We analytically calculate the cross sections of double charmonium production in $e^+ e^- \to J/ψ(ψ(2S))χ_{cJ}$ (J=0,1,2) at next-to-leading order (NLO) in $α_s$ in nonrelativistic QCD, and confirm factorization of these processes. In contrast to $χ_{c0}$ production, for which the NLO correction is large and positive, the NLO corrections for $χ_{c1,2}$ production can be negative, resulting in decreased $K$ factors of 0.91 and 0.78 for J=1 and 2 respectively when $μ= 2 m_{c}$. Consequently, the NLO QCD corrections markedly enlarge the difference between cross sections of $χ_{c0}$ and $χ_{c1,2}$. This may explain why $e^+ e^- \to J/ψ(ψ(2S))χ_{c0}$ but not $e^+ e^- \to J/ψ(ψ(2S))χ_{c1,2}$ is observed experimentally. Moreover, for $J/ψ(ψ(2S))χ_{c1,2}$, the NLO QCD corrections substantially reduce the $μ$ dependence and lead to predictions with small theoretical uncertainties.
The next-to-leading order (NLO) quantum chromodynamics (QCD) corrections for $χ_{cJ}(^3P_J^{[1]},^3S_1^{[8]})$, the P-wave charmoniums inclusive production at $B$ factories are calculated utilizing the non-relativistic QCD (NRQCD) factorization formalism. Large NLO corrections are found, especially for $^3P_0^{[1]}$ and $^3S_1^{[8]}$ configurations. Numerical evaluation indicates that the total cross sections of $χ_{cJ}$ inclusive production processes are at the order of $10$fb, which are accessible in BELLE II(super-B) experiment.
We calculate the next-to-leading order (NLO) quantum chromodynamics (QCD) corrections to double charmonium production processes $e^+e^-\toγ^*\toη_c+h_c(1P)/ψ_{1,2}(1D)$ within the non-relativistic QCD (NRQCD) factorization framework. We find that the corrections to $η_c+h_c(1P)$ production are positive, while those to $η_c+ψ_{1,2}(1D)$ are negative. Unlike the $J/ψ+ η_c$ case, all the corrections here are not large. Uncertainties in the renormalization scale, quark mass and running energy of center-of-mass are discussed, and the scale dependence of these processes is found to be greatly reduce…
We study production of the tetraquark state $T_{cc}$ via virtual photon at the B-factories in the QCD factorization framework. We predict the cross section of tetraquark state production in the leading order at the B-factories.
In this paper, we calculate the next-to-next-to-leading-order (NNLO) QCD corrections to $e^+e^- \to J/ψ+η_c$ at the $B$ factories. After including the NNLO corrections, the cross section of $e^+e^- \to J/ψ+η_c$ is enhanced by about $17\%$, and the perturbative series of the prediction shows the convergent behavior. It is also found that the contribution from bottom quark starts at the $α_s^3$-order, which is about $2.4\%$ of the total prediction. The renormalization scale $μ_R$ dependence of the cross section is reduced at the NNLO level, but the prediction is sensitive to the charm quark mass…
We calculate the next-to-leading-order (NLO) QCD corrections to $e^+e^-\to J/ψg g$ via color singlet $J/ψ(^3{-0.8mm}S_1)$ at the B factories. The result shows that the cross section is enhanced to $0.373\pb$ by a K factor (NLO/LO) of about 1.21. By considering its dependence on the charm quark mass and renormalization scale, the NLO cross section can range from 0.294 to $0.409\pb$. Further including the $ψ^\prime$ feed-down, $σ(e^+e^-\to \jpsi X(\mathrm{non} c\bar{c}))$ is enhanced by another factor of about 1.29 and reaches $0.482\pb$. In addition, the momentum distributions of $J/ψ$ producti…
We study the production of $C=+$ charmonium states $X$ in $e^+e^-\to γ+ X$ at B factories with $X=η_c(nS)$ (n=1,2,3), $χ_{cJ}(mP)$ (m=1,2), and $^1D_2(1D)$. In the S and P wave case, contributions of tree-QED with one-loop QCD corrections are calculated within the framework of nonrelativistic QCD(NRQCD) and in the D-wave case only the tree-QED contribution are considered. We find that in most cases the QCD corrections are negative and moderate, in contrast to the case of double charmonium production $e^+e^-\to J/ψ+ X$, where QCD corrections are positive and large in most cases. We also find th…
