arXiv subjects

Christoph Hanhart

Publications and source records attributed to Christoph Hanhart.

At least 37 records · Page 2Linked to original sources

arXiv2025

Internal structure of the $T_{cc}(3875)^+$ from its light-quark mass dependence

We employ a chiral effective field theory-based approach to connect $DD^*$ scattering observables at the physical and variable pion masses accessible in lattice QCD simulations. We incorporate all relevant scales associated with three-body $DDπ$ dynamics and the left-hand cut induced by the one-pion exchange for pion masses higher than the physical one, as required by analyticity and unitarity. By adjusting the contact interactions to match experimental data at the physical pion mass and lattice finite-volume energy levels at $m_π = 280$ MeV, we predict the trajectory of the $T_{cc}$ pole as a function of the pion mass, finding it consistent with the hadronic-molecule scenario. In particular, we find that the explicit treatment of the one-pion exchange has a pronounced effect on the pole trajectory for $m_π\gtrsim 230$ MeV by pushing it into the complex energy plane.

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arXiv2024

Dispersive analysis of the isospin breaking in the $X(3872)~\to~J/ψπ^+π^-$ and $X(3872)~\to~J/ψπ^+π^0π^-$ decays

We analyze the latest LHCb data on the $π^+π^-$ spectrum in the isospin-violating $X(3872)\to J/ψπ^+π^-$ decay, based on dispersion theory to deal with the $ππ$ final state interactions. Additionally, the isospin breaking effects are properly introduced, allowing for a reliable and accurate extraction of the ratio, $R_X$, between the $X(3872)$ couplings to the $J/ψρ$ and $J/ψω$ channels from the data. We find very good agreement with the LHCb data for the whole range of the $π^+π^-$ invariant mass, and $R_X$ is determined to be {$0.26\pm 0.03$}. Using this value, we make predictions for the $π^+π^0π^-$ mass distribution in the $X(3872)\to J/ψπ^+π^0π^-$ process, which is currently accessible by the BESIII Collaboration, and update a prediction for the pole positions of the isovector partner states of the $X(3872)$, $W_{c1}$, with $I(J^{PC})=1(1^{++})$.

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arXiv2024

On the scalar $πK$ form factor beyond the elastic region

Pion-kaon ($πK$) final states, often appearing in heavy-particle decays at the precision frontier, are important for Standard-Model tests, to describe crossed channels with exotic states, and for spectroscopy of excited kaon resonances. We construct a representation of the $πK$ $S$-wave form factor using the elastic $πK$ scattering phase shift via dispersion relations in the elastic region and extend this model into the inelastic region using resonance exchange, while maintaining unitarity and the correct analytic structure. As a first application, we successfully described the $τ\to K_S πν_τ$ spectrum to not only achieve a better distinction between $S$- and $P$-wave contributions, but also to provide an improved estimate of the $CP$ asymmetry produced by a tensor operator as well as the forward-backward asymmetry, both of which can be confronted with future data at Belle II.

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arXiv2024

Predicting isovector charmonium-like states from X(3872) properties

Using chiral effective field theory, we predict that there must be isovector charmonium-like $D\bar D^*$ hadronic molecules with $J^{PC}=1^{++}$ denoted as $W_{c1}$. The inputs are the properties of the $X(3872)$, including its mass and the ratio of its branching fractions of decays into $J/ψρ^0$ and $J/ψω$. The predicted states are virtual state poles of the scattering matrix, pointing at a molecular nature of the $X(3872)$ as well as its spin partners. They should show up as either a mild cusp or dip at the $D\bar D^*$ thresholds, explaining why they are elusive in experiments. The so far negative observation also indicates that the $X(3872)$ is either a bound state with non-vanishing binding energy or a virtual state, only in these cases the $X(3872)$ signal dominates over that from the $W_{c1}^0$. The pole positions are $3881.2^{+0.8}_{-0.0}- i 1.6^{+0.7}_{-0.9}$ MeV for $W_{c1}^0$ on the fourth Riemann sheet of the $D^0\bar D^{*0}$-$D^+D^{*-}$ coupled-channel system, and $3866.9^{+4.6}_{-7.7}- i (0.07\pm0.01)$ MeV for $W_{c1}^\pm$ on the second Riemann sheet of the $(D\bar D^*)^\pm$ single-channel system. The findings imply that the peak in the $J/ψπ^+π^-$ invariant mass distribution is not purely from the $X(3872)$ but contains contributions from $W_{c1}^0$ predicted here. The states should have isovector heavy quark spin partners with $J^{PC}=0^{++}$, $2^{++}$ and $1^{+-}$, with the last one corresponding to $Z_c$. We suggest to search for the charged $0^{++}$, $1^{++}$ and $2^{++}$ states in $J/ψπ^\pm π^0$.

