We study real-time scalar $$\phi ^4$$ -theory in 2+1 dimensions near criticality. Specifically, we compute the single-particle spectral function and that of the $\textit{s}$-channel four-point function in and outside the scaling regime. The computation is done with the spectral functional Callan–Symanzik equation, which exhibits manifest Lorentz invariance and preserves causality. We extract the scaling exponent $$\eta $$ from the spectral function and compare our result with that from a Euclidean fixed point analysis.

Germany

Konrad Kockler

Jan Pawlowski

Jonas Wessely

Critical scaling for spectral functions

We present a general formula for the amplitude of forward exclusive hadronic processes in the semihard regime of perturbative Quantum Chromodynamics (QCD), by means of the $\textit{next-to-leading order}$ eigenfunctions of the Balitsky–Fadin–Kuraev–Lipatov (BFKL) kernel, as constructed by Chirilli and Kovchegov. We discuss some formal subtleties in the check of compatibility with the similar formula based on the use of the $\textit{leading-order}$ BFKL eigenfunctions. Finally, in the specific case of the electroproduction of two light vector mesons, we consider the numerical stability of the amplitude when one or the other set of eigenfunctions is adopted.

Italy

Ada Polizzi

Poland

Michael Fucilla

Alessandro Papa

High-energy factorization via eigenfunctions of the next-to-leading-order BFKL kernel

The concept of complexity related to the celestial systems is elaborated within the context of distinct revised gravity theories. However, its interpretation in $\textit{f}$($\textit{R}$, $\textit{G}$) gravity is the main idea of our manuscript. We assume that the inner configuration of the system is a cylindrically symmetric geometry comprising the anisotropic configuration of matter. In our case study, we determine the revised equations of motion combined with the orthogonal decomposition of the Riemann tensor. The implications of anisotropic pressure and nonhomogeneous energy density are relevant. Decisive results relating to the Tolman mass, Weyl scalar, and the complexity factor are derived by incorporating dark source terms corresponding to the $\textit{f}$($\textit{R}$, $\textit{G}$) theory. Additionally, the structure scalars calculated in our manuscript are employed to derive the expression for the complexity factor, after considering reducing the complexity constraint to obtain the solutions for the specific models. The compact structures with anisotropic pressure and non-homogeneous energy density claim the maximum complexity. However, these fluids might not demonstrate any complexity if the implications of non-homogeneous energy density and anisotropic pressure are eradicated because of dark source terms corresponding to the $\textit{f}$($\textit{R}$, $\textit{G}$) theory.

Pakistan

A. Rehman

Azerbaijan

M. Yousaf

China

Faisal Javed

Thailand

Phongpichit Channuie

Interpretation of complexity associated with cylindrically symmetric configuration in $\textit{f}$($\textit{R}$, $\textit{G}$) theory

Using the data samples of 102 million Υ(1$\textit{S}$) and 158 million Υ(2$\textit{S}$) events collected by the Belle detector, we search for a pentaquark state in the $\textit{pJ/ψ}$ final state from Υ(1$\textit{,}$ 2$\textit{S}$) inclusive decays. Here, the charge-conjugate $$\overline{p }J/\psi $$ is included. We observe clear $\textit{pJ/ψ}$ production in Υ(1$\textit{,}$ 2$\textit{S}$) decays and measure the branching fractions to be $$\mathcal{B}[\Upsilon (1S)\to pJ/\psi +anything]=[8.1\pm 0.6(stat.)\pm 0.5(syst.)]\times {10}^{-5}$$ and $$\mathcal{B}[\Upsilon (2S)\to pJ/\psi +anything]=[4.3\pm 0.5(stat.)\pm 0.4(syst.)]\times {10}^{-5}$$ . We also measure the cross section of inclusive $\textit{pJ/ψ}$ production in $\textit{e}$ $\textit{e}$ annihilation to be $\textit{σ}$($\textit{e}$ $\textit{e}$ → $\textit{pJ/ψ}$ + $\textit{anything}$) = [108 ± 11($\textit{stat.}$) ± 6($\textit{syst.}$)] fb at $$\sqrt{s}=10.52$$ GeV using an 89$\textit{.}$5 fb continuum data sample. There is no significant $\textit{P}$ (4312) , $\textit{P}$ (4440) or $\textit{P}$ (4457) signal found in the $\textit{pJ/ψ}$ final states in Υ(1$\textit{,}$ 2$\textit{S}$) inclusive decays. We determine the upper limits of $$\mathcal{B}\left[\Upsilon \left({1},{2}S\right)\to {P}_{c}^{+}+anything\right]\cdot \mathcal{B}\left({P}_{c}^{+}\to pJ/\psi \right)$$ to be at the 10 level.