We evaluate the QED corrections due to initial state radiation (ISR) to associated Higgs boson production in electron-positron ($e^+ e^-$) annihilation at typical energies of interest for the measurement of the Higgs properties at future $e^+ e^-$ colliders, such as CEPC and FCC-ee. We apply the QED Structure Function approach to the four-fermion production process $e^+ e^- \to μ^+ μ^- b \bar b$, including both signal and background contributions. We emphasize the relevance of the ISR corrections particularly near threshold and show that finite third order collinear contributions are mandatory…
Within the nonrelativistic QCD (NRQCD) factorization framework, we compute the long-awaited ${\mathcal O}(α_s^2)$ correction for the exclusive double charmonium production process at $B$ factories, {\it i.e.}, $e^+e^-\to J/ψ+η_c$ at $\sqrt{s}=10.58$ GeV. For the first time, we confirm that NRQCD factorization does hold at next-to-next-to-leading-order (NNLO) for exclusive double charmonium production. It is found that including the NNLO QCD correction considerably reduces the renormalization scale dependence, and also implies the reasonable perturbative convergence behavior for this process. O…
In nonrelativistic Quantum Chromodynamics (NRQCD), we study the next-to-leading order (NLO) QCD radiative correction to the color-octet $J/ψ$ inclusive production at B Factories. Compared with the leading-order (LO) result, the NLO QCD corrections are found to enhance the short-distance coefficients in the color-octet $J/ψ$ production $ e^+ e^-\to c \bar c (^3P_0^{(8)} {\rm or} ^3P_0^{(8)})g$ by a factor of about 1.9. Moreover, the peak at the endpoint in the $J/ψ$ energy distribution predicted at LO can be smeared by the NLO corrections, but the major color-octet contribution still comes from…
We calculate the next-to-leading-order (NLO) QCD correction to $e^+e^-\to J/ψc \bar{c}$ at the B factories, and present theoretical predictions on the momentum and production angular distribution for $J/ψ$ production, and momentum distribution for $J/ψ$ polarization at NLO for the first time. By applying Brodsky, Lepage and Mackenzie scale setting for the renormalization scale, it is found that the QCD perturbative expansion is significantly improved with the unique scale choice $μ^*=1.65$GeV. Together with the $ψ^\prime$ feed-down contribution, the total cross section and momentum distributio…
We calculate the relativistic correction to $J/ψ$ production in the color-singlet process $e^{+}e^{-}\to J/ψ+gg$ at B-factories. We employ the non-relativistic QCD (NRQCD) factorization approach, where the short-distance coefficients are calculated perturbatively and the long-distance matrix elements are extracted from the decays of $J/ψ$ into $e^{+}e^{-}$ and light hadrons. We find that the $O(v^2)$ relativistic correction can enhance the cross section by a factor of 20-30%, comparable to the enhancement due to the $O(α_s)$ radiative correction obtained earlier. Combining the relativistic cor…
Based on Monte Carlo techniques, we analyze the initial state radiation (ISR) effects in prompt $\jpsi$ inclusive production at B factories. ISR enhances cross section $σ(e^-e^+\to\jpsi+gg+X)$ by about $15-25\%$, which is almost the same size as the QCD and relativistic correction. Moreover, ISR slightly changes $σ(e^-e^+\to\jpsi+c\bar{c}+X)$. The $\jpsi$ momentum spectrum in $e^-e^+\to\jpsi+gg+X$ and in $e^-e^+\to\jpsi+c\bar{c}+X$ is softer after the photon showering from the initial $e^{\pm}$ beam radiation. After combining the QCD,relativistic, and ISR corrections,a more precise theoretical…
I discuss topics in the strong QCD dynamics that are of relevance to studies of the $B$ mesons and to the spectroscopy of heavy hadrons. In particular the limitations from the hadronic dynamics for the determination of the weak-interaction parameters are discussed as well as some models for the newly observed apparently exotic resonances with hidden charm.
