Papers

Many experiments have provided possible hints of gluon saturation, including geometric scaling in deep inelastic scattering (DIS) at HERA, the suppression of forward particle yields in d+Au collisions relative to p+p collisions at RHIC, and the suppression of away-side peaks in di-hadron correlations at forward rapidities in proton-nucleus collisions at RHIC and the LHC. Previous studies within the Color Glass Condensate (CGC) framework have primarily focused on fits to HERA deep inelastic scattering data, using the resulting dipole amplitudes to predict hadronic observables in proton-nucleus and proton-proton collisions. A simultaneous fit of DIS and forward particle production data, and a systematic study of their interplay, has so far been absent. In the work presented here, we focus on two processes: inclusive DIS and forward single inclusive hadron production in p+p collisions, incorporating data from HERA, RHIC, and the LHC. We solve the Balitsky-Kovchegov (BK) small-x evolution equation and perform a global fit to the combined datasets. Our analysis accounts for uncertainties in fragmentation functions and provides final uncertainties for the fitted parameters. The outcomes demonstrate the potential of the CGC formalism to provide a universal description of these diverse processes at the level of the dipole amplitude. In these proceedings, after very briefly summarizing the setup and our results, we highlight one particular aspect of the analysis, namely the complete uncertainty treatment. We validated the final uncertainties with two independent methods: the Hessian method and the Bayesian inference method, finding very good agreement.

We compute the combinations $E_M=H^{u+d}+E^{u+d}$ and $H_E=H^{u-d}+tE^{u-d}/(4M_N^2)$ of unpolarized generalized parton distributions (GPDs) of the nucleon in the chiral quark soliton model at nonzero skewness $\xi$ and nonzero momentum transfer $t$. The combinations contain the GPDs $H^{u-d}$ and $E^{u+d}$, which are subleading in the expansion in the inverse number of colors. Both combinations are double sums over the quark states. A multipole expansion of the light-cone operators makes the sums computable at every $\xi$ and every $t\le0$. The contribution of the Dirac continuum is summed over the quark states, without an interpolation formula and without a gradient expansion. The first moments satisfy the form-factor sum rules, and the second moments satisfy polynomiality.

We present a complete analytic calculation of the next-to-leading-order (NLO) QCD cross sections for the production of an electroweak vector boson ($W^\pm$, $Z/\gamma^*$) at finite transverse momentum, decomposed into the full set of helicity cross sections that determine the angular coefficients $A_0$-$A_7$ of the lepton-pair angular distribution in the Collins-Soper frame. The calculation includes the unpolarised cross section and all eight helicity projections for both neutral- and charged-current Drell-Yan production, the axial quark-triangle contributions in the $m_t\to\infty$ limit and with full top-quark-mass dependence, and closed-form expressions for all coefficient functions. The results are implemented in the DYTurbo program and validated at the level of a few times $10^{-4}$ against its numerical implementation derived from MCFM, as well as through the analytic $q_T\to0$ limit. The analytic implementation achieves a speed-up of more than five orders of magnitude with respect to the numerical code, enabling fast and numerically stable predictions for precision electroweak measurements at the LHC. The calculation was carried out with extensive use of large language models (Anthropic Claude) as autonomous agents; we document the methodology and the associated computational and token budgets.

We investigate the structure of the pion in a magnetized nuclear medium at finite temperature by analyzing the in-medium modifications of its parton distribution functions (PDFs) and electromagnetic form factors (EMFFs). We use a unified framework combining the chiral SU(3) quark mean field (CQMF) model and the light-cone quark model (LCQM) where the in-medium quark masses are evaluated using the CQMF model and subsequently employed as inputs in the light-cone formalism. The study systematically explores the effects of magnetic field, baryon density, temperature, and isospin asymmetry on the pion structure. In addition, Dirac sea contributions are incorporated to account for vacuum polarization effects in the medium. Our results of PDFs and EMFFs provide valuable insights into the modification of pion properties under extreme conditions, highlighting the significant role of the surrounding medium in altering its internal structure.

