arXiv subjects

Otto Nachtmann

Publications and source records attributed to Otto Nachtmann.

At least 19 recordsLinked to original sources

arXiv2026

Addendum: Production of $π^{+} π^{-}$ pairs in diffractive photon-proton and in proton-proton collisions revisited, in particular concerning the Drell-Söding contribution

We update our analyses concerning the non-resonant (Drell-Söding) contribution to the reaction $γ^{(*)} p \to π^{+} π^{-} p$, now including general vertex functions for the coupling of pomeron, $f_{2 \mathbb{R}}$, and $ρ_{\mathbb{R}}$, to pions. This takes into account the off-shellness of the pions. We present a comparison of our tensor-pomeron model, including our new Drell-Söding and $ρ$, $ω$ vector-meson contributions, with data for the $γp \to π^{+} π^{-} p$ reaction measured by the ZEUS and H1 Collaborations. We find very good agreement of our theory with the experimental data for the $π^{+} π^{-}$ invariant mass ($M_{ππ}$) and for angular distributions. Here we restrict our analysis to the region $M_{ππ} \lesssim 1.2$ GeV. For higher values of $M_{ππ}$ we will have to consider production of higher-mass mesons. The purpose of the present article is to show that our tensor-pomeron model gives a very good fit to the so-called skewing of the $ρ$-resonance contribution in photoproduction. In fact, it is an old problem/puzzle to understood the difference of the shapes of the $M_{ππ}$ distributions in the region of the $ρ(770)$ resonance in $e^{+} e^{-}$ annihilation and photoproduction. We think that with our results we have obtained for this problem a solution which is very satisfactory from the Quantum-Field-Theory point of view. Our results are also relevant for central-exclusive $π^{+} π^{-}$ production in ultraperipheral $pp$, A$p$, and AA collisions at the LHC and for photo- and electroproduction of $π^{+} π^{-}$ at future electron-proton/ion colliders, EIC and LeHC.

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arXiv2026

Production of $π^{+}π^{-}$ pairs in diffractive photon-proton and in proton-proton collisions revisited, in particular concerning the Drell-Söding contribution

We discuss the exclusive photoproduction of $π^{+}π^{-}$ pairs in photon-proton and in proton-proton collisions at high energies. The $ρ^{0}$, $ω$, $f_{2}(1270)$, and non-resonant (Drell-Söding) contributions are considered. The calculation is based on the tensor-pomeron model. In the Drell-Söding contribution we have different subenergies for the $π^{+}p$ and $π^{-}p$ systems. In the method which we propose now we take this into account. Respecting the gauge-invariance constraints is then a nontrivial problem for which, however, we present a solution here. In the present paper we give in this way a substantial improvement of the calculations for real photoproduction of $π^{+}π^{-}$ from JHEP 01, 151 (2015), and we extend the calculations to low $Q^{2}$ electroproduction, $0 \leqslant Q^{2} \leqslant 0.5$ GeV$^{2}$. The photo- and electroproduction amplitudes are then the basis for the calculation of central exclusive production (CEP) of $π^{+}π^{-}$ pairs in $pp$ collisions, where at least one proton participates in the CEP via a virtual-photon emission. The revised model leads to enhanced cross sections and gives an increased skewing of the $ρ^{0}$ spectral shape. For the $pp \to pp π^{+}π^{-}$ reaction, we calculate differential cross sections as function of the two-pion invariant mass, pion transverse momentum and pion pseudorapidity. This research is relevant in the context of ALICE, ATLAS, CMS, and LHCb measurements in $pp$ collisions. Our results can also serve as basis for the description of coherent $π^{+}π^{-}$ production in ultra-peripheral $p$A and AA collisions at the LHC. The formulas given in our paper can be used for the analysis of photoproduction and small-$Q^{2}$ electroproduction in $ep$ collisions at high energies. Such data exist from the HERA experiments and will be obtained in the future at the electron-ion colliders.

