Nonperturbative Part Research Articles

Phenomenology of TMD parton distributions in Drell-Yan and Z0 boson production in a hadron structure oriented approach

We present a first practical implementation of a recently proposed hadron structure oriented (HSO) approach to transverse momentum dependent (TMD) phenomenology applied to Drell-Yan-like processes, including lepton pair production at moderate Q2 and Z0 boson production. We compare and contrast general features of our methodology with other common practices and emphasize aspects that we view as improvements. Separately, we discuss the importance of treatments that preserve various theoretical properties of the nonperturbative parts of TMD parametrizations for future applications that have the extraction of hadron structure as a primary goal. These include the HSO’s preservation of a basic TMD parton-model-like framework even while accounting for full TMD factorization and evolution, explicit preservation of the integral relationship between TMD and collinear parton density functions, and the ability to meaningfully compare different theoretical models of nonperturbative TMD parton distributions. In our examples, we show that there is significant sensitivity at moderate Q2 to both the form of the nonperturbative transverse momentum dependence and the parametrization of collinear parton densities. However, we also find that evolving to Q2=MZ2, without fitting, results in a satisfactory postdiction of existing data for Z0 production, nearly independently of the modeling of nonperturbative transverse momentum behavior. We argue that this demonstrates that moderate Q measurements should be given greater weight than high Q measurements in extractions of nonperturbative transverse momentum dependence. We also obtain new extractions of the nonperturbative Collins-Soper kernel within the HSO approach. We discuss its features and compare with some earlier extractions. Published by the American Physical Society 2024

Perturbative approach to time-dependent quantum solitons

Recently we have introduced a lightweight, perturbative approach to quantum solitons. Thus far, our approach has been largely limited to configurations consisting of a single soliton plus a finite number of mesons, whose classical limit is an isolated stationary or rigidly moving soliton. In this paper, with an eye to soliton collisions and oscillons, we generalize this approach to quantum states whose classical limits are genuinely time-dependent. More precisely, we use a unitary operator, inspired by the coherent state approach to solitons, to factor out the nonperturbative part of the state, which includes the classical motion. The solution for the quantum state and its evolution is then reduced to an entirely perturbative problem.

Rotating SU(2) gluon matter and deconfinement at finite temperature

In this work a non-abelian gauge theory is reformulated in a rotating frame. With this new formalism, the influence of the background rotation on the color deconfinement transition for a pure SU(2) gluon system has been studied. The KvBLL caloron, which is a color neutral and topologically nontrivial solution of Yang-Mills equation at finite temperature, is reexamined under rotation and adopted as the confined vacuum of such a system. With rotation-modified solutions of the caloron's constituent solitons, i.e. dyons, the non-perturbative part of effective potential of the rotating system has been obtained. Combining with the perturbative potential by Gaussian fluctuations, the critical temperature of confinement-deconfinement phase transition is investigated. It is found that neither the rotational semi-classical potential nor Gaussian fluctuations can confine color charges more tightly when the rotation becomes faster. While only a stronger coupling constant is able to make the critical temperature increase with angular velocity, as what indicated in lattice simulations. And it is found a non-monotonic dependence of the critical temperature on the angular velocity is established because of the competition between these two contrary contributions.

Black hole/black ring transition

We consider BPS states in M theory compactified on a Calabi-Yau threefold with one Kähler parameter, and investigate their relation to black holes and black rings. On the microscopic side, a characterization of the BPS degeneracy can be obtained from the non-perturbative part of the topological string free energy according to the Gopakumar-Vafa conjecture. On the macroscopic side, the Wald entropy of relevant black objects in the four-dimensional IIA description is computed from the perturbative part of the same topological string free energy following the work of Cardoso-de Wit-Mohaupt and then lifted to five-dimensional M theory through the Gaiotto-Strominger-Yin correspondence. For a given value of the M2 brane charge, we find that for small angular momenta, the microscopic BPS degeneracy matches the entropy of a rotating black hole, whereas an apparent transition occurs at a critical value of the angular momentum. Beyond this value, we find encouraging evidence that the microscopic counting is well approximated by the entropy of a black ring. We conclude by formulating a new puzzle involving the corrections due to degenerate worldsheet instantons.

