arXiv subjects

Wen-Long Sang

Publications and source records attributed to Wen-Long Sang.

At least 37 records · Page 2Linked to original sources

arXiv2023

$Z$ boson radiative decays to a $S$-wave quarkonium at NNLO and NLL accuracy

Within the framework of nonrelativistic QCD (NRQCD) factorization formalism, we compute QCD next-to-next-to-leading order (NNLO) corrections to the helicity amplitudes as well as the decay width of $Z\to H+γ$, where $H$ can be $η_Q (Q=c,b), J/ψ$, or $Υ$. In addition, we resum the next-to-leading logarithms (NLL) of ${m_Z^2}/{m_Q^2}$ to all orders of $α_s$ for the leading-twist helicity amplitude by employing the light-cone factorization approach. It is worth mentioning that we obtain the analytic expressions of the truncated NLL at $α_s^2$. We find that the $\mathcal{O}(α_s)$ corrections are around 10\% for $η_c$ and $Υ$ productions, however insignificant for $J/ψ$ and $η_b$ productions. The $\mathcal{O}(α_s^2)$ corrections are moderate for charmonium production, while very small for bottomonium production. Moreover, it is found that the NLL resummation can considerably alter the NRQCD prediction, especially for $J/ψ$ production. Combining the NRQCD and light-cone computation, we make phenomenological predictions on the decay widths and branching fractions. In addition, we investigate the dependence of the theoretical results on the heavy quark mass, and find the branching fraction of $Z\to H+γ$ monotonically decreases as $m_Q$ increases.

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arXiv2023

Optimized ${\cal O}(α_s^2)$ correction to exclusive double $J/ψ$ production at $B$ factories

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.

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arXiv2023

Inclusive production of fully-charmed tetraquarks at LHC

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 $α_s$ 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.

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arXiv2023

Decay constant of $B_c^*$ accurate up to $\mathcal{O}(α_s^3)$

In this paper, we evaluate, up to QCD next-to-next-to-next-to-leading order, the $B_c^*$ decay constant, which, within the nonrelativistic QCD (NRQCD) framework, is factorized as the product of the short-distance coefficient (SDC) and the long-distance matrix element. For the first time, the renormalization constant and the anomalous dimension for the NRQCD vector current composed of $c\bar{b}$, which are functions of the charm quark mass $m_c$, the bottom quark mass $m_b$ and the factorization scale $μ_Λ$, are obtained analytically at $\mathcal{O}(α_s^2)$ and $\mathcal{O}(α_s^3)$. The SDC is calculated up to $\mathcal{O}(α_s^3)$ in perturbative expansion. Explicitly, the $\mathcal{O}(α_s^2)$ correction to the SDC is analytically calculated in terms of logarithmic and polylogarithmic functions of $r\equiv m_b/m_c$, and the $\mathcal{O}(α_s^3)$ correction to the SDC is numerically calculated at a series of values of $r$, ranging from $2.1$ to $4.0$. Surprisingly, we find that the nontrivial part of the SDC at $\mathcal{O}(α_s^3)$ can be well estimated by a linear function of $r$. In addition, We find that the $\mathcal{O}(α_s^2)$ and $\mathcal{O}(α_s^3)$ corrections to the decay constant and decay width are considerable and very significant, which indicates a very poor convergence for the perturbative expansion.

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arXiv2023

$Z$ boson radiative decays to a $P$-wave quarkonium at NNLO and LL accuracy

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, are resummed to all orders of $α_s$ by employing the light-cone factorization. We find the radiative corrections are considerable for $χ_{Q2}$ and $h_Q$ productions, while are moderate or even minor for other channels. We also notice that the LL resummation can change the leading-order predictions for decay widths by more than 25\% for $χ_{c0,2}$ and $h_c$ productions, and by around 50\% for $χ_{c1}$ production. However, effects of the LL resummation on the next-to-leading-order and NNLO predictions are notably mitigated. Some phenomenological explorations are also performed.

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arXiv2022

Next-to-next-to-leading-order QCD corrections to $e^+e^-\to J/ψ+η_c$ at $B$ factories

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. Our state-of-the-art prediction is consistent with the BaBar measurement within errors.

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arXiv2022

Higher-order QCD corrections to $Υ$ decay into double charmonia

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.

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arXiv2022

Three-loop QCD corrections to the decay constant of $B_c$

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.