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arXiv2024

How many vector charmonium(-like) states sit in the energy range from $4.2$ to $4.35$ GeV?

In recent years many vector charmonium(-like) states were reported by different electron-positron collider experiments above $4.2$ GeV. However, so far, there not only exists sizable tension in the parameters of those states, but there is also no consensus on the number of the vector states in this energy range. To some extend, this might be caused by the fact that the experimental data were typically analyzed in single channel analyses employing overlapping Breit-Wigner functions, in particular ignoring the effect of opening thresholds. In this study, we focus on the mass range between $4.2$ and $4.35$ GeV, conducting a comprehensive analysis of eight different final states in $e^+ e^-$ annihilation. Our findings demonstrate that, within this mass range, a single vector charmonium-like state, exhibiting properties consistent with a $D_1\bar D$ molecular structure and characterized by a pole location $\sqrt{s_\text{pole}^{Y(4230)}}=\left( 4227{\pm} 3 {-} \frac{i}{2}(50^{+10}_{-5}) \right) \text{MeV}$, can effectively describe all the collected data. This is made possible by allowing for an interference with the well-established vector chamonium $ψ(4160)$ along with the inclusion of the $D_1\bar D$ threshold effect. Moreover, in contrast to experimental analyses, our study reveals that the highly asymmetric total cross sections for $e^+e^-\to J/ψππ$ and $e^+e^-\to J/ψK\bar K$ around 4230 MeV stem from the same physics, rooted in the approximate SU(3) flavor symmetry of QCD.

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arXiv2024

How does the $X(3872)$ show up in $e^+e^-$ collisions: dip versus peak

We demonstrate that the dip observed near the total energy of 3872 MeV in the recent cross section data from the BESIII Collaboration for $e^+e^-\to J/ψπ^+π^- $ admits a natural explanation as a coupled-channel effect: it is a consequence of unitarity and a strong $S$-wave $D\bar D^*$ attraction that generates the state $X(3872)$. We anticipate the appearance of a similar dip in the $e^+e^-\to J/ψπ^+π^-π^0$ final state near the $D^*\bar{D}^*$ threshold driven by the same general mechanism, then to be interpreted as a signature of the predicted spin-two partner of the $X(3872)$.

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arXiv2024

Analysis of the $ψ(3770)$ resonance in line with unitarity and analyticity constraints

We study the inclusive and exclusive cross sections of $e^+e^-\to \text{hadrons}$ for center-of-mass energies between 3.70 GeV and 3.83 GeV to infer the mass, width, and couplings of the $ψ(3770)$ resonance. By using a coupled-channel K-matrix approach, we setup our analysis to respect unitarity and the analyticity properties of the underlying scattering amplitudes. We fit several models to the full dataset and identify our nominal results through a statistical model comparison. We find that, accounting for the interplay between the $ψ(2S)$ and the $ψ(3770)$, no further pole is required to describe the $ψ(3770)$ line shape. In particular we derive from the pole location $M_{ψ(3770)} = 3778.8 \pm 0.3$ MeV and $Γ_{ψ(3770)} = 25.0 \pm 0.5$ MeV. Moreover, we find the decay to $D^+D^-$ and $D^0\bar{D}^0$ to be consistent with isospin symmetry and derive an upper bound on the branching ratio $\mathcal{B}(ψ(3770) \to \textrm{non-}D\bar{D}) < 6\%$ at $90\%$ probability.

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arXiv2024

Production of the $X(4014)$ as the spin-2 partner of $X(3872)$ in $e^+e^-$ collisions

In 2021, the Belle collaboration reported the first observation of a new structure in the $ψ(2S) γ$ final state produced in the two-photon fusion process. In the hadronic molecule picture, this new structure can be associated with the shallow isoscalar $D^*\bar{D}^*$ bound state and as such is an excellent candidate for the spin-2 partner of the $X(3872)$ with the quantum numbers $J^{PC}=2^{++}$ conventionally named $X_2$. In this work we evaluate the electronic width of this new state and argue that its nature is sensitive to its total width, the experimental measurement currently available being unable to distinguish between different options. Our estimates demonstrate that the planned Super $τ$-Charm Facility offers a promising opportunity to search for and study this new state in the invariant mass distributions for the final states $J/ψγ$ and $ψ(2S)γ$.

