Within the nonrelativistic QCD (NRQCD) factorization framework, we have computed the ${\mathcal O}(α_s^2)$ corrections to the exclusive production of $P$-wave spin-triplet charmonia $χ_{cJ}(J=0,1,2)$ accompanied by a hard photon at $B$ factories. For the first time, we have explicitly verified the validity of NRQCD factorization for exclusive $P$-wave quarkonium production at two-loop order. Unlike the $χ_{cJ}$ electromagnetic decay processes, the $\mathcal{O}(α_s^2)$ corrections are found to be smaller than the $\mathcal{O}(α_s)$ corrections in all three channels $e^+e^-\to χ_{c0,1,2}+γ$. In particular, the ${\mathcal O}(α_s^2)$ corrections appear moderate for $χ_{c1}$ case, and insignificant for $χ_{c0}$. In addition, the next-to-next-to-leading order (NNLO) predictions for the production rates of $χ_{c0,1}+γ$ are insensitive to the renormalization and factorization scales. All of these features may indicate that perturbative expansion in these two channels exhibits a decent convergence behavior. By contrast, both the ${\mathcal O}(α_s)$ and ${\mathcal O}(α_s^2)$ corrections to the $χ_{c2}+γ$ production cross section are sizable, which even reduces the Born order cross section by one order of magnitude after including the NNLO perturbative correction. Taking the values of the long-distance NRQCD matrix elements from nonrelativistic potential model, our prediction to $χ_{c1}+γ$ production rate is consistent with the recent {\tt Belle} measurement. The NNLO predictions for the $χ_{c0,2}+γ$ production rates are much smaller than that for $χ_{c1}+γ$, which seems to naturally explain why the $e^+e^-\to χ_{c0,2}+γ$ channels have escaped experimental detection to date.
We apply the newly developed NRQCD factorization formula to analyze the exclusive production of the fully-charmed tetraquark $T_{4c}$ plus a hard photon at $B$ factory. For simplicity, in this work we have concentrated on the associated production of the $0^{++}$ and $2^{++}$ tetraquarks with a photon. With some rough estimates about the size of the unknown nonperturbative NRQCD matrix elements, we predict the production rates of these types of exclusive channels at $\sqrt{s}=10.6$ GeV and also assess their observation prospect at {\tt Belle 2} experiment.
This paper presents the first calculations of the parity-violating polarization asymmetry and forward-backward asymmetry of the $e^- e^+ \rightarrow μ^+ μ^- (γ)$ process at a center-of-mass energy of 10.58 GeV with up to one-loop electroweak radiative corrections. The calculations are relevant for future precision electroweak measurements at the Belle~II experiment, which is now collecting data at the SuperKEKB $e^- e^+$ collider with a center-of-mass energy at the mass of the $Υ(4S)$ resonance. In this paper we take under full control the bremsstrahlung process at the conditions of Belle II/S…
In view of their physics goals, future neutrino factories from muon decay aim at an overall flux precision of ${\cal O}(1%)$ or better. We analytically study the QED radiative corrections to the neutrino differential distributions from muon decay. Kinematic uncertainties due to the divergence of the muon beam are considered as well. The resulting corrections to the neutrino flux turn out to be of order ${\cal O}(0.1%)$, safely below the required precision.
