arXiv subjects

Wan-Li Ju

Publications and source records attributed to Wan-Li Ju.

At least 19 recordsLinked to original sources

arXiv2025

Saddle-point method for resummed form factors in QCD

We consider the form factor appearing in QCD resummation formalism for event shape distributions in the two-jet (or Sudakov) region. We present an analytic formula for the inverse transform of the form factor, namely from the conjugate moment space to the (physical) momentum space, based on the saddle-point method. The saddle-point itself is determined by means of an analytic recursion method as well as by standard numerical methods. The results we have found are in very good agreement with the exact (numerical) evaluation of the inverse transform, while they significantly differ from classical analytical formulations of resummation in momentum space. The latter are based on a Taylor expansion of the form factor around the free-theory saddle point.

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arXiv2025

Dihadron Angular Correlations in the $e^+e^-$ Collision

The precision of fixed-order calculations on the dihadron production in electron-positron annihilation is paramount for probing QCD factorization and constraining non-perturbative inputs. This paper investigates the QCD corrections to the angular separation distribution $\theta_{12}$ between two observed hadrons, $H_1$ and $H_2$, in the process $e^+e^- \to H_1 H_2 + X$ up to $\mathcal{O}(\alpha_s^2)$, with particular emphasis on the intermediate region $\theta_{12} \in (0,\pi)$. The partonic processes at this accuracy consist of two sorts of contributions, the real-virtual and double-real corrections. Of them, the evaluation of four-body phase space integrals in the latter case is at the core of this study. To address them, we first employ the integration-by-parts (IBP) identities to reduce the number of independent integrals and then apply the differential equations (DE) method to recursively solve the resulting master integrals. In kinematic regions where the invariant mass of the unresolved partons vanishes, IBP coefficients can develop divergences. To this end, we resum higher-order terms in the dimensional regulator for each master integral based on the asymptotic behavior of the canonical DEs. After combining the real and virtual corrections with the counter terms from fragmentation function renormalization, we demonstrate that the pole terms in the final analytic expressions exactly cancel out in all partonic channels, thereby providing a non-trivial validation of collinear factorization at the next-to-leading order (NLO). Eventually, when presenting our analytic expressions of the finite partonic coefficients, we transform the transcendental functions resulting from the DE solutions into classical (poly)logarithmic functions, in order to facilitate the implementation in event generators.

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arXiv2025

Thrust distribution in electron-positron annihilation at full NNNLL+NNLO (and beyond) in QCD

We consider the thrust ($T$) distribution in electron-positron ($e^+e^-$) annihilation into hadrons and we perform the all-order resummation of the large logarithms of $1-T$ up to next-to-next-to-next-to-next-to-leading logarithmic (N$^4$LL) accuracy in QCD. We consistently combine resummed predictions with the known fixed-order results up to next-to-next-to-leading order (NNLO). All perturbative terms up to order $\alpha_S^3$ are included in our calculation which, thanks to a unitarity constraint, exactly reproduce after integration over the variable $T$ the next-to-next-to-next-to-leading order (N$^3$LO) result for the total cross section of $e^+e^-$ into hadrons. We resum the large logarithms in the Laplace-conjugated space and compare our results with those obtained with the analytic resummation formalism in the physical ($T$) space. We find that the differences in the spectra obtained with the two different formalisms are sizable. Non-perturbative corrections have been included through an analytic hadronization model depending on two free parameters. Finally, we present a comparison of our spectra with experimental data at the $Z$-boson mass ($m_Z$) energy, which enables us to extract the value of the QCD coupling $\alpha_S(m_Z^2)=0.1181 \pm 0.0018$ fully consistent with the world average.