X. Dong

S. Zou

H. Zhang

X. Wang

I. Adachi

J. Ahn

H. Aihara

S. Said

D. Asner

H. Atmacan

R. Ayad

S. Bahinipati

Sw. Banerjee

M. Bessner

V. Bhardwaj

D. Biswas

D. Bodrov

A. Bozek

M. Bračko

P. Branchini

T. Browder

A. Budano

M. Campajola

D. Červenkov

M.C. Chang

P. Chang

B. Cheon

H. Cho

K. Cho

S.K. Choi

Y. Choi

S. Choudhury

S. Das

G. Nardo

G. Pietro

R. Dhamija

F. Capua

J. Dingfelder

Z. Doležal

T. Dong

P. Ecker

D. Epifanov

T. Ferber

D. Ferlewicz

B. Fulsom

R. Garg

V. Gaur

A. Giri

P. Goldenzweig

E. Graziani

T. Gu

Y. Guan

K. Gudkova

C. Hadjivasiliou

H. Hayashii

S. Hazra

M. Hedges

W.S. Hou

C.L. Hsu

K. Inami

N. Ipsita

A. Ishikawa

R. Itoh

M. Iwasaki

W. Jacobs

S. Jia

Y. Jin

D. Kalita

T. Kawasaki

D. Kim

K.H. Kim

Y. Kim

Y.K. Kim

K. Kinoshita

P. Kodyš

A. Korobov

S. Korpar

E. Kovalenko

P. Križan

P. Krokovny

T. Kuhr

R. Kumar

T. Kumita

A. Kuzmin

Y.J. Kwon

Y.T. Lai

T. Lam

J. Lange

D. Levit

L. Li

Y. Li

L. Gioi

J. Libby

D. Liventsev

Y. Ma

M. Masuda

T. Matsuda

S. Maurya

F. Meier

Search for a pentaquark state decaying into $\textit{pJ/ψ}$ in Υ(1$\textit{,}$ 2$\textit{S}$) inclusive decays at Belle

In this article we study, via analytical methods, 1/$\textit{Q}$ non-perturbative power corrections to event shape mean values, addressing in particular the question of their interplay with soft perturbative emissions. Specifically we point out that energy-ordered soft perturbative emissions that precede a non-perturbative emission, give rise to terms of the form $$ \frac{1}{Q}{\left({\alpha}_s\ln \frac{Q}{\Lambda}\right)}^n $$ . While such terms are formally higher order in the strong coupling, their form suggests that they can numerically compete with the leading 1/$\textit{Q}$ term while also modifying the $\textit{Q}$ dependence of the result. The resummation of such power-suppressed but logarithmically enhanced terms lends an anomalous dimension to the leading 1/$\textit{Q}$ power correction. In order to argue for the presence of such an anomalous dimension, we formulate a method to compute the first order in $\textit{α}$ correction for the mean values of the thrust 1 – $\textit{T}$ and $\textit{C}$-parameter observables. We comment on our findings in light of the standard picture of universality of 1/$\textit{Q}$ power corrections for event shape variables and implications for phenomenology.

