We present a method for obtaining an initial-state parton shower model where the (backward) evolution fully consistent with the (forward) evolution of the collinear parton density used. As a proof-of-concept we use parton densities obtained with the parton branching (PB) approach, and modify the default initial-state shower in 8 with this method to be consistent with them. PB is ideally suited for checking the validity of our method since, in addition to producing collinear parton densities, it also produces the corresponding transverse-dependent (TMD) ones, and these can then be directly compared to the transverse momentum distribution obtained from the parton shower. We show that TMD distributions which we in this way obtain from our modified 8 shower using leading order (LO) parton densities and splitting functions are fully consistent with the corresponding leading order TMD densities. At next-to-leading order (NLO) it is not possible to achieve the same consistency using the built-in LO splitting functions in the shower, but we show that by introducing NLO splitting functions using a reweighting procedure, we can achieve consistency also at NLO. The method presented here, which we have named , can be easily extended to any collinear parton densities, as long as the exact conditions for the evolution are known. With the method we obtain an initial-state parton shower which in principle has no free parameters, and is fully consistent with collinear parton densities at LO and NLO.

Germany

H. Jung

Sweden

L. Lönnblad

M. Mendizabal

Sara Taheri Monfared

A parton shower consistent with parton densities at LO and NLO:

In this paper, we explore the properties of the Ellis-Jaffe Sum Rule (EJSR) by employing the Principle of Maximum Conformality (PMC) approach to address its perturbative part up to next-to-next-to-next-to-leading order ( <math altimg='si1.svg'><msup><mrow><mi mathvariant='normal'>N</mi></mrow><mrow><mn mathvariant='normal'>3</mn></mrow></msup><mi mathvariant='normal'>LO</mi></math>) QCD contributions. By applying the PMC, we achieve a precise perturbative QCD prediction for the EJSR, free from conventional ambiguities associated with the renormalization scale choices. Considering the presence of the <math altimg='si2.svg'><msub><mrow><mi>&#945;</mi></mrow><mrow><mi>s</mi></mrow></msub></math> Landau pole near the asymptotic scale, we incorporate the low-energy <math altimg='si2.svg'><msub><mrow><mi>&#945;</mi></mrow><mrow><mi>s</mi></mrow></msub></math> model based on analytic perturbation theory (APT) to refine the EJSR behavior in the infrared region. By combining the PMC approach with the low-energy APT model, the agreement between theoretical calculations and experimental measurements of EJSR is significantly improved, as evidenced by the reduced discrepancy from <math altimg='si3.svg'><msup><mrow><mi>&#967;</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy='false'>/</mo><mi>d</mi><mo>.</mo><mi>o</mi><mo>.</mo><mi>f</mi><msub><mrow><mo stretchy='false'>|</mo></mrow><mrow><mi mathvariant='normal'>Conv</mi><mo>.</mo></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>1.86</mn></math> to <math altimg='si4.svg'><msup><mrow><mi>&#967;</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy='false'>/</mo><mi>d</mi><mo>.</mo><mi>o</mi><mo>.</mo><mi>f</mi><msub><mrow><mo stretchy='false'>|</mo></mrow><mrow><mi mathvariant='normal'>PMC</mi></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>1.19</mn></math>, thereby validating the effectiveness of our approach.

China

Hua Zhou

Qing Yu

Xing-Gang Wu

Updated determination of Ellis-Jaffe sum rules up to N <sup>3</sup>LO QCD corrections

We discuss the modeling of the hadronic phase of QCD at finite magnetic field in the framework of hadron resonance gas (HRG). We focus on the statistical description of particle yields that include contribution from resonance decays. We demonstrate that the swift increase in the number of protons with magnetic field predicted in the HRG is due to the assumption of structureless resonances. We discuss fluctuations of conserved charges and show that at present the qualitative comparison of the model predictions with the lattice QCD data should be treated with care. We also discuss the principle of detailed balance which allows us to study the magnetic field dependence of neutral resonances.

