A. V. Luchinsky
Muon pair production in exclusive radiative decays $χ_{cJ}\to J/ψμμ$, $χ_{bJ}\toΥμμ$ are considered. We present numerical values of the branching fractions and distributions over various kinematical variables.
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We consider the inclusive radiative decays quarkonium -> gamma + hadrons and examine the effects of soft QCD radiation on the photon energy spectrum near the endpoint.
We study infrared QCD effects in radiative quarkonia decays. We examine the endpoint region z -> 1 of the photon spectrum. We point out a cancellation mechanism for the corrections in $α_s^n \ln^{m} (1-z)$, $m \leq 2 n$, in the short-distance coefficient for the color-singlet Fock state in the quarkonium. The cancellation is due to the coherence of the color radiation, and applies even though logarithmic contributions are present in the jet distributions associated with the decay. We comment on the implications of our results for the modeling of hadronization in the endpoint region and for the…
We argue that the photon spectra in radiative decays of various heavy quarkonium states provide important information on their nature. If two of these states are in the strong coupling regime, we are able to produce a parameter-free model independent formula, which holds at next-to-leading order and includes both direct and fragmentation contributions. When the formula is checked against recent CLEO data it favors Upsilon (2S) and Upsilon (3S) in the strong coupling regime and disfavors Upsilon (1S) in it.
In this work we study the radiative decay widths of vector quarkonia for the process of $J/ψ(nS)\rightarrowη_{c}(nS)γ$ and $Υ(nS)\rightarrowη_{b}(nS)γ$ (for principal quantum numbers $n=1, 2, 3$) in the framework of Bethe-Salpeter equation under the covariant instantaneous ansatz using a $4\times 4$ form of BSE. The parameters of the framework were determined by a fit to the mass spectrum of ground states of pseudoscalar and vector quarkonia, such as; $η_{c}$, $η_{b}$, $J/ψ$ and $Υ$. These input parameters so fixed were found to give good agreements with data on mass spectra of ground and exci…
Non-relativistic QCD (NRQCD) predicts colour octet contributions to be significant not only in many production processes of heavy quarkonia but also in their radiative decays. We investigate the photon energy distributions in these processes in the endpoint region. There the velocity expansion of NRQCD breaks down which requires a resummation of an infinite class of colour octet operators to so-called shape functions. We model these non-perturbative functions by the emission of a soft gluon cluster in the initial state. We found that the spectrum in the endpoint region is poorly understood if …
In this work we study the radiative decays of heavy-light quarkonia through M1 and E1 transitions, that involve quark-triangle diagrams with two hadron vertices, and are difficult to evaluate in BSE-CIA. We have expressed the transition amplitude, $M_{fi}$ as a linear superposition of terms involving all possible combinations of $++$, and $--$ components of Salpeter wave functions of final and initial hadron, with coefficients being related to results of pole integrals over complex $σ$- plane. We evaluate the decay widths for $M1$ transitions ($^3S_1 \rightarrow ^1S_0 +γ$), and $E1$ transition…
The radiative spin-flip transition rates of heavy quarkonium states depend sensitively on the matrix elements of the effective confining interaction through the associated two-quark exchange current operator. The Hamiltonian model based on a scalar linear confining interaction with a single gluon exchange hyperfine term is shown to provide an adequate description of the $J/ψ\to η_cγ$ and $ψ(2S)\to η_cγ$ decay widths once the relativistic single quark magnetic moment operator is treated without approximation and the exchange current is taken into account. Predictions are given for the radiative…
The Operator Product Expansion, in conjunction with the power counting of non-relativistic field theory, is used to examine the end-point region of the radiative decay of heavy quark bound states with $^3S_1$ quantum numbers, $Q\bar{Q}\rightarrow γ+X$. We identify an infinite class of operators that determine the shape of the photonic end-point spectrum. These operators can be resummed to form an octet structure function which parameterizes the energy of the dynamical gluon content of the leading octet Fock state component of the quarkonium. This color-octet contribution is important when the …
We revisit the calculation of the width for the radiative decay of a $1^{+-}$ heavy $Q \bar Q$ meson via the channel $1^{+-} \to 0^{-+} +γ$ in the covariant light-front quark model. We carry out the reduction of the light-front amplitude in the non-relativistic limit, explicitly computing the leading and next-to-leading order relativistic corrections. This shows the consistency of the light-front approach with the non-relativistic formula for this electric dipole transition. Furthermore, the theoretical uncertainty in the predicted width is studied as a function of the inputs for the heavy qua…
Axion-Like Particles in Radiative Quarkonia Decays
本文综述了B和Charm工厂中通过 $e^+ e^- \ o γ\,a$ 过程产生类轴子粒子（ALP）的机制，基于Belle II和BESIII实验数据推导了对ALP与标准模型场耦合的约束，并区分了不可见与可见衰变情景。
Decay rates of quarkonia are studied within the framework of NRQCD formalism. The basic parameters of the formalism have been obtained from different potential schemes studied for the spectra of quarkonia. We estimate the heavy quarkonia mass spectra, radiative and leptonic widths and compare them with other contemporary theoretical approaches and experimental results.
