We present the first full analytic evaluation of the scattering amplitude for the process $q {\bar q} \to Q {\bar Q}$ up-to two loops in Quantum Chromodynamics, for a massless $(q)$ and a massive $(Q)$ quark flavour. The interference terms of the one- and two-loop amplitudes with the Born amplitude, decomposed in terms of gauge invariant form factors depending on the colour and flavour structure, are analytically calculated by keeping complete dependence on the squared center-of-mass energy, the squared momentum transfer, and the heavy-quark mass. The results are expressed as Laurent series around four space-time dimensions, with coefficients given in terms of generalised polylogarithms and transcendental constants up-to weight four. Our results validate the known, purely numerical calculations of the squared amplitude, and extend the analytic knowledge, previously limited to a subset of form factors, to their whole set, coming from both planar and non-planar diagrams, up-to the second order corrections in the strong coupling constant.
The CDF 3.7 sigma evidence of pure annihilation $B_s \to π^+ π^-$ decays, if confirmed, would imply a large annihilation scenario in the QCD factorization approach. This is somewhat unexpected as the large annihilation scenario was disfavored in previous studies. In this paper we reinvestigate the role of annihilation topology in QCD factorization. We find that it is not easy to reach the CDF central value of $B_s \to π^+ π^-$ decays when other decay channels are considered. Our analysis also reveals that, for well-measured charmless B decays into two final pseudoscalar mesons, the QCD factori…
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.
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 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…
The multiple hadron production in the events induced by the heavy primary quarks in $e^+e^-$ annihilation is reconsidered with account of corrected experimental data. New value for the multiplicity in $b\bar{b}$ events is presented on the basis of pQCD estimates.
In this paper we present an analysis of the multiple hadron production induced by primary heavy quarks in e+e- annihilation with the account of most complete and corrected experimental data. In the framework of perturbative QCD, new theoretical bounds on the asymptotically constant differences of the multiplicities in processes with light and heavy quarks are given.
We calculate the full one-loop SUSY-QCD corrections to stop annihilation into gluons and light quarks including the Sommerfeld enhancement effect and discuss their impact on the neutralino relic density in the MSSM.
We provide a brief summary of recent developments in QCD calculations in and beyond fixed-order perturbation theory, for observables in $e^{+}e^{-}$ annihilation as well as hadron collisions.
We present full QCD and SUSY-QCD corrections to neutralino pair annihilation into quark-antiquark pairs. We show results and numerically evaluate their impact on the neutralino annihilation cross section and the relic density in scenarios with non-universal gaugino masses. By comparing to the relic density obtained from a pure leading order calculation, we demonstrate that the corrections strongly influence the extraction of SUSY mass parameters from cosmological data.
We present a complete calculation of the QCD and SUSY-QCD corrections to neutralino pair annihilation into bottom quark-antiquark pairs through exchange of a pseudoscalar Higgs boson, which is the dominant process in the cosmological A-funnel region of the mSUGRA model. We present numerical predictions for the annihilation cross section and discuss the influence of the correction terms on the cold dark matter relic density with respect to recent cosmological data.
We calculate QCD correction to the neutralino annihilation cross section into quark anti-quark final state and discuss its implications to the calculation of neutralino relic density. We see that the QCD correction enhances the pair-annihilation cross section by O(10 %) when final-state quarks are non-relativistic. Consequently, when the lightest neutralinos dominantly annihilate into a t\bar{t} pair, the relic density of the lightest neutralino is significantly affected by the QCD correction, in particular when the lightest-neutralino mass is close to the top-quark mass.
We use classical or large Nc QCD to describe the mesons (pion, rho, omega) coming from proton-antiproton annihilation at rest as classical fields, which we then quantize as coherent states. This treatment gives a nearly parameter free account of the pion branching ratios in annihilation.