Poland

Michał Marczenko

Michał Szymański

Pok Man Lo

Bithika Karmakar

Pasi Huovinen

Japan

Chihiro Sasaki

Krzysztof Redlich

Magnetic effects in the hadron resonance gas

We evaluate all nuclear matrix elements (NMEs) up to next-to-next-to leading order (N$^{2}$LO) in chiral effective field theory (χEFT) for the neutrinoless double-beta (<math><mn>0</mn><mi>ν</mi><mi>β</mi><mi>β</mi></math>) decay of the nuclei most relevant for experiments, including $^{76}$Ge, $^{100}$Mo, and $^{136}$Xe. We use the proton-neutron quasiparticle random-phase approximation (pnQRPA) and the nuclear shell model to calculate the N$^{2}$LO NMEs from very low-momentum (ultrasoft) neutrinos and from loop diagrams usually neglected in <math><mn>0</mn><mi>ν</mi><mi>β</mi><mi>β</mi></math> studies. Our results indicate that the overall N$^{2}$LO contribution is centered around <math><mo>−</mo><mo>(</mo><mn>5</mn></math>-<math><mn>10</mn><mo>)</mo><mtext>%</mtext></math> for the shell model and <math><mo>+</mo><mo>(</mo><mn>10</mn></math>-<math><mn>15</mn><mo>)</mo><mtext>%</mtext></math> for the pnQRPA, with sizable uncertainties due to the scale dependence of the ultrasoft NMEs and the short-range nature of the loop NMEs. The sign discrepancy between many-body methods is common to all studied nuclei and points to the different behavior of the intermediate states of the <math><mn>0</mn><mi>ν</mi><mi>β</mi><mi>β</mi></math> decay. Within uncertainties, our results for the ultrasoft NME are of similar size as contributions usually referred to as “beyond the closure approximation”.

Spain

Daniel Castillo

Canada

Lotta Jokiniemi

Pablo Soriano

Javier Menéndez

Neutrinoless decay nuclear matrix elements complete up to N LO in heavy nuclei

We investigate the effect of screening of the four-quarks contact interactions by the ring diagram at finite temperature and density in an effective chiral model inspired by QCD in the Coulomb gauge. As a consequence, a medium-dependent coupling naturally emerges which, in a class of chiral models, brings the chiral crossover temperature down to the value calculated in lattice QCD at low net-baryon density. Furthermore, it implies a stronger divergence of the chiral susceptibility at the critical point compared to the mean-field dynamics. At high densities, the screening induces a substantial instability region and its size depends on the regularization schemes. We discuss the properties of an effective potential for a class of models described by momentum-independent gap equations. In particular, we introduce the method to construct an approximate effective potential from the gap equations to determine the location of the first-order phase transition.

Influence of dynamical screening of four-quarks interaction on the chiral phase diagram

We present the first determination of the value of the strong coupling via a simultaneous global fit of the proton parton distribution functions (PDFs) at approximate  $$\textrm{N}^3$$  <math> <msup> <mtext>N</mtext> <mn>3</mn> </msup> </math>  LO (a $$\textrm{N}^3$$  <math> <msup> <mtext>N</mtext> <mn>3</mn> </msup> </math>  LO) order in QCD. This makes use of the MSHT global PDF fitting framework, and in particular the recent theoretical advances t l;;mhat allow a PDF fit to now be performed at this order. The value of the strong coupling is found to be  $$\alpha _{S}(M_Z^2)(\mathrm{aN^3LO}) = 0.1170 \pm 0.0016$$  <math> <mrow> <msub> <mi>α</mi> <mi>S</mi> </msub> <mrow> <mo>(</mo> <msubsup> <mi>M</mi> <mi>Z</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <msup> <mi>aN</mi> <mn>3</mn> </msup> <mi>LO</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.1170</mn> <mo>±</mo> <mn>0.0016</mn> </mrow> </math>  . This is in excellent agreement with the NNLO value of  $$ \alpha _{S}(M_Z^2)(\textrm{NNLO}) = 0.1171 \pm 0.0014$$  <math> <mrow> <msub> <mi>α</mi> <mi>S</mi> </msub> <mrow> <mo>(</mo> <msubsup> <mi>M</mi> <mi>Z</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mtext>NNLO</mtext> <mo>)</mo> </mrow> <mo>=</mo> <mn>0.1171</mn> <mo>±</mo> <mn>0.0014</mn> </mrow> </math>  , indicating that good perturbative convergence has been found. The resulting uncertainties, calculated using the MSHT dynamic tolerance procedure, are somewhat larger, but more accurate, at a $$\textrm{N}^3$$  <math> <msup> <mtext>N</mtext> <mn>3</mn> </msup> </math>  LO, due to the missing higher order theoretical uncertainties that are included at this order, but not at NNLO. We in addition present a detailed breakdown of the individual dataset sensitivity to the value of the strong coupling, with special focus on the impact of fitting dijet rather than inclusive jet data. This choice is found to have a non-negligible impact, but with overall good consistency found, especially at a $$\textrm{N}^3$$  <math> <msup> <mtext>N</mtext> <mn>3</mn> </msup> </math>  LO.