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arXiv2026

Central exclusive production of $η$ and $η'$ mesons in diffractive proton-proton collisions at the LHC and the nature of the pomeron

Central exclusive production (CEP) of $η$ and $η'$ mesons in proton-proton collisions at high-energies is discussed. At the LHC the main mechanism for the production of these mesons should be double-pomeron ($\rm I\!P$-$\rm I\!P$) exchange, that is, the fusion reactions ${\rm I\!P I\!P} \to η, η'$. We show that for a scalar pomeron these fusion reactions are not possible. In contrast, in the tensor-pomeron model CEP of $η$ and $η'$ mesons via double-pomeron exchange is allowed. We discuss these reactions for the c.m. energy $\sqrt{s} = 29.1$ GeV realised at the WA102 experiment and for $\sqrt{s} = 13$ TeV corresponding to the LHC experiments. Cross sections and distributions are presented and discussed.

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arXiv2026

Charm associated production of the pseudoscalar Higgs boson $h''$ in the MCPM' at the LHC

We discuss charm associated production of the pseudoscalar Higgs boson $h''$ in the MCPM'. In our analysis we assume $m_{h''}$ = 95.4 GeV, which corresponds to an enhancement observed by the CMS collaboration in the $γγ$ channel. As discussed recently, the MCPM' is consistent with the CMS enhancement. In this model the $h''$ Higgs boson of this mass decays dominantly into $c \bar c$ jets. The cross section for the associated $h''$ production in $p p \to h'' c \bar c$ is found to be almost as big as that for the Drell-Yan (DY) $c \bar c \to h''$ production, much larger than that for two-gluon fusion $g g \to h''$. Since in the MCPM' the dominant $h''$ decay is into the $c \bar c$ channel we have to deal with the $p p \to c \bar c c \bar c$ process with $c$ and $\bar c$ jets. In addition to the signal processes, we have sizeable single parton scattering (SPS) and double parton scattering (DPS) nonresonant background. In our analysis we include diagrams of gluon-gluon fusion $g g \to h''$ which lead to the $c \bar c c \bar c$ final state. We discuss also the possible role of the reaction $p p \to h'' h''$. Assuming 100\% c and $\bar c$ jet tagging we discuss in detail how to improve the signal-to-background ratio. Our analysis shows promising resonance-like enhancements and relatively large cross sections in the $c \bar c c \bar c$ channel within the MCPM'. In an appendix we discuss the total cross section for $h''$ production at the LHC. We also compare distributions for the reactions $p p \to h'' X$ and $p p \to Z X$ with $h''$ and $Z$ decaying to $c\bar c$ and $μ^{+}μ^{-}$. We hope that the LHC collaborations will in the future perform the experimental studies corresponding to the theoretical studies discussed here.

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arXiv2025

Central exclusive production of $η$ and $η'$ mesons in diffractive proton-proton collisions at the LHC within the tensor-pomeron approach

We present a study of the central exclusive production (CEP) of $η$ and $η'(958)$ mesons in diffractive proton-proton collisions at high energies. The amplitudes, including pomeron and $f_{2 \mathbb{R}}$ reggeon exchanges, are calculated within the tensor-pomeron model. Absorption effects are also taken into account at the amplitude level. We fit some undetermined model parameters (coupling constants and cutoff parameters in form factors) to the WA102 experimental data and then make predictions for the LHC energy $\sqrt{s} = 13$ TeV. Both, total cross sections and several differential distributions are presented. For $pp \to pp η$, we find an upper limit for the total cross section of 2.5 $μ$b for pseudorapidity of the $η$ meson $|η_{M}| < 1$ and 5.6 $μ$b for $2 < η_{M} < 5$. For $pp \to pp η'$, we predict the cross section to be in the range of 0.3-0.7 $μ$b for pseudorapidity of the $η'$ meson $|η_{M}| < 1$ and 0.9-2.1 $μ$b for $2 < η_{M} < 5$. This opens the possibility to study diffractive production of pseudoscalar mesons in experiments at the LHC. We discuss if there are arguments from SU(3)-flavor symmetry which would forbid pomeron-pomeron fusion giving an $η$ meson. In our opinion such arguments do not exist. We also consider CEP of the pseudoscalars $η$ and $η'(958)$ and the pseudovector meson $f_{1}(1285)$ in diffractive proton-proton collisions in a theory with a scalar pomeron. We show that none of these particles can be produced in this way in the scalar-pomeron theory. Thus, experimental observation of any of these particles in the above CEP processes at the LHC would give striking evidence against a scalar character of the pomeron.

