Singularities in Forward Multiparticle Scattering Amplitudes and the S‐Matrix Interpretation of Higher Virial Coefficients

1971 ◽  
Vol 12 (4) ◽  
pp. 689-715 ◽  
Author(s):  
Roger Dashen ◽  
Shang‐Keng Ma
Keyword(s):  
Scattering Amplitudes ◽  
Virial Coefficients ◽  
S Matrix ◽  
Multiparticle Scattering

Interacting Hadron resonance gas model within S-matrix formalism

2019 ◽  
Vol 28 (09) ◽  
pp. 1940001 ◽  
Author(s):  
Ashutosh Dash ◽  
Subhasis Samanta
Keyword(s):  
Virial Coefficients ◽  
Heavy Ion ◽  
Phase Shifts ◽  
Matrix Formalism ◽  
Ion Collisions ◽  
S Matrix ◽  
Scattering Phase ◽  
Thermodynamic Variables ◽  
K Matrix ◽  
Dynamical Information

A noninteracting hadron resonance gas model is used often to study the hadronic phase formed in heavy ion collisions. Interaction among various hadronic constituents can be included using an S-matrix-based virial expansion approach. The virial coefficients require the dynamical information about the scattering phase shifts, which is used to compute various thermodynamic observables of an interacting hadronic gas. The attractive part of the phase shifts are calculated using K-matrix formalism while the repulsive part is obtained by fitting to experimental data. Calculation of various thermodynamic variables like pressure, energy density, specific heat capacity, etc., along with the second and higher-order correlations and fluctuations of conserved charges are done, first with only attraction and then with both attraction and repulsion included. Comparison of S-matrix results indicate a better agreement with lattice QCD data than the ideal HRG model across all thermodynamic variables.

scholarly journals ANALYTICITY AND THE Nc COUNTING RULE OF S MATRIX POLES

2007 ◽  
Vol 22 (01) ◽  
pp. 55-63 ◽  
Author(s):  
Z. G. XIAO ◽  
H. Q. ZHENG
Keyword(s):  
Scattering Amplitudes ◽  
Pole Position ◽  
Counting Rule ◽  
Large N ◽  
S Matrix

By studying ππ scattering amplitudes in the large-N c limit, we clarify the N c dependence of the S matrix pole position. It is demonstrated that analyticity and the N c counting rule exclude the existence of S-matrix poles with [Formula: see text]. Especially the properties of σ and f0(980) with respect to the 1/N c expansion are discussed. We point out that in general tetra-quark resonances do not exist.

scholarly journals On an exponential representation of the gravitational S-matrix

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Poul H. Damgaard ◽  
Ludovic Planté ◽  
Pierre Vanhove
Keyword(s):  
Scattering Amplitudes ◽  
Classical Limit ◽  
Body Problem ◽  
Radiation Reaction ◽  
Einstein Gravity ◽  
Isotropic Coordinates ◽  
Two Body Problem ◽  
Maximal Supergravity ◽  
S Matrix ◽  
Gravitational Scattering

Abstract An exponential representation of the S-matrix provides a natural framework for understanding the semi-classical limit of scattering amplitudes. While sharing some similarities with the eikonal formalism it differs from it in details. Computationally, rules are simple because pieces that must be subtracted are given by combinations of unitarity cuts. Analyzing classical gravitational scattering to third Post-Minkowskian order in both maximal supergravity and Einstein gravity we find agreement with other approaches, including the contributions from radiation reaction terms. The kinematical relation for the two-body problem in isotropic coordinates follows immediately from this procedure, again with the inclusion of radiation reaction pieces up to third Post-Minkowskian order.

EVALUATION OF ELASTIC NΔ SCATTERING AMPLITUDE FROM INELASTIC pp→NΔ AMPLITUDE

1990 ◽  
Vol 05 (03) ◽  
pp. 207-214 ◽  
Author(s):  
N. HIROSHIGE ◽  
M. KAWASAKI ◽  
W. WATARI ◽  
M. YONEZAWA
Keyword(s):  
Matrix Element ◽  
Scattering Amplitudes ◽  
Partial Wave ◽  
Energy Region ◽  
Scattering Amplitude ◽  
Transition Amplitude ◽  
Channel Approximation ◽  
S Matrix

In the dibaryon energy region we have evaluated the NΔ→NΔ (5S2) partial-wave S-matrix element from recently obtained pp→NΔ transition amplitude by combining with the information on pp→pp, pp→πd, and πd→πd scattering amplitudes in the three-channel approximation. One of the two solutions allowed by the unitarity shows an anticlockwise rotating behavior.

Scattering processes

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Scattering Amplitudes ◽  
Cross Sections ◽  
Decay Rates ◽  
Optical Theorem ◽  
Green Functions ◽  
Matrix Elements ◽  
Reduction Formula ◽  
S Matrix ◽  
Feynman Amplitudes

The unitarity of the S-matrix is used to derive the optical theorem. The connection between Green functions and scattering amplitudes given by the LSZ reduction formula is derived. The trace and the helicity method are developed and applied to the calculation of QED processes. The emission of soft photons and gravitons is discussed. In an appendix, the connection between S-matrix elements, Feynman amplitudes and decay rates or cross-sections is derived.

scholarly journals Spinning S-matrix bootstrap in 4d

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Aditya Hebbar ◽  
Denis Karateev ◽  
João Penedones
Keyword(s):  
Scattering Amplitudes ◽  
Scattering Amplitude ◽  
Bootstrap Method ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Yukawa Couplings ◽  
S Matrix ◽  
Mandelstam Analyticity

Abstract We review unitarity and crossing constraints on scattering amplitudes for particles with spin in four dimensional quantum field theories. As an application we study two to two scattering of neutral spin 1/2 fermions in detail. Assuming Mandelstam analyticity of its scattering amplitude, we use the numerical S-matrix bootstrap method to estimate various non-perturbative bounds on quartic and cubic (Yukawa) couplings.

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