T. Cridge

United Kingdom

L. Harland-Lang

R. Thorne

A first determination of the strong coupling  $$\alpha _S$$  <math> <msub> <mi>α</mi> <mi>S</mi> </msub> </math>   at approximate  $$\textrm{N}^3$$  <math> <msup> <mtext>N</mtext> <mn>3</mn> </msup> </math>  LO order in a global PDF fit

We study the transverse momentum (<math><msub><mi>q</mi><mi>T</mi></msub></math>) spectrum of the Higgs boson produced via the annihilation of massive quarks (<math><mrow><mi>s</mi></mrow></math>, <math><mrow><mi>c</mi></mrow></math>, <math><mrow><mi>b</mi></mrow></math>) in proton-proton collisions. Using soft-collinear effective theory (SCET) and working in the five-flavor scheme, we provide predictions at three-loop order in resummed perturbation theory (<math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>L</mi><msup><mrow><mi>L</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></math>). We match the resummed calculation to full fixed-order results at next-to-next-to-leading order (NNLO), and introduce a decorrelation method to enable a consistent matching to an approximate <math><msup><mi>N</mi><mn>3</mn></msup><mi>LO</mi></math> (<math><msup><mi>aN</mi><mn>3</mn></msup><mi>LO</mi></math>) result. Since the <math><mi>b</mi></math>-quark initiated process exhibits large nonsingular corrections, it requires special care in the matching procedure and estimation of associated theoretical uncertainties, which we discuss in detail. Our results constitute the most accurate predictions to date for these processes in the small <math><msub><mi>q</mi><mi>T</mi></msub></math> region and could be used to improve the determination of Higgs Yukawa couplings from the shape of the measured Higgs <math><msub><mi>q</mi><mi>T</mi></msub></math> spectrum.

Pedro Cal

Rebecca von Kuk

Matthew A. Lim

Frank J. Tackmann

<math><msub><mi>q</mi><mi>T</mi></msub></math> spectrum for Higgs boson production via heavy quark annihilation at <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msup><msup><mrow><mi>LL</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>+</mo><msup><mrow><mi>aN</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>LO</mi></mrow></math>

We present NNPDF4.0MC, a variant of the NNPDF4.0 set of parton distributions (PDFs) at LO, NLO and NNLO, with and without inclusion of the photon PDF, suitable for use with Monte Carlo (MC) event generators, which require PDFs to satisfy additional constraints in comparison to standard PDF sets. These requirements include PDF positivity down to a low scale Q ~ 1 GeV, smooth extrapolation in the very small and large x regions, and numerically stable results even in extreme regions of phase space for all PDFs. We compare the NNPDF4.0MC PDFs to their baseline NNPDF4.0 counterparts, and to the NNPDF2.3LO set entering the Monash tune of the Pythia8 event generator. We briefly assess the phenomenological impact of these PDFs on the cross-sections for hard and soft QCD processes at the LHC.

CERN

Juan Cruz-Martinez

Italy

Stefano Forte

Niccolò Laurenti

Netherlands

Tanjona Rabemananjara

Juan Rojo

LO, NLO, and NNLO parton distributions for LHC event generators

We extend the existing leading (LO), next-to-leading (NLO), and next-to-next-to-leading order (NNLO) NNPDF4.0 sets of parton distribution functions (PDFs) to approximate next-to-next-to-next-to-leading order ( $$\hbox {aN}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>aN</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>  ). We construct an approximation to the  $$\hbox {N}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>N</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   splitting functions that includes all available partial information from both fixed-order computations and from small and large x resummation, and estimate the uncertainty on this approximation by varying the set of basis functions used to construct the approximation. We include known  $$\hbox {N}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>N</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   corrections to deep-inelastic scattering structure functions and extend the FONLL general-mass scheme to  $$\mathcal {O}\left( \alpha _s^3\right) $$  <math> <mrow> <mi>O</mi> <mfenced> <msubsup> <mi>α</mi> <mi>s</mi> <mn>3</mn> </msubsup> </mfenced> </mrow> </math>   accuracy. We determine a set of  $$\hbox {aN}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>aN</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   PDFs by accounting both for the uncertainty on splitting functions due to the incomplete knowledge of  $$\hbox {N}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>N</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   terms, and to the uncertainty related to missing higher corrections (MHOU), estimated by scale variation, through a theory covariance matrix formalism. We assess the perturbative stability of the resulting PDFs, we study the impact of MHOUs on them, and we compare our results to the  $$\hbox {aN}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>aN</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   PDFs from the MSHT group. We examine the phenomenological impact of  $$\hbox {aN}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>aN</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   corrections on parton luminosities at the LHC, and give a first assessment of the impact of  $$\hbox {aN}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>aN</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   PDFs on the Higgs and Drell–Yan total production cross-sections. We find that the  $$\hbox {aN}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>aN</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   NNPDF4.0 PDFs are consistent within uncertainties with their NNLO counterparts, that they improve the description of the global dataset and the perturbative convergence of Higgs and Drell–Yan cross-sections, and that MHOUs on PDFs decrease substantially with the increase of perturbative order.