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arXiv2024

Soft-photon theorem for pion-proton elastic scattering revisited

We discuss the reactions $πp \to πp$ and $πp \to πp γ$ from a general quantum field theory (QFT) point of view, describing these reactions in QCD and lowest relevant order of electromagnetism. We consider the pion-proton elastic scattering both off shell and on shell. The on-shell amplitudes for $π^{\pm} p \to π^{\pm} p$ scattering are described by two invariant amplitudes, while the off-shell amplitudes contain eight invariant amplitudes. We study the photon emission amplitudes in the soft-photon limit where the c.m. photon energy $ω\to 0$. The Laurent expansion in $ω$ of the $π^{\pm} p \to π^{\pm} p γ$ amplitudes is considered and the terms of the orders $ω^{-1}$ and $ω^{0}$ are derived. These terms can be expressed by the on-shell invariant amplitudes and their partial derivatives with respect to $s$ and $t$. The pole term $\propto ω^{-1}$ in the amplitudes corresponds to Weinberg's soft-photon theorem and is well known from the literature. We derive the next-to-leading term $\propto ω^{0}$ using only rigorous methods of QFT. We give the relation of the Laurent series for $π^{0} p \to π^{0} p γ$ and Low's soft-photon theorem. Our formulas for the amplitudes in the limit $ω\to 0$ are valid for photon momentum $k$ satisfying $k^{2} \geqslant 0$, $k^{0} = ω\geqslant 0$, that is, for both real and virtual photons. Here we consider a limit where with $ω\to 0$ we have also $k^{2} \to 0$. We discuss the behavior of the corresponding cross-sections for $π^{-} p \to π^{-} p γ$ with respect to $ω$ for $ω\to 0$. We consider cross sections for unpolarized as well as polarized protons in the initial and final states.

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arXiv2024

High-energy $ππ$ scattering without and with photon radiation

We discuss the processes $ππ\to ππ$ and $ππ\to ππγ$ from a general quantum field theory (QFT) point of view. We study the soft-photon limit where the photon energy $ω\to 0$ and where we have the theorems due to F.E. Low and S. Weinberg. We consider for the radiative amplitude the Laurent expansion in $ω$ and calculate the terms of order $ω^{-1}$ and $ω^{0}$. The pole term $\propto ω^{-1}$ is given by Weinberg's soft-photon theorem. Then we calculate the amplitudes for the above reactions for high center-of-mass energies and small momentum transfers, that is, in the soft-diffraction regime using the tensor-pomeron model. We identify places where "anomalous" soft photons could come from. Three soft-photon approximations (SPAs) are introduced. The corresponding SPA results are compared to those obtained from the full tensor-pomeron model for center-of-mass energies $\sqrt{s} = 10$ GeV and 100 GeV. The kinematic regions where the SPAs are a good representation of the full amplitude are determined. Finally we make some remarks on the type of fundamental information one could obtain from high-energy exclusive hadronic reactions without and with soft photon radiation.

