$Apart: A generalized Mathematica Apart function

Feng, Feng

doi:10.1016/j.cpc.2012.03.025

Cited by 129 publications

(82 citation statements)

References 40 publications

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“…Therefore, for the "Virtual-Real" and "Double Real"-type diagrams, we can also utilize the packages Apart [27] and FIRE [28] to conduct partial fraction and the corresponding IBP reduction. Finally, we end up with 93 MIs for the "Double Virtual" type of diagrams, 89 MIs for the "Virtual-Real" type of diagrams, and 32 MIs for "Double Real" type of diagrams, respectively.…”

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confidence: 99%

Next-to-Next-to-Leading-Order QCD Corrections to the Hadronic Width of Pseudoscalar Quarkonium

2017

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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 2 s . As a byproduct, the renormalization group equation (RGE) of the leading NRQCD 4-fermion operator O1( 1 S0) 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 ηc hadronic width, and in particular the branching fraction of ηc → γγ. NRQCD appears to be capable of accounting for η b hadronic decay to a satisfactory degree, and our most refined prediction is Br(η b → γγ) = (4.8 ± 0.7) × 10 −5 . Heavy quarkonium decay has historically played a preeminent role in establishing asymptotic freedom of QCD [1,2]. Due to the nonrelativistic nature of heavy quark inside a quarkonium, the decay rates are traditionally expressed as the squared bound-state wave function at the origin multiplying the short-distance quarkantiquark annihilation decay rates. With the advent of the modern effective-field-theory approach, the nonrelativistic QCD (NRQCD), this factorization picture has been put on a firmer ground, and one is allowed to systematically include the QCD radiative and relativistic corrections when tackling various quarkonium decay and production processes [3].

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Next-to-Next-to-Leading-Order QCD Corrections to the Hadronic Width of Pseudoscalar Quarkonium

2017

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“…We then use FeynCalc/FormLink [26,27] to carry out the trace over Dirac/color matrices. The packages Apart [28] and FIRE [29] are utilized to conduct partial fraction together with integration-by-parts (IBP) reduction. Finally, we end up with around 80 master integrals (MI).…”

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confidence: 99%

Next-to-next-to-leading-order QCD corrections to χc0,2→γγ

et al. 2016

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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 2 s 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 BESIII measurements, especially fail to account for the measured χc2 → γγ 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 χc0 and χc2 toward the wrong direction. We also present the order-α 2 s predictions to χ b0,2 → γγ, which await the future experimental test. Charmonium decay has historically played an important role in establishing the asymptotic freedom of QCD, and served as a clean platform to probe the interplay between pertubative and nonperturbative dynamics [1,2]. Among them, the electromagnetic decay χ c0,2 → γγ provide a particularly interesting, and, rich testing ground of QCD [3,4]. In the past decades, these decay channels have been extensively studied from various theoretical angles, such as nonrelativistic potential model [5,6], relativistic quark model [7][8][9], Bethe-Salpeter approach [10], nonrelativistic QCD (NRQCD) factorization [11,12], as well as lattice QCD [13]. On the experimental side, they were previously measured by . BESIII experiment [15] has recently reported their high precision results, Γ γγ (χ c0 ) = (2.33 ± 0.20 ± 0.13 ± 0.17) keV, (1a) Γ γγ (χ c2 ) = (0.63 ± 0.04 ± 0.04 ± 0.04) keV. (1b)

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“…In our analytic calculation, we use our Mathematica package with the employment of FeynArts [37], FeynCalc [38], FIRE [39] and Apart [40]. As a cross check, we also compute the processes using the FDC package [41], except for the process (9).…”

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confidence: 99%

Is the color-octet mechanism consistent with the double $$J/\psi $$ J / ψ production measurement at B-factories?

2017

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Double J/ψ production in e + e − collisions involving color-octet channels are evaluated up to order α 2 α 3 s . Having implemented the variation of the parameters (m c , μ r and long-distance matrix elements), we found that the cross sections for producing double J/ψ at B-factories range from −0.016 to 0.245 fb, which are even much smaller than that via the color-singlet mechanism. Accordingly, this result is consistent with the measurement by the Belle and BABAR Collaborations.

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$Apart: A generalized Mathematica Apart function

Cited by 129 publications

References 40 publications

Next-to-Next-to-Leading-Order QCD Corrections to the Hadronic Width of Pseudoscalar Quarkonium

Next-to-Next-to-Leading-Order QCD Corrections to the Hadronic Width of Pseudoscalar Quarkonium

Next-to-next-to-leading-order QCD corrections to χc0,2→γγ

Is the color-octet mechanism consistent with the double $$J/\psi $$ J / ψ production measurement at B-factories?

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