We present a first model-independent calculation of $ππ$ intermediate states in the hadronic-light-by-light (HLbL) contribution to the anomalous magnetic moment of the muon $(g-2)_μ$ that goes beyond the scalar QED pion loop. To this end we combine a recently developed dispersive description of the HLbL tensor with a partial-wave expansion and demonstrate that the known scalar-QED result is recovered after partial-wave resummation. Using dispersive fits to high-statistics data for the pion vector form factor, we provide an evaluation of the full pion box, $a_μ^{π\text{-box}}=-15.9(2)\times 10^{-11}$. We then construct suitable input for the $γ^*γ^*\toππ$ helicity partial waves based on a pion-pole left-hand cut and show that for the dominant charged-pion contribution this representation is consistent with the two-loop chiral prediction and the COMPASS measurement for the pion polarizability. This allows us to reliably estimate $S$-wave rescattering effects to the full pion box and leads to our final estimate for the sum of these two contributions: $a_μ^{π\text{-box}} + a_{μ,J=0}^{ππ,π\text{-pole LHC}}=-24(1)\times 10^{-11}$.
A method for modelling the prompt production of molecular states using the hadronic rescattering framework of the general-purpose Pythia event generator is introduced. Production cross sections of possible exotic hadronic molecules via hadronic rescattering at the LHC are calculated for the $χ_{c1}(3872)$ resonance, a possible tetraquark state, as well as three possible pentaquark states, $P_c^+(4312)$, $P_c^+(4440)$, and $P_c^+(4457)$. For the $P_c^+$ states, the expected cross section from $Λ_b$ decays is compared to the hadronic-rescattering production. The $χ_{c1}(3872)$ cross section is c…
A kinematic model based on the superposition of p+p collisions, relativistic geometry and final-state hadronic rescattering is used to predict various hadronic observables in \surd sNN = 2.76 TeV Pb+Pb collisions. Predictions for rapidity and transverse momentum distributions, elliptic flow, and two-boson femtoscopy are presented. A short proper time for hadronization is assumed. Previous calculations using this model which were performed for \surd sNN = 200 GeV Au+Au collisions were shown to describe reasonably well the trends of observables in experiments carried out at that energy, giving t…
In a recent article we presented a model for hadronic rescattering, and some results were shown for pp collisions at LHC energies. In order to extend the studies to pA and AA collisions, the Angantyr model for heavy-ion collisions is taken as the starting point. Both these models are implemented within the general-purpose Monte Carlo event generator Pythia, which makes the matching reasonably straightforward, and allows for detailed studies of the full space--time evolution. The rescattering rate is significantly higher than in pp, especially for central AA collisions, where the typical primar…
We study the effects of hadronic rescattering on hadron distributions in high-energy nuclear collisions by using an integrated dynamical approach. This approach is based on a hybrid model combining (3+1)-dimensional ideal hydrodynamics for the quark gluon plasma (QGP), and a transport model for the hadron resonance gas. Since the hadron distributions are the result of the entire expansion history of the system, understanding the QGP properties requires investigating how rescattering during the hadronic stage affects the final distributions of hadrons. We include multistrange hadrons in our stu…
The $σ$ resonance was observed as a conspicuous $π^+π^-$ peak in hadronic decays like $J/ψ\to π^+π^-ω$ or $D^+\toπ^+π^-π^+$. The phase of the $σ\toπ^+π^-$ amplitude, extracted from production data within the conventional isobar model, is assumed to coincide with that in $ππ$ elastic scattering. We check the validity of this assumption by using Lehmann-Symanzik-Zimmermann (LSZ) reduction and unitarity. The rescattering effects in the final three-particle states are shown to generate a correction to the phase given by a naive application of Watson theorem. We briefly discuss the implications of …
In this article, a framework for hadronic rescattering in the general-purpose Pythia event generator is introduced. The starting point is the recently presented space-time picture of the hadronization process. It is now extended with a tracing of the subsequent motion of the primary hadrons, including both subsequent scattering processes among them and decays of them. The major new component is cross-section parameterizations for a range of possible hadron-hadron combinations, applicable from threshold energies upwards. The production dynamics in these collisions has also been extended to cope…
