Heavy fermion pair production in $e^+e^-$ annihilation is a fundamental process in hadron physics and is of considerable interest for various phenomena. In this paper, we will apply the Principle of Maximum Conformality (PMC) to provide a comprehensive analysis of these processes. The PMC provides a systematic, unambiguous method for determining the renormalization scales of the QCD coupling constant for single-scale and multiple-scale applications. The resulting predictions eliminate any renormalization scheme-and-scale ambiguities, eliminate the factorial renormalon divergences, and are consistent with the requirements of the renormalization group. It is remarkable that two distinctly different scales are determined by using the PMC for heavy fermion pair production near the threshold region. One scale is the order of the fermion mass $m_f$, which enters the hard virtual corrections, and the other scale is of order $ v\,m_f$, where $v$ is the quark velocity, which enters the Coulomb rescattering amplitude. The PMC scales yield the correct physical behavior and reflect the virtuality of the propagating gluons (photons) for the QCD (QED) processes. Moreover, we demonstrate the consistency of PMC scale setting from QCD to QED. Perfect agreement between the Abelian unambiguous Gell-Mann-Low and the PMC scale-setting methods in the limit of zero number of colors is demonstrated.
Using renormalization-group methods, we derive differential equations for the all-orders summation of logarithmic corrections to the QCD series for R(s) = sigma(e^+ e^- --> hadrons)/sigma(e^+ e^- --> mu^+ mu^-), as obtained from the imaginary part of the purely-perturbative vector-current correlation function. We present explicit solutions for the summation of leading and up to three subsequent subleading orders of logarithms. The summations accessible from the four-loop vector-correlator not only lead to a substantial reduction in sensitivity to the renormalization scale, but necessarily impo…
A threshold singularity in a heavier meson channel, e.g. $D^* {\bar D}^*$, generally reflects in the amplitudes of $e^+e^-$ annihilation into lighter meson pairs, such as $D^* {\bar D}$, $D {\bar D}$, and $D_s {\bar D}_s$, due to the channel coupling. The behavior of the cross section of the $e^+e^-$ annihilation into each channel in this situation is considered using general properties of the amplitudes near the new threshold. It is argued that the effects of the channel coupling can be quite significant in the observable cross section, in particular near the $D^* {\bar D}^*$ threshold.
We argue that the recent CLEO-c data on $e^+e^-$ annihilation into pairs of charmed mesons at c.m. energy around 4.0 GeV are not well described by a single resonance $ψ(4040)$, but can be better understood if there is an additional narrow resonance with mass within few MeV from the $D^* {\bar D}^*$ threshold.
We show that higher-order coefficients required to perform threshold resummation for electroweak annihilation processes, such as Drell-Yan or Higgs production via gluon fusion, can be computed using perturbative results derived in Deep Inelastic Scattering. As an example, we compute the three-loop coefficient D_3, generating most of the fourth tower of threshold logarithms for the Drell-Yan cross section in the MSbar scheme, using the recent three-loop results for splitting functions and for the quark form factor, as well as a class of exponentiating two-loop contributions to the Drell-Yan pro…
We investigate a contribution of the $d$ wave to the cross section of $e^+e^-$ annihilation to the pair of charged leptons or nucleons close to threshold of the process. In contrast to the point of view accepted in literature, due to the Coulomb final state interaction this contribution does not vanish even at zero relative velocity of produced particles. This results in the nonzero asymmetry in angular distribution at threshold. Though value of the asymmetry is small, observation of this effect is not hopeless.
We show that the longitudinal polarization of the top quarks produced in the annihilation of e+ e- or mu+ mu- into tbar t at energies near the threshold is not affected by the large Coulomb-type corrections, which greatly modify the total cross section. Thus the longitudinal polarization, although small, may provide an independent information on the mass and the width of the top quark, largely independent of the uncertainty in alpha_s.
We study the structures in cross sections and R ratios concerning electron-positron annihilation reactions, for open-strangeness, open-charm and open-beauty hadron-pair production, from the perspective of a recently developed production formalism. Special attention is paid to non-resonant contributions. Known, tentative, and yet unknown resonances are spotted, with estimates for their masses and widths.
