The Kaon bag parameter $$ {\hat{B}}_K $$ plays a critical role in constraining the parameters of the CKM matrix and in probing physics beyond the Standard Model. In this work, we improve the precision of $$ {\hat{B}}_K $$ to next-to-next-to-leading order (NNLO) and provide world averages for both 3- and 4-flavour theories. In the course of this, as our main technical development, we carry out the two-loop matching between the RI-(S)MOM and $$ \overline{\textrm{MS}} $$ schemes. Our world averages combine all available lattice data, including conversion between the 3- and 4-flavour theories as appropriate. We obtain the result $$ {\hat{B}}_K^{\left(f=3\right)}=0.7627(60) $$ , which comprises the complete set of 3- and 4-flavour lattice results and can be used directly in phenomenological applications. The error is dominated by lattice uncertainties and missing higher-order corrections (residual scale dependence). Our averages include a PDG rescaling factor of 1.28 reflecting a mild tension among the lattice inputs after inclusion of NNLO corrections in the scheme conversion and matching across flavour thresholds. Our averages imply an updated value |$\textit{ϵ}$ | = 2$\textit{.}$171(65) (71) (153) × 10 . We briefly discuss applications of our results to $\textit{D}$-meson mixing.

United Kingdom

Martin Gorbahn

Sebastian Jäger

Spain

Sandra Kvedaraitė

RI-(S)MOM to $$ \overline{\textrm{MS}} $$ conversion for $\textit{B}$

The jet energy calibration and its uncertainties are derived from measurements of the calorimeter response to single particles in both data and Monte Carlo simulation using proton–proton collisions at $$\sqrt{s} = 13$$ TeV collected with the ATLAS detector during Run 2 at the Large Hadron Collider. The jet calibration uncertainty for anti- $$k_T$$ jets with a jet radius parameter of $\textit{R}$ $$_\textrm{jet} = 0.4$$ and in the central jet rapidity region is about 2.5% for transverse momenta ( $$p_{\text {T}}$$ ) of 20 $$\text {GeV}$$ , about $$0.5\%$$ for $$p_{\text {T}} =300$$ $$\text {GeV}$$ and $$0.7\%$$ for $$p_{\text {T}} =4$$ $$\text {TeV}$$ . Excellent agreement is found with earlier determinations obtained from $$p_\textrm{T}$$ -balance based in situ methods ( $$Z/\gamma $$ +jets). The combination of these two independent methods results in the most precise jet energy measurement achieved so far with the ATLAS detector with a relative uncertainty of $$0.3\%$$ at $$p_\textrm{T}=300$$ GeV and $$0.6\%$$ at 4 TeV. The jet energy calibration is also derived with the single-particle calorimeter response measurements separately for quark- and gluon-induced jets and furthermore for jets with $\textit{R}$ $$_\textrm{jet}$$ varying from 0.2 to 1.0 retaining the correlations between these measurements. Differences between inclusive jets and jets from boosted top-quark decays, with and without grooming the soft jet constituents, are also studied.

France

G. Aad

Norway

E. Aakvaag

United States

B. Abbott

United Arab Emirates

S. Abdelhameed

Germany

K. Abeling

N. Abicht

S. Abidi

M. Aboelela

Morocco

A. Aboulhorma

Israel

H. Abramowicz

H. Abreu

Y. Abulaiti

Italy

B. Acharya

A. Ackermann

C. Bourdarios

Poland

L. Adamczyk

S. Addepalli

M. Addison

J. Adelman

Türkiye

A. Adiguzel

T. Adye

A. Affolder

Y. Afik

M. Agaras

J. Agarwala

A. Aggarwal

Romania

C. Agheorghiesei

Azerbaijan

F. Ahmadov

Canada

W. Ahmed

S. Ahuja

China

X. Ai

G. Aielli

A. Aikot

M. Tamlihat

B. Aitbenchikh

M. Akbiyik

Sweden

T. Åkesson

A. Akimov

Japan

D. Akiyama

N. Akolkar

S. Aktas

K. Khoury

G. Alberghi

J. Albert

P. Albicocco

G. Albouy

S. Alderweireldt

Z. Alegria

Switzerland

M. Aleksa

I. Aleksandrov

C. Alexa

Greece

T. Alexopoulos

F. Alfonsi

M. Algren

M. Alhroob

Czechia

B. Ali

Saudi Arabia

H. Ali

S. Ali

S. Alibocus

South Africa

M. Aliev

G. Alimonti

W. Alkakhi

C. Allaire

B. Allbrooke

J. Allen

Chile

C. Flores

P. Allport

A. Aloisio

Argentina

F. Alonso

C. Alpigiani

Z. Alsolami

M. Estevez

A. Fernandez

M. Cardoso

M. Alviggi

M. Aly

Brazil

Y. Coutinho

A. Ambler

C. Amelung

M. Amerl

C. Ames

D. Amidei

B. Amini

K. Amirie

Portugal

S. Santos

K. Amos

D. Amperiadou

S. An

V. Ananiev

C. Anastopoulos

T. Andeen

J. Anders

A. Anderson

S. Andrean

A. Andreazza

S. Angelidakis

A. Angerami

A. Anisenkov

A. Annovi

A precise measurement of the jet energy scale derived from single-particle measurements and in situ techniques in proton–proton collisions at $$\sqrt{s}=$$ 13 TeV with the ATLAS detector

