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Hadronic Light-by-light Scattering Contribution to Muon $ g - 2 $  [PDF]
M. Hayakawa,T. Kinoshita,A. I. Sanda
Physics , 1996, DOI: 10.1103/PhysRevD.54.3137
Abstract: The hadronic light-by-light scattering contribution to muon $g-2$ is examined based on the low energy effective theories of QCD, the Nambu-Jona-Lasinio model and hidden local symmetry approach, supplemented by a general information concerning the asymptotic behavior of QCD. Our result is $- 52 \times 10^{-11}$ with an uncertainty of $\pm 18 \times 10^{-11}$, which includes our best estimate of model dependence. This is within the expected measurement uncertainty of $40\times 10^{-11}$ in the forthcoming experiment at Brookhaven National Laboratory. Our result removes one of the main theoretical obstacles in verifying the existence of the weak contribution to the muon $g-2$.
Pseudoscalar pole terms in the hadronic light-by-light scattering contribution to muon $ g - 2 $  [PDF]
M. Hayakawa,T. Kinoshita
Physics , 1997, DOI: 10.1103/PhysRevD.66.019902
Abstract: The pseudoscalar pole contribution is the dominant source of the $ {\cal O}(\alpha^3) $ hadronic light-by-light scattering effect in muon $g - 2$. We have examined this contribution taking account of the off-shell structure of the pseudoscalar-photon-photon anomaly vertex deduced from available experimental data. Our work leads to an improved estimate, $ -79.2 (15.4) \times 10^{-11}$, for the total hadronic light-by-light scattering contribution to the muon $g - 2$.
Hadronic light-by-light scattering contribution to the muon g-2 from lattice QCD : Methodology  [PDF]
Masashi Hayakawa,Thomas Blum,Taku Izubuchi,Norikazu Yamada
Physics , 2005,
Abstract: The hadronic light-by-light scattering contribution to the muon g-2 is the most troublesome component of its theoretical prediction; (1) it cannot be determined from the other measurable quantities, (2) the dimensional argument and the estimation based on hadronic models imply that the magnitude of this contribution may be comparable to the discrepancy between the standard model prediction and the experimental value. The direct approach to evaluate the hadronic light-by-light scattering contribution requires the evaluation of the correlation function of {\it four} hadronic electromagnetic currents, and the summation of it over two independent four-momenta of off-shell photons, which is far from the reach of direct lattice simulation. Here we propose an alternative method using combined (QCD + QED) lattice simulations to evaluate the hadronic light-by-light scattering contribution.
Hadronic light-by-light scattering contribution to the muon g-2: an effective field theory approach  [PDF]
M. Knecht,A. Nyffeler,M. Perrottet,E. de Rafael
Physics , 2001, DOI: 10.1103/PhysRevLett.88.071802
Abstract: The hadronic light-by-light contribution to a_{mu}, the anomalous magnetic moment of the muon, is discussed from the point of view of an effective low-energy theory. As an application, the coefficient of the leading logarithm arising from the two-loop graphs involving two anomalous vertices is computed, and found to be positive. This corresponds to a positive sign for the pion-pole contribution to the hadronic light-by-light correction to a_{mu}, and to a sizeable reduction of the discrepancy between the present experimental value of a_{mu} and its theoretical counterpart in the standard model.
Hadronic light-by-light corrections to the muon g-2: the pion-pole contribution  [PDF]
Marc Knecht,Andreas Nyffeler
Physics , 2001, DOI: 10.1103/PhysRevD.65.073034
Abstract: The correction to the muon anomalous magnetic moment from the pion-pole contribution to the hadronic light-by-light scattering is considered using a description of the pi0 - gamma* - gamma* transition form factor based on the large-Nc and short-distance properties of QCD. The resulting two-loop integrals are treated by first performing the angular integration analytically, using the method of Gegenbauer polynomials, followed by a numerical evaluation of the remaining two-dimensional integration over the moduli of the Euclidean loop momenta. The value obtained, a_{mu}(LbyL;pi0) = +5.8 (1.0) x 10^{-10}, disagrees with other recent calculations. In the case of the vector meson dominance form factor, the result obtained by following the same procedure reads a_{mu}(LbyL;pi0)_{VMD} = +5.6 x 10^{-10}, and differs only by its overall sign from the value obtained by previous authors. Inclusion of the eta and eta-prime poles gives a total value a_{mu}(LbyL;PS) = +8.3 (1.2) x 10^{-10} for the three pseudoscalar states. This result substantially reduces the difference between the experimental value of a_{mu} and its theoretical counterpart in the standard model.