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arXiv2024

The $q_{\mathrm{T}}$ and $\Delta\phi_{t\bar{t}}$ spectra in top-antitop hadroproduction at NNLL+NNLO: the interplay of soft-collinear resummation and Coulomb singularities

In this paper, we present the resummation-improved differential transverse momentum and azimuthal decorrelation cross sections, $d\sigma_{t\bar{t}}/dq_{\mathrm{T}}$ and $d\sigma_{t\bar{t}}/d\Delta\phi_{t\bar{t}}$, in top-antitop pair production at the LHC. Our calculation is based on the observation that both cross sections are dominated by topologies where the top-quark pair is well separated, expressed in their relative velocity $\beta_{t\bar{t}}\sim\mathcal{O}(1)$, at colliding energies of $\sqrt{s}=13\,\text{TeV}$ or higher. Therefore, the asymptotic behaviour in the limits $q_{\mathrm{T}}\to0$ and $\Delta\phi_{t\bar{t}}\to0$ can mostly be captured by the soft and collinear resummation in the HQET$+$SCET framework. Nevertheless, starting at NNLL, Coulomb singularities emerge in the threshold regime, $\beta_{t\bar{t}}\to0$, in both the hard sector and its evolution kernels, leading to unphysical results upon integration over the entire $\beta_{t\bar{t}}$ range. To this end, two prescriptions, dubbed the D- and R-prescription, are introduced to regularise these Coulomb singularities. They embody two fundamentally different methods to truncate the threshold enhanced terms, rendering their contribution finite. In the absence of a combined threshold and small-transverse-momentum resummation, we present a quantitative assessment of the ambiguity introduced by the choice of prescription, itself a test of the sensitivity of our calculation to such threshold enhancements, for both the $d\sigma_{t\bar{t}}/dq_{\mathrm{T}}$ and $d\sigma_{t\bar{t}}/d\Delta\phi_{t\bar{t}}$ spectra.

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arXiv2024

Zero-bin subtraction and the $q_{\mathrm{T}}$ spectrum beyond leading power

In this paper, we present an algorithm to construct the qT distribution at NLO accuracy to arbitrary power precision, including the assembly of suitable zero-bin subtrahends, in a mathematically well-defined way for a generic choice of rapidity-divergence regularisation prescription. In its derivation, we divide the phase space into two sectors, the interior of the integration domain as well as the integration boundary, which we include here for the first time. To demonstrate the applicability and usefulness of our algorithm, we calculate the NNLP corrections for Higgs hadroproduction for the first time. We observe that our approximate NNLP-accurate qT spectra replicate the asymptotic behaviour of the full QCD calculation to a much better degree than the previously available results, both within the $q_{\mathrm{T}}\to 0$ limit and in the large-qT domain for all the involved partonic processes. While playing a minor role at larger transverse momenta, we show that the newly incorporated boundary contribution plays a vital role in the $q_{\mathrm{T}}\to 0$ limit, where any subleading power accuracy would be lost without them. In particular, our NNLP-accurate qT expansion can approximate the exact qT distribution up to $q_{\mathrm{T}}\sim30\,\text{GeV}$ at the percent level for rapidities $|Y_H|\lesssim 3$.

