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Abstract Hadronic matrix elements involving tensor currents play an important rôle in decays that allow to probe the consistency of the Standard Model via precision lattice QCD calculations. The non-singlet tensor current is a scale-dependent (anomalous) quantity. We fully resolve its renormalisation group (RG) running in the continuum by carrying out a recursive finite-size scaling technique. In this way ambiguities due to a perturbative RG running and matching to lattice data at low energies are eliminated. We provide the total renormalisation factor at a hadronic scale of 233 MeV, which converts the bare current into its RG-invariant form. Our calculation features three flavours of O(a) improved Wilson fermions and tree-level Symanzik-improved gauge action. We employ the (massless) Schrödinger functional renormalisation scheme throughout and present the first non-perturbative determination of the Symanzik counterterm c T derived from an axial Ward identity. We elaborate on various details of our calculations, including two different renormalisation conditions.

Abstract X-space schemes are gauge-invariant, regulator-independent renormalization schemes that are defined by requiring position-space correlation functions of gauge-invariant operators to be equal to their noninteracting values at particular kinematic points. These schemes can be used to nonperturbatively renormalize composite operators in Lattice Quantum Chromodynamics (LQCD), and by computing matching coefficients between the X-space scheme and MS ¯ $$ \overline{\textrm{MS}} $$ in the dimensionally-regulated continuum, matrix elements calculated with LQCD can be converted to MS ¯ $$ \overline{\textrm{MS}} $$ -renormalized matrix elements. Using X-space schemes for Heavy Quark Effective Theory (HQET) operators has the additional benefit that appropriate ratios of position-space correlation functions cancel the power-divergent static-quark self-energy of Lattice HQET nonperturbatively. This work presents the O(α S ) matching coefficients between X-space renormalized four-quark flavor-nonsinglet HQET operators relevant for the lifetimes of charm- and bottom-hadrons, and four-quark HQET operators relevant for mixing between neutral mesons containing a heavy quark, such as B − B ¯ $$ \overline{B} $$ mixing.

Abstract We present a comprehensive investigation of leading-twist lightcone distribution amplitudes (LCDAs) and quasi distribution amplitudes (quasi-DAs) for light octet and decuplet baryons within large momentum effective theory. In LaMET, LCDAs can be factorized in terms of a hard kernel and quasi-DAs that are defined as spatial correlators and calculable on Lattice QCD. To renormalize quasi-DAs and eliminate the singular terms ln( μ 2 z i 2 $$ {\mu}^2{z}_i^2 $$ ) in them, which undermine the efficacy in perturbative expansion, we adopt a hybrid renormalization scheme that combines the self-renormalization and ratio scheme. Through self-renormalization, we eliminate UV divergences and linear divergences at large spatial separations in quasi distribution amplitudes without introducing additional nonperturbative effects. By taking a ratio with respect to the zero-momentum matrix element, we effectively remove UV divergences at small spatial separations. Under the hybrid renormalization scheme, we calculate the hard kernels up to one-loop accuracy. It turns out that only four different hard kernels are needed for all leading-twist LCDAs of octet and decuplet baryons. These results are crucial for the lattice-based exploration of the LCDAs of a light baryon from the first principle of QCD.

We present a comprehensive investigation of leading-twist lightcone distribution amplitudes (LCDAs) and quasi distribution amplitudes (quasi-DAs) for light octet and decuplet baryons within large momentum effective theory. In LaMET, LCDAs can be factorized in terms of a hard kernel and quasi-DAs that are defined as spatial correlators and calculable on Lattice QCD. To renormalize quasi-DAs and eliminate the singular terms ln( μ 2 z i 2 ) in them, which undermine the efficacy in perturbative expansion, we adopt a hybrid renormalization scheme that combines the self-renormalization and ratio scheme. Through self-renormalization, we eliminate UV divergences and linear divergences at large spatial separations in quasi distribution amplitudes without introducing additional nonperturbative effects. By taking a ratio with respect to the zero-momentum matrix element, we effectively remove UV divergences at small spatial separations. Under the hybrid renormalization scheme, we calculate the hard kernels up to one-loop accuracy. It turns out that only four different hard kernels are needed for all leading-twist LCDAs of octet and decuplet baryons. These results are crucial for the lattice-based exploration of the LCDAs of a light baryon from the first principle of QCD. [ABSTRACT FROM AUTHOR]

