Dimension-Six Matrix Elements from Sum Rules

2019 ◽  
pp. 125-157
Author(s):  
Matthew John Kirk
Keyword(s):  
Sum Rules ◽  
Matrix Elements

scholarly journals Light-cone sum rules for proton decay

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ulrich Haisch ◽  
Amando Hala
Keyword(s):  
Lattice Qcd ◽  
Light Cone ◽  
Sum Rules ◽  
State Of The Art ◽  
Form Factors ◽  
Baryon Number ◽  
Proton Decay ◽  
Matrix Elements ◽  
Decay Channels ◽  
Systematic Uncertainties

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.

THE CHIRAL LIMIT K → ππ MATRIX ELEMENTS OF THE ELECTROWEAK PENGUIN OPERATORS Q7,8

2003 ◽  
Vol 18 (02n06) ◽  
pp. 366-369
Author(s):  
K. MALTMAN ◽  
V. CIRIGLIANO ◽  
J. F. DONOGHUE ◽  
E. GOLOWICH
Keyword(s):  
Sum Rules ◽  
Chiral Limit ◽  
Finite Energy ◽  
Matrix Elements ◽  
Decay Data ◽  
Electroweak Penguin

The SU(3) chiral limit K → ππ matrix elements of the electroweak penguin operators, Q7,8, are determined using hadronic τ decay data, and dispersive and finite energy sum rules.

The Zeeman effect

2021 ◽  
pp. 212-226
Author(s):  
Geoffrey Brooker
Keyword(s):  
Sum Rules ◽  
Zeeman Effect ◽  
Matrix Elements ◽  
Quantum Numbers ◽  
Spectral Components ◽  
Working Out

The Zeeman effect is described, including the relative intensities of the spectral components. There are three intensity patterns: “shaded in”, “shaded out”, and a more symmetrical possibility. These patterns are helpful for diagnosis: the assignment of quantum numbers to the states involved in a transition. An example is worked in detail. In simple cases, intensity sum rules give an alternative to working out matrix elements.

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