Two recent experimental observations at the ATOMKI Institute of the Hungarian Academy of Sciences (regarding the angular emission pattern of electron-positron pairs from nuclear transitions from excited states in 8Be and 4He) indicate the possible existence of a particle of a rest mass energy of roughly 17 MeV. The so-called X17 particle constitutes a virtual state in the process, preceding the emission of the electron-positron pair. Based on the symmetry of the nuclear transitions ($1^+$ to $0^+$ and $0^-$ to $0^+$), the X17 could either be a vector, or a pseudoscalar particle. Here, we calculate the effective potentials generated by the X17, for hyperfine interactions in simple atomic systems, for both the pseudoscalar as well as the vector X17 hypotheses. The effective Hamiltonians are obtained in a general form which is applicable to both electronic as well as muonic bound systems. The effect of virtual annihilation and its contribution to the hyperfine splitting also is considered. Because of the short range of the X17-generated potentials, the most promising pathway for the observation of the X17-mediated effects in bound systems concerns hyperfine interactions, which, for $S$ states, are given by modifications of short-range (Dirac-delta) potentials in coordinate space. For the pseudoscalar hypothesis, the exchange of one virtual X17 quantum between the bound lepton and the nucleus exclusively leads to hyperfine effects, but does not affect the Lamb shift. Effects due to the X17 are shown to be drastically enhanced for muonic bound systems. Prospects for the detection of hyperfine effects mediated by X17 exchange are analyzed for muonic deuterium, muonic hydrogen, muonium, true muonium ($μ^+μ^-$ bound system), and positronium.
Three-loop corrections to hyperfine splitting in muonium generated by the gauge invariant sets of diagrams with muon and tauon loop light-by-light scattering blocks are calculated. These results complete calculations of all light-by-light scattering contributions to hyperfine splitting in muonium.
The muon and tauon light-by-light scattering contributions to hyperfine splitting in muonium are calculated. These results conclude calculation of all hard three-loop contributions to hyperfine splitting containing graphs with closed fermion loops. We discuss the special role that the lepton anomalous magnetic moments play in these calculations. The full result for all three-loop radiative-recoil corrections to hyperfine splitting generated by the graphs with closed lepton loops is presented.
We calculate radiative corrections to the Lamb shift of order $α^3(Zα)^5m$ and radiative corrections to hyperfine splitting of order $α^3(Zα)E_F$ generated by the diagrams with insertions of radiative photons and electron polarization loops in the graphs with two external photons. We also obtain the radiative-recoil correction to hyperfine splitting in muonium generated by the diagrams with the $τ$ polarization loop.
We calculate radiative-recoil corrections of order $α^2(Zα)(m/M)E_F$ to hyperfine splitting in muonium generated by the diagrams with electron and muon polarization loops. These corrections are enhanced by the large logarithm of the electron-muon mass ratio. The leading logarithm cubed and logarithm squared contributions were obtained a long time ago. The single-logarithmic and nonlogarithmic contributions calculated here improve the theory of hyperfine splitting, and affect the value of the electron-muon mass ratio extracted from the experimental data on the muonium hyperfine splitting.
We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by the gauge invariant set of diagrams with virtual light-by-light scattering block. These corrections are enhanced by the large logarithms of the electron-muon mass ratio. We present the results of an analytic calculation of the single-logarithmic radiative-recoil corrections of order $α^2(Zα)(m/M)E_F$ to hyperfine splitting in muonium generated by these diagrams.
The single photon annihilation contributions for the positronium ground state hyperfine splitting are calculated analytically to order $m_eα^6$ using NRQED. Based on intuitive physical arguments the same result can also be determined by a trivial calculation using results from existing literature. Our result completes the hyperfine splitting calculation to order $m_eα^6$. We compare the theoretical prediction with the most recent experimental measurement.
We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by diagrams with one-loop radiative photon insertions both in the electron and muon lines. An analytic result for these nonlogarithmic corrections of order $α(Z^2α)(Zα)(m/M)\widetilde E_F$ is obtained. This result constitutes a next step in the implementation of the program of reduction of the theoretical uncertainty of hyperfine splitting below 10 Hz.
Corrections of order $α^3(Zα)^5m$ to the Lamb shift and corrections of order $α^3(Zα)E_F$ to hyperfine splitting generated by the insertions of the three-loop one-particle reducible diagrams with radiative photons in the electron line are calculated. The calculations are performed in the Yennie gauge.