Exact conditions for quasi-normal modes of extremal M5-branes and exact WKB analysis

We study the quasi-normal modes (QNMs) of a massless scalar perturbation to the extremal M5-branes metric by using the exact WKB analysis. The exact WKB analysis provides two exact QNMs conditions depending on the argument of the complex frequency of the perturbation. The exact conditions show that the discontinuity of the perturbative part of the QNMs leads the non-perturbative part of themselves. We also find a new example of the Seiberg-Witten/gravity correspondence, which helps us to compute the QNMs from our conditions.

New determination of |Vcb| using the three-loop QCD corrections for the B → D⁎ semi-leptonic decays

We present a new determination of the Cabibbo-Kobayashi-Maskawa matrix element |Vcb| by using the three-loop perturbative QCD corrections for the B→D⁎ semi-leptonic decay. The decay width of B→D⁎ semi-leptonic decay can be factorized as perturbatively calculable short-distance part and the non-perturbative but universal long-distance part. We adopt the principle of maximum conformality (PMC) single-scale setting approach to deal with the perturbative series so as to achieve a precise fixed-order prediction for the short-distance parameter ηA. By applying the PMC, an overall effective αs value is achieved by recursively using the renormalization group equation, which inversely results in a precise scale-invariant pQCD series. Such scale-invariant series also provides a reliable basis for predicting the contributions from uncalculated perturbative terms. We then obtain ηA=0.9225−0.0168+0.0117, where the error is the squared average of those from Δαs(MZ)=±0.0010 and the uncertainties caused by the uncalculated higher-order perturbative terms. By using the data of B→D⁎ℓν¯ℓ, we finally obtain |Vcb|PMC=(40.60−0.57+0.53)×10−3, which is consistent with the PDG value within errors.

Nonperturbative effects in neutrino magnetic moments

In this paper, we calculate the QCD nonperturbative contributions of the neutrino-quark tensor operators to the neutrino magnetic moments by matching onto the chiral perturbation theory at low energies. These nonperturbative contributions can be compared to the perturbative ones, which are induced from one-loop mixing when performing the renormalization group evolutions from $\mu=m_W$ down to $\mu=2~\mathrm{GeV}$. We then constrain the dipole and tensor Wilson coefficients of the low-energy neutrino effective field theory (LNEFT) separately from the neutrino-electron scattering with Borexino data and coherent elastic neutrino-nucleus scattering (CE$\nu$NS) with COHERENT data to show the competition between these two contributions, at the renormalization scales $\mu=2~\mathrm{GeV}$ and $\mu=m_W$ in the $\bar{\mathrm{MS}}$ scheme. In the neutrino-electron scattering, it is found that the nonperturbative contributions dominate for the coefficients involving up and down quarks, while they are expected to be of the same order of magnitude as the perturbative contributions for the coefficients involving strange quark. As for constraints in the CE$\nu$NS, the tensor operators can contribute to the process through either direct or indirect way. As a result, the indirect contributions including nonperturbative and perturbative parts for all couplings become negligible in comparison with the direct ones. As the nonperturbative contributions crucially depend on the value of $c_T$, its inputs will affect the extraction of limits on the tensor LNEFT Wilson coefficients. We compute the upper bounds on these coefficients with $c_T$ quoting from the model and lattice estimates.

Transverse momentum dependent fragmentation functions from recent BELLE data

A new formalism for the factorization of the cross section for single hadron production in $e^+e^-$ annihilations, differential in $z_h$, $P_T$ and thrust, is applied to the phenomenological analysis of data recently measured by the BELLE Collaboration. Within this scheme the $e^+e^- \to hX$ cross section can be recast in the convolution of a perturbatively calculable coefficient and a universal transverse momentum dependent fragmentation function. While performing a next-to-leading order calculation of the perturbative part of the process to next-to-leading logarithmic accuracy, we examine and thoroughly discuss the suitability of a number of possible ansatz to model the non-perturbative part of this universal transverse momentum dependent fragmentation function, showing the extent to which present experimental data can actually constrain its shape and functional form in terms of $z_h$, $P_T$ and thrust.

