Strangeness Production in √sNN = 3 GeV Au+Au Collisions at RHIC
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73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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First measurement of D* + vector meson spin alignment in Pb–Pb collisions at $\sqrt{{s}_{\text{NN}}}={5}.0{2}$ TeV
The first measurement of prompt D *+ -meson spin alignment in ultrarelativistic heavy-ion collisions with respect to the direction orthogonal to the reaction plane is presented. The spin alignment is quantified by measuring the element ρ 00 of the diagonal spin-density matrix for prompt D *+ mesons with 4 < p T < 30 GeV/c in two rapidity intervals, |y| < 0.3 and 0.3 < |y| < 0.8, in central (0–10%) and midcentral (30–50%) Pb–Pb collisions at $\sqrt{{s}_{\text{NN}}}={5}.0{2}$ TeV. Evidence of spin alignment ρ 00 > 1/3 has been found for p T > 15 GeV/c and 0.3 < |y| < 0.8 with a significance of 3.1σ. The measured spin alignment of prompt D *+ mesons is compared with the one of inclusive J/ψ mesons measured at forward rapidity (2.5 < y < 4).
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Chaos on the hypercube
We analyze the spectral properties of a d-dimensional HyperCubic (HC) lattice model originally introduced by Parisi. The U(1) gauge links of this model give rise to a magnetic flux of constant magnitude φ but random orientation through the faces of the hypercube. The HC model, which also can be written as a model of 2d interacting Majorana fermions, has a spectral flow that is reminiscent of Maldacena-Qi (MQ) model, and its spectrum at φ = 0, actually coincides with the coupling term of the MQ model. As was already shown by Parisi, at leading order in 1/d, the spectral density of this model is given by the density function of the Q-Hermite polynomials, which is also the spectral density of the double-scaled Sachdev-Ye-Kitaev model. Parisi demonstrated this by mapping the moments of the HC model to Q-weighted sums on chord diagrams. We point out that the subleading moments of the HC model can also be mapped to weighted sums on chord diagrams, in a manner that descends from the leading moments. The HC model has a magnetic inversion symmetry that depends on both the magnitude and the orientation of the magnetic flux through the faces of the hypercube. The spectrum for fixed quantum number of this symmetry exhibits a transition from regular spectra at φ = 0 to chaotic spectra with spectral statistics given by the Gaussian Unitary Ensembles (GUE) for larger values of φ. For small magnetic flux, the ground state is gapped and is close to a Thermofield Double (TFD) state.
1/N expansion↗
Quark sivers function at small x: spin-dependent odderon and the sub-eikonal evolution
We apply the formalism developed earlier for studying transverse momentum dependent parton distribution functions (TMDs) at small Bjorken x to construct the small- x asymptotics of the quark Sivers function. First, we explicitly construct the complete fundamental “polarized Wilson line” operator to sub-sub-eikonal order: this object can be used to study a variety of quark TMDs at small x . We then express the quark Sivers function in terms of dipole scattering amplitudes containing various components of the “polarized Wilson line” and show that the dominant (eikonal) term which contributes to the quark Sivers function at small x is the spin-dependent odderon, confirming the re- cent results of Dong, Zheng and Zhou. Our conclusion is also similar to the case of the gluon Sivers function derived by Boer, Echevarria, Mulders and Zhou. We also analyze the sub-eikonal corrections to the quark Sivers function using the constructed “polarized Wilson