scholarly journals Three-loop vertex integrals at symmetric point

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Andrey Pikelner
Keyword(s):  
Renormalization Group ◽  
Differential Equations ◽  
Basis Functions ◽  
Composite Operator ◽  
Operator Matrix ◽  
Matrix Elements ◽  
Root Of Unity ◽  
Loop Level ◽  
Symmetric Point ◽  
Group Functions

Abstract This paper provides details of the massless three-loop three-point integrals calculation at the symmetric point. Our work aimed to extend known two-loop results for such integrals to the three-loop level. Obtained results can find their application in regularization-invariant symmetric point momentum-subtraction (RI/SMOM) scheme QCD calculations of renormalization group functions and various composite operator matrix elements. To calculate integrals, we solve differential equations for auxiliary integrals by transforming the system to the ε-form. Calculated integrals are expressed through the basis of functions with uniform transcendental weight. We provide expansion up to the transcendental weight six for the basis functions in terms of harmonic polylogarithms with six-root of unity argument.

scholarly journals p-adic confluence of q-difference equations

2008 ◽  
Vol 144 (4) ◽  
pp. 867-919 ◽  
Author(s):  
Andrea Pulita
Keyword(s):  
Differential Equation ◽  
Difference Equation ◽  
Differential Equations ◽  
Difference Equations ◽  
Root Of Unity

AbstractWe develop the theory of p-adic confluence of q-difference equations. The main result is the fact that, in the p-adic framework, a function is a (Taylor) solution of a differential equation if and only if it is a solution of a q-difference equation. This fact implies an equivalence, called confluence, between the category of differential equations and those of q-difference equations. We develop this theory by introducing a category of sheaves on the disk D−(1,1), for which the stalk at 1 is a differential equation, the stalk at q isa q-difference equation if q is not a root of unity, and the stalk at a root of unity ξ is a mixed object, formed by a differential equation and an action of σξ.

scholarly journals Another SMEFT story: Z′ facing new results on ε′/ε, ∆MK and K → $$ \pi \nu \overline{\nu} $$

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Jason Aebischer ◽  
Andrzej J. Buras ◽  
Jacky Kumar
Keyword(s):  
Renormalization Group ◽  
Mass Difference ◽  
Branching Ratios ◽  
New Physics ◽  
Matrix Elements ◽  
Isospin Breaking ◽  
Left Handed ◽  
The Standard Model ◽  
First Time ◽  
Group Effects

Abstract Recently the RBC-UKQCD lattice QCD collaboration presented new results for the hadronic matrix elements relevant for the ratio ε′/ε in the Standard Model (SM) albeit with significant uncertainties. With the present knowledge of the Wilson coefficients and isospin breaking effects there is still a sizable room left for new physics (NP) contributions to ε′/ε which could both enhance or suppress this ratio to agree with the data. The new SM value for the K0 − $$ {\overline{K}}^0 $$ K ¯ 0 mass difference ∆MK from RBC-UKQCD is on the other hand by 2σ above the data hinting for NP required to suppress ∆MK. Simultaneously the most recent results for K+ → $$ {\pi}^{+}\nu \overline{\nu} $$ π + ν ν ¯ from NA62 and for KL → $$ {\pi}^0\nu \overline{\nu} $$ π 0 ν ν ¯ from KOTO still allow for significant NP contributions. We point out that the suppression of ∆MK by NP requires the presence of new CP-violating phases with interesting implications for K → $$ \pi \nu \overline{\nu} $$ πν ν ¯ , KS → μ+μ− and KL → π0ℓ+ℓ− decays. Considering a Z′-scenario within the SMEFT we analyze the dependence of all these observables on the size of NP still allowed by the data on ε′/ε. The hinted ∆MK anomaly together with the εK constraint implies in the presence of only left-handed (LH) or right-handed (RH) flavour-violating Z′ couplings strict correlation between K+ → $$ {\pi}^{+}\nu \overline{\nu} $$ π + ν ν ¯ and KL → $$ {\pi}^0\nu \overline{\nu} $$ π 0 ν ν ¯ branching ratios so that they are either simultaneously enhanced or suppressed relative to SM predictions. An anticorrelation can only be obtained in the presence of both LH and RH couplings. Interestingly, the NP QCD penguin scenario for ε′/ε is excluded by SMEFT renormalization group effects in εK so that NP effects in ε′/ε are governed by electroweak penguins. We also investigate for the first time whether the presence of a heavy Z′ with flavour violating couplings could generate through top Yukawa renormalization group effects FCNCs mediated by the SM Z-boson. The outcome turns out to be very interesting.

scholarly journals Three loop massive operator matrix elements and asymptotic Wilson coefficients with two different masses

2017 ◽  
Vol 921 ◽  
pp. 585-688 ◽  
Author(s):  
J. Ablinger ◽  
J. Blümlein ◽  
A. De Freitas ◽  
A. Hasselhuhn ◽  
C. Schneider ◽  
...  
Keyword(s):  
Operator Matrix ◽  
Matrix Elements
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