In our previous work [2], it has been found that sizable charmonium events via the channel $e^+e^- \to γ^*/Z^0 \to H(|c\bar{c}\rangle) +γ$ can be produced at the suggested super $Z$ factory, where $H(|c\bar{c}\rangle)$ represents the dominant color-singlet $S$-wave and $P$-wave charmonium states $J/ψ$, $η_c$, $h_c$ and $χ_{cJ}$ ($J=0, 1, 2$), respectively. As an important step forward, in the present paper, we present a next-to-leading order (NLO) QCD analysis within the framework of nonrelativistic QCD. In different to the case of $B$ factory in which the single charmonium production is domin…
We investigate the Higgs-strahlung production process e^+ e^- \to Z h at the future Higgs factory such as TLEP by including radiative corrections in the Minimal Dilaton Model (MDM), which extends the SM by one singlet scalar called dilaton. We consider various theoretical and experimental constraints on the model, and perform fits to the Higgs data taken from ATLAS, CMS and CDF+D0. Then for the 1σsurviving samples, we calculate the MDM predictions on the inclusive production rate σ(e^+e^-\to Zh) at the 240-GeV Higgs factory, and also the signal rates of e^+e^-\to Zh with the Higgs boson decayi…
Motivated by the future precision test of the Higgs boson at an $e^+e^-$ Higgs factory, we calculate the production $e^+e^- \to ZHγ$ in the Standard Model with complete next-to-leading order electroweak corrections. We find that for $\sqrt{s}=240$ (350) GeV the cross section of this production is sizably reduced by the electroweak corrections, which is $1.03$ (5.32) fb at leading order and 0.72 (4.79) fb at next-to-leading order. The transverse momentum distribution of the photon in the final states is also presented.
The lowest order QED radiative corrections to the radiative large angle Bhabha scattering process in the region where all kinematic invariants are large compared to the electron mass are considered. We show that the leading logarithmic corrections do not factorize before the Born cross section, contrary to the picture assumed in the renormalization group approach. The leading and non leading contributions for typical kinematics of the hard process at the energy of the $Φ$ factory are estimated.
Contributions from the reaction e+e- --> pi+pi- e+e- to the pion form factor measurement via radiative return method are discussed basing on the results of a Monte Carlo generator (EKHARA). The generator contains contributions from the initial and final state emission of a e+e- pair from e+e- --> pi+pi- production diagrams and the pi+pi- pair production from space-like and time-like Bhabha diagrams. A detailed study is performed for the Phi- factory energy. Tests of the generation procedure are also presented.
For high energy long baseline neutrino oscillation experiments, we propose a Figure of Merit criterion to compare the statistical quality of experiments at various oscillation distances under the condition of identical detectors and a given neutrino beam. We take into account all possible experimental errors under general consideration. In this way the Figure of Merit is closely related to the usual statistical criterion of number of sigmas. We use a realistic neutrino beam for an entry level neutrino factory and a possible superbeam from a meson source and a 100 kt detector for the calculatio…
We review the current status of neutrino oscillations after 1258 days of Super-Kamiokande, assess their future prospects over the next 10 years as the next generation of experiments come on-line, and discuss the longer-term opportunities presented by a Neutrino Factory. We also give an introduction to the see-saw mechanism and its application to atmospheric and solar neutrinos.
The prospective Higgs factories, exemplified by ILC, FCC-ee and CEPC, plan to conduct the precision Higgs measurements at the $e^+e^-$ center-of-mass energy around 250 GeV. The cross sections for the dominant Higgs production channel, the Higgsstrahlung process, can be measured to a (sub-) percent accuracy. Merely incorporating the well-known next-to-leading order (NLO) electroweak corrections appears far from sufficient to match the unprecedented experimental precision. In this work, we make an important advancement toward this direction by investigating the mixed electroweak-QCD corrections …
We have analyzed how much the $CP$ angles to be measured at B factories can deviate from the geometrical ones defined in unitarity triangle under the existence of new physics. The measurements are given in rephasing invariant form. If KM matrix is not a $3\times 3$ and unitary matrix, $\tildeϕ_1$ and $\tildeϕ_3$ is affected, and the value of $\tildeϕ_3$ depends on the decay mode. The deviation is constrained to be less than the experimental precision attained in the next decade by the available data of the magnitude of KM matrix elements. Deviation of the sum of three angles from $π$ cannot be…
