arXiv subjects

Wen-Long Sang

Publications and source records attributed to Wen-Long Sang.

At least 55 records · Page 3Linked to original sources

arXiv2019

Statistical analysis of the azimuthal asymmetry in the $J/ψ$ leptoproduction in unpolarized $ep$ collisions

In this paper, we study the azimuthal asymmetry in the $J/ψ$ leptoproduction in unpolarized $ep$ collisions. There are two independent azimuthal asymmetry modulations, namely $\mathrm{cos}(ψ)$ and $\mathrm{cos}(2ψ)$, where $ψ$ is the azimuthal angle of the lepton scattering plane with respect to the hadron-interacting plane. We calculate the two modulations as functions of four kinematic variables, and find that they provide a very good laboratory to distinguish several models describing the heavy quarkonium production, including the color-singlet (CS) model, the nonrelativistic QCD (NRQCD) associated with the $^1S_0^{[8]}$ dominance picture, and the NRQCD in which the values of all the three color-octet (CO) long-distance matrix elements are of the same order. In order to make definite conclusions, we restrict our calculation in a specific kinematic region, where the CS and CO mechanisms can be distinguished by scrutinizing the values of the $\mathrm{cos}(ψ)$ modulation, while the $^1S_0^{[8]}$ dominance picture can be tested by measuring the values of the $\mathrm{cos}(2ψ)$ modulation. Calculating their values and carrying out a meticulous statistical analysis, we find that at an integrated luminosity $\mathcal{L}=1000\mathrm{pb}^{-1}$, the statistical uncertainties of the two quantities are small enough to tell the three models apart. When this experiment is implemented at the future $ep$ colliders such as the EIC, crucial information for the $J/ψ$ production mechanism might be discovered.

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arXiv2019

Optimized predictions for $W \to B_c + γ$ by combining light-cone and NRQCD approaches

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 $Λ_{\rm QCD}$, we carry out a joint analysis that combines both light-cone and NRQCD factorization approaches, and compute the order-$α_s$ correction to $W \to B_c+γ$. With the aid of the celebrated Efremov-Radyushkin-Brodsky-Lepage (ERBL) evolution equation, we resum the leading collinear logarithms $α_s \ln\! {M_W\over m_Q}$ to all orders in $α_s$. We also explore some phenomenological implications of our predictions.

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arXiv2019

Kinematic distributions of the $η_c$ photoproduction in $ep$ collisions within the nonrelativistic QCD framework

We study the $η_c$ photoproduction in $ep$ collisions in this paper. The short-distance coefficients for $c\bar{c}(^1S_0^{[1]})$, $c\bar{c}(^1S_0^{[8]})$, $c\bar{c}(^3S_1^{[8]})$, and $c\bar{c}(^1P_1^{[8]})$ photoproductions are evaluated at leading order in $α_s$ expansion, where the color-singlet contribution is achieved for the first time. We have carefully analyzed different kinematic distributions of the cross sections and found that the color-singlet contribution is considerably suppressed comparing with the color-octet parts. This feature renders the $η_c$ photoproduction process an ideal laboratory to test the color-octet mechanism in nonrelativistic QCD. By taking different sets of long-distance matrix elements, we have observed some apparently distinguishable predictions, which can be utilized to scrutinize the validity of these matrix elements.

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arXiv2018

Mixed electroweak-QCD corrections to $e^+e^-\to μ^+μ^- H$ at CEPC with finite-width effect

The associated production of Higgs boson with a muon pair, $e^+e^-\to μ^+μ^- H$, 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 ${\mathcal O}(α)$ weak correction and the ${\mathcal O}(αα_s)$ mixed electroweak-QCD corrections for this channel, appropriately taking into account the effect of finite $Z^0$ width. The $μ^+μ^-$ 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.

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arXiv2018

A solution to the $γγ^*\rightarrowη_c$ puzzle using the Principle of Maximum Conformality

The next-to-next-to-leading order (NNLO) pQCD prediction for the $γγ^* \to η_c$ form factor was evaluated in 2015 using nonrelativistic QCD (NRQCD). A strong discrepancy between the NRQCD prediction and the BaBar measurements was observed. Until now there has been no solution for this puzzle. In this paper, we present a NNLO analysis by applying the Principle of Maximum Conformality (PMC) to set the renormalization scale. By carefully dealing with the light-by-light diagrams at the NNLO level, the resulting high precision PMC prediction agrees with the BaBar measurements within errors, and the conventional renormalization scale uncertainty is eliminated. The PMC is consistent with all of the requirements of the renormalization group, including scheme-independence. The application of the PMC thus provides a rigorous solution for the $γγ^* \to η_c$ form factor puzzle, emphasizing the importance of correct renormalization scale-setting. The results also support the applicability of NRQCD to hard exclusive processes involving charmonium.

