In these conference proceedings, we discuss recent progress in high-order perturbative studies of the thermodynamic and transport properties of dense quark matter. Special emphasis will be placed in the introduction of a promising new computational tool, thermal Loop Tree Duality, which enables pushing the existing weak-coupling calculations to higher perturbative orders.

A bstract We compute the contributions of heavy quarks to the deep-inelastic scattering structure functions F 4 and F 5 at next-to-leading order of perturbative QCD in the ACOT scheme. Both analytic results including the details of the calculation as well as numerical results for the neutral and charged current cases are presented. Our study thus lays the groundwork for future measurements of these two structure functions in experiments such as the SHiP experiment.

A measurement oftt¯production is presented in the invariant-mass region near the pair production threshold,mtt¯∼345 GeV, in final states with two charged leptons and multiple jets. The measurement is based on140fb-1of proton-proton collision data collected ats=13 TeV with the ATLAS detector at the Large Hadron Collider. The data are compared to two models oftt¯production: a baseline model including only perturbative quantum chromodynamics (pQCD) predictions for the hard process at approximate next-to-next-to leading order accuracy in the strong coupling, and an extended model that, in addition, incorporates non-relativistic QCD simulations that also include the formation of colour-singlet quasi-bound-states near thett¯threshold. The agreement between the data and the models is quantified via a profile-likelihood fit to the reconstructedmtt¯distributions, in bins of two angular observables sensitive to spin-correlations in thett¯system. An excess of events is observed over the baseline pQCD prediction, with an observed significance over 8 standard deviations. This excess is consistent with the formation of colour-singlet and spin-singletS-wave quasi-boundtt¯states, as predicted by non-relativistic QCD, and corresponds to an observed cross-section of9.3-1.3+1.4 pb.

Beyond leading order, perturbative QCD calculations require the choice of a factorisation scheme to define the coefficient functions and parton distribution functions. Through the years, a number of different schemes were proposed, with different motivations and purposes. We present the first-ever comparison of these factorisation schemes on a common basis. We compare their features, both at the analytical and numerical level, and assess the impact of this choice on phenomenology at the LHC. Abstract Published by the Jagiellonian University 2026 authors

In this paper, we investigate the Quantum Chromodynamics (QCD)-like running coupling, αsAdS(Q2), and its associated β-function within a tachyonic Anti-de Sitter (AdS)/QCD framework. The AdS5 bulk geometry is deformed through the introduction of a color dielectric function G(ϕ(z)), associated with a tachyon field ϕ(z). This function governs the behavior of αsAdS(Q2) across all momentum scales by modifying the AdS background at both small and large values of the holographic coordinate z. In the ultraviolet (UV) regime (small z), the deformation is driven by free tachyons and reproduces features consistent with perturbative QCD. In contrast, in the infrared (IR) regime (large z), tachyon condensation dominates, yielding behavior characteristic of nonperturbative QCD. This construction enables a unified description of the running coupling and its β-function over the full range of momentum transfer Q2, where Q2 denotes the space-like momentum scale.

A bstract A measurement of the substructure of bottom quark jets (b jets) in proton-proton (pp) collisions is presented. The measurement uses data collected in pp collisions at $$ \sqrt{s}=5.02 $$ s = 5.02 TeV, with a low number of simultaneous interactions per bunch crossing, recorded by the CMS experiment in 2017, corresponding to an integrated luminosity of 301 pb − 1 . An algorithm to identify and cluster the charged decay daughters of b hadrons is developed for this analysis, which facilitates the exposure of the gluon radiation pattern of b jets using iterative Cambridge-Aachen declustering. The soft-drop-groomed jet radius, R g , and momentum balance, z g , of b quark jets are presented. These observables can be used to test perturbative quantum chromodynamics predictions that account for mass effects. Because the b hadron is partially reconstructed from its charged decay daughters, only charged particles are used for the jet substructure studies. In addition, a jet fragmentation function, z b,ch , is measured, which is defined as the distribution of the ratio of the transverse momentum ( p T ) of the partially reconstructed b hadron with respect to the charged-particle component of the jet p T . The substructure variable distributions are unfolded to the charged-particle level. The b jet substructure is compared to the substructure of jets in an inclusive jet sample that is dominated by light-quark and gluon jets in order to assess the role of the b quark mass. A strong suppression of emissions at small R g values is observed for b jets when compared to inclusive jets, consistent with the dead-cone effect. The measurement is also compared with theoretical predictions from Monte Carlo event generators. This is the first substructure measurement of b jets that clusters together the b hadron decay daughters independent of the b hadron species and decay channel.