We calculate the next-to-leading order (NLO) radiative correction to the color-octet $h_c$ inclusive production in $e^+e^-$ annihilation at Super $B$ factory, within the nonrelativistic QCD factorization framework. The analytic expression for the NLO short-distance coefficient (SDC) accompanying the color-octet production operator $\mathcal{O}_8^{h_c}(^1S_0)$ is obtained after summing both virtual and real corrections. The size of NLO correction for the color-octet production channel is found to be positive and substantial. The NLO prediction to the $h_c$ energy spectrum is plagued with unphys…
Z and Higgs Factory Implications of Two Higgs Doublets with First-Order Phase Transitions
Karlsruhe Institute of Technology (KIT)（卡尔斯鲁厄理工学院）；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器）；University of Glasgow（格拉斯哥大学）；University of Manchester（曼彻斯特大学）
In order to study the interactions and structure of various types of matter one typically needs to carry out scattering experiments utilizing many different particles as projectiles. Whereas beams of $e^\pm$, $μ^\pm$, $π^\pm$, $K^\pm$, proton, antiproton, and of various heavy ions have been produced and have enabled many scientific breakthroughs, beams of antineutrons, hyperons ($Λ$, $Σ$ and $Ξ$) and their antiparticles are typically not easy to obtain. Here we point out and investigate a new high-quality source of these particles: a super $J/ψ$ factory with capability of accumulating trillion…
Radiative effects in the electroproduction of photons in polarized $ep$-scattering are calculated with the next-to-leading (NLO) accuracy. The contributions of loops and two photon emission were presented in analytical form. The covariant approach of Bardin and Shumeiko was used to extract the infrared divergence. All contributions to the radiative correction were presented in the form of the correction to the leptonic tensor thus allowing for further applications in other experiments, e.g., deep inelastic scattering. The radiative corrections (RC) to the cross sections and polarization asymme…
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…
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.
The 3 X 3 CKM matrix defines six unitarity triangles in the complex plane, which will be carefully explored in the LHCb experiment and at the Super-B factory. We calculate the running effects of nine different inner angles and eighteen different sides of the six triangles from the electroweak scale to a superhigh-energy scale by using the one-loop renormalization-group equations, and demonstrate that all the nine angles are stable against radiative corrections. In particular, we find that the CP-violating angle αis most insensitive to the changes of energy scales.
We make a detailed discussion on the one-loop QCD correction to the bottomonium production associated with a photon, i.e. via the channel $e^{+}e^{-} \toγ^*/Z^0 \to |H_{b\bar{b}}\rangle + γ$, where $|H_{b\bar{b}}\rangle$ stands for the color-singlet bottomonium state as $η_b$, $Υ$, $h_b$ or $χ_{bJ}$ ($J$=0, 1 or 2), respectively. At the super $Z$ factory with the collision energy $E_{cm} \sim m_Z$, by summing up the cross sections for all bottomonium states, we obtain a large one-loop QCD correction, i.e. $|R|\sim 30\%$. This ensures the necessity and importance of the one-loop QCD corrections…
We present a detailed study of the exclusive radiative decays $Z\toη^{(\prime)}γ$ employing the QCD factorization approach. We derive a factorization formula for the decay amplitudes valid at leading power in an expansion in $(Λ_{QCD}/m_Z)^2$, which includes convolutions of calculable hard-scattering kernels with the leading-twist quark and gluon light-cone distribution amplitudes of the mesons. Large logarithms arising in the evolution from the high scale $m_Z$ down to hadronic scales are resummed using the renormalization group, carefully accounting for the effects of the heavy bottom and ch…
We study the potential of a Neutrino Factory in constraining the parameter space of a scheme with one sterile neutrino separated from three active ones by an O(1) eV^2, mass-squared difference. We present approximated analytic expressions for the oscillation probabilities, showing that the greatest sensitivity to sterile neutrinos at a Neutrino Factory can be achieved using the ν_μ->ν_μand the ν_μ->ν_τoscillations. We have studied two setups: a Neutrino Factory with 50 GeV (20 GeV) stored muons, with two detectors of the Hybrid-MIND type (a magnetized ECC next to a magnetized iron calorimeter)…