We present nCTEQ26OHF, a global analysis of nuclear parton distribution functions (nPDFs) within the nCTEQ framework. In this analysis, constrasting the main nCTEQ26 release, we replace the Crystal-Ball function, an effective matrix element that is used in nCTEQ26 for open heavy-flavor (OHF) and quarkonium production, by an SACOT GM-VFNS calculation for the OHF predictions. The resulting nCTEQ26OHF PDFs are compatible with the nCTEQ26 PDFs within uncertainties, implying that the OHF data alone provide ample constraint.

Electroweak penguin $B$ decays with neutrinos or $\tau$ leptons in the final state are sensitive probes of physics beyond the Standard Model. Using the full Belle and Run 1 Belle II datasets, the first search for $B^0 \to K^0_S\tau^+\tau^-$ sets the upper limit on the branching fraction to $\mathcal{B} < 8.3 \times 10^{-4}$, the search for $B^+ \to K^+\tau^+\tau^-$ sets $\mathcal{B} < 5.6 \times 10^{-4}$, and their isospin combination gives $\mathcal{B}(B \to K\tau^+\tau^-) < 5.4 \times 10^{-4}$, all at 90% confidence level (CL$_s$). The first search for inclusive $B \to X_s\nu\bar\nu$ decays at Belle II sets $\mathcal{B} < 3.3 \times 10^{-4}$. Finally, the Belle II $B^+ \to K^+\nu\bar\nu$ result is reinterpreted in the Weak Effective Theory using its published likelihood. The data prefer an enhanced vector contribution and mildly favour a nonzero tensor contribution.

Coleman–De Luccia tunneling can exhibit an infinite tower of rapidly oscillating negative modes, complicating the semiclassical evaluation of the path integral. We show that this tower does not represent infinitely many bounce-specific instabilities, but instead is tied to a single underlying gravitational conformal sector. This sector is exposed in two different ways: by a large scalar gradient near the bubble wall and by the turning point of a compact Euclidean geometry. The corresponding conformal sector is already present in fluctuations about the false vacuum. Treating the bounce and the false vacuum in the same well-defined gauge and with a common regulator, we find that their high-frequency negative spectra approach one another. The ultraviolet tower therefore cancels from the relative negative-mode count, leaving a single bounce-specific negative mode. This finite-backreaction spectral cancellation provides a corresponding picture of the result obtained in the small-backreaction limit.

We infer the initial condition for the Balitsky-Kovchegov (BK) evolution equation at next-to-leading order accuracy from HERA proton structure function data. A simultaneous description of both the total cross section and charm production measurements is obtained. We then show that inclusive hadron production in deep inelastic scattering can provide complementary constraints on the non-perturbative initial condition of the BK equation. As a more differential observable, it serves as a sensitive probe of gluon saturation phenomena. We demonstrate this by calculating predictions for the nuclear modification factor in hadron production in photon-nucleus scattering at leading order in the dipole picture. We find that saturation effects lead to significant nuclear suppression at small $x_\mathrm{Bj}$.

We introduce the basics of Effective Field Theories, using the Standard Model Effective Field Theory as our central example. The first part of this chapter gives a pedagogical introduction to EFTs - including matching, resummation and the construction of an operator basis - with explicit examples and provides a starting point for newcomers. The second part reviews the current status of SMEFT and collects suitable references for those who want to go deeper.