The annihilation type diagrams are difficult to calculate in any kind of models or method. Encouraged by the the successful calculation of pure annihilation type B decays in the perturbative QCD factorization approach, we calculate the pure annihilation type $D\to PP(V)$ decays in the perturbative QCD approach based on the $k_T$ factorization. Although the expansion parameter $1/m_D$ is not very small, our leading order numerical results agree with the existing experiment data for most channels. We expect the more accurate observation from experiments, which can help us learn about the dynamic…
We report on a complete calculation of electroweak production of top quark pairs in $e^+e^-$ annihilation at next-to-next-to-leading order in Quantum Chromodynamics. Our setup is fully differential and can be used to calculate any infrared-safe observable. Especially we calculated the next-to-next-to-leading order corrections to top-quark forward-backward asymmetry and found sizable effects. Our results show a large reduction of the theoretical uncertainties in predictions of the forward-backward asymmetry, and allow a precision determination of the top quark electroweak couplings at future $e…
We present the first results on the two-loop massless QCD corrections to the four-point amplitude $b+\overline{b} \rightarrow H+H$ in the five flavor scheme, treating bottom quarks as massless. This amplitude is sensitive to the trilinear Higgs boson coupling. Our two-loop result for this amplitude constitutes of purely virtual contributions to the next-to-next-to-leading order QCD predictions for the production of a pair of Higgs bosons at the Large Hadron Collider. Using these two loop amplitudes and exploiting the universality of the soft contributions in perturbative QCD, we obtain the NNL…
Within the framework of nonrelativistic quark-antiquark Cornell potential model formalism, we study the annihilation of heavy quarkonia. We determine their annihilation widths resulting into digluon, dilepton, $3γ$, $3g$ and $γgg$ and compare our findings with the available theoretical results and experimental data. We also provide the charge radii and absolute square of radial Schrödinger wave function at zero quark-antiquark separation for heavy quarkonia and $B_c$ mesons.
We report on two recent calculations of QCD corrections to neutralino annihilation cross sections: (1) the next-to-leading order corrections to chi chi -> g g, and (2) the contribution to the cross section for chi chi -> q qbar g arising from interference between the tree-level and loop-induced processes.
We present a new implementation of the NNLO QCD corrections to three-jet final states and related event-shape observables in electron--positron annihilation. Our implementation is based on the antenna subtraction method, and is performed in the NNLOJET framework. The calculation improves upon earlier results by taking into account the full kinematical information on the initial state momenta, thereby allowing the event orientation to be computed to NNLO accuracy. We find the event-orientation distributions at LEP and SLC to be very robust under higher order QCD corrections.
We report on our computation of the mixed QCD and weak corrections to $q {\bar q} \to t\bar{t}$ including $t, \bar t$ spin effects, in particular on single top spin asymmetries.
The calculation of the cosmological relic density of the dark matter candidate within supersymmetric models is an interesting possibility to obtain additional constraints on the supersymmetric parameter space with respect to collider, electroweak precision, and low-energy data. Considering future cosmological precision measurements, radiative corrections can play an important role in the analysis. We present full QCD and SUSY-QCD corrections to neutralino pair annihilation into quark-antiquark pairs and analyze their impact on the neutralino annihilation cross section and the relic density. By…
We consider the Adler $D$-function, which is defined in the spacelike region, and the $e^+e^-$ annihilation ratio smeared, according to the Poggio, Quinn, and Weinberg method, which is determined for timelike argument. We show that the method of the nonperturbative $a$-expansion allows one to describe these Euclidean and Minkowskian characteristics of the process of $e^+e^-$ annihilation down to the lowest energy scales.
We describe in detail our calculation of the full supersymmetric (SUSY) QCD corrections to neutralino annihilation into heavy quarks and extend our numerical analysis of the resulting dark matter relic density to scenarios without scalar or gaugino mass unification. In these scenarios, the final state is often composed of top quarks and the annihilation proceeds through Z^0-boson or scalar top-quark exchanges. The impact of the corrections is again shown to be sizable, so that they must be taken into account systematically in global analyses of the supersymmetry parameter space.
We compute the full O(alpha_s) supersymmetric (SUSY) QCD corrections for neutralino annihilation into massive quarks through gauge or Higgs bosons and squarks in the Minimal Supersymmetric Standard Model (MSSM), including the known resummation of logarithmically enhanced terms. The numerical impact of the corrections on the extraction of SUSY mass parameters from cosmological data is analyzed for gravity-mediated SUSY breaking scenarios and shown to be sizable, so that these corrections must be included in common analysis tools.
In Perturbative QCD (PQCD) approach we study the direct $CP$ violation in the pure annihilation decay process of $\bar{B}^0_{s}\rightarrowπ^+π^-π^+π^-$ induced by the $ρ$ and $ω$ double resonance effect. Generally, the $CP$ violation is small in the pure annihilation type decay process. However, we find that the $CP$ violation can be enhanced by double $ρ-ω$ interference when the invariant masses of the $π^+π^-$ pairs are in the vicinity of the $ω$ resonance. For the decay process of $\bar{B}^0_{s}\rightarrowπ^+π^-π^+π^-$, the maximum $CP$ violation can reach 28.64{\%}.
