Hadronic Systems Research Articles

Using an amplitude analysis to measure the photon polarisation in B rightarrow Kpi pi gamma decays

A method is proposed to measure the photon polarisation parameter lambda _{gamma } in {{b}} !rightarrow {s} {gamma } transitions using an amplitude analysis of B!rightarrow Kpi pi {gamma } decays. Simplified models of the {K} {pi } {pi } system are used to simulate {{{B} ^+}} !rightarrow {{K} ^+} {{pi } ^-} {{pi } ^+} {gamma } and {{B} ^0} !rightarrow {{K} ^+} {{pi } ^-} {{pi } ^0} {gamma } decays, validate the amplitude analysis method, and demonstrate the feasibility of a measurement of the lambda _{gamma } parameter irrespective of the model parameters. Similar sensitivities to lambda _{gamma } are obtained with both the charged and neutral hadronic systems. In the absence of any background and distortion due to experimental effects, the statistical uncertainty expected from an analysis of {{{B} ^+}} !rightarrow {{K} ^+} {{pi } ^-} {{pi } ^+} {gamma } decays in an LHCb data set corresponding to an integrated luminosity of 9 ,hbox {fb}^{-1} is estimated to be 0.009. A similar measurement using {{B} ^0} !rightarrow {{K} ^+} {{pi } ^-} {{pi } ^0} {gamma } decays in a Belle II data sample corresponding to an integrated luminosity of 5 hbox {,ab}^{-1} would lead to a statistical uncertainty of 0.018.

Benchmarking a nonequilibrium approach to photon emission in relativistic heavy-ion collisions

In this work, the production of photons through binary scattering processes is investigated for equilibrated hadronic systems. More precisely, a non-equilibrium hadronic transport approach to describe relativistic heavy-ion collisions is benchmarked with respect to photon emission. Cross sections for photon production in $\pi + \rho \to \pi + \gamma$ and $\pi + \pi \to \rho + \gamma$ scattering processes are derived from an effective chiral field theory and implemented into the hadronic transport approach, SMASH (Simulating Many Accelerated Strongly-interacting Hadrons). The implementation is verified by systematically comparing the thermal photon rate to theoretical expectations. Further, the impact of form factors is discussed, scattering processes mediated by $\omega$ mesons are found to contribute significantly to the total photon production. Several comparisons of the yielded photon rates are performed: to parametrizations of the very same rates, as used in hydrodynamic simulations, to previous works relying on different cross sections for the production of direct photons from the hadronic stage, and to partonic rates. Finally, the impact of considering the finite width of the $\rho$ meson is investigated, where a significant enhancement of photon production in the low-energy region is observed. This benchmark is the first step towards a consistent treatment of photon emission in hybrid hydrodynamics+transport approaches and a genuine dynamical description.

RMF models with $\sigma$-scaled hadron masses and couplings for the description of heavy-ion collisions below 2 A GeV

Within the relativistic mean-field framework with hadron masses and coupling constants dependent on the mean scalar field we study properties of nuclear matter at finite temperatures, baryon densities and isospin asymmetries relevant for heavy-ion collisions at laboratory energies below 2$A$ GeV. Previously constructed (KVORcut-based and MKVOR-based) models for the description of the cold hadron matter, which differ mainly by the density dependence of the nucleon effective mass and symmetry energy, are extended for finite temperatures. The baryon equation of state, which includes nucleons and $\Delta$ resonances is supplemented by the contribution of the pion gas described either by the vacuum dispersion relation or with taking into account the $s$-wave pion-baryon interaction. Distribution of the charge between components is found. Thermodynamical characteristics on $T-n$ plane are considered. The energy-density and entropy-density isotherms are constructed and a dynamical trajectory of the hadron system formed in heavy-ion collisions is described. The effects of taking into account the $\Delta$ isobars and the $s$-wave pion-nucleon interaction on pion differential cross sections, pion to proton and $\pi^-/\pi^+$ ratios are studied. The liquid-gas first-order phase transition is studied within the same models in isospin-symmetric and asymmetric systems. We demonstrate that our models yield thermodynamic characteristics of the phase transition compatible with available experimental results. In addition, we discuss the scaled variance of baryon and electric charge in the phase transition region. Effect of the non-zero surface tension on spatial redistribution of the electric charge is considered for a possible application to heavy-ion collisions at low energies.

