Non-perturbative aspects of Sp(2N) gauge theories

Yang-Mills theories based on the symplectic groups – denoted by Sp(2N) – are inter-esting for both theoretical and phenomenological reasons. Sp(2N) theories with two fundamental Dirac fermions give rise to pseudo-Nambu-Goldstone bosons which can be interpreted as a composite Higgs particle. This framework can describe the existing Higgs boson without the need for unnatural fine-tuning. This justifies a programme of wider investigations of Sp(2N) gauge theories aimed at understanding their general behaviour. In this work, we study the glueball mass spectrum for Sp(2N) Yang-Mills theories using the variational method applied to Monte-Carlo generated gauge config-urations. This is carried out both for finite N and in the limit N → ∞. The results are compared to existing results for SU(N) Yang-Mills theories, again, for finite- and large-N. Our glueball analysis is then used to investigate some conjectures related to the behaviour of the spectrum in Yang-Mills theories based on a generic non-Abeliangauge group G. We also find numerical evidence that Sp(2N) groups confine both for finite and large N. As well as studying the glueball spectrum, we examine the quenched-meson spectrum for fermions in the fundamental, antisymmetric and sym-metric representations for N = 2 and N = 3. This study enables us to provide a first account of how the related observables vary with N. The investigations presented in this work contribute to our understanding of the non-perturbative dynamics of Sp(2N) gauge theories in connection with Higgs compositeness and, more in general, with fun-damental open problems in non-Abelian gauge theories such as confinement and global symmetry breaking

Leading Power Accuracy in Lattice Calculations of Parton Distributions

In lattice-QCD calculations of parton distribution functions (PDFs) via large-momentum effective theory, the leading power (twist-three) correction appears as ${\cal O}(\Lambda_{\rm QCD}/P^z)$ due to the linear-divergent self-energy of Wilson line in quasi-PDF operators. For lattice data with hadron momentum $P^z$ of a few GeV, this correction is dominant in matching, as large as 30\% or more. We show how to eliminate this uncertainty through choosing the mass renormalization parameter consistently with the resummation scheme of the infrared-renormalon series in perturbative matching coefficients. An example on the lattice pion PDF data at $P^z = 1.9$ GeV shows an improvement of matching accuracy by a factor of more than $3\sim 5$ in the expansion region $x= 0.2\sim 0.5$.Comment: Updated to version published on PL

Sp(2N) Yang-Mills towards large N.

Non-perturbative aspects of the physics of Sp(2N) gauge theories are interesting for phenomeno- logical and theoretical reasons, and little studied so far, particularly in the approach to the large-N limit. We examine the spectrum of glueballs and the string tension of Yang-Mills theories based upon these groups. Glueball masses are calculated numerically with a variational method from Monte-Carlo generated lattice gauge configurations. After taking continuum limits for N = 1, 2, 3 and 4, we extrapolate the results towards large N. We compare the resulting spectrum with that of SU(N) gauge theories, both at finite N and as N approaches infinity

Progress in Sp(2N)Sp(2N) lattice gauge theories

Lattice studies of gauge theories with symplectic gauge groups provide valuable information about gauge dynamics, and complement the results of lattice investigations focused on unitary gauge groups. These theories play a central role in phenomenological contexts such as composite Higgs and strongly interacting dark matter models. We report on recent progress of our lattice research programme, starting from the glueball mass spectrum and the topology of the pure gauge theory. We present our results on the mass spectrum of mesons in the quenched approximation, by varying the number of colours in the symplectic group. For the (4) theory, we focus on results obtained with dynamical fermion matter content comprising both fundamental and 2-index antisymmetric representations of the gauge group, as dictated by a well known model of composite Higgs with partial top compositeness