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arXiv2017

Next-to-leading-order QCD corrections to $e^+e^-\to H+γ$

The associated production of Higgs boson with a hard photon at lepton collider, i.e., $e^+e^-\to Hγ$, 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 $H\to γγ, Zγ$, the $e^+e^-\to Hγ$ 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 $H+γ$ 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 ($\sqrt{s}<300$ GeV), thus of negligible impact on Higgs factory such as CEPC. Nevertheless, when the energy is boosted to the ILC energy range ($\sqrt{s}\approx 400$ GeV), QCD corrections may enhance the leading-order cross section by $20\%$. In any event, the $e^+e^-\to Hγ$ process has a maximal production rate $σ_{\rm max}\approx 0.08$ fb around $\sqrt{s}= 250$ GeV, thus CEPC turns out to be the best place to look for this rare Higgs production process. In the high energy limit, the effect of NLO QCD corrections become completely negligible, which can be simply attributed to the different asymptotic scaling behaviors of the LO and NLO cross sections, where the former exhibits a milder decrement $\propto 1/s$ , but the latter undergoes a much faster decrease $\propto 1/s^2$.

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arXiv2017

Next-to-next-to-leading-order QCD corrections to hadronic width of pseudoscalar quarkonium

We compute the next-to-next-to-leading order (NNLO) QCD corrections to the hadronic decay rates of the pseudoscalar quarkonia, at the lowest order in velocity expansion. The validity of NRQCD factorization for inclusive quarkonium decay process, for the first time, is verified to relative order $α_s^2$. As a byproduct, the renormalization group equation (RGE) of the leading NRQCD 4-fermion operator ${\cal O}_1({}^1S_0)$ is also deduced to this perturbative order. By incorporating this new piece of correction together with available relativistic corrections, we find that there exists severe tension between the state-of-the-art NRQCD predictions and the measured $η_c$ hadronic width, and in particular the branching fraction of $η_c\to γγ$. NRQCD appears to be capable of accounting for $η_b$ hadronic decay to a satisfactory degree, and our most refined prediction is ${\rm Br}(η_b\to γγ) = (4.8\pm 0.7)\times 10^{-5}$.

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arXiv2017

Mixed electroweak-QCD corrections to $e^+e^-\to HZ$ at Higgs factory

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.

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arXiv2015

Next-to-next-to-leading-order QCD corrections to $χ_{c0,2}\rightarrow γγ$

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-$α_s^2$ 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 $χ_{c2}\toγγ$ 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 $χ_{c0}$ and $χ_{c2}$ toward the wrong direction. We also present the order-$α_s^2$ predictions to $χ_{b0,2}\toγγ$, which await the future experimental test.

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arXiv2015

Can NRQCD explain the $γγ^* \to η_c$ transition form factor data?

Unlike the bewildering situation in the $γγ^*\to π$ form factor, a widespread view is that perturbative QCD can decently account for the recent \textsc{BaBar} measurement of $γγ^*\to η_c$ transition form factor. The next-to-next-to-leading order (NNLO) perturbative correction to the $γγ^*\to η_{c,b}$ form factor, is investigated in the NRQCD factorization framework for the first time. As a byproduct, we obtain by far the most precise order-$α_s^2$ NRQCD matching coefficient for the $η_{c,b}\to γγ$ process. After including the substantial negative order-$α_s^2$ correction, the good agreement between NRQCD prediction and the measured $γγ^*\to η_c$ 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.

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arXiv2015

Relativistic corrections to $Υ$ exclusive decay into double $S-$wave charmonia

Within the framework of nonrelativisitic QCD factorization formalism, we present the next-to-leading-order relativistic corrections to $Υ$ exclusive decay into $η_c$ plus $J/ψ$. The double charmonia can be produced through several immediate channels, i.e. $Υ\to g^*g^*g^*\to η_c+J/ψ$, $Υ\to g^*g^*γ^*\to η_c+J/ψ$, and $Υ\to γ^*\to η_c+J/ψ$. The amplitudes of these three channels are obtained accurate up to ${\cal O}(α_s^3 v^2)$, ${\cal O}(αα_s^2 v^2)$, and ${\cal O}(αα_s^2 v^2)$ respectively, where $v$ indicates the typical heavy quark velocity in bottomonium and/or charmonium rest frame. The decay rates are also presented. We find the next-to-leading-order relativistic corrections to the short distance coefficients as well as the decay rates are both significant and negative, especially for the corrections from bottomonium. More seriously, the decay rates are even brought into negative by including the relativistic corrections, which indicates the poor convergence for the velocity expansion in this kind of processes. Detailed analysis is given in the paper.

