We point out that the odd-in-velocity contribution to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mi>G</mi><mn>4</mn></msup><mo stretchy="false">)</mo></math> radiated angular momentum for two-body scattering is determined by the radiation-reaction (RR) term in the one-loop waveform. This RR term is actually proportional to the tree-level waveform, and this reduces the calculation of the odd-in-velocity contribution to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mi>G</mi><mn>4</mn></msup><mo stretchy="false">)</mo></math> angular momentum loss, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>J</mi></mrow><mrow><mn>2</mn><mtext> </mtext><mtext> </mtext><mi>rad</mi></mrow></msub></mrow></math>, to two loops, instead of three loops as one would expect by power counting. We exploit this simplification, which follows from unitarity, to obtain a closed-form expression for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>J</mi></mrow><mrow><mn>2</mn><mtext> </mtext><mtext> </mtext><mi>rad</mi></mrow></msub></mrow></math> for generic velocities, which resums all fractional post-Newtonian (PN) corrections to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mi>G</mi><mn>4</mn></msup><mo stretchy="false">)</mo></math> angular momentum loss starting at 1.5PN.

France

Carlo Heissenberg

Radiation-reaction and angular momentum loss at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mrow><mi>G</mi></mrow><mrow><mn>4</mn></mrow></msup><mo stretchy="false">)</mo></mrow></math>

The production yields of the orbitally excited charm-strange mesons <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mi mathvariant="normal">s</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>2536</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">D</mi><mrow><mi mathvariant="normal">s</mi><mn>2</mn></mrow><mo>*</mo></msubsup><mo stretchy="false">(</mo><msup><mn>2</mn><mo>+</mo></msup><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>2573</mn><msup><mo stretchy="false">)</mo><mo>+</mo></msup></math> were measured for the first time in proton-proton (pp) collisions at a center-of-mass energy of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> with the ALICE experiment at the LHC. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">D</mi><mrow><mi mathvariant="normal">s</mi><mn>1</mn></mrow><mo>+</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">D</mi><mrow><mi mathvariant="normal">s</mi><mn>2</mn></mrow><mrow><mo>*</mo><mo>+</mo></mrow></msubsup></math> mesons were measured at midrapidity (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><mi>y</mi><mo stretchy="false">|</mo><mo>&lt;</mo><mn>0.5</mn></math>) in minimum-bias and high-multiplicity pp collisions in the transverse-momentum interval <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>&lt;</mo><msub><mrow><mi>p</mi></mrow><mrow><mi mathvariant="normal">T</mi></mrow></msub><mo>&lt;</mo><mn>24</mn><mtext> </mtext><mtext> </mtext><mrow><mi>GeV</mi><mo>/</mo><mi>c</mi></mrow></mrow></math>. Their production yields relative to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">D</mi><mi mathvariant="normal">s</mi><mo>+</mo></msubsup></math> ground-state yield were found to be compatible between minimum-bias and high-multiplicity collisions, as well as with previous measurements in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">e</mi><mo>±</mo></msup><mi mathvariant="normal">p</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi mathvariant="normal">e</mi><mo>+</mo></msup><msup><mi mathvariant="normal">e</mi><mo>−</mo></msup></math> collisions. The measured <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">D</mi><mrow><mi mathvariant="normal">s</mi><mn>1</mn></mrow><mo>+</mo></msubsup><mo>/</mo><msubsup><mi mathvariant="normal">D</mi><mi mathvariant="normal">s</mi><mo>+</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi mathvariant="normal">D</mi><mrow><mi mathvariant="normal">s</mi><mn>2</mn></mrow><mrow><mo>*</mo><mo>+</mo></mrow></msubsup><mo>/</mo><msubsup><mi mathvariant="normal">D</mi><mi mathvariant="normal">s</mi><mo>+</mo></msubsup></math> yield ratios are described by statistical hadronization models and can be used to tune the parameters governing the production of excited charm-strange hadrons in Monte Carlo generators, such as pythia 8.