This work is an extension of our previous work in \cite{bhatnagar20} to calculate M1 transitions, $0^{-+}\rightarrow 1^{--} γ$, and E1 transitions involving axial vector mesons such as, $1^{+-} \rightarrow 0^{-+}γ$, and $0^{-+}\rightarrow 1^{+-} γ$ for which very little data is available as of now. We make use of the general structure of the transition amplitude, $M_{fi}$ derived in our previous work \cite{bhatnagar20} as a linear superposition of terms involving all possible combinations of $++$, and $--$ components of Salpeter wave functions of final and initial hadrons. In the present work,…
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.
Two-photon decay rates of pseudoscalar, scalar and tensor states of charmonium and bottomonium are calculated in the framework of the relativistic quark model. Both relativistic effects and one-loop radiative corrections are taken into account. The obtained results are compared with other theoretical predictions and available experimental data.
Three-gluon decays of radially excited quarkonia $ψ(2S)$ and $Υ(2S)$ with both relativistic and QCD radiative corrections
研究$ψ(2S)$和$Υ(2S)$的三胶子衰变，结合相对论和QCD修正，通过波函数节点结构分析，推导极化衰变宽度关系，预测衰变率与实验相符，提取参数反映更局域的动量空间波函数。
Radiative Leptonic Decay of Heavy Quarkonia
本研究在NRQCD框架下重新计算重夸克偶素辐射轻子衰变分支比，建立与纯轻子衰变宽度联系，发现Ψ(2S)的τ通道比值比文献大四倍，对QED/QCD过程和新物理研究有重要意义。
Production cross-sections and Radiative Decay widths of Heavy Quarkonia in magnetized matter
本文利用手征有效模型研究了磁化核物质中重夸克偶素的生产截面和辐射衰变宽度，发现磁场导致的PV混合会显著改变介子质量并产生双峰结构，对重离子碰撞实验具有可观测影响。
Rare Exclusive Decays of the Z-boson into S-wave Quarkonia within the Bethe-Salpeter Formalism
利用Bethe-Salpeter形式论研究Z玻色子衰变到双S波夸克偶素及辐射衰变到单S波夸克偶素，考虑QCD和QED领头阶贡献，发现粲偶素结果大于NRQCD而底偶素较小，体现相对论效应差异。
It is shown that $BR(χ_{b1}(1P)\rightarrow Z\rightarrow e^+e^-)\simeq 3.3\cdot 10^{-7}$, $BR(χ_{b1}(2P)\rightarrow Z\rightarrow e^+e^-)\simeq 4.1\cdot 10^{-7}$ and $BR(χ_{c1}(1P)\rightarrow Z\rightarrow e^+e^-)\simeq 10^{-8}$ that give a good chance to search for the direct production of pseudovector $^3P_1$ heavy quarkonia in $e^+e^-$ collisions ($e^+e^-\rightarrow Z\rightarrow ^3P_1$) even at current facilities not to mention $b$ and $c-τ$ factories. Leading radiative corrections to annihilation of quarkonia in QCD are discussed.
Using the expression of the dynamical gluon mass obtained through the operator product expansion we discuss the relevance of gluon mass effects in the decays V -> hadrons (V = J/Psi, Upsilon). Relativistic and radiative corrections are also introduced to calculate alpha_s(m_c) and alpha_s(m_b) comparing them with other values available in the literature. The effects of dynamical gluon masses are negligible for Upsilon decay but important for J/Psi decay.