By including the interference effect between the QCD and the QED diagrams, we carry out a complete analysis on the exclusive productions of $e^+e^- \to J/ψ+χ_{cJ}$ ($J=0,1,2$) at the $B$ factories with $\sqrt{s}=10.6$ GeV at the next-to-leading-order (NLO) level in $α_s$, within the nonrelativistic QCD framework. It is found that the $\mathcal O (α^3α_s)$-order terms that represent the tree-level interference are comparable with the usual NLO QCD corrections, especially for the $χ_{c1}$ and $χ_{c2}$ cases. To explore the effect of the higher-order terms, namely $\mathcal O (α^3α_s^2)$, we perf…
In this paper the cross sections of the processes $e^+ e^- \to H+γ, H=η_c, η_c', χ_{c0}, χ_{c1}, χ_{c2}$ are calculated. The calculation is carried out at the leading twist approximation of light cone formalism. Within this approach the leading logarithmic radiative and relativistic corrections to the amplitudes are resumed. For the processes $e^+ e^- \to η_c, η_c'+γ$ one loop radiative corrections are taken into account. It is also shown that one loop leading logarithmic radiative corrections calculated within light cone formalism for the processes under study coincide with that obtained by d…
In heavy quarkonium production, the measured ratio $R_{c \bar c}=σ[J/ψ+ c\bar c + X]/σ[J/ψ+X]$ at B factories is much larger than existing theoretical predictions. To clarify this discrepancy, in nonrelativistic QCD (NRQCD) we find the next-to-leading-order (NLO) QCD correction to $e^+ e^- \to J/ψ+gg$ can enhance the cross section by about 20%. Together with the calculated NLO result for $e^+ e^- \to J/ψ+c\bar c$, we show that the NLO corrections can significantly improve the fit to the ratio $R_{c \bar c}$. The effects of leading logarithm resummation near the end point on the $J/ψ$ momentum …
The full one-loop corrections, both the weak and QED corrections, to the process $e^+ e^- \to Z ϕ$ ($ϕ=h^0,H^0$) in the two Higgs doublet model (2HDM) at the Higgs factories are presented. Up to the $O(α_{em})$ level, the virtual corrections are evaluated by using the FeynArts/FormCalc packages. The real emission corrections are computed using the Feynman Diagram Calculation (FDC) package and the collinear divergences are regularized by the structure functions of an electron. Using the FeynArts/FormCalc and the FDC packages, we study the corrections in the Standard Model (SM) and the 2HDM, res…
Virtual fermionic N_f = 1 and N_f = 2 contributions to Bhabha scattering are combined with realistic real corrections at next-to-next-to-leading order in QED. The virtual corrections are determined by the package bha_nnlo_hf, and real corrections with the Monte Carlo generators Bhagen-1Ph, Helac-Phegas and Ekhara. Numerical results are discussed at the energies of and with realistic cuts used at the Phi factory DAFNE, at the B factories PEP-II and KEK, and at the charm/tau factory BEPC II. We compare these complete calculations with the approximate ones realized in the generator BabaYaga@NLO u…
We investigate the ${\cal O}(α_s)$ corrections to $e^+e^-\to J/ψ(ψ')+χ_{cJ}$ ($J=0,1,2$) in the NRQCD factorization approach. These next-to-leading order (NLO) corrections are calculated at the level of helicity amplitude. We have made a detailed analysis for both polarized and unpolarized cross sections, and compared our predictions with the measurements at the $B$ factories. We also derive the asymptotic expressions for each of the NLO helicity amplitudes, and confirm the earlier speculation that at NLO in $α_s$, the double logarithm of type $\ln^2 (s/m_c^2)$ appearing in the NRQCD short-dis…
