RI-MOM Scheme Research Articles

Kaon mixing beyond the standard model with physical masses

We present nonperturbative results for beyond the standard model kaon mixing matrix elements in the isospin symmetric limit (mu=md) of QCD, including a complete estimate of all dominant sources of systematic error. Our results are obtained from numerical simulations of lattice QCD with Nf=2+1 flavors of dynamical domain wall fermions. For the first time, these quantities are simulated directly at the physical pion mass mπ∼139 MeV for two different lattice spacings. We include data at three lattice spacings in the range a=0.11–0.07 fm and with pion masses ranging from the physical value up to 450 MeV. Compared to our earlier work, we have added both direct calculations at physical quark masses and a third lattice spacing making the removal of discretization effects significantly more precise and eliminating the need for any significant mass extrapolation beyond the range of simulated data. We renormalize the lattice operators nonperturbatively using RI-SMOM off-shell schemes. These schemes eliminate the need to model and subtract nonperturbative pion poles that arises in the RI-MOM scheme and, since the calculations are performed with domain wall fermions, the unphysical mixing between chirality sectors is suppressed. Our results for the bag parameters in the MS¯ scheme at 3 GeV are BK≡B1=0.5240(17)(54), B2=0.4794(25)(35), B3=0.746(13)(17), B4=0.897(02)(10) and B5=0.6882(78)(94), where the first error is from lattice uncertainties and the second is the uncertainty due to the perturbative matching to MS¯. Published by the American Physical Society 2024

Valence parton distribution function of pion from fine lattice

We present a lattice QCD study of valence parton distribution inside the pion within the framework of Large Momentum Effective Theory. We use a mixed action approach with 1-HYP smeared valence Wilson clover quarks on 2+1 flavor HISQ sea with the valence quark mass tuned to 300 MeV pion mass. We use $48^3 \times 64$ lattice at a fine lattice spacing $a=0.06$ fm for this computation. We renormalize the quasi-PDF matrix element in the non-perturbative RI-MOM scheme. As a byproduct, we test the validity of 1-loop matching procedure by comparing the RI-MOM renormalized quasi-PDF matrix element with off-shell quark external states as computed in the continuum 1-loop perturbation theory with the lattice results at $a=0.04$ and 0.06 fm. By applying the RI-MOM to ${\bar{\rm MS}}$ one-loop matching, implemented through a fit to phenomenologically motivated PDFs, we obtain the valence PDF of pion.

Neutral kaon mixing beyond the Standard Model with nf = 2 + 1 chiral fermions. Part 2: non perturbative renormalisation of the \u0394F = 2 four-quark operators

We compute the renormalisation factors (Z-matrices) of the ΔF = 2 four-quark operators needed for Beyond the Standard Model (BSM) kaon mixing. We work with nf = 2+1 flavours of Domain-Wall fermions whose chiral-flavour properties are essential to maintain a continuum-like mixing pattern. We introduce new RI-SMOM renormalisation schemes, which we argue are better behaved compared to the commonly-used corresponding RI-MOM one. We find that, once converted to overline{mathrm{MS}} , the Z-factors computed through these RI-SMOM schemes are in good agreement but differ significantly from the ones computed through the RI-MOM scheme. The RI-SMOM Z-factors presented here have been used to compute the BSM neutral kaon mixing matrix elements in the companion paper [1]. We argue that the renormalisation procedure is responsible for the discrepancies observed by different collaborations, we will investigate and elucidate the origin of these differences throughout this work.

ΔS=2andΔC=2bag parameters in the standard model and beyond fromNf=2+1+1twisted-mass lattice QCD

We present unquenched lattice QCD results for the matrix elements of four-fermion operators relevant to the description of the neutral K and D mixing in the Standard Model and its extensions. We have employed simulations with Nf = 2 + 1 + 1 dynamical sea quarks at three values of the lattice spacings in the interval 0.06 - 0.09 fm and pseudoscalar meson masses in the range 210 - 450 MeV. Our results are extrapolated to the continuum limit and to the physical pion mass. Renormalization constants have been determined non-perturbatively in the RI-MOM scheme. In particular, for the Kaon bag-parameter, which is relevant for the \overline{K}^0-K^0 mixing in the Standard Model, we obtain B_K^{RGI} = 0.717(24).

