The vector and scalar form factors of the pion to two loops

Bijnens, Johan; Colangelo, Gilberto; Talavera, P.

doi:10.1088/1126-6708/1998/05/014

Cited by 230 publications

(501 citation statements)

References 32 publications

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“…One recovers then [8] the standard χPT Lagrangian, which leads to the following result for the VFF [35,36]:…”

Section: Low-energy Limitmentioning

confidence: 95%

“…[4,5,36,39]. The running of the O(p 6 ) coupling r V 2 (µ)/F 4 receives of course additional 2-loop contributions which are of O(1/N 2 C ).…”

Section: Low-energy Limitmentioning

confidence: 99%

“…The χPT couplings ℓ 6 and r V 2 have been phenomenologically extracted from a fit to the VFF data at low momenta. This determines [36] the scale-invariant combination…”

Section: Low-energy Limitmentioning

confidence: 99%

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Quantum Loops in the Resonance Chiral Theory: The Vector Form-Factor

Rosell

Sanz-Cillero

Pich

2004

J. High Energy Phys.

172

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We present a calculation of the Vector Form Factor at the next-to-leading order in the 1/N C expansion, within the framework of Resonance Chiral Theory. The calculation is performed in the chiral limit, and with two dynamical quark flavours. The ultraviolet behaviour of quantum loops involving virtual resonance propagators is analyzed, together with the kind of counterterms needed in the renormalization procedure. Using the lowest-order equations of motion, we show that only a few combinations of local couplings appear in the final result. The low-energy limit of our calculation reproduces the standard Chiral Perturbation Theory formula, allowing us to determine the resonance contribution to the chiral low-energy couplings, at the next-to-leading order in 1/N C , keeping a full control of their renormalization scale dependence.

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“…One recovers then [8] the standard χPT Lagrangian, which leads to the following result for the VFF [35,36]:…”

Section: Low-energy Limitmentioning

confidence: 95%

“…[4,5,36,39]. The running of the O(p 6 ) coupling r V 2 (µ)/F 4 receives of course additional 2-loop contributions which are of O(1/N 2 C ).…”

Section: Low-energy Limitmentioning

confidence: 99%

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Quantum Loops in the Resonance Chiral Theory: The Vector Form-Factor

Rosell

Sanz-Cillero

Pich

2004

J. High Energy Phys.

172

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“…At very low energies, F (s) has been studied within the χPT framework up to O(p 6 ) [2,23]. RχT and the 1/N C expansion have also been used to determine F (s) at the ρ meson peak, including appropriate resummations of subleading logarithms from two pseudo-Goldstone channels [24,25].…”

Section: The Vector Form Factor Of the Pionmentioning

confidence: 99%

“…The low-momentum expansion of F (s) is determined by χPT [2,23]. The corresponding expression in the chiral limit reads …”

Section: The Vector Form Factor Of the Pionmentioning

confidence: 99%

The vector form factor at the next-to-leading order in 1/N C : chiral couplings L9(μ) and C88(μ) − C90(μ)

Pich

Rosell

Sanz-Cillero

2011

J. High Energ. Phys.

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Using the Resonance Chiral Theory Lagrangian, we perform a calculation of the vector form factor of the pion at the next-to-leading order (NLO) in the 1/N C expansion. Imposing the correct QCD short-distance constraints, one fixes the amplitude in terms of the pion decay constant F and resonance masses. Its low momentum expansion determines then the corresponding O(p 4 ) and O(p 6 ) low-energy chiral couplings at NLO, keeping control of their renormalization scale dependence. At µ 0 = 0.77 GeV, we obtain L 9 (µ 0 ) = (7.9 ± 0.4) · 10 −3 and C 88 (µ 0 ) − C 90 (µ 0 ) = (−4.6 ± 0.4) · 10 −5 .

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Renormalization of Chiral Perturbation Theory to Order p6

2000

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The renormalization of chiral perturbation theory is carried out to next-tonext-to-leading order in the meson sector. We calculate the divergent part of the generating functional of Green functions of quark currents to O(p 6 ) for chiral SU (n), involving one-and two-loop diagrams. The renormalization group equations for the renormalized low-energy constants of O(p 6 ) are derived. We compare our results with previous two-loop calculations in chiral perturbation theory.

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The vector and scalar form factors of the pion to two loops

Cited by 230 publications

References 32 publications

Quantum Loops in the Resonance Chiral Theory: The Vector Form-Factor

Quantum Loops in the Resonance Chiral Theory: The Vector Form-Factor

The vector form factor at the next-to-leading order in 1/N C : chiral couplings L9(μ) and C88(μ) − C90(μ)

Renormalization of Chiral Perturbation Theory to Order p6

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