Next-to-leading order corrections are an important aspect in the extraction of the Cabibbo- Kobayashi-Maskawa matrix elements $|V_{\text{cb}}|$ and $|V_{\text{ub}}|$ at $B$-factory experiments: virtual and real photons couple to all charged particles of the decay, alter the resulting decay dynamics and enhance the total decay rate. We present a phenomenologically motivated model and a Monte-Carlo implementation to study electromagnetic radiative corrections to differential and total decay rates for semileptonic $B$-meson decays into exclusive pseudoscalar and scalar final states and apply it t…
We have calculated the next-to-leading order perturbative QCD corrections to the photon energy spectrum in radiative Upsilon decays. The higher-order corrections significantly modify the shape of the spectrum, in particular at large photon energies, and thereby reduce the discrepancy between experimental data and previous leading-order predictions. The next-to-leading order calculation of the photon energy spectrum allows a more reliable determination of the strong coupling constant from radiative Upsilon decays by restricting the analysis to the region of the energy spectrum that can be descr…
We compute the next-to-leading order corrections in $α_s$ to prompt diphoton production in association with a jet at hadron colliders. We use a next-to-leading order general-purpose partonic Monte Carlo event generator that allows the computation of a rate differential in the produced photons and hadrons.
We show how leading radiative corrections can be implemented in the general description of $h\to 4\ell$ decays by means of Pseudo Observables (PO). With the inclusion of such corrections, the PO description of $h\to 4\ell$ decays can be matched to next-to-leading-order electroweak calculations both within and beyond the Standard Model (SM). In particular, we demonstrate that with the inclusion of such corrections the complete next-to-leading-order Standard Model prediction for the $h\to 2e2μ$ dilepton mass spectrum is recovered within 1% accuracy. The impact of radiative corrections for non-st…
We evaluate the complete four-loop anomalous dimension matrix that is necessary for determining the effective flavour-changing neutral current couplings qbar-q'-gamma and qbar-q'-g at the next-to-next-to-leading order in QCD. The resulting O(alpha_s^2(mu_b)) correction to the B -> X_s gamma branching ratio amounts to around -2.9% for mu_b = 5 GeV, and -4.4% for mu_b = 2.5 GeV
This paper is devoted to the calculation of the quark-gluon-Reggeized quark effective vertex in perturbative QCD in the next-to-leading order. The case of QCD with massive quarks is considered. This vertex has a number of applications, in particular, the result can be used for determination of the next-to-leading correction to the massive Reggeized quark trajectory.
We provide a model-independent framework for the analysis of the radiative B-meson decays B -> K* gamma and B -> rho gamma. In particular, we give a systematic discussion of the various contributions to these exclusive processes based on the heavy-quark limit of QCD. We propose a novel factorization formula for the consistent treatment of B -> V gamma matrix elements involving charm (or up-quark) loops, which contribute at leading power in Lambda_QCD/m_B to the decay amplitude. Annihilation topologies are shown to be power suppressed. In some cases they are nevertheless calculable. The approac…
We investigate the neutral Higgs sector in the next-to-minimal supersymmetric standard model (NMSSM) with explicit CP violation at the one-loop level by using the effective potential method. In general, explicit CP violation is possible at the tree-level in the Higgs potential of the NMSSM, which may possess a complex phase. The tree-level Higgs potential can be made CP conserving by assuming that all the relevant parameters are real. However, the CP-conserving Higgs potential at the tree level may still develop complex phases at the one-loop level through radiative corrections. These complex …
In this short review, the calculation of the next-to-next-to-leading order QCD corrections to the inclusive radiative decay B -> X_s gamma is described. I summarize the salient features of the calculational framework adopted, discuss the results obtained in the last few years, and indicate the technical tools that made the NNLO calculations possible. I conclude by comparing the current NNLO theoretical estimate for the branching ratio with the experimental measurement and by briefly discussing the size and origin of the residual theoretical uncertainty.
