Dispersion relations with crossing symmetry for ππ D- and F1-wave amplitudes

2011 ◽  
Author(s):  
R. Kamiński
Keyword(s):  
Dispersion Relations ◽  
Crossing Symmetry

scholarly journals NEW DISPERSION RELATIONS IN THE DESCRIPTION OF ππ SCATTERING AMPLITUDES

2009 ◽  
Vol 24 (02n03) ◽  
pp. 402-409 ◽  
Author(s):  
R. KAMIŃSKI ◽  
R. GARCIA-MARTIN ◽  
P. GRYNKIEWICZ ◽  
J. R. PELAEZ ◽  
F. YNDURAIN
Keyword(s):  
Scattering Amplitudes ◽  
Partial Wave ◽  
Dispersion Relations ◽  
Crossing Symmetry ◽  
Stringent Test

We present a set of once subtracted dispersion relations which implement crossing symmetry conditions for the ππ scattering amplitudes below 1 GeV. We compare and discuss the results obtained for the once and twice subtracted dispersion relations, known as Roy's equations, for three ππ partial JI waves, S0, P and S2. We also show that once subtracted dispersion relations provide a stringent test of crossing and analyticity for ππ partial wave amplitudes, remarkably precise in the 400 to 1.1 GeV region, where the resulting uncertainties are significantly smaller than those coming from standard Roy's equations, given the same input.

scholarly journals Dispersion relations and exact bounds on CFT correlators

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Miguel F. Paulos
Keyword(s):  
Sum Rules ◽  
Dispersion Relations ◽  
Lower And Upper Bounds ◽  
Equivalent Formulation ◽  
Ising Spin ◽  
Crossing Symmetry ◽  
Free Fields ◽  
Exact Bounds ◽  
Regge Limit ◽  
Spin Correlator

Abstract We derive new crossing-symmetric dispersion formulae for CFT correlators restricted to the line. The formulae are equivalent to the sum rules implied by what we call master functionals, which are analytic extremal functionals which act on the crossing equation. The dispersion relations provide an equivalent formulation of the constraints of the Polyakov bootstrap and hence of crossing symmetry on the line. The built in positivity properties imply simple and exact lower and upper bounds on the values of general CFT correlators on the Euclidean section, which are saturated by generalized free fields. Besides bounds on correlators, we apply this technology to determine new universal constraints on the Regge limit of arbitrary CFTs and obtain very simple and accurate representations of the 3d Ising spin correlator.

ONCE SUBTRACTED DISPERSION RELATIONS IN DESCRIPTION OF THE ππ D- AND F-WAVE AMPLITUDES

2011 ◽  
Vol 26 (03n04) ◽  
pp. 656-657
Author(s):  
ROBERT KAMIŃSKI
Keyword(s):  
Experimental Data ◽  
Dispersion Relations ◽  
Symmetry Condition ◽  
Crossing Symmetry ◽  
F Wave

Once subtracted dispersion relations with imposed crossing symmetry condition are applied in description of the ππ D- and F-wave amplitudes. We show that these equations impose strong constraints on experimental data and model amplitudes.

scholarly journals DISPERSIVE BOUNDS ON THE SHAPE OF $\Lambda_b\to \Lambda_b l\bar{\nu}_l$ FORM FACTORS

1999 ◽  
Vol 14 (15) ◽  
pp. 2385-2395 ◽  
Author(s):  
DEBRUPA CHAKRAVERTY ◽  
TRIPTESH DE ◽  
BINAYAK DUTTA-ROY ◽  
K. S. GUPTA
Keyword(s):  
Experimental Data ◽  
Heavy Quark ◽  
Charge Radius ◽  
Form Factors ◽  
Heavy Baryon ◽  
Dispersion Relations ◽  
Effective Theory ◽  
Heavy Quark Effective Theory ◽  
Input Information ◽  
Crossing Symmetry

We derive a theoretically allowed domain for the charge radius ρ and the curvature c of the Isgur–Wise function describing the decay [Formula: see text]. Our method uses crossing symmetry, dispersion relations and analyticity in the context of the heavy quark effective theory (HQET), but is independent of the specifics of any given model. The experimentally determined values of the ϒ masses have been used as input information. The results are of interest for testing different models employed to calculate the heavy baryon form factors which are used for the extraction of |Vcb| from experimental data.

scholarly journals Scalar and tensor ππ resonances in dispersive analysis

2015 ◽  
Vol 39 ◽  
pp. 1560087 ◽  
Author(s):  
Robert Kamiński
Keyword(s):  
Experimental Data ◽  
Mathematical Proof ◽  
Precise Determination ◽  
Dispersion Relations ◽  
Interaction Parameters ◽  
Symmetry Condition ◽  
Crossing Symmetry ◽  
Text Interaction

Role of the dispersive method in analysis of the [Formula: see text] amplitudes in all important partial waves: [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] is presented. Widely discussed is the role of new (GKPY) and old (Roy) dispersion relations with imposed crossing symmetry condition. Example of a successful application of the GKPY and Roy’s equations in test of [Formula: see text] amplitudes fitted to both experimental data and dispersion relations is presented. Short and purely mathematical proof of the uniqueness and correctness of the dispersive method used to precise determination of [Formula: see text] interaction parameters is presented.

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