Search

The $X(6900)$ resonance, originally discovered by the \texttt{LHCb} collaboration and later confirmed by both \texttt{ATLAS} and \texttt{CMS} experiments, has sparked broad interests in the fully-charmed tetraquark states. Relative to the mass spectra and decay properties of fully-heavy tetraquarks, our knowledge on their production mechanism is still rather limited. In this work we investigate the inclusive production of fully-charmed $S$-wave tetraquarks at \texttt{LHC} within the nonrelativistic QCD (NRQCD) factorization framework. The partonic cross sections are computed at lowest order in $\alpha_s$ and velocity, while the long-distance NRQCD matrix elements are estimated from phenomenological potential models. We predict the differential $p_T$ spectra of various fully-charmed $S$-wave tetraquarks at the \texttt{LHC}, and compare with the results predicted from the fragmentation mechanism at large $p_T$ end., Comment: 12 pages, 5 figures, 2 tables. SDCs in .m attachment

The failure of observing the $e^+ e^- \to J/ψ+J/ψ$ events at $B$ factories to date is often attributed to the significant negative order-$α_s$ correction. In this work we compute the ${\cal O}(α^2_s)$ correction to this process for the first time. The magnitude of the next-to-next-to-leading order (NNLO) perturbative correction is substantially negative so that the standard NRQCD prediction would suffer from an unphysical, negative cross section. This dilemma may be traced in the fact that the bulk contribution of the fixed-order radiative corrections stems from the perturbative corrections to the $J/ψ$ decay constant. We thus implement an improved NRQCD factorization framework, by decomposing the amplitude into the photon-fragmentation piece and the non-fragmentation piece. With the measured $J/ψ$ decay constant as input, which amounts to resumming a specific class of radiative and relativistic corrections to all orders, the fragmentation-induced production rate can be predicted accurately and serves a benchmark prediction. The non-fragmentation type of the amplitude is then computed through NNLO in $α_s$ and at lowest order in velocity. Both the ${\cal O}(α_s)$ and ${\cal O}(α^2_s)$ corrections in the interference term become positive and exhibit a decent convergence behavior. Our finest prediction is $σ(e^+ e^- \to J/ψ+J/ψ)= 2.13^{+0.30}_{-0.06}$ fb at $\sqrt{s}=10.58$ GeV. With the projected integrated luminosity of 50 ${\rm ab}^{-1}$, the prospect to observe this exclusive process at \texttt{Belle} 2 experiment appears to be bright., 13 pages, 8 figures, 3 tables

Within the framework of nonrelativistic QCD (NRQCD) factorization, we compute the three-loop QCD corrections to the decay constant of $B_c$. We reconstruct the analytical expressions for the three-loop renormalization constant and the corresponding anomalous dimension affiliated with the pseudoscalar current composed of two different heavy flavors in NRQCD, which are functions of the ratio between the charm and bottom quark masses. Meanwhile, the short-distance coefficient is obtained with very high numerical accuracy. The three-loop QCD correction turns out to be overwhelmingly large. The phenomenological implication of this new piece of radiative corrections for the $B_c$ leptonic decay is also addressed., 9 pages, 4 figures and 2 tables

In this work, we study the exclusive decay of $Υ$ into $J/ψ$ in association with $η_c$ ($χ_{c0,1,2}$). The decay widths for different helicity configurations are evaluated up to QCD next-to-leading order within the nonrelativistic QCD framework. We find that the QCD corrections notably mitigate the renormalization scale dependence of the decay widths for all the processes. The branching fraction of $Υ\rightarrow J/ψ+χ_{c1}$ is obtained as $3.73^{+5.10+0.10}_{-2.06-1.19}\times 10^{-6}$, which agrees well with the Belle measurement, i.e., ${\rm Br}(Υ\rightarrow J/ψ+χ_{c1})=(3.90\pm1.21\pm0.23)\times10^{-6}$. For the other processes, our results of the branching fractions are compatible with the upper limits given by the Belle experiments, except for $Υ(2S)\to J/ψ+χ_{c1}$, where some tension exists between theory and experiment. Having the polarized decay widths, we study the $J/ψ$ polarization, which turn out to be independent of any nonperturbative parameters. Further, according to our calculation, it is promising to measure all the processes at Super B factory thanks to the high luminosity., 13 pages, 2 figures, 3 tables, to match the version accepted for publication in PRL