We compute the complete O(alphas^2) anomalous dimension matrix relevant for the b to s gamma, b to s gluon and b to s l+l- transitions in the standard model and some of its extensions. For radiative decays we confirm the results of Misiak and Munz, and of Chetyrkin, Misiak and Munz. The O(alphas^2) mixing of four-quark into semileptonic operators is instead a new result and represents one of the last missing ingredients of the next-to-next-to-leading-order analysis of rare semileptonic B meson decays.
We study the amplitude of deeply virtual Compton scattering in next-to-leading order of perturbation theory including the two-loop evolution effects for different sets of skewed parton distributions (SPDs). It turns out that in the minimal subtraction scheme the relative radiative corrections are of order 20-50%. We analyze the dependence of our predictions on the choice of SPD, that will allow to discriminate between possible models of SPDs from future high precision experimental data, and discuss shortly theoretical uncertainties induced by the radiative corrections.
We present the calculation of the next-to-leading corrections to the tree amplitudes which appear in the description of non-leptonic B-decays in the factorization approach. These corrections, together with radiative corrections to the jet functions, represent the full next-to-leading contributions to the dominant hard spectator scattering term generated by operators $O_{1,2}$ in the decay amplitudes. Using obtained analytical results we estimate $B\toππ$ branchings fractions in the physical (or BBNS) factorization scheme. We have also found that the imaginary part generated in the hard spectat…
Recent advances in the theoretical description of radiative Upsilon decays are reviewed, including the calculation of next-to-leading order QCD corrections to the photon spectrum.
I present a first determination of a set of collinear fragmentation functions of charged pions using the NNPDF methodology. The analysis is based on a wide set of single-inclusive electron-positron annihilation data, including recent measurements from $B$-factory experiments, and is performed up to next-to-next-to-leading order accuracy in perturbative quantum chromodynamics. I discuss the results of the fits, highlighting their quality in the description of the data, their stability upon the inclusion of higher-order corrections, and their comparison to other sets of fragmentation functions.
We calculate radiative corrections to decay rates of CP-odd Higgs boson $A$ for various decay modes in the four types of two Higgs doublet models with the softly broken discrete $Z_{2}$ symmetry. The decay branching ratios are evaluated at the next-to-leading order for electroweak corrections and the next-to-next-to-leading order for QCD corrections. We comprehensively study the impact of the electroweak corrections on the decay rates and the branching ratios. We find that the radiative corrections can sizably modify the branching ratios, especially for the $A\to Zh$ decay mode in the nearly a…
We study radiative corrections to deeply virtual Compton scattering in the kinematics of HERA collider experiments to next--to--leading and next--to--next--to--leading order. In the latter case the radiative corrections are evaluated in a special scheme that allows us to employ the predictive power of conformal symmetry. As observed before, the size of next--to--leading order corrections strongly depends on the gluonic input, as gluons start to contribute at this order. Beyond next--to--leading order we find, in contrast, that the corrections for an input scale of few GeV^2 are small enough to…
Next-to-leading order electroweak and QCD radiative corrections to the Drell-Yan process with high dimuon masses for experiments CMS LHC at CERN have been studied in fully differential form. The FORTRAN code READY for numerical analysis of Drell-Yan observables has been presented. The radiative corrections are found to become significant for CMS LHC experiment setup.
We review some selected rare B decays calculated in next-to-leading order accuracy in the Standard Model (SM). These include the radiative decays $B \to (X_s,K^*,ρ)γ$ and the semileptonic decays $B \to (X_s,K,K^*) \ell^+ \ell^-$, for which new data from the BABAR and BELLE collaborations have been presented at this conference. SM is in agreement with the current measurements within the theoretical and experimental errors. The impact of rare B-decays on the CKM phenomenology is quantitatively discussed.