line” operator. We derive new small- x evolution equations re-summing double-logarithmic powers of α s ln 2 (1 /x ) with α s the strong coupling constant. We solve the corresponding novel evolution equations in the large- N c limit, obtaining a sub-eikonal correction to the spin-dependent odderon contribution. We conclude that the quark Sivers function at small x receives contributions from two terms and is given by ${f}_{1T}^{\perp q}\left(x,{k}_T^2\right)={C}_O\left(x,{k}_T^2\right)\frac{1}{x}+{C}_1\left({k}_T^2\right){\left(\frac{1}{x}\right)}^0+\cdots$ with the function C O ( x, ${k}_T^2$) varying slowly with x and the ellipsis denoting the subasymptotic and sub-sub-eikonal (order- x ) corrections.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Dijet impact factor in DIS at next-to-leading order in the Color Glass Condensate
In this work, we compute the next-to-leading order impact factor for inclusive dijet production in deeply inelastic electron-nucleus scattering at small x Bj . Our computation, performed in the framework of the Color Glass Condensate effective field theory, includes all real and virtual contributions in the gluon shock wave background of all-twist lightlike Wilson line correlators. We demonstrate explicitly that the rapidity evolution of these correlators, to leading logarithmic accuracy, is described by the JIMWLK Hamiltonian. When combined with the next-to-leading order JIMWLK Hamiltonian, our results for the impact factor improve the accuracy of the inclusive dijet cross-section to \( \mathcal{O} \) ( \( {\alpha}_s^2 \) ln( x f /x Bj )), where x f is a rapidity factorization scale. These results are an essential ingredient in assessing the discovery potential of inclusive dijets to uncover the physics of gluon saturation at the Electron-Ion Collider.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
T-odd leading-twist quark TMDs at small x
We study the small-x asymptotics of the flavor non-singlet T-odd leading-twist quark transverse momentum dependent parton distributions (TMDs), the Sivers and Boer-Mulders functions. While the leading eikonal small-x asymptotics of the quark Sivers function is given by the spin-dependent odderon [1, 2], we are interested in revisiting the sub-eikonal correction considered by us earlier in [3]. We first simplify the expressions for both TMDs at small Bjorken x and then construct small-x evolution equations for the resulting operators in the large-N c limit, with N c the number of quark colors. For both TMDs, the evolution equations resum all powers of the double-logarithmic parameter α s ln 2 (1/x), where α s is the strong coupling constant, which is assumed to be small. Solving these evolution equations numerically (for the Sivers function) and analytically (for the Boer-Mulders function) we arrive at the following leading small-x asymptotics of these TMDs at large N c :$$ {\displaystyle \begin{array}{l}{f}_{1T}^{\perp NS}\left(x\ll 1,{k}_T^2\right)={C}_O\left(x,{k}_T^2\right)\frac{1}{x}+{C}_1\left(x,{k}_T^2\right){\left(\frac{1}{x}\right)}^{3.4\sqrt{\frac{\alpha_s{N}_c}{4\pi }}}\\ {}{h}_1^{\perp \textrm{NS}}\left(x\ll 1,{k}_T^2\right)=C\left(x,{k}_T^2\right){\left(\frac{1}{x}\right)}^{-1}.\end{array}} $$ The functions C O (x,$ {k}_T^2 $), C 1 (x,$ {k}_T^2 $), and C(x,$ {k}_T^2 $) can be readily obtained in our formalism: they are mildly x-dependent and do not strongly affect the power-of-x asymptotics shown above. The function C O , along with the 1/x factor, arises from the odderon exchange. For the sub-eikonal contribution to the quark Sivers function (the term with C 1 ), our result shown above supersedes the one obtained in [3] due to the new contributions identified recently in [4].