Heavy-quark spin and flavor symmetry partners of the X(3872) revisited: What can we learn from the one boson exchange model?

Heavy-quark symmetry as applied to heavy hadron systems implies that their interactions are independent of their heavy-quark spin (heavy-quark spin symmetry) and heavy flavour contents (heavy flavour symmetry). In the molecular hypothesis the $X(3872)$ resonance is a $1^{++}$ $D^*\bar{D}$ bound state. If this is the case, the application of heavy-quark symmetry to a molecular $X(3872)$ suggests the existence of a series of partner states, the most obvious of which is a possible $2^{++}$ $D^*\bar{D}^*$ bound state for which the two-body potential is identical to that of the $1^{++}$ $D^*\bar{D}$ system, the reason being that these two heavy hadron-antihadron states have identical light-spin content. As already discussed in the literature this leads to the prediction of a partner state at $4012\,{\rm MeV}$, at least in the absence of other dynamical effects which might affect the location of this molecule. However the prediction of further heavy-quark symmetry partners cannot be done solely on the basis of symmetry and requires additional information. We propose to use the one boson exchange model to fill this gap, in which case we will be able to predict or discard the existence of other partner states. Besides the isoscalar $2^{++}$ $D^*\bar{D}^*$ bound state, we correctly reproduce the location and quantum numbers of the isovector hidden-bottom $Z_b(10610)$ and $Z_b(10650)$ molecular candidates. We also predict the hidden-bottom $1^{++}$ $B^*\bar{B}^*$ and $2^{++}$ $B^*\bar{B}^*$ partners of the $X(3872)$, in agreement with previous theoretical speculations, plus a series of other states. The isoscalar, doubly charmed $1^+$ $D D^*$ and $D^* D^*$ molecules and their doubly bottomed counterparts are likely to bind, providing a few instances of explicitly exotic systems.

Thermodynamical Investigation of the Quark-Gluon Plasma Phase near the Deconfining Phase Transition

We investigate, in the present work, some thermodynamical properties of a Quark-Gluon Plasma (QGP), near the thermal deconfining phase transition, at vanishing chemical potential. We project the QGP partition function onto the color-singlet SU(3) representation using a density of states once containing the volume term only, then containing the curvature and the volume terms, according to the Multiple Reflection Expansion approximation. We study the evolution of some physical quantities well describing the mixed hadronic gas-QGP system. We compare the present results to those obtained in our previous works.

Study of the decay K^{+}rightarrow pi ^{+}pi ^{-}pi ^{+}gamma in the OKA experiment

A high statistics data sample of the decays of K^+ mesons to three charged particles was accumulated by the OKA experiment in 2012 and 2013. This allowed to select a clean sample of about 450 events with K^{+}rightarrow pi ^{+}pi ^{-}pi ^{+}gamma decays with the energy of the photon in the kaon rest frame greater than 30 MeV. The measured branching fraction of the K^{+}rightarrow pi ^{+}pi ^{-}pi ^{+}gamma , with E_{gamma }^{*} > 30 hbox {MeV} is equal to (0.71 pm 0.05) times 10^{-5}. The measured differential branching fraction over photon energy is compared with the prediction of the chiral perturbation theory to {mathcal {O}}(p^{4}). A search for an up-down asymmetry of the photon with respect to the hadronic system decay plane is also performed.

Maximum Entropy Principle in Statistical Inference: Case for Non-Shannonian Entropies.

In this Letter, we show that the Shore-Johnson axioms for the maximum entropy principle in statistical estimation theory account for a considerably wider class of entropic functional than previously thought. Apart from a formal side of the proof where a one-parameter class of admissible entropies is identified, we substantiate our point by analyzing the effect of weak correlations and by discussing two pertinent examples: two-qubit quantum system and transverse-momentum behavior of hadrons in high-energy proton-proton collisions.