We examine the spectra and radiative decays of the cc-bar and bb-bar systems using a model which incorporates the complete one-loop spin-dependent perturbative QCD short distance potential, a linear confining term including (spin-dependent) relativistic corrections to order v^2/c^2, and a fully relativistic treatment of the kinetic energy. We compare the predictions of this model to experiments, including states and decays recently measured at Belle, BaBar, CLEO and CDF.
We examine the electronic width ratios of Upsilon resonances below the BBbar threshold by means of an effective (Cornell-type) QCD potential incorporating 1/m_b corrections obtained from a prior fit to the bottomonium spectrum. From our analysis we conclude that the Upsilon(2S) and Upsilon(3S) states should belong to the strong-coupling (nonperturbative) regime while the Upsilon(1S) state should belong to the weak-coupling (perturbative) regime, in agreement with a previous study based on radiative decays.
We extend our treatment of the the spectroscopy and decays of the charm-strange quarkonium system to include the effect of using the full three-loop QCD correction to the static short distance potential. As before, our potential model consists of the relativistic kinetic energy term, a scalar linear confining term including its relativistic corrections and the perturbative QCD spin-dependent terms. A set of unperturbed wave functions for the various states is obtained using a variational technique that is further constrained by requiring that the wave functions also satisfy the relativistic vi…
We present calculations of radiative transitions between vector and pseudoscalar quarkonia in the light-front Hamiltonian approach. The valence sector light-front wavefunctions of heavy quarkonia are obtained from the Basis Light-Front Quantization (BLFQ) approach in a holographic basis. We study the transition form factor with both the traditional "good current" $J^+$ and the transverse current $\vec J_\perp$ (in particular, $J^R=J^x+i J^y$). This allows us to investigate the role of rotational symmetry by considering vector mesons with different magnetic projections ($m_j=0,\pm 1$). We use t…
We calculate the dynamical relativistic corrections, originating from radiative one-gluon-exchange, to the leptonic decay width of heavy quarkonia in the framework of a covariant formulation of Light-Front Dynamics. Comparison with the non-relativistic calculations of the leptonic decay width of J=1 charmonium and bottomonium S-ground states shows that relativistic corrections are large. Most importantly, the calculation of these dynamical relativistic corrections legitimate a perturbative expansion in $α_s$, even in the charmonium sector. This is in contrast with the ongoing belief based on c…
One-loop QED corrections to the differential width of radiative muon decay are considered. Results can be used to analyze high statistics data of modern and future experiments.
New double ratios of exponential moments of different two-point functions, which are less sensitive to the heavy quark mass and to the continuum effects than the commonly used ratio of moments, are presented for a more refined analysis of the mass-splittings between the different heavy quarkonia states. We show that at the $c$ and $b$ quark mass scales the $1/m$-expansion does not converge for these quarkonia channels, while a connection of our mass and width formulae, with the potential model ones is done. Using the present value of the QCD coupling $α_s$, we deduce the value: $<α_s G^2> = (7…
Radiative muon and tau lepton decays are described within the model-independent approach with the help of generalized Michel parameters. The exact dependence on charged lepton masses is taken into account. The results are relevant for modern and future experiments on muon and tau lepton decays.
The first order QED corrections to the polarized muon decay spectrum are considered. The exact dependence on electron and muon masses is kept. Numerical results are presented.
The radiative decay of muon-neutrinos in matter with a scheme of mass-degenerate neutrinos could be the common origin of the appearance of anti-electron-neutrinos at LSND and the disappearance of muons-neutrinos at SuperKamiokande. With the decay probability fixed by the LSND signal, the deficit of atmospheric neutrinos can be satisfactorily reproduced.