Hadronic matrix elements involving tensor currents play an important rôle in decays that allow to probe the consistency of the Standard Model via precision lattice QCD calculations. The non-singlet tensor current is a scale-dependent (anomalous) quantity. We fully resolve its renormalisation group (RG) running in the continuum by carrying out a recursive finite-size scaling technique. In this way ambiguities due to a perturbative RG running and matching to lattice data at low energies are eliminated. We provide the total renormalisation factor at a hadronic scale of 233 MeV, which converts the bare current into its RG-invariant form. Our calculation features three flavours of O(a) improved Wilson fermions and tree-level Symanzik-improved gauge action. We employ the (massless) Schrödinger functional renormalisation scheme throughout and present the first non-perturbative determination of the Symanzik counterterm cT derived from an axial Ward identity. We elaborate on various details of our calculations, including two different renormalisation conditions. [ABSTRACT FROM AUTHOR]

X-space schemes are gauge-invariant, regulator-independent renormalization schemes that are defined by requiring position-space correlation functions of gauge-invariant operators to be equal to their noninteracting values at particular kinematic points. These schemes can be used to nonperturbatively renormalize composite operators in Lattice Quantum Chromodynamics (LQCD), and by computing matching coefficients between the X-space scheme and MS ¯ in the dimensionally-regulated continuum, matrix elements calculated with LQCD can be converted to MS ¯ -renormalized matrix elements. Using X-space schemes for Heavy Quark Effective Theory (HQET) operators has the additional benefit that appropriate ratios of position-space correlation functions cancel the power-divergent static-quark self-energy of Lattice HQET nonperturbatively. This work presents the O(αS) matching coefficients between X-space renormalized four-quark flavor-nonsinglet HQET operators relevant for the lifetimes of charm- and bottom-hadrons, and four-quark HQET operators relevant for mixing between neutral mesons containing a heavy quark, such as B − B ¯ mixing. [ABSTRACT FROM AUTHOR]

Abstract In this work, we establish a direct connection between generative diffusion models (DMs) and stochastic quantization (SQ). The DM is realized by approximating the reversal of a stochastic process dictated by the Langevin equation, generating samples from a prior distribution to effectively mimic the target distribution. Using numerical simulations, we demonstrate that the DM can serve as a global sampler for generating quantum lattice field configurations in two-dimensional ϕ 4 theory. We demonstrate that DMs can notably reduce autocorrelation times in the Markov chain, especially in the critical region where standard Markov Chain Monte-Carlo (MCMC) algorithms experience critical slowing down. The findings can potentially inspire further advancements in lattice field theory simulations, in particular in cases where it is expensive to generate large ensembles.

In this work, we establish a direct connection between generative diffusion models (DMs) and stochastic quantization (SQ). The DM is realized by approximating the reversal of a stochastic process dictated by the Langevin equation, generating samples from a prior distribution to effectively mimic the target distribution. Using numerical simulations, we demonstrate that the DM can serve as a global sampler for generating quantum lattice field configurations in two-dimensional ϕ4 theory. We demonstrate that DMs can notably reduce autocorrelation times in the Markov chain, especially in the critical region where standard Markov Chain Monte-Carlo (MCMC) algorithms experience critical slowing down. The findings can potentially inspire further advancements in lattice field theory simulations, in particular in cases where it is expensive to generate large ensembles. [ABSTRACT FROM AUTHOR]

Abstract With Wilson quarks, on-shell O(a) improvement of the lattice QCD action is achieved by including the Sheikholeslami-Wohlert term and two further operators of mass dimension 5, which amount to a mass-dependent rescaling of the bare parameters. We here focus on the rescaled bare coupling, g ~ 0 2 = g 0 2 1 + b g a m q $$ {\tilde{g}}_0^2={g}_0^2\left(1+{b}_{\textrm{g}}a{m}_{\textrm{q}}\right) $$ , and the determination of b g g 0 2 $$ {b}_{\textrm{g}}\left({g}_0^2\right) $$ which is currently only known to 1-loop order of perturbation theory. We derive suitable improvement conditions in the chiral limit and in a finite space-time volume and evaluate these for different gluonic observables, both with and without the gradient flow. The choice of β-values and the line of constant physics are motivated by the ALPHA collaboration’s decoupling strategy to determine α s (m Z ) [1]. However, the improvement conditions and some insight into systematic effects may prove useful in other contexts, too.