Chromo-Electric Field Energy in Quark Models

We study the contribution of the chromo-electric field to the total energy of the hadrons. We analyze the case of quarks considered as extended sources of the field. Specific forms of the interaction potential of the quarks are obtained. Moreover, the color charge distribution of these sources allows to determine the zero point energy that is commonly introduced, as a free (independent) parameter, in the total quark model Hamiltonian of the hadronic systems. The ground states of charmonium ($q \bar q$) and nucleon ($ q q q$) are studied in more detail: their mass is calculated within a relativized dynamical model and the expectation value of the chromo-electric field energy is consistently obtained. \end{abstract}

Theoretical aspects of quantum electrodynamics in a finite volume with periodic boundary conditions

First-principles studies of strongly-interacting hadronic systems using lattice quantum chromodynamics (QCD) have been complemented in recent years with the inclusion of quantum electrodynamics (QED). The aim is to confront experimental results with more precise theoretical determinations, e.g. for the anomalous magnetic moment of the muon and the CP-violating parameters in the decay of mesons. Quantifying the effects arising from enclosing QED in a finite volume remains a primary target of investigations. To this end, finite-volume corrections to hadron masses in the presence of QED have been carefully studied in recent years. This paper extends such studies to the self-energy of moving charged hadrons, both on and away from their mass shell. In particular, we present analytical results for leading finite-volume corrections to the self-energy of spin-0 and spin-$\frac{1}{2}$ particles in the presence of QED on a periodic hypercubic lattice, once the spatial zero mode of the photon is removed, a framework that is called $\mathrm{QED}_{\mathrm{L}}$. By altering modes beyond the zero mode, an improvement scheme is introduced to eliminate the leading finite-volume corrections to masses, with potential applications to other hadronic quantities. Our analytical results are verified by a dedicated numerical study of a lattice scalar field theory coupled to $\mathrm{QED}_{\mathrm{L}}$. Further, this paper offers new perspectives on the subtleties involved in applying low-energy effective field theories in the presence of $\mathrm{QED}_{\mathrm{L}}$, a theory that is rendered non-local with the exclusion of the spatial zero mode of the photon, clarifying recent discussions on this matter.

Finite-Volume Spectrum of π^{+}π^{+} and π^{+}π^{+}π^{+} Systems.

The abinitio understanding of hadronic three-body systems above threshold, such as exotic resonances or the baryon spectrum, requires the mapping of the finite-volume eigenvalue spectrum, produced in lattice QCD calculations, to the infinite volume. We present the first application of such a formalism to a physical system in form of three interacting positively charged pions. The results for the ground state energies agree with the available lattice QCD results by the NPLQCD collaboration at unphysical pion masses. Extrapolations to physical pion masses are performed using input from effective field theory. The excited energy spectrum is predicted. This demonstrates the feasibility to determine three-body amplitudes above threshold from lattice QCD, including resonance properties of axial mesons, exotics, and excited baryons.

Electromagnetic currents for dressed hadrons

We propose an extension of the minimal-substitution prescription for coupling the electromagnetic field to hadronic systems with internal structure. The resulting rules of extended substitution necessarily distinguish between couplings to scalar and Dirac particles. Moreover, they allow for the incorporation of electromagnetic form factors for virtual photons in an effective phenomenological framework. Applied to pions and nucleons, assumed to be fully dressed to all orders, the resulting dressed currents are shown to be locally gauge invariant. Moreover, half-on-shell expressions of (hadron propagator)$\times$(electromagnetic current) needed in all descriptions of physical processes will lose \textit{all} information about hadronic dressing for real photons. The Ball-Chiu ansatz for the spin-1/2 current is seen to suffer from an incomplete coupling procedure where some essential aspects of the Dirac particle are effectively treated as those of a scalar particle. Applied to real Compton scattering on pions and nucleons, we find that \emph{all} dressing information cancels exactly when external hadrons are on shell, leaving only gauge-invariant bare Born-type contributions with physical masses. Hence, nontrivial descriptions necessarily require contact-type two-photon processes obtained by hadrons looping around two photon insertion points.