S. Acharya

India

A. Agarwal

CERN

G. Aglieri Rinella

Italy

L. Aglietta

M. Agnello

N. Agrawal

Z. Ahammed

S. Ahmad

South Korea

S.U. Ahn

Slovakia

I. Ahuja

A. Akindinov

Germany

V. Akishina

M. Al-Turany

D. Aleksandrov

B. Alessandro

China

H.M. Alfanda

Mexico

R. Alfaro Molina

B. Ali

A. Alici

United States

N. Alizadehvandchali

A. Alkin

Norway

J. Alme

G. Alocco

T. Alt

A.R. Altamura

I. Altsybeev

J.R. Alvarado

M.N. Anaam

Romania

C. Andrei

United Kingdom

N. Andreou

A. Andronic

E. Andronov

V. Anguelov

F. Antinori

P. Antonioli

N. Apadula

L. Aphecetche

H. Appelshäuser

C. Arata

S. Arcelli

R. Arnaldi

Brazil

J.G.M.C.A. Arneiro

I.C. Arsene

M. Arslandok

A. Augustinus

R. Averbeck

D. Averyanov

M.D. Azmi

Japan

H. Baba

A. Badalà

J. Bae

Y.W. Baek

X. Bai

R. Bailhache

Y. Bailung

R. Bala

A. Balbino

A. Baldisseri

Poland

B. Balis

Z. Banoo

V. Barbasova

F. Barile

L. Barioglio

Greece

M. Barlou

B. Barman

Hungary

G.G. Barnaföldi

L.S. Barnby

E. Barreau

V. Barret

L. Barreto

C. Bartels

K. Barth

E. Bartsch

N. Bastid

Sweden

S. Basu

G. Batigne

D. Battistini

B. Batyunya

D. Bauri

Peru

J.L. Bazo Alba

Denmark

I.G. Bearden

C. Beattie

P. Becht

D. Behera

I. Belikov

A.D.C. Bell Hechavarria

F. Bellini

R. Bellwied

S. Belokurova

L.G.E. Beltran

Y.A.V. Beltran

G. Bencedi

A. Bensaoula

S. Beole

Y. Berdnikov

A. Berdnikova

L. Bergmann

M.G. Besoiu

L. Betev

P.P. Bhaduri

First measurement of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi>s</mi><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>2536</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi><mn>2</mn></mrow><mrow><mo>*</mo></mrow></msubsup><mo stretchy="false">(</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>2573</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> production in proton-proton collisions at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> at the LHC

The low-energy spectrum relevant to the lattice calculation of the hadronic vacuum polarization contribution to muon anomalous magnetic moment <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>a</mi><mi>μ</mi><mrow><mi>HVP</mi><mo>,</mo><mi>LO</mi></mrow></msubsup></math> is dominantly given by two-pion states satisfying Lüscher’s finite-volume quantization condition. Finite-volume effects from those states may exhibit power-law dependence on the volume, contrary to an exponential suppression as suggested by chiral effective theory. Employing the finite-volume state decomposition of Euclidean correlators, we systematically investigate the volume dependence and identify the different volume scalings depending on the volume and Euclidean-time region. Using phenomenological inputs for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math> phase shift and the timelike pion form factor, we obtain an estimate for the finite-volume effects on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>a</mi><mi>μ</mi><mrow><mi>HVP</mi><mo>,</mo><mi>LO</mi></mrow></msubsup></math>, which is consistent with previous works. Numerical results are given for the “window” observables of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mi>μ</mi></msub></math>.

Sakura Itatani

Hidenori Fukaya

Shoji Hashimoto

Anatomy of finite-volume effects on the hadronic vacuum polarization contribution to the muon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math>