We present a complete study of the associated production of the $η_c$ meson with light hadrons in $e^+e^-$ collisions at the B-factory energy, which is demonstrated to be one of the best laboratories for testing the colour-octet (CO) mechanism. The colour-siglet contributions are evaluated up to $O(α^2α_s^3)$ while the CO ones are evaluated up to $O(α^2α_s^2)$. For the first time, the angular distribution of the $^1S_0^{[8]}$ production is studied at QCD next-to-leading order. We find that the $^1S_0^{[8]}$ channel dominate the total cross section, while the $^1P_1^{[8]}$ one exhibit its impor…
The Semileptonic B Frontier: LHC, B-factories, Lattice QCD & the Hunt for Precision
INFN, Sezione di Bari（意大利国家核物理研究所巴里分部）；Laboratori Nazionali di Frascati（弗拉斯卡蒂国家实验室）；PRISMA ++ Cluster of Excellence & Mainz Institute for Theoretical Physics, Johannes Gutenberg University（约翰内斯·古腾堡大学）；ICCUB, Universitat de Barcelona（巴塞罗那大学）；Department of Physics and Astronomy, University of Manchester（曼彻斯特大学）；Aix Marseille Univ, CNRS/IN2P3, CPPM（艾克斯-马赛大学）；Dipartimento di Fisica e Astronomia Galileo Galilei & INFN, Università di Padova（帕多瓦大学）；Dipartimento di Fisica & INFN, Università di Torino（都灵大学）；INFN, Sezione di Roma Tre（意大利国家核物理研究所罗马第三大学分部）
As a test of the color-singlet mechanism of the nonrelativistic QCD (NRQCD) factorization approach, we consider the exclusive two-quarkonium productions in electron-positron annihilation e+ e- -> eta_c + gamma and e+ e- -> J/psi + J/psi at B factories. The cross sections are computed to the next-to-leading order in alpha_s and are resummed to all orders in half the relative velocity v of the charm quark in each meson rest frame. The available theoretical prediction of the cross section for e+ e- -> J/psi + eta_c at the same level of theoretical accuracies is consistent with the available exper…
We investigate the ${\mathcal O}(α_s v^2)$ correction to the $e^+e^-\to J/ψ+η_c$ process in the nonrelativistic QCD (NRQCD) factorization approach. Within some reasonable choices of the relative order-$v^2$ NRQCD matrix elements, we find that including this new ingredient of correction only mildly enhances the existing NRQCD predictions. We have also deduced the asymptotic expressions for the ${\mathcal O}(α_s v^2)$ short-distance coefficients, and reconfirm the early speculation that at next-to-leading order in $α_s$, the double logarithm of type $\ln^2 (s/m_c^2)$ appearing in various NRQCD s…
Photon pair production at flavour factories with per mille accuracy
我们提出了一个高精度的QED计算，与0.1%的理论精度，双光子产生的$e^+ e^-$湮灭，要求越来越精确的光度监测在香料工厂。该方法的准确性，这是基于精确的下一个到领先的阶校正与QED Parton Shower算法匹配，证明通过详细分析的辐射校正的各种来源的实验相关的观测量的影响。该计算是在事件发生器BabaYaga的最新版本中实现的，可用于精确模拟中等高能量的$e^+ e^-$对撞机的光子对生产。
We consider the production of the $η_c$ and $χ_{cJ}$ states recoiled with a photon up to $\mathcal{O}(α_s v^2)$ at BESIII and B-factories within the frame of NRQCD factorization. With the corrections, we revisit the numerical calculations to the cross sections for the $η_c(nS)$ and the $χ_{cJ}(mP)$ states. We argue that the search for $XYZ$ states with even charge conjugation such as $X(3872)$, $X(3940)$, $X(4160)$, and $X(4350)$ recoiled with a photon at BESIII may help clarify the nature of these states. For completeness, the production of charmonium with even charge conjugation recoiled wit…
To understand the direct $J/ψ+X_{\mathrm{non-c\bar{c}}}$ production mechanism in $e^{+}e^{-}$ annihilation, in this work, we propose to measure the inclusive $J/ψ$ plus light hadrons (LH) production at B-factories and present a detailed study on its QED production due to $ψ(2S)$ feed-down, where the $ψ(2S)$ are produced in $e^{+}e^{-}\to ψ(2S)+γ$ and $e^{+}e^{-}\to ψ(2S)+f\bar{f}, f=lepton,light quark$, and QED contribution to direct $J/ψ+q\bar{q}$ production with $q=u,d,s$ quark. We find that the QED contribution is huge in the whole phase space region, but can be reduced largely and is in th…
