Perturbative vs non-perturbative renormalization: the case of the quark mass

Chapter 4 deals with the stability of the proton, hence of hydrogen, and how to reconcile that stability with the baryon number nonconservation (or baryon conservation) needed to establish a matter–antimatter imbalance in the infant universe. Sakharov’s three conditions for establishing a matter–antimatter imbalance are presented. Grand unified theories and experimental searches for proton decay are described. The concept of spontaneous symmetry breaking is introduced in describing the electroweak phase transition in the infant universe. That transition is treated as the potential site for introducing the imbalance between quarks and antiquarks, via either baryogenesis or leptogenesis models. The up–down quark mass difference is presented as essential for providing the stability of hydrogen and of the deuteron, which serves as a crucial stepping stone in stellar hydrogen-burning reactions that generate the energy and elements needed for life. Constraints on quark masses from lattice QCD calculations and violations of chiral symmetry are discussed.

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Quark mass differences and isospin violation in the pion-nucleon coupling constants

Physical Review C ◽

10.1103/physrevc.39.2054 ◽

1989 ◽

Vol 39 (5) ◽

pp. 2054-2056 ◽

Cited By ~ 11

Author(s):

Véronique Bernard ◽

Ulf-G. Meissner

Keyword(s):

Quark Mass ◽

Coupling Constants ◽

Isospin Violation ◽

Pion Nucleon

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Heavy-flavor hadro-production with heavy-quark masses renormalized in the $$ \overline{\mathrm{MS}} $$, MSR and on-shell schemes

Journal of High Energy Physics ◽

10.1007/jhep04(2021)043 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

M. V. Garzelli ◽

L. Kemmler ◽

S. Moch ◽

O. Zenaiev

Keyword(s):

Heavy Quark ◽

Cross Sections ◽

Top Quark ◽

Quark Mass ◽

Production Cross ◽

Hadron Collider ◽

Distribution Functions ◽

Heavy Flavor ◽

Parton Distribution Functions ◽

Heavy Quark Mass

Abstract We present predictions for heavy-quark production at the Large Hadron Collider making use of the $$ \overline{\mathrm{MS}} $$ MS ¯ and MSR renormalization schemes for the heavy-quark mass as alternatives to the widely used on-shell renormalization scheme. We compute single and double differential distributions including QCD corrections at next-to-leading order and investigate the renormalization and factorization scale dependence as well as the perturbative convergence in these mass renormalization schemes. The implementation is based on publicly available programs, MCFM and xFitter, extending their capabilities. Our results are applied to extract the top-quark mass using measurements of the total and differential $$ t\overline{t} $$ t t ¯ production cross-sections and to investigate constraints on parton distribution functions, especially on the gluon distribution at low x values, from available LHC data on heavy-flavor hadro-production.

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Double parton distributions in the pion from lattice QCD

Journal of High Energy Physics ◽

10.1007/jhep02(2021)067 ◽

2021 ◽

Vol 2021 (2) ◽

Author(s):

Gunnar S. Bali ◽

Luca Castagnini ◽

Markus Diehl ◽

Jonathan R. Gaunt ◽

Benjamin Gläßle ◽

...

Keyword(s):

Spatial Distribution ◽

Lattice Qcd ◽

Quark Mass ◽

Matrix Elements ◽

Parton Distributions ◽

Almost All ◽

The Relationship

Abstract We perform a lattice study of double parton distributions in the pion, using the relationship between their Mellin moments and pion matrix elements of two local currents. A good statistical signal is obtained for almost all relevant Wick contractions. We investigate correlations in the spatial distribution of two partons in the pion, as well as correlations involving the parton polarisation. The patterns we observe depend significantly on the quark mass. We investigate the assumption that double parton distributions approximately factorise into a convolution of single parton distributions.

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Isospin-1/2 Dπ scattering and the lightest $$ {D}_0^{\ast } $$ resonance from lattice QCD

Journal of High Energy Physics ◽

10.1007/jhep07(2021)123 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Luke Gayer ◽

Nicolas Lang ◽

Sinéad M. Ryan ◽

David Tims ◽

Christopher E. Thomas ◽

...

Keyword(s):

Scattering Amplitudes ◽

Lattice Qcd ◽

Quark Mass ◽

Light Quark ◽

Energy Levels ◽

Experimental Result ◽

Infinite Volume ◽

Resonance Pole ◽

Strongly Coupled ◽

Light Quark Mass

Abstract Isospin-1/2 Dπ scattering amplitudes are computed using lattice QCD, working in a single volume of approximately (3.6 fm)3 and with a light quark mass corresponding to mπ ≈ 239 MeV. The spectrum of the elastic Dπ energy region is computed yielding 20 energy levels. Using the Lüscher finite-volume quantisation condition, these energies are translated into constraints on the infinite-volume scattering amplitudes and hence enable us to map out the energy dependence of elastic Dπ scattering. By analytically continuing a range of scattering amplitudes, a $$ {D}_0^{\ast } $$ D 0 ∗ resonance pole is consistently found strongly coupled to the S-wave Dπ channel, with a mass m ≈ 2200 MeV and a width Γ ≈ 400 MeV. Combined with earlier work investigating the $$ {D}_{s0}^{\ast } $$ D s 0 ∗ , and $$ {D}_0^{\ast } $$ D 0 ∗ with heavier light quarks, similar couplings between each of these scalar states and their relevant meson-meson scattering channels are determined. The mass of the $$ {D}_0^{\ast } $$ D 0 ∗ is consistently found well below that of the $$ {D}_{s0}^{\ast } $$ D s 0 ∗ , in contrast to the currently reported experimental result.

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Eigenvalue spectrum and scaling dimension of lattice $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills

Journal of High Energy Physics ◽

10.1007/jhep04(2021)260 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Georg Bergner ◽

David Schaich

Keyword(s):

Anomalous Dimension ◽

Finite Lattice ◽

Continuum Theory ◽

Lattice Volume ◽

Yang Mills ◽

Lattice Regularization ◽

Perturbative Renormalization ◽

Zero Values ◽

Definition Of ◽

Group Flow

Abstract We investigate the lattice regularization of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory, by stochastically computing the eigenvalue mode number of the fermion operator. This provides important insight into the non-perturbative renormalization group flow of the lattice theory, through the definition of a scale-dependent effective mass anomalous dimension. While this anomalous dimension is expected to vanish in the conformal continuum theory, the finite lattice volume and lattice spacing generically lead to non-zero values, which we use to study the approach to the continuum limit. Our numerical results, comparing multiple lattice volumes, ’t Hooft couplings, and numbers of colors, confirm convergence towards the expected continuum result, while quantifying the increasing significance of lattice artifacts at larger couplings.

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