United Kingdom

Mrinal Dasgupta

Farid Hounat

Exploring soft anomalous dimensions for 1/$\textit{Q}$ power corrections

<p>We report the first observation of the two-body baryonic decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msub><mi mathvariant="normal">Σ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2455</mn><msup><mo stretchy="false">)</mo><mrow><mo>+</mo><mo>+</mo></mrow></msup><msubsup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mo>−</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msub><mi mathvariant="normal">Σ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2455</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup><msubsup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mn>0</mn></msubsup></math> with significances of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>7.3</mn><mi>σ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>6.2</mn><mi>σ</mi></math>, respectively, including statistical and systematic uncertainties. The branching fractions are measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msub><mi mathvariant="normal">Σ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2455</mn><msup><mo stretchy="false">)</mo><mrow><mo>+</mo><mo>+</mo></mrow></msup><msubsup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mo>−</mo></msubsup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>5.74</mn><mo>±</mo><mn>1.11</mn><mo>±</mo><mn>0.4</mn><msubsup><mn>2</mn><mrow><mo>−</mo><mn>1.53</mn></mrow><mrow><mo>+</mo><mn>2.47</mn></mrow></msubsup><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msub><mi mathvariant="normal">Σ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2455</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup><msubsup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mn>0</mn></msubsup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>4.83</mn><mo>±</mo><mn>1.12</mn><mo>±</mo><mn>0.3</mn><msubsup><mn>7</mn><mrow><mo>−</mo><mn>0.60</mn></mrow><mrow><mo>+</mo><mn>0.72</mn></mrow></msubsup><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>. The first and second uncertainties are statistical and systematic, respectively, while the third ones arise from the absolute branching fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mo>−</mo></msubsup></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mn>0</mn></msubsup></math> decays. The data samples used for this analysis have integrated luminosities of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>711</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>365</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>, and were collected at the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">ϒ</mi><mo stretchy="false">(</mo><mn>4</mn><mi>S</mi><mo stretchy="false">)</mo></math> resonance by the Belle and Belle II detectors operating at the KEKB and SuperKEKB asymmetric-energy <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> colliders, respectively.</p>

M. Abumusabh

L. Aggarwal

H. Ahmed

Y. Ahn

N. Akopov

S. Alghamdi

M. Alhakami

A. Aloisio

N. Althubiti

K. Amos

N. Anh Ky

D.M. Asner

T. Aushev

V. Aushev

V. Babu

H. Bae

N.K. Baghel

P. Bambade

M. Barrett

M. Bartl

J. Baudot

A. Baur

A. Beaubien

F. Becherer

J. Becker

J.V. Bennett

F.U. Bernlochner

V. Bertacchi

M. Bertemes

E. Bertholet

S. Bettarini

B. Bhuyan

F. Bianchi

A. Bobrov

A. Bondar

G. Bonvicini

J. Borah

A. Boschetti

R.A. Briere

T.E. Browder

S. Bussino

Q. Campagna

L. Cao

G. Casarosa

C. Cecchi

P. Cheema

L. Chen

B.G. Cheon

K. Chilikin

J. Chin

K. Chirapatpimol

H.E. Cho

S.J. Cho

L. Corona

J.X. Cui

E. De La Cruz-Burelo

S.A. De La Motte

G. De Nardo

G. De Pietro

R. de Sangro

M. Destefanis

S. Dey

A. Di Canto

I. Domínguez Jiménez

T.V. Dong

M. Dorigo

K. Dugic

G. Dujany

J. Eppelt

R. Farkas

P. Feichtinger

Observation of the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>+</mo></msup><mo stretchy="false">→</mo><msub><mi mathvariant="normal">Σ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2455</mn><msup><mo stretchy="false">)</mo><mrow><mo>+</mo><mo>+</mo></mrow></msup><msubsup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mo>−</mo></msubsup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msub><mi mathvariant="normal">Σ</mi><mi>c</mi></msub><mo stretchy="false">(</mo><mn>2455</mn><msup><mo stretchy="false">)</mo><mn>0</mn></msup><msubsup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo stretchy="false">¯</mo></mover><mi>c</mi><mn>0</mn></msubsup></math>