We consider three-loop corrections to hyperfine splitting in muonium generated by the gauge invariant set of diagrams with virtual light-by-light scattering block. These diagrams produce both recoil and nonrecoil contributions to hyperfine splitting. Recoil corrections are enhanced by large logarithms of the muon-electron mass ratio. Both nonrecoil and logarithmically enhanced radiative-recoil corrections where calculated some time ago. Here we calculate nonlogarithmic radiative-recoil corrections generated by the insertions of the light-by-light scattering block.
We calculate three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by the diagrams with the first order electron and muon polarization loop insertions in graphs with two exchanged photons. These corrections are enhanced by the large logarithm of the electron-muon mass ratio. The leading logarithm squared contribution was obtained a long time ago. Here we calculate the single-logarithmic and nonlogarithmic contributions. We previously calculated the three-loop radiative-recoil corrections generated by two-loop polarization insertions in the exchanged photons. The c…
We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium. These corrections are enhanced by the large logarithm of the electron-muon mass ratio. The leading logarithm cubed and logarithm squared contributions were obtained a long time ago. We calculate the single-logarithmic and nonlogarithmic contributions of order $α^3(m/M)E_F$ generated by gauge invariant sets of diagrams with one- and two-loop polarization insertions in diagrams with two exchanged photons and radiative photons, and by diagrams with one-loop radiative photon insertions both in the electron and m…
The two-photon-annihilation contribution to the true muonium hyperfine splitting arising from $e$ and $τ$ loops is obtained analytically at order $m_μα^6$. The contribution to the hyperfine splitting is $-2.031092873 m_μα^6/n^3π^2=-793.926988/n^3$ MHz. The contribution to the triplet true muonium decay rate has also been obtained and was found to be $9.825708266 m_μα^6/n^3π^2=3840.737698/n^3$ MHz. Additional results have been computed for other purely leptonic bound states.
We calculate corrections of order $α^3(Zα)E_F$ to hyperfine splitting in muonium generated by the gauge invariant set of diagrams with polarization insertions in the light by light scattering diagrams. This nonrecoil contribution turns out to be -2.63 Hz. The total contribution of all known corrections of order $α^3(Zα)E_F$ is equal to -4.28 Hz.
We consider hard three-loop nonlogarithmic corrections of order $mα^7$ to hyperfine splitting in positronium. All these contributions are generated by the graphs with photon and/or electron loop radiative insertions in the two-photon exchange diagrams. We calculate contributions of six gauge invariant sets of diagrams. The total result for all these diagrams is $ΔE=-1.2917(1)mα^7/π^3=-5.672$ kHz.
We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium due to insertions of one-loop polarization operator in the muon factor. The contribution produced by electron polarization insertions are enhanced by the large logarithm of the electron-muon mass ratio. We obtained all single-logarithmic and nonlogarithmic radiative-recoil corrections of order $α^3(m/M)E_F$ generated by the diagrams with electron and muon polarization insertions.
Radiative-recoil corrections to hyperfine splitting in muonium of orders $α(Zα)(m/M)^2E_F$ and $(Z^2α)(Zα)(m/M)^2E_F$ are calculated. These corrections are of the second order in the small electron-muon mass ratio. An analytic expression $[(-6 \ln2- \frac{3}{4})α(Zα) - \frac{17}{12} (Z^2 α) (Zα)](\frac{m}{M})^2 E_F$ is obtained. Numerically the correction is equal to $-0.0351\:\mbox{kHz}$ and is of the same order of magnitude as the expected accuracy of the current Los Alamos experiment to measure the hyperfine splitting.
We consider three-loop radiative corrections to the Lamb shift and hyperfine splitting. Corrections of order $α^3(Zα)^5m$ are the largest still unknown contributions to the Lamb shift in hydrogen. We calculated radiative corrections to the Lamb shift and hyperfine splitting generated by the diagrams with insertions of one radiative photon and electron polarization loops in the graphs with two external photons. We also obtained corrections generated by the gauge invariant sets of diagrams with two reducible radiative photon insertions in the electron line and polarization operator insertion in …
We consider hard three-loop corrections to hyperfine splitting in muonium and positronium generated by the diagrams with closed electron loops. There are six gauge-invariant sets of such diagrams that generate corrections of order $mα^7$. The contributions of these diagrams are calculated for an arbitrary electron-muon mass ratio without expansion in the small mass ratio. We obtain the formulae for contributions to hyperfine splitting that in the case of small mass ratio describe corrections for muonium and in the case of equal masses describe corrections for positronium. First few terms of th…
We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium due to insertions of one-loop polarization operator in the electron factor. The contribution generated by electron polarization insertions is a cubic polynomial in the large logarithm of the electron-muon mass ratio. The leading logarithm cubed and logarithm squared terms are well known for some time. We calculated all single-logarithmic and nonlogarithmic radiative-recoil corrections of order $α^3(m/M)E_F$ generated by the diagrams with electron and muon polarization insertions.
