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Volumn 74, Issue 9, 2006, Pages

Constraints on the form factors for K→πlν and implications for |Vus|

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EID: 33751182649     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.74.096006     Document Type: Article
Times cited : (53)

References (36)
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    • By the Riemann mapping theorem, this conformal transformation is unique up to the choice of t0 and an overall phase See e.g..
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    • For heavy-quark systems the choice of in 8 14 also ensures that AF does not scale as some power of the heavy-quark mass.
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    • This value of t0 is insensitive to the precise form factor shape, e.g. whether F+ is assumed constant, or is input from experimental data. Since Ref. measures a distribution in transverse momentum, t π=mK2+mπ2-2mKmπ2+p 2, the partial rates dΓ/dt π involve a smearing over different t values. Taking this into account, the correlations remain very insensitive to the form factor shape, and are minimized in the ideal case for t0 ≈0.37t- (at Q2=2GeV2).
    • This value of t0 is insensitive to the precise form factor shape, e.g. whether F+ is assumed constant, or is input from experimental data. Since Ref. measures a distribution in transverse momentum, t π=mK2+mπ2-2mKmπ2+p 2, the partial rates dΓ/dt π involve a smearing over different t values. Taking this into account, the correlations remain very insensitive to the form factor shape, and are minimized in the ideal case for t0 ≈ 0.37t- (at Q2=2GeV2).
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    • Another commonly used parametrization, the pole model, suffers from similar difficulties. To avoid biases, this model would need to be generalized. A pedestrian, but rigorous, approach is to break apart the dispersive integral into the sum of effective poles. Although there is no analogue of the OPE here, we can establish a bound on the coefficients of the effective poles using the τ-decay data in (and a negligible perturbative contribution) to obtain (1/π)∫t+∞dt′|F+(t′)|/t′ 2.3±0.4.
    • Another commonly used parametrization, the pole model, suffers from similar difficulties. To avoid biases, this model would need to be generalized. A pedestrian, but rigorous, approach is to break apart the dispersive integral into the sum of effective poles. Although there is no analogue of the OPE here, we can establish a bound on the coefficients of the effective poles using the τ-decay data in (and a negligible perturbative contribution) to obtain (1/π)∫t+∞dt′|F+(t′)|/t′ 2.3±0.4.
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    • Semileptonic data combined with the bound 17 yields a more precise value for the slope than is obtained from combining unitarity with the Callan-Treiman point in the absence of data, cf.
    • Semileptonic data combined with the bound 17 yields a more precise value for the slope than is obtained from combining unitarity with the Callan-Treiman point in the absence of data, cf.
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    • For some recent analysis along these lines, see: PRVDAQ 0556-2821 10.1103/PhysRevD.74.074009
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