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arXiv2023

Projected transverse momentum resummation in top-antitop pair production at LHC

The transverse momentum distribution of the $t\bar{t}$ system is of both experimental and theoretical interest. In the presence of the azimuthally asymmetric divergences, pursuing the resummation at the high logarithmic precision is rather demanding in general. In this paper, we propose the projected transverse momentum spectrum $\mathrm{d}σ_{t\bar{t}}/\mathrm{d} q_τ$, which is derived from the classical $\vec{q}_{\mathrm{T}}$ spectrum by integrating out the rejection component $q_{τ_{\perp}}$ with respect to a reference unit vector $\vecτ$, to serve as an alternative resolution to curb those asymmetric influences, in additional to the azimuthally averaged case $\mathrm{d}σ_{t\bar{t}}/\mathrm{d} |\vec{q}_{\mathrm{T}}|$. In the context of the effective field theories, SCET$_{\mathrm{II}}$ and HQET, we will demonstrate that in spite of the $q_{τ_{\perp}}$ integrations, the leading asymptotic terms of $\mathrm{d}σ_{t\bar{t}}/\mathrm{d} q_τ$ still observe the factorization pattern in terms of the hard, beam, and soft functions in the vicinity of $ q_τ=0$~GeV. With the help of the renormalisation group equation techniques, we evaluate the resummed spectra $\mathrm{d}σ_{t\bar{t}}/\mathrm{d} q_{\mathrm{T,in}}$, $\mathrm{d}σ_{t\bar{t}}/\mathrm{d} q_{\mathrm{T,out}}$, and $\mathrm{d}σ_{t\bar{t}}/\mathrm{d} ΔΦ_{t\bar{t}}$ at NLL+NLO, NNLL+NNLO, and approximate NNLL'+NNLO accuracy. This is the first time the azimuthal spectrum $ΔΦ_{t\bar{t}}$ is appraised at or beyond the NNLL level including a consistent treatment of both beam collinear and soft radiation.

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arXiv2023

Thrust distribution in Higgs decays up to the fifth logarithmic order

In this work, we extend the resummation for the thrust distribution in Higgs decays up to the fifth logarithmic order. We show that one needs the accurate values of the three-loop soft functions for reliable predictions in the back-to-back region. This is especially true in the gluon channel, where the soft function exhibits poor perturbative convergence.

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arXiv2022

Thrust distribution in Higgs decays at the next-to-leading order and beyond

We present predictions for the thrust distribution in hadronic decays of the Higgs boson at the next-to-leading order and the approximate next-to-next-to-leading order. The approximate NNLO corrections are derived from a factorization formula in the soft/collinear phase-space regions. We find large corrections, especially for the gluon channel. The scale variations at the lowest orders tend to underestimate the genuine higher order contributions. The results of this paper is therefore necessary to control the perturbative uncertainties of the theoretical predictions. We also discuss on possible improvements to our results, such as a soft-gluon resummation for the 2-jets limit, and an exact next-to-next-to-leading order calculation for the multi-jets region.

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arXiv2021

The $q_T$ and $Δϕ$ spectra in W and Z production at the LHC at N$^3$LL'+N$^2$LO

The production of weak gauge bosons, $W^{\pm}$ and $Z$, are at the core of the LHC precision measurement program. Their transverse momentum spectra as well as their pairwise ratios are key theoretical inputs to many high-precision analyses, ranging from the $W$ mass measurement to the determination of parton distribution functions. Owing to the different properties of the $W$ and $Z$ boson and the different accessible fiducial regions for their measurement, a simple one-dimensional correlation is insufficient to capture the differing vector and axial-vector dynamics of the produced lepton pair. We propose to correlate them in two observables, the transverse momentum $q_T$ of the lepton pair and its azimuthal separation $Δϕ$. Both quantities are purely transverse and therefore accessible in all three processes, either directly or by utilising the missing transverse momentum of the event. We calculate all the single-differential $q_T$ and $Δϕ$ as well as the double-differential $(q_T,Δϕ)$ spectra for all three processes at N$^3$LL'+N$^2$LO accuracy, resumming small transverse momentum logarithms in the soft-collinear effective theory approach and including all singlet and non-singlet contributions. Using the double-differential cross sections we build the pairwise ratios $\mathcal{R}_{W^+/Z},~\mathcal{R}_{W^-/Z},~\mathcal{R}_{W^+/W^-}$ and determine their uncertainties assuming fully correlated, partially correlated, and uncorrelated uncertainties in the respective numerators and denominators. In the preferred partially correlated case we find uncertainties of less than 1% in most phase space regions and up to 3% in the lowest $q_T$ region.

