arXiv subjects

Igor Danilkin

Publications and source records attributed to Igor Danilkin.

29 records · Page 2Linked to original sources

arXiv2021

Data-driven dispersive analysis of the $ππ$ and $πK$ scattering

We present a data-driven analysis of the resonant S-wave $ππ\to ππ$ and $πK \to πK$ reactions using the partial-wave dispersion relation. The contributions from the left-hand cuts are accounted for using the Taylor expansion in a suitably constructed conformal variable. The fits are performed to experimental and lattice data as well as Roy analyses. For the $ππ$ scattering we present both a single- and coupled-channel analysis by including additionally the $K\bar{K}$ channel. For the latter the central result is the Omnès matrix, which is consistent with the most recent Roy and Roy-Steiner results on $ππ\to ππ$ and $ππ\to K\bar{K}$, respectively. By the analytic continuation to the complex plane, we found poles associated with the lightest scalar resonances $σ/f_0(500)$, $f_0(980)$, and $κ/K_0^*(700)$ for the physical pion mass value and in the case of $σ/f_0(500)$, $κ/K_0^*(700)$ also for unphysical pion mass values.

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arXiv2020

Light-by-light scattering sum rule for radiative transitions of bottomonia

We generalize a forward light-by-light scattering sum rule to the case of heavy quarkonium radiative transitions. We apply such sum rule to the bottomonium states, and use available data on radiative transitions in its evaluation. For the transitions that are not known experimentally, we provide theoretical estimates within a potential model, and consider the spread between similar approaches in the literature as an estimate for the model error. For the $Υ(1S)$, $Υ(2S)$, and $Υ(3S)$ states we observe that, due to a cancellation between transitions involving $χ_{b0}, χ_{b1}$, and $χ_{b2}$ states, the sum rule is satisfied within experimental and theoretical error estimates. Having tested this sum rule for the low-lying bottomonium states, it may be used as a tool to investigate the nature of exotic states in the charmonium and bottomonium spectrum through the corresponding radiative transitions.

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arXiv2020

Simultaneous description of the $e^+e^- \to J/ ψ\, ππ\, (K \bar{K})$ processes

In this work, we provide a simultaneous and accurate description of the $π^+π^-$ and $π^{\pm} J/ψ$ invariant mass distributions of the recent BESIII data on $e^+ e^- \to J/ψ\; π^+ π^-$ together with the $e^+ e^- \to J/ψ\; K^+K^-$ cross sections at $e^+e^-$ center-of-mass energies $q=4.23$ GeV and $q=4.26$ GeV. The rescattering effects between pions in the S and D-waves are taken into account through the Muskhelishvili-Omnès formalism. Since the physical region of the $ππ$ invariant mass extends above 1 GeV, the important $K\bar{K}$ intermediate state in the S-wave is implemented through coupled-channel unitarity. For the left-hand cuts, we account for the well established charged exotic state $Z_c(3900)$ in $t$- and $u$-channels, while the other contributions are absorbed in the subtraction constants. For the $e^+ e^- \to J/ψ\, K \bar{K}$ we provide the prediction of the two-kaon invariant mass distribution. The constructed amplitudes serve as an essential framework to interpret the present and forthcoming measurements by the BESIII and Belle II Collaborations.

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arXiv2020

Dispersive analysis of the $γ^{}γ^{} \to ππ$ process

In this paper, we present a dispersive analysis of the double-virtual photon-photon scattering to two pions up to 1.5 GeV. Through unitarity, this process is very sensitive to hadronic final state interaction. For the $s$-wave, we use a coupled-channel $ππ,\, K\bar{K}$ analysis which allows a simultaneous description of both $f_0(500)$ and $f_{0}(980)$ resonances. For higher energies, $f_2(1270)$ shows up as a dominant structure which we approximate by a single channel $ππ$ rescattering in the $d$-wave. In the dispersive approach, the latter requires taking into account $t$- and $u$-channel vector-meson exchange left-hand cuts which exhibit an anomalous-like behavior for large space-like virtualities. In our paper, we show how to readily incorporate such behavior using a contour deformation. Besides, we devote special attention to kinematic constraints of helicity amplitudes and show their correlations explicitly.

