Preparation of 4‐Alkyl‐and 4‐Halobenzoyl Chlorides: 4‐Pentylbenzoyl Chloride

Neubert, Mary E.; Fishel, D. L.

doi:10.1002/0471264180.os061.03

Cited by 1 publication

(3 citation statements)

References 16 publications

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“…in e + e − annihilation, one might as well stick with formula (15) for the cross section, evolve the partonic cross section down to a scale µ = m b (for details see [16]), and model the fragmentation function D b/B (x, µ = m b ) directly. At this stage, all perturbative logarithms of (1 − x) have already been extracted and absorbed into the partonic cross section.…”

Section: Phenomenological Resultsmentioning

confidence: 99%

“…In fact, these are the only large logarithms that can be extracted from the fragmentation functions in a meaningful way. In a forthcoming paper we will show that the µ-dependent terms in (12) combine with other terms in the resummed expression for the partonic cross section dσ Q /dx in such a way that the running coupling α s (µ) is converted from the (n l + 1)-flavor to the n l -flavor theory [16]. The constant pieces give rise to matching corrections, which are analogous to the matching correction creating a discontinuity in the running coupling constant at three-loop order.…”

Section: Decoupling Of Real and Virtual Heavy-quark Pairsmentioning

confidence: 99%

“…2 More transparently, it is possible to formulate a factorization theorem for the partonic cross sections using methods of effective field theory and to perform the resummation of large logarithms directly in x space, applying a novel approach developed recently in [14,15]. This will be discussed in a forthcoming paper [16]. In the x → 1 limit, the fragmentation functions are sensitive to contributions associated with three different mass scales:…”

Section: Introductionmentioning

confidence: 99%

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Factorization analysis for the fragmentation functions of hadrons containing a heavy quark

Neubert

2007

Preprint

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Using methods of effective field theory, a systematic analysis of the fragmentation functions D a/H (x, m Q , µ) of a hadron H containing a heavy quark Q is performed (with a = Q, Q, q, q, g). By integrating out pair production of virtual and real heavy quarks, the fragmentation functions are matched onto a single nonperturbative function describing the fragmentation of the heavy quark Q into the hadron H in "partially quenched" QCD. All calculable, short-distance dependence on x is extracted in this step. For x → 1, the remaining fragmentation function can be matched further onto a universal function defined in heavy-quark effective theory in order to factor off its residual dependence on the heavy-quark mass. By solving the evolution equation in the effective theory analytically, large logarithms of the ratio µ/m Q are resummed to all orders in perturbation theory. Connections with existing approaches to heavy-quark fragmentation are discussed. In particular, it is shown that previous attempts to extract ln n (1 − x) terms from the fragmentation function D Q/H (x, m Q , µ) are incompatible with a proper separation of short-and long-distance effects.

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Section: Phenomenological Resultsmentioning

confidence: 99%

Section: Decoupling Of Real and Virtual Heavy-quark Pairsmentioning

confidence: 99%