In the framework of potential NRQCD, we obtain the next-to-leading-log renormalization-group running of the matching coefficients for the heavy quarkonium production currents near threshold. This allows to obtain S-wave heavy-quarkonium production/annihilation observables with next-to-leading-log accuracy within perturbative QCD. In particular, we give expressions for the decays of heavy quarkonium to e^+e^- and to two photons. We also compute the O(mα^8\ln^3α) corrections to the Hydrogen spectrum.
We present the third-order QCD prediction for the production of top-anti-top quark pairs in electron-positron collisions close to the threshold in the dominant S-wave state. We observe a significant reduction of the theoretical uncertainty and discuss the sensitivity to the top quark mass and width.
The threshold behavior of $e^+ e^-$ annihilation is considered in the channels $B_{s0} \bar B_s^* + c.c.$, $B_{s1} \bar B_s + c.c.$, and $B_{s1} \bar B_s^* +c.c.$, where $B_{s0}$ and $B_{s1}$ are the excited bottom-strange $J^P=0^+$ and $J^P = 1^+$ mesons. It is argued that due to the heavy quark spin symmetry (HQSS) only one coherent combination of the first two channels is produced in the $S$ wave as well as the third channel. Thus, if there exist threshold molecular peaks in the considered channels, only two of such peaks can be formed in the annihilation. The properties of such threshold s…
We discuss the $p\bar{p}$ annihilation into a pair of charmed $D$ mesons not far from the threshold of the reaction. An interesting interference pattern in the differential cross section is predicted to arise from the existence of both $t$-channel charmed-baryon exchange and $s$-channel $Ψ^{''}$ charmonium resonance amplitudes. We argue that the experimental study of this process would provide new and valuable information about the unknown $p\bar{p}Ψ^{''}$ and $Λ_c N D$ couplings. These are important to know to solve the long-standing puzzle of the heavy flavour contents of baryons and to test…
We present analytic all-order results for the highest three threshold logarithms of the space-like and time-like off-diagonal splitting functions and the corresponding coefficient functions for inclusive deep-inelastic scattering (DIS) and semi-inclusive e^+ e^- annihilation. All these results, obtained through an order-by-order analysis of the structure of the corresponding unfactorized quantities in dimensional regularization, can be expressed in terms of the Bernoulli functions introduced by one of us and leading-logarithmic soft-gluon exponentials. The resulting numerical corrections are s…
By exploiting the analyticity properties of the two-point current-current correlator we obtain numerical predictions for the $e^+e^-$ moments in terms of the $τ$ decay rate. We perform a partial resummation of the pertinent perturbative series expansion by solving the renormalization group equation for Adler's function. Our predictions are renormalization scheme independent but depend on the order of the perturbative $β$-function expansion. The analysis involves the unknown five-loop coefficient $k_3$ for which we give some new estimates.
The processes of muons (tau) and charged pions pairs production at electron-positron annihilation with first order radiative corrections are considered. The calculation results are presented assuming the energies of final particles (cms implied) to be not far significantly from threshold production. The invariant mass distributions for the muon (tau) and pion pairs are obtained both for the initial and final state radiation. Some analytical calculations are illustrated numerically. The pions were assumed to be point-like objects and scalar QED was applied for calculation. The QED radiative cor…
The completion of the third-order QCD corrections to the inclusive top-pair production cross section near threshold demonstrates that the strong dynamics is under control at the few percent level. In this paper we consider the effects of the Higgs boson on the cross section and, for the first time, combine the third-order QCD result with the third-order P-wave, the leading QED and the leading non-resonant contributions. We study the size of the different effects and investigate the sensitivity of the cross section to variations of the top-quark Yukawa coupling due to possible new physics effec…
The subject of the charged-to-neutral yield ratio for B{\bar B} and D{\bar D}pairs near their respective thresholds in e^+e^- annihilation is revisited. As previously argued for the B mesons, this ratio should exhibit a substantial variation across the Upsilon(4S) resonance due to interference of the resonance scattering phase with the Coulomb interaction between the charged mesons. A simple alternative derivation of the expression describing this effect is presented here, and the analysis is extended to include the D meson production in the region of the psi(3770) resonance. The available dat…
Top quark pair production close to threshold at a next linear collider is discussed, with special focus on the influence of rescattering corrections. Numerical results are shown for the differential cross-section, i.e. the momentum distribution and the forward backward asymmetry, and for moments of the angular distribution of leptons arising from the semileptonic top quark decay.