Nonperturbative renormalization of overlap quark bilinears on2+1-flavor domain wall fermion configurations

We present renormalization constants of overlap quark bilinear operators on $2+1$-flavor domain wall fermion configurations. This setup is being used by the $\ensuremath{\chi}\mathrm{QCD}$ Collaboration in calculations of physical quantities such as strangeness in the nucleon and the strange and charm quark masses. The scale-independent renormalization constant for the axial-vector current is computed using the Ward identity. The renormalization constants for scalar, pseudoscalar, and vector currents are calculated in the RI-MOM scheme. Results in the $\overline{\mathrm{MS}}$ scheme are also given. The step scaling function of quark masses in the RI-MOM scheme is computed as well. The analysis uses, in total, six different ensembles of three sea quarks, each on two lattices with sizes ${24}^{3}\ifmmode\times\else\texttimes\fi{}64$ and ${32}^{3}\ifmmode\times\else\texttimes\fi{}64$ at spacings $a=(1.73\text{ }\text{ }\mathrm{GeV}{)}^{\ensuremath{-}1}$ and $(2.28\text{ }\text{ }\mathrm{GeV}{)}^{\ensuremath{-}1}$, respectively.

Kaon mixing beyond the SM from Nf = 2 tmQCD and model independent constraints from the UTA

Abstract We present the first unquenched, continuum limit, lattice QCD results for the matrix elements of the operators describing neutral kaon oscillations in extensions of the Standard Model. Owing to the accuracy of our calculation on ∆S = 2 weak Hamiltonian matrix elements, we are able to provide a refined Unitarity Triangle analysis improving the bounds coming from model independent constraints on New Physics. In our nonperturbative computation we use a combination of N f = 2 maximally twisted sea quarks and Osterwalder-Seiler valence quarks in order to achieve both O(a)-improvement and continuum-like renormalization properties for the relevant four-fermion operators. The calculation of the renormalization constants has been performed non-perturbatively in the RI-MOM scheme. Based on simulations at four values of the lattice spacing and a number of quark masses we have extrapolated/interpolated our results to the continuum limit and physical light/strange quark masses.

Neutral kaon mixing beyond the standard model withnf=2+1chiral fermions

We compute the hadronic matrix elements of the four-quark operators needed for the study of ${K}^{0}\ensuremath{-}{\overline{K}}^{0}$ mixing beyond the Standard Model (SM). We use ${n}_{f}=2+1$ flavors of domain-wall fermion that exhibit good chiral-flavor symmetry. The renormalization is performed nonperturbatively through the RI-MOM scheme and our results are converted perturbatively to $\overline{\mathrm{MS}}$. The computation is performed on a single lattice spacing $a\ensuremath{\sim}0.086$ with a lightest unitary pion mass of 290 MeV. The various systematic errors, including the discretization effects, are estimated and discussed. Our results confirm a previous quenched study, where large ratios of non-SM to SM matrix elements were obtained.

Non-perturbative renormalization in coordinate space for [formula omitted] maximally twisted mass fermions with tree-level Symanzik improved gauge action

We present results of a Lattice QCD application of a coordinate space renormalization scheme for the extraction of renormalization constants for flavour non-singlet bilinear quark operators. The method consists in the analysis of the small-distance behaviour of correlation functions in Euclidean space and has several theoretical and practical advantages, in particular: it is gauge invariant, easy to implement and has relatively low computational cost. The values of renormalization constants in the X-space scheme can be converted to the MS¯ scheme via 4-loop continuum perturbative formulae. Our results for Nf=2 maximally twisted mass fermions with tree-level Symanzik improved gauge action are compared to the ones from the RI-MOM scheme and show full agreement with this method.