Status of the Hadronic Light-by-Light Contribution to the Muon Anomalous Magnetic Moment
Bijnens, Johan;Prades, Joaquim
High Energy Physics - Phenomenology , 2007,
Abstract: We review the present status of the hadronic light-by-light contribution to muon g-2 and critically compare recent calculations.
Status of the Hadronic Light-by-Light Contribution to the Muon Anomalous Magnetic Moment  [PDF]
Johan Bijnens,Joaquim Prades
Physics , 2007,
Abstract: We review the present status of the hadronic light-by-light contribution to muon g-2 and critically compare recent calculations.
Lattice Calculation of the Connected Hadronic Light-by-Light Contribution to the Muon Anomalous Magnetic Moment  [PDF]
Luchang Jin,Thomas Blum,Norman Christ,Masashi Hayakawa,Taku Izubuchi,Christoph Lehner
Physics , 2015,
Abstract: The anomalous magnetic moment of muon, $g-2$, is a very precisely measured quantity. However, the current measurement disagrees with standard model by about 3 standard deviations. Hadronic vacuum polarization and hadronic light by light are the two types of processes that contribute most to the theoretical uncertainty. I will describe how lattice methods are well-suited to provide a first-principle's result for the hadronic light by light contribution, the various numerical strategies that are presently being used to evaluate it, our current results and the important remaining challenges which must be overcome.
Analysis of the Hadronic Light-by-Light Contributions to the Muon $g-2$  [PDF]
Johan Bijnens,Elisabetta Pallante,Joaquim Prades
Physics , 1995, DOI: 10.1016/0550-3213(96)00288-X
Abstract: We calculate the hadronic light-by-light contributions to the muon $g-2$. We use both $1/N_c$ and chiral counting to organize the calculation. Then we calculate the leading and next-to-leading order in the $1/N_c$ expansion low energy contributions using the Extended Nambu--Jona-Lasinio model as hadronic model. We do that to all orders in the external momenta and quark masses expansion. Although the hadronic light-by-light contributions to muon $g-2$ are not saturated by these low energy contributions we estimate them conservatively. A detailed analysis of the different hadronic light-by-light contributions to muon $g-2$ is done. The dominant contribution is the twice anomalous pseudoscalar exchange diagram. The final result we get is $a_\mu^{\rm light-by-light}= (-9.2\pm3.2 ) \cdot 10^{-10}$. This is between two and three times the expected experimental uncertainty at the forthcoming BNL muon $g-2$ experiment.
Hadronic Light-by-light Scattering Effect on Muon g-2  [PDF]
M. Hayakawa,T. Kinoshita,A. I. Sanda
Physics , 1995, DOI: 10.1103/PhysRevLett.75.790
Abstract: The hadronic light-by-light scattering contribution to muon $g-2$ is examined using low energy effective theories of QCD, the Nambu-Jona-Lasinio model and hidden local chiral symmetry, as guides. Our result is $- 36 \times 10^{-11}$ with an uncertainty of $\pm 16 \times 10^{-11}$, which includes our best estimate of model dependence. This is within the expected measurement uncertainty of $40\times 10^{-11}$ in the forthcoming experiment at Brookhaven National Laboratory. Our result removes one of the main theoretical obstacles in verifying the existence of the weak contribution to the muon $g-2$.
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