We consider the $π^+π^-π_0γ$ final state in electron-positron annihilation at cms energies not far from the threshold. Both initial and final state radiations of the hard photon is considered but without interference between them. The amplitude for the final state radiation is obtained by using the effective Wess-Zumino-Witten Lagrangian for pion-photon interactions valid for low energies. In real experiments energies are never such small that $ρ$ and $ω$ mesons would have negligible effect. So a phenomenological Breit-Wigner factor is introduced in the final state radiation amplitude to accou…
We present a novel method for precisely determining the running QCD coupling constant $α_s(Q^2)$ over a wide range of $Q^2$ from event shapes for electron-positron annihilation measured at a single annihilation energy $\sqrt{s}$. The renormalization scale $Q^2$ of the running coupling depends dynamically on the virtuality of the underlying quark and gluon subprocess and thus the specific kinematics of each event. The determination of the renormalization scale for event shape distributions is obtained by using the Principle of Maximum Conformality (PMC), a rigorous scale-setting method for gaug…
It is demonstrated how perturbative O(alpha_s^2) relativistic corrections to the non-relativistic stable heavy quark-antiquark production cross section in e^+e^- annihilation based on a Coulombic QCD potential can be systematically calculated using the concept of effective field theories. The O(alpha_s^2) corrections from the relativistic energy-momentum relation, the relativistic phase space corrections and the O(alpha_s^2) corrections involving the group theoretical factors C_F^2 and C_F T are determined explicitly. For the case of $t\bar t$ production the sum of these corrections amounts to…
We consider non-relativistic "dark" particles interacting through gauge boson exchange. At finite temperature, gauge exchange is modified in many ways: virtual corrections lead to Debye screening; real corrections amount to frequent scatterings of the heavy particles on light plasma constituents; mixing angles change. In a certain temperature and energy range, these effects are of order unity. Taking them into account in a resummed form, we estimate the near-threshold spectrum of kinetically equilibrated annihilating TeV scale particles. Weakly bound states are shown to "melt" below freeze-out…
Next-to-Leading-Order(NLO) QCD corrections to double J/psi production in e^+e^- annihilation at sqrt{s}=10.6 GeV are calculated. We find that they greatly decrease the cross section, with a K factor (NLO/LO) ranging from -0.31 to 0.25 depending on the renormalization scale. Although the renormalization scale dependence indicates a large uncertainty, when combined with the NLO QCD corrections to J/psi + eta_c production, it can explain why the double J/psi$ production could not be found at B factories while the J/psi + eta_c production could, despite the fact that cross section of the former is…
We derive the 1-loop Renormalization Group Equations for the parameters of the Minimal Supersymmetric Standard Model (MSSM) taking into account the successive decoupling of each sparticle below its threshold. This is realized by a step function at the level of each graph contributing to the Renormalization Group Equations.
We present the O(alpha_s) corrections to the cross section for the reaction e+e- --> gamma^* --> Q \bar Q in the energy region close to the threshold. We assume that the energy of the reaction is such that both the perturbative expansion in the strong coupling constant and expansion in the relative velocity of the heavy quarks can be used. We explicitly obtain terms O(alpha_s^2/beta^2, alpha_s^2/beta, alpha_s^2) in the relative correction to the threshold cross section. Using the ideas of asymptotic expansions, we demonstrate how an expansion of Feynman diagrams in the threshold region is cons…
We present threshold enhanced QCD corrections to the bottom quark energy distribution in Higgs boson decay and to hadroproduction in $l^+l^-$ annihilation beyond leading order in the strong coupling constant. This is achieved using the resummed decay distribution obtained using renormalisation group invariance and the mass factorisation theorem that they satisfy and Sudakov resummation of soft gluons.
The complete soft-enhanced and virtual-gluon contributions are derived for the quark coefficient functions in semi-inclusive e^+e^- annihilation to the third order in massless perturbative QCD. These terms enable us to extend the soft-gluon resummation for the fragmentation functions by two orders to the next-to-next-to-next-to-leading logarithmic (N^3LL) accuracy. The resummation exponent is found to be the same as for the structure functions in inclusive deep-inelastic scattering. This finding, together with known results on the higher-order quark form factor, facilitates the determination o…
We consider the threshold effect on the renormalization group (RG) evolution of the neutrino masses and mixing angles in TeV scale seesaw models. We obtain the analytic expressions using the factorization method in presence of threshold effects. We also perform numerical study of RG effects in two specific low scale seesaw models following the bottom-up approach and ascertain the role of seesaw thresholds in altering the values of masses and mixing angles during RG evolution.