The Unpolarized Proton PDF at NNLO from Lattice QCD with Physical Quark Masses

We present a lattice QCD calculation of the unpolarized isovector quark parton distribution function (PDF) of the proton utilizing a perturbative matching at next-to-next-leading-order (NNLO). The calculations are carried out using a single ensemble of gauge configurations generated with $N_f = 2 + 1$ highly improved staggered quarks with physical masses and a lattice spacing of $a = 0.076$ fm. We use one iteration of hypercubic smearing on these gauge configurations, and the resulting smeared configurations are then used for all aspects of the subsequent calculation. For the valence quarks, we use the Wilson-clover action with physical quark masses. We consider several methods for extracting information on the PDF. We first extract the lowest four Mellin moments using the leading-twist operator product expansion approximation. Then, we determine the $x$ dependence of the PDF through a deep neural network within the pseudo-PDF approach and additionally through the framework of large-momentum effective theory utilizing a hybrid renormalization scheme. This is the first application of the NNLO matching coefficients for the nucleon directly at the physical point.Comment: 19 pages, 17 figures, and 3 table

Glueballs and strings in Sp(2N) Yang-Mills theories

Motivated in part by the pseudo-Nambu Goldstone Boson mechanism of electroweak symmetry breaking in Composite Higgs Models, in part by dark matter scenarios with strongly coupled origin, as well as by general theoretical considerations related to the large-N extrapolation, we perform lattice studies of the Yang-Mills theories with Sp(2N) gauge groups. We measure the string tension and the mass spectrum of glueballs, extracted from appropriate 2-point correlation functions of operators organised as irreducible representations of the octahedral symmetry group. We perform the continuum extrapolation and study the magnitude of finite-size effects, showing that they are negligible in our calculation. We present new numerical results for N = 1, 2, 3, 4, combine them with data previously obtained for N = 2, and extrapolate towards N ! 1. We confirm explicitly the expectation that, as already known for N = 1, 2 also for N = 3, 4 a confining potential rising linearly with the distance binds a static quark to its antiquark. We compare our results to the existing literature on other gauge groups, with particular attention devoted to the large-N limit. We find agreement with the known values of the mass of the 0++, 0++⇤ and 2++ glueballs obtained taking the large-N limit in the SU(N) groups. In addition, we determine for the first time the mass of some heavier glueball states at finite N in Sp(2N) and extrapolate the results towards N ! +1 taking the limit in the latter groups. Since the large-N limit of Sp(2N) is the same as in SU(N), our results are relevant also for the study of QCD-like theories

Sp(2N) Lattice Gauge Theories and Extensions of the Standard Model of Particle Physics

We review the current status of the long-term programme of numerical investigation of (2) gauge theories with and without fermionic matter content. We start by introducing the phenomenological as well as theoretical motivations for this research programme, which are related to composite Higgs models, models of partial top compositeness, dark matter models, and in general to the physics of strongly coupled theories and their approach to the large-N limit. We summarise the results of lattice studies conducted so far in the (2) Yang–Mills theories, measuring the string tension, the mass spectrum of glueballs and the topological susceptibility, and discuss their large-N extrapolation. We then focus our discussion on (4), and summarise the numerical measurements of mass and decay constant of mesons in the theories with fermion matter in either the fundamental or the antisymmetric representation, first in the quenched approximation, and then with dynamical fermions. We finally discuss the case of dynamical fermions in mixed representations, and exotic composite fermion states such as the chimera baryons. We conclude by sketching the future stages of the programme. We also describe our approach to open access

Precision control in lattice calculation of x-dependent pion distribution amplitude

We present a new Bjorken x-dependence analysis of a previous lattice quantum chromodynamics data for the pion distribution amplitude from MILC configurations with three lattice spacing a=0.06,0.09,0.12 fm. A leading renormalon resummation in renormalization as well as the perturbative matching kernel in the framework of large momentum expansion generates the power accuracy of the matching to the light-cone amplitude. Meanwhile, a small momentum log resummation is implemented for both the quark momentum xPz and the antiquark momentum (1−x)Pz inside a meson of boost momentum Pz up to 1.72 GeV along the z direction, allowing us to have more accurate determination of the x-dependence in the middle range. Finally, we use the complementarity between the short-distance factorization and the large momentum expansion to constrain the endpoint regions x∼0,1, thus obtaining the full-range x-dependence of the amplitude