arXiv subjects

Mauro Papinutto

Publications and source records attributed to Mauro Papinutto.

At least 19 recordsLinked to original sources

arXiv2025

On the structure of the large-$N$ expansion in SU($N$) Yang-Mills theory

Recently, we have computed the short-distance asymptotics of the generating functional of Euclidean correlators of single-trace twist-$2$ operators in the large-$N$ expansion of SU($N$) Yang-Mills (YM) theory to the leading-nonplanar order. Remarkably, it has the structure of the logarithm of a functional determinant, but with the sign opposite to the one that would follow from the spin-statistics theorem for the glueballs. In order to solve this sign puzzle, we have reconsidered the proof in the literature that in the 't Hooft topological expansion of large-$N$ YM theory the leading-nonplanar contribution to the generating functional consists of the sum over punctures of $n$-punctured tori. We have discovered that for twist-$2$ operators it contains -- in addition to the $n$-punctured tori -- the normalization of tori with $1 \leq p \leq n$ pinches and $n-p$ punctures. Once the existence of the new sector is taken into account, the violation of the spin-statistics theorem disappears. Moreover, the new sector contributes trivially to the nonperturbative $S$ matrix because -- for example -- the $n$-pinched torus represents nonperturbatively a loop of $n$ glueball propagators with no external leg. This opens the way for an exact solution limited to the new sector that may be solvable thanks to the vanishing $S$ matrix.

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arXiv2025

Test of a two-level algorithm for the glueball spectrum in $SU(N_c)$ Yang-Mills theory

We present preliminary results obtained using a new code for $SU (N_c)$ Yang-Mills theory which performs a 2-level sampling of glueball correlators obtained from a suitably chosen basis of (APE) smeared and unsmeared operators. The code builds loop operators of any shape and length and classifies them according to the irreducible representations of the cubic group. We report on the performances of the algorithm and on the computation of the first low-lying glueball states choosing $N_c = 3$ as a reference to compare our results with the literature.

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arXiv2025

Generating functional of correlators of twist-$2$ operators in $\mathcal{N} = 1$ SUSY Yang-Mills theory, I

The present paper is the first installment where, extending our previous work in pure Yang-Mills (YM) theory, we compute the generating functional of correlators of collinear twist-$2$ operators that enter the components of balanced superfields -- i.e., superfields with an equal number of dotted and undotted indices in their spinor representation -- in $\mathcal{N} = 1$ SUSY SU($N$) YM theory in Minkowskian and Euclidean space-time, in the conformal limit and renormalization-group (RG) improved form, and to the leading and next-to-leading order in the large-$N$ expansion. Moreover, we compare our asymptotic RG-improved generating functional to the next-to-leading large-$N$ order with the corresponding nonperturbative object arising from the glueball/gluinoball one-loop effective action, which it should be asymptotic to at short distances because of the asymptotic freedom. Remarkably, we find that both have the structure of the logarithm of a functional superdeterminant. Hence, our large-$N$ computation sets strong ultraviolet asymptotic constraints on the nonperturbative solution of large-$N$ $\mathcal{N} = 1$ SUSY YM theory that may be a pivotal guide for the search of such a solution.

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arXiv2023

Nonperturbative running of the tensor operator for $N_\rm{f}=3$ QCD from the chirally rotated Schrödinger Functional

We study the Renormalisation Group (RG) running of the non-singlet tensor operator, for $N_\mathrm{\scriptstyle f}=3$ QCD with Wilson fermions in a mixed action setup, with standard Schrödinger Functional (SF) boundary conditions for sea quarks and chirally rotated Schrödinger Functional ($χ$SF) boundary conditions for valence quarks. Based on a recursive finite-size scaling technique we compute non-perturbatively the tensor step-scaling function for an energy range between a hadronic scale and an electroweak scale, above which perturbation theory may be safely applied. Our result is expressed as the RG-running factor $T^{\mathrm{RGI}}/[ T(μ_{\mathrm{had}})]_{\scriptstyle \rm R}$, where the numerator is the scale independent (Renormalisation Group Invariant - RGI) tensor operator and the denominator is its renormalised counterpart at a hadronic scale $μ_{\mathrm{had}} = 233(8)$~MeV in a given scheme. We determine the step-scaling function in four distinct renormalisation schemes. We also compute the renormalisation parameters of these schemes at $μ_{\mathrm{had}}$ which, combined with the RG-running factor, gives the scheme-independent quantity $Z^{\mathrm{RGI}}_{\mathrm T}(g_0^2)$ in four schemes and for a range of bare gauge couplings in which large volume hadronic matrix element simulations are performed by the CLS consortium in $N_\mathrm{\scriptstyle f}=2+1$ QCD. All four results are compatible and also agree with a recent determination based on a unitary setup for Wilson quarks with Schrödinger Functional boundary conditions~arXiv:2309.04314 . This provides a strong universality test.