We compute the next-to-next-to-leading-order (NNLO) perturbative corrections to the exclusive channels $e^+e^-\to J/ψ+χ_{cJ}$ ($J=0,1,2$) at $\sqrt{s}=10.58$ GeV within the nonrelativistic QCD (NRQCD) factorization framework. The validity of NRQCD factorization at ${\cal O}(α_s^2)$ has been confirmed for these double-charmonium exclusive production processes. We analyze the impact of the NNLO perturbative corrections on the polarized and unpolarized cross sections, as well as the $J/ψ$ angular distributions, which largely reduce the renormalization scale dependence but lower the NLO NRQCD predictions to some extent for $χ_{c0,1}$. With high numerical accuracy, our NNLO predictions for $σ(J/ψ+χ_{c1,2})$ are compatible with the upper limit of the \texttt{Belle} measurement. Although the finest prediction for $σ(J/ψ+χ_{c0})$ is consistent with both \texttt{Belle} and \texttt{BaBar} measurements within uncertainties, there still exists serious tension between the predicted and the measured profiles for the $J/ψ$ angular distribution. Regarding the bright observation prospect of the $e^+e^-\to J/ψ+χ_{c1,2}$ channels in \texttt{Belle 2} experiment, it is interesting to compare the future measurements with our NNLO predictions. The more accurate measurement of $e^+e^-\to J/ψ+χ_{0}$ at \texttt{Belle 2} will also help to clarify the long-standing puzzle of $J/ψ$ angular distribution., 17 pages, 4 tables, 2 figures. b quark loop contributions explicitly included

Within the framework of nonrelativistic QCD (NRQCD) factorization, we calculate the next-to-leading-order (NLO) perturbative corrections to the radiative decay $\Upsilon\to \eta_c(\chi_{cJ})+\gamma$. Both the helicity amplitudes and the helicity decay widths are obtained. It is the first computation for the processes involving both bottomonium and charmonium at two-loop accuracy. By employing the Cheng-Wu theorem, we are able to convert most of complex-valued master integrals (MIs) into real-valued MIs, which makes the numerical integration much efficient. Our results indicate the $\mathcal{O}(\alpha_s)$ corrections are moderate for $\eta_c$ and $\chi_{c2}$ production, and are quite marginal for $\chi_{c0}$ and $\chi_{c1}$ production. It is impressive to note the NLO corrections considerably reduce the renormalization scale dependence in both the decay widths and the branching fractions for $\chi_{cJ}$, and slightly improve that for $\eta_c$. With the NRQCD matrix elements evaluated via the Buchm\"uller-Tye potential model, we find the decay width for $\eta_c$ production is one-order-of-magnitude larger than $\chi_{cJ}$ production, which may provide a good opportunity to search for $\Upsilon\to \eta_c+\gamma$ in experiment. In addition, the decay width for $\chi_{c1}$ production is several times larger than those for $\chi_{c0,2}$. Finally, we find the NLO NRQCD prediction for the branching fraction of $\Upsilon\to \chi_{c1}+\gamma$ is only half of the lower bound of the experimental data measured recently by {\tt Belle}. Moreover, there exists serious contradiction between theory and experiment for $\Upsilon\to \eta_c+\gamma$. The discrepancies between theory and experiment deserve further research efforts., Comment: 24 pages, 2 figures, 6 tables. Significantly improved in writing; Matches version published in JHEP

Inspired by the recent discovery of the $X(6900)$ meson at {\tt LHCb} experiment, we investigate the inclusive production rate of the $C$-odd fully-charmed tetraquarks associated with light hadrons at the $B$ factory within the nonrelativistic QCD (NRQCD) factorization framework. The short-distance coefficient is computed at lowest order in velocity and $\alpha_s$. Employing the diquark-antidiquark model to roughly estimate the long-distance NRQCD matrix elements, we predict the rate for inclusive production of the $1^{+-}$ $T_{4c}$ state and discuss the observation prospects at {\tt Belle 2} experiment., Comment: 11 pages, 3 figures