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arXiv2023

The $Y(4230)$ as a $D_1 \bar{D}$ molecule

We show that the currently available data are consistent with $Y(4230)$ being a $D_1 \bar{D}$ hadronic molecule. By a simultaneous fit to data from $e^+ e^- \rightarrow D^0 D^{* -} π^+,\: J/ψπ^+ π^-,\: J/ψK^+ K^-,\: h_c π^+ π^-,\: J/ψη,\: χ_{c0} ω,\: χ_{c1}(3872) γ$ and $μ^+ μ^-$, we demonstrate that this single state can explain the experimental signals in the mass range from $4.2$ to $4.35\, \rm{GeV}.$

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arXiv2023

Role of left-hand cut contributions on pole extractions from lattice data: Case study for $T_{cc}(3875)^+$

We discuss recent lattice data for the $T_{cc}(3875)^+$ state to stress, for the first time, a potentially strong impact of left-hand cuts from the one-pion exchange on the pole extraction for near-threshold exotic states. In particular, if the left-hand cut is located close to the two-particle threshold, which happens naturally in the $DD^*$ system for the pion mass exceeding its physical value, the effective-range expansion is valid only in a very limited energy range up to the cut and as such is of little use to reliably extract the poles. Then, an accurate extraction of the pole locations requires the one-pion exchange to be implemented explicitly into the scattering amplitudes. Our findings are general and potentially relevant for a wide class of hadronic near-threshold states.

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arXiv2023

Can the two-pole structure of the $D_0^*(2300)$ be understood from recent lattice data?

It was demonstrated in a series of papers employing unitarized chiral perturbation theory that the phenomenology of the scalar open-charm state, the $D_0^*(2300)$, can be understood as the interplay of two poles, corresponding to two scalar-isospin doublet states with different SU(3) flavor content. Within this formalism the lightest open charm positive parity states emerge as being dynamically generated from the scattering of the Goldstone-boson octet off $D$ mesons, a picture that at the same time solves various problems that the experimental observations posed. However, in recent lattice studies of $Dπ$ scattering at different pion masses only one pole was reported in the $D_0^*$ channel, while it was not possible to extract reliable parameters of a second pole from the lattice data. In this paper we demonstrate how this seeming contradiction can be understood and that imposing SU(3) constraints on the fitting amplitudes allows one to extract information on the second pole from the lattice data with minimal bias. The results may also be regarded as a showcase how approximate symmetries can be imposed in the $K$-matrix formalism to reduce the number of parameters.

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arXiv2023

Update on strong and radiative decays of the $D_{s0}^{*}(2317)$ and $D_{s1}(2460)$ and their bottom cousins

The isospin breaking and radiative decay widths of the positive-parity charm-strange mesons, $D^{*}_{s0}$ and $D_{s1}$, and their predicted bottom-strange counterparts, $B^{*}_{s0}$ and $B_{s1}$, as hadronic molecules are revisited. This is necessary, since the $B^{*}_{s0}$ and $B_{s1}$ masses used in Eur. Phys. J. A 50 (2014) 149 were too small, in conflict with the heavy quark flavour symmetry. Furthermore, not all isospin breaking contributions were considered. We here present a method to restore heavy quark flavour symmetry, correcting the masses of $B^{*}_{s0}$ and $B_{s1}$, and include the complete isospin breaking contributions up to next-to-leading order. With this we provide updated hadronic decay widths for all of $D^{*}_{s0}$, $D_{s1}$, $B^{*}_{s0}$ and $B_{s1}$. Results for the partial widths of the radiative deays of $D_{s0}^*(2317)$ and $D_{s1}(2460)$ are also renewed in light of the much more precisely measured $D^{*+}$ width. We find that $B_sπ^0$ and $B_sγ$ are the preferred channels for searching for $B_{s0}^*$ and $B_{s1}$, respectively.

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arXiv2023

Isospin-conserving hadronic decay of the ${D_{s1}(2460)}$ into ${D_sπ^+π^-}$

The internal structure of the charm-strange mesons $D_{s0}^*(2317)$ and $D_{s1}(2460)$ are subject of intensive studies. Their widths are small because they decay dominantly through isospin-breaking hadronic channels $D_{s0}^*(2317)^+\to D_s^+π^0$ and $D_{s1}(2460)^+\to D_s^{*+}π^0$. The $D_{s1}(2460)$ can also decay into the hadronic final states $D_s^+ππ$, conserving isospin. In that case there is, however, a strong suppression from phase space. We study the transition $D_{s1}(2460)^+\to D_s^+π^+π^-$ in the scenario that the $D_{s1}(2460)$ is a $D^*K$ hadronic molecule. The $ππ$ final state interaction is taken into account through dispersion relations. We find that the ratio of the partial widths of the $Γ(D_{s1}(2460)^+\to D_s^+π^+π^-)/Γ(D_{s1}(2460)^+\to D_s^{*+}π^0)$ obtained in the molecular picture is consistent with the existing experimental measurement. More interestingly, we demonstrate that the $π^+π^-$ invariant mass distribution shows a double bump structure, which can be used to disentangle the hadronic molecular picture from the compact state picture for the $D_{s1}(2460)^+$. Predictions on the $B_{s1}^0\to B_s^0π^+π^-$ are also made.