The electron-positron Future Circular Collider will provide an unprecedented opportunity for precision studies at the $Z$ pole. In addition to improving the electroweak measurements pioneered at LEP, Tera-$Z$ statistics and modern jet flavor reconstruction could make rare, flavor-resolved final states accessible as precision observables. We study the exclusive four-body processes $e^+e^-\to Z\to Q\bar Q\ell^+\ell^-$ with $ Q=c,\,b$ and $\ell=\mu,\,\tau$ as probes of flavor-specific new physics contact interactions. A fast analysis yields representative multi-TeV reaches for vector-current interactions involving bottom or charm quarks and muons or taus, providing a baseline for future detector-level studies. For charm-current interactions, the projected direct sensitivities are comparable to those obtained indirectly from electroweak precision observables. Two-dimensional fits further show that these processes retain quark-flavor information that can be poorly resolved by the renormalization-group-induced electroweak response. These results illustrate how flavor-resolved four-body $Z$ processes can bridge the electroweak and flavor programs at FCC-ee, opening a new class of complementary precision observables.

The $J^{P}=2^{+}$ $cc\bar c\bar s$ and $bb\bar b\bar s$ tetraquarks are studied in parallel within the two-point QCD Sum Rules framework using the same symmetric axial-vector$\otimes$axial-vector interpolating current. The current-specific OPE sectors retained through dimension seven within the stated background-field truncation are evaluated with a common symbolic construction, with the bottom channel obtained by the heavy-flavour replacement $c\to b$. The same pole-dominance and OPE-convergence criteria are imposed in both channels. The adopted charm region is $\sqrt{s_0}=5.7\GeV$ with $3.6\le M_B^2\le4.3\GeVsq$, whereas the bottom region is $\sqrt{s_0}=14.3\GeV$ with $9.8\le M_B^2\le10.8\GeVsq$. At representative Borel points, the extracted masses are $5.239\GeV$ and $13.832\GeV$, respectively. After the QCD-input, continuum-threshold, and Borel-window variations are combined, the final results are $m_{cc\bar c\bar s,\,2^+}=5.239\pm0.061\GeV$ and $m_{bb\bar b\bar s,\,2^+}=13.832\pm0.059\GeV$.

New physics beyond the Standard Model (SM) may induce new four-fermion interactions. We investigate the sensitivity of radiative muon decay, $\mu^-\to e^-\bar\nu_e\nu_\mu\gamma$, to such four-fermion interactions of mass dimension seven and eight. For each operator, we calculate its interference with the SM amplitude and obtain an analytic expression for the decay rate. We apply these to a log-likelihood comparison for a benchmark sample of $10^5$ events, and find that these operator contributions can be distinguished from the SM prediction at characteristic coefficient magnitudes between $10^{-9}$ and $10^{-8}$.

The LUX-ZEPLIN (LZ) Collaboration has reported a nuclear-recoil candidate at $248\pm23~({\rm stat})\pm23~({\rm sys})~{\rm keV}$ in an extended high energy search window. We investigate whether this event can arise from the hyperfine excitation of hydrogen-like atomic dark matter. For a TeV-scale dark atom, a hyperfine splitting near $340~{\rm keV}$ places xenon scattering close to the observed value by naturally selecting the high-velocity tail of the Galactic halo while suppressing the leading low-energy elastic response. The resulting endothermic kinematics predict a pronounced target hierarchy: the benchmark transition is inaccessible on Ar and Ge, lies close to threshold on Xe, and remains open on heavier targets such as W, which is specific to our model parameters. Because xenon probes the extreme high-speed tail, the signal exhibits a large annual modulation and a strong dependence on the assumed halo distribution. We also examine how the infall of the Large Magellanic Cloud enhances the high-speed tail of the Milky Way's local dark matter distribution, extending the kinematic reach to larger hyperfine splittings.

A black hole growing adiabatically inside a dark matter halo is expected to develop a dense spike, with a power-law slope between 1.5 and 2.5, depending on redshift and baryonic activity. Direct dynamical tests of this prediction are almost non-existent. Here we show that water megamaser disks offer one; their masers orbit within a parsec of the black hole and are mapped individually with very long baseline interferometry, so the enclosed mass at each radius can be read off the rotation curve. We develop a search method and apply it to eleven megamaser disks with public kinematics. Compared with a black hole alone, a spike is preferred in NGC 1194 and NGC 4258 and moderately improves the fit in several others. Allowing the disks to warp removes this preference in all but NGC 4258 and NGC 6264. No combination of disks, warped or not, allows a spike heavier than about ten per cent of the black hole mass, a sensitivity validated with mock injection tests. Mapping the warps with maser accelerations and detecting fainter inner masers, where a spike and a tilt differ most, can break the remaining degeneracy. Megamaser disks open a window onto dark matter around supermassive black holes, and, importantly, one that enables population statistics.