We consider three-loop radiative-recoil corrections to hyperfine splitting in muonium generated by the diagrams with electron and muon vacuum polarizations. We calculate single-logarithmic and nonlogarithmic contributions of order $α^3(m/M)E_F$ generated by gauge invariant sets of diagrams with electron and muon polarization insertions in the electron and muon factors. Combining the new contributions with our older results we present complete result for all three-loop radiative-recoil corrections generated by the diagrams with electron and muon polarization loops.
We present a precise determination of the polarizability and other proton structure dependent contributions to the hydrogen hyperfine splitting, based heavily on the most recent published data on proton spin dependent structure functions from the EG1 experiment at the Jefferson Laboratory. As a result, the total calculated hyperfine splitting now has a standard deviation slightly under 1 part-per-million, and is about 1 standard deviation away from the measured value. We also present results for muonic hydrogen hyperfine splitting, taking care to ensure the compatibility of the recoil and pola…
We consider a set of radiative contributions from one-loop lepton vacuum polarization to the hyperfine splitting of true muonium. Improving previous results, we obtain values for the electron-loop coefficients and extract their leading dependence upon $β=m_μ/m_e$. The coefficients are $C^μ_{20,1{\rm VPCT}}=0.734931603β$, $C^μ_{20,1{\rm VPCA}}=0.551198702β$, and $C^μ_{20,1{\rm VPT}}=0.419149715β$. The mass-independent contribution from three one-loop vacuum polarization is $C_{40,{\rm VPX}}=\frac{1}{127575}\left(-5255-2016π^2+51840ζ(3)\right)$. Contributions from $τ$ up to $\mathcal{O}(m_μα^8)$…
We present the derivation of the formulas for the proton structure-dependent terms in the hyperfine splitting of muonic hydrogen. We use compatible conventions throughout the calculations to derive a consistent set of formulas that reconcile differences between our results and some specific terms in earlier work. Convention conversion corrections are explicitly presented, which reduce the calculated hyperfine splitting by about 46 ppm. We also note that using only modern fits to the proton elastic form factors gives a smaller than historical spread of Zemach radii and leads to a reduced uncert…
We present the leading-order prediction of baryon chiral perturbation theory for the proton polarizability contribution to the 2S hyperfine splitting in muonic hydrogen, and compare with the results of dispersive calculations.
In the last twenty years, the theory of hyperfine splitting in muonium developed without any experimental input. Finally, this situation is changing and a new experiment on measuring hyperfine splitting in muonium is now in progress at J-PARC. The goal of the MuSEUM experiment is to improve by an order of magnitude experimental accuracy of the hyperfine splitting and muon-electron mass ratio. Uncertainty of the theoretical prediction for hyperfine splitting will be crucial for comparison between the forthcoming experimental data and the theory in search of a possible new physics. In the curren…
The hyperfine mass splittings of baryons in large $N$ QCD are proved to be proportional to ${\bf J}^2$. Hyperfine mass splittings are first allowed at order $1/N$ in the $1/N$ expansion.
We show that the non-spherical charge distribution of the proton manifests itself in hydrogen hyperfine splitting as an increase (in absolute value) of the proton Zemach radius and polarization contributions.
The self-energy corrections to the hyperfine splitting is evaluated for higher excited states in hydrogenlike ions, using an expansion in the binding parameter Zalpha, where Z is the nuclear charge number, and alpha is the fine-structure constant. We present analytic results for D, F and G states, and for a number of highly excited Rydberg states with principal quantum numbers in the range 13 <= n <= 16, and orbital angular momenta l = n-2 and l = n-1. A closed-form, analytic expression is derived for the contribution of high-energy photons, valid for any state with l <= 2$ and arbitrary n, l …
We compute O(alpha^3 ln alpha) relative corrections to the ground state hyperfine splitting of a QED two body bound state with different masses of constituents. The general result is then applied to muonium and positronium. In particular, a new value of the muon to electron mass ratio is derived from the muonium ground state hyperfine splitting.
We present a high-precision calculation of the recoil--finite-size correction to the hyperfine splitting (HFS) in muonic and electronic hydrogen based on nucleon electromagnetic form factors obtained from dispersion theory. This will help guide the upcoming searches of the HFS transition in muonic hydrogen, and will allow a precise determination of the polarizability and Zemach radius contributions when this transition is found.