Abstract We develop a hybrid scheme to renormalize quasi distribution amplitudes of a light baryon on the lattice, which combines the self-renormalization and ratio scheme. By employing self-renormalization, the UV divergences and linear divergence at large spatial separations in quasi distribution amplitudes are removed without introducing extra nonperturbative effects, while making a ratio with respect to the zero-momentum matrix element can properly remove the UV divergences in small spatial separations. As a specific application, distribution amplitudes of the Λ baryon made of uds are investigated, and the requisite equal-time correlators, which define quasi distribution amplitudes in coordinate space, are perturbatively calculated up to the next-to-leading order in strong coupling constant α s . These perturbative equal-time correlators are used to convert lattice QCD matrix elements to the continuum space during the renormalization process. Subsequently, quasi distribution amplitudes are matched onto lightcone distribution amplitudes by integrating out hard modes and the corresponding hard kernels are derived up to next-to-leading order in α s including the hybrid counterterms. These results are valuable in the lattice-based investigation of the lightcone distribution amplitudes of a light baryon from the first principles of QCD.

We develop a hybrid scheme to renormalize quasi distribution amplitudes of a light baryon on the lattice, which combines the self-renormalization and ratio scheme. By employing self-renormalization, the UV divergences and linear divergence at large spatial separations in quasi distribution amplitudes are removed without introducing extra nonperturbative effects, while making a ratio with respect to the zero-momentum matrix element can properly remove the UV divergences in small spatial separations. As a specific application, distribution amplitudes of the Λ baryon made of uds are investigated, and the requisite equal-time correlators, which define quasi distribution amplitudes in coordinate space, are perturbatively calculated up to the next-to-leading order in strong coupling constant αs. These perturbative equal-time correlators are used to convert lattice QCD matrix elements to the continuum space during the renormalization process. Subsequently, quasi distribution amplitudes are matched onto lightcone distribution amplitudes by integrating out hard modes and the corresponding hard kernels are derived up to next-to-leading order in αs including the hybrid counterterms. These results are valuable in the lattice-based investigation of the lightcone distribution amplitudes of a light baryon from the first principles of QCD. [ABSTRACT FROM AUTHOR]

Abstract The translation of experimental limits on the neutron electric dipole moment into constraints on heavy CP-violating physics beyond the Standard Model requires knowledge about non-perturbative matrix elements of effective operators, which ideally should be computed in lattice QCD. However, this necessitates a matching calculation as an interface to the effective field theory framework, which is based on dimensional regularization and renormalization by minimal subtraction. We calculate the one-loop matching between the gradient-flow and minimal-subtraction schemes for the CP-violating four-quark operators contributing to the neutron electric dipole moment. The gradient flow is a modern regularization-independent scheme amenable to lattice computations that promises, e.g., better control over power divergences than traditional momentum-subtraction schemes. Our results extend previous work on dimension-five operators and provide a necessary ingredient for future lattice-QCD computations of the contribution of four-quark operators to the neutron electric dipole moment.

Abstract We study the “three particle coupling” Γ 11 1 ξ $$ {\Gamma}_{11}^1\left(\xi \right) $$ , in 2d Ising Field Theory in a magnetic field, as the function of the scaling parameter ξ := h/(−m)15/8, where m ∼ T c − T and h ∼ H are scaled deviation from the critical temperature and scaled external field, respectively. The “φ 3 coupling” Γ 11 1 $$ {\Gamma}_{11}^1 $$ is defined in terms of the residue of the 2 → 2 elastic scattering amplitude at its pole associated with the lightest particle itself. We limit attention to the High-Temperature domain, so that m is negative. We suggest “standard analyticity”: Γ 11 1 2 $$ {\left({\Gamma}_{11}^1\right)}^2 $$ , as the function of u := ξ 2, is analytic in the whole complex u-plane except for the branch cut from – ∞ to – u 0 ≈ – 0.03585, the latter branching point – u 0 being associated with the Yang-Lee edge singularity. Under this assumption, the values of Γ 11 1 $$ {\Gamma}_{11}^1 $$ at any complex u are expressed through the discontinuity across the branch cut. We suggest approximation for this discontinuity which accounts for singular expansion of Γ 11 1 $$ {\Gamma}_{11}^1 $$ near the Yang-Lee branching point, as well as its known asymptotic at u → +∞. The resulting dispersion relation agrees well with known exact data, and with numerics obtained via Truncated Free Fermion Space Approach. This work is part of extended project of studying the S-matrix of the Ising Field Theory in a magnetic field.