In this letter, we present the first measurement of direct photons at the transverse momentum of <math altimg='si2.svg'><mn>1</mn><mo linebreak='goodbreak' linebreakstyle='after'>&lt;</mo><msub><mrow><mi>p</mi></mrow><mrow><mi mathvariant='normal'>T</mi></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>&lt;</mo><mn>6</mn></math> GeV/ <italic>c</italic> at midrapidity <math altimg='si3.svg'><mo stretchy='false'>|</mo><mi>&#951;</mi><mo stretchy='false'>|</mo><mo linebreak='goodbreak' linebreakstyle='after'>&lt;</mo><mn>0.8</mn></math> in inelastic and high-multiplicity proton&#8211;proton collisions at a centre-of-mass energy of <math altimg='si1.svg'><msqrt><mrow><mi>s</mi></mrow></msqrt><mo linebreak='goodbreak' linebreakstyle='after'>=</mo></math> 13 TeV. The fraction of virtual direct photons in the inclusive virtual photon spectrum is obtained from a fit to the dielectron invariant mass spectrum. In the limit of zero invariant mass, this fraction is equal to the relative contribution of real direct photons in the inclusive real photon spectrum. Contributions from decays of light-flavour neutral mesons are estimated using independent measurements in proton&#8211;proton collisions at the same energy and the same event class. For the first time at the LHC energies, a direct-photon signal is observed at low <math altimg='si4.svg'><msub><mrow><mi>p</mi></mrow><mrow><mi mathvariant='normal'>T</mi></mrow></msub></math> in both inelastic and high-multiplicity event classes, with a significance of 3.2 <italic>&#963;</italic> and 1.9 <italic>&#963;</italic> in terms of standard deviations, correspondingly. The yield of direct photons in inelastic pp collisions is compared to perturbative QCD calculations. The integrated photon yield is studied as a function of charged-particle multiplicity and is compared to the results from other experiments and theoretical calculations. The results show a significant increase of direct-photon yield with charged-particle multiplicity.

Switzerland

Y. Bae

Direct-photon production in inelastic and high-multiplicity proton–proton collisions at <math altimg='si1.svg'><msqrt><mrow><mi>s</mi></mrow></msqrt><mo linebreak='goodbreak' linebreakstyle='after'>=</mo></math> 13 TeV

We present a calculation of the leading two-loop corrections to the axial-vector coupling constant <math altimg='si1.svg'><msub><mrow><mi>g</mi></mrow><mrow><mi>A</mi></mrow></msub></math> in two covariant versions of two-flavor baryon chiral perturbation theory. Taking the low-energy constants from a combined analysis of elastic and inelastic pion-nucleon scattering, we find that these corrections are rather moderate.

Véronique Bernard

Georgia

Jambul Gegelia

Shayan Ghosh

Ulf-G. Meißner

Calculation of the axial-vector coupling constant <italic>g</italic> <inf><italic>A</italic></inf> to two loops in covariant chiral perturbation theory

The novel Branching-Ratio Method (BRM) for the determination of effective value <math altimg='si1.svg'><msubsup><mrow><mi>g</mi></mrow><mrow><mi mathvariant='normal'>A</mi></mrow><mrow><mi mathvariant='normal'>eff</mi></mrow></msubsup></math> of the weak axial coupling <math altimg='si2.svg'><msub><mrow><mi>g</mi></mrow><mrow><mi mathvariant='normal'>A</mi></mrow></msub></math> for forbidden non-unique (FNU) <math altimg='si3.svg'><msup><mrow><mi>&#946;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup></math>/electron-capture(EC) decays is introduced. The method offers new possibilities for testing the fitness of nuclear Hamiltonians in modeling the physics of complex <math altimg='si3.svg'><msup><mrow><mi>&#946;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup></math>/EC decays. The constraint of simultaneously reproducing the branching to <math altimg='si3.svg'><msup><mrow><mi>&#946;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup></math> and EC transitions offers an additional constraint in tackling the problem of <math altimg='si1.svg'><msubsup><mrow><mi>g</mi></mrow><mrow><mi mathvariant='normal'>A</mi></mrow><mrow><mi mathvariant='normal'>eff</mi></mrow></msubsup></math> determination. In the BRM the ambiguity in the choice of the values of <math altimg='si1.svg'><msubsup><mrow><mi>g</mi></mrow><mrow><mi mathvariant='normal'>A</mi></mrow><mrow><mi mathvariant='normal'>eff</mi></mrow></msubsup></math> and s-NME (small relativistic vector nuclear matrix element) is lifted when constraints of the branching ratios of <math altimg='si3.svg'><msup><mrow><mi>&#946;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup></math> and EC decays are applied. As an example, in the present work we apply BRM to the case of second FNU <math altimg='si3.svg'><msup><mrow><mi>&#946;</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup></math>/EC decay of 59Ni. This decay is treated with three different nuclear shell-model (NSM) Hamiltonians demonstrating the effects of different nuclear-structure aspects in application of the BRM.

