Renormalization Scale-Fixing for Complex Scattering Amplitudes

Brodsky, Stanley J.; Llanes-Estrada, Felipe J.

doi:10.2172/877458

Cited by 3 publications

(13 citation statements)

References 16 publications

(14 reference statements)

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“…( 14), (12). (Notice that the DVCS cross section is enhanced at high momentum transfer by a factor Q 2 f 2 ρ and eventually crosses over and dominates over ρ 0 production in spite of the extra α EM suppression in Compton scattering [23]). For this example we have chosen kinematics such that Q 2 /t is 2 or more as a compromise between theory and experimental uncertainties.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…This is due to the extra gluon necessary to construct the LO distribution amplitude of the emitted meson and is a striking manifestation of the J = 0 fixed pole which appears in the Compton amplitude due to the quasi-local coupling of two currents to the propagating quark. [23] Let us now turn to setting the BLM renormalization scale for meson electroproduction. We shall disregard the µ evolution of H as an irrelevant complication for our application.…”

Section: Meson Electroproductionmentioning

confidence: 99%

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Renormalization scale-fixing for complex scattering amplitudes

Brodsky

Llanes-Estrada

2006

Eur. Phys. J. C

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Abstract. We show how to fix the renormalization scale for hard-scattering exclusive processes such as deeply virtual meson electroproduction by applying the BLM prescription to the imaginary part of the scattering amplitude and employing a fixed-t dispersion relation to obtain the scale-fixed real part. In this way we resolve the ambiguity in BLM renormalization scale-setting for complex scattering amplitudes. We illustrate this by computing the H generalized parton distribution at leading twist in an analytic quark-diquark model for the parton-proton scattering amplitude which can incorporate Regge exchange contributions characteristic of the deep inelastic structure functions.PACS. 11.55.Fv Dispersion relations -11.10.Gh Renormalization 1 BLM renormalization scale setting A typical QCD amplitude for an exclusive process can be calculated as a power series in the strong coupling constantThe renormalization scale µ of the running coupling in such processes can be set systematically in QCD without ambiguity at each order in perturbation theory using the Brodsky-Lepage-Mackenzie (BLM) method [1,2,3]. The BLM scale is derived order-by-order by incorporating the non-conformal terms associated with the β function into the argument of the running coupling. This can be done systematically using the skeleton expansion [4,5]. The scale determined by the BLM method is consistent with (a) the transitivity and other properties of the renormalization group [6] (b) the renormalization group principle that relations between observables must be independent of the choice of intermediate renormalization scheme [7,8], and (c) the location of the analytic cut structure of amplitudes at each flavor threshold. The nonconformal terms involving the QCD β function are all absorbed by the scale choice. The coefficients of the perturbative series remaining after BLM-scale-setting are thus the same as those of a conformally invariant theory with β = 0. In practice, one can often simply use the flavor Send offprint requests to:dependence of the series to tag the nonconformal β dependence in perturbation theory; i.e., the BLM procedure resums the terms involving n f associated with the running of the QCD coupling.Non-Abelian gauge theory based on SU (N C ) symmetry becomes an Abelian QED-like theory in the limit N C → 0 while keeping α = C F α s and n ℓ = n eff /2C F fixed [9]. Here C F = (N 2 C − 1)/2N C . The BLM scale reduces properly to the standard QED scale in this analytic limit. For example, consider the vacuum polarization leptonloop correction to e + e − → e + e − in QED. The amplitude must be proportional to α(s) since this gives the correct cut of the forward amplitude at the lepton pair threshold s = 4m 2 ℓ . Thus the renormalization scale µ 2 R = s is exact and unambiguous in the conventional QED GoldbergerLow scheme [10]. If one chooses any other scale µ 2 R = s, the scale µ 2 R = s will be restored when one sums all bubble graphs. The BLM procedure is thus consistent with the Abelian limit and the proper cut structure of amp...

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Meson Electroproductionmentioning

confidence: 99%

Renormalization scale-fixing for complex scattering amplitudes

Brodsky

Llanes-Estrada

2006

Eur. Phys. J. C

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“…One can test the similarities of their wavefunctions and form factors in exclusive reactions such as e + e − → πT where T is a tetraquark [23]. Quark counting rules for hadron form factors and other hard exclusive amplitudes are also a property of these nonperturbative solutions [22,23]. One can thus use counting rules to identify the field content of mesons, baryons, tetraquarks, and gluonium.…”

Section: Discussionmentioning

confidence: 99%

“…For example, the asymptotic power-law falloff of the exclusive annihilation cross sections for σ (e + e − → H a +H b ) ∝ (1/s) 1+n H a +n H b , where n H is the number of valence constituent fields (the leading twist ) of a meson (n=2), baryon (n=3 ), tetraquark (n=4), gluonium (n=2,3), or pentaquark (n=5). [22,23].…”

Section: Pos(confinement2018)040mentioning

confidence: 99%

Color Confinement, Hadron Dynamics, and Hadron Spectroscopy from Light-Front Holography and Superconformal Algebra

Brodsky¹,

Téramond²,

Deur³

et al. 2019

Proceedings of XIII Quark Confinement and the Hadron Spectrum — PoS(Confinement2018)

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“…

S. Brodsky, F. J. Llanes-Estrada, and A. Szczepaniak emphasized the importance of the J = 0 fixed pole manifestation in real and (deeply) virtual Compton scattering measurements and argued that the J = 0 fixed pole is universal, i.e., independent on the photon virtualities [1]. In this paper we review the J = 0 fixed pole issue in deeply virtual Compton scattering.

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confidence: 96%

J=0fixed pole andD-term form factor in deeply virtual Compton scattering

Mueller

Semenov-Tian-Shansky

2015

Phys. Rev. D

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emphasized the importance of the J = 0 fixed pole manifestation in real and (deeply) virtual Compton scattering measurements and argued that the J = 0 fixed pole is universal, i.e., independent on the photon virtualities [1]. In this paper we review the J = 0 fixed pole issue in deeply virtual Compton scattering. We employ the dispersive approach to derive the sum rule that connects the J = 0 fixed pole contribution and the subtraction constant, called the D-term form factor for deeply virtual Compton scattering. We show that in the Bjorken limit the J = 0 fixed pole universality hypothesis is equivalent to the conjecture that the D-term form factor is given by the inverse moment sum rule for the Compton form factor. This implies that the D-term is an inherent part of corresponding generalized parton distribution (GPD). Any supplementary D-term added to a GPD results in an additional J = 0 fixed pole contribution and implies the violation of the universality hypothesis. We argue that there exists no theoretical proof for the J = 0 fixed pole universality conjecture.

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Renormalization Scale-Fixing for Complex Scattering Amplitudes

Cited by 3 publications

References 16 publications

Renormalization scale-fixing for complex scattering amplitudes

Renormalization scale-fixing for complex scattering amplitudes

Color Confinement, Hadron Dynamics, and Hadron Spectroscopy from Light-Front Holography and Superconformal Algebra

J=0fixed pole andD-term form factor in deeply virtual Compton scattering

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