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arXiv2023

UV asymptotics of $n$-point correlators of twist-$2$ operators in SU($N$) Yang-Mills theory

The generating functional $\mathcal{W}[J_{\mathcal O}]$ of Euclidean correlators of twist-$2$ operators in SU($N$) Yang-Mills theory admits the 't Hooft large-$N$ expansion: $\mathcal{W}[J_{\mathcal O}]=\mathcal{W}_{sphere}\,\,\,\,[J_{\mathcal O}]+\mathcal{W}_{torus} \,\,\,[J_{\mathcal O}]+ \cdots$. Nonperturbatively, $\mathcal{W}_{sphere} \,\,\,\,[J_{\mathcal O}]$ is a sum of tree diagrams involving glueball propagators and vertices, while $\mathcal{W}_{torus} \,\,\,[J_{\mathcal O}]$ is a sum of glueball one-loop diagrams. Moreover, it has been predicted that $\mathcal{W}_{torus } \,\,\,[J_{\mathcal O}]$ should admit the structure of the logarithm of a functional determinant summing glueball one-loop diagrams. We work out in a closed form the ultraviolet (UV) asymptotics of $\mathcal{W}_{sphere} \,\,\,\,[J_{\mathcal O},λ] \sim \mathcal{W}_{asym \, sphere} \,\,\,\,\,\,\,[J_{\mathcal O},λ]$ and $\mathcal{W}_{torus} \,\,\,[J_{\mathcal O},λ] \sim \mathcal{W}_{asym \, torus} \,\,\,\,\,\,[J_{\mathcal O},λ]$ in the coordinate representation as all the coordinates of the correlators are uniformly rescaled by a factor $λ\rightarrow 0$. Remarkably, we verify the above prediction that $\mathcal{W}_{asym \, torus} \,\,\,\,\,\,[J_{\mathcal O},λ]$ -- being asymptotic in the UV to $\mathcal{W}_{torus} \,\,\,[J_{\mathcal O}, λ]$ -- admits the structure of the logarithm of a functional determinant as well. Hence, the computation above sets strong UV asymptotic constraints on the nonperturbative solution of large-$N$ YM theory and it may be a pivotal guide for the search of such a solution.

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arXiv2022

RG-running of the tensor currents for $N_f$ =3 QCD in a $χSF$ setup

We present the preliminary results of the non-perturbative running of the flavour non-singlet tensor operator in the high-energy range $2~\rm{GeV}\lesssim μ\lesssim 128~\rm{GeV}$ in $N_f=3$ massless QCD, comparing four different definitions of the renormalisation constant. We use the configuration ensembles of arXiv:1802.05243 and arXiv:1607.06423, subject to Schrödinger functional (SF) boundary conditions, and valence quarks with chirally rotated Schrödinger functional ($χ$SF) boundary conditions. Provided that boundary counterterms have been appropriately tuned, this results in O($a$) improvement of the tensor operator, without the need of a dimension-4 Symanzik counterterm (proportional to $c_T$).

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arXiv2021

Nonperturbative running of the quark mass for $N_f=3$ QCD from the chirally rotated Schrödinger Functional

We study the Renormalisation Group (RG) running of the quark mass, for $N_f=3$ QCD with Wilson fermions in a mixed action setup, with standard Schrödinger Functional (SF) boundary conditions for sea quarks and chirally rotated Schrödinger Functional ($χ$SF) boundary conditions for valence quarks. This necessitates the tuning of the boundary factor $z_f(g_0^2)$ of the $χ$SF valence action, in order to ensure that QCD symmetries are fully recovered in the continuum. The properties of this novel setup are monitored through the ratios $Z_S/Z_P$ and $Σ_S/Σ_P$ of the renormalisation parameters and step scaling functions of the scalar and pseudoscalar densities. Where comparison is possible, our $Z_S/Z_P$ results are found to agree with previous determinations, based on a mass ratio method arXiv:1906.03445 and Ward identities arXiv:2005.01352, arXiv:2101.10969, with Schrödinger Functional boundary conditions. The behaviour of $Σ_S/Σ_P$ confirms the theoretical expectations of $χ$SF QCD, related to the restoration of the theory's symmetries in the continuum limit. From the step scaling function of the pseudoscalar density we obtain the quark mass RG-running function from hadronic to perturbative energy scales. This is fully compatible with the earlier result obtained in a similar setup for Wilson quarks with Schrödinger Functional boundary conditions arXiv:1802.05243 and provides a strong universality test for the two lattice setups.