In this work, we present for the first time, the simultaneous analysis of the non-standard neutrino interactions (NSI) and a light sterile neutrino in the 3+1 framework for the future long- and medium-baseline experiments DUNE and MOMENT, respectively. We show that treating the two sectors separately yields over optimistic sensitivities. The simultaneous presence of sterile-neutrino mixing and complex NSI weakens the $|\varepsilon_{e\mu}|$ sensitivity by a factor of $\sim (2-3)$ with the dominant degradation associated with the additional parameter freedom in the flavor-changing NSI sector. DUNE alone fails to achieve $5\sigma$ CP-violation discovery, once NSI phases are marginalized over. The DUNE+MOMENT combination recovers $>5\sigma$ sensitivity over a wide range of $\delta_{\rm CP}$ space, constrains $\sin^2\theta_{24}\lesssim10^{-2}$ and $|\varepsilon_{e\mu}|\lesssim0.025$ at $95\%$~C.L., and resolves degeneracies that are intractable for either experiment alone. Our results establish that a multi-baseline strategy combining matter-rich and near-vacuum baselines is necessary for robust parameter extraction in the simultaneous presence of two new physics scenarios. It is also important to perform simultaneous new physics analyses to reliably interpret future precision neutrino oscillation data.

Extracting the intrinsic transverse-momentum structure of quarks from deep-inelastic scattering data requires separating nonperturbative effects from perturbative radiation, which broadens the measured transverse-momentum distributions. We address this problem in electron–proton scattering, $ep\to eX$, by introducing the fiducial imbalance $\boldsymbol{q}_T$, defined as the vector sum of the scattered electron's transverse momentum and all hadronic transverse momenta within a specified rapidity window. This construction reduces radiative recoil without requiring jet reconstruction or an explicit jet veto. We account for non-global logarithms (NGLs) arising from correlated soft emissions across the acceptance boundary. The azimuthally averaged NGL contribution is resummed to all orders at leading-logarithmic accuracy in the large-$N_c$ limit using Banfi–Marchesini–Smye evolution, while the leading NGL correction to the first azimuthal harmonic is included at $\mathcal{O}(\alpha_s^2)$. For the EIC and EicC kinematics considered, widening the rapidity window increases the cross section at low $q_T$, a region particularly sensitive to nonperturbative transverse dynamics, and reduces the dilution of spin asymmetries by azimuthally symmetric soft recoil. Both the Sivers single-spin asymmetry $A_{UT}$ and the worm-gear double-spin asymmetry $A_{LT}$ increase in magnitude, while the $\boldsymbol{q}_T$ integrated cross section remains unchanged. The unpolarized $\cos\phi$ moment generated by soft gluon radiation is sensitive to NGL effects, with its ratio definition reducing common normalization uncertainties. The absence of jet reconstruction makes this observable particularly relevant at the lower collision energies of EicC, providing a way to study nonperturbative spin–momentum correlations by varying the fiducial acceptance.

The future Electron-Ion Collider (EIC) will offer new opportunities to search for physics beyond the Standard Model. We study resonant anomaly detection using machine learning and the full particle content of an event. We consider a new neutral gauge boson and a heavy neutral lepton as illustrative signals with different electron-jet topologies. Weakly supervised learning uses this event information to enhance the sensitivity of an invariant-mass search without identifying individual signal events during training. Comparisons with high-level observables show that the electron kinematics account for an important part of the separation, while correlations among the particles provide further sensitivity. We also construct a conditional full-event generator by adapting a model pretrained on LHC jets to produce EIC background events. A scan over signal fractions demonstrates substantial signal enhancement using the learned background reference, providing a proof of concept for this approach at the EIC. Finally, we consider a fully unsupervised graph autoencoder that provides modest signal enhancement but retains sensitivity at signal fractions too small for effective weak supervision. Our results motivate full-event anomaly detection as part of the EIC physics program and identify directions for developing methods suited to its distinct kinematics.

