamental constituents) for exclusive processes when high energy scales are present, have been known for decades, and have been borne out in a number of experiments. Such scaling would be sensitive, in particular, to possible exotic multiquark content. Here we examine how one may use the rules to test for pentaquarks in electroproduction, or for tetraquarks in e^+ e^- annihilation. An interesting new type of scaling (separate Mandelstam s and t behavior) arises in the forward scattering direction. The correct scaling arises naturally in AdS/QCD, in which the amplitudes can be computed explicitly.

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arXiv2018

Heavy-Quark Hybrid Mass Splittings: Hyperfine and "Ultrafine"

It is argued that the heavy-quark limit of QCD requires a certain combination of hyperfine mass splittings in heavy-quark hybrid-meson multiplets to be unusually small. This observation will assist in the exploration of the heavy-quark hybrid spectrum at facilities such as PANDA. Alternatively, a large measured value for this mass splitting indicates that at least one member of the multiplet must contain significant light-quark degrees of freedom.

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arXiv2017

QCD Constituent Counting Rules for Neutral Vector Mesons

QCD constituent counting rules define the scaling behavior of exclusive hadronic scattering and electromagnetic scattering amplitudes at high momentum transfer in terms of the total number of fundamental constituents in the initial and final states participating in the hard subprocess. The scaling laws reflect the twist of the leading Fock state for each hadron and hence the leading operator that creates the composite state from the vacuum. Thus, the constituent counting scaling laws can be used to identify the twist of exotic hadronic candidates such as tetraquarks and pentaquarks. Effective field theories must consistently implement the scaling rules in order to be consistent with the fundamental theory. Here we examine how one can apply constituent counting rules for the exclusive production of one or two neutral vector mesons $V^0$ in $e^+ e^-$ annihilation, processes in which the $V^0$ can couple via intermediate photons. In case of a (narrow) real $V^0$, the photon virtuality is fixed to a precise value $s_1 = m_{V^0}^2$, in effect treating the $V^0$ as a single fundamental particle. Each real $V^0$ thus contributes to the constituent counting rules with $N_{V_0} = 1$. In effect, the leading operator underlying the $V^0$ has twist 1. Thus, in the specific physical case of single or double on-shell $V^0$ production via intermediate photons, the predicted scaling from counting rules coincides with Vector Meson Dominance (VMD), an effective theory that treats $V^0$ as an elementary field. However, the VMD prediction fails in the general case where the $V^0$ is not coupled through an elementary photon field, and then the leading-twist interpolating operator has twist $N_{V_0} = 2$. Analogous effects appear in $pp$ scattering processes.

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arXiv2017

Spectroscopy of Exotic Hadrons Formed from Dynamical Diquarks

The dynamical diquark picture asserts that exotic hadrons can be formed from widely separated colored diquark or triquark components. We use the Born-Oppenheimer (BO) approximation to study the spectrum of states thus constructed, both in the basis of diquark spins and in the basis of heavy quark-antiquark spins. We develop a compact notation for naming these states, and use the results of lattice simulations for hybrid mesons to predict the lowest expected BO potentials for both tetraquarks and pentaquarks. We then compare to the set of exotic candidates with experimentally determined quantum numbers, and find that all of them can be accommodated. Once decay modes are also considered, one can develop selection rules of both exact ($J^{PC}$ conservation) and approximate (within the context of the BO approximation) types and test their effectiveness. We find that the most appealing way to satisfy both sets of selection rules requires including additional low-lying BO potentials, a hypothesis that can be checked on the lattice.

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arXiv2017

Model-independent constraints on hadronic form factors with above-threshold poles

Model-independent constraints on hadronic form factors, in particular those describing exclusive semileptonic decays, can be derived from the knowledge of field correlators calculated in perturbative QCD, using analyticity and unitarity. The location of poles corresponding to below-threshold resonances, i.e., stable states that cannot decay into a pair of hadrons from the crossed channel of the form factor, must be known a priori, and their effect, accounted for through the use of Blaschke factors, is to reduce the strength of the constraints in the semileptonic region. By contrast, above-threshold resonances appear as poles on unphysical Riemann sheets, and their presence does not affect the original model-independent constraints. We discuss the possibility that the above-threshold poles can provide indirect information on the form factors on the first Riemann sheet, either through information from their residues or by constraining the discontinuity function. The bounds on form factors can be improved by imposing, in an exact way, the additional information in the extremal problem. The semileptonic $K\to π\ell ν$ and $D\to π\ellν$ decays are considered as illustrations.

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arXiv2017

Quarkonium $h$ States As Arbiters of Exoticity

The mass splitting between the quarkonium spin-singlet state $h$ ($J^{PC} = 1^{+-}$) and the spin average of the quarkonium spin-triplet states $χ$ ($J^{PC} = 0^{++}, 1^{++}, 2^{++}$) is seen to be astonishingly small, not only in the charmonium and bottomonium cases where the relevant masses have been measured, but in positronium as well. We find, both in nonrelativistic quark models and in NRQCD, that this hyperfine splitting is so small that it can be used as a test of the pure $Q\bar Q$ content of the states. We discuss the $2P$ states of charmonium in the vicinity of $3.9$ GeV, where the putative exotics $X(3872)$ and $X(3915)$ have been seen and a new $χ_{c0}(2P)$ candidate has been observed at Belle.