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
All order factorization for virtual Compton scattering at next-to-leading power
We discuss all-order factorization for the virtual Compton process at next-to leading power (NLP) in the Λ QCD /Q and $\sqrt{-t}$/Q expansion (twist-3), both in the double deeply-virtual case and the single-deeply-virtual case. We use the soft-collinear efective theory (SCET) as the main theoretical tool. We conclude that collinear factorization holds in the double-deeply virtual case, where both photons are far of-shell. The agreement is found with the known results for the hard matching coefcients at leading order $α^0_s$, and we can therefore connect the traditional approach with SCET. In the single-deeply-virtual case, commonly called deeply virtual Compton scattering (DVCS), the contribution of non-target collinear regions complicates the factorization. These include momentum modes collinear to the real photon and (ultra)soft interactions between the photon-collinear and target-collinear modes. However, such contributions appear only for the transversely polarized virtual photon at the NLP accuracy and in fact it is the only NLP ~ (Λ QCD /Q) 1 ~ ( $\sqrt{-t}$/Q) 1 contribution in that case. We therefore conclude that the DVCS amplitude for a longitudinally polarized virtual photon, where the leading power ~ (Λ QCD /Q) 0 ~ ($\sqrt{-t}$/Q) 0 contribution vanishes, is free of non-target collinear contributions and the collinear factorization in terms of twist-3 GPDs holds in that case as well.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Advancing the understanding of energy-energy correlators in heavy-ion collisions
We investigate the collinear limit of the energy-energy correlator (EEC) in a heavy-ion context. First, we revisit the leading-logarithmic (LL) resummation of this observable in vacuum following a diagrammatic approach. We argue that this route allows to naturally incorporate medium-induced effects into the all-orders structure systematically. As an example, we show how the phase-space constraints imposed by the static medium on vacuum-like emissions can be incorporated into the LL result by modifying the anomalous dimensions. On the fixed-order side, we calculate the $\mathcal{O}$(α s ) expansion of the in-medium EEC for a γ → $q\overline{q}$ splitting with arbitrary kinematics including, for the first time, subleading colour corrections. When comparing this result to previously used approximations in the literature, we find up to $\mathcal{O}$(1) deviations in the regime of interest for jet quenching signatures. Energy loss effects are also quantified and further suppress the EEC at large angles. These semi-analytic studies are complemented with a phenomenological study using the jet quenching Monte Carlo JetMed. Finally, we argue that the imprint of medium-induced effects in energy-energy correlators can be enhanced by using an alternative definition that takes as input Lund primary declusterings instead of particles.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Effective theory tower for μ → e conversion
We present theoretical predictions for μ → e conversion rates using a tower of effective field theories connecting the UV to nuclear physics scales. The interactions in nuclei are described using a recently developed nonrelativistic effective theory (NRET) that organizes contributions according to bound nucleon and muon velocities, ${\overrightarrow{v}}_N$ and ${\overrightarrow{v}}_μ$, with |${\overrightarrow{v}}_N$| > |${\overrightarrow{v}}_μ$|. To facilitate the top-down matching, we enlarge the set of Lorentz covariant nucleon-level interactions mapped onto the NRET operators to include those mediated by tensor interactions, in addition to the scalar and vector interactions already considered previously, and then match NRET nonperturbatively onto the Weak Effective Theory (WET). At the scale μ ≈ 2 GeV WET is formulated in terms of u, d, s quarks, gluons and photons as the light degrees of freedom, along with the flavor-violating leptonic current. We retain contributions from WET operators up to dimension 7, which requires the full set of 26 NRET operators. The results are encoded in the open-source Python- and Mathematica-based software suite MuonBridge, which we make available to the theoretical and experimental communities interested in μ → e conversion.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Measurement of beauty production via non-prompt charm hadrons in p–Pb collisions at $\sqrt{s_{\textrm{NN}}}$ = 5.02 TeV
