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Gauhar Abbas

Publications and source records attributed to Gauhar Abbas.

43 records · Page 3Linked to original sources
arXiv2011

Constraining the properties of K_{l3} form factors with analyticity and unitarity

Bounds on the shape parameters of K_{l3} form factors are investigated in a general model independent framework. Using the method of unitarity bounds for correlators evaluated in pQCD, chiral symmetry and experimental information on the phase and modulus of πK form factors up to an energy t_{in}=1 GeV^2, we constrain the shape parameters of the scalar and vector form factors, the value of the scalar form factor at t=M_π^2-M_K^2, and exclude regions where zeros can exist on the real energy line and in the complex energy plane.

hep-ph↗
arXiv2010

Improving the phenomenology of K_{l3} form factors with analyticity and unitarity

The shape of the vector and scalar K_{l3} form factors is investigated by exploiting analyticity and unitarity in a model-independent formalism. The method uses as input dispersion relations for certain correlators computed in perturbative QCD in the deep Euclidean region, soft-meson theorems, and experimental information on the phase and modulus of the form factors along the elastic part of the unitarity cut. We derive constraints on the coefficients of the parameterizations valid in the semileptonic range and on the truncation error. The method also predicts low-energy domains in the complex $t$-plane where zeros of the form factors are excluded. The results are useful for K_{l3} data analyses and provide theoretical underpinning for recent phenomenological dispersive representations for the form factors.

hep-ph↗
arXiv2010

Theory of unitarity bounds and low energy form factors

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 beincluded 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 K_l3 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.

hep-ph↗
arXiv2010

Stringent constraints on the scalar K pi form factor from analyticity, unitarity and low-energy theorems

We investigate the scalar K pi form factor at low energies by the method of unitarity bounds adapted so as to include information on the phase and modulus along the elastic region of the unitarity cut. Using at input the values of the form factor at t=0 and the Callan-Treiman point, we obtain stringent constraints on the slope and curvature parameters of the Taylor expansion at the origin. Also, we predict a quite narrow range for the higher order ChPT corrections at the second Callan-Treiman point.

hep-ph↗
arXiv2009

Improved bounds on the radius and curvature of the K pi scalar form factor and implications to low-energy theorems

We obtain stringent bounds in the < r^2 >_S^{K pi}-c plane where these are the scalar radius and the curvature parameters of the scalar pi K form factor respectively using analyticity and dispersion relation constraints, the knowledge of the form factor from the well-known Callan-Treiman point m_K^2-m_pi^2, as well as at m_pi^2-m_K^2 which we call the second Callan-Treiman point. The central values of these parameters from a recent determination are accomodated in the allowed region provided the higher loop corrections to the value of the form factor at the second Callan-Treiman point reduce the one-loop result by about 3% with F_K/F_pi=1.21. Such a variation in magnitude at the second Callan-Treiman point yields 0.12 fm^2 \lesssim < r^2>_S^{K pi} \lesssim 0.21 fm^2 and 0.56 GeV^{-4} \lesssim c \lesssim 1.47 GeV^{-4} and a strong correlation between them. A smaller value of F_K/F_pi shifts both bounds to lower values.

hep-ph↗
arXiv2009

New constraints on the Pion EM form factor using Pi'(-Q^2)

We study the constraints arising on the expansion parameters c and d of the Pion electromagnetic form factor from the inclusion of pure space-like data and the phase of time-like data along with one space-like datum, using as input the first derivative of the QCD polarization amplitude Pi'(-Q^2). These constraints when combined with other analyses, provide a valuable check on a determination of c due to Guo et al. and on our previous work where pionic contribution to the (g-2) of the muon was used as the input. This work further illustrates the power of analyticity techniques in form factor analysis.

hep-ph↗