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arXiv2021

Quark mass RG-running for $N_f$ =3 QCD in a $χSF$ setup

We compute the nonperturbative quark mass RG-running in the range $Λ_{QCD}\lessapproxμ\lessapprox M_W$ for $N_f=3$ massless QCD with a mixed action approach: sea quarks are regularised using nonperturbatively $O(a)$-improved Wilson fermions with Schrödinger functional (SF) boundary conditions, employing the configurations of 1802.05243, while valence quarks are regularised using nonperturbatively $O(a)$-improved Wilson fermions with chirally rotated Schrödinger functional boundary conditions ($χ$SF). Our result is compatible with its SF counterpart of ref.1802.05243, confirming the universality of $χ$SF and SF in the continuum limit. We also establish the optimal tuning strategy for the critical hopping parameter $κ_c$ and the $χ$SF boundary counterterm coefficient $z_{\rm f}$. We work in two energy regimes with two different definitions of the coupling: SF-coupling for 2 GeV $\lessapproxμ\lessapprox M_W$ and GF-coupling for $Λ_{QCD} \lessapproxμ\lessapprox 2 GeV$.

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arXiv2021

Renormalization $\&$ improvement of the tensor operator for $N_f=3$ QCD in a $χ$SF setup

We present preliminary results of the non-perturbative renormalization group (RG) running of the flavor non-singlet tensor operator. We employ the $χ$SF scheme for $N_f=3$ QCD using ensembles generated by the ALPHA collaboration for the computation of the quark mass running. The $χ$SF property of automatic $O(a)$ improvement prevents the $O(a)$ mixing of the correlation functions.

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arXiv2021

$n$-point correlators of twist-$2$ operators in $SU(N)$ Yang-Mills theory to the lowest perturbative order

We compute, to the lowest perturbative order in $SU(N)$ Yang-Mills theory, $n$-point correlators in the coordinate and momentum representation of the gauge-invariant twist-$2$ operators with maximal spin along the $p_+$ direction, both in Minkowskian and -- by analytic continuation -- Euclidean space-time. We also construct the corresponding generating functionals. Remarkably, they have the structure of the logarithm of a functional determinant of the identity plus a term involving the effective propagators that act on the appropriate source fields.

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arXiv2021

Operator mixing, UV asymptotics of nonplanar/planar $2$-point correlators, and nonperturbative large-$N$ expansion of QCD-like theories

We work out the interplay between lowest-order perturbative computations in the 't Hooft coupling, $g^2=g^2_{YM} N$, operator mixing, renormalization-group (RG) improved ultraviolet (UV) asymptotics of leading-order (LO) nonplanar/planar contributions to $2$-point correlators, and nonperturbative large-$N$ expansion of perturbatively massless QCD-like theories. As concrete examples, we compute to the lowest perturbative order in $SU(N)$ YM theory the ratios, $r_i$, of LO-nonplanar to planar contributions to the $2$-point correlators in the orthogonal basis in the coordinate representation of the gauge-invariant dimension-$8$ scalar operators and all the twist-$2$ operators. We demonstrate that -- if $\frac{γ_0}{β_0}$ has no LO-nonplanar contribution, with $γ_0$ and $β_0$ the one-loop coefficients of the anomalous-dimension matrix and beta function respectively -- $r_i$ actually coincides with the corresponding ratio in the large-$N$ expansion of the RG-improved UV asymptotics of the $2$-point correlators, provided that a certain canonical nonresonant diagonal renormalization scheme exists for the corresponding operators. Contrary to the aforementioned scalar operators, for the first $10^3$ twist-$2$ operators we actually verify the above conditions, and we get the universal value $r_i=-\frac{1}{N^2}$. Hence, nonperturbatively such $r_i$ must coincide with the UV asymptotics of the ratio of the glueball self-energy loop to the glueball tree contribution to the $2$-point correlators above. As a consequence, the universality of $r_i$ reflects the universality of the effective coupling in the nonperturbative large-$N$ YM theory for the twist-$2$ operators in the coordinate representation.

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arXiv2019

$χ$SF near the electroweak scale

We employ the chirally rotated Schrödinger functional ($χ$SF) to study two-point fermion bilinear correlation functions used in the determination of $Z_{A,V,S,P,T}$ on a series of well-tuned ensembles. The gauge configurations, which span renormalisation scales from 4 to 70~GeV, are generated with $N_{\rm f}=3$ massless flavors and Schrödinger Functional (SF) boundary conditions. Valence quarks are computed with $χ$SF boundary conditions. We show preliminary results on the tuning of the $χ$SF Symanzik coefficient $z_f$ and the scaling of the axial current normalization $Z_{\rm A}$. Moreover we carry out a detailed comparison with the expectations from one-loop perturbation theory. Finally we outline how automatically $\mathrm{O}(a)$-improved $B_{\rm K}$ matrix elements, including BSM contributions, can be computed in a $χ$SF renormalization scheme.