A bstract We consider dijet production in e + e − collisions and in $$ H\to b\overline{b} $$ H → b b ¯ decays at next-to-next-to-leading order (NNLO) in perturbative QCD. A new non-local subtraction scheme is applied, for the first time, to obtain the fully differential cross section for these benchmark processes. We discuss and explicitly evaluate the perturbative ingredients needed in the computation, and we compare the performance of different slicing variables to obtain the NNLO corrections.

This Letter reports the first measurement of photonuclear D^{0} meson production in ultraperipheral heavy ion collisions. The study is performed using lead-lead collision data, with an integrated luminosity of 1.34 nb^{-1}, collected by the CMS experiment at a nucleon-nucleon center-of-mass energy of 5.36TeV. Photonuclear events, where one of the colliding nuclei breaks up and the other remains intact, are selected based on breakup neutron emissions and by requiring no particle activity in a large rapidity interval in the direction of the photon-emitting nucleus. The D^{0} mesons are reconstructed via the D^{0}→K^{-}π^{+} decay channel, with the cross section measured as a function of D^{0} meson transverse momentum and rapidity. The results are compared with next-to-leading-order perturbative QCD calculations that employ recent parametrizations of the lead nuclear parton distribution functions, as well as with predictions based on the color glass condensate framework. This measurement is the first photonuclear collision study characterizing parton distribution functions of lead nuclei for parton fractional momenta x (relative to the nucleon) ranging approximately from a few 10^{-4} to 10^{-2} for different hard energy scale Q^{2} selections.

Abstract We present the first high-twist study of the proton form factors $$F_{1,2}(Q^2)$$ F 1 , 2 ( Q 2 ) in ep elastic scattering based on the perturbative QCD $$k_T$$ k T factorization, $$Q^2$$ Q 2 being momentum transfer squared. It is motivated by unexpectedly large higher-power contributions from subleading-twist light-cone distribution amplitudes (LCDAs), which are attributed to the enhancement in endpoint regions of parton momentum fractions. We highlight that the endpoint enhancement, tamed by the $$k_T$$ k T resummation effect, is crucial for accommodating the approximate scaling behavior of the $$Q^4F_1(Q^2)$$ Q 4 F 1 ( Q 2 ) data at intermediate $$Q^2\sim \mathcal{O}(10)$$ Q 2 ∼ O ( 10 ) GeV $$^2$$ 2 . The proton LCDAs up to twist 6 are then extracted, and verified by the charge-parity asymmetries observed in hadronic heavy baryon decays. Our work provides new insights into the proton three-dimensional structure and manifests the precision requirement for reliable perturbative analyses of baryonic exclusive processes.

