Pion and kaon electromagnetic form factors

Bijnens, Johan; Talavera, P.

doi:10.1088/1126-6708/2002/03/046

Cited by 181 publications

(247 citation statements)

References 66 publications

(128 reference statements)

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“…Besides the decay constant at the chiral limit, the SU(2) formula (22) involves l r 6 as the only unknown LEC, and the same situation holds for the SU(3) case, (23), with L r 9 as the unknown LEC. Calculating the slope at the origin of the momentum transfer yields the expressions for the charge radius:…”

Section: Pion Electromagnetic Form Factor and Charge Radiusmentioning

confidence: 92%

Electromagnetic form factor of pion from N f = 2 + 1 dynamical flavor QCD

Nguyen

Ishikawa

Ukawa

et al. 2011

J. High Energ. Phys.

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We present a calculation of the electromagnetic form factor of the pion in N f = 2+1 flavor lattice QCD. Calculations are made on the PACS-CS gauge field configurations generated using Iwasaki gauge action and Wilson-clover quark action on a 32 3 × 64 lattice volume with the lattice spacing estimated as a = 0.0907(13) fm at the physical point. Measurements of the form factor are made using the technique of partially twisted boundary condition to reach small momentum transfer as well as periodic boundary condition with integer momenta.Additional improvements including random wall source techniques and a judicious choice of momenta carried by the incoming and outgoing quarks are employed for error reduction.Analyzing the form factor data for the pion mass at M π ≈ 411 MeV and 296 MeV, we find that the NNLO SU(2) chiral perturbation theory fit yields r 2 = 0.441 ± 0.046 fm 2 for the pion charge radius at the physical pion mass. Albeit the error is quite large, this is consistent with the experimental value of 0.452 ± 0.011 fm 2 . Below M π ≈ 300 MeV, we find that statistical fluctuations in the pion two-and three-point functions become too large to extract statistically meaningful averages on a 32 3 spatial volume. We carry out a sample calculation on a 64 4 lattice with the quark masses close to the physical point, which suggests that form factor calculations at the physical point become feasible by enlarging lattice sizes to M π L ≈ 4.

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Section: Pion Electromagnetic Form Factor and Charge Radiusmentioning

confidence: 92%

Electromagnetic form factor of pion from N f = 2 + 1 dynamical flavor QCD

Nguyen

Ishikawa

Ukawa

et al. 2011

J. High Energ. Phys.

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“…[41], and R and c 9 , which also depend on m π , m K and f π , are completely known once Q 2 , µ, m π , m K and f π are specified. The NLO LEC L r 9 (µ) is well known from an NNLO analysis of π and K electromagnetic form factors [42] and we take advantage of this determination in the exploratory fits to the τ -based model data below.…”

Section: Chiral Representations Of the Subtracted Polarizationmentioning

confidence: 99%

New strategy for the lattice evaluation of the leading order hadronic contribution to(g−2)μ

Golterman¹,

Maltman

Peris

2014

Phys. Rev. D

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A reliable evaluation of the integral giving the hadronic vacuum polarization contribution to the muon anomalous magnetic moment should be possible using a simple trapezoid-rule integration of lattice data for the subtracted electromagnetic current polarization function in the Euclidean momentum interval Q 2 > Q 2 min , coupled with an N -parameter Padé or other representation of the polarization in the interval 0 < Q 2 < Q 2 min , for sufficiently high Q 2 min and sufficiently large N . Using a physically motivated model for the I = 1 polarization, and the covariance matrix from a recent lattice simulation to generate associated fake "lattice data," we show that systematic errors associated with the choices of Q 2 min and N can be reduced to well below the 1% level for Q 2 min as low as 0.1 GeV 2 and rather small N . For such low Q 2 min , both an NNLO chiral representation with one additional NNNLO term and a low-order polynomial expansion employing a conformally transformed variable also provide representations sufficiently accurate to reach this precision for the low-Q 2 contribution. Combined with standard techniques for reducing other sources of error on the lattice determination, this hybrid strategy thus looks to provide a promising approach to reaching the goal of a sub-percent precision determination 2 of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment on the lattice.

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“…V. For the strong low-energy constants L i , we take as estimates the central values of the so-called O(p 4 ) fit in Refs. [60,61], and assign an uncertainty of ±0.5 · 10 −3 to each of the low-energy constants. For the electromagnetic counterterms k i and K i , we use resonance estimates obtained in N f = 2 and N f = 3 χPT [62,63].…”

Section: B Isospin Breaking In the Two-loop Phasesmentioning

confidence: 99%

Isospin breaking in the phases of the K e4 form factors

2013

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Isospin breaking in the K ℓ4 form factors induced by the difference between charged and neutral pion masses is studied. Starting from suitably subtracted dispersion representations, the form factors are constructed in an iterative way up to two loops in the low-energy expansion by implementing analyticity, crossing, and unitarity due to two-meson intermediate states. Analytical expressions for the phases of the two-loop form factors of the K ± → π + π − e ± νe channel are given, allowing one to connect the difference of form-factor phase shifts measured experimentally (out of the isospin limit) and the difference of S-and P -wave ππ phase shifts studied theoretically (in the isospin limit). The isospin-breaking correction consists of the sum of a universal part, involving only ππ rescattering, and a process-dependent contribution, involving the form factors in the coupled channels. The dependence on the two S-wave scattering lengths a 0 0 and a 2 0 in the isospin limit is worked out in a general way, in contrast to previous analyses based on one-loop chiral perturbation theory. The latter is used only to assess the subtraction constants involved in the dispersive approach. The two-loop universal and process-dependent contributions are estimated and cancel partially to yield an isospin-breaking correction close to the one-loop case. The recent results on the phases of K ± → π + π − e ± νe form factors obtained by the NA48/2 collaboration at the CERN SPS are reanalysed including this isospin-breaking correction to extract values for the scattering lengths a 0 0 and a 2 0 , as well as for low-energy constants and order parameters of two-flavour χPT.

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Pion and kaon electromagnetic form factors

Cited by 181 publications

References 66 publications

Electromagnetic form factor of pion from N f = 2 + 1 dynamical flavor QCD

Electromagnetic form factor of pion from N f = 2 + 1 dynamical flavor QCD

New strategy for the lattice evaluation of the leading order hadronic contribution to(g−2)μ

Isospin breaking in the phases of the K e4 form factors

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