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arXiv2024

Different versions of soft-photon theorems exemplified at leading and next-to-leading terms for pion-pion and pion-proton scattering

We investigate the photon emission in pion-pion and pion-proton scattering in the soft-photon limit where the photon energy $ω\to 0$. The expansions of the $π^{-} π^{0} \to π^{-} π^{0} γ$ and the $π^{\pm} p \to π^{\pm} p γ$ amplitudes, satisfying the energy-momentum relations, to the orders $ω^{-1}$ and $ω^{0}$ are derived. We show that these terms can be expressed completely in terms of the on-shell amplitudes for $π^{-} π^{0} \to π^{-} π^{0}$ and $π^{\pm} p \to π^{\pm} p$, respectively, and their partial derivatives with respect to $s$ and $t$. The~structure term which is non singular for $ω\to 0$ is determined to the order $ω^{0}$ from the gauge-invariance constraint using the generalized Ward identities for pions and the proton. For the reaction $π^{-} π^{0} \to π^{-} π^{0} γ$ we discuss in detail the soft-photon theorems in the versions of both F.E. Low and S. Weinberg. We show that these two versions are different and must not be confounded. Weinberg's version gives the pole term of a Laurent expansion in $ω$ of the amplitude for $π^{-} π^{0} \to π^{-} π^{0} γ$ around the phase-space point of zero radiation. Low's version gives an approximate expression for the above amplitude at a fixed phase-space point, corresponding to non-zero radiation. Clearly, the leading and next-to-leading terms in theses two approaches must be, and are indeed, different. We show their relation. We also discuss the expansions of differential cross sections for $π^{-} π^{0} \to π^{-} π^{0} γ$ with respect to $ω$ for $ω\to 0$.

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arXiv2024

Exclusive Bremsstrahlung of One and Two Photons in Proton-Proton Collisions

We discuss the diffractive bremsstrahlung of a single photon in the $pp \to pp γ$ reaction at LHC energies and at forward photon rapidities. We compare the results for our standard approach, based on QFT and the tensor-Pomeron model, with two versions of soft-photon approximations, SPA1 and SPA2, where the radiative amplitudes contain only the leading terms proportional to $ω^{-1}$ (the inverse of the photon energy). SPA1, which does not have the correct energy-momentum relations, performs surprisingly well in the kinematic range considered, namely at very forward photon rapidities and $0.02 < ξ_{1,2} < 0.1$, the relative energy loss of the protons, corresponding to small values of the photon transverse momentum. Azimuthal correlations between outgoing particles are presented. We discuss also the role of the $p p \to p p π^0$ background for single photon production. We discuss also the possibility of a measurement of the $pp \to pp γγ$ reaction. Our predictions can be verified by ATLAS-LHCf combined experiments.

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arXiv2023

Exclusive diffractive bremsstrahlung of one and two photons at forward rapidities: Possibilities for experimental studies in $pp$ collisions at the LHC

We evaluate the cross section for diffractive bremsstrahlung of a single photon in the $pp \to pp γ$ reaction at high energies and at forward photon rapidities. Several differential distributions, for instance, in $y$, $k_{\perp}$ and $ω$, the rapidity, the absolute value of the transverse momentum, and the energy of the photon, respectively, are presented. We compare the results for our standard approach, based on QFT and the tensor-pomeron model, with two versions of soft-photon-approximations, SPA1 and SPA2, where the radiative amplitudes contain only the leading terms proportional to $ω^{-1}$. The SPA1, which does not have the correct energy-momentum relations, performs surprisingly well in the kinematic range considered. We discuss also azimuthal correlations between outgoing particles. The azimuthal distributions are not isotropic and are different for our standard model and SPAs. We discuss also the possibility of a measurement of two-photon-bremsstrahlung in the $pp \to pp γγ$ reaction. In our calculations we impose a cut on the relative energy loss ($0.02 < ξ_{i} < 0.1$, $i = 1,2$) of the protons where measurements by the ATLAS Forward Proton (AFP) detectors are possible. The AFP requirement for both diffractively scattered protons and one forward photon (measured at LHCf) reduces the cross section for $p p \to p p γ$ almost to zero. On the other hand, much less cross-section reduction occurs for $pp \to pp γγ$ when photons are emitted in opposite sides of the ATLAS interaction point and can be measured by two different arms of LHCf. For the SPA1 ansatz we find $σ(pp \to pp γγ) \simeq 0.03$ nb at $\sqrt{s} = 13$ TeV and with the cuts $0.02 < ξ_{i} < 0.1$, $8.5 < y_{3} < 9$, $-9 < y_{4} < -8.5$. Our predictions can be verified by ATLAS and LHCf combined experiments.