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arXiv2022

Complete three-loop QCD corrections to leptonic width of vector quarkonium

Within the nonrelativistic QCD (NRQCD) factorization framework, we compute the order-$α_s^3$ perturbative corrections to the leptonic decay of the $Υ$ and $J/ψ$ with high numerical accuracy, at the lowest order in velocity expansion. We confirm the existing three-loop results in literature. Furthermore, we explicitly consider the complex-valued light-by-light (singlet) contributions. We for the first time also consider the finite charm quark mass effect for $Υ$ leptonic decay, and obtain a new piece of 3-loop contribution to the anomalous dimension related to the composite NRQCD bilinear of vector current that arises from the nonzero charm quark mass. Based on the complete three-loop NRQCD short-distance coefficients, we also present a comprehensive phenomenological analysis for $Υ(J/ψ)$ leptonic width.

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arXiv2021

Next-to-leading-order QCD corrections to a vector bottomonium radiative decay into a charmonium

Within the framework of nonrelativistic QCD (NRQCD) factorization, we calculate the next-to-leading-order (NLO) perturbative corrections to the radiative decay $Υ\to η_c(χ_{cJ})+γ$. 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 $\mathcal{O}(α_s)$ corrections are moderate for $η_c$ and $χ_{c2}$ production, and are quite marginal for $χ_{c0}$ and $χ_{c1}$ 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 $χ_{cJ}$, and slightly improve that for $η_c$. With the NRQCD matrix elements evaluated via the Buchmüller-Tye potential model, we find the decay width for $η_c$ production is one-order-of-magnitude larger than $χ_{cJ}$ production, which may provide a good opportunity to search for $Υ\to η_c+γ$ in experiment. In addition, the decay width for $χ_{c1}$ production is several times larger than those for $χ_{c0,2}$. Finally, we find the NLO NRQCD prediction for the branching fraction of $Υ\to χ_{c1}+γ$ 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 $Υ\to η_c+γ$. The discrepancies between theory and experiment deserve further research efforts.

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arXiv2021

Next-to-leading-order QCD corrections to heavy quark fragmentation into ${}^1S^{(1,8)}_0$ quarkonia

Within NRQCD factorization framework, in this work we compute, at the lowest order in velocity expansion, the next-to-leading-order (NLO) perturbative corrections to the short-distance coefficients associated with heavy quark fragmentation into the ${}^1S_0^{(1,8)}$ components of a heavy quarkonium. Starting from the Collins and Soper's operator definition of the quark fragmentation function, we apply the sector decomposition method to facilitate the numerical manipulation. It is found that the NLO QCD corrections have a significant impact.

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arXiv2021

Inclusive production of fully-charmed ${\bm 1}^{\bm{+}\bm{-}}$ tetraquark at $\bm B$ factory

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 $α_s$. 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.

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arXiv2020

Scale-Fixed Predictions for $γ+ η_c$ production in electron-positron collisions at NNLO in perturbative QCD

In the paper, we present QCD predictions for $η_{c} + γ$ production at an electron-position collider up to next-to-next-to-leading order (NNLO) accuracy without renormalization scale ambiguities. The NNLO total cross-section for $e^{+}+e^{-}\toγ+η_{c}$ using the conventional scale-setting approach has large renormalization scale ambiguities, usually estimated by choosing the renormalization scale to be the $e^+ e^-$ center-of-mass collision energy $\sqrt{s}$. The Principle of Maximum Conformality (PMC) provides a systematic way to eliminate such renormalization scale ambiguities by summing the nonconformal $β$ contributions into the QCD coupling $α_s(Q^2)$. The renormalization group equation then sets the value of $α_s$ for the process. The PMC renormalization scale reflects the virtuality of the underlying process, and the resulting predictions satisfy all of the requirements of renormalization group invariance, including renormalization scheme invariance. After applying the PMC, we obtain a scale-and-scheme independent prediction, $σ|_{\rm NNLO, PMC}\simeq 41.18$ fb for $\sqrt{s}$=10.6 GeV. The resulting pQCD series matches the series for conformal theory and thus has no divergent renormalon contributions. The large $K$ factor which contributes to this process reinforces the importance of uncalculated NNNLO and higher-order terms. Using the PMC scale-and-scheme independent conformal series and the $\rm Pad\acute{e}$ approximation approach, we predict $σ|_{\rm NNNLO, PMC+Pade} \simeq 21.36$ fb, which is consistent with the recent BELLE measurement $σ^{\rm obs}$=$16.58^{+10.51}_{-9.93}$ fb at $\sqrt{s} \simeq 10.6$ GeV. This procedure also provides a first estimate of the NNNLO contribution.