The $X(6900)$ resonance, very recently discovered in the double-$J/\psi$ channel at LHCb experiment, has spurred intensive interest in unravelling the nature of the fully charmed tetraquark state. The aim of this paper is to present a model-independent theoretical framework to study the inclusive production of this novel species of exotic hadrons, the resonances composed of four heavy quark (commonly referred to as $T_{4c}$), at large $p_T$ in hadron collision experiments. Appealing to asymptotic freedom and the fact $m_c\gg \Lambda_{\rm QCD}$, we propose that the nonpertubative yet universal gluon-to-$T_{4c}$ fragmentation function, can be decomposed into the product of the perturbatively calculable short-distance coefficient and the long-distance NRQCD matrix elements. We compute the short-distance coefficient at lowest-order in $\alpha_s$ and velocity expansion. Adopting the diquark ansatz to roughly estimate those not-yet-known NRQCD matrix elements, together with the standard QCD factorization theorem, we predict the differential production rates for the $T_{4c/4b}(0^{++})$ and $T_{4c/4b}(2^{++})$ at large $p_T$ in $pp$ collision, which eagerly awaits the confrontation with the future LHC experiments., Comment: 9 pages, 1 table, 3 figures

Within the nonrelativistic QCD (NRQCD) factorization framework, we compute the ${\mathcal O}(��_s v^2)$ corrections to the hadronic decay rate of vector quarkonia, exemplified by $J/��$ and $��$. Setting both the renormalization and NRQCD factorization scales to be $m_Q$, we obtain $��(J/��\to {\rm LH})= 0.0716\frac{��_s^3}{m_c^2} \langle \mathcal{O}_1({}^3S_1)\rangle_{J/��} [1-1.19��_s+(-5.32+3.03��_s)\langle v^2\rangle_{J/��}]$ and $��(��\to {\rm LH})= 0.0716\frac{��_s^3}{m_b^2}\langle\mathcal{O}_1({}^3S_1)\rangle_��[1-1.56��_s+(-5.32+4.61��_s)\langle v^2\rangle_��]$. We confirm the previous calculation of $\mathcal{O}(��_s)$ corrections on a diagram-by-diagram basis, with the accuracy significantly improved. For $J/��$ hadronic decay, we find that the ${\mathcal O}(��_sv^2)$ corrections are moderate and positive, nevertheless unable to counterbalance the huge negative corrections. On the other hand, the effect of ${\mathcal O}(��_sv^2)$ corrections for $��(nS)$ is sensitive to the $\mathcal{O}(v^2)$ NRQCD matrix elements. With the appropriate choice of the NRQCD matrix elements, our theoretical predictions for the decay rates may be consistent with the experimental data for $��(1S,2S)\to {\rm LH}$. As a byproduct, we also present the theoretical predictions for the branching ratio of $J/��(��)\to 3��$ accurate up to $\mathcal{O}(��_s v^2)$., 21 pages, 5 figures, 3 tables

The rare process of $W$ radiative decay into the $B_c$ meson can serve as an interesting play ground for testing two influential perturbative QCD approaches: non-relativistic quantum chromodynamics (NRQCD) and ligh-cone (LC) factorization. Since the $B_c$ meson is a genuine heavy quarkonium which is composed of two different species of heavy quarks, it is natural to employ NRQCD factorization to tackle this exclusive quarkonium production process; on the other hand, since the mass of the $W$ boson is much greater than that of the $B_c$, the collinear factorization is also a viable approach. To fully disentangle the contributions from several distinct scales $M_W$, $m_Q$, $m_Q v$ ($v$ represents the typical velocity of the $c/\bar{b}$ quarks inside $B_c$), and $��_{\rm QCD}$, we carry out a joint analysis that combines both light-cone and NRQCD factorization approaches, and compute the order-$��_s$ correction to $W \to B_c+��$. With the aid of the celebrated Efremov-Radyushkin-Brodsky-Lepage (ERBL) evolution equation, we resum the leading collinear logarithms $��_s \ln\! {M_W\over m_Q}$ to all orders in $��_s$. We also explore some phenomenological implications of our predictions., 16 pages, 3 figures

