The European Physical Journal A

, Volume 45, Issue 3, pp 389–399 | Cite as

Theory of unitarity bounds and low-energy form factors

  • Gauhar Abbas
  • B. Ananthanarayan
  • I. Caprini
  • I. Sentitemsu Imsong
  • S. Ramanan
Special Article - Tools for Experiment and Theory

Abstract.

We present a general formalism for deriving bounds on the shape parameters of the weak and electromagnetic form factors using as input correlators calculated from perturbative QCD, and exploiting analyticity and unitarity. The values resulting from the symmetries of QCD at low energies or from lattice calculations at special points inside the analyticity domain can be included in an exact way. We write down the general solution of the corresponding Meiman problem for an arbitrary number of interior constraints and the integral equations that allow one to include the phase of the form factor along a part of the unitarity cut. A formalism that includes the phase and some information on the modulus along a part of the cut is also given. For illustration we present constraints on the slope and curvature of the Kl3 scalar form factor and discuss our findings in some detail. The techniques are useful for checking the consistency of various inputs and for controlling the parameterizations of the form factors entering precision predictions in flavor physics.

Keywords

Form Factor Lagrange Multiplier Electromagnetic Form Factor Unitarity Bound Outer Function 

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Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Gauhar Abbas
    • 1
  • B. Ananthanarayan
    • 1
  • I. Caprini
    • 2
  • I. Sentitemsu Imsong
    • 1
  • S. Ramanan
    • 1
  1. 1.Centre for High Energy PhysicsIndian Institute of ScienceBangaloreIndia
  2. 2.National Institute of Physics and Nuclear EngineeringBucharestRomania

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