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arXiv2020

Exclusive radiative production of fully-charmed tetraquarks at $B$ Factory

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.

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arXiv2020

Next-to-Next-to-Leading-Order Radiative Corrections to $e^+e^-\toχ_{cJ}+γ$ at $B$ factory

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.

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arXiv2020

Study on $η_{c2}(η_{b2})$ electromagnetic decay into double photons

Within the framework of nonrelativistic QCD (NRQCD) factorization formalism, we compute the helicity amplitude as well as the decay width of $η_{Q2}$ ($Q=c,b$) electromagnetic decay into two photons up to next-to-next-to-leading order (NNLO) in $α_s$ expansion. For the first time, we verify the validity of NRQCD factorization for the D-wave quarkonium decay at NNLO. We find that the $\mathcal{O}(α_s)$ and $\mathcal{O}(α_s^2)$ corrections to the helicity amplitude are negative and moderate, nevertheless both corrections combine to suppress the leading-order prediction for the decay width significantly. By approximating the total decay width of $η_{Q2}$ as the sum of those for the hadronic decay and the electric $E1$ transition, we obtain the branching ratios ${\rm Br}(η_{c2}\to 2γ)\approx 5\times10^{-6}$ and ${\rm Br}(η_{b2}\to 2γ)\approx 4\times10^{-7}$. To explore the potential measurement on $η_{Q2}$, we further evaluate the production cross section of $η_{Q2}$ at LHCb at the lowest order in $α_s$ expansion. With the kinematic constraint on the longitudinal rapidity $4.5>y>2$ and transverse momentum $P_T>(2-4)m_Q$ for $η_{Q2}$, we find the cross section can reach $2-50$ nb for $η_{c2}$, and $1-22$ pb for $η_{b2}$. Considering the integrated luminosity $\mathcal{L}=10\, {\rm fb}^{-1}$ at $\sqrt{s}=7$ TeV and $\sqrt{s}=13$ TeV, we estimate that there are several hundreds events of $pp\to η_{c2}\to 2γ$. Since the background is relatively clean, it is promising to reconstruct $η_{c2}$ through its electromagnetic decay. On the contrary, due to small branching ratio and production cross section, it is quite challenging to detect $η_{b2}\to 2γ$ at LHCb.

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arXiv2020

${\cal O}(α_sv^2)$ corrections to hadronic decay of vector quarkonia

Within the nonrelativistic QCD (NRQCD) factorization framework, we compute the ${\mathcal O}(α_s v^2)$ corrections to the hadronic decay rate of vector quarkonia, exemplified by $J/ψ$ and $Υ$. Setting both the renormalization and NRQCD factorization scales to be $m_Q$, we obtain $Γ(J/ψ\to {\rm LH})= 0.0716\frac{α_s^3}{m_c^2} \langle \mathcal{O}_1({}^3S_1)\rangle_{J/ψ} [1-1.19α_s+(-5.32+3.03α_s)\langle v^2\rangle_{J/ψ}]$ and $Γ(Υ\to {\rm LH})= 0.0716\frac{α_s^3}{m_b^2}\langle\mathcal{O}_1({}^3S_1)\rangle_Υ[1-1.56α_s+(-5.32+4.61α_s)\langle v^2\rangle_Υ]$. We confirm the previous calculation of $\mathcal{O}(α_s)$ corrections on a diagram-by-diagram basis, with the accuracy significantly improved. For $J/ψ$ hadronic decay, we find that the ${\mathcal O}(α_sv^2)$ corrections are moderate and positive, nevertheless unable to counterbalance the huge negative corrections. On the other hand, the effect of ${\mathcal O}(α_sv^2)$ corrections for $Υ(nS)$ 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 $Υ(1S,2S)\to {\rm LH}$. As a byproduct, we also present the theoretical predictions for the branching ratio of $J/ψ(Υ)\to 3γ$ accurate up to $\mathcal{O}(α_s v^2)$.

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arXiv2020

Fragmentation production of fully-charmed tetraquarks at LHC

The $X(6900)$ resonance, very recently discovered in the double-$J/ψ$ 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 $m_c\gg Λ_{\rm QCD}$, 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 $α_s$ 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.

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