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arXiv2021

Top quark pair production near threshold: single/double distributions and mass determination

We investigate top quark pair production near the threshold where the pair invariant mass $M_{t\bar{t}}$ approaches $2m_t$, which provides sensitive observables to extract the top quark mass $m_t$. Using the effective field theory methods, we derive a factorization and resummation formula for kinematic distributions in the threshold limit up to the next-to-leading power, which resums higher order Coulomb corrections to all orders in the strong coupling constant. Our formula is similar to those in the literature but differs in several important aspects. We apply our formula to the $M_{t\bar{t}}$ distribution, as well as to the double differential cross section with respect to $M_{t\bar{t}}$ and the rapidity of the $t\bar{t}$ pair. We find that the resummation effects significantly increase the cross sections near the threshold, and lead to predictions better compatible with experimental data than the fixed-order ones. We demonstrate that incorporating resummation effects in the top quark mass determination can shift the extracted value of $m_t$ by as large as 1.4 GeV. The shift is much larger than the estimated uncertainties in previous experimental studies, and leads to a value of the top quark pole mass more consistent with the current world average.

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arXiv2021

Invariant-mass distribution of top-quark pairs and top-quark mass determination

We investigate the invariant-mass distribution of top-quark pairs near the $2m_t$ threshold, which has strong impact on the determination of the top-quark mass $m_t$. We show that higher-order non-relativistic corrections lead to large contributions which are not included in the state-of-the-art theoretical predictions. We derive a factorization formula to resum such corrections to all orders in the strong-coupling, and calculate necessary ingredients to perform the resummation at next-to-leading power. We combine the resummation with fixed-order results and present phenomenologically relevant numeric results. We find that the resummation effect significantly enhances the differential cross section in the threshold region, and makes the theoretical prediction more compatible with experimental data. We estimate that using our prediction in the determination of $m_t$ will lead to a value closer to the result of direct measurement.

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arXiv2019

Resummation of soft and Coulomb corrections for $t\bar{t}h$ production at the LHC

In this paper, a combined resummation of soft and Coulomb corrections is performed for the associated production of the Higgs boson with a top quark pair at the LHC. We illustrate the similarities and critical differences between this process and the $t\bar{t}$ production process. We show that up to the next-to-leading power, the total cross section for $t\bar{t}h$ production admits a similar factorization formula in the threshold limit as that for $t\bar{t}$ production. This fact, however, is not expected to hold at higher powers. Based on the factorization formula, we perform the resummation at the improved next-to-leading logarithmic accuracy, and match to the next-to-leading order result. This allows us to give NLL$'$+NLO predictions for the total cross sections at the LHC. We find that the resummation effects enhance the NLO cross sections by about 6\%, and significantly reduce the scale dependence of the theoretical predictions.

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arXiv2016

Rare radiative decays of the $B_c$ meson

In this paper, we study the rare radiative processes $B_c\to D_{sJ} ^{(*)}γ$ within the Standard Model, where $D_{sJ}^{(*)}$ stands for the meson $D_s^*$,~$D_{s1}(2460,2536)$ or ~$D_{s2}^*(2573)$. During the investigations, we consider the contributions from the penguin, annihilation, color-suppressed and color-favored cascade diagrams. Our results show that: 1) the penguin and annihilation contributions are dominant in the branching fractions; 2) for the processes $B_c\to D_s^{*}γ$ and $B_c\to D_{s1}(2460,2536)γ$, the effects from the color-suppressed and color-favored cascade diagrams are un-negligible.

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arXiv2015

The nonleptonic charmless decays of $B_c$ meson

In this paper, with the framework of (p)NRQCD and SCET, the processes $B_c\to M_1 M_2$ are investigated. Here $M_{1(2)}$ denotes the light charmless meson, such as $π$, $ρ$, $K$ or $K^*$. Based on the SCET power counting rules, the leading transition amplitudes are picked out, which include $A_{wA}^2$, $A_{wB}^2$, $A_{wC}^2$, $A_{wD}^2$ and $A_{c}^0$. From SCET, their factorization formulae are proven. Based on the obtained factorization formulae, in particular, the numerical calculation on $A_{wB}^2$ is performed.