Corrections of orders alpha^5, alpha^6 are calculated in the hyperfine splitting of the 2S state in the muonic hydrogen. The nuclear structure effects are taken into account in the one- and two-loop Feynman amplitudes by means of the proton electromagnetic form factors. Total numerical value of the 2S state hyperfine splitting 22.8148 meV in the (μp) can be considered as reliable estimation for the corresponding experiment with the accuracy 10^{-5}. The value of the Sternheim's hyperfine splitting interval [8ΔE^{HFS}(2S)-ΔE^{HFS}(1S)] is obtained with the accuracy 10^{-6}.
A detailed presentation is given of the analytic calculation of the single-photon annihilation contributions to the positronium ground state hyperfine splitting to order $m_eα^6$ in the framework of non-relativistic effective theories. The current status of the theoretical description of the positronium ground state hyperfine splitting is reviewed.
We investigate the influence of the spatial extent of the proton magnetization and charge densities on the 2S hyperfine splitting in muonic hydrogen. The use of a non-perturbative relativistic Dirac approach leads to corrections of 15% to values obtained from the perturbative treatment encapsulated by the Zemach radius, which surpass the next-leading order contribution in the perturbation series by an order of magnitude.
The contribution of hadronic vacuum polarization (HVP) to the hyperfine splitting of the muonium ground state is evaluated with the account of modern experimental data on the cross section of $e^+e^- \to$ annihilation into hadrons.
The contribution of Δisobar to the correction on proton polarizability in the hyperfine splitting of hydrogen and muonic hydrogen is calculated with the account of the experimental data on N-Δtransition form factors.
We evaluate the two-photon exchange corrections to the Lamb shift and hyperfine splitting of S states in electronic hydrogen relying on modern experimental data and present the two-photon exchange on a neutron inside the electronic and muonic atoms. These results are relevant for the precise extraction of the isotope shift as well as in the analysis of the ground state hyperfine splitting in usual and muonic hydrogen.
The contribution of the proton polarizability to the ground state hyperfine splitting in muonic hydrogen is evaluated on the basis of modern experimental and theoretical results on the proton polarized structure functions. The value of this correction is equal to 4.6(8)\cdot 10^{-4} times the Fermi splitting E_F.
Corrections of orders alpha^5, alpha^6 are calculated in the hyperfine splitting of the muonic hydrogen ground state. The nuclear structure effects are taken into account in the one- and two-loop Feynman amplitudes by means of the proton electromagnetic form factors. The modification of the hyperfine splitting part of the Breit potential due to the electron vacuum polarization is considered. Total numerical value of the 1S state hyperfine splitting 182.638 meV in the (mu p) can play the role of proper estimation for the corresponding experiment with the accuracy 30 ppm.
We present the complete result for the ${\cal O}(α^7m_e)$ one-photon annihilation contribution to the hyperfine splitting of the ground state energy levels in positronium. Numerically it increases the prediction of quantum electrodynamics by $217\pm 1$ kHz.
We obtain a model-independent prediction for the two-photon exchange contribution to the hyperfine splitting in muonic hydrogen. We use the relation of the Wilson coefficients of the spin-dependent dimension-six four-fermion operator of NRQED applied to the electron-proton and to the muon-proton sectors. Their difference can be reliably computed using chiral perturbation theory, whereas the Wilson coefficient of the electron-proton sector can be determined from the hyperfine splitting in hydrogen. This allows us to give a precise model-independent determination of the Wilson coefficient for th…
Recent measurements of the $η_b(1S)$, the ground state of the $b\bar{b}$ system, show the splitting between it and the $\Up(1S)$ to be 69.5$\pm$3.2 MeV, considerably larger than lattice QCD and potential model predictions, including recent calculations published by us. The models are unable to incorporate such a large hyperfine splitting within the context of a consistent description of the energy spectrum and decays. We demonstrate that in our model, which incorporates a relativistic kinetic energy term, a linear confining term including its scalar-exchange relativistic corrections, and the c…
The contribution of hadronic vacuum polarization to the hyperfine splitting of the muonic hydrogen ground state is calculated with the account of experimental data on the cross section of e^+e^-\to annihilation into hadrons and the dipole parameterization of electromagnetic proton form factors.
The one-loop self-energy correction to the hyperfine splitting of the 1s and 2s levels in H-like low-Z atoms is evaluated to all orders in Zα. The results are compared to perturbative calculations. The residual higher-order contribution is evaluated. Implications to the specific difference of the hyperfine structure intervals 8Δν_2 - Δν_1 in He^+ are investigated.