A model for the $B^\pm \to π^-π^+π^\pm$ decay amplitude is proposed to study the large CP violation observed at the high mass region of the Dalitz plane. A short distance $ b \to u $ amplitude with the weak phase $γ$ is considered together with the contribution of a hadronic charm loop and a s-wave $D\bar{D}\to ππ$ rescattering. In the model, the $χ_c^0$ appears as a narrow resonant state of the $D\bar D$ system below threshold. It is introduced in an unitary two channel S-matrix model of the coupled $D\bar D$ and $ππ$ channels, where the $χ_c^0$ complex pole in $D\bar D$ channel shows its sig…
Higher-order hadronic corrections to the anomalous magnetic moment of the muon have been evaluated including next-to-next-to-leading-order insertions of hadronic vacuum polarization and next-to-leading-order corrections to hadronic light-by-light scattering. This leaves a set of mixed leptonic and hadronic corrections in the form of double-bubble topologies as the only remaining hadronic effect at ${\mathcal O}(α^4)$. Here, we estimate these contributions by analyzing the respective cuts of the diagrams, suggesting that the impact is limited to $\lesssim 1\times 10^{-11}$ and thus negligible a…
We study effects of the hadronic rescattering on final observables especially for multi-strange hadrons such as $ϕ$, $Ξ$ and $Ω$ in high-energy heavy-ion collisions within an integrated dynamical approach. In this approach, (3+1)-dimensional ideal hydrodynamics is combined with a microscopic transport model, JAM. We simulate the collisions with or without hadronic rescatterings and compare observables between these two options so that we quantify the effects of the hadronic rescattering. We find that the mean transverse momentum and the elliptic flow parameter of multi-strange hadrons are less…
We study phi photoproduction with various hadronic rescattering contributions included, in addition to the Pomeron and pseudoscalar meson-exchange diagrams. We find that the hadronic box diagrams can explain the recent experimental data in the vicinity of the threshold. In particular, the bump-like structure at the photon energy E_gamma \approx 2.3$ GeV is well explained by the K Lambda(1520) rescattering amplitude in the intermediate state, which is the dominant contribution among other hadronic contributions. We also find that the hadronic box diagrams are consistent with the observed spin-d…
The hadronic phase in ultrarelativistic nuclear collisions has a large influence on final state observables like multiplicity, flow and $p_t$ spectra, as studied in the UrQMD approach. In this model one assumes that a non-equilibrium decoupling phase follows a fluid dynamical description of the high density phase. Hadrons are produced assuming local thermal equilibrium and dynamically decouple during the hadronic rescattering until the particles are registered in the detectors. This rescattering of hadrons modifies every hadronic bulk observable. The apparent multiplicity of resonances is supp…
Hadronic resonance propagators which take into account the analytical properties of decay processes are built in terms of the dispersion relation technique. Such propagators can describe multi-component systems, for example, those when quark degrees of freedom create a resonance state, and decay products correct the corresponding pole by adding hadronic deuteron-like components. Meson and baryon states are considered, examples of particles with different spins are presented.
There exist many experimental indications that final-state interactions (FSIs) may play a prominent role not only in charmful B decays but also in charmless B ones. We examine the final-state rescattering effects on the hadronic B decay rates and their impact on direct CP violation. The color-suppressed neutral modes such as $B^0\to D^0π^0,π^0π^0,ρ^0π^0,K^0π^0$ can be substantially enhanced by long-distance rescattering effects. The direct CP-violating partial rate asymmetries in charmless B decays to $ππ/πK$ and $ρπ$ are significantly affected by final-state rescattering and their signs are g…
We discuss the hadronic contributions to the muon anomalous magnetic moment. They are dominated by light quark contributions which are constrained by the mechanism of chiral symmetry breaking. Using the leading order result based on $e^+ e^-$ scattering data, we show that the next-to-leading order contributions in the fine structure constant $α$ can be reliably calculated. Extending this idea to the hadronic four-point function we give a prediction for the light-by-light contribution.