The associated production of Higgs boson with a muon pair, $e^+e^-\to ��^+��^- H$, is one of the golden channels to pin down the properties of the Higgs boson in the prospective Higgs factories exemplified by \textsf{CEPC}. The projected accuracy of the corresponding cross section measurement is about per cent level at CEPC. In this work, we investigate both ${\mathcal O}(��)$ weak correction and the ${\mathcal O}(����_s)$ mixed electroweak-QCD corrections for this channel, appropriately taking into account the effect of finite $Z^0$ width. The $��^+��^-$ invariant mass spectrum is also predicted. The mixed electroweak-QCD correction turns out to reach 1.5\% of the Born-order result, and thereby must be included in future confrontation with the data. We also observe that, after including higher-order corrections, the simplified prediction for the integrated cross section employing the narrow-width-approximation may deviate from our full result by a few per cents., v2, 15 pages, 5 figures, 3 tables. Typos corrected, references added, the version to appear in Chinese Physics C

The associated production of Higgs boson with a hard photon at lepton collider, i.e., $e^+e^-\to H��$, is known to bear a rather small cross section in Standard Model, and can serve as a sensitive probe for the potential new physics signals. Similar to the loop-induced Higgs decay channels $H\to ����, Z��$, the $e^+e^-\to H��$ process also starts at one-loop order provided that the tiny electron mass is neglected. In this work, we calculate the next-to-leading-order (NLO) QCD corrections to this associated $H+��$ production process, which mainly stem from the gluonic dressing to the top quark loop. The QCD corrections are found to be rather modest at lower center-of-mass energy range ($\sqrt{s}, v4, 11 pages, 6 figures, 2 tables; errors in Appendix are fixed; version accepted for publication at PLB

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 to $e^+e^-\to HZ$ at next-to-next-to-leading order (NNLO) for both unpolarized and polarized $Z$ boson. The corrections turn out to reach one percent level of the Born-order results, thereby must be incorporated in the future confrontation with the data., 7 pages, 3 figures, 2 tables; version accepted for publication in PRD RC

We calculate the next-to-next-to-leading-order (NNLO) perturbative corrections to $P$-wave quarkonia annihilation decay to two photons, in the framework of nonrelativistic QCD (NRQCD) factorization. The order-$��_s^2$ short-distance coefficients associated with each helicity amplitude are presented in a semi-analytic form, including the "light-by-light" contributions. With substantial NNLO corrections, we find disquieting discrepancy when confronting our state-of-the-art predictions with the latest \textsf{BESIII} measurements, especially fail to account for the measured $��_{c2}\to����$ width. Incorporating the effects of spin-dependent forces would even exacerbate the situation, since it lifts the degeneracy between the nonperturbative NRQCD matrix elements of $��_{c0}$ and $��_{c2}$ toward the wrong direction. We also present the order-$��_s^2$ predictions to $��_{b0,2}\to����$, which await the future experimental test., 6 pages, 2 figures, 1 table; v2, typos fixed, minor changes in text

Unlike the bewildering situation in the $����^*\to ��$ form factor, a widespread view is that perturbative QCD can decently account for the recent \textsc{BaBar} measurement of $����^*\to ��_c$ transition form factor. The next-to-next-to-leading order (NNLO) perturbative correction to the $����^*\to ��_{c,b}$ form factor, is investigated in the NRQCD factorization framework for the first time. As a byproduct, we obtain by far the most precise order-$��_s^2$ NRQCD matching coefficient for the $��_{c,b}\to ����$ process. After including the substantial negative order-$��_s^2$ correction, the good agreement between NRQCD prediction and the measured $����^*\to ��_c$ form factor is completely ruined over a wide range of momentum transfer squared. This eminent discrepancy casts some doubts on the applicability of NRQCD approach to hard exclusive reactions involving charmonium., 6 pages, 3 figures and 1 table; adding Eqs.(8) and (9) as well as some references, correcting errors in Table 1, updating Fig.3 to include the "light-by-light" contributions, devoting a paragraph to discuss why our strategy of interpreting the NNLO corrections is justified; Accepted by PRL