The multiplicity of heavy quarks from gluon splitting in e+e- annihilation has now been theoretically calculated and experimentally measured at LEP. However, the experimental measurement requires theoretical input for the shape of the multiplicity with respect to an event shape. In this paper we calculate the multiplicity of heavy quarks from gluon splitting in e+e- annihilation as a function of the heavy jet mass of the event, to next-to-leading logarithmic accuracy. We compare our result with Monte Carlo predictions.
We study the decays into six quarks of off-shell pairs of W bosons produced in electron-positron annihilations, through the O(as^2) order in the strong coupling constant. We give explicit helicity amplitude formulae. We present numerical results in the context of phenomenological analyses of relevance at LEP2 and future Linear Colliders: such as MW determinations, New Physics and Higgs searches.
Using the method of QCD light-cone sum rules, we calculate the $B \to ππ$ hadronic matrix elements with annihilation topology. We obtain a finite result, including the related strong phase. Numerically, the annihilation effects in $B\to ππ$ turn out to be small with respect to the factorizable emission mechanism. Our predictions, together with the earlier sum rule estimates of emission and penguin contributions, are used for the phenomenological analysis of $B\to ππ$ channels. We predict a $ΔI=1/2$ transition amplitude which significantly differs from this amplitude extracted from the current …
We present the first genuine QCD five-loop calculation of the vacuum polarization functions: analytical terms of order alpha_s^4 n_f^2 to the absorptive parts of vector and scalar correlators. These corrections form an important gauge-invariant subset of the full O(alpha_s^4) correction to $e^+ e^- annihilation into hadrons and the Higgs decay rate into hadrons respectively. They discriminate between different widely used estimates of the full result.
Expressions for Sudakov form factors for heavy quarks are presented. They are used to construct resummed jet rates in electron-positron annihilation. Predictions are given for production of bottom quarks at LEP and top quarks at the Linear Collider.
We calculate the QCD radiative corrections to the production of supersymmetric scalar partners of quarks in e+e- annihilation. We include both the standard gluonic corrections and the genuine supersymmetric QCD corrections due to quark--gluino loops, and allow for mixing between left-- and right--handed scalar quarks which leads to the possibility that the two final state particles have different masses. The corrections are found to be much larger than the ones affecting the production of spin 1/2 particles.
Through this article, we present the two-loop massless QCD corrections to the production of di-Higgs and di-pseudo-Higgs boson through quark annihilation in the large top quark mass limit. Within dimensional regularisation, we employ the non-anticommuting $γ_5$ and treat it under the Larin prescription. We discover the absence of any additional renormalisation, so-called contact renormalisation, that could arise from the short distance behaviour of two local operators. This finding is in corroboration with the operator product expansion. By examining the results, we discover the lack of simila…
The heavy meson-antimeson pairs, where one is an excited $\bigl ({3 \over 2} \bigr) ^+ $ meson and the other is a ground state $\bigl ({1 \over 2} \bigr) ^-$ meson, namely the pairs ($D_1(2420) \bar D$ + c.c.), ($D_1(2420) \bar D^*$ + c.c.), ($D_2(2460) \bar D^*$ + c.c.) in the charm sector and ($B_1(5721) \bar B$ + c.c.), ($B_1(5721) \bar B^*$ + c.c.), ($B_2(5747) \bar B^*$ + c.c.) in the bottom sector, are allowed, by the quantum numbers, to be produced in the $S$ wave in $e^+e^-$ annihilation. We show, however, that such $S$-wave production is forbidden by the heavy quark spin symmetry. Thu…
The next-to-leading order (NLO) QCD corrections are calculated for the pair-annihilation of spin-1 dark matter (DM) by dimensionally regularizing both ultraviolet and infrared singularities in non-relativistic limit (v<<1). The complete O(alphas) correction is about 8% due to the massless gluon contribution. An extra 5% will be added if there is a new interaction from a massive gluon of approximately same mass as the DM particle. The NLO QCD correction could give the sizable shift to the DM mass constrained by relic density measurements.
The revised version contains two additional references i.e. [13], [14] w.r.t. to the original paper. Furthermore Eq. (33) in [11] at the end of the paragraph below (3.17) must be Eq. (33) in [10]. Misprints in the list of references are corrected.
We present the two-loop QCD corrections to the amplitude of the Higgs production associated with a $Z$ boson via the bottom quark-antiquark annihilation channel with a non-vanishing bottom-quark Yukawa coupling. The computation is performed by projecting the D-dimensional scattering amplitude directly onto a set of Lorentz structures related to the linear polarisation states of the $Z$ boson. We cross-check the finite remainders through a computation based on conventional form factor decomposition. We show that for physical observables, an ultimate D-dimensional form factor decomposition of am…
We compute the full O(alpha_s) SUSY-QCD corrections to dark matter annihilation in the Higgs-funnel, resumming potentially large mu tan beta and A_b contributions and keeping all finite O(m_b,s,1/tan^2 beta) terms. We demonstrate numerically that these corrections strongly influence the extraction of SUSY mass parameters from cosmological data and must therefore be included in common analysis tools such as DarkSUSY or micrOMEGAs.