Finland

Aagrah Agnihotri

Jouni Suhonen

Novel way of evaluating <italic>g</italic> <inf><italic>A</italic></inf> quenching in <italic>&#946;</italic> +/EC decays: Introducing the Branching-Ratio Method (BRM)

In this paper, we consider hard-wall anti–de Sitter/quantum chromodynamics (AdS/QCD) models extended by a string-theory inspired Chern-Simons action in terms of a superconnection involving a bifundamental scalar field which corresponds to the open-string tachyon of brane-antibrane configurations and which is naturally identified with the holographic dual of the quark condensate in chiral symmetry breaking. This realizes both the axial and chiral anomalies of QCD with a Witten-Veneziano mechanism for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>η</mi><mo>′</mo></msup></math> mass in addition to current quark masses, but somewhat differently than in the Katz-Schwartz AdS/QCD model used previously by us to evaluate pseudoscalar and axial vector transition form factors and their contribution to the hadronic light-by-light (HLBL) piece of the muon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math>. Compared to the Katz-Schwartz model, we obtain a significantly more realistic description of axial-vector mesons with regard to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>1</mn></msub><mo>−</mo><msubsup><mi>f</mi><mn>1</mn><mo>′</mo></msubsup></math> mixing and equivalent photon rates. Moreover, predictions of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">→</mo><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> branching ratios are found to be in line with a recent phenomenological study. However, pseudoscalar transition form factors compare less well with experiment; in particular the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>π</mi><mn>0</mn></msup></math> transition form factor turns out to be overestimated at moderate nonzero virtuality. For the combined HLBL contribution to the muon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi><mo>−</mo><mn>2</mn></math> from the towers of axial vector mesons and excited pseudoscalars we obtain, however, a result very close to that of the Katz-Schwartz model.

Austria

Josef Leutgeb

Jonas Mager

Anton Rebhan

Superconnections in AdS/QCD and the hadronic light-by-light contribution to the muon <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>g</mi><mo>−</mo><mn>2</mn></mrow></math>

We propose a novel method to determine the strong coupling of quantum chromodynamics (QCD) and fix its running behavior at all scales by using the Bjorken sum rules (BSR). The BSR defines an effective coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow><mrow><msub><mrow><mi>g</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msubsup><mo stretchy="false">(</mo><mi>Q</mi><mo stretchy="false">)</mo></mrow></math> which includes the nonperturbative higher-twist corrections and perturbative QCD (pQCD) corrections to the leading-twist part. For the leading-twist part of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>α</mi><mi>s</mi><msub><mi>g</mi><mn>1</mn></msub></msubsup><mo stretchy="false">(</mo><mi>Q</mi><mo stretchy="false">)</mo></math>, we adopt the infinite-order scale-setting procedure of the principle of maximum conformality (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>PMC</mi><mi>∞</mi></msub></math>) to deal with its pQCD corrections, which reveals the intrinsic conformality of the series and eliminates conventional renormalization scheme-and-scale ambiguities. Using the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>PMC</mi><mi>∞</mi></msub></math> approach, we not only eliminate the first kind of residual scale dependence due to uncalculated higher-order terms, but also resolve the previous “self-consistency problem.” The light-front holographic QCD model is used for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>α</mi><mi>s</mi><msub><mi>g</mi><mn>1</mn></msub></msubsup><mo stretchy="false">(</mo><mi>Q</mi><mo stretchy="false">)</mo></math> in the infrared region, which also reveals a conformal behavior at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Q</mi><mo stretchy="false">→</mo><mn>0</mn></math>. As a combination, we obtain a precise <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>α</mi><mi>s</mi><msub><mi>g</mi><mn>1</mn></msub></msubsup><mo stretchy="false">(</mo><mi>Q</mi><mo stretchy="false">)</mo></math> at all scales, which matches well with the known experimental data with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi></math>-value <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>∼</mo><mn>98</mn><mo>%</mo></math>, and determines the strong coupling constant at the scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>M</mi><mi>Z</mi></msub></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub><mo stretchy="false">(</mo><msub><mi>M</mi><mi>Z</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mn>0.122</mn><msubsup><mn>0</mn><mrow><mo>−</mo><mn>0.0012</mn></mrow><mrow><mo>+</mo><mn>0.0011</mn></mrow></msubsup><mo stretchy="false">(</mo><mi mathvariant="normal">Δ</mi><mi>κ</mi><msubsup><mo stretchy="false">)</mo><mrow><mo>+</mo><mn>0.0007</mn></mrow><mrow><mo>−</mo><mn>0.0046</mn></mrow></msubsup><mo stretchy="false">(</mo><mrow><mi>the</mi><mo>.</mo></mrow><mo stretchy="false">)</mo></math>, where the first error comes from <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mi>κ</mi></math> of LFHQCD model and the second error is from the second kind of residual scale dependence.