Electric dipole moments of atoms, molecules, nuclei, and particles

A permanent electric dipole moment (EDM) of a particle or system is a separation of charge along its angular-momentum axis and is a direct signal of T-violation and, assuming CPT symmetry, CP violation. For over sixty years EDMs have been studied, first as a signal of a parity-symmetry violation and then as a signal of CP violation that would clarify its role in nature and in theory. Contemporary motivations include the role that CP violation plays in explaining the cosmological matter-antimatter asymmetry and the search for new physics. Experiments on a variety of systems have become ever-more sensitive, but provide only upper limits on EDMs, and theory at several scales is crucial to interpret these limits. Nuclear theory provides connections from Standard-Model and Beyond-Standard-Model physics to the observable EDMs, and atomic and molecular theory reveal how CP-violation is manifest in these systems. EDM results in hadronic systems require that the Standard Model QCD parameter of $\bar\theta$ must be exceptionally small, which could be explained by the existence of axions - also a candidate dark-matter particle. Theoretical results on electroweak baryogenesis show that new physics is needed to explain the dominance of matter in the universe. Experimental and theoretical efforts continue to expand with new ideas and new questions, and this review provides a broad overview of theoretical motivations and interpretations as well as details about experimental techniques, experiments, and prospects. The intent is to provide specifics and context as this exciting field moves forward.

Constituent quark models for hadronic systems

In this work we introduce two different potential models for hadronic systems such that the QCD concepts of the quark-quark and quark-antiquark interactions be satisfied. We present the simple methods to solve two- and three-body equation of meson and baryon systems respectively. The introduced models are studied in the relativistic and non-relativistic limits.

Equilibration in fermionic systems

The time evolution of a finite fermion system towards local statistical equilibrium is investigated using analytical solutions of a nonlinear partial differential equation that had been derived earlier from the Boltzmann collision term. The solutions of this fermionic diffusion equation are rederived in closed form, evaluated exactly for simplified initial conditions, and applied to hadron systems at low energies in the MeV-range, as well as to quark systems at relativistic energies in the TeV-range where antiparticle production is abundant. Conservation laws for particle number including created antiparticles, and for the energy are discussed.

Hadronic Paschen–Back effect

We find a novel phenomenon induced by the interplay between a strong magnetic field and finite orbital angular momenta in hadronic systems, which is analogous to the Paschen–Back effect observed in the field of atomic physics. This effect allows the wave functions to drastically deform. We discuss anisotropic decay from the deformation as a possibility to measure the strength of the magnetic field in high-energy heavy-ion collisions, which has not been measured experimentally. As an example we investigate charmonia with a finite orbital angular momentum in a strong magnetic field. We calculate the mass spectra and mixing ratios. To obtain anisotropic wave functions, we apply the cylindrical Gaussian expansion method. There we use different extension parameters for the parallel and transverse directions to the magnetic field.

K− over K+ multiplicity ratio for kaons produced in DIS with a large fraction of the virtual-photon energy

The K− over K+ multiplicity ratio is measured in deep-inelastic scattering, for the first time for kaons carrying a large fraction z of the virtual-photon energy. The data were obtained by the COMPASS collaboration using a 160 GeV muon beam and an isoscalar 6LiD target. The regime of deep-inelastic scattering is ensured by requiring Q2>1(GeV/c)2 for the photon virtuality and W>5GeV/c2 for the invariant mass of the produced hadronic system. Kaons are identified in the momentum range from 12 GeV/c to 40 GeV/c, thereby restricting the range in Bjorken-x to 0.01<x<0.40. The z-dependence of the multiplicity ratio is studied for z>0.75. For very large values of z, i.e.z>0.8, we observe the kaon multiplicity ratio to fall below the lower limits expected from calculations based on leading and next-to-leading order perturbative quantum chromodynamics. Also, the kaon multiplicity ratio shows a strong dependence on the missing mass of the single-kaon production process. This suggests that within the perturbative quantum chromodynamics formalism an additional correction may be required, which takes into account the phase space available for hadronisation.