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arXiv2015

The Electromagnetic Decays of $B^{\pm}_c(2S)$

We calculate the electromagnetic (EM) decay widths of the $B^{\pm}_c(2S)$ meson, which is observed recently by the ATLAS Collaboration. The main EM decay channels of this particle are $1{^3S_1}γ$ and $1{P}γ$, which, in literature, are estimated to have the branching ratio of about $1/10$. In this work, we get the partial decay widths: $Γ(2{^1S_0}\rightarrow 1{^3S_1}γ)=0.192$ keV, $Γ(2{^1S_0}\rightarrow 1{P_1}γ) = 2.24$ keV and $Γ(2{^1S_0}\rightarrow 1{P_1^\prime}γ) = 11.4$ keV. In the calculation, the instantaneous approximated Bethe-Salpeter method is used. For the $P$-wave $B_c$ mesons, the wave functions are given by mixing the $^3P_1$ and $^1P_1$ states. Within the Mandelstam formalism, the decay amplitude is given, which includes the relativistic corrections.

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arXiv2015

The rare semi-leptonic $B_c$ decays involving orbitally excited final mesons

The rare processes $B_c\to D_{(s)J} ^{(*)}μ\barμ$, where $D_{(s)J}^{(*)}$ stands for the final meson $D_{s0}^*(2317)$, $D_{s1}(2460,2536)$,~$D_{s2}^*(2573)$, $D_0^*(2400)$, $D_{1}(2420,2430)$ or~$D_{2}^*(2460)$, are studied within the Standard Model. The hadronic matrix elements are evaluated in the Bethe-Salpeter approach and furthermore a discussion on the gauge-invariant condition of the annihilation hadronic currents is presented. Considering the penguin, box, annihilation, color-favored cascade and color-suppressed cascade contributions, the observables $\text{d}Br/\text{d}Q^2$, $A_{LPL}$, $A_{FB}$ and $P_L$ are calculated.

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arXiv2014

The Study of Rare $B_c\rightarrow D^{(*)}_{s,d}l\bar{l}$ Decays

In this paper, we study rare decays $B_c\rightarrow D^{(*)}_{s,d}l\bar{l}$ within the Standard Model. The penguin, box, annihilation, color-favored cascade and color-suppressed cascade contributions are included. Based on our calculation, the annihilation and color-favored cascade diagrams play important roles in the differential branching fractions, forward-backward asymmetries, longitudinal polarizations of the final vector mesons and leptonic longitudinal polarization asymmetries. More importantly, color-favored cascade decays largely enhance the resonance cascade contributions. To avoid the resonance cascade contribution pollution, new cutting regions are put forward.

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arXiv2013

Why X(3915) is so narrow as a $χ_{c0}(2P)$ state

New resonance X(3915) was identified as the charmonium $χ_{c0}(2P)$ by BABAR Collaboration, but there seems still open question of this assignment: why its full width is so narrow? To answer this question, we calculate the Okubo-Zweig-Iizuka (OZI) allowed strong decays $X(3915)\to D \bar D$, where X(3915) is assigned as a $χ_{c0}(2P)$ state, and estimate its full width in the cooperating framework of $^3/!P_0^{}$ model and the Bethe-Salpeter (BS) method using the Mandelstam Formalism, during which non-perturbative QCD effects of the hadronic matrix elements are well considered by overlapping integral over the relativistic Salpeter wave functions of the initial and finial states. We find the node structure of $χ_{c0}(2P)$ wave function resulting in the narrow width of X(3915) and show the dependence of the decay width on the variation of the initial mass of X(3915). We point out that the rate of $\frac{Γ(X(3915)\to D^+ D^-)}{Γ(X(3915)\to D^0 \bar D^0)}$ is crucial to confirm whether X(3915) is the $χ_{c0}(2P)$ state or not.

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