Abstract Rapid uniformly rotating neutron stars are expected to be formed, for instance, in the collapse of some massive stars, the accretion of compact object binaries, and double neutron star mergers. The huge amount of rotational energy has been widely believed to be the source of some cosmic gamma-ray bursts and superluminous supernovae. Benefiting from the constraints on the equation of state of the neutron star matter set by the latest multimessenger data, the chiral effective field theory, and perturbative quantum chromodynamics, here we present the maximum gravitational mass as well as the rotational energy for a neutron star at a given spin period. Our nonparametric equation-of-state analysis reveals that the critical Keplerian configurations ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="normal">Ω</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">kep</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">crit</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mn>1.0</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.07</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.06</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>×</mml:mo> <mml:mn>1</mml:mn> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.25em"/> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">rad</mml:mi> <mml:mspace width="0.25em"/> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> ) can sustain maximum gravitational masses of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi>kep</mml:mi> <mml:mi>crit</mml:mi> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mn>2.73</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.09</mml:mn> <mml:mspace width="0.25em"/> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:math> with the corresponding rotational energy reaching <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">rot</mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant="normal">kep</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">crit</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mn>2.3</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>6</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.22</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.24</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>×</mml:mo> <mml:mn>1</mml:mn> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>53</mml:mn> </mml:mrow> </mml:msup> </mml:math> erg. However, the maximum rotational energy that can be feasibly extracted from a neutron star is limited to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>1.4</mml:mn> <mml:msubsup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.13</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.14</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>×</mml:mo> <mml:mn>1</mml:mn> <mml:msup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>53</mml:mn> </mml:mrow> </mml:msup> </mml:math> erg, which holds for a baryon mass of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>2.6</mml:mn> <mml:msubsup> <mml:mn>6</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.09</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.10</mml:mn> </mml:mrow> </mml:msubsup> <mml:mspace width="0.25em"/> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:math> . All these parameters, obtained via the nonparametric reconstruction of the equation of state, are at the 68.3% confidence level, and the adoption of a quarkonic model yields rather similar results. These findings are found to have already set some intriguing constraints on the millisecond magnetar interpretation of some exciting data.

The energy density generated by a vector current is characterized by a single parameter a_{E} bounded by unitarity to -1/2≤a_{E}≤1, with extremal values saturated by free theories of different matter content. Through confinement, QCD transmutes fermionic matter into scalars, revealing a nontrivial flow between extremal correlators. We reconstruct this flow using perturbative QCD and chiral perturbation theory. The observable is accessible with currently available experimental data.

We use conformal symmetry to calculate the next to next to leading order (NNLO) anomalous dimension matrix (three loops) for flavor-singlet axial-vector QCD operators for spin <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>N</a:mi> <a:mo>≤</a:mo> <a:mn>8</a:mn> </a:math> from a set of gauge-invariant two-point correlation functions. Combining this result with the recent calculation of the two-loop coefficient functions, we carry out the calculation of the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>γ</c:mi> <c:msup> <c:mi>γ</c:mi> <c:mo>*</c:mo> </c:msup> <c:mo stretchy="false">→</c:mo> <c:mi>η</c:mi> </c:math> and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mi>γ</f:mi> <f:msup> <f:mi>γ</f:mi> <f:mo>*</f:mo> </f:msup> <f:mo stretchy="false">→</f:mo> <f:msup> <f:mi>η</f:mi> <f:mo>′</f:mo> </f:msup> </f:math> form factors at large momentum transfers to the NNLO accuracy in perturbative QCD.

Based on the (2712.4±14.4)×10^{6} ψ(3686) events collected with the BESIII detector, we present a high-precision study of the π^{+}π^{-} mass spectrum in ψ(3686)→π^{+}π^{-}J/ψ decays. A clear resonancelike structure is observed near the π^{+}π^{-} mass threshold for the first time. A fit with a Breit-Wigner function yields a mass of 285.6±2.5 MeV/c^{2} and a width of 16.3±0.9 MeV with a statistical significance exceeding 10σ. To interpret the data, we incorporate final-state interactions (FSI) within two theoretical frameworks: chiral perturbation theory (ChPT) and QCD multipole expansion (QCDME). ChPT describes the spectrum above 0.3 GeV/c^{2} but fails to reproduce the threshold enhancement. In contrast, the QCDME model-assuming the ψ(3686) is an admixture of S- and D-wave charmonium-reproduces the data well. The pronounced dip near 0.3 GeV/c^{2} offers new insight into the interplay between chiral dynamics and low-energy QCD.