Erratum to: Differential branching fraction and angular analysis of Λ b 0 → Λμ + μ − decays

The differential branching fraction of the rare decay $\Lambda^{0}_{b} \rightarrow \Lambda \mu^+\mu^-$ is measured as a function of $q^{2}$, the square of the dimuon invariant mass. The analysis is performed using proton-proton collision data, corresponding to an integrated luminosity of $3.0 \mbox{ fb}^{-1}$, collected by the LHCb experiment. Evidence of signal is observed in the $q^2$ region below the square of the $J/\psi$ mass. Integrating over $15 < q^{2} < 20 \mbox{ GeV}^2/c^4$ the branching fraction is measured as $d\mathcal{B}(\Lambda^{0}_{b} \rightarrow \Lambda \mu^+\mu^-)/dq^2 = (1.18 ^{+ 0.09} _{-0.08} \pm 0.03 \pm 0.27) \times 10^{-7} ( \mbox{GeV}^{2}/c^{4})^{-1}$, where the uncertainties are statistical, systematic and due to the normalisation mode, $\Lambda^{0}_{b} \rightarrow J/\psi \Lambda$, respectively. In the $q^2$ intervals where the signal is observed, angular distributions are studied and the forward-backward asymmetries in the dimuon ($A^{l}_{\rm FB}$) and hadron ($A^{h}_{\rm FB}$) systems are measured for the first time. In the range $15 < q^2 < 20 \mbox{ GeV}^2/c^4$ they are found to be $A^{l}_{\rm FB} = -0.05 \pm 0.09 \mbox{ (stat)} \pm 0.03 \mbox{ (syst)}$ and $A^{h}_{\rm FB} = -0.29 \pm 0.07 \mbox{ (stat)} \pm 0.03 \mbox{ (syst)}$.

Beautiful mathematics for beauty-full and other multi-heavy hadronic systems

In most non-perturbative methods in hadron physics the calculations are started with a correlation function in terms of some interpolating and transition currents in $ x $-space. For simplicity, the calculations are then transformed to the momentum space by a Fourier transformation. To suppress the contributions of the higher states and continuum; and enhance the ground state contribution, Borel transformation as well as continuum subtraction are applied by the help of quark-hadron duality assumption. In the present study we work out the mathematics required for these processes in the case of light and multi-heavy hadrons. We address a well-known problem in subtraction of the effects of the higher states and continuum and discuss how we find finite results without any divergence by using an appropriate representation of the modified Bessel functions, appearing in the heavy quark propagator, and successive applications of the Borel transformations, which lead to more suppression of the higher states and continuum contributions. The results obtained can be used in determination of the spectroscopic and decay properties of the multi-heavy standard and non-conventional (exotic) systems in many non-perturbative methods, specially the QCD sum rules.

Energy reconstruction of hadrons in highly granular combined ECAL and HCAL systems

This paper discusses the hadronic energy reconstruction of two combined electromagnetic and hadronic calorimeter systems using physics prototypes of the CALICE collaboration: the silicon-tungsten electromagnetic calorimeter (Si-W ECAL) and the scintillator-SiPM based analog hadron calorimeter (AHCAL); and the scintillator-tungsten electromagnetic calorimeter (ScECAL) and the AHCAL. These systems were operated in hadron beams at CERN and FNAL, permitting the study of the performance in combined ECAL and HCAL systems. Two techniques for the energy reconstruction are used, a standard reconstruction based on calibrated sub-detector energy sums, and one based on a software compensation algorithm making use of the local energy density information provided by the high granularity of the detectors. The software compensation-based algorithm improves the hadronic energy resolution by up to 30% compared to the standard reconstruction. The combined system data show comparable energy resolutions to the one achieved for data with showers starting only in the AHCAL and therefore demonstrate the success of the inter-calibration of the different sub-systems, despite of their different geometries and different readout technologies.

Quasielastic neutrino charged-current scattering off C12 : Effects of the meson exchange currents and large nucleon axial mass

The quasi-elastic scattering of muon neutrino and electrons on a carbon target are analyzed using the relativistic distorted-wave impulse approximation (RDWIA). We also evaluate the contribution of the two-particle and two-hole meson exchange current ($2p-2h$ MEC) to electroweak response functions. The nuclear model dependence of the (anti)neutrino cross sections is studied within the RDWIA+MEC approach and RDWIA model with the large nucleon axial mass. It is shown that the results for the squared momentum transfer distribution $d\sigma/dQ^2$ and for invariant mass of the final hadronic system distribution $d\sigma/dW$ obtained within these models are substantially different.