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.
We present the full $\mathcal{O}(α_s)$ supersymmetric QCD corrections for stop-anti-stop annihilation into electroweak final states within the Minimal Supersymmetric Standard Model (MSSM). We also incorporate Coulomb corrections due to gluon exchange between the incoming stops. Numerical results for the annihilation cross sections and the predicted neutralino relic density are presented. We show that the impact of the radiative corrections on the cosmologically preferred region of the parameter space can become larger than the current experimental uncertainty, shifting the relic bands within t…
We have calculated the full O(alpha_s) supersymmetric QCD corrections to neutralino-stop co-annihilation into electroweak vector and Higgs bosons within the Minimal Supersymmetric Standard Model (MSSM). We performed a parameter study within the phenomenological MSSM and demonstrated that the studied co-annihilation processes are phenomenologically relevant, especially in the context of a 126 GeV Higgs-like particle. By means of an example scenario we discuss the effect of the full next-to-leading order corrections on the co-annihilation cross section and show their impact on the predicted neut…
We study the scaling regime of hadron-(anti)-hadron annihilation into a deeply virtual photon and a real photon, H anti-H -> gamma^* gamma, and deep backward virtual Compton scattering, gamma^* H -> H gamma. We advocate that there is a kinematical region where the scattering amplitude factorizes into a short-distance matrix element and a long-distance dominated object: a transition distribution amplitude which describes the hadron to photon transition.
We present theoretical analysis of paired $B_c$ mesons production in $e^+e^-$ annihilation at different energy scales taking into account full next-to-leading order QCD corrections. Both possible electroweak channels are considered: production via virtual photon and via virtual $Z$-boson. We study in detail the role of radiative QCD corrections, which were found to be significant especially at low energies. It is shown that the contribution from $Z$-boson is significant at high energies ($\sqrt{s} > M_Z/2$) especially in the case of paired production of pseudo-scalar and vector ($B_c + B_c^*$)…
We show that in the presence of sufficiently strong $ν_τ$ annihilations to majorons, primordial nucleosynthesis constraints can not rule out any values of the $ν_τ$ mass up the present laboratory limit.
Precision studies of QCD at electron-positron colliders are based on measurements of event shapes and jet rates. To match the high experimental accuracy, theoretical predictions to next-to-next-to-leading order (NNLO) in QCD are needed for a reliable interpretation of the data. We report the first calculation of NNLO corrections O(alpha_s^3) to three-jet production and related event shapes, and discuss their phenomenological impact.
We present the analytic calculation of the Master Integrals for the two-loop, non-planar topologies that enter the calculation of the amplitude for top-quark pair hadroproduction in the quark-annihilation channel. Using the method of differential equations, we expand the integrals in powers of the dimensional regulator $ε$ and determine the expansion coefficients in terms of generalized harmonic polylogarithms of two dimensionless variables through to weight four.
QCD corrections to all the allowed decays of superheavy groundstate quarkonia into electroweak gauge and Higgs bosons are presented. For quick estimates, approximations that reproduce the exact results within less than at worst two percent are also given.
We apply Heavy Quark Effective Theory to the production of $0^-$ and $1^-$ $Q\bar{q}$ states in $e^+ e^-$ annihilation. We show that HQET implies that the electric quadrupole amplitudes vanish and we propose tests for this theory. We also show how HQET can be applied to distinguish the $^3D_1$ and $^3S_1$ $Q\bar{Q}$ states.
We compute production rates for two, three, four and five jets in electron-positron annihilation at the third order in the QCD coupling constant. At this order, three-jet production is described to next-to-next-to-leading order (NNLO) in perturbation theory while the two-jet rate is obtained at next-to-next-to-next-to-leading order (N$^3$LO). Our results yield an improved perturbative description of the dependence of jet multiplicity on the jet resolution parameter, $\ycut$, particularly at small values of $\ycut$.
We begin with short review of the analytic approach (AA) to QCD recently developed and applied to the process of $e^+e^-$ annihilation into hadrons at low energies. Besides summary of the theoretical description of smeared experimental data for the $R$ cross-section ratio we give fresh analogous result for the corresponding Adler function, $D(Q^2)$, and demonstrate excellent agreement between the AA theoretical results and data in the low $Q^2$ region.