In this work, we study the radiative decay of $Z$ boson to a $P$-wave quarkonium $H$ in association with a photon, where $H$ can be $χ_{QJ}$, $h_Q$ with $Q=c,b$ and $J=0,1,2$. The helicity amplitudes and the unpolarized decay widths are evaluated up to QCD next-to-next-to-leading order (NNLO) within the framework of nonrelativistic QCD (NRQCD). For the first time, we check the NRQCD factorization for $h_Q$ exclusive production at two-loop order. The leading logarithms (LL) of $m_Z^2/m_Q^2$ in the leading-twist short-distance coefficients, which may potentially ruin the perturbative convergence…
We present our results for three-loop anomalous dimensions necessary in analyzing $B{\to}X_sγ$ decay at the next-to-leading order in QCD. We combine them with other recently calculated contributions, obtaining a practically complete next-to-leading order prediction for the branching ratio ${\cal B}(B{\to}X_sγ) = (3.28 \pm 0.33) \times 10^{-4}$. The uncertainty is more than twice smaller than in the previously available leading order theoretical result. The Standard Model prediction remains in agreement with the CLEO measurement at the $2 σ$ level.
The impact of final-state radiation (FSR) on the radiative return method for the extraction of the e+e- hadronic cross section is discussed in detail. Possible experimental tests of the model dependence of FSR are proposed for the pi+pi- hadronic final state. The importance of the (pi+pi-photon) final state contribution to the muon anomalous magnetic moment is investigated, and a method based on the radiative return is proposed to extract these contributions from data.
The annihilation of proton and antiproton to electron-positron pair, including radiative corrections due to the emission of virtual and real photons is considered. The results are generalized to leading and next-to leading approximations. The relevant distributions are derived and numerical applications are given in the kinematical range accessible to the PANDA experiment at the FAIR facility.
Born cross section and the radiative corrections to its lowest order are considered in the frame work of QED with structureless nucleons including the emission of virtual and real photons. Result is generalized to take into account radiative corrections in higher orders of perturbation theory in the leading and next-to leading logarithmic approximation. Crossing processes are considered in the leading approximation.
We analyze in the framework of pQCD the properties of the single spin asymmetry in heavy flavor production by linearly polarized photons. At leading order, the parallel- perpendicular asymmetry in azimuthal distributions of both charm and bottom quark is predicted to be about 20% in a wide region of initial energy. Using the soft gluon resummation formalism, we have calculated the next-to-leading order corrections to the asymmetry to next-to-leading logarithmic accuracy. It is shown that radiative corrections practically do not affect the Born predictions for the azimuthal asymmetry at energie…
We discuss the next to the leading order (NLO) electroweak radiative corrections to the $e^- e^+ \rightarrow f^- f^+ (γ)$ cross section asymmetry, for polarized and unpolarized beam scenario. The left-right and forward-backward amplitudes, with and without radiative corrections, are evaluated and compared for various kinematics. The hard bremsstrahlung is included for arbitrary energy cuts. The radiative corrections are shown to be significant and having a non-trivial dependency on the kinematic conditions. The calculations are relevant for the ultra-precise low-energy experiment Belle~II plan…
The radiative corrections to double-Dalitz ($P\to\bar{\ell}\ell\bar{\ell'}\ell'$) decays are revisited and completed up to next-to-leading order in QED, finding mild differences with respect to previous studies. These might be relevant for extracting information about the mesons transition form factors, which play an important role in determining the hadronic light-by-light contribution to the anomalous magnetic moment of the muon.
We discuss QCD radiative corrections to the production of a heavy neutral resonance $Z'$ at the LHC assuming that it decays into a $ t\bar t$ final state. Compared to previous studies, our computation includes top quark decays as well as interference between the $Z'$ signal process and the QCD $t \bar t$ background. The interference contribution appears for the first time at next-to-leading order (NLO) QCD and requires new one-loop amplitudes that are not present when signal and background are treated separately. We describe some examples of how QCD radiative corrections may influence both the…