Self-similar behavior of the neutron fracture functions

In this paper, we have employed Fractal formalism to calculate the Fracture Functions of the Leading neutron produced in [Formula: see text] collisions. The Fractal concept describes the self-similar behavior of the proton structure at Leading neutron production of semi-inclusive Deep Inelastic Scattering at the low values of the fractional momentum variable [Formula: see text]. The Fracture Functions (FFs) parameterized the non-perturbative part of the fragmentation process at the initial scale of Q[Formula: see text]. In this analysis, we benefit from the Leading neutron (Ln) experimental data published by H1 Collaboration and in order to estimate the uncertainty of neutron FFs and corresponding observables, we used the Hessian method. As a consequence of this Next-to-Leading order QCD analysis, we achieve a nice agreement between the prediction of our model for neutron FFs and experimental data. It seems that the Fractal approach based on the self-similar behavior of these conditional parton distribution functions can nicely describe the experimental data at low [Formula: see text].

The sin 2phi _h azimuthal asymmetry of pion production in SIDIS within TMD factorization

We study the sin 2phi _h azimuthal asymmetry of charged and neutral pion productions off the longitudinally polarized nucleon targets in semi-inclusive deeply inelastic scattering (SIDIS) process within the transverse momentum dependent (TMD) factorization. The asymmetry is contributed by the convolution of the TMD distribution h_{1L}^{perp } and the Collins fragmentation function H_{1}^perp . We adopt the Wandzura–Wilczek-type (WW-type) approximation for h_{1L}^{perp } and two different parametrizations on the nonperturbative Sudakov form factor for h_{1L}^{perp } and H_{1}^perp . We estimate the sin 2phi _h asymmetry at HERMES and CLAS and compare them with the corresponding experimental data. We also provide the prediction at kinematical configuration of CLAS12. It is shown that our theoretical calculation can describe the HERMES and CLAS data, except the asymmetry of the pi ^- production off proton target at HERMES and CLAS. We also find that different choices of the nonperturbative part of TMD evolution lead qualitatively similar results.

Phenomenological extraction of a universal TMD fragmentation function from single hadron production in $e^+ e^-$ annihilations

Factorizing the cross section for single hadron production in e^+e^-e+e− annihilations, differential in z_hzh, P_TPT and thrust, is a highly non trivial task. We have devised a factorization scheme that allows us to recast the e^+e^- \to hXe+e−→hX cross section in the convolution of a calculable hard coefficient and a universal Transverse Momentum Dependent (TMD) Fragmentation Function (FF). The predictions obtained from our NLO-LL perturbative computation, together with a simple ansatz to model the non-perturbative part of the TMD, are applied to the experimental measurements of the BELLE Collaboration for the phenomenological extraction of this process independent TMD FF.

Field, current, and charge distribution in a pure gauge SU(3) flux tube

The quark confinement in QCD is achieved by concentration of the chromoelectric field between the quark-antiquark pair into a flux tube, which gives rise to a linear quark-antiquark potential. We study the structure of the flux tube created by a static quark-antiquark pair in the pure gauge SU(3) theory, using lattice Monte-Carlo simulations. We calculate the spatial distribution of all three components of the chromoelectric field and perform the “zero curl subtraction” procedure to obtain the nonperturbative part of the longitudinal component of the field, which we identify as the part responsible for the formation of the flux tube. Taking the spatial derivatives of the obtained field allows us to extract the electric charge and magnetic current densities in the flux tube. The behavior of these observables under smearing and with respect to continuum scaling is investigated. Finally, we briefly discuss the role of magnetic currents in the formation of the string tension.

Black hole evolution in a quantum-gravitational framework

Abstract We investigated black hole evolution on a quantum-gravitational scattering framework with the aim of tackling the black hole information paradox. With this setup, various pieces of system information are explicit from the start and unitary evolution is manifest throughout. The scattering amplitudes factorize into a perturbative part and a non-perturbative part. The non-perturbative part is dominated by an instanton-type contribution, i.e. a black hole analogue of the Coleman–De Luccia bounce solution, and we propose that the Hawking radiation be identified with the particles generated by the vacuum decay. Our results indicate that the black hole degrees of freedom are entangled not only with the Hawking modes but also with the pre-Hawking modes. The Wald’s entropy charge measures their entanglement. The full quantum-gravitational entropy is defined as the vacuum expectation value of the Wald entropy charge. With this definition, a shifted Page-like curve is generically generated and its quantum extension is readily defined.