XENONnT has measured a low-energy solar-neutrino signal dominated by $pp$ neutrinos. At these energies, an ultra-small pseudo-Dirac mass-squared splitting induces detectable active-sterile oscillations over the Sun–Earth baseline. We study pseudo-Dirac oscillations of the first mass eigenstate, compute the resulting modification of the $pp+{}^7$Be electron-recoil spectrum, and construct a likelihood from the published XENONnT energy spectra. We find that the XENONnT data exclude $5.9\times10^{-13}\,\mathrm{eV}^2\lesssim \delta m_1^2 \leq 10^{-11}\,\mathrm{eV}^2$ at the $2\sigma$ level, extending current solar-neutrino sensitivity to smaller mass splittings and approaching a regime previously discussed for future $pp$-sensitive detectors.

$t\bar{t}$ spin correlations originating from theoretical models assuming on one side toponium bound state formation in proton-proton collisions at 13 TeV are compared against predictions from non-relativistic QCD ressumation effects via Green's function formalism that go beyond the perturbative $t\bar{t}$ baseline with no bound state but could justify extra yield of events in the $t\bar{t}$ mass spectrum recently observed by ATLAS and CMS Collaborations, still awaiting an explanation. Toponium production comprises two scenarios, a simplified Effective Field Theory (EFT) with $\eta_t\rightarrow t\bar{t}$ decays and an additional model with scalar and vector toponium states with $\eta_t\rightarrow HZ$ and $J_t\rightarrow ZW^+W^-$ decays. Experimental measurements on $t\bar{t}$ system are added to the comparisons. Fitted diagonal spin correlation $C_{kk}$, $C_{rr}$, $C_{nn}$ matrix terms show a relative increase in value ranging from 200%-2330% for toponium $t\bar{t}$ decays with respect the perturbative NLO baseline. Relative contribution from resummation effect ranges from 0.6% to 10.4% and its combination with perturbative baseline improves agreement with Data distributions, with $\chi^2/N_\mathrm{dof}$ value reduced by $\sim$4.5%-60.0% . Equivalent fitted cross-section for resummation effect $\sigma_{res}$, ranges from 7.3 to 9.1 pb in consistency with excess yield reported by LHC experiments. $\sigma_{res}$ $>$ 50 pb range is excluded at 95% C.L. A classifier performing at detector level achieves a ROC curve area of $0.91$ leading to toponium signal to background significances over 55. These results indicate that efficient isolation of observed $t\bar{t}$ excess events from background is feasible and a characterisation via spin correlation measurements would reveal their consistency with either toponium production or non-relativistic effects beyond the perturbative baseline.

Effective kinematic variables are proposed in the rest frame of the common cluster of the top quark and mediator decay products for searching for and determining the type of dark matter mediator particles and measuring their masses in single top quark production processes. The efficiency of the variables is confirmed by full Monte Carlo simulation taking into account the response of the LHC detectors.

Against a background supported by the three pillars of emergent mass, this contribution challenges the fidelity of vector meson dominance as an instrument for relating the electromagnetic vector-meson (V) production reaction $e + p \to e^\prime + V + p$ to the hadronic process $V + p \to V + p$. It also describes a viable reaction model for exclusive photoproduction of light and heavy vector mesons from the proton, which exposes the $q\bar q$ content of the photon. That model's successes reveal that it is premature to link extant $V + p \to V + p$ data with, for instance, in-proton gluon distributions, the QCD trace anomaly, or pentaquark production. Improved reaction theory and more precise data are required before the validity of such links can objectively be assessed.