A bstract We compute squared matrix elements at next-to-next-to-leading order in perturbative quantum chromodynamics for the production of two or three (on- or off-shell) photons mediated via (light or heavy) quark loops. Our method handles all cases in a unified framework, using simultaneous subtraction of infrared, ultraviolet, and threshold singularities in loop momentum space to produce a locally finite integrand suitable for numerical integration. We confirm agreement with available analytic benchmarks at fixed phase-space points and provide new results otherwise. We also compute the double-virtual corrections to the cross section for on- and off-shell diphoton and on-shell triphoton production by combining the Monte Carlo integration over loop and phase space.

A bstract We argue that collider observables such as hadron number flux can be matched onto a linear combination of detectors/light-ray operators in perturbative QCD. The spectrum of detectors in QCD is subtle, due to recombination between the DGLAP and BFKL trajectories. We explain how to define and renormalize these trajectories at one-loop, systematically incorporating their recombination. The leading and subleading soft gluon theorems play an important role, and our analysis suggests the presence of an infinite series of further subleading soft theorems for squared-amplitudes/form factors. Combined with our light-ray matching hypothesis, the anomalous dimensions of recombined DGLAP/BFKL detectors yield a prediction for the energy dependence of the number of particles in a jet, as well as other predictions for more general energy-weighted hadron measurements. We compare these predictions to Monte-Carlo simulations, finding good agreement.

A bstract At the Large Hadron Collider, the WbWb final state is expected to be dominated by $$ t\overline{t} $$ t t ¯ production with a contribution from single-top processes. Differential cross-sections for WbWb production in the dilepton decay channel are measured at the particle level as a function of various kinematic variables. The analysis is based on data from proton-proton collisions at a centre-of-mass energy of $$ \sqrt{s}=13 $$ s = 13 TeV, recorded by the ATLAS detector at the Large Hadron Collider over the period from 2015 to 2018, corresponding to an integrated luminosity of 140 fb − 1 . Measurements are performed within the fiducial phase-space defined by the presence of two b -jets and one electron and one muon of opposite charges. The differential cross-sections are corrected for detector effects and unfolded to the particle level. Results are compared with predictions from Monte Carlo event generators at next-to-leading order in perturbative quantum chromodynamics; overall the measurements are in reasonable agreement with several generator setups, although no single prediction is able to describe all measured distributions simultaneously. These measurements provide valuable constraints on the modelling of WbWb production and the interference between doubly resonant and singly resonant WbWb production.

Abstract The determination of whether the ground state of baryon matter in Quantum Chromodynamics (QCD) is the ordinary nucleus or a quark matter state remains a long-standing question in physics. A critical parameter in this investigation is the bag parameter B , which quantifies the QCD vacuum energy and can be computed using nonperturbative methods such as Lattice QCD (LQCD). By combining the equation of state derived from perturbative QCD (pQCD) with the bag parameter to fit the LQCD-simulated data for isospin-dense matter, we address the stability of quark matter within the LQCD+pQCD framework. Our findings suggest that the current data imposes an upper bound on $$B^{1/4} \lesssim 160$$ B 1 / 4 ≲ 160 MeV, approaching a conclusive statement on quark matter stability. Given the lower bound on B from the quark condensate contribution to the vacuum energy, the stable 2-flavor quark matter remains possible, whereas the stable 2+1-flavor quark matter is excluded, assuming complete deconfinement and chiral-symmetry restoration and the reliability of pQCD at baryon chemical potentials around the proton mass. Additionally, we derive more general thermodynamic bounds on the quark matter energy-per-baryon and B , which, while weaker, provide complementary insights.