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arXiv2023

Central exclusive diffractive production of a single photon in high-energy proton-proton collisions within the tensor-Pomeron approach

We discuss central-exclusive production (CEP) of photons via different fusion processes in the reaction $pp \to pp γ$ at high energies, available at RHIC and LHC, within the tensor-pomeron model. We consider two types of processes, the photoproduction contribution via the photon-pomeron and photon-reggeon fusion reactions, and the purely diffractive contribution via the reggeon-pomeron and odderon-pomeron fusion reactions. We present predictions for the measurements of photons at midrapidity, $|{\rm y}| < 2.5$, and at relatively low transverse momentum, $0.1~{\rm GeV} < k_{\perp} < 1~{\rm GeV}$. To check the main results of our study the measurement of the outgoing protons is not necessary. This is of relevance, e.g., for the present version of the ALICE detector at the LHC. Several differential distributions, for instance, in ${\rm y}$, $k_{\perp}$ and $ω$, the rapidity, the absolute value of the transverse momentum, and the energy of the photon, respectively, are presented. We show that the photoproduction is an important process in the kinematic region specified above. There it gives a much larger cross section than diffractive bremsstrahlung. This is remarkable as the CEP cross section is of order $α_{\rm em}^{3}$ whereas the bremsstrahlung one is only of order $α_{\rm em}$. On the other hand, the soft-photon bremsstrahlung where the basic $pp \to pp$ reaction is due to strong interaction diffraction is more important than CEP in the forward rapidity range, $|{\rm y}| > 4$, and/or at very low $k_{\perp}$. We leave it as a challenge for the planned ALICE 3 experiment at the LHC to study these two contributions to soft photon production in $pp$ collisions. This could shed new light on the so called ``soft photon puzzle'' in hadron-hadron collisions.

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arXiv2023

The Tensor Pomeron and Low-x Deeply Virtual Compton Scattering

The two-tensor-pomeron model is applied to deeply virtual Compton scattering (DVCS) on a proton. A good description of the DVCS HERA data at small Bjorken-$x$ is achieved due to a sizeable interference of soft and hard pomeron contributions. We present two fits which differ somewhat in the strength of the hard pomeron contribution. We describe, in the same framework, both the low $Q^{2}$ and high $Q^{2}$ regimes and the transition between them. We find that the soft-pomeron contribution is considerable up to $Q^{2} \sim 20$ GeV$^{2}$. The reggeon exchange term is particularly relevant for describing the scattering of a real photon on a proton measured at lower $γp$ energies at FNAL. We find that the ratio of $γ^{*} p \to γp$ cross-sections for longitudinally and transversely polarized virtual photons strongly increases with $t$. Our findings may be checked in future lepton-nucleon scattering experiments in the low-$x$ regime, for instance, at a future Electron-Ion Collider (EIC) at the BNL and LHeC at the LHC.

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arXiv2022

Deeply virtual Compton scattering in the tensor-pomeron approach

The two-tensor-pomeron model proposed previously to describe low $x$ DIS data is applied to real and virtual Compton scattering on a proton. The model includes two tensor pomerons, a soft and a hard one, and tensor reggeons. We include contributions of both transverse and longitudinal virtual photons. We show that this model gives a very good description of experimental data at small Bjorken $x$ on deeply virtual Compton scattering (DVCS) from HERA. The reggeon exchange term is particularly relevant for describing the real-photon-proton scattering measured at lower $γp$ energies at FNAL. We present two fits which differ somewhat in the strength of the hard pomeron contribution. In both fits we find that the interference between soft- and hard-pomeron exchange plays an important role. We find that in DVCS the soft-pomeron contribution is considerable up to $Q^{2} \sim 20$ GeV$^{2}$. Our model allows to study the transition from the small-$Q^{2}$ regime, including the photoproduction ($Q^{2} = 0$) limit, to the large-$Q^{2}$ regime, the DIS limit. We also discuss the ratio of cross sections for longitudinally and transversely polarized virtual photons in $γ^{*} p \to γp$ as a function of $|t|$ and $Q^2$. The ratio $\tilde{R}(Q^{2},W^{2},t) = (dσ_{\rm L} / dt) / (dσ_{\rm T} / dt)$ strongly increases with $t$. Our findings may be checked in future lepton-nucleon scattering experiments in the low-$x$ regime, for instance, at a future Electron-Ion Collider at the BNL (EIC), and, if LHeC is realized, at the LHC.

