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Wolfgang Lucha

Publications and source records attributed to Wolfgang Lucha.

At least 19 recordsLinked to original sources
arXiv2026

$B_{(s)}\to V M_X$ decays as probes of dark-matter scenarios of Belle II enhancement in $B\to KM_X$ decays

Recently, we have shown that the hypothesis of the dark-matter (DM) origin of the Belle II excess events in $B\to K M_X$ decays allows for a successful description of the data. The DM parameters (masses and couplings) in two DM scenarios with either scalar (S-scenario) or vector (V-scenario) mediator have been extracted with rather small uncertainty from fits to the $B\to K M_X$ data. The same mechanism leads to a similar enhancement of the $B_s\to (η,η',ϕ) M_X$ decay rates. We present a detailed analysis of $B\to K^* M_X$ and $B_s\to ϕM_X$ decays and show that these decays provide a clear probe of the S- and V-scenarios: Compared to the Standard Model, in the S-scenario an enhancement by a factor $\sim 1.6$ is expected, whereas the V-scenario leads to a much larger enhancement by a factor $\sim 3.5$. For the $B\to K^* M_X$ decays, we provide the expected number of events at Belle II for the sample for which a rather large enhancement of $B\to K M_X$ decays compared to the Standard Model expectations has been reported.

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arXiv2025

Scrutinizing dark-matter scenarios with $B\to(K,K^*)\barνν$ decays

Conceivable explanations of Belle-II measurements of a (surprising) excess of missing-energy decays of the $B$ meson to the $K$ meson not covered by standard-model neutrino-antineutrino pairs might be offered by additional contributions of dark-matter fermion-antifermion pairs. Assuming the excessive missing-energy events to be mediated by a (generic) scalar or vector boson, a simultaneous inspection of both of the missing-energy $B$ decays into a pseudoscalar $K$ meson or a vector $K^*$ meson allows to gain information on the nature of bosons relating standard-model and dark-matter sectors, irrespective of any (unknown) dark-sector details. Upon availability of indispensable experimental data, most prominent among such insights might be the identification of the mediator spin from the differential $B$-meson decay widths.

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arXiv2025

Probing vector- vs scalar-mediator dark-matter scenarios in $B\to (K,K^*) M_X$ decays

Within the hypothesis of the dark-matter origin of the excess in $B\to K M_X$ decays over the standard-model expectation, observed by Belle-II, we show that: (i) Scalar- and vector-medator scenarios may be unambiguously discriminated by measuring the differential distributions in $B\to K M_X$ and $B\to K^* M_X$ decays. (ii) Combining the available data on $Γ(B\to K M_X)$ and the upper limit on $Γ(B\to K^* M_X)$ provides a tight constraint on the vector mediator mass $M_V\lesssim 3$ GeV. At the same time, no constraints on the scalar-mediator mass are imposed by these data. (iii) Both scalar- and vector-mediator scenarios allow a good description of the differential distributions in $B\to K M_X$ measured by Belle-II and an extraction of dark-model parameters within both scenarios.

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arXiv2025

Analysis of $B\to KM_X$ and $B\to K^* M_X$ decays in scalar- and vector-mediator dark-matter scenarios

The surprising excess of missing-energy events far beyond all standard-model expectations in the weak decays of the charged ground-state $B^+$ meson into some charged strange meson, rather recently observed by the Belle-II experiment, may (easily) be explained by the decay of the $B$ meson into the strange meson and a pair of dark-matter fermion and antifermion, mediated by an (intermediate) scalar or vector boson. Thorough inspections of both the total and the differential widths of these decays provide, among others, a simple means for the (straightforward) discrimination of such mediator boson's scalar or vector nature.

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arXiv2025

Analysis of $q_\mathrm{rec}^2$-distribution for $B\to K M_X$ and $B\to K^* M_X$ decays in a scalar-mediator dark-matter scenario

We demonstrate that the scalar-mediator dark-matter scenario is consistent with the experimental data on the decay $B\to K M_X$ and provides a good description of the shape of the observed excess. Within this scenario, the interaction with dark-matter particles leads to approximately the same excess in $Γ(B\to K^* M_X)$ and $Γ(B\to K M_X)$ compared to the Standard Model; also the differential distributions of the excess events are similar in shape in the variable $q_\mathrm{rec}^2$ measured by experiment.