As an extension of our prior work, we analyze the resonance contributions for the kaon pair originating from the intermediate , , and their excited states in the three-body decays within the perturbative quantum chromodynamics approach. The information of subprocesses and are included in the distribution amplitudes for the system using the kaon vector time-like form factors. We calculate the charge-conjugation parity (CP)-averaged branching fractions and direct CP asymmetries for the relevant quasi-two-body B meson decays. The branching fractions of the virtual contributions for from the Breit-Wigner formula tails of and for these decays are found comparable to the corresponding contributions from the resonances and . Consequently, they comprise a significant component that should be accounted for in the considered three-body decays. All predictions in this work are expected to be tested by the LHCb and Belle-II experiments in future.

We consider the most general form of soft and collinear factorization for hard-scattering amplitudes to all orders in perturbative quantum chromodynamics. Specifically, we present the generalization of collinear factorization to configurations with several collinear directions, where the most singular behavior is encoded by generalized collinear splitting amplitudes that manifestly embed the breaking of strict collinear factorization in spacelike collinear configurations. We also extend the analysis to the simultaneous soft-collinear factorization with multiple collinear directions where naive multiplicative factorization does not hold. As an illustrative example of factorization breaking, we present explicit results at the one-loop level in the soft-collinear limit.

The Collins-Soper (CS) kernel governs the rapidity evolution of transverse-momentum-dependent (TMD) parton distributions, a cornerstone for QCD factorization and linking nucleon structure data across scales. Its nonperturbative behavior at large transverse separations ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>b</a:mi> <a:mo>⊥</a:mo> </a:msub> </a:math> ) remains weakly constrained due to phenomenological model dependencies. We present a first-principles determination of the CS kernel at the continuum limit and physical pion mass from lattice QCD in the large-momentum effective theory framework. Using ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mn>2</c:mn> <c:mo>+</c:mo> <c:mn>1</c:mn> </c:mrow> </c:math> )-flavor configurations (lattice spacings <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>a</e:mi> <e:mo>∈</e:mo> <e:mo stretchy="false">[</e:mo> <e:mn>0.052</e:mn> <e:mo>,</e:mo> <e:mn>0.105</e:mn> <e:mo stretchy="false">]</e:mo> <e:mtext> </e:mtext> <e:mtext> </e:mtext> <e:mi>fm</e:mi> </e:math> , and pion mass <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msub> <i:mi>m</i:mi> <i:mi>π</i:mi> </i:msub> <i:mo>≈</i:mo> <i:mo stretchy="false">(</i:mo> <i:mn>136</i:mn> <i:mo>,</i:mo> <i:mn>230</i:mn> <i:mo>,</i:mo> <i:mn>300</i:mn> <i:mo>,</i:mo> <i:mn>320</i:mn> <i:mo stretchy="false">)</i:mo> <i:mtext> </i:mtext> <i:mtext> </i:mtext> <i:mi>MeV</i:mi> </i:math> ), we simulating the nonlocal equal-time correlation function and extract the quasi-TMD wave functions. Taking into account systematic improvements including hypercubic smearing, nonperturbative renormalization, and a <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msub> <m:mi>b</m:mi> <m:mo>⊥</m:mo> </m:msub> </m:math> -unexpanded matching kernel, we obtain the CS kernel at the continuum, chiral, and infinite-momentum limits. Our results are determined up to <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>b</o:mi> <o:mo>⊥</o:mo> </o:msub> <o:mo>∼</o:mo> <o:mn>1</o:mn> <o:mtext> </o:mtext> <o:mtext> </o:mtext> <o:mi>fm</o:mi> </o:math> , with controllable uncertainties, and agree with perturbative QCD at small <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msub> <q:mi>b</q:mi> <q:mo>⊥</q:mo> </q:msub> </q:math> and global TMD phenomenological extractions. We conduct a global analysis integrated with phenomenological fits and demonstrate the impact of our results on such fits. This work yields the most precise nonperturbative constraint on the CS kernel’s long-distance behavior from lattice QCD, which not only bridges lattice QCD, perturbation theory, and nucleon structure experiments for TMD studies, but also boosts the utility of our constraint for future global TMD analyses.