We perform a rigorous analysis of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math> scattering at an unphysical pion mass 391 MeV using the Roy-Steiner equations, which satisfy unitarity, analyticity, and crossing symmetry, for the first time. Stable solutions of the Roy-Steiner equations with different quantum numbers of isospin and angular momentum are obtained in the elastic energy region, by taking inputs from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math> lattice data in the inelastic region, the lattice data from the crossed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi><mo stretchy="false">→</mo><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math> channels, the masses of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>500</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup></math> at the same pion mass from previous study, and the Regge model. Predictions on the elastic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math> scattering phase shifts and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>700</mn><mo stretchy="false">)</mo></math> pole content are made. Contrary to the virtual pole scenario obtained using the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math>-matrix method in the literature, we find that lightest strange scalar meson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow><mrow><mo>*</mo></mrow></msubsup><mo stretchy="false">(</mo><mn>700</mn><mo stretchy="false">)</mo></mrow></math> remains a broad resonance at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>=</mo><mn>391</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. The cross-channel dynamics is found to play a crucial role in deriving the proper pole position.

Xiong-Hui Cao

Feng-Kun Guo

Zhi-Hui Guo

Qu-Zhi Li

Rigorous Roy-Steiner equation analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math> scattering at unphysical quark masses

In this work, real photon production scattering kernels from jet-medium interactions in the QCD medium are perturbatively calculated using the higher-twist (HT) formalism. Focus is given towards real photon production from a highly virtual (and highly energetic) quark, taking into account heavy-quark mass scales [<a href="http://dx.doi.org/10.1103/PhysRevC.94.054902">Phys. Rev. C 94, 054902 (2016)</a>], fermion-boson conversion processes [<a href="http://dx.doi.org/10.1016/j.nuclphysa.2007.06.009">Nucl. Phys. A 793, 128 (2007)</a>], as well as coherence effects [<a href="http://dx.doi.org/10.1103/PhysRevC.105.024908">Phys. Rev. C 105, 024908 (2022)</a>]. A generalized factorization procedure, such as that used in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>e</mi><mtext>−</mtext><mi>A</mi></mrow></math> deep-inelastic scattering, is employed to derive an improved single-scattering medium-induced photon emission kernels that go beyond the traditional in-medium gluon exchange approximation. Diagrams with real-photon emission from the hard quark are classified based on the final-state particles, and include two types of scattering kernels at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>O</mi><mo>(</mo><msub><mi>α</mi><mi>em</mi></msub><msub><mi>α</mi><mi>s</mi></msub><mo>)</mo></mrow></math> giving the following final states: (i) real photon and real quark, (ii) real photon and real gluon. The collisional kernels, thus derived, include full phase factors from all nonvanishing diagrams and complete second-order derivative terms in the transverse momentum gradient expansion. Moreover, the calculation includes heavy-quark mass effects, thus exploring heavy-quark energy loss. The in-medium parton distribution functions and the related jet transport coefficients have a hard transverse momentum dependence (of the emitted gluon or photon) present within the phase factor. It is observed that the jet transport coefficients resemble the transverse-momentum-dependent parton distribution functions.

Amit Kumar

Gojko Vujanovic

Bremsstrahlung photon contributions to parton energy loss at high virtuality <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>Q</mi><mn>2</mn></msup></math>: A perturbative calculation at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>O</mi><mo>(</mo><msub><mi>α</mi><mi>s</mi></msub><msub><mi>α</mi><mtext>em</mtext></msub><mo>)</mo></mrow></math>

This paper presents the primary charged-particle multiplicity distributions in proton–lead collisions at a centre-of-mass energy per nucleon–nucleon collision of $$\sqrt{s_{\textrm{NN}}}~=~5.02$$ TeV. The distributions are reported for non-single diffractive collisions in different pseudorapidity ranges. The measurements are performed using the combined information from the Silicon Pixel Detector and the Forward Multiplicity Detector of ALICE. The multiplicity distributions are parametrised with a double negative binomial distribution function which provides satisfactory descriptions of the distributions for all the studied pseudorapidity intervals. The data are compared to models and analysed quantitatively, evaluating the first four moments (mean, standard deviation, skewness, and kurtosis). The shape evolution of the measured multiplicity distributions is studied in terms of KNO variables and it is found that none of the considered models reproduces the measurements. This paper also reports on the average charged-particle multiplicity, normalised by the average number of participating nucleon pairs, as a function of the collision energy. The multiplicity results are then compared to measurements made in proton–proton and nucleus–nucleus collisions across a wide range of collision energies.

S. Acharya

India

A. Agarwal

G. Rinella

L. Aglietta

M. Agnello

N. Agrawal

Z. Ahammed

S. Ahmad

South Korea

S. Ahn

Slovakia

I. Ahuja

A. Akindinov

V. Akishina

M. Al-Turany

D. Aleksandrov

B. Alessandro

H. Alfanda

Mexico

R. Molina

A. Alici

N. Alizadehvandchali

A. Alkin

J. Alme

G. Alocco

T. Alt

A. Altamura

I. Altsybeev

J. Alvarado

M. Anaam

C. Andrei

N. Andreou

A. Andronic

E. Andronov

V. Anguelov

F. Antinori

P. Antonioli

N. Apadula

H. Appelshäuser

C. Arata

S. Arcelli

R. Arnaldi

J. Arneiro

I. Arsene

M. Arslandok

A. Augustinus

R. Averbeck

D. Averyanov

M. Azmi

H. Baba

A. Badalà

J. Bae

Y. Bae

Y. Baek

X. Bai

R. Bailhache

Charged-particle multiplicity distributions over a wide pseudorapidity range in p–Pb collisions at $$\sqrt{{{\varvec{s}}}_{{\textbf {NN}}}}={\textbf {5.02}}$$ TeV