The production cross sections of D 0 , D + , and Λ$^{+}_{c}$ hadrons originating from beauty-hadron decays (i.e. non-prompt) were measured for the first time at midrapidity in proton–lead (p–Pb) collisions at the center-of-mass energy per nucleon pair of $\sqrt{s_{\textrm{NN}}}$ = 5.02 TeV. Nuclear modification factors (R pPb ) of non-prompt D 0 , D + , and Λ$^{+}_{c}$ are calculated as a function of the transverse momentum (p T ) to investigate the modification of the momentum spectra measured in p–Pb collisions with respect to those measured in proton–proton (pp) collisions at the same energy. The R pPb measurements are compatible with unity and with the measurements in the prompt charm sector, and do not show a significant p T dependence. The p T -integrated cross sections and p T -integrated R pPb of non-prompt D 0 and D + mesons are also computed by extrapolating the visible cross sections down to p T = 0. The non-prompt D-meson R pPb integrated over p T is compatible with unity and with model calculations implementing modification of the parton distribution functions of nucleons bound in nuclei with respect to free nucleons. The non-prompt Λ$^{+}_{c}$/D 0 and D + /D 0 production ratios are computed to investigate hadronisation mechanisms of beauty quarks into mesons and baryons. The measured ratios as a function of p T display a similar trend to that measured for charm hadrons in the same collision system.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
The metamorphosis of semi-classical mechanisms of confinement: from monopoles on ℝ 3 × S 1 to center-vortices on ℝ 2 × T 2
There are two distinct regimes of Yang-Mills theory where we can demonstrate confinement, the existence of a mass gap, and the multi-branch structure of the effective potential as a function of the theta angle using a reliable semi-classical calculation. The two regimes are deformed Yang-Mills theory on ℝ 3 × S 1 , and Yang-Mills theory on ℝ 2 × T 2 where the torus is threaded by a ’t Hooft flux. The weak coupling regime is ensured by the small size of the circle or torus. In the first case the confinement mechanism is related to self-dual monopoles, whereas in the second case self-dual center-vortices play a crucial role. These two topological objects are distinct. In particular, they have different mutual statistics with Wilson loops. On the other hand, they carry the same topological charge and action. We consider the theory on ℝ × T 2 × S 1 and extrapolate both the monopole and vortex regimes to a quantum mechanical domain, where a cross-over takes place. Both sides of the cross-over are described by a deformed ℤ N TQFT. On ℝ 2 × S 1 × S 1 , we derive an effective field theory (EFT) of vortices from the EFT of monopoles in the presence of a ’t Hooft flux. This construction is based on a two-stage Higgs mechanism, reducing SU(N) to U(1) N−1 in 3d first, followed by reduction to a ℤ N EFT in 2d in the second step. This result shows how monopoles transmute into center-vortices, and suggests adiabatic continuity between the two confinement mechanisms. The basic mechanism is flux fractionalization: the magnetic flux of the monopoles splits up and is collimated in such a way that 2d Wilson loops detect it as a center vortex.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Study of $\langle {p}_{\text{T}}\rangle$ and its higher moments, and extraction of the speed of sound in Pb-Pb collisions with ALICE
Ultrarelativistic heavy-ion collisions produce a state of hot and dense strongly interacting QCD matter called quark-gluon plasma (QGP). On an event-by-event basis, the volume of the QGP in ultracentral collisions is mostly constant, while its total entropy can vary significantly due to quantum fluctuations, leading to variations in the temperature of the system. Exploiting this unique feature of ultracentral collisions allows for the interpretation of the correlation of the mean transverse momentum ($\langle$p T $\rangle$) of produced charged hadrons and the number of charged hadrons as a measure for the speed of sound, c s . This speed is related to the rate at which compression waves travel in the QGP and is determined by fitting the relative increase in $\langle$p T $\rangle$ with respect to the relative change in the average charged-particle density ($\langle$dN ch /dη$\rangle$) measured at mid-rapidity. This study reports the event-average $\langle$p T $\rangle$ of charged particles as well as the variance, skewness, and kurtosis of the event-by-event transverse momentum per charged particle ([p T ]) distribution in ultracentral Pb-Pb collisions at a center-of-mass energy of 5.02 TeV per nucleon pair using the ALICE detector. Different centrality estimators based on charged-particle multiplicity or the transverse energy of the event are used to select ultracentral collisions. By ensuring a pseudorapidity gap between the region used to define the centrality and the region used to perform the measurement, the influence of biases and their potential effects on the rise of the mean transverse momentum is tested. The measured c$^{2}_{s}$ is found to strongly depend on the exploited centrality estimator and ranges between 0.1146±0.0028 (stat.)