Three-loop calculation of the anomalous field dimension in the full four-fermionU N -symmetric model

Two-loop anomalous dimensions and one-loop renormalization scheme matching factors are calculated for six-quark operators responsible for neutron-antineutron transitions. When combined with lattice QCD determinations of the matrix elements of these operators, our results can be used to reliably predict the neutron-antineutron vacuum transition time, τnn, in terms of basic parameters of baryon-number violating beyond-the-Standard-Model theories. The operators are classified by their chiral transformation properties, and a basis in which there is no operator mixing due to strong interactions is identified. Operator projectors that are required for non-perturbative renormalization of the corresponding lattice QCD six-quark operator matrix elements are constructed. A complete calculation of δm = 1/τnn in a particular beyond-the-Standard-Model theory is presented as an example to demonstrate how operator renormalization and results from lattice QCD are combined with experimental bounds on δm to constrain the scale of new baryon-number violating physics. At the present computationally accessible lattice QCD matching scale of ∼ 2 GeV, the next-to-nextto-leading-order effects calculated in this work correct the leading-order plus next-to-leading-order δm predictions of beyond-the-Standard-Model theories by < 26%. Next-to-next-to-next-to-leadingorder effects provide additional unknown corrections to predictions of δm that are estimated to be < 7%.

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“…[67,72,74,75], and in particular many results and techniques for D-dimensional tensor reduction can be found in Refs. [83,96].…”

Section: Dirac Algebramentioning

confidence: 99%

Perturbative renormalization of neutron-antineutron operators

Buchoff¹,

Wagman

2016

Phys. Rev. D

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“…A systematic way to achieve this is to use a specific basis for all possible combinations of γ-matrices that can arise. These have been discussed at length in [32,33,34,35,36] and are defined as…”

Section: Formalismmentioning

confidence: 99%

“…This is important since we will use dimensional regularization to evaluate all the Feynman integrals. Clearly for an integer dimension the basis will truncate to a finite set but they allow one to systematically construct the projection matrix from the basis tensors P L naturally partitions spinor space due to the property, [32,33,34,35,36], tr Γ µ 1 ...µm…”

Section: Formalismmentioning

confidence: 99%

Off-shell quark bilinear operator Green’s functions at two loops

Gracey

2019

Phys. Rev. D

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“…So a trace over these indices is also included implicitly within our construction. In addition we use the generalized γ matrices of [38][39][40][41][42] denoted by Γ μ 1 …μ n ðnÞ which are defined by…”

Section: Introductionmentioning

confidence: 99%