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arXiv2014

Impact of $η_c$ hadroproduction data on charmonium production and polarization within NRQCD framework

With the recent LHCb data on $η_c$ production and based on heavy quark spin symmetry, we obtain the long-distance matrix elements for both $η_c$ and $J/ψ$ productions, among which, the color-singlet one for $η_c$ is obtained directly by the fit of experiment for the first time. Using our long-distance matrix elements, we can provide good description of the $η_c$ and $J/ψ$ hadroproduction measurements. Our predictions on $J/ψ$ polarization are in good agreement with the LHCb data and pass through the two sets of CDF measurements in medium $p_t$ region. Considering all the possible uncertainties carefully, we obtained quite narrow bands of the $J/ψ$ polarization curves.

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arXiv2014

Short-range force between two Higgs bosons

The $S$-wave scattering length and the effective range of the Higgs boson in Standard Model are studied using effective-field-theory approach. After incorporating the first-order electroweak correction, the short-range force between two Higgs bosons remains weakly attractive for $M_H=126$ GeV. It is interesting to find that the force range is about two order-of-magnitude larger than the Compton wavelength of the Higgs boson, almost comparable with the typical length scale of the strong interaction.

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arXiv2013

Reconciling the nonrelativistic QCD prediction and the $J/ψ\to 3γ$ data

It has been a long-standing problem that the rare electromagnetic decay process $J/ψ\to 3γ$ 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 $J/ψ\to 3γ$ 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 ${\mathcal O}(α_s v^2)$ correction, where $v$ denotes the characteristic velocity of the charm quark inside the $J/ψ$) 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.

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arXiv2012

Inclusive $h_c$ production at $B$ factories

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 associated with charmed hadrons, the total production rate is about one order of magnitude smaller, and dominated by the color-singlet channel.

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arXiv2012

Order-$v^4$ Relativistic Corrections to $Υ$ Inclusive Decay into a Charm pair

In this work, we determine the short-distance coefficients for $Υ$ inclusive decay into a charm pair through relative order $v^4$ within the framework of NRQCD factorization formula. The short-distance coefficient of the order-$v^4$ color-singlet NRQCD matrix element is obtained through matching the decay rate of $b\bar{b}(^3S^{[1]}_1)\to c\bar{c}gg$ in full QCD to that in NRQCD. The double and single IR divergences appearing in the decay rate are exactly canceled through the next-to-next-to-leading-order renormalization of the operator ${\mathcal O}(^3S^{[8]}_1)$ and the next-to-leading-order renormalization of the operators ${\mathcal O}(^3P^{[8]}_J)$. To investigate the convergence of the relativistic expansion arising from the color-singlet contributions, we study the ratios of the order-$v^2$ and -$v^4$ color-singlet short-distance coefficients to the leading-order one. Our results indicate that though the order-$v^4$ color-singlet short-distance coefficient is quite large, the relativistic expansion for the color-singlet contributions in the process $Υ\to c\bar{c}+X$ is well convergent due to a small value of $v$. In addition, we extrapolate the value of the mass ratio of the charm quark to the bottom quark, and find the relativistic corrections rise quickly with increase of the mass ratio.

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arXiv2012

Relativistic corrections to the semi-inclusive decay of $\bmψ$ and $\bmΥ$

In the framework of the nonrelativistic quantum chromodynamics factorization formalism, we study the processes of $ψ(nS)$ and $Υ(nS)$ decay into a lepton pair or a charm pair associated with two jets up to the next-to-leading order in velocity expansion. We present the analytic expressions for the differential decay rate to the invariant mass of the lepton pair or charm pair. We find that the ratio of the next-to-leading order short-distance coefficient to the leading order one is in the range from -5.5 to -12.4. The relativistic corrections are so large that they modify the leading order prediction significantly. Utilizing the analytic expressions, we also investigate the relativistic corrections in different kinematic regions and their dependence on the masses of the initial-state quarkonium and the final-state fermion. In addition, we study the momentum distribution of $D^{*+}$ in the process $Υ(1S)\to c\bar{c}gg\to D^{*+}X$.

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arXiv2011

Relativistic Corrections to the Exclusive Decays of C-even Bottomonia into S-wave Charmonium Pairs

Within the nonrelativistic quantum chromodynamics (NRQCD) factorization formalism, we compute the relativistic corrections to the exclusive decays of bottomonia with even charge conjugation parity into $S$-wave charmonium pairs at leading order in the strong coupling constant. Relativistic corrections are resummed for a class of color-singlet contributions to all orders in the charm-quark velocity $v_c$ in the charmonium rest frame. Almost every process that we consider in this work has negative relativistic corrections ranging from -20 to -35,%. Among the various processes, the relativistic corrections of the next-to-leading order in $v_c$ to the decay rate for $χ_{b2}\to η_c(mS)+η_c(nS)$ with $m,$ $n=1$ or 2 are very large. In every case, the resummation of the relativistic corrections enhances the rate in comparison with the next-to-leading-order results. We compare our results with available predictions based on the NRQCD factorization formalism. The NRQCD predictions are significantly smaller than those based on the light-cone formalism by an or two orders of magnitudes.

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