We study the elliptic flow coefficient v_2(eta,b) in Au+Au collisions at sqrt(s)=200 A GeV as a function of pseudorapidity eta and impact parameter b. Using a hybrid approach which combines early ideal fluid dynamical evolution with late hadronic rescattering, we demonstrate strong dissipative effects from the hadronic rescattering stage on the elliptic flow. With Glauber model initial conditions, hadronic dissipation is shown to be sufficient to fully explain the differences between measured v_2 values and ideal hydrodynamic predictions. Initial conditions based on the Color Glass Condensate …
Recently, it was shown that insertions of hadronic vacuum polarization at O(alpha^4) generate non-negligible effects in the calculation of the anomalous magnetic moment of the muon. This result raises the question if other hadronic diagrams at this order might become relevant for the next round of g-2 measurements as well. In this note we show that a potentially enhanced such contribution, hadronic light-by-light scattering in combination with electron vacuum polarization, is already sufficiently suppressed.
Final-state rescattering effects on the hadronic B decays and their impact on direct CP violation are examined. The phenomenology of the polarization anomaly in $B\toϕK^*$ decays is discussed.
I discuss the effect of final state interactions on the determination of the CKM angle γfrom B -> K + pi decays. Using a simple Regge-based model for rescattering processes, I argue that such effects could be substantial enough to make it problematic to obtain reliable limits on γin this way. Fortunately, an analysis of B -> K + K decays may provide model-independent bounds on rescattering contributions.
A calculation of the hadronic matrix elements for K\toππincluding π-πrescattering effects in a dispersion integral is presented. I study the dependence of the results on the matching scale μand use them to calculate the CP-parameter (ε\prime/ε). I find improved stability on the matching scale and good agreement with the experimental results.
We present the status of the MUonE experimental proposal which aims at determining the leading order hadronic contribution to the muon g-2 by measuring the hadronic part of the photon vacuum polarization in the spacelike region. The challenges posed by this measurement on the detector, the proposed solution, and the status of this proposal will be discussed.
The MUonE proposal at the CERN SPS consists in extracting the value of the hadronic vacuum polarization self-energy function (HVP) from its contribution to the differential cross-section of elastic muon-electron scattering. The HVP contribution to the muon anomalous magnetic moment can then be obtained from a weighted integral of the measured HVP self-energy function. This, however, requires a knowledge of the HVP function in its full integration domain. This paper discusses a procedure to reconstruct the HVP function in the regions not directly accessible to measurement. The method is based o…
We report on our progress toward the computation of the $π^0$, $η$ and $η^{\prime}$ transition form factors using staggered quarks on $N_f=2+1+1$ gauge ensembles generated by the Budapest-Marseille-Wuppertal collaboration. These form factors are essential ingredients to evaluate the pseudoscalar-pole contributions to the hadronic light-by-light scattering in the muon $g-2$. Preliminary results for the pseudoscalar-pole contributions are presented, at finite lattice spacing, for all three light mesons.
Using a relativistic hydrodynamics + hadronic afterburner simulation we explore resonance production in PbPb collisions at 5.02 TeV, and demonstrate that many resonance yields, mean transverse momenta, and flows are very sensitive to the late stage hadronic rescattering. Out of all measured resonances $Λ(1520)$ is affected strongest by the hadronic rescattering stage, which allows to estimate its duration, and even constrain branching ratios of $Σ^* \to Λ(1520)π$ decays. Strong suppression of $Λ(1520)$, which in vacuum has a lifetime of 12.6 fm/$c$, is explained by its small lifetime in a hadr…
We present a calculation of the hadronic vacuum polarization (HVP) tensor within the framework of Dyson--Schwinger equations. To this end we use a well-established phenomenological model for the quark-gluon interaction with parameters fixed to reproduce hadronic observables. From the HVP tensor we compute both the Adler function and the HVP contribution to the anomalous magnetic moment of the muon, $a_μ$. We find $a_μ^{HVP}= 6760\times 10^{-11}$ which deviates about two percent from the value extracted from experiment. Additionally, we make comparison with a recent lattice determination of $a_…
We present a Lorentz-covariant, Euclidean coordinate-space expression for the hadronic vacuum polarisation, the Adler function and the leading hadronic contribution to the anomalous magnetic moment of the muon. The representation offers a lot of flexibility for an implementation in lattice QCD. We expect it to be particularly helpful for the quark-line disconnected contributions.
In view of the current 3 - 4 $σ$ deviation between theoretical and experimental values for the muon's anomalous magnetic moment, we review the ongoing efforts in constraining the hadronic light-by-light contribution to $a_μ$ by using dispersive techniques combined with a dedicated experimental program to obtain the required hadronic input.
