One-loop structure of parton distribution for the gluon condensate and “zero modes”

Abstract We present results for one-loop corrections to the recently introduced “gluon condensate” PDF F(x). In particular, we give expression for the gg-part of its evolution kernel. To enforce strict compliance with the gauge invariance requirements, we have used on-shell states for external gluons, and have obtained identical results both in Feynman and light-cone gauges. No “zero mode” δ(x) terms were found for the twist-4 gluon PDF F(x). However a q2δ(x) term was found for the ξ = 0 GPD F(x, q2) at nonzero momentum transfer q. Overall, our results do not agree with the original attempt of one-loop calculations of F(x) for gluon states, which sets alarm warning for calculations that use matrix elements with virtual external gluons and for lattice renormalization procedures based on their results.

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Light-cone sum rules for proton decay

Journal of High Energy Physics ◽

10.1007/jhep05(2021)258 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Ulrich Haisch ◽

Amando Hala

Keyword(s):

Lattice Qcd ◽

Light Cone ◽

Sum Rules ◽

State Of The Art ◽

Form Factors ◽

Baryon Number ◽

Proton Decay ◽

Matrix Elements ◽

Decay Channels ◽

Systematic Uncertainties

Abstract We estimate the form factors that parametrise the hadronic matrix elements of proton-to-pion transitions with the help of light-cone sum rules. These form factors are relevant for semi-leptonic proton decay channels induced by baryon-number violating dimension-six operators, as typically studied in the context of grand unified theories. We calculate the form factors in a kinematical regime where the momentum transfer from the proton to the pion is space-like and extrapolate our final results to the regime that is relevant for proton decay. In this way, we obtain estimates for the form factors that show agreement with the state-of-the-art calculations in lattice QCD, if systematic uncertainties are taken into account. Our work is a first step towards calculating more involved proton decay channels where lattice QCD results are not available at present.

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Majorana zero modes in impurity-assisted vortex of LiFeAs superconductor

Nature Communications ◽

10.1038/s41467-021-24372-6 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Lingyuan Kong ◽

Lu Cao ◽

Shiyu Zhu ◽

Michał Papaj ◽

Guangyang Dai ◽

...

Keyword(s):

Quantum Computation ◽

Zero Mode ◽

Scanning Tunneling ◽

Homogeneous Material ◽

Dirac Fermions ◽

Tunneling Microscopy ◽

Zero Modes ◽

Topological Quantum ◽

One Step ◽

Topological Quantum Computation

AbstractThe iron-based superconductor is emerging as a promising platform for Majorana zero mode, which can be used to implement topological quantum computation. One of the most significant advances of this platform is the appearance of large vortex level spacing that strongly protects Majorana zero mode from other low-lying quasiparticles. Despite the advantages in the context of physics research, the inhomogeneity of various aspects hampers the practical construction of topological qubits in the compounds studied so far. Here we show that the stoichiometric superconductor LiFeAs is a good candidate to overcome this obstacle. By using scanning tunneling microscopy, we discover that the Majorana zero modes, which are absent on the natural clean surface, can appear in vortices influenced by native impurities. Our detailed analysis reveals a new mechanism for the emergence of those Majorana zero modes, i.e. native tuning of bulk Dirac fermions. The discovery of Majorana zero modes in this homogeneous material, with a promise of tunability, offers an ideal material platform for manipulating and braiding Majorana zero modes, pushing one step forward towards topological quantum computation.

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DEFINITION AND EVOLUTION OF TRANSVERSE MOMENTUM DISTRIBUTIONS

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194512009130 ◽

2012 ◽

Vol 20 ◽

pp. 92-108 ◽

Cited By ~ 5

Author(s):

MIGUEL G. ECHEVARRÍA ◽

AHMAD IDILBI ◽

IGNAZIO SCIMEMI

Keyword(s):

Transverse Momentum ◽

Evolution Equation ◽

Gauge Invariance ◽

Parton Distribution ◽

Ultra Violet ◽

Distribution Functions ◽

Parton Distribution Functions ◽

Transverse Momentum Dependent ◽

Momentum Distributions ◽

Definition Of

We consider the definition of unpolarized transverse-momentum-dependent parton distribution functions while staying on-the-light-cone. By imposing a requirement of identical treatment of two collinear sectors, our approach, compatible with a generic factorization theorem with the soft function included, is valid for all non-ultra-violet regulators (as it should), an issue which causes much confusion in the whole field. We explain how large logarithms can be resummed in a way which can be considered as an alternative to the use of Collins-Soper evolution equation. The evolution properties are also discussed and the gauge-invariance, in both classes of gauges, regular and singular, is emphasized.

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Light-Cone Parton Distribution Functions from Lattice QCD

Physical Review Letters ◽

10.1103/physrevlett.121.112001 ◽

2018 ◽

Vol 121 (11) ◽

Cited By ~ 52

Author(s):

Constantia Alexandrou ◽

Krzysztof Cichy ◽

Martha Constantinou ◽

Karl Jansen ◽

Aurora Scapellato ◽

...