We study the radiative (E1 and M1) decays of P-wave quarkonia in a strong magnetic field based on the Lagrangian of potential nonrelativistic QCD. To investigate their properties, we implement a polarized wave function basis justified in the Paschen-Back limit. In a magnetic field stronger than the spin-orbit coupling, the wave functions of the P-wave quarkonia are drastically deformed by the Hadronic Paschen-Back effect. Such deformation leads to the anisotropy of the direction of decays from the P-wave quarkonia. The analytic formulas for the radiative decay widths in the nonrelativistic lim…
The electromagnetic radiative transition widths for heavy quarkonia, as well as digamma and digluon decay widths, are computed in the framework of the extended harmonic confinement model (ERHM) and Coulomb plus power potential (CPP$_ν$) with varying potential index $ν$. The outcome is compared with the values obtained from other theoretical models and experimental results. While the mass spectra, digamma and digluon widths from ERHM as well as CPP$_{ν=1}$ are in good agreement with experimental data, the electromagnetic transition widths span over a wide range for the potential models consider…
We investigate the implications of spin symmetry for heavy quarkonia production and decay. We first compare spin symmetry predictions for charmonia and bottomonia radiative transitions with data and find they agree quite well. We next use spin symmetry along with nonrelativistic QCD power counting to determine the leading order alignment of P and D-wave orthoquarkonia that are produced through gluon fragmentation. Finally, we discuss a mechanism which may resolve the current factor of 30 discrepancy between theoretical predictions and experimental measurements of prompt $ψ'$ production at the …
We compute the energy loss of heavy quarkonia in high temperature QCD plasmas and investigate the energy loss effects on quarkonium suppression. Based on the effective vertex derived from the Bethe-Salpeter amplitude for quarkonium, the collisional and radiative energy loss are determined by quarkonium-gluon elastic scattering and the associated gluon-bremsstrahlung, respectively. In the energy regime $E<m_Υ^2/T$ the collisional energy loss is dominant over the radiative one, and the total energy loss increases with the plasma temperature and the initial energy of quarkonium. Our numerical ana…
High-energy muons can travel large thicknesses of matter. For underground neutrino and cosmic ray detectors the energy loss of muons has to be known accurately for simulations. In this article the next-to-leading order correction to the average energy loss of muons through bremsstrahlung is calculated using a modified Weizsäcker-Williams method. An analytical parametrisation of the numerical results is given.
Recent measurements of the Higgs-muon coupling are directly probing muon mass generation for the first time. We classify minimal models with a one-loop radiative mass mechanism and show that benchmark models are consistent with current experimental results. We find that these models are best probed by measurements of $(g-2)_μ$, even when taking into account the precision of Higgs measurements expected at future colliders. The current $(g-2)_μ$ anomaly, if confirmed, could therefore be a first hint that the muon mass has a radiative origin.
We calculate in closed analytical form the one-photon loop radiative corrections to muon Compton scattering $μ^- γ\to μ^- γ$. Ultraviolet and infrared divergencies are both treated in dimensional regularization. Infrared finiteness of the (virtual) radiative corrections is achieved (in the standard way) by including soft photon radiation below an energy cut-off $λ$. We find that the anomalous magnetic moment $α/2π$ provides only a very small portion of the full radiative corrections. Furthermore, we extend our calculation of radiative corrections to the muon-nucleus bremsstrahlung process (or …
Process of muon (pion) pair production with small invariant mass in the electron-positron high-energy annihilation, accompanied by emission of hard photon at large angles, is considered. We find that the Dell-Yan picture for differential cross section is valid in the charge-even experimental set-up. Radiative corrections both for electron block and for final state block are taken into account.
The lowest order radiative correction to the differential cross-section of process of muon pair production with emission of hard photon at high energy electron-positron annihilation are calculated. Taking into account the emission of additional soft and hard photon the cross-section can be put in the form of Drell-Yan process in leading logarithmical approximation. Applying the crossing transformation we obtain the cross section of radiative electron-muon high-energy scattering process. Virtual and soft photon emission contributions of non-leading form are tabulated for several typical kinemat…
The leptons are viewed as composite objects, exhibiting anomalous magnetic moments and anomalous flavor-changing transition moments. The decay $μ\to e γ$ is expected to occur with a branching ratio of the same order as the present experimental limit.
