KRAMERS--KRONIG RELATIONS AND SUM RULES.

1972 ◽  
Author(s):  
R Kubo ◽  
M Ichimura
Keyword(s):  
1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.


2021 ◽  
Vol 103 (2) ◽  
Author(s):  
B. P. Kay ◽  
J. P. Schiffer ◽  
S. J. Freeman ◽  
T. L. Tang ◽  
B. D. Cropper ◽  
...  

2020 ◽  
Vol 2020 (3) ◽  
Author(s):  
Daniel King ◽  
Matthew Kirk ◽  
Alexander Lenz ◽  
Thomas Rauh
Keyword(s):  

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
A. de Giorgi ◽  
S. Vogl

Abstract The Kaluza-Klein (KK) decomposition of higher-dimensional gravity gives rise to a tower of KK-gravitons in the effective four-dimensional (4D) theory. Such massive spin-2 fields are known to be connected with unitarity issues and easily lead to a breakdown of the effective theory well below the naive scale of the interaction. However, the breakdown of the effective 4D theory is expected to be controlled by the parameters of the 5D theory. Working in a simplified Randall-Sundrum model we study the matrix elements for matter annihilations into massive gravitons. We find that truncating the KK-tower leads to an early breakdown of perturbative unitarity. However, by considering the full tower we obtain a set of sum rules for the couplings between the different KK-fields that restore unitarity up to the scale of the 5D theory. We prove analytically that these are fulfilled in the model under consideration and present numerical tests of their convergence. This work complements earlier studies that focused on graviton self-interactions and yields additional sum rules that are required if matter fields are incorporated into warped extra-dimensions.


2021 ◽  
Vol 1007 ◽  
pp. 122113
Author(s):  
R. Albuquerque ◽  
S. Narison ◽  
D. Rabetiarivony ◽  
G. Randriamanatrika
Keyword(s):  

2021 ◽  
Vol 104 (1) ◽  
Author(s):  
Muslem Rahimi ◽  
Marcel Wald
Keyword(s):  
B Meson ◽  

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ulrich Haisch ◽  
Amando Hala

Abstract We estimate the form factors that parametrise the hadronic matrix elements of proton-to-pion transitions with the help of light-cone sum rules. These form factors are relevant for semi-leptonic proton decay channels induced by baryon-number violating dimension-six operators, as typically studied in the context of grand unified theories. We calculate the form factors in a kinematical regime where the momentum transfer from the proton to the pion is space-like and extrapolate our final results to the regime that is relevant for proton decay. In this way, we obtain estimates for the form factors that show agreement with the state-of-the-art calculations in lattice QCD, if systematic uncertainties are taken into account. Our work is a first step towards calculating more involved proton decay channels where lattice QCD results are not available at present.


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