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arXiv2019

The role of charged exotic states in $e^+e^- \to ψ(2S) \; π^+ π^-$

In this work, we use the dispersion theory to provide a physical description of recent BESIII data on the reaction $ e^+ e^- \to ψ(2S) \, π^+ \, π^-$. Taking into account explicitly the effects of charged exotic intermediate states in the $t$- and $u$-channels as well as the two-pion final state interaction, we describe the invariant mass distribution for four different $e^+ e^-$ center-of-mass energies. The effects of the $ππ$ rescattering are accounted for within a model-independent single channel approach which is found to explain the $ππ$-invariant mass distributions at all $e^+ e^-$ center-of-mass energies. For $q= 4.226$ GeV and $q= 4.258$ GeV the already established charged exotic state $Z_c(3900)$ is considered as the intermediate state, whereas for $q= 4.358$ GeV the rescattering of pions dominates the fits. For the highest energy, $q= 4.416$ GeV, a heavier charged exotic state with mass $m_{Z_c} = 4.016(4)$ GeV and width $Γ_{Z_c} = 52(10)$ MeV is essential to describe the experimental data. Although the mass of this state is consistent with the established $Z_c(4020)$, its width is significantly larger.

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arXiv2019

The hadronic light-by-light contribution to the muon's anomalous magnetic moment

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.

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arXiv2019

Dispersive analysis of the $γγ^{*} \to ππ$ process

We present a theoretical study of the $γγ^{*} \to π^+π^-, π^0π^0$ processes from the threshold through the $f_2(1270)$ region in the $ππ$ invariant mass. We adopt the Omnès representation in order to account for rescattering effects in both s- and d-partial waves. For the description of the $f_0(980)$ resonance, we implement a coupled-channel unitarity. The constructed amplitudes serve as an essential framework to interpret the current experimental two-photon fusion program at BESIII. They also provide an important input for the dispersive analyses of the hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment.

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arXiv2018

Theoretical analysis of the $γγ^{(*)} \to π^0η$ process

The theoretical analysis of the $γγ\to π^0η$ process is presented within the energy range up to 1.4 GeV. The $S$-wave resonance $a_0(980)$ is described involving the coupled channel dispersive framework and the $D$-wave $a_2(1320)$ is approximated as a Breit-Wigner resonance. For the $a_0(980)$ the pole is found on the IV Riemann sheet resulting in a two-photon decay width of $Γ_{a_0\toγγ}=0.27(4)$ keV. The first dispersive prediction is provided for the single-virtual $γγ^*(Q^2)\toπ^0η$ process in the spacelike region up to $Q^2=1$ GeV$^2$.

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arXiv2017

Theoretical analysis of the $γγ\to π^0 η$ process

We present a theoretical study of the $γγ\to πη$ process from the threshold up to 1.4 GeV in the $πη$ invariant mass. For the s-wave $a_0(980)$ resonance state we adopt a dispersive formalism using a coupled-channel Omnès representation, while the d-wave $a_2(1320)$ state is described as a Breit-Wigner resonance. An analytic continuation to the $a_0(980)$ pole position allows us to extract its two-photon decay width as $Γ_{a_0\toγγ}=0.27(4)$ keV.

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arXiv2017

Light-by-light forward scattering sum rules for charmonium states

We apply three forward light-by-light scattering sum rules to charmonium states. We show that these sum rules imply a cancellation between charmonium bound state contributions, which are mostly known from the $γγ$ decay widths of these states, and continuum contributions above $D \bar D$ threshold, for which we provide a duality estimate. We also show that two of these sum rules allow to predict the yet unmeasured $γ^\ast γ$ coupling of the $χ_{c1}(1P)$ state, which can be tested at present high-luminosity $e^+ e^-$ colliders.

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arXiv2017

Light-by-light scattering sum rules in light of new data

We evaluate the light-quark meson contributions to three exact light-by-light scattering sum rules in light of new data by the Belle Collaboration, which recently has extracted the transition form factors of the tensor meson $f_2(1270)$ as well as of the scalar meson $f_0(980)$. We confirm a previous finding that the $η, η^\prime$ and helicity-2 $f_2(1270)$ contributions saturate one of these sum rules up to photon virtualities around 1 GeV$^2$. At larger virtualities, our sum rule analysis shows an important contribution of the $f_2(1565)$ meson and provides a first empirical extraction of its helicity-2 transition form factor. Two further sum rules allow us to predict the helicity-0 and helicity-1 transition form factors of the $f_2(1270)$ meson. Furthermore, our analysis also provides an update for the scalar and tensor meson hadronic light-by-light contributions to the muon's anomalous magnetic moment.

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