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 $$; for the $h_c$ production associated with charmed hadrons, the total production rate is about one order of magnitude smaller, and dominated by the color-singlet channel., Comment: v2, 23 pages, 1 table, 6 figures. Minor corrections, and a note added, accepted for publication in PRD

It has been a long-standing problem that the rare electromagnetic decay process $J/��\to 3��$ is plagued with both large and negative radiative and relativistic corrections. To date it remains futile to make a definite prediction to confront with the branching fraction of $J/��\to 3��$ recently measured by the \textsf{CLEO-c} and \textsf{BESIII} Collaborations. In this work, we investigate the joint perturbative and relativistic correction (i.e. the ${\mathcal O}(��_s v^2)$ correction, where $v$ denotes the characteristic velocity of the charm quark inside the $J/��$) for this decay process, which turns out to be very significant. After incorporating the contribution from this new ingredient, with the reasonable choice of the input parameters, we are able to account for the measured decay rates in a satisfactory degree., 7 pages, 1 figure, version accepted for publication in PRD RC

We investigate the $O(��_s v^2)$ correction to the process of pseudoscalar quarkonium decay to two photons in nonrelativistic QCD (NRQCD) factorization framework. The short-distance coefficient associated with the relative-order $v^2$ NRQCD matrix element is determined to next-to-leading order in $��_s$ through the perturbative matching procedure. Some technical subtleties encountered in calculating the ${O(��_s)$ QCD amplitude are thoroughly addressed., v2, 28 pages, 2 figures and 2 tables, matching the published version; typos corrected, references added, as well as a "Note added in the proof"

The very recent analysis by BaBar Collaboration indicates that the $X(3872)$ may favor the quantum number $J^{PC}=2^{-+}$ rather than the previously assumed $1^{++}$. By pretending the $\eta_{c2}(1D)$ charmonium to be the $X(3872)$, we study the parity-even radiative transition processes $\eta_{c2}(1D)\to J/\psi(\psi')+\gamma$ within several phenomenological potential models. We take the ${}^3D_1$ admixture in $\psi'$ into account, and consider the contributions from the magnetic dipole ($M1$), electric quadrupole ($E2$), and magnetic octupole ($M3$) amplitudes. It is found that the ratio of the branching fractions of these two channels, as well as the absolute branching fraction of $\eta_{c2}\to \psi'\gamma$, are in stark contradiction with the existing \textsc{BaBar} measurements. This may indicate that the $2^{-+}$ assignment for the $X(3872)$ is highly problematic., Comment: v2; 14 pages, 3 tables; references, a new table and several footnotes added, text refined; a minus sign added for the definition of J1 in (14b), accordingly Table I and II and equations (21,22,23) are corrected to reflect this change, but the conclusion remains

The Circular Electron Positron Collider (CEPC) is a large international scientific facility proposed by the Chinese particle physics community to explore the Higgs boson and provide critical tests of the underlying fundamental physics principles of the Standard Model that might reveal new physics. The CEPC, to be hosted in China in a circular underground tunnel of approximately 100 km in circumference, is designed to operate as a Higgs factory producing electron-positron collisions with a center-of-mass energy of 240 GeV. The collider will also operate at around 91.2 GeV, as a Z factory, and at the WW production threshold (around 160 GeV). The CEPC will produce close to one trillion Z bosons, 100 million W bosons and over one million Higgs bosons. The vast amount of bottom quarks, charm quarks and tau-leptons produced in the decays of the Z bosons also makes the CEPC an effective B-factory and tau-charm factory. The CEPC will have two interaction points where two large detectors will be located. This document is the second volume of the CEPC Conceptual Design Report (CDR). It presents the physics case for the CEPC, describes conceptual designs of possible detectors and their technological options, highlights the expected detector and physics performance, and discusses future plans for detector R&D and physics investigations. The final CEPC detectors will be proposed and built by international collaborations but they are likely to be composed of the detector technologies included in the conceptual designs described in this document. A separate volume, Volume I, recently released, describes the design of the CEPC accelerator complex, its associated civil engineering, and strategic alternative scenarios., 424 pages