±0.0065 (syst.) and 0.4374±0.0006 (stat.)±0.0184 (syst.) in natural units. The self-normalized variance shows a steep decrease towards ultracentral collisions, while the self-normalized skewness variables show a maximum, followed by a fast decrease. These non-Gaussian features are understood in terms of the vanishing of the impact-parameter fluctuations contributing to the event-to-event [p T ] distribution.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Strong constraints on the b → sγ photon polarisation from B0 → K*0e+e-decays
An angular analysis of the B 0 → K* 0 e + e - decay is performed using a data sample corresponding to an integrated luminosity of 9 fb - 1 of pp collisions collected with the LHCb experiment. The analysis is conducted in the very low dielectron mass squared ( q 2 ) interval between 0 . 0008 and 0 . 257 GeV 2 , where the rate is dominated by the B 0 → K * 0 γ transition with a virtual photon. The fraction of longitudinal polarisation of the K * 0 meson, F L , is measured to be F L = (4 . 4 ± 2 . 6 ± 1 . 4)%, where the first uncertainty is statistical and the second systematic. The \( {A}_{\mathrm{T}}^{\mathrm{Re}} \) observable, which is related to the lepton forward-backward asymmetry, is measured to be \( {A}_{\mathrm{T}}^{\mathrm{Re}} \) = - 0 . 06 ± 0 . 08 ± 0 . 02. The \( {A}_{\mathrm{T}}^{(2)} \) and \( {A}_{\mathrm{T}}^{\mathrm{Im}} \) transverse asymmetries, which are sensitive to the virtual photon polarisation, are found to be \( {A}_{\mathrm{T}}^{(2)} \) = 0 . 11 ± 0 . 10 ± 0 . 02 and \( {A}_{\mathrm{T}}^{\mathrm{Im}} \) = 0 . 02 ± 0 . 10 ± 0 . 01. The results are consistent with Standard Model predictions and provide the world’s best constraint on the b → sγ photon polarisation.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Positivity and geometric function theory constraints on pion scattering
This paper presents the fascinating correspondence between the geometric function theory and the scattering amplitudes with O(N) global symmetry. A crucial ingredient to show such correspondence is a fully crossing symmetric dispersion relation in the z-variable, rather than the fixed channel dispersion relation. We have written down fully crossing symmetric dispersion relation for O(N) model in z-variable for three independent combinations of isospin amplitudes. We have presented three independent sum rules or locality constraints for the O(N) model arising from the fully crossing symmetric dispersion relations. We have derived three sets of positivity conditions. We have obtained two-sided bounds on Taylor coefficients of physical Pion amplitudes around the crossing symmetric point (for example, π + π – → π 0 π 0 ) applying the positivity conditions and the Bieberbach-Rogosinski inequalities from geometric function theory.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Measurement of the effective leptonic weak mixing angle
Using pp collision data at $\sqrt{s}$ = 13 TeV, recorded by the LHCb experiment between 2016 and 2018 and corresponding to an integrated luminosity of 5.4 fb −1 , the forward-backward asymmetry in the pp → Z/γ* → μ + μ − process is measured. The measurement is carried out in ten intervals of the difference between the muon pseudorapidities, within a fiducial region covering dimuon masses between 66 and 116 GeV, muon pseudorapidities between 2.0 and 4.5 and muon transverse momenta above 20 GeV. These forward-backward asymmetries are compared with predictions, at next-to-leading order in the strong and electroweak couplings. The measured effective leptonic weak mixing angle is ${\sin}^2{\theta}_{\textrm{eff}}^{\ell }=0.23147\pm 0.00044\pm 0.00005\pm 0.00023,$ where the first uncertainty is statistical, the second arises from systematic uncertainties associated with the asymmetry measurement, and the third arises from uncertainties in the fit model used to extract ${\sin}^2{\theta}_{\textrm{eff}}^{\ell }$ from the asymmetry measurement. This result is based on an arithmetic average of results using the CT18, MSHT20, and NNPDF31 parameterisations of the proton internal structure, and is consistent with previous measurements and with predictions from the global electroweak fit.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