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arXiv2022

A dispersive analysis of $η'\toπ^+π^-γ$ and $η'\to \ell^+\ell^-γ$

We present a dispersive representation of the $η'$ transition form factor that allows one to account, in a consistent way, for the effects of $ρ$-$ω$ mixing in both the isoscalar and the isovector contributions. Using this formalism, we analyze recent data on $η'\to π^+π^-γ$ to constrain the isovector part of the form factor, individually and in combination with data for the pion vector form factor. As a first application, we use our results, in combination with the most recent input for the isoscalar part of the form factor, to predict the corresponding spectrum of $η'\to\ell^+\ell^-γ$, in particular we find the slope parameter $b_{η'}=1.431(23)\, \text{GeV}^{-2}$. With forthcoming data on the latter process, our results establish the necessary framework to improve the evaluation of the $η'$-pole contribution to the anomalous magnetic moment of the muon using experimental input from both $η'$ decay channels.

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arXiv2022

Do near-threshold molecular states mix with neighbouring $\bar QQ$ states?

The last two decades are marked by a renaissance in hadronic spectroscopy caused by the arrival of vast experimental information on exotic states in the spectrum of charmonium and bottomonium. Most of such states have properties at odds with the predictions of the quark model and reside very close to strong hadronic thresholds. Prominent examples are provided by the glorious $X(3872)$ charmonium-like state and the doubly charmed tetraquark $T_{cc}^+$ with the masses within less than 1 MeV from the $D\bar{D}^*$ and $DD^*$ open-charm thresholds, respectively. The universality of this feature hints towards the existence of a general pattern for such exotic states. In this work we discuss a possible generic mechanism for the formation of near-threshold molecular states as a result of the strong coupling of compact quark states with a hadronic continuum channel. The compact states that survive the strong coupling limit decouple from the continuum channel and therefore also from the formed hadronic molecule - if realised this scenario would provide a justification to treat hadronic molecules isolated, ignoring the possible influence from surrounding, compact quark-model states. We confront the phenomenology of the $D_{s1}(2460)$ and $D_{s1}(2536)$ with this picture and find consistency, although other explanations remain possible for those states.

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arXiv2022

Hadronic molecules

A large number of experimental discoveries especially in the heavy quarkonium sector that did not at all fit to the expectations of the until then very successful quark model led to a renaissance of hadron spectroscopy. Among various explanations of the internal structure of these excitations, hadronic molecules, being analogues of light nuclei, play a unique role since for those predictions can be made with controlled uncertainty. We review experimental evidences of various candidates of hadronic molecules, and methods of identifying such structures. Nonrelativistic effective field theories are the suitable framework for studying hadronic molecules, and are discussed in both the continuum and finite volumes. Also pertinent lattice QCD results are presented. Further, we discuss the production mechanisms and decays of hadronic molecules, and comment on the reliability of certain assertions often made in the literature.

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arXiv2022

Substructure of Multiquark Hadrons (Snowmass 2021 White Paper)

In recent years there has been a rapidly growing body of experimental evidence for existence of exotic, multiquark hadrons, i.e. mesons which contain additional quarks, beyond the usual quark-antiquark pair and baryons which consist of more than three quarks. In all cases with robust evidence they contain at least one heavy quark Q=c or b, the majority including two heavy quarks. Two key theoretical questions have been triggered by these discoveries: (a) how are quarks organized inside these multiquark states -- as compact objects with all quarks within one confinement volume, interacting via color forces, perhaps with an important role played by diquarks, or as deuteron-like hadronic molecules, bound by light-meson exchange? (b) what other multiquark states should we expect? The two questions are tightly intertwined. Each of the interpretations provides a natural explanation of parts of the data, but neither explains all of the data. It is quite possible that both kinds of structures appear in Nature. It may also be the case that certain states are superpositions of the compact and molecular configurations. This Whitepaper brings together contributions from many leading practitioners in the field, representing a wide spectrum of theoretical interpretations. We discuss the importance of future experimental and phenomenological work, which will lead to better understandingof multiquark phenomena in QCD.

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arXiv2022

Effective range expansion for narrow near-threshold resonances

We discuss some general features of the effective range expansion, the content of its parameters with respect to the nature of the pertinent near-threshold states and the necessary modifications in the presence of coupled channels, isospin violations and unstable constituents. As illustrative examples, we analyse the properties of the $χ_{c1}(3872)$ and $T_{cc}^+$ states supporting the claim that these exotic states have a predominantly molecular nature.

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