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arXiv2022

Soft-photon radiation in high-energy proton-proton collisions within the tensor-Pomeron approach: Bremsstrahlung

We discuss diffractive processes in proton-proton collisions at small momentum transfers without and with photon radiation. We consider the soft exclusive reactions $pp \to pp$, $p\bar{p} \to p\bar{p}$, and $pp \to pp γ$ within the tensor-pomeron and vector-odderon approach. We compare our results with the data for $pp$ and $p\bar{p}$ total cross sections, for the ratio of real to imaginary part of the forward scattering amplitude, and for the elastic $pp$ cross sections, especially those from TOTEM. To describe the low-energy data more accurately the secondary reggeons must be included. We write down the amplitudes for the photon bremsstrahlung in high-energy proton-proton collisions using the tensor-pomeron model. These results are relevant for the c.m. energies presently available at the Relativistic Heavy Ion Collider and at the LHC. We present predictions for the proposed measurements of soft photons with the planned future upgrade of the ALICE experiment at the LHC. We investigate the limits of applicability of the soft-photon approximation (SPA) based on Low's theorem. The corresponding SPA results are compared to those obtained from our complete model. The regions of phase space are given quantitatively where SPA and our complete tensor-pomeron results are close to each other. As an example, let $k_{\perp}$, $\rm y$, and $ω$, be the absolute value of the transverse momentum, the rapidity, and the energy of the photon, respectively, in the overall c.m. system. For the region $1 \; {\rm MeV} < k_{\perp} < 100 \; {\rm MeV}$ and $3.5 < |\rm y| < 5.0$, we find that the SPA Ansatz with only the pole terms $\propto ω^{-1}$ agrees at the percent level with our complete model result up to $ω\cong 2$ GeV.

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arXiv2021

Probing the tau electric dipole moment at BEPC-II collider energies

We investigate the prospects of the search for a nonzero $τ$ EDM form factor $d_τ(s)$ in $τ$ pair production by $e^+ e^-$ collisions at BEPC-II collider energies. We compute the expectation values and covariances of simple and optimal $CP$-odd observables for $τ$-pair production at $\sqrt{s}=4.18$ GeV and $4.95$ GeV with subsequent decays of $τ^\pm$ into major leptonic or semihadronic modes. For the $τ$ decays to two pions and three charged pions we take the full kinematic information of the hadronic system into account. Applying cuts and using realistic assumptions on the eventually attainable integrated luminosities at these energies, ${\cal L}(4.18) = 3\times 10^4~{\rm pb}^{-1}$ and ${\cal L}(4.95) = 10^4~{\rm pb}^{-1}$, respectively, we find the following. By taking into account purely semihadronic and semihadronic-leptonic $τ^+τ^-$ decays one can achieve with optimal $CP$-odd observables the 1 s.d. sensitivities $δ{\rm Re} d_τ= 4.5\times 10^{-18}$ ecm ($5.3\times 10^{-18}$ ecm) and $δ{\rm Im} d_τ= 2.2 \times 10^{-18}$ ecm ($2.7\times 10^{-18}$ ecm) at $\sqrt{s}=4.18$ GeV ($4.95$ GeV).