Keyword(s):

Lattice Qcd ◽

Parton Distribution ◽

Light Cone ◽

Distribution Functions ◽

Parton Distribution Functions

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ZERO MODE OF GRAVITINO ON SCALAR FLAT THICK BRANES

Modern Physics Letters A ◽

10.1142/s0217732309030515 ◽

2009 ◽

Vol 24 (25) ◽

pp. 2005-2011

Author(s):

LI-JIE ZHANG ◽

SHAO-FENG WU ◽

GUO-HONG YANG

Keyword(s):

Yukawa Coupling ◽

Zero Mode ◽

Fermionic Field ◽

Zero Modes ◽

Gravitino Field ◽

Thick Branes

The localization of the spin-3/2 gravitino field on thick branes with a Yukawa coupling is studied in this paper. We show that, for spin-3/2 fermionic field, there exist normalizable zero modes which can be localized on the flat thick branes under certain conditions.

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CHIRAL ZERO MODES ON VORTEX-TYPE INTERSECTING HETEROTIC FIVE-BRANES

Modern Physics Letters A ◽

10.1142/s0217732312500721 ◽

2012 ◽

Vol 27 (12) ◽

pp. 1250072 ◽

Cited By ~ 1

Author(s):

MASAYA YATA

Keyword(s):

Dirac Equation ◽

Zero Mode ◽

The Other ◽

Two Dimensional ◽

Complete Spectrum ◽

Type Solution ◽

Heterotic String Theory ◽

Zero Modes ◽

Brane Solution ◽

Opposite Chirality

We solve the gaugino Dirac equation on a smeared intersecting five-brane solution in E8×E8 heterotic string theory to search for localized chiral zero modes on the intersection. The background is chosen to depend on the full two-dimensional overall transverse coordinates to the branes. Under some appropriate boundary conditions, we compute the complete spectrum of zero modes to find that, among infinite towers of Fourier modes, there exist only three localized normalizable zero modes, one of which has opposite chirality to the other two. This agrees with the result previously obtained in the domain-wall type solution, supporting the claim that there exists one net chiral zero mode localized on the heterotic five-brane system.

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QCD Factorization and PDFs from Lattice QCD Calculation

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194515600411 ◽

2015 ◽

Vol 37 ◽

pp. 1560041 ◽

Cited By ~ 20

Author(s):

Yan-Qing Ma ◽

Jian-Wei Qiu

Keyword(s):

Euclidean Space ◽

Minkowski Space ◽

Lattice Qcd ◽

Correlation Functions ◽

Parton Distribution ◽

Distribution Functions ◽

Matrix Elements ◽

Parton Distribution Functions ◽

Qcd Factorization ◽

The Matrix

In this talk, we review a QCD factorization based approach to extract parton distribution and correlation functions from lattice QCD calculation of single hadron matrix elements of quark-gluon operators. We argue that although the lattice QCD calculations are done in the Euclidean space, the nonperturbative collinear behavior of the matrix elements are the same as that in the Minkowski space, and could be systematically factorized into parton distribution functions with infrared safe matching coefficients. The matching coefficients can be calculated perturbatively by applying the factorization formalism on to asymptotic partonic states.

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Light Cone Singularities and the Asymptotic Behavior of Matrix Elements of Operator Products in Momentum Space

Fortschritte der Physik ◽

10.1002/prop.19730210502 ◽

1973 ◽

Vol 21 (5) ◽

pp. 205-263 ◽

Cited By ~ 3

Author(s):

Fritz Schwarz

Keyword(s):

Asymptotic Behavior ◽

Momentum Space ◽

Light Cone ◽

Matrix Elements

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DUALITY THROUGH THE SYMPLECTIC EMBEDDING FORMALISM

International Journal of Modern Physics A ◽

10.1142/s0217751x07036932 ◽

2007 ◽

Vol 22 (21) ◽

pp. 3605-3620 ◽

Cited By ~ 15

Author(s):

E. M. C. ABREU ◽

A. C. R. MENDES ◽

C. NEVES ◽

W. OLIVEIRA ◽

F. I. TAKAKURA

Keyword(s):

Phase Space ◽

Gauge Invariance ◽

Zero Mode ◽

Mass Term ◽

Gauge Invariant ◽

Embedding Method ◽

Symplectic Embedding ◽

The One ◽

Topological Term

In this work we show that we can obtain dual equivalent actions following the symplectic formalism with the introduction of extra variables which enlarge the phase space. We show that the results are equal as the one obtained with the recently developed gauging iterative Noether dualization method. We believe that, with the arbitrariness property of the zero mode, the symplectic embedding method is more profound since it can reveal a whole family of dual equivalent actions. We illustrate the method demonstrating that the gauge-invariance of the electromagnetic Maxwell Lagrangian broken by the introduction of an explicit mass term and a topological term can be restored to obtain the dual equivalent and gauge-invariant version of the theory.

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