Charmed-Hadron Production in ϒ(1
                    <i>S</i>
                    ) Semi-inclusive Decay

Chen, Hai-Ting; Sang, Wen-Long; Wu, Pei Jung

doi:10.1088/0253-6102/57/4/22

Cited by 2 publications

(4 citation statements)

References 45 publications

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“…We may learn a lesson from this kind of process and the example Υ → ccgg in Refs. [20,21]. Despite a rather small NRQCD matrix element v 2 Υ , it is not always reasonable to discard the relativistic corrections from Υ, which actually have not been considered carefully in most references.…”

Section: Numerical Predictions For the Decay Ratesmentioning

confidence: 99%

“…To see the dependence on α and α s , we retain these two constants in the SDCs explicitly. From (19)(20)(21), we notice some characteristics. First, Υ → g * g * g * → η c J/ψ is the dominant channel for the SDCs and therefore also for the decay rates.…”

Section: B Numerical Predictions For the Sdcsmentioning

confidence: 99%

“…[19] indicated that the O(α s v 2 ) corrections to J/ψ → 3γ are also huge; meanwhile, the study in Refs. [20,21] indicates that the relativistic corrections to Υ → g * gg → ccgg are extraordinarily large, despite the small O(v 2 ) NRQCD matrix element for Υ. The common feature for these processes is that Υ first annihilates into three gluons (photons).…”

Section: Introductionmentioning

confidence: 99%

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Relativistic corrections toϒexclusive decay into doubleS-wave charmonia

Sang¹,

Feng²,

Chen³

2015

Phys. Rev. D

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Within the framework of nonrelativisitic QCD factorization formalism, we present the next-toleading-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 → g * g * g * → η c + J/ψ, Υ → g * g * γ * → η c + J/ψ, and Υ → γ * → η c + J/ψ. The amplitudes of these three channels are obtained accurate, and O(αα 2 s 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 that 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 process. Detailed analysis is given in the paper.

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Section: Numerical Predictions For the Decay Ratesmentioning

confidence: 99%

Section: B Numerical Predictions For the Sdcsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Relativistic corrections toϒexclusive decay into doubleS-wave charmonia

Sang¹,

Feng²,

Chen³

2015

Phys. Rev. D

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“…For the quarkonium production, typical examples are the double charmonia J/ψ + η c production at the B factories [2,3] and the double η c production through η b decay [4]. For the quarkonium annihilate decay, it happens in the J/ψ inclusive decay and J/ψ(Υ) inclusive decay into a lepton pair or charm pair [5][6][7]. It may arouse worries about the relativistic expansion in the NRQCD approach.…”

Section: Introductionmentioning

confidence: 99%

Order-v4relativistic corrections toΥinclusive decay into a charm pair

Sang

Chen

2012

Phys. Rev. D

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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 shortdistance coefficient of the order-v 4 color-singlet NRQCD matrix element is obtained through matching the decay rate of bb( 3 S[1] 1 ) → ccgg 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-leadingorder renormalization of the operator O( 3 S [8] 1 ) and the next-to-leading-order renormalization of the operators O( 3 P [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 → cc + 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. 12.38.Bx, 12.39.St, 13.20.Gd where m indicates the mass of the bottom quark b, O( 2S+1 L [c] J ) indicates the NRQCD operator with the spectroscopic state 2S+1 L [c] J with the spin S, orbital angular momentum L, total angular momentum J, and color quantum number c, and O( 2S+1 L [c] J ) H ≡ H|O( 2S+1 L [c] J )|H indicates the NRQCD matrix element averaged over the spin states of H. The color quantum number c = 1 and 8 in the NRQCD operators denote the color-singlet and the color-octet respectively. The NRQCD operators in the factorization formula (1) are1 When we were doing this work, a work about order-v 4 corrections to gluon fragmentation appeared at arXiv recently [12]. In that work, the authors applied the similar techniques to cancel IR divergences. (46)We can utilize (25) to calculate the decay rates in full QCD. First, we need to obtain H( 3 P [8] J ) defined in (26). To understand the IR structure and show the IR cancelation, here we separate H( 3 P [8] J ) into two parts: H( 3 P [8] J ) = H d ( 3 P [8] J ) + H s ( 3 P [8] J ). H d ( 3 P [8] J ) include the terms proportional to 1/(1−z), which contribute the whole IR divergences to the decay rates from the region with the real gluon being soft. H s ( 3 P [8] J ) take in charge of the remainder, which is absent of any singularity. Correspondingly, we use the subscripts d, s in both dΓ( 3 P [8] J ) and dF ( 3 P [8]J ) to denote the contributions from the two parts. The advantage of this classification will be recognized when we determine the short-distance coefficient

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Charmed-Hadron Production in ϒ(1 S ) Semi-inclusive Decay

Cited by 2 publications

References 45 publications

Relativistic corrections toϒexclusive decay into doubleS-wave charmonia

Relativistic corrections toϒexclusive decay into doubleS-wave charmonia

Order-v4relativistic corrections toΥinclusive decay into a charm pair

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