We extend the interpolation of the Poincaré algebra between instant form dynamics (IFD) and light-front dynamics (LFD) to the conformal algebra in $(3+1)$ dimensions. Building upon our recent formulation of the interpolating conformal algebra in $(1+1)$ dimensions, we propose an interpolation method for the conformal group $SO(4,2)$. A central feature of this work is classifying the $15$ conformal generators into kinematic and dynamic categories as a function of the interpolation angle ($0 \leq \delta \leq \frac{\pi}{4}$). We show that among the five additional generators beyond the Poincaré group, the dilatation generator remains strictly kinematic across the entire interpolation region. We also find that in the exact light-front limit ($\delta = \frac{\pi}{4}$), one additional generator from the Special Conformal Transformations (SCT) becomes kinematic in $(1+1)$ but dynamical in $(3+1)$. This behavior shows the advantage of LFD in maximizing kinematic generators and minimizing dynamical complexity. To support this algebraic framework, we construct a $6 \times 6$ interpolating projective spacetime matrix representation. We detail the explicit transformations of the interpolating time under all $15$ generators, providing a systematic view of conformal symmetry across the relativistic dynamics.

We study the dark-matter phase space distribution of Milky Way-mass halos in the Auriga simulations, considering both hydrodynamic and dark-matter-only runs. In a spherically averaged potential, we test whether the coarse-grained distribution function can be approximated as a function of the integrals of motion $E$ and $L$. We find that $f(E,L)$ provides a useful description of the simulated halos: although the deviations from this form are formally statistically significant, the median fractional residuals between radial shells are typically $\lesssim 15\%$, with 90th-percentile residuals of order tens of percent. An energy-only approximation, $f(E)$, gives similar median residuals but is systematically disfavored by $\chi^2$ tests, indicating that angular momentum dependence is statistically preferred. Ultimately we find that neither $f(E)$ nor $f(E,L)$ fully describes the particle data at high precision. The remaining residuals likely reflect departures from spherical equilibrium, including anisotropy, triaxiality, substructure, and baryonic effects.

We obtain a general decay rate between Kaluza-Klein (KK) gravitons, resolving an ambiguity in the literature concerning these decays. The amplitude is determined not only by the mass $m_n$ of the decaying particle, but also by the momentum $q$ of the decay products in the parent's rest frame, and is suppressed relative to the expression commonly used in the literature by $(q/m_n)^2$. Phase space gives a general $q^5$-dependent decay rate obtained earlier in Randall-Sundrum models. We identify the cancellation that gives this result as a consequence of the massless 5D graviton, and argue for its universality even with scalar-induced KK violation by absorbing non-minimally coupled scalar fields into the warp-factor. This has significant implications for the potential for cascading dark matter models, and can be used to rule out existing Dark Dimension models, because the rapid cascade that was needed to evade constraints is severely suppressed. The amplitude is established by an explicit calculation that accounts for the backreaction of fields and branes and applies broadly to non-minimal diffeomorphism invariant two-derivative couplings between scalar fields and gravity.

The local dark matter (DM) velocity distribution is significantly altered by the gravitational impact of the Large Magellanic Cloud (LMC), which creates a high-velocity tail. We evaluate how the LMC reshapes the DM landscape for a wide variety of theoretical models in light of the recent putative LZ DM event. We show that the LMC-induced velocity shifts substantially modify the parameter space for inelastic endothermic DM models across a broad range of possible interactions, driving the viable regions towards larger mass splittings, which are more susceptible to collider and indirect detection constraints. By contrast, models for elastically colliding DM are less impacted, and some remain viable candidates – for example, the simple light Singlet-Doublet Majorana DM candidate at the Higgs blind spot. Our work confirms that accurately accounting for LMC effects is essential when high-velocity DM is probed, rather than relying on the simplified Standard Halo Model.