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arXiv2024

Various Illustrative Brief Glances at the Flavour-Cryptoexotic Tetraquark States

Constituting the largest subset of multiquark states so far observed by experiment, tetraquark mesons carrying overall quark flavour quantum numbers identical to those of the (conventional) quark-antiquark mesons necessitate their particularly deliberate phenomenological analyses. A collection of (more or less recent) insights specific to the latter subclass of exotic hadrons bears the promise to enable even significant improvement in the understanding of these hadrons by theoretical approaches such as, among others, the framework of QCD sum rules.

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arXiv2023

Mission Target: Tetraquark Mesons of Flavour-Cryptoexotic Type

Currently, flavour-cryptoexotic tetraquarks form the most common sort of all experimentally established exotic multiquark hadrons. This note points out a few promising concepts that should help improve theoretical (but, for several reasons, not quite straightforward) analyses of such kind of states: among others, their scope of application encompasses the strong interactions in the limit of (arbitrarily) large numbers of colours, and equally analytical and nonperturbative approaches to multiquark states.

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arXiv2023

Mission Target: Exotic Multiquark Hadrons -- Sharpened Blades

Motivated by recent experimental progress in establishing the likely existence of (variants of) exotic hadrons, predicted to be formed by the strong interactions, various proposed concepts and ideas are compiled in an attempt to draft a coherent picture of the achievable improvement in the theoretical interpretation of exotic hadrons in terms of the underlying quantum field theory of strong interactions.

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arXiv2022

Zooming in on Multiquark Hadrons within QCD Sum-Rule Approaches

Aiming at self-consistent descriptions of multiquark hadrons (such as tetraquarks, pentaquarks, hexaquarks) by means of QCD sum rules, we note that the totality of contributions to two-point or three-point correlation functions that involve, respectively, either two or just a single operator capable of interpolating the particular multiquark under study can be straightforwardly disentangled into two disjoint classes defined by unambiguously identifiable members. The first is formed by so-called multiquark-phile contributions which indeed might support multiquarks. In the case of flavour-exotic tetraquarks, by definition composed of four (anti-) quarks of mutually different flavours, a tetraquark-phile contribution has to exhibit two or more gluon exchanges of appropriate topology. The second consists of contributions evidently not bearing any relation to multiquarks; these must be discarded when studying multiquarks by QCD sum rules. The first class only should enter the "multiquark-adequate" QCD sum rules for exotic hadrons.

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arXiv2022

Bethe-Salpeter Bound-State Solutions: Examining Semirelativistic Approaches

Within the formalism of relativistic quantum field theory an adequate framework for the description of two-particle bound states, such as, for instance, all conventional (i.e., non-exotic) mesons, is provided by the Poincaré-covariant homogeneous Bethe-Salpeter equation. In applications, however, this approach usually proves to be rather involved, whence it is not always quite easy to extract the predictions sought. In view of this, a coarse idea of the bound-state spectrum to be expected might be gained by adhering to some simplifying approximations - which constitutes an entirely legitimate first step. The reliability of the insights inferred from the arising simpler bound-state equation may be straightforwardly examined by taking into account a couple of rigorous constraints on the obtained discrete spectrum. Application of these tools is illustrated for popular potentials.

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arXiv2022

Semirelativistic Potential Modelling of Bound States: Advocating Due Rigour

The Poincaré-covariant quantum-field-theoretic description of bound states by the homogeneous Bethe-Salpeter equation usually exhibits an intrinsic complexity that can be attenuated by allowing this formalism to undergo various simplifications. The resulting approximate outcome's reliability can be assessed by applying several rigorous constraints on the nature of the bound-state spectra; most prominent here are existence, number and location of discrete eigenvalues.

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arXiv2022

Multiquark-Oriented QCD Sum Rules

We propose to increase the factual reliability of descriptions of exotic multiquark hadrons utilizing the approach to bound states of strongly interacting constituents known as QCD sum rules, by allowing exclusively all contributions that potentially bear some relevance for multiquark states to enter the correlation functions that form the main ingredient of this framework. The route to this goal is illustrated for the (presumably least involved) special case of tetraquark states.