We give a status report on the hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment from the Dyson-Schwinger approach. We discuss novel, model-independent properties of the light-by-light amplitude: we give its covariant decomposition in view of electromagnetic gauge invariance and Bose symmetry, and we identify the relevant kinematic regions that are probed under the integral. The decomposition of the amplitude at the quark level and the importance of its various diagrams are discussed and related to model approaches.
We present simple analytic expressions to compute the hadronic vacuum polarization contribution to the muon $g$-2 in the space-like region up to next-to-next-to-leading order. These results can be employed in lattice QCD calculations of this contribution as well as in space-like determinations based on scattering data, like that expected from the proposed MUonE experiment at CERN.
The Standard Model prediction for muon-electron scattering beyond leading order requires the inclusion of QCD contributions which cannot be computed perturbatively. At next-to- and next-to-next-to-leading order, they arise from one- and two-loop diagrams with hadronic vacuum polarization insertions in the photon propagator. We present their evaluation using the dispersive approach with hadronic $e^+e^-$ annihilation data and estimate their uncertainty. We find that these corrections are crucial for the analysis of future high-precision muon-electron scattering data, like those of the recently …
Contributions of hadronic effects to the muonium physics and anomalous magnetic moment of muon are considered. Special attention is paid to higher-order effects and the uncertainty related to the hadronic contribution to the hyperfine structure interval in the ground state of muonium.
I present a preliminary calculation of the hadronic vacuum polarization for 2+1 flavors of improved Kogut-Susskind quarks by utilizing a set of gauge configurations recently generated by the MILC collaboration. The polarization function $Π(q^2)$ is then used to calculate the lowest order (in $α_{QED}$) hadronic contribution to the muon anomalous magnetic moment.
Hadronic light-by-light scattering in the anomalous magnetic moment of the muon $a_μ$ is one of two hadronic effects limiting the precision of the Standard Model prediction for this precision observable, and hence the new-physics discovery potential of direct experimental determinations of $a_μ$. In this contribution, we report on recent progress in the calculation of this effect achieved both via dispersive and lattice QCD methods.
After a brief self-contained introduction to the muon anomalous magnetic moment, (g-2), we review the status of lattice calculations of the hadronic vacuum polarization contribution and present first results from lattice QCD for the hadronic light-by-light scattering contribution. The signal for the latter is consistent with model calculations. While encouraging, the statistical error is large and systematic errors are mostly uncontrolled. The method is applied first to pure QED as a check.
The hadronic contributions to the anomalous magnetic moment of the muon which are relevant for the confrontation between theory and experiment at the present level of accuracy, are evaluated within the same framework: the constituent chiral quark model. This includes the contributions from the dominant hadronic vacuum polarization as well as from the next--to--leading order hadronic vacuum polarization, the contributions from the hadronic light-by-light scattering, and the contributions from the electroweak hadronic $Zγγ$ vertex. They are all evaluated as a function of only one free parameter:…
The concept of multiple partonic interactions in hadronic events is vital for the understanding of both minimum-bias and underlying-event physics. The area is rather little studied, however, and current models offer a far from complete coverage, even of the effects we know ought to be there. In this article we address one such topic, namely that of rescattering, where an already scattered parton is allowed to take part in another subsequent scattering. A framework for rescattering is introduced for the Pythia 8 event generator and fully integrated with normal multiparton interactions and initi…
The complete set of relations, which mutually express the spacelike and timelike kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment $a^{\text{HVP}}_μ$ in terms of each other, is obtained. By making use of the derived relations the explicit expression for the next-to-leading order spacelike kernel function, which enters the representation for $a^{\text{HVP}}_μ$ involving the hadronic vacuum polarization function, is obtained. The corresponding next-to-leading order spacelike kernel function, which appears in the representation for $a^{\text{…
We give a short overview of the theory of the muon anomalous magnetic moment with emphasis on the hadronic light-by-light and the pion loop contribution. We explain the difference between the hidden local symmetry and full VMD pion loop and discuss leading logarithms in the anomalous sector of 2-flavour chiral perturbation theory.
The form factor that yields the light-by-light scattering contribution to the muon anomalous magnetic moment is computed in lattice QCD+QED and QED. A non-perturbative treatment of QED is used and is checked against perturbation theory. The hadronic contribution is calculated for unphysical quark and muon masses, and only the diagram with a single quark loop is computed. Statistically significant signals are obtained. Initial results appear promising, and the prospect for a complete calculation with physical masses and controlled errors is discussed.