Recently methods have been developed to extend the resummation of large-x double logarithms in inclusive deep-inelastic scattering (DIS) to terms not addressed by the soft-gluon exponentiation. Here we briefly outline our approach based on fixed-order results, the general large-x structure in dimensional regularization and the all-order factorization of mass singularities, which is directly applicable also to semi-inclusive e+e- annihilation (SIA). We then present some main results for the corresponding timelike splitting functions and transverse and longitudinal fragmentation functions. The c…
We revisit the problem of interplay between the strong and the Coulomb interaction in the charged-to-neutral yield ratio for $B {\bar B}$ and $D {\bar D}$ pairs near their respective thresholds in $e^+e^-$ annihilation. We consider here a realistic situation with a resonant interaction in the isospin I=0 channel and a nonresonant strong scattering amplitude in the I=1 state. We find that the yield ratio has a smooth behavior depending on the scattering phase in the I=1 channel. The same approach is also applicable to the $K {\bar K}$ production at the $ϕ(1020)$ resonance, where the Coulomb eff…
We find model-independent upper limits on rates of dark matter annihilation in galactic halos. The Born approximation generally fails, while exotic threshold enhancements akin to "Sommerfeld factors" also turn out to be baseless The most efficient annihilation mechanism involves perturbatively small decay widths that have largely been ignored. Widths that are very small compared to TeV mass scales suffice to effectively saturate unitarity bounds on annihilation rates. Bound state formation in weakly coupled theories produces small effects due to wave function normalizations. Unitarity shows th…
We present threshold enhanced N$^3$LO QCD corrections to inclusive Higgs production through bottom anti-bottom annihilation at hadron colliders using threshold resummed cross section. The resummed cross section is obtained using factorization properties and Sudakov resummation of the inclusive cross section. We use the recent results on threshold N$^3$LO corrections in QCD for Drell-Yan production and three loop QCD corrections to Higgs form factor with bottom anti-bottom quark to achieve this task. This is the first step towards the evaluation of complete N$^3$LO result. We have numerically d…
We use the Paris nucleon-antinucleon optical potential for explanation of experimental data in the process $e^+e^- \rightarrow p\bar p$ near threshold. It turns out that final-state interaction due to Paris optical potential allows us to reproduce available experimental data. It follows from our consideration that the isoscalar form factor is much larger than the isovector one.
We present the rapidity distribution of the Higgs boson produced through bottom quark annihilation at third order in QCD using the threshold approximation. We provide a framework, based on the factorization properties of the QCD amplitudes along with Sudakov resummation and the renormalization group invariance, that allows one to perform the computation of the threshold corrections in a consistent, systematic and accurate way. The recent results on threshold N$^3$LO correction in QCD for the Drell-Yan production and on three loop QCD correction to Higgs form factor with bottom anti-bottom quar…
We calculate the cross section for s-wave neutralino annihilation to three-body final states below the W^+ W^- and t-bar t thresholds. Such three-body channels may dominate the annihilation cross section if the neutralino mass is not too much less than m_t and m_W respectively. Furthermore, because neutrinos produced in these channels are much more energetic than those from the $b\bar{b}$ or tau^+ tau^- channels, they can dominate the energetic-neutrino fluxes from neutralino annihilation in the Sun or Earth far below these thresholds and significantly enhance the neutrino signal in certain re…
Top quark polarization in $e^+e^-$ annihilation into $t\bar t$ is calculated for linearly polarized beams. The Green function formalism is applied to this reaction near threshold. The Lippmann--Schwinger equations for the $S$-wave and $P$-wave Green functions are solved numerically for the QCD chromostatic potential given by the two-loop formula for large momentum transfer and Richardson's ansatz for intermediate and small momenta. $S$-$P$--wave interference contributes to all components of the top quark polarization vector. Rescattering of the decay products is considered. The mean values $\l…
The next-next-to-leading order QCD corrections to the e+e- annihilation into hadrons are considered. The stability of the predictions with respect to change of the renormalization scheme is discussed in detail for the case of five, four and three active quark flavors. The analysis is based on the recently proposed condition for selecting renormalization schemes according to the degree of cancellation that they introduce in the expression for the scheme invariant combination of the expansion coefficients. It is demonstrated that the scheme dependence ambiguity in the predictions obtained with t…
Multiparticle production in (2+1) dimensions is investigated. We show that in a small region around the threshold the perturbation theory becomes unapplicable due to infrared divergencies in a class of Feynman graphs with rescattering in final state. We develop a technique based on renormalization group for summing up leading logarithms and apply it to the $ϕ^4$ models with and without symmetry breaking and to the $O(N)$ $ϕ^4$ theory.