Qing Yu

Xing-Gang Wu

Hua Zhou

Jian-Ming Shen

Determination of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>α</mi><mi>s</mi></msub><mo stretchy="false">(</mo><msub><mi>M</mi><mi>Z</mi></msub><mo stretchy="false">)</mo></math> via a high-precision effective coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>α</mi><mi>s</mi><msub><mi>g</mi><mn>1</mn></msub></msubsup><mo stretchy="false">(</mo><mi>Q</mi><mo stretchy="false">)</mo></math>

In this paper, we evaluate the complexity of the non static cylindrical geometry with anisotropic matter configuration in the framework of modified Gauss–Bonnet theory. In this perspective, we calculate modified field equations, the $\textit{C}$ energy formula and the mass function that help to understand the astrophysical structures in this modified gravity. Furthermore, we use the Weyl tensor and obtain different structure scalars by orthogonally splitting the Riemann tensor. One of these scalars, $$Y_{TF}$$ is referred to as the complexity factor. This parameter measures the system’s complexity due to non-uniform energy density and non-isotropic pressure. We select the identical complexity factor for the structure as used in the non-static scenario, while considering the analogous criterion for the most elementary pattern of development. This technique involves formulating structural scalars that illustrate the fundamental features of the system. A fluid distribution that satisfies the vanishing complexity requirement and evolves homologously is characterized as isotropic, geodesic, homogeneous, and shear-free. In the dissipative scenario, the fluid remains geodesic while exhibiting shear, resulting in an extensive array of solutions.

Pakistan

Azerbaijan

M. Gul

W. Ahmad

M. Nasir

Faisal Javed

Kuwait

Orhan Donmez

Saudi Arabia

Bander Almutairi

Study of complexity factor and stability of dynamical systems in $$f(\mathcal {G})$$ gravity

In previous works, an operator was developed for heterotic compactifications on ℝ × $\textit{G}$ and $\textit{AdS}$ × $\textit{G}$ , which preserves $\textit{N}$ = 1 $\textit{d}$ = 3 supersymmetry and whose kernel is related to the moduli of the compactification. The operator is described in terms of non-physical spurious degrees of freedom, specifically, deformations of a connection on the tangent bundle. In this paper, we eliminate these spurious degrees of freedom by linking deformations of the spin connection to the moduli of the $\textit{G}$ manifold $\textit{Y}$. This results in an operator $$ \overset{\check{} }{D} $$ that captures the physical moduli space of the $\textit{G}$ heterotic string theory. When $\textit{Y}$ = $\textit{X}$ × $\textit{S}$ , with $\textit{X}$ an SU(3) manifold, we show $$ \overset{\check{} }{D} $$ produces results that align with existing literature. This allows us to propose a $\textit{G}$ moduli space metric. We check that this metric reduces to the SU(3) moduli metric constructed in the literature. We then define an adjoint operator $$ {\overset{\check{} }{D}}^{\dagger } $$ . We show the $\textit{G}$ moduli correspond to the intersection of the kernels of $$ \overset{\check{} }{D} $$ and $$ {\overset{\check{} }{D}}^{\dagger } $$ . These kernels reduce to the SU(3) F-terms and D-terms respectively on $\textit{X}$ × $\textit{S}$ . This gives two non-trivial consistency checks of our proposed moduli space metric. Working perturbatively in $\textit{α}$‵, we also demonstrate that the heterotic $\textit{G}$ moduli problem can be characterised in terms of a double extension of ordinary bundles, just like in the SU(3) case.

Australia

Jock McOrist

Martin Sticka

Eirik Svanes

The physical moduli of heterotic $\textit{G}$