Asymptotic expansions in limits of large momenta and masses

Smirnov, Vladimir A.

doi:10.1007/bf02102092

Cited by 130 publications

(100 citation statements)

References 46 publications

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“…It is not possible to give a general proof, but it seems to be a rule, that one needs the leading power as a "boundary condition". An efficient way to calculate the leading power of Feynman integrals is provided by the method of regions [17,18,19,20], whereas the subleading powers can be obtained from a differential equation. In the present section I will discuss which conditions the differential equation has to fulfil in order for this to work.…”

Section: Calculation Of Feynman Diagrams With Differential Equationsmentioning

confidence: 99%

Hard spectator interactions in at order

Pilipp

2008

Nuclear Physics B

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I compute the hard spectator interaction amplitude in B → ππ at NLO i.e. at O(α 2 s ). This special part of the amplitude, whose LO starts at O(α s ), is defined in the framework of QCD factorization. QCD factorization allows to separate the shortand the long-distance physics in leading power in an expansion in Λ QCD /m b , where the short-distance physics can be calculated in a perturbative expansion in α s .In this calculation it is necessary to obtain an expansion of Feynman integrals in powers of Λ QCD /m b . I will present a general method to obtain this expansion in a systematic way once the leading power is given as an input. This method is based on differential equation techniques and easy to implement in a computer algebra system.The numerical impact on amplitudes and branching ratios is considered. The NLO contributions of the hard spectator interactions are important but small enough for perturbation theory to be valid.

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Section: Calculation Of Feynman Diagrams With Differential Equationsmentioning

confidence: 99%

Hard spectator interactions in at order

Pilipp

2008

Nuclear Physics B

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“…The asymptotic expansion of Feynman integrals in limits typical of Euclidean space is given by well-known prescriptions as a sum over certain subgraphs [76,77,78,79,80]. …”

Section: B Expansion By Regionsmentioning

confidence: 99%

The two-loop vector form factor in the Sudakov limit

Jantzen

Smirnov

2006

Eur. Phys. J. C

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Abstract. Recently two-loop electroweak corrections to the neutral current four-fermion processes at high energies have been presented. The basic ingredient of this calculation is the evaluation of the two-loop corrections to the Abelian vector form factor in a spontaneously broken SU (2) gauge model. Whereas the final result and the derivation of the four-fermion cross sections from evolution equations have been published earlier, the calculation of the form factor from the two-loop Feynman diagrams is presented for the first time in this paper. We describe in detail the individual contributions to the form factor and their calculation with the help of the expansion by regions method and Mellin-Barnes representations.

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“…(24) and (25) contain all the terms constant or linear in quark masses in the expansion of F 2 π and F 2 K , whereas ε P denote remainders of order O(m 2 quark ). There is also a formula for F η , which can be written as:…”

Section: Role Of Lmentioning

confidence: 99%

“…The basic idea is to follow the flow of this large external momentum through the Feynman diagram, in order to Taylor expand correctly the propagators [24]. This procedure relies on the asymptotic expansion theorem [25] and can be formally expressed as:…”

Section: A3 Pseudoscalar Masses For M →mentioning

confidence: 99%

Zweig rule violation in the scalar sector and values of low-energy constants

Descotes

2001

J. High Energy Phys.

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We discuss the role of the Zweig rule (ZR) violation in the scalar channel for the determination of low-energy constants and condensates arising in the effective chiral Lagrangian of QCD. The analysis of the Goldstone boson masses and decay constants shows that the three-flavor condensate and some low-energy constants are very sensitive to the value of the ZR violating constant L 6 . A similar study is performed in the case of the decay constants. A chiral sum rule based on experimental data in the 0 ++ channel is used to constrain L 6 , indicating a significant decrease between the two-and the three-flavor condensates. The analysis of the scalar form factors of the pion at zero momentum suggests that the pseudoscalar decay constant could also be suppressed from N f = 2 to 3.

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Asymptotic expansions in limits of large momenta and masses

Cited by 130 publications

References 46 publications

Hard spectator interactions in at order

Hard spectator interactions in at order

The two-loop vector form factor in the Sudakov limit

Zweig rule violation in the scalar sector and values of low-energy constants

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