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J. A. Gracey

Publications and source records attributed to J. A. Gracey.

At least 37 records · Page 2Linked to original sources
arXiv2022

Three loop effective potential for $\langle \frac{1}{2} { A_μ^a }^2 \rangle$ in the Landau gauge in QCD

We apply the Local Composite Operator method to construct the three loop effective potential for the dimension two operator $\frac{1}{2} { A_μ^a }^2$ in the Landau gauge in Quantum Chromodynamics. For $SU(3)$ we show that the three loop value of the effective mass of the gluon is similar to the two loop estimates when the number of massless quarks is strictly less than five for $SU(3)$.

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arXiv2022

Exploring interpolating momentum schemes

We compute the renormalisation factors of the quark mass and wave function using IMOM (Interpolating MOMenta) schemes. The framework is the Rome-Southampton non-renormalisation method, but the momentum transfer in the quark bilinears is not restricted to zero or to the symmetric point. We study the scale dependence, infrared contamination and lattice artefacts for different values of this momentum transfer and for two different kinds of projectors. For the numerical simulations, we use data generated by the RBC-UKQCD collaborations, with $N_f = 2+1$ flavours of Domain-Wall fermions, and inverse lattice spacing of $1.79 $ and $2.38$ GeV.

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arXiv2021

Five loop renormalization of the Wess-Zumino model

We renormalize the Wess-Zumino model at five loops in both the minimal subtraction (MSbar) and momentum subtraction (MOM) schemes. The calculation is carried out automatically using a routine that performs the D-algebra. Generalizations of the model to include $O(N)$ symmetry as well as the case with real and complex tensor couplings are also considered. We confirm that the emergent SU(3) symmetry of six dimensional O(N) phi^3 theory is also a property of the tensor O(N) model. With the new loop order precision we compute critical exponents in the epsilon expansion for several of these generalizations as well as the XYZ model in order to compare with conformal bootstrap estimates in three dimensions. For example at five loops our estimate for the correction to scaling exponent is in very good agreement for the Wess-Zumino model which equates to the emergent supersymmetric fixed point of the Gross-Neveu-Yukawa model. We also compute the rational number that is part of the six loop MSbar beta-function.

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arXiv2021

Five loop renormalization of $ϕ^3$ theory with applications to the Lee-Yang edge singularity and percolation theory

We apply the method of graphical functions that was recently extended to six dimensions for scalar theories, to $ϕ^3$ theory and compute the $β$ function, the wave function anomalous dimension as well as the mass anomalous dimension in the $\overline{\mbox{MS}}$ scheme to five loops. From the results we derive the corresponding renormalization group functions for the Lee-Yang edge singularity problem and percolation theory. After determining the $\varepsilon$ expansions of the respective critical exponents to $\mathcal{O}(\varepsilon^5)$ we apply recent resummation technology to obtain improved exponent estimates in 3, 4 and 5 dimensions. These compare favourably with estimates from fixed dimension numerical techniques and refine the four loop results. To assist with this comparison we collated a substantial amount of data from numerical techniques which are included in tables for each exponent.

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arXiv2021

Critical exponent $η$ at $O(1/N^3)$ in the chiral XY model using the large $N$ conformal bootstrap

We compute the $O(1/N^3)$ correction to the critical exponent $η$ in the chiral XY or chiral Gross-Neveu model in $d$-dimensions. As the leading order vertex anomalous dimension vanishes, the direct application of the large $N$ conformal bootstrap formalism is not immediately possible. To circumvent this we consider the more general Nambu-Jona-Lasinio model for a general non-abelian Lie group. Taking the abelian limit of the exponents of this model produces those of the chiral XY model. Subsequently we provide improved estimates for $η$ in the three dimensional chiral XY model for various values of $N$.