We develop two hybrid techniques that approach the performance of neural simulation-based inference (NSBI) analyses while substantially reducing the computational cost of inference and preserving some or all of the reliability guarantees of parametric methods. The first approach is broadly applicable, while the second is tailored to a class of particle physics analyses that admit a semi-parametric NSBI formulation. With only a modest compromise in raw sensitivity, these methods represent an important step toward computationally efficient NSBI in offline analyses and also open the door to the exploration of trigger-level applications in the future. Based on our comparison studies, we recommend the use of our first approach, Latent Categories, for robust and efficient inference.

We address the breakdown of fixed-order perturbation theory due to logarithms in $s/p_t^2$ for processes involving two jets or more at the energies currently explored at the LHC. The problem manifests itself in various ways: an obvious breakdown of the perturbative series for some kinematic distributions, highly asymmetric scale variations in other distributions, and the need for an artificially large renormalisation scale to even achieve numerical stability. As we demonstrate, the problem is solved through the resummation of these high-energy logarithms. The customary choice of a large renormalisation scale of $m_{j_1j_2}$ offers no systematic resolution. This breakdown in fixed order predictions is illustrated for the production of $Z$+dijets. We show that resummed predictions obtained using \HighEJ matched to fixed order obtain accurate predictions for all the relevant distributions investigated in a recent ATLAS measurement.

Electric dipole moments (EDMs) provide some of the most sensitive probes of CP-violating interactions beyond the Standard Model (SM). Within the Standard Model Effective Field Theory (SMEFT), we investigate constraints on CP-violating top-quark interactions using current and projected leptonic and hadronic EDM measurements. Our analysis incorporates the complete chain of relevant effects, including one- and two-loop matching, Barr-Zee contributions, Weinberg operator and heavy-quark threshold corrections, and renormalization-group induced operator mixing. We demonstrate the strong complementarity between leptonic and hadronic EDM observables and show that future proton EDM searches could significantly strengthen constraints on several CP-violating top-quark interactions.

We make use of unique properties of scaling functions to estimate the chiral phase transition temperature and corresponding universal critical parameters of this phase transition directly from (2+1)-flavor QCD simulations with highly improved staggered fermions on lattices with temporal extent $N_\tau=8$. Working with an improved chiral order parameter for quantifying chiral symmetry breaking, we analyze the finite-volume dependence of this observable for a wide range of lattice volumes and light quark masses, and quantitatively estimate the deviations from the expected universal scaling behaviour as a function of the light-to-strange quark mass ratio.

We present AI-developed local infrared subtraction, building on projection to Born and EFT matching. The framework separates an integrable radiation term from a finite contribution at Born kinematics, referred to as the Born contact. The contact is determined using the EFT singular distribution in a resolution observable such as N-jettiness $\tau_N$. Under human physics guidance, an LLM develops two implementations. One uses a neural network for phase space projection and fits the contact by matching to EFT cumulants. The other uses an analytic construction that keeps the Born momenta fixed while integrating over radiation. It combines the EFT $\delta(\tau_N)$ coefficient with finite 4-dimensional radiation integrals to calculate the contact term directly. This gives a local subtraction formula without a slicing parameter, while reusing existing lower-order radiation calculations and EFT singular predictions. As a demonstration, we reconstruct the full NLO correction for massless 3- and 4-jet production in electron-positron annihilation. The attempt to the NNLO dijet production is also made by recursively using the NLO P2B construction with the LLM designing machine-learning controls to reduce the variance of the contact integral. The tested predictions are in good agreement with EERAD3. The numerical calculation and projection-network training use a 2020 Apple M1 MacBook, without GPU acceleration, illustrating the feasibility of the construction with modest computing resources. The appendices develop an extension of the local subtraction to 3-jet NNLO, giving explicit radiation maps and a proposed contact formula. We also show how to integrate over NNLO radiation while keeping the Born momenta fixed, for any number of massless final-state jets. Our results demonstrate how AI can help higher-order calculations by constructing infrared subtraction and improving its numerical integration.