The translation of experimental limits on the neutron electric dipole moment into constraints on heavy CP-violating physics beyond the Standard Model requires knowledge about non-perturbative matrix elements of effective operators, which ideally should be computed in lattice QCD. However, this necessitates a matching calculation as an interface to the effective field theory framework, which is based on dimensional regularization and renormalization by minimal subtraction. We calculate the one-loop matching between the gradient-flow and minimal-subtraction schemes for the CP-violating four-quark operators contributing to the neutron electric dipole moment. The gradient flow is a modern regularization-independent scheme amenable to lattice computations that promises, e.g., better control over power divergences than traditional momentum-subtraction schemes. Our results extend previous work on dimension-five operators and provide a necessary ingredient for future lattice-QCD computations of the contribution of four-quark operators to the neutron electric dipole moment. [ABSTRACT FROM AUTHOR]

We study the "three particle coupling" Γ 11 1 ξ , in 2d Ising Field Theory in a magnetic field, as the function of the scaling parameter ξ := h/(−m)15/8, where m ∼ Tc − T and h ∼ H are scaled deviation from the critical temperature and scaled external field, respectively. The "φ3 coupling" Γ 11 1 is defined in terms of the residue of the 2 → 2 elastic scattering amplitude at its pole associated with the lightest particle itself. We limit attention to the High-Temperature domain, so that m is negative. We suggest "standard analyticity": Γ 11 1 2 , as the function of u := ξ2, is analytic in the whole complex u-plane except for the branch cut from – ∞ to – u0 ≈ – 0.03585, the latter branching point – u0 being associated with the Yang-Lee edge singularity. Under this assumption, the values of Γ 11 1 at any complex u are expressed through the discontinuity across the branch cut. We suggest approximation for this discontinuity which accounts for singular expansion of Γ 11 1 near the Yang-Lee branching point, as well as its known asymptotic at u → +∞. The resulting dispersion relation agrees well with known exact data, and with numerics obtained via Truncated Free Fermion Space Approach. This work is part of extended project of studying the S-matrix of the Ising Field Theory in a magnetic field. [ABSTRACT FROM AUTHOR]

We study the "three particle coupling" Γ 11 1 ξ , in 2d Ising Field Theory in a magnetic field, as the function of the scaling parameter ξ := h/(−m)15/8, where m ∼ Tc − T and h ∼ H are scaled deviation from the critical temperature and scaled external field, respectively. The "φ3 coupling" Γ 11 1 is defined in terms of the residue of the 2 → 2 elastic scattering amplitude at its pole associated with the lightest particle itself. We limit attention to the High-Temperature domain, so that m is negative. We suggest "standard analyticity": Γ 11 1 2 , as the function of u := ξ2, is analytic in the whole complex u-plane except for the branch cut from – ∞ to – u0 ≈ – 0.03585, the latter branching point – u0 being associated with the Yang-Lee edge singularity. Under this assumption, the values of Γ 11 1 at any complex u are expressed through the discontinuity across the branch cut. We suggest approximation for this discontinuity which accounts for singular expansion of Γ 11 1 near the Yang-Lee branching point, as well as its known asymptotic at u → +∞. The resulting dispersion relation agrees well with known exact data, and with numerics obtained via Truncated Free Fermion Space Approach. This work is part of extended project of studying the S-matrix of the Ising Field Theory in a magnetic field. [ABSTRACT FROM AUTHOR]