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arXiv2020

Symmetric point flavour singlet axial vector current renormalization at two loops

We calculate the two loop correction to the quark 2-point function with the non-zero momentum insertion of the flavour singlet axial vector current at the fully symmetric subtraction point for massless quarks in the modified minimal subtraction (MSbar) scheme. The Larin method is used to handle $γ^5$ within dimensional regularization at this loop order ensuring that the effect of the chiral anomaly is properly included within the construction.

hep-ph↗
arXiv2020

Theory for the FCC-ee : Report on the 11th FCC-ee Workshop

The Future Circular Collider (FCC) at CERN, a proposed 100-km circular facility with several colliders in succession, culminates with a 100 TeV proton-proton collider. It offers a vast new domain of exploration in particle physics, with orders of magnitude advances in terms of Precision, Sensitivity and Energy. The implementation plan foresees, as a first step, an Electroweak Factory electron-positron collider. This high luminosity facility, operating between 90 and 365 GeV centre-of-mass energy, will study the heavy particles of the Standard Model, Z, W, Higgs, and top with unprecedented accuracy. The Electroweak Factory $e^+e^-$ collider constitutes a real challenge to the theory and to precision calculations, triggering the need for the development of new mathematical methods and software tools. A first workshop in 2018 had focused on the first FCC-ee stage, the Tera-Z, and confronted the theoretical status of precision Standard Model calculations on the Z-boson resonance to the experimental demands. The second workshop in January 2019, which is reported here, extended the scope to the next stages, with the production of W-bosons (FCC-ee-W), the Higgs boson (FCC-ee-H) and top quarks (FCC-ee-tt). In particular, the theoretical precision in the determination of the crucial input parameters, alpha_QED, alpha_QCD, M_W, m_t at the level of FCC-ee requirements is thoroughly discussed. The requirements on Standard Model theory calculations were spelled out, so as to meet the demanding accuracy of the FCC-ee experimental potential. The discussion of innovative methods and tools for multi-loop calculations was deepened. Furthermore, phenomenological analyses beyond the Standard Model were discussed, in particular the effective theory approaches. The reports of 2018 and 2019 serve as white papers of the workshop results and subsequent developments.

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arXiv2020

Six dimensional ultraviolet completion of the $CP(N)$ $σ$ model at two loops

We extend the recent one loop analysis of the ultraviolet completion of the $CP(N)$ nonlinear $σ$ model in six dimensions to two loop order in the MSbar scheme for an arbitrary covariant gauge. In particular we compute the anomalous dimensions of the fields and $β$-functions of the four coupling constants. We note that like Quantum Electrodynamics (QED) in four dimensions the matter field anomalous dimension only depends on the gauge parameter at one loop. As a non-trivial check we verify that the critical exponents derived from these renormalization group functions at the Wilson-Fisher fixed point are consistent with the $ε$ expansion of the respective large $N$ exponents of the underlying universal theory. Using the Ward-Takahashi identity we deduce the three loop MSbar renormalization group functions for the six dimensional ultraviolet completeness of scalar QED.

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arXiv2020

Asymptotic freedom from the two loop term of the $β$-function in a cubic theory

We renormalize a six dimensional cubic theory to four loops in the MSbar scheme where the scalar is in a bi-adjoint representation. The underlying model was originally derived in a problem relating to gravity being a double copy of Yang-Mills theory. As a field theory in its own right we find that it has a curious property in that while unexpectedly there is no one loop contribution to the $β$-function the two loop coefficient is negative. It therefore represents an example where asymptotic freedom is determined by the two loop term of the $β$-function. We also examine a multi-adjoint cubic theory in order to see whether this is a more universal property of these models.

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arXiv2019

On the self-consistency of off-shell Slavnov-Taylor identities in QCD

Using Hopf-algebraic structures as well as diagrammatic techniques for determining the Slavnov-Taylor identities for QCD we construct the relations for the triple and quartic gluon vertices at one loop. By making the longitudinal projection on an external gluon of a Green's function we show that the gluon self-energy of that leg is consistently replaced by a ghost self-energy. The resulting identities are then studied by evaluating all the graphs for an off-shell non-exceptional momentum configuration. In the case of the 3-point function this is for the most general momentum case and for the 4-point function we consider the fully symmetric point.

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arXiv2019

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

We construct the two loop Green's functions for a quark bilinear operator inserted at non-zero momentum in a quark 2-point function for the most general off-shell configuration. In particular we consider the quark mass operator, vector and tensor currents as well as the second moment of the flavour non-singlet Wilson operator.