The Ghent Hybrid model in NuWro: a new neutrino single-pion production model in the GeV regime
Neutrino-induced single-pion production constitutes an essential interaction channel in modern neutrino oscillation experiments, with its products building up a significant fraction of the observable hadronic final states. Frameworks of oscillation analyses strongly rely on Monte Carlo neutrino event generators, which provide theoretical predictions of neutrino interactions on nuclear targets. Thus, it is crucial to integrate state-of-the-art single-pion production models with Monte Carlo simulations to prepare for the upcoming systematics-dominated landscape of neutrino measurements. In this work, we present the implementation of the Ghent Hybrid model for neutrino-induced single-pion production in the NuWro Monte Carlo event generator. The interaction dynamics includes coherently-added contributions from nucleon resonances and a non-resonant background, merged into the pythia branching predictions in the deep-inelastic regime, as instrumented by NuWro. This neutrino-nucleon interaction model is fully incorporated into the nuclear framework of the generator, allowing it to account for the influence of both initial- and final-state nuclear medium effects. We compare the predictions of this integrated implementation with recent pion production data from accelerator-based neutrino experiments. The results of the novel model show improved agreement of the generator predictions with the data and point to the significance of the refined treatment of the description of pion-production processes beyond the ∆ region.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Entanglement entropy of a color flux tube in (2+1)D Yang-Mills theory
We construct a novel flux tube entanglement entropy (FTE 2 ), defined as the excess entanglement entropy relative to the vacuum of a region of color flux stretching between a heavy quark-anti-quark pair in pure gauge Yang-Mills theory. We show that FTE 2 can be expressed in terms of correlators of Polyakov loops, is manifestly gauge-invariant, and therefore free of the ambiguities in computations of the entanglement entropy in gauge theories related to the choice of the center algebra. Employing the replica trick, we compute FTE 2 for SU(2) Yang-Mills theory in (2+1)D and demonstrate that it is finite in the continuum limit. We explore the properties of FTE 2 for a half-slab geometry, which allows us to vary the width and location of the slab, and the extent to which the slab cross-cuts the color flux tube. Following the intuition provided by computations of FTE 2 in (1+1)D, and in a thin string model, we examine the extent to which our FTE 2 results can be interpreted as the sum of an internal color entropy and a vibrational entropy corresponding to the transverse excitations of the string.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Multiplicity dependence of ${\Xi }_{\text{c}}^{+}$ and ${\Xi }_{\text{c}}^{0}$ production in pp collisions at $\sqrt{s}=13$ TeV
The first measurement at midrapidity (|y| < 0.5) of the production yield of the strange-charm baryons $Ξ$$^{+}_{c}$ and $Ξ$$^{0}_{c}$ as a function of transverse momentum (p T ) in different charged-particle multiplicity classes in proton-proton collisions at $\sqrt{s}$ = 13 TeV with the ALICE experiment at the LHC is reported. The $Ξ$$^{+}_{c}$ baryon is reconstructed via the $Ξ$$^{+}_{c}$ → $Ξ$ – π + π + decay channel in the range 4 < p T < 12 GeV/c, while the $Ξ$$^{0}_{c}$ baryon is reconstructed via both the $Ξ$$^{0}_{c}$ → $Ξ$ – π + and $Ξ$$^{0}_{c}$ → $Ξ$ – e + ν e decay channels in the range 2 < p T < 12 GeV/c. The baryon-to-meson ($Ξ$$^{0}_{c}$ + /D 0 ) and the baryon-to-baryon ($Ξ$$^{0}_{c}$ + /Λ$^{+}_{c}$) production yield ratios show no significant dependence on multiplicity. In addition, the observed yield ratios are not described by theoretical predictions that model charm-quark fragmentation based on measurements at e + e − and e − p colliders, indicating differences in the charm-baryon production mechanism in pp collisions. A comparison with different event generators and tunings, including different modelling of the hadronisation process, is also discussed.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