We review some recent progress in understanding various exclusive double charmonium production processes at $B$ factories, within the nonrelativistic QCD factorization framework. First we investigate the impact of the joint perturbative and relativistic correction on the process that has attracted a great amount of attention in the past decade, $e^+e^-\to J/ψ+η_c$. We then briefly discuss the phenomenological implication of the next-to-leading order perturbative correction to the processes $e^+e^-\to J/ψ+χ_{c0,1,2} (η_{c2})$. We further emphasize a novel theoretical challenge, which is recentl…
We investigate the ${\cal O}(α_s)$ correction to $e^+e^-\to J/ψ+η_{c2}$ in the NRQCD factorization approach. A detailed comparative study between $e^+e^-\to J/ψ+η_{c2}$ and $e^+e^-\to J/ψ+χ^\prime_{c1}$ at $B$ factory energy is also carried out. After incorporating the ${\cal O}(α_s)$ correction, we predict the cross section for the former process to be around 0.3 fb, while that of the latter about 6 times greater. The outgoing $J/ψ$ is found to be dominantly transversely-polarized in the former process, while longitudinally-polarized in the latter. These features may provide valuable guidance…
We study the first-order relativistic correction to the associated production of $J/ψ$ with light hadrons at $B$ factory experiments at $\sqrt{s}=10.58$ GeV, in the context of NRQCD factorization. We employ a strategy for NRQCD expansion that slightly deviates from the orthodox doctrine, in that the matching coefficients are not truly of ``short-distance" nature, but explicitly depend upon physical kinematic variables rather than partonic ones. Our matching method, with validity guaranteed by the Gremm-Kapustin relation, is particularly suited for the inclusive quarkonium production and decay …
A comparison of theoretical results on NNLO leptonic and hadronic corrections to Bhabha scattering with the Monte Carlo generator BabaYaga@NLO used at meson factories is given. Complete NLO virtual corrections to the $e^+e^- \to μ^+ μ^- γ$ process are discussed.
Within the nonrelativistic QCD (NRQCD) factorization framework, we investigate the inclusive production of the $h_c$ meson associated with either light hadrons or charmed hadrons at $B$ factory energy $\sqrt{s}=10.58$ GeV. Both the leading color-singlet and color-octet channels are included. For the $h_c$ production associated with light hadrons, the total production rate is dominated by the color-octet channel, thus the future measurement of this process may impose useful constraint on the value of the color-octet matrix element $<{\cal O}^{h_c}_8({}^1S_0)>$; for the $h_c$ production associat…
SuperB experiment could represent an ideal environment to test a new U (1) symmetry related to light dark forces candidates. A promising discovery channel is represented by the resonant production of a boson U, followed by its decay into lepton pairs. Beyond approximations adopted in the literature, an exact tree level calculation of the radiative processes $e+ e- \rightarrow γ, U \rightarrow μ^+ μ^- γ, e^+ e^- γ$ and corresponding QED backgrounds is performed, including also the most important higher-order corrections. The calculation is implemented in a release of the generator BabaYaga@NLO …
We present an estimate of the next-to-leading order QCD corrections to mixed QCD-electroweak contribution to Higgs boson production cross section in gluon fusion, combining the recently computed three-loop virtual corrections and the approximate treatment of real emission in the soft approximation. We find that the NLO QCD corrections to mixed QCD-electroweak contributions are nearly identical to NLO QCD corrections to QCD Higgs production. Our result confirms an earlier estimate of these ${\cal O}\left( α\, α_s^2 \right)$ effects in arXiv:0811.3458 [hep-ph] and provides further support for th…
Branching Ratio and CP Violation of B to pi pi Decays in Perturbative QCD Approach
用微扰QCD方法计算了B^0到pi^+pi^-，B^+到pi^+ pi ^0和B^0到pi ^0 pi ^0衰变的分支比和CP不对称性.在这种方法中，我们计算非因式分解和湮灭型的贡献，除了通常的因式分解的贡献。我们发现湮没图的贡献并不像以前的论点那么小。我们的结果与CLEO合作组测得的B对π ^+ π ^-的分支比一致。由于湮灭图和一个大的强相位的不可忽略的贡献，我们预测B^0中的大的直接CP不对称性为pi^+pi^-和pi^0pi^0，这可以通过当前运行的B工厂进行测试。