Abstract The nature of the three narrow hidden-charm pentaquark P c states, i.e., P c (4312), P c (4440) and P c (4457), is under intense discussion since their discovery from the updated analysis of the process Λ b 0 → J / ψ pK − $$ {\Lambda}_b^0\to J/\psi {pK}^{-} $$ by LHCb. In this work we extend our previous coupled-channel approach [Phys. Rev. Lett. 124, 072001 (2020)], in which the P c states are treated as Σ c ∗ D ¯ ∗ $$ {\Sigma}_c^{\left(\ast \right)}{\overline{D}}^{\left(\ast \right)} $$ molecules, by including the Λ c D ¯ ∗ $$ {\Lambda}_c{\overline{D}}^{\left(\ast \right)} $$ and η c p as explicit inelastic channels in addition to the J/ψp, as required by unitarity and heavy quark spin symmetry (HQSS), respectively. Since inelastic parameters are very badly constrained by the current data, three calculation schemes are considered: (a) scheme I with pure contact interactions between the elastic, i.e., Σ c ∗ D ¯ ∗ $$ {\Sigma}_c^{\left(\ast \right)}{\overline{D}}^{\left(\ast \right)} $$ , and inelastic channels and without the Λ c D ¯ ∗ $$ {\Lambda}_c{\overline{D}}^{\left(\ast \right)} $$ interactions, (b) scheme II, where the one-pion exchange (OPE) is added to scheme I, and (c) scheme III, where the Λ c D ¯ ∗ $$ {\Lambda}_c{\overline{D}}^{\left(\ast \right)} $$ interactions are included in addition. It is shown that to obtain cutoff independent results, OPE in the multichannel system is to be supplemented with S-wave-to-D-wave mixing contact terms. As a result, in line with our previous analysis, we demonstrate that the experimental data for the J/ψp invariant mass distribution are consistent with the interpretation of the P c (4312) and P c (4440)/P c (4457) as Λ c D ¯ $$ {\Lambda}_c\overline{D} $$ and Σ c D ¯ ∗ $$ {\Sigma}_c{\overline{D}}^{\ast } $$ hadronic molecules, respectively, and that the data show clear evidence for a new narrow state, P c (4380), identified as a Σ c ∗ D ¯ $$ {\Sigma}_c^{\ast}\overline{D} $$ molecule, which should exist as a consequence of HQSS. While two statistically equally good solutions are found in scheme I, only one of these solutions with the quantum numbers of the P c (4440) and P c (4457) being J P = 3/2 − and 1/2 − , respectively, survives the requirement of regulator independence once the OPE is included. Moreover, we predict the line shapes in the elastic and inelastic channels and demonstrate that those related to the P c (4440) and the P c (4457) in the Σ c ∗ D ¯ $$ {\Sigma}_c^{\left(\ast \right)}\overline{D} $$ and η c p mass distributions from Λ b 0 → Σ c ∗ D ¯ K − $$ {\Lambda}_b^0\to {\Sigma}_c^{\left(\ast \right)}\overline{D}{K}^{-} $$ and Λ b 0 → η c pK − $$ {\Lambda}_b^0\to {\eta}_c{pK}^{-} $$ will shed light on the quantum numbers of those states, once the data are available. We also investigate possible pentaquark signals in the Λ c D ¯ ∗ $$ {\Lambda}_c{\overline{D}}^{\left(\ast \right)} $$ final states.

Abstract We discuss composite UV completions of the Nelson-Barr(NB) solution to the strong CP problem. In our construction, the CP symmetry is broken spontaneously by the dynamics of a hidden QCD at θ = π. We focus on the minimal implementation of the NB construction, where the visible sector contains one extra pair of vector-like up/down quarks. We show that the minimal NB theory suffers from a quality problem and discuss how composite UV completions may resolve it. We present a simple calculable scheme, free of a quality problem, where dynamical CP violation in the hidden sector is mediated through a scalar portal to the visible sector, which successfully realizes the NB construction.