We show that, in the low-scale type-I seesaw model, renormalization group running of neutrino parameters may lead to significant modifications of the leptonic mixing angles in view of so-called seesaw threshold effects. Especially, we derive analytical formulas for radiative corrections to neutrino parameters in crossing the different seesaw thresholds, and show that there may exist enhancement factors efficiently boosting the renormalization group running of the leptonic mixing angles. We find that, as a result of the seesaw threshold corrections to the leptonic mixing angles, various flavor …
We consider the production of $B^* \bar B^*$ meson pairs in $e^+e^-$ annihilation near the threshold. The rescattering due to pion exchange between the mesons results in a mixing between three partial wave amplitudes: two $P$-wave with the total spin of the meson pair S=0 and S=2 and an F-wave amplitude. The mixing due to pion exchange with a low momentum transfer is calculable up to c.m. energy $E \approx 15 ÷20$\,MeV above the threshold. We find that the $P-F$ mixing is numerically quite small in this energy range, while the mixing of the two P-wave amplitudes is rapidly changing with energy…
The energy dependence of the cross sections of $p\bar p$, $n\bar n$, and meson production in $e^+e^-$ annihilation in the vicinity of the $p\bar p$ and $n\bar n$ thresholds is studied. The proton-neutron mass difference and the $p\bar p$ Coulomb interaction are taken into account. The values of the cross sections are very sensitive to the parameters of the optical potential. It is shown that the commonly accepted factorization approach for the account of the Coulomb interaction does not work well enough in the vicinity of the threshold due to the finite size of the optical potential well.
We study the effect of final state interactions at the threshold of Higgs boson pair production in the Glashow-Weinberg-Salam model. We consider three major processes of the pair production in the model: lepton pair annihilation, ZZ fusion, and WW fusion. We find that the corrections caused by the effect for these processes are markedly different. According to our results, the effect can cause non-negligible corrections to the cross sections for lepton pair annihilation and small corrections for ZZ fusion, and this effect is negligible for WW fusion.
Two-loop threshold corrections for both the strong coupling constant and Yukawa couplings of heavy SM fermions are considered in the context of Minimal Supersymmetric Standard Model (MSSM). With the help of the well-known SOFTSUSY code the dependence of the corrections on universal MSSM parameters is analyzed. For a consistent study of the influence of the corrections on SUSY mass spectrum three-loop renormalization group equations are implemented. A particular scenario (SPS4) is considered and the shifts of the particle masses due to contributions of different threshold corrections are presen…
In a physical renormalization scheme, gauge couplings are defined directly in terms of physical observables. Such effective charges are analytic functions of physical scales, and thus mass thresholds are treated with their correct analytic dependence. In particular, particles will contribute to physical predictions even at energies below their threshold. This is in contrast to unphysical renormalization schemes such as MS-bar, where mass thresholds are treated as step functions. In this paper we analyze supersymmetric grand unification in the context of physical renormalization schemes and fin…
Production of $p\bar{p}$ and $n\bar{n}$ pairs in $e^{+}e^{-}$ annihilation near the threshold of the process is discussed with account for the new experimental data appeared recently. Since a significant part of these new data was obtained at energies noticeably exceeding the threshold, we also take into account the form factor describing the amplitude of $N\bar{N}$ pair production at small distances. The effective optical potential, which describes a sharp dependence of the $N\bar{N}$ production cross sections near the threshold, consists of the central potential for $S$ and $D$ waves and the…
In this paper, we give comprehensive analyses for event shape observables in electron-positron annihilation by using the Principle of Maximum Conformality (PMC) which is a rigorous scale-setting method to eliminate the renormalization scheme and scale ambiguities in perturbative QCD predictions. Conventionally the renormalization scale and theoretical uncertainties in event shape observables are often evaluated by setting the scale to the center-of-mass energy $\sqrt{s}$. The event shape distributions using this conventional scale setting are plagued by the large renormalization scale uncertai…