The associated production of a $J/ψ$ and a $π$-meson in antiproton-nucleon annihilation is studied in the framework of QCD collinear factorization. In this approach, a hard subprocess responsible for the production of the heavy quark-antiquark pair factorizes from soft hadronic matrix elements, such as the antiproton (nucleon) distribution amplitude and the nucleon-to-pion (antiproton-to-pion) transition distribution amplitude. This reaction mechanism should dominate the forward and backward kinematical regions, where the cross sections are expected to be measurable in the set-up of the PANDA …
We analyze the decay $B\to ϕK$ within the framework of QCD-improved factorization. We found that although the twist-3 kaon distribution amplitude dominates the spectator interactions, it will suppress the decay rates slightly. The weak annihilation diagrams induced by $(S-P)(S+P)$ penguin operators, which are formally power-suppressed by order $(Λ/m_b)^2$, are chirally and logarithmically enhanced. Therefore, these annihilation contributions are not subject to helicity suppression and can be sizable. The predicted branching ratio of $B^-\toϕK^-$ is $(3.8\pm0.6)\times 10^{-6}$ in the absence of…
The process pp -> top anti-top bottom anti-bottom + X represents a very important background reaction to searches at the LHC, in particular to top anti-top H production where the Higgs boson decays into a bottom anti-bottom pair. A successful analysis of top anti-top H at the LHC requires the knowledge of direct top anti-top bottom anti-bottom production at NLO in QCD. We take the first step in this direction upon calculating the NLO QCD corrections to the subprocess initiated by quark anti-quark annihilation.
We analyze the exclusive charmonium $J/ψ+η_c$ pair production in $e^+e^-$ annihilation using the nonfactorized perturbative QCD and the light-front quark model(LFQM) that goes beyond the peaking approximation. We effectively include all orders of higher twist terms in the leading order of QCD coupling constant and compare our nonfactorized analysis with the usual factorized analysis in the calculation of the cross section. We also calculate the quark distribution amplitudes, the Gegenbauer moments, and the decay constants for $J/ψ$ and $η_c$ mesons using our LFQM. Our nonfactorized result enha…
In the framework of nonrelativistic QCD, we compute the leading double-logarithmic corrections of order alpha_s^3 ln^2(1/alpha_s) to the heavy-quark-antiquark bound-state wave function at the origin, which determines the production and annihilation rates of heavy quarkonia. The phenomenological implications for the top-antitop and Upsilon systems are discussed.
We report on the analytic calculation of the second-order QCD corrections to semi-inclusive hadron production in electron-positron annihilation. The calculation of the single-particle inclusive cross-section in time-like kinematics is performed in Mellin N-space and uses an algorithmic evaluation of inclusive phase-space integrals, based on the unitarity cutting rules and integration-by-parts. We obtain splitting functions and coefficient functions up to second order in the strong coupling alpha_s. Our results are in agreement with earlier calculations in the literature by Rijken and van Neerv…
For $B_{d,s} \to π^\mp K^\pm$ and $K^{(\ast)} K^{(\ast)}$ decays, the flavor symmetry breaking effects may be particularly small since the final state interactions should be the same between the corresponding $B_d$ and $B_s$ decays due to the charge conjugation symmetry of the final states. This is consistent with the newly measured direct CP asymmetry of $B_s \to π^+ K^-$. These decays are thus supposed to be important in testing the Standard Model and in probing new physics effects. However, the observation of pure annihilation decay $B_s \to π^+ π^-$ appears to imply a large annihilation sc…
Next-to-leading order calculations for heavy quark three-jet production in e+e- annihilation are reviewed. Their applications for the measurement of the b-quark mass at LEP/SLC and for the test of flavour independence of the strong coupling constant are discussed.
We calculate the O(alpha_s^3 ln(alpha_s)) contributions to the heavy-quarkonium production and annihilation rates. Our result sheds new light on the structure of the high-order perturbative corrections and opens a new perspective for a high-precision theoretical analysis. We also determine the three-loop anomalous dimensions of the nonrelativistic vector and pseudoscalar currents.
We report on a calculation of the vector current contributions to the electroweak production of top quark pairs in $e^+e^-$ annihilation at next-to-next-to-leading order in Quantum Chromodynamics. Our setup is fully differential and can be used to calculate any infrared-safe observable. The real emission contributions are handled by a next-to-next-to-leading order generalization of the phase-space slicing method. We demonstrate the power of our technique by considering its application to various inclusive and exclusive observables.