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arXiv2018

New extended interpolating fields built from three-dimensional fermions

New extended interpolating operators made of quenched three dimensional fermions are introduced in the context of lattice QCD. The mass of the 3D fermions can be tuned in a controlled way to find a better overlap of the extended operators with the states of interest. The extended operators have good renormalization properties and are easy to control when taking the continuum limit. Moreover the short distance behaviour of the two point functions built from these operators is greatly improved. A numerical comparison with point sources and Jacobi smeared sources on dynamical 2+1 flavour configurations is presented.

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arXiv2018

On the perturbative renormalisation of four-quark operators for new physics

We discuss the renormalisation properties of the full set of $ΔF=2$ operators involved in BSM processes, including the definition of RGI versions of operators that exhibit mixing under RG transformations. As a first step for a fully non-perturbative determination of the scale-dependent renormalization factors and their runnings, we introduce a family of appropriate Schrödinger Functional schemes, and study them in perturbation theory. This allows, in particular, to determine the NLO anomalous dimensions of all $ΔF=1,2$ operators in these schemes. Finally, we discuss the systematic uncertainties related to the use of NLO perturbation theory for the RG running of four-quark operators to scales in the GeV range, in both our SF schemes and standard $\overline{MS}$ and RI-MOM schemes. Large truncation effects are found for some of the operators considered.

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arXiv2018

Non-Perturbative Renormalisation and Running of BSM Four-Quark Operators in $N_f = 2$ QCD

We perform a non-perturbative study of the scale-dependent renormalisation factors of a complete set of dimension-six four-fermion operators. The renormalisation-group (RG) running is determined in the continuum limit for a specific Schrdinger Functional (SF) renormalisation scheme in the framework of lattice QCD with two dynamical flavours ( $N_f = 2$ ). The theory is regularised on a lattice with a plaquette Wilson action and $\mathcal{O}(a)$-improved Wilson fermions. For one of these operators, the computation had been performed in ref. [1]; the present work completes the study for the rest of the operator basis, on the same simulations (configuration ensembles). The related weak matrix elements arise in several operator product expansions; in $ΔF = 2$ transitions they contain the QCD long-distance effects, including contributions from beyond-Standard Model (BSM) processes. Some of these operators mix under renormalisation and their RG-running is governed by anomalous dimension matrices. In ref. [2] the RG formalism for the operator basis has been worked out in full generality and the anomalous dimension matrix has been calculated in NLO perturbation theory. Here the discussion is extended to the matrix step-scaling functions (matrix-SSFs), which are used in finite-size recursive techniques. We rely on these matrix-SSFs to obtain non-perturbative estimates of the operator anomalous dimensions for scales ranging from $\mathcal{O}(Λ_{\rm QCD})$ to $\mathcal{O}(M_W)$.

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arXiv2016

New extended interpolating operators for hadron correlation functions

New extended interpolating operators made of quenched three dimensional fermions are introduced in the context of lattice QCD. The mass of the 3D fermions can be tuned in a controlled way to find a better overlap of the extended operators with the states of interest. The extended operators have good renormalisation properties and are easy to control when taking the continuum limit. Moreover the short distance behaviour of the two point functions built from these operators is greatly improved. The operators have been numerically implemented and a comparison to point sources and Jacobi smeared sources has been performed on the new CLS configurations.

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arXiv2016

Perturbative renormalization of $ΔF = 2$ four-fermion operators with the chirally rotated Schrödinger functional

The chirally rotated Schrödinger functional ($χ$SF) renders the mechanism of automatic $O(a)$ improvement compatible with Schrödinger functional (SF) renormalization schemes. Here we define a family of renormalization schemes based on the $χ$SF for a complete basis of $ΔF = 2$ parity-odd four-fermion operators. We compute the corresponding scale-dependent renormalization constants to one-loop order in perturbation theory and obtain their NLO anomalous dimensions by matching to the $\overline{\textrm{MS}}$ scheme. Due to automatic $O(a)$ improvement, once the $χ$SF is renormalized and improved at the boundaries, the step scaling functions (SSF) of these operators approach their continuum limit with $O(a^{2})$ corrections without the need of operator improvement.

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arXiv2015

Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions

We describe a new set of gauge configurations generated within the CLS effort. These ensembles have N_f=2+1 flavors of non-perturbatively improved Wilson fermions in the sea with the Luescher-Weisz action used for the gluons. Open boundary conditions in time are used to address the problem of topological freezing at small lattice spacings and twisted-mass reweighting for improved stability of the simulations. We give the bare parameters at which the ensembles have been generated and how these parameters have been chosen. Details of the algorithmic setup and its performance are presented as well as measurements of the pion and kaon masses alongside the scale parameter t_0.

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