Abstract We define a regularization-independent momentum-subtraction scheme for the C P -odd three-gluon operator at dimension six. This operator appears in effective field theories for heavy physics beyond the Standard Model, describing the indirect effect of new sources of C P-violation at low energies. In a hadronic context, it induces permanent electric dipole moments. The hadronic matrix elements of the three-gluon operator are non-perturbative objects that should ideally be evaluated with lattice QCD. We define a non-perturbative renormalization scheme that can be implemented on the lattice and we compute the scheme transformation to MS ¯ $$ \overline{\mathrm{MS}} $$ at one loop. Our calculation can be used as an interface to future lattice-QCD calculations of the matrix elements of the three-gluon operator, in order to obtain theoretically robust constraints on physics beyond the Standard Model from measurements of the neutron electric dipole moment.

Abstract To set the stage, I discuss the β-function of the massless O(N) model in three dimensions, which can be calculated exactly in the large N limit. Then, I consider SU(N) Yang-Mills theory in 2+1 space-time dimensions. Relating the β-function to the expectation value of the action in lattice gauge theory, and the latter to the trace of the energy-momentum tensor, Is how that d ln g 2 / μ d ln μ = − 1 $$ \frac{d\ln {g}^2/\mu }{d\ln \mu }=-1 $$ for all g and all N in one particular renormalization scheme. As a consequence, I find that the Yang-Mills β-function in three dimensions must have the same sign for all finite and positive bare coupling parameters in any renormalization scheme, and all non-trivial infrared fixed points are unreachable in practice.

The nature of the three narrow hidden-charm pentaquark Pc states, i.e., Pc(4312), Pc(4440) and Pc(4457), is under intense discussion since their discovery from the updated analysis of the process Λ b 0 → J / ψ pK − by LHCb. In this work we extend our previous coupled-channel approach [Phys. Rev. Lett. 124, 072001 (2020)], in which the Pc states are treated as Σ c ∗ D ¯ ∗ molecules, by including the Λ c D ¯ ∗ and ηcp as explicit inelastic channels in addition to the J/ψp, as required by unitarity and heavy quark spin symmetry (HQSS), respectively. Since inelastic parameters are very badly constrained by the current data, three calculation schemes are considered: (a) scheme I with pure contact interactions between the elastic, i.e., Σ c ∗ D ¯ ∗ , and inelastic channels and without the Λ c D ¯ ∗ interactions, (b) scheme II, where the one-pion exchange (OPE) is added to scheme I, and (c) scheme III, where the Λ c D ¯ ∗ interactions are included in addition. It is shown that to obtain cutoff independent results, OPE in the multichannel system is to be supplemented with S-wave-to-D-wave mixing contact terms. As a result, in line with our previous analysis, we demonstrate that the experimental data for the J/ψp invariant mass distribution are consistent with the interpretation of the Pc(4312) and Pc(4440)/Pc(4457) as Λ c D ¯ and Σ c D ¯ ∗ hadronic molecules, respectively, and that the data show clear evidence for a new narrow state, Pc(4380), identified as a Σ c ∗ D ¯ molecule, which should exist as a consequence of HQSS. While two statistically equally good solutions are found in scheme I, only one of these solutions with the quantum numbers of the Pc(4440) and Pc(4457) being JP = 3/2− and 1/2−, respectively, survives the requirement of regulator independence once the OPE is included. Moreover, we predict the line shapes in the elastic and inelastic channels and demonstrate that those related to the Pc(4440) and the Pc(4457) in the Σ c ∗ D ¯ and ηcp mass distributions from Λ b 0 → Σ c ∗ D ¯ K − and Λ b 0 → η c pK − will shed light on the quantum numbers of those states, once the data are available. We also investigate possible pentaquark signals in the Λ c D ¯ ∗ final states. [ABSTRACT FROM AUTHOR]

Abstract Higgs-portal interactions of fermionic dark matter — in contrast to fermions coupled via Yukawa interactions — can have a stabilizing effect on the standard-model Higgs potential. A non-perturbative renormalization-group analysis reveals that, similar to higher-order operators in the Higgs potential itself, the fermionic portal coupling can increase the metastability scale by only about one order of magnitude. Assuming a thermal freeze-out via the Higgs-portal coupling, this regime of very weakly coupled dark matter is in conflict with relic-density constraints. Conversely, fermionic dark matter with the right relic abundance requires either a low cutoff scale of the effective field theory or a strongly interacting scalar sector. This results in a triviality problem in the scalar sector which persists at the non-perturbative level. The corresponding breakdown of the effective field theory suggests a larger dark sector to be present not too far above the dark-fermion mass-scale.