Final-state rescattering effects on the hadronic B decays and their impact on direct and mixing-induced CP asymmetries are examined. Implications for some phenomenologies are briefly discussed.
We discuss hadronic effects in the muonium hyperfine structure and derive an expression for the hadronic contribution to the hfs interval in form of the one-dimensional integral of the cross section of e+e- annihilation into hadrons. Higher-order hadronic contributions are also considered.
We report preliminary results for the hadronic light-by-light scattering contribution to the muon anomalous magnetic moment. Several ensembles using 2+1 flavors of Möbius domain-wall fermions, generated by the RBC/UKQCD collaborations, are employed to take the continuum and infinite volume limits of finite volume lattice QED+QCD. We find $a_μ^{\rm HLbL} = (7.41\pm6.33)\times 10^{-10}$
The lowest order hadronic contribution to the $g-2$ factor of the muon is analyzed in the framework of the operator product expansion at short distances, and a QCD finite energy sum rule designed to quench the role of the $e^+ e^-$ data. This procedure reduces the discrepancy between experiment and theory, $Δa_μ\equiv a^{EXP}_μ- a^{SM}_μ$, from $Δa_μ= 28.7 (8.0) \times 10^{-10}$ to $Δa_μ= 19.2 (8.0) \times 10^{-10}$, i.e. without changing the uncertainty.
Some short-distance properties of the fourth-rank hadronic vacuum polarization tensor are re-examined.Their consequences are critically discussed in the context of the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon.
The well-known discrepancy in the muon $g-2$ between experiment and theory demands further theory investigations in view of the upcoming new experiments. One of the leading uncertainties lies in the hadronic light-by-light scattering contribution (HLbL), that we address with our position-space approach. We focus on exploratory studies of the pion-pole contribution in a simple model and the fermion loop without gluon exchanges in the continuum and in infinite volume. These studies provide us with useful information for our planned computation of HLbL in the muon $g-2$ using full QCD.
The leading hadronic contribution to the muon anomalous magnetic moment is given by a weighted integral over euclidean momentum of the hadronic vacuum polarization. This integral is dominated by momenta of order the muon mass. Since the finite volume in lattice QCD makes it difficult to compute the vacuum polarization at a large number of low momenta with high statistics (combined with the fact that one cannot compute it at zero momentum), a parametrization of the vacuum polarization is required to extrapolate the data. A much used functional form is based on vector meson dominance, which intr…
We propose a novel approach to determine the leading hadronic corrections to the muon g-2. It consists in a measurement of the effective electromagnetic coupling in the space-like region extracted from Bhabha scattering data. We argue that this new method may become feasible at flavor factories, resulting in an alternative determination potentially competitive with the accuracy of the present results obtained with the dispersive approach via time-like data.
We evaluate the hadronic contribution to the $g-2$ of the muon by deriving the low-energy limit of quantum chromodynamics (QCD) and computing in this way the hadronic vacuum polarization. The low-energy limit is a non-local Nambu--Jona-Lasinio (NJL) model that has all the parameters fixed from QCD, and the only experimental input used is the confinement scale that is known from measurements of hadronic physics. Our estimations provide a novel analytical alternative to the current lattice computations and we find that our result is close to the similar computation performed from experimental da…
The hadronic light-by-light contribution to a_{mu}, the anomalous magnetic moment of the muon, is discussed from the point of view of an effective low-energy theory. As an application, the coefficient of the leading logarithm arising from the two-loop graphs involving two anomalous vertices is computed, and found to be positive. This corresponds to a positive sign for the pion-pole contribution to the hadronic light-by-light correction to a_{mu}, and to a sizeable reduction of the discrepancy between the present experimental value of a_{mu} and its theoretical counterpart in the standard model…
Using the gauge/gravity duality, we compute the leading order hadronic (HLO) contribution to the anomalous magnetic moment of muon, amu(HLO). Holographic renormalization is used to obtain a finite vacuum polarization. We find amu(HLO) =470.5 x 10^{-10} in AdS/QCD with two light flavors, which is compared with the currently revised BABAR data estimated from e^+ e^- -> pi^+ pi^- events, amu(HLO)[pipi]=(514.1 +- 3.8) x 10^{-10}.