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arXiv2018

Large $N_f$ quantum field theory

We review the development of the large $N$ method, where $N$ indicates the number of flavours, used to study perturbative and nonperturbative properties of quantum field theories. The relevant historical background is summarized as a prelude to the introduction of the large $N$ critical point formalism. This is used to compute large $N$ corrections to $d$-dimensional critical exponents of the universal quantum field theory present at the Wilson-Fisher fixed point. While pedagogical in part the application to gauge theories is also covered and the use of the large $N$ method to complement explicit high order perturbative computations in gauge theories is also highlighted. The usefulness of the technique in relation to other methods currently used to study quantum field theories in $d$-dimensions is also summarized.

hep-th↗
arXiv2018

Fermion bilinear operator critical exponents at $O(1/N^2)$ in the QED-Gross-Neveu universality class

We use the critical point large $N$ formalism to calculate the critical exponents corresponding to the fermion mass operator and flavour non-singlet fermion bilinear operator in the universality class of Quantum Electrodynamics (QED) coupled to the Gross-Neveu model for an $SU(N)$ flavour symmetry in $d$-dimensions. The $ε$ expansion of the exponents in $d$ $=$ $4$ $-$ $2ε$ dimensions are in agreement with recent three and four loop perturbative evaluations of both renormalization group functions of these operators. Estimates of the value of the non-singlet operator exponent in three dimensions are provided.

hep-th↗
arXiv2018

Loop calculations for models of graphene

The various Gross-Neveu classes of quantum field theories are of interest in the study of a particular phase transition in graphene. We review recent activity in the determination of several critical exponents in the chiral Heisenberg Gross-Neveu universality class using the critical point large $N$ technique which includes the use of the large $N$ conformal bootstrap method.

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arXiv2018

Large $N$ critical exponents for the chiral Heisenberg Gross-Neveu universality class

We compute the large $N$ critical exponents $η$, $η_ϕ$ and $1/ν$ in $d$-dimensions in the chiral Heisenberg Gross-Neveu model to several orders in powers of $1/N$. For instance, the large $N$ conformal bootstrap method is used to determine $η$ at $O(1/N^3)$ while the other exponents are computed to $O(1/N^2)$. Estimates of the exponents for a phase transition in graphene are given which are shown to be commensurate with other approaches. In particular the behaviour of the exponents in $2$ $<$ $d$ $<$ $4$ is in qualitative agreement with a functional renormalization group analysis. The $ε$-expansion of the exponents near four dimensions are in agreement with recent four loop perturbation theory.

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arXiv2018

Renormalization of QCD in the interpolating momentum subtraction scheme at three loops

We introduce a more general set of kinematic renormalization schemes than the original momentum (MOM) subtraction schemes of Celmaster and Gonsalves. These new schemes will depend on a parameter $ω$ which tags the external momentum of one of the legs of the $3$-point vertex functions in Quantum Chromodynamics (QCD). In each of the three new schemes we renormalize QCD in the Landau and maximal abelian gauges and establish the three loop renormalization group functions in each gauge. As an application we evaluate two critical exponents at the Banks-Zaks fixed point and demonstrate that their values appear to be numerically scheme independent in a subrange of the conformal window.

hep-th↗
arXiv2018

Eight dimensional QCD at one loop

The Lagrangian for a non-abelian gauge theory with an $SU(N_{\! c})$ symmetry and a linear covariant gauge fixing is constructed in eight dimensions. The renormalization group functions are computed at one loop with the special cases of $N_{\! c}$ $=$ $2$ and $3$ treated separately. By computing the critical exponents derived from these in the large $N_{\! f}$ expansion at the Wilson-Fisher fixed point it is shown that the Lagrangian is in the same universality class as the two dimensional non-abelian Thirring model and Quantum Chromodynamics (QCD). As the eight dimensional Lagrangian contains new quartic gluon operators not present in four dimensional QCD, we compute in parallel the mixing matrix of four dimensional dimension $8$ operators in pure Yang-Mills theory.

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