We investigate the spectroscopy and decays of the charm-strange quarkonium system in a potential model consisting of a relativistic kinetic energy term, a linear confining term including its scalar and vector relativistic corrections and the complete perturbative one-loop quantum chromodynamic short distance potential. The masses and wave functions of the various states are obtained using a variational technique, which are then used in a perturbative treatment of the potential to find the mass spectrum of the $c\bar{s}$ system and radiative decay widths. Our results compare well with the avail…
We explore muon anomalous magnetic moment (muon $g-2$) in a scotogenic neutrino model with a gauged lepton number symmetry $U(1)_{μ-τ}$. In this model, a dominant muon $g-2$ contribution comes not from an additional gauge sector but from a Yukawa sector. In our numerical $Δχ^2$ analysis, we show that our model is in favor of normal hierarchy with some features. We demonstrate one benchmark point, satisfying muon $g-2$ at the best fit value $25.1\times10^{-10}$.
Here we present the two-photon and two-gluon decay widths of the S-wave ($η_{Q\in c,b}$) and P-wave ($χ_{Q\in c,bJ}$) charmonium and bottonium states and the radiative transition decay widths of $c\bar c$, $b\bar b$ and $c\bar b$ systems based on Coulomb plus power form of the inter-quark potential ($CPP_ν$) with exponent $ν$. The Schr$\ddot{o}$dinger equation is solved numerically for different choices of the exponent $ν$. We employ the masses of different states and their radial wave functions obtained from the study to compute the two-photon and two-gluon decay widths and the E1 and M1 radi…
A description and a detailed comparison of the Mo and Tsai and the Dubna radiative correction schemes is presented. Numerical comparisons made in the kinematical region of the NMC high energy deep inelastic electroproduction experiment are discussed. An overall agreement between the two approaches in the region of low $x$ and high $y$, where the radiative corrections are largest, is better than 2$\%$.
We study the NNLO radiative corrections of enhanced electroweak strength to the lineshape of the Higgs boson in the processes ($μ^+μ^- \to H \to ZZ$) and ($μ^+μ^- \to H \to t\bar t$), which are of interest for Higgs searches at a possible muon collider. We give the radiative corrections both in the on-shell renormalization scheme and in the pole renormalization scheme. The pole scheme appears to have better convergence properties, in agreement with previous results regarding the position of the Higgs pole in the complex plane.
Radiative corrections of the order $\mathcal{O}(α^3L^3)$ to unpolarized muon decay spectrum
本文研究非极化μ子衰变能谱的高阶辐射修正，计算并给出了$\mathcal{O}(α^2 L)$、$\mathcal{O}(α^3 L^3)$和$\mathcal{O}(α^3 L^2)$阶的结果。
The process of the muon (pion) pair production with small invariant mass in the electron--positron high--energy annihilation, accompanied by emission of hard photon at large angles, is considered. We find that the Drell--Yan picture for differential cross section is valid in the charge--even experimental set--up. Radiative corrections both for electron block and for final state block are taken into account.
We have noted that the electron spectrum of muon decay in the leading logarithmic approximation calculated in two lowest orders of the perturbation theory in the paper of Berman (1958), can be reproduced by the parton language. This fact permits one to generalize the result to all orders of the perturbation theory using the structure function method.
We present results for the corrections of order alpha^2 (Z alpha) E_F to the hyperfine splitting of muonium. We compute all the contributing Feynman diagrams in dimensional regularization and a general covariant gauge using a mixture of analytical and numerical methods. We improve the precision of previous results.
Electroweak radiative corrections to muon capture on nuclei are computed and found to be sizable. They enhance the capture rates for hydrogen and helium by 2.8% and 3.0% respectively. As a result, the value of the induced pseudoscalar coupling, g_P^exp, extracted from a recent hydrogen 1S singlet capture experiment is increased by about 21% to g_P^exp = 7.3 +/- 1.2 and brought into good agreement with the prediction of chiral perturbation theory, g_P^theory=8.2 +/- 0.2. Implications for helium capture rate predictions are also discussed.
Self-consistent $M1$ radiative transitions of excited $B_c$ and heavy quarkonia with different polarizations in the light-front quark model
本文在光前夸克模型中用变分法和 QCD 有效哈密顿量研究重夸克偶素及 $B_c$ 介子的 $M1$ 辐射跃迁，验证了不同流分量与极化结果的一致性，并通过 $M_0$ 替换实现自洽，给出了与实验和格点 QCD 相符的预言。
The evidence for dark matter signals a new class of particles at the TeV scale, which may manifest themselves indirectly through loop effects. In a simple model we show that these loop effects may be responsible for the enhanced muon anomalous magnetic moment, for the neutrino mass, as well as for leptogenesis in a novel way. This scenario can be verified at LHC experiments.