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arXiv2016

QCD Compositeness as Revealed in Exclusive Vector Boson Reactions through Double-Photon Annihilation: $e^+ e^- \to γγ^\ast \to γV^0 $ and $e^+ e^- \to γ^\ast γ^\ast \to V^0 V^0$

We study the exclusive double-photon annihilation processes, $e^+ e^- \to γγ^\ast\to γV^0$ and $e^+ e^- \to γ^\ast γ^\ast \to V^0_a V^0_b,$ where the $V^0_i$ is a neutral vector meson produced in the forward kinematical region: $s \gg -t$ and $-t \gg Λ_{\rm QCD}^2$. We show how the differential cross sections $\frac{dσ}{dt}$, as predicted by QCD, have additional falloff in the momentum transfer squared $t$ due to the QCD compositeness of the hadrons, consistent with the leading-twist fixed-$θ_{\rm CM} $ scaling laws. However, even though they are exclusive channels and not associated with the conventional electron-positron annihilation process $e^+ e^- \to γ^\ast \to q \bar q,$ these total cross sections $σ(e^+ e^- \to γV^0) $ and $σ(e^+ e^- \to V^0_a V^0_b),$ integrated over the dominant forward- and backward-$θ_{\rm CM}$ angular domains, scale as $1/s$, and thus contribute to the leading-twist scaling behavior of the ratio $R_{e^+ e^-}$. We generalize these results to exclusive double-electroweak vector-boson annihilation processes accompanied by the forward production of hadrons, such as $e^+ e^- \to Z^0 V^0$ and $e^+ e^- \to W^-ρ^+$. These results can also be applied to the exclusive production of exotic hadrons such as tetraquarks, where the cross-section scaling behavior can reveal their multiquark nature.

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arXiv2016

Heavy-Quark QCD Exotica

This review presents an overview of the remarkable progress in the field of heavy-quark exotic hadrons over the past 15 years. It seeks to be pedagogical rather than exhaustive, summarizing both the progress and specific results of experimental discoveries, and the variety of theoretical approaches designed to explain these new states.

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arXiv2016

Exotic Discoveries in Familiar Places: Theory of the Onia and Exotics

This brief overview presents an introduction to the heavy-quark exotic hadron candidates, $X$, $Y$, $Z$, $P_c$, believed to be tetraquark and pentaquark states. After an abridged account of their discovery, we outline the various theoretical pictures employed to describe their structure, with special focus on the new dynamical diquark picture.

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arXiv2016

How Often Do Diquarks Form? A Very Simple Model

Starting from a textbook result, the nearest-neighbor distribution of particles in an ideal gas, we develop estimates for the probability with which quarks $q$ in a mixed $q$, $\bar q$ gas are more strongly attracted to the nearest $q$, potentially forming a diquark, than to the nearest $\bar q$. Generic probabilities lie in the range of tens of percent, with values in the several percent range even under extreme assumptions favoring $q\bar q$ over $qq$ attraction.

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arXiv2016

$χ^{\vphantom\dagger}_{c0}(3915)$ As the Lightest $c\bar c s \bar s$ State

The state $χ^{\vphantom\dagger}_{c0}(3915)$ has recently been demoted by the Particle Data Group from its previous status as the conventional $c\bar c$ $2 {}^3P_0$ state, largely due to the absence of expected $D\bar D$ decays. We propose that $χ^{\vphantom\dagger}_{c0}(3915)$ is actually the lightest $c\bar c s \bar s$ state, and calculate the spectrum of such states using the diquark model, identifying many of the observed charmoniumlike states that lack open-charm decay modes as $c\bar c s \bar s$. Among other results, we argue that $Y(4140)$ is a $J^{PC} = 1^{++}$ $c\bar c s \bar s$ state that has been not been seen in two-photon fusion largely as a consequence of the Landau-Yang theorem.

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arXiv2016

Nonperturbative True Muonium on the Light Front with TMSWIFT

The true muonium $(μ\barμ)$ bound state presents an interesting test of light-cone quantization techniques. In addition to exhibiting the standard problems of handling non-perturbative calculations, true muonium requires correct treatment of $e\bar{e}$ Fock-state contributions. Having previously produced a crude model of true muonium using the method of iterated resolvents, our current work has focused on the inclusion of the box diagrams to improve the cutoff-dependent issues of the model. Further, a parallel computer code, TMSWIFT, allowing for smaller numerical uncertainties, has been developed. This work focuses on the current state of these efforts to develop a model of true muonium that is testable at near-term experiments.

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arXiv2015

Do the $P_c^+$ Pentaquarks Have Strange Siblings?

The recent LHCb discovery of states $P_c^+(4380)$, $P_c^+(4450)$, believed to be $c\bar c uud$ pentaquark resonances, begs the question of whether equivalent states with $c\bar c \to s\bar s$ exist, and how they might be produced. The precise analogue to the $P_c^+$ discovery channel $Λ_b \to J/ψ\, K^- \! p$, namely, $Λ_c \to ϕπ^0 \! p$, is feasible for this study and indeed is less Cabibbo-suppressed, although its limited phase space suggests that evidence of a $s\bar s uud$ resonance $P_s^+$ would be confined to the kinematic endpoint region.

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