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arXiv2021

Central exclusive diffractive production of axial-vector $f_{1}$ mesons in proton-proton collisions

Exclusive production of axial-vector $f_{1}(1285)$ meson in proton-proton collisions via pomeron-pomeron fusion within the tensor-pomeron approach is discussed. Two ways to construct the pomeron-pomeron-$f_{1}$ coupling are presented. We adjust the parameters of our model to the WA102 experimental data and compare with predictions of the Sakai-Sugimoto model. Predictions for LHC experiments are given.

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arXiv2021

Exclusive $f_{1}(1285)$ meson production for energy ranges available at the GSI-FAIR with HADES and PANDA

We evaluate the cross section for the $p p \to p p f_{1}(1285)$ and $p \bar{p} \to p \bar{p} f_{1}(1285)$ reactions at near threshold energies relevant for the HADES and PANDA experiments at GSI-FAIR. We assume that at energies close to the threshold the $ωω\to f_{1}(1285)$ and $ρ^{0} ρ^{0} \to f_{1}(1285)$ fusion processes are the dominant production mechanisms. The vertex for the $VV \to f_{1}$ coupling is derived from an effective coupling Lagrangian. The $g_{ρρf_1}$ coupling constant is extracted from the decay rate of $f_{1}(1285) \to ρ^{0} γ$ using the vector-meson-dominance ansatz. We assume $g_{ωωf_1} = g_{ρρf_1}$, equality of these two coupling constants, based on arguments from the naive quark model and vector-meson dominance. The amplitude for the $VV \to f_{1}$ fusion, supplemented by phenomenological vertex form factors for the process, is given. The differential cross sections at energies close to the threshold are calculated. In order to determine the parameters of the model the $γp \to f_{1}(1285) p$ reaction is discussed in addition and results are compared with the CLAS data. The possibility of a measurement by HADES@GSI is presented and discussed. We performed a Monte Carlo feasibility simulations of the $p p \to p p f_1$ reaction for $\sqrt{s}$ = 3.46 GeV in the $π^+ π^- π^+ π^-$ (not shown explicitly) and $π^+ π^- π^+ π^- π^0$ final states using the PLUTO generator. The latter one is especially promising as a peak in the $π^+ π^- η$ should be observable by HADES.

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arXiv2021

The electric dipole moment of the tau lepton revisited

We reconsider the issue of the search for a nonzero electric dipole form factor (EDM) $d_τ(s)$ using optimal observables in $τ^+τ^-$ production by $e^+ e^-$ collisions in the center-of-mass energy range from the $τ$-pair threshold to about $\sqrt{s} \sim 15$ GeV. We discuss the general formalism of optimal observables and apply it to two $CP$-odd observables that are sensitive to the real and imaginary part of $d_τ(s)$, respectively. We compute the expectation values and covariances of these optimal $CP$ observables for $τ$-pair production at $\sqrt{s}=10.58$ GeV with subsequent decays of $τ^\pm$ into major leptonic or semihadronic modes. For the $τ$ decays to two pions and three charged pions we take the full kinematic information of the hadronic system into account. Assuming that the Belle II experiment at the KEKB accelerator will eventually analyze data corresponding to an integrated luminosity of 50 ab$^{-1}$ and applying acceptance cuts on the final-state pions we find that 1~s.d. sensitivities $δ{\rm Re} d_τ= 6.8 \times 10^{-20}$ e cm and $δ{\rm} Im d_τ= 4.0 \times 10^{-20}$ e cm can be obtained with events where both $τ$'s decay semihadronically. In the ideal case where no cuts on the final-state particles are applied we find with 50 ab$^{-1}$ at $\sqrt{s}=10.58$ GeV corresponding to $4.5 \times 10^{10}$ $τ^+ τ^-$ events the 1 s.d. sensitivities $δ{\rm Re} d_τ= 5.8 \times 10^{-20}$ e cm and $δ{\rm} Im d_τ= 3.2 \times 10^{-20}$ e cm, again for events where both $τ$ leptons decay semihadronically. Furthermore, we analyze the potential magnitude of the $τ$ EDM form factor in the type-II two-Higgs doublet extension and in two scalar leptoquark extensions of the Standard Model.

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