The contribution of the proton polarizability to the hydrogen hyperfine splitting is evaluated on the basis of modern experimental and theoretical results on the proton polarized structure functions. The value of this correction is equal to 1.4 ppm.
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 reevaluate the Zemach, recoil and polarizability corrections to the hyperfine splitting in muonic hydrogen expressing them through the low-energy proton structure constants and obtain the precise values of the Zemach radius and two-photon exchange (TPE) contribution. The uncertainty of TPE correction to S energy levels in muonic hydrogen of 105 ppm exceeds the ppm accuracy level of the forthcoming 1S hyperfine splitting measurements at PSI, J-PARC and RIKEN-RAL.
The hyperfine mass splittings of baryons containing a heavy quark are derived at leading order in large $N$ QCD. Hyperfine splittings either preserve or violate heavy quark spin symmetry. Previous work proves that the splittings which preserve heavy quark spin symmetry are proportional to ${\bf J}^2$ at order $1/N$, where $J$ is the angular momentum of the light degrees of freedom of the baryon. This work proves that the splittings which violate heavy quark spin symmetry are proportional to ${\bf J} \cdot {\bf S_Q}$ at order $1/(N m_Q)$ in the $1/N$ and $1/m_Q$ expansions.
We provide an accurate evaluation of the two-photon exchange correction to the hyperfine splitting of S energy levels in muonic hydrogen exploiting the corresponding measurements in electronic hydrogen. The proton structure uncertainty in the calculation of $α^5$ contribution is sizably reduced.
We calculate the contribution from the two-photon exchange on the neutron to the hyperfine splitting of S energy levels. We update the value of the neutron Zemach radius, estimate total recoil and polarizability corrections. The resulting two-photon exchange in electronic atoms exceeds by an order of magnitude the leading Zemach term and has different sign both in electronic and muonic hydrogen.
The hyperfine splitting in heavy quarkonia is considered in its relation to the leptonic decay rates with the account of relativistic and radiative corrections. The calculated decay rates agree well with the available experimental data, while the predicted η_c(2S) mass is significantly smaller than the value measured recently by the Belle Collaboration.
The $Σ_c^*-Σ_c$ and $Σ_b^*-Σ_b$ hyperfine mass splittings are computed in the Skyrme model. The hyperfine splittings are suppressed by both $1/N_c$ and by $1/m_Q$, where $N_c$ is the number of colors and $m_Q$ is the mass of the heavy quark. The $Σ_c$, $Σ_c^*$, $Σ_b$, $Σ_b^*$, and $Λ_b$ masses are predicted in terms of the known values of the $Λ_c$, $D$, $D^*$, $B$ and $B^*$ masses.
This paper aims at proving the fundamental role of a relativistic formulation for quarkonia models. We present a completely covariant description of a two-quark system interacting by the Cornell potential with a Breit term describing the hyperfine splitting. Using an appropriate procedure to calculate the Breit correction, we find heavy meson masses in excellent agreement with experimental data. Moreover, also when applied to light quarks and even taking average values of the running coupling constant, we prove that covariance properties and hyperfine splitting are sufficient to explain the li…
We compute the next-to-leading, O(m alpha^5), contribution to the hyperfine splitting in positronium within the framework of NRQED. When applied to the ground state, our calculation reproduces known results, providing a further test of NRQED techniques. Besides providing a very simple method of calculation of the standard result, we also obtain new expressions for excited states of positronium with negligible additional effort. Our calculation requires the complete next-to-leading matching of the lowest-dimension NRQED four-fermi couplings, which we publish here for the first time.
We consider the proton structure corrections to hydrogen ground-state hyperfine structure, focusing on a state-of-the-art evaluation of the inelastic nucleon corrections--the polarizability corrections--using analytic fits to the most recent data. We find a value for the fractional correction Delta_{pol} of 1.3 \pm 0.3 ppm. This is 1--2 ppm smaller than the value of Delta_{pol}$ one would deduce using hyperfine splitting data and elastic proton structure corrections obtained from modern form factor fits. In addition, we discuss the derivations of the relevant formulas, paying attention to lept…
By relating fine and hyperfine spittings for l=1 states in bottomium we can factor out the less tractable part of the perturbative and nonperturbative effects. Reliable predictions for one of the fine splittings and the hyperfine splitting can then be made calculating in terms of the remaining fine splitting, which is then taken from experiment; perturbative and nonperturbative corrections to these relations are under full control. The method (which produces reasonable results even for the $c{\bar c}$ system) predicts a value of 1.5 MeV for the $(s=1)-(s=0)$ splitting in $b{\bar b}$, opposite …