We discuss composite UV completions of the Nelson-Barr(NB) solution to the strong CP problem. In our construction, the CP symmetry is broken spontaneously by the dynamics of a hidden QCD at θ = π. We focus on the minimal implementation of the NB construction, where the visible sector contains one extra pair of vector-like up/down quarks. We show that the minimal NB theory suffers from a quality problem and discuss how composite UV completions may resolve it. We present a simple calculable scheme, free of a quality problem, where dynamical CP violation in the hidden sector is mediated through a scalar portal to the visible sector, which successfully realizes the NB construction. [ABSTRACT FROM AUTHOR]

We define a regularization-independent momentum-subtraction scheme for the C P -odd three-gluon operator at dimension six. This operator appears in effective field theories for heavy physics beyond the Standard Model, describing the indirect effect of new sources of C P-violation at low energies. In a hadronic context, it induces permanent electric dipole moments. The hadronic matrix elements of the three-gluon operator are non-perturbative objects that should ideally be evaluated with lattice QCD. We define a non-perturbative renormalization scheme that can be implemented on the lattice and we compute the scheme transformation to MS ¯ at one loop. Our calculation can be used as an interface to future lattice-QCD calculations of the matrix elements of the three-gluon operator, in order to obtain theoretically robust constraints on physics beyond the Standard Model from measurements of the neutron electric dipole moment. [ABSTRACT FROM AUTHOR]

To set the stage, I discuss the β-function of the massless O(N) model in three dimensions, which can be calculated exactly in the large N limit. Then, I consider SU(N) Yang-Mills theory in 2+1 space-time dimensions. Relating the β-function to the expectation value of the action in lattice gauge theory, and the latter to the trace of the energy-momentum tensor, Is how that d ln g 2 / μ d ln μ = − 1 for all g and all N in one particular renormalization scheme. As a consequence, I find that the Yang-Mills β-function in three dimensions must have the same sign for all finite and positive bare coupling parameters in any renormalization scheme, and all non-trivial infrared fixed points are unreachable in practice. [ABSTRACT FROM AUTHOR]

Abstract 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 n f = 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 M S ¯ $$ \overline{\mathrm{MS}} $$ , 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.

Abstract We present the results of a lattice study of the normalization constants and second moments of the light-cone distribution amplitudes of longitudinally and transversely polarized ρ mesons. The calculation is performed using two flavors of dynamical clover fermions at lattice spacings between 0.060 fm and 0.081 fm, different lattice volumes up to m π L = 6.7 and pion masses down to m π = 150 MeV. Bare lattice results are renormalized non-perturbatively using a variant of the RI′-MOM scheme and converted to the M S ¯ $$ \overline{\mathrm{MS}} $$ scheme. The necessary conversion coefficients, which are not available in the literature, are calculated. The chiral extrapolation for the relevant decay constants is worked out in detail. We obtain for the ratio of the tensor and vector coupling constants f ρ T /f ρ = 0.629(8) and the values of the second Gegenbauer moments a 2 ‖ = 0.132(27) and a 2 ⊥ = 0.101(22) at the scale μ = 2 GeV for the longitudinally and transversely polarized ρ mesons, respectively. The errors include the statistical uncertainty and estimates of the systematics arising from renormalization. Discretization errors cannot be estimated reliably and are not included. In this calculation the possibility of ρ → ππ decay at the smaller pion masses is not taken into account.

