Lattice QCD determination of neutron-antineutron matrix elements with physical quark masses

Abstract

Matrix elements of six-quark operators are needed to extract new physics constraints from experimental searches for neutron-antineutron oscillations. This work presents in detail the first lattice quantum chromodynamics calculations of the necessary neutron-antineutron transition matrix elements including calculation methods and discussions of systematic uncertainties. Implications of isospin and chiral symmetry on the matrix elements, power counting in the isospin limit, and renormalization of a chiral basis of six-quark operators are discussed. Calculations are performed with a chiral-symmetric discretization of the quark action and physical light quark masses in order to avoid the need for chiral extrapolation. Non-perturbative renormalization is performed, including a study of lattice cutoff effects. Excited-state effects are studied using two nucleon operators and multiple values of source-sink separation. Results for the dominant matrix elements are found to be significantly larger compared to previous results from the MIT bag model. Future calculations are needed to fully account for systematic uncertainties associated with discretization and finite-volume effects but are not expected to significantly affect this conclusion. * erinaldi@bnl.gov †

Baryon-number-violating nucleon and dinucleon decays in a model with large extra dimensions

“…The matrix elements n|O (nn) r |n have dimensions of (mass) 6 , and since they are determined by hadronic physics, one expects on general grounds that they are ∼ Λ 6 QCD , where, as above, Λ QCD ≃ 0.25 GeV. This is borne out by quantitative studies [6,7,57]. Requiring that |δm| must be less than the experimental upper bound (4.3) yields a lower bound on M BN V (denoted M X in [23]).…”

Neutron-Antineutron Oscillations from Lattice QCD

“…An extended discussion of the operators and their chiral properties is reported in Ref. [23]. There are three Standard Model (SM) gaugesinglet operators 1 that provide the dominant contributions to n-n transitions in SM EFT,…”

“…These operators transform in the same chiral irreducible representation but describe different chiral multiplet components and do not mix under renormalization [22,23]. Isospin SU (2) symmetry leads to the following relation between matrix elements…”

“…where |m, ↑ (|n, ↑ ) denote the spin-up (anti)neutron states, (τ, t) are the Euclidean time intervals from the source to the operator and the sink, respectively. The n-n ground-state matrix elements are extracted with two-state fits using optimal shrinkage [30], variable projection (VarPro) [31], and weighted averages of results for a variety of source/sink separations that are described at length in our companion paper [23]. First, G P P 2pt and G P S 2pt are fitted in order to determine E 0,1 and Z P,S 0 .…”

“…where Z RI q is the quark field renormalization and Λ JK (p) are amputated Green's functions of the lattice operators Q J and quark fields carrying momenta ±p projected onto the spin-color-flavor structure of Q K . All steps to calculate the renormalization factors numerically can be found in the companion paper [23]. We find that the matrices Λ IJ and therefore Z RI IJ are diagonal in the chiral basis (2-4) up to O(10 −3 ) [23], thanks to chiral symmetry of the lattice action we use.…”