Unified coupled-channel description for the five near-threshold structures $ψ(3770)$, $G(3900)$, $R(3760)$, $R(3780)$ and $R(3810)$ from $e^+e^-$ annihilation
We discuss hadron mass corrections and threshold resummation for deep-inelastic scattering $\ell N\rightarrow\ell' X$ and semi-inclusive annihilation $e^+e^-\rightarrow h X$ processes, and provide a prescription how to consistently combine these two corrections respecting all kinematic thresholds. We find an interesting interplay between threshold resummation and target mass corrections for deep-inelastic scattering at large values of Bjorken $x_B$. In semi-inclusive annihilation, on the contrary, the two considered corrections are relevant in different kinematic regions and do not affect each…
We present a partonic Monte Carlo event generator that can be used for calculating the group independent kinematical functions of any infrared safe four-jet observable at NLO accuracy. As an example, we calculate the differential distribution of the $Π_1$ and $Π_4$ Fox-Wolfram moments. We find large K factors (K $>$ 2). The effect of the radiative correction is to increase the overall normalization, but not to reduce the renormalization scale dependence significantly.
We calculate the radiative corrections to the annihilation of the Dark Matter particles into leptons. Lepton masses are taken into account. As the Dark Matter particles are considered both Dirac and Majorana fermions. We sum up all the leading logarithms contributions where it is possible. We show that in the Dirac fermion case the resulting cross-section is consistent with the renormalization group prediction: the cross-section have the Drell-Yan form. Whereas, in the Majorana fermions case we have two essentially different limits of the resulting cross-section and quantitively the answer str…
The cross section for vector leptoquark pair production in $e^+e^-$ annihilation is calculated for the case of finite anomalous gauge boson couplings $κ_{γ, Z}$ and $λ_{γ, Z}$. The minimal cross section is found to behave $\propto β^7$, leading to weaker mass bounds in the threshold range than in models studied previously.
We determine the O(alpha_s^2) corrections to the partonic hemisphere soft function relevant for thrust and jet mass distributions in e+e- annihilation in the dijet limit. In this limit the distributions can be described by a factorization theorem that sums large logarithmic terms and separates perturbative from nonperturbative effects. Using the known O(alpha_s^2) contributions of the jet functions and the hard coefficients in the factorization theorem, constraints from renormalization group evolution and nonabelian exponentiation, and results from numerical integration of O(alpha_s^2) QCD mat…
We calculate the supersymmetric QCD corrections in order $α_s$ to the cross section $e^+ e^- \to \sq_i \bar\sq_j$ $(i,j = 1, 2)$ within the Minimal Supersymmetric Standard Model. We pay particular attention to the case of the left--right squark mixing and to the renormalization of the mixing angle. The corrections due to gluino exchange turn out to be smaller than those due to gluon exchange, but they can be significant at higher energies even for a gluino mass of a few hundred GeV.
In the reaction of the antiproton-deuteron electromagnetic annihilation pbar + d --> e+e-n the value of the invariant mass M of the (e+e-) pair can be near or below the (pbar p) mass even for enough high momentum of incident antiproton. This allows to access the proton electromagnetic form factors in the time-like region of q^2 near the (pbar p) threshold. We estimate the cross section dsigma(pbar + d --> e+e-n)/dM for an antiproton beam momentum of 1.5 GeV/c. We find that near the (pbar p) threshold this cross section is about 1 pb/MeV. The case of heavy nuclei target is also discussed. Eleme…
The deployment of DeepCore array significantly lowers IceCube's energy threshold to about 10 GeV and enhances the sensitivity of detecting neutrinos from annihilations and decays of light dark matter. To match this experimental development, we calculate the track event rate in DeepCore array due to neutrino flux produced by annihilations and decays of galactic dark matter. We also calculate the background event rate due to atmospheric neutrino flux for evaluating the sensitivity of DeepCore array to galactic dark matter signatures. Unlike previous approaches, which set the energy threshold for…