Richard Ball

Andrea Barontini

Alessandro Candido

Stefano Carrazza

Luigi Del Debbio

Tommaso Giani

Finland

Felix Hekhorn

Zahari Kassabov

Giacomo Magni

Emanuele Nocera

Christopher Schwan

Roy Stegeman

Maria Ubiali

The path to  $$\hbox {N}^3\hbox {LO}$$  <math> <mrow> <msup> <mtext>N</mtext> <mn>3</mn> </msup> <mtext>LO</mtext> </mrow> </math>   parton distributions

In this paper, we analyze the top-quark decay <math><mi>t</mi><mo>→</mo><mi>W</mi><mi>b</mi></math> up to next-to-next-to-next-to-leading order (<math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>LO</mi></mrow></math>) QCD corrections. For the purpose, we first adopt the principle of maximum conformality (PMC) to deal with the initial perturbative QCD (pQCD) series. Then we adopt the Bayesian analysis approach, which quantifies the unknown higher-order terms’ contributions in terms of a probability distribution, to estimate the possible magnitude of the uncalculated <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>4</mn></mrow></msup><mi>LO</mi></mrow></math> terms. In our calculation, an effective strong coupling constant <math><mrow><msub><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>(</mo><msub><mrow><mi>Q</mi></mrow><mrow><mo>*</mo></mrow></msub><mo>)</mo></mrow></math> is determined by using all nonconformal <math><mo>{</mo><msub><mi>β</mi><mi>i</mi></msub><mo>}</mo></math> terms associated with the renormalization group equation. This leads to a next-to-leading-log PMC scale <math><msubsup><mi>Q</mi><mo>*</mo><mrow><mo>(</mo><mi>NLL</mi><mo>)</mo></mrow></msubsup><mo>=</mo><mn>10.3048</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, which can be regarded as the correct momentum flow of the process. Consequently, we obtain an improved scale-invariant pQCD prediction for the top-quark decay width, e.g., <math><msubsup><mi>Γ</mi><mi>t</mi><mrow><mi>tot</mi></mrow></msubsup><mo>=</mo><mn>1.3120</mn><mo>±</mo><mn>0.0038</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, whose error is the squared average of the uncertainties from the decay width of <math><mi>W</mi></math>-boson <math><mi>Δ</mi><msub><mi>Γ</mi><mi>W</mi></msub><mo>=</mo><mo>±</mo><mn>0.042</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, the coupling constant <math><mi>Δ</mi><msub><mi>α</mi><mi>s</mi></msub><mo>(</mo><msub><mi>m</mi><mi>Z</mi></msub><mo>)</mo><mo>=</mo><mo>±</mo><mn>0.0009</mn></math>, and the predicted <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>4</mn></mrow></msup><mi>LO</mi></mrow></math>-terms. The magnitude of the top-quark pole mass greatly affects the total decay width. By further taking the PDG top-quark pole mass error from cross-section measurements into consideration, e.g., <math><mi>Δ</mi><msub><mi>m</mi><mi>t</mi></msub><mo>=</mo><mo>±</mo><mn>0.7</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, we obtain <math><msubsup><mi>Γ</mi><mi>t</mi><mrow><mi>tot</mi></mrow></msubsup><mo>=</mo><mn>1.312</mn><msubsup><mn>0</mn><mrow><mo>−</mo><mn>0.0192</mn></mrow><mrow><mo>+</mo><mn>0.0194</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>.

Jiang Yan

Hong-Tai Li

Jing-Hao Shan

Improved analysis of the decay width of <math><mrow><mi>t</mi><mo>→</mo><mi>W</mi><mi>b</mi></mrow></math> up to <math><mrow><msup><mi>N</mi><mn>3</mn></msup><mi>LO</mi></mrow></math> QCD corrections