Improvement of the radiative correction scheme for the deep inelastic scattering on the heavy targets is discussed. Arguments that the contribution of the radiative tail from the elastic peak should be calculated without use of the Born approximation in the case of the heavy target scattering are presented. The semianalytical approach based on the classical solution of the old bremsstrahlung problem is shortly described. The numerical results for the new correction factor are presented for the scattering on tin and lead.
An expression for the Dalitz plot of the semileptonic decay of a charged kaon, including radiative corrections to order O[απ)(q/M_1)], where q is the four-momentum transfer and M_1 is the mass of the decaying kaon, is obtained. Contributions of both the three- and four-body regions are accounted for. Besides, the emitted muon is considered to be polarized so the analysis is also focused on evaluating the radiative corrections to the longitudinal, transverse, and normal polarization components of the muon. The final formulas, with the triple integration of the bremsstrahlung photon variables re…
Radiative Corrections to the Muon Polarization in the Semileptonic Decay of a Neutral Kaon
本文给出含$\ncalO[(α/ π)(q/M_1)]$阶辐射修正的中性K介子半轻衰变$K_{μ3}^0$达利兹图模型无关表达式，数值计算μ子三个极化分量的辐射修正，发现修正值远小于未修正值，可用于模型无关实验分析。
Electrons emitted in the radiative decay mu^- -> e^- anti-nu_e nu_mu gamma have a significant probability of being right-handed, even in the limit m_e -> 0. Such ``wrong-helicity'' electrons, arising from helicity-flip bremsstrahlung, contribute an amount alpha/(4 pi) Gamma_0 to the muon decay width (Gamma_0 = G_F^2 m^5_mu/ (192 pi^3)). We use the helicity-flip splitting function D_hf (z) of Falk and Sehgal (Phys. Lett. B 325, 509 (1994)) to obtain the spectrum of the right-handed electrons and the photons that accompany them. For a minimum photon energy E_gamma = 10 MeV (20 MeV), approximatel…
Muon pair production through the radiative return is of importance for a measurement of the hadronic production cross section in two ways: it provides an independent calibration and it may give rise to an important background for a measurement of the pion form factor. With this motivation the Monte Carlo event generator PHOKHARA is extended to include next-to-leading order radiative corrections to the reaction $e^+e^-\to μ^+μ^-γ$. Furthermore, virtual ISR corrections to FSR from pions are introduced, which extends the applicability of the generator into a new kinematical regime. Finally, the e…
The recent experimental status, including the confirmation of the muon $g-2$ anomaly at Fermilab, indicates a Beyond Standard Model (BSM) satisfying the following properties: 1) it enhances the $g-2$ 2) suppresses flavor violations, such as $μ\to e γ$, 3) suppresses CP violations, such as the electron electric dipole moment (EDM). In this letter, I show that if the masses of heavy leptons are generated radiatively, the eigenbasis of the mass matrix and higher dimensional photon operators can be automatically aligned. As a result, the muon $g-2$ is enhanced but the EDM of the electron and $μ\to…
The mass spectra and electromagnetic decay rates of charmonium, bottomonium and B_c mesons are comprehensively investigated in the relativistic quark model. The presence of only heavy quarks allows the expansion in powers of their velocities. All relativistic corrections of order v^2/c^2, including retardation effects and one-loop radiative corrections, are systematically taken into account in the computations of the mass spectra. The obtained wave functions are used for the calculation of radiative magnetic dipole (M1) and electric dipole (E1) transitions. It is found that relativistic effect…
This writeup summarizes recent CMS results on quarkonia measurements in pp, pPb and PbPb collisions at LHC. The excellent muon detection capability of CMS allows measurement of charmonia states at high transverse momentum ($p_T$) while the $Υ$ states can be reconstructed starting at zero $p_T$. The absolute and relative yields of different charmonia and bottomonia states modified in PbPb collisions (over pp collisions) are described. The vertexing capability of CMS enables measurement of B meson energy loss via its decay to J/$ψ$. An overview of these measurements is given. How these measureme…
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