Precision computation of the kaon bag parameter

Indirect CP violation in K→ππ decays plays a central role in constraining the flavor structure of the Standard Model (SM) and in the search for new physics. For many years the leading uncertainty in the SM prediction of this phenomenon was the one associated with the nonperturbative strong interaction dynamics in this process. Here we present a fully controlled lattice QCD calculation of these effects, which are described by the neutral kaon mixing parameter BK. We use a two step HEX smeared clover-improved Wilson action, with four lattice spacings from a≈0.054 fm to a≈0.093 fm and pion masses at and even below the physical value. Nonperturbative renormalization is performed in the RI-MOM scheme, where we find that operator mixing induced by chiral symmetry breaking is very small. Using fully nonperturbative continuum running, we obtain our main result BKRI(3.5 GeV)=0.531(6)stat(2)sys. A perturbative 2-loop conversion yields BKMS¯-NDR(2 GeV)=0.564(6)stat(3)sys(6)PT and BˆK=0.773(8)stat(3)sys(8)PT, which is in good agreement with current results from fits to experimental data.

BK-parameter fromNf=2twisted mass lattice QCD

We present an unquenched ${N}_{f}=2$ lattice computation of the ${B}_{K}$ parameter which controls ${K}^{0}\ensuremath{-}{\overline{K}}^{0}$ oscillations. A partially quenched setup is employed with two maximally twisted dynamical (sea) light Wilson quarks, and valence quarks of both the maximally twisted and the Osterwalder-Seiler variety. Suitable combinations of these two kinds of valence quarks lead to a lattice definition of the ${B}_{K}$ parameter which is both multiplicatively renormalizable and $\mathrm{O}(a)$ improved. Employing the nonperturbative RI-MOM scheme, in the continuum limit and at the physical value of the pion mass we get ${B}_{K}^{\mathrm{RGI}}=0.729\ifmmode\pm\else\textpm\fi{}0.030$, a number well in line with the existing quenched and unquenched determinations.

Perturbative and nonperturbative renormalization in lattice QCD

We investigate the perturbative and nonperturbative renormalization of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields (quark-antiquark operators). These include operators which are relevant to the calculation of moments of hadronic structure functions. The nonperturbative computations are based on Monte Carlo simulations with two flavors of clover fermions and utilize the Rome-Southampton method also known as the RI-MOM scheme. We compare the results of this approach with various estimates from lattice perturbation theory, in particular with recent two-loop calculations.

Non-perturbative renormalization of quark bilinear operators with N f = 2 (tmQCD) Wilson fermions and the tree-level improved gauge action

We present results for the renormalization constants of bilinear quark operators obtained by using the tree-level Symanzik improved gauge action and the Nf=2 twisted mass fermion action at maximal twist, which guarantees automatic O(a)-improvement. Our results are also relevant for the corresponding standard (un-twisted) Wilson fermionic action since the two actions only differ, in the massless limit, by a chiral rotation of the quark fields. The scale-independent renormalization constants ZV, ZA and the ratio ZP/ZS have been computed using the RI-MOM approach, as well as other alternative methods. For ZA and ZP/ZS, the latter are based on both standard twisted mass and Osterwalder-Seiler fermions, while for ZV a Ward Identity has been used. The quark field renormalization constant Zq and the scale dependent renormalization constants ZS, ZP and ZT are determined in the RI-MOM scheme. Leading discretization effects of O(g^2 a^2), evaluated in one-loop perturbation theory, are explicitly subtracted from the RI-MOM estimates.

Hadron spectrum, quark masses, and decay constants from light overlap fermions on large lattices

We present results from a simulation of quenched overlap fermions with Luescher-Weisz gauge field action on lattices up to 24{sup 3}48 and for pion masses down to {approx_equal}250 MeV. Among the quantities we study are the pion, rho, and nucleon masses; the light and strange quark masses; and the pion decay constant. The renormalization of the scalar and axial vector currents is done nonperturbatively in the RI-MOM scheme. The simulations are performed at two different lattice spacings, a{approx_equal}0.1 fm and {approx_equal}0.15 fm, and on two different physical volumes, to test the scaling properties of our action and to study finite volume effects. We compare our results with the predictions of chiral perturbation theory and compute several of its low-energy constants. The pion mass is computed in sectors of fixed topology as well.

Non-perturbative renormalisation of four fermion operators and B0 − B¯0 mixing with Wilson fermions

We present new results for the renormalisation and subtraction constants for the four fermionΔ F = 2 operators, computed non-perturbatively in the RI-MOM scheme (in the Landau gauge). From our preliminary analysis of the lattice data at β = 6.45, for the B 0 − B¯ 0 mixing bag-parameter we obtain B B RGI = 1.46(7)(1).