We present the results of a lattice study of the normalization constants and second moments of the light-cone distribution amplitudes of longitudinally and transversely polarized ρ mesons. The calculation is performed using two flavors of dynamical clover fermions at lattice spacings between 0.060 fm and 0.081 fm, different lattice volumes up to m L = 6.7 and pion masses down to m = 150 MeV. Bare lattice results are renormalized non-perturbatively using a variant of the RI′-MOM scheme and converted to the $$ \overline{\mathrm{MS}} $$ scheme. The necessary conversion coefficients, which are not available in the literature, are calculated. The chiral extrapolation for the relevant decay constants is worked out in detail. We obtain for the ratio of the tensor and vector coupling constants f / f = 0.629(8) and the values of the second Gegenbauer moments a = 0.132(27) and a = 0.101(22) at the scale μ = 2 GeV for the longitudinally and transversely polarized ρ mesons, respectively. The errors include the statistical uncertainty and estimates of the systematics arising from renormalization. Discretization errors cannot be estimated reliably and are not included. In this calculation the possibility of ρ → ππ decay at the smaller pion masses is not taken into account. [ABSTRACT FROM AUTHOR]

The $$s-d$$ model describes a chain of spin-1/2 electrons interacting magnetically with a two-level impurity. It was introduced to study the Kondo effect, in which the magnetic susceptibility of the impurity remains finite in the 0-temperature limit as long as the interaction of the impurity with the electrons is anti-ferromagnetic. A variant of this model was introduced by Andrei, which he proved was exactly solvable via Bethe Ansatz. A hierarchical version of Andrei's model was studied by Benfatto and the authors. In the present letter, that discussion is extended to a hierarchical version of the $$s-d$$ model. The resulting analysis is very similar to the hierarchical Andrei model, though the result is slightly simpler. [ABSTRACT FROM AUTHOR]

In this paper, a fermionic hierarchical model is defined, inspired by the Kondo model, which describes a 1-dimensional lattice gas of spin-1/2 electrons interacting with a spin-1/2 impurity. This model is proved to be exactly solvable, and is shown to exhibit a Kondo effect, i.e. that, if the interaction between the impurity and the electrons is antiferromagnetic, then the magnetic susceptibility of the impurity is finite in the 0-temperature limit, whereas it diverges if the interaction is ferromagnetic. Such an effect is therefore inherently non-perturbative. This difficulty is overcome by using the exact solvability of the model, which follows both from its fermionic and hierarchical nature. [ABSTRACT FROM AUTHOR]

Abstract: 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 scheme via 4-loop continuum perturbative formulae. Our results for 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. [Copyright &y& Elsevier]

Abstract: High luminosity accelerators have greatly increased the interest in semi-exclusive and exclusive reactions involving nucleons. The relevant theoretical information is contained in the nucleon wave function and can be parametrized by moments of the nucleon distribution amplitudes, which in turn are linked to matrix elements of local three-quark operators. These can be calculated from first principles in lattice QCD. Defining an RI-MOM renormalization scheme, we renormalize three-quark operators corresponding to low moments non-perturbatively and take special care of the operator mixing. After performing a scheme matching and a conversion of the renormalization scale we quote our final results in the scheme at . [Copyright &y& Elsevier]

Abstract: We discuss kinematical enhancements of cutoff effects at short and intermediate distances. Starting from a pedagogical example with periodic boundary conditions, we switch to the case of the Schrödinger functional, where the theoretical analysis is checked by precise numerical data with dynamical -improved Wilson quarks. Finally we present an improved determination of the renormalization of the axial current in that theory. [Copyright &y& Elsevier]

Abstract: We investigate the spectrum of the free Neuberger–Dirac operator on the Schrödinger functional (SF). We check that the lowest few eigen-values of the Hermitian operator in unit of converge to the continuum limit properly. We also perform a one-loop calculation of the SF coupling, and then check the universality and investigate lattice artifacts of the step scaling function. It turns out that the lattice artifacts for the Neuberger–Dirac operator are comparable to those of the clover action. [Copyright &y& Elsevier]

We non-perturbatively calculate the scale dependence of the static axial current in the Schro¨dinger functional scheme by means of a recursive finite-size scaling technique, taking the continuum limit in each step. The bare current in the O(a) improved theory as well as in the original Wilson regularization is thus connected to the renormalization group invariant one. The latter may then be related to the current at the B-scale defined such that its matrix elements differ from the physical (QCD) ones by O(1/M). At present, a (probably small) perturbative uncertainty enters in this step. As an application, we renormalize existing unimproved data on FBbare and extrapolate to the continuum limit. We also study an interesting function h(d/L,u) derived from the Schro¨dinger functional amplitude describing the propagation of a static quark–antiquark pair. [Copyright &y& Elsevier]