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arXiv2021

Cluster Reducibility of Multiquark Operators and Tetraquark-Adequate QCD Sum Rules

If connecting properties of a multiquark hadron with those exhibited by its constituents, QCD sum rules inferred along the routes of traditional wisdom necessarily involve contributions not related at all to and thus not presenting information about multiquarks. Realizing this deficiency, we propose to increase, for the example of tetraquarks, the predictive power of the QCD sum-rule formalism by disposal of all of the unwanted contributions from the very beginning; this move is easily accomplished by subjecting the contributions to our perspicuous selection criterion.

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arXiv2021

Tetraquarks in large-$N_c$ QCD

The present work reviews the various aspects of the extension of the large-$N_c$ approach, as had been proposed and developed by 't Hooft, to the case of tetraquark states, which are a category of the general class of exotic states, also called multiquark states, whose internal valence-quark structure does not match with that of ordinary hadrons, and which have received, in recent years, many experimental confirmations. The primary question of describing, or probing, on theoretical grounds, multiquark states is first examined. The signature of such states inside Feynman diagrams in relation with their singularities is highlighted. The main mechanisms of formation of tetraquark states, provided by the diquark model and the molecular scheme, are considered together with their specific implications. The properties of tetraquark states at large $N_c$ are analyzed through the Feynman diagrams that describe two-meson scattering amplitudes. It turns out that, in that limit, the possible formation of tetraquark states is mainly due to the mutual interactions of their internal mesonic clusters. These essentially arise from the quark-rearrangement, or quark-interchange, mechanism. In coupled-channel meson-meson scattering amplitudes, one may expect the occurrence of two independent tetraquark states, each having priviledged couplings with the two mesons of their dominant channel. The question of the energy balance of various schemes in the static limit is also analyzed. The clarification of the mechanisms that are at work in the formation of tetraquarks is the main outcome from the large-$N_c$ approach to this problem.

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arXiv2020

OPE and quark-hadron duality for two-point functions of tetraquark currents in $1/N_c$ expansion

We discuss the Operator Product Expansion (OPE) and quark-hadron duality for two-point Green functions of tetraquark currents. We emphasize that the factorizable part of the OPE series for such Green functions, including nonperturbative contributions described by QCD condensates, is saturated by the full system of ordinary hadrons and therefore cannot have any relationship to the possible tetraquark bound states. Possible tetraquark bound states may be contained in nonfactorizable parts of these Green functions. In the framework of the $1/N_c$ expansion in QCD$(N_c)$, nonfactorizable parts of the two-point Green functions of tetraquark currents provide $N_c$-suppressed contributions compared to the $N_c$-leading factorizable parts. A possible exotic tetraquark state may appear only in $N_c$-subleading contributions to the QCD Green functions, in full accord with the well-known rigorous properties of large-$N_c$ QCD.

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arXiv2020

Tetraquark Properties at Large $N_{\rm c}$

Considering quantum chromodynamics in the consistent limit of simultaneous correlated increase of the number of colours, $N_{\rm c}$, beyond bounds and decrease of the strong coupling to zero allows for solid statements about qualitative features of the class of "truly exotic" tetraquark mesons carrying four mutually distinct quark flavours. Consistency criteria extracted from correlation functions for two-ordinary-meson scattering suggest the existence of more than one such tetraquarks, at least, of two tetraquarks of identical quark-flavour content and large-$N_{\rm c}$ behaviour of the total decay widths but differing in, and hence discriminable by, their predominant decay modes into two conventional mesons. This pairwise appearance is in conflict with the unique variant of such a four-quark bound state arising from the binding of diquark and antidiquark to a tetraquark by the strong interactions.

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arXiv2019

Cluster reducibility of multiquark operators

It is shown that the multiquark gauge-invariant operators can, in general, be decomposed into combinations of products of ordinary hadronic operators, exhibiting their cluster reducibility. The latter property inhibits the formation of completely compact multiquark bound states. Multiquark operators still play a crucial role in the description of exotic states in regions of configuration space where the hadronic clusters are close to each other. Our proof gives a foundation for a unified viewpoint, where the multiquark-type and the molecular-type approaches play complementary roles, at the gauge-invariant nonlocal operator level.

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