Factorization of e+e\u2212 \u2192 H X cross section, differential in zh, PT and thrust, in the 2-jet limit

Factorizing the cross section for single hadron production in e+e− annihilations is a highly non trivial task when the transverse momentum of the outgoing hadron with respect to the thrust axis is taken into account. We work in a scheme that allows to factorize the e+e−→ H X cross section as a convolution of a calculable hard coefficient and a Transverse Momentum Dependent (TMD) fragmentation function. The result, differential in zh, PT and thrust, will be given to all orders in perturbation theory and explicitly computed to Next to Leading Order (NLO) and Next to Leading Log (NLL) accuracy. The predictions obtained from our computation, applying the simplest and most natural ansatz to model the non-perturbative part of the TMD, are in exceptional agreement with the experimental measurements of the BELLE Collaboration. The factorization scheme we propose relates the TMD parton densities defined in 1-hadron and 2-hadron processes, restoring the possi- bility to perform global phenomenological studies of TMD physics including experimental data from semi-inclusive deep inelastic scattering, Drell-Yan processes, e+e−→ H1H2X and e+e−→ H X annihilations.

Short-distance HLbL contributions to the muon anomalous magnetic moment beyond perturbation theory

The hadronic light-by-light contribution to the muon anomalous magnetic moment depends on an integration over three off-shell momenta squared ( {Q}_i^2 ) of the correlator of four electromagnetic currents and the fourth leg at zero momentum. We derive the short-distance expansion of this correlator in the limit where all three {Q}_i^2 are large and in the Euclidean domain in QCD. This is done via a systematic operator product expansion (OPE) in a background field which we construct. The leading order term in the expansion is the massless quark loop. We also compute the non-perturbative part of the next-to-leading contribution, which is suppressed by quark masses, and the chiral limit part of the next-to-next-to leading contributions to the OPE. We build a renormalisation program for the OPE. The numerical role of the higher-order contributions is estimated and found to be small.

The confining color field in SU(3) gauge theory

We extend a previous numerical study of SU(3) Yang–Mills theory in which we measured the spatial distribution of all components of the color fields surrounding a static quark–antiquark pair and provided evidence that the simulated gauge invariant chromoelectric field can be separated into a Coulomb-like ‘perturbative’ field and a ‘non-perturbative’ confining field. In this paper we hypothesize that the fluctuating color fields not measured in our simulations do not contribute to the string tension. Under this assumption the string tension is determined by the color fields we measure, which form a field strength tensor pointing in a single direction in color space. We call this the ‘Maxwell picture of confinement’. We provide an additional procedure to isolate the confining field. We then extract the string tension from a stress energy-momentum tensor having the Maxwell form, constructed from the simulated non-perturbative part of the field strength tensor. To test our hypothesis we calculate the string tension for values of the quark–antiquark separation ranging from 0.37 fm to 1.2 fm. We also calculate the spatial distributions of the energy-momentum tensor surrounding static quarks for this range of separations, and we compare with the distributions obtained from direct simulations of the energy-momentum tensor.

$$\Omega _{ccc}$$ baryon production from gluon in vector diquark fragmentation

Hadronization is known as the nonperturbative part of hadron production process which is described by the process-independent fragmentation functions. These functions refer to the probability densities for the initial partons to fragment into observed hadrons carrying away the momentum fractions of parent partons. In this work, using the quark-diquark approximative model we compute the fragmentation density of gluon into polarized triply heavy baryon $$\Omega _{ccc}$$ in a vector cc-diquark fragmentation. To impose the polarization effect of baryon into the corresponding fragmentation function we shall apply three different scenarios and compare all results.

Probing transverse-momentum distributions with groomed jets

We present the transverse momentum spectrum of groomed jets in di-jet events for e+e− collisions and semi-inclusive deep inelastic scattering (SIDIS). The jets are groomed using a soft-drop grooming algorithm which helps in mitigating effects of non-global logarithms and underlying event. At the same time, by reducing the final state hadronization effects, it provides a clean access to the non-perturbative part of the evolution of transverse momentum dependent (TMD) distributions. In SIDIS experiments we look at the transverse momentum of the groomed jet measured w.r.t. the incoming hadron in the Breit frame. Because the final state hadronization effects are significantly reduced, the SIDIS case allows to probe the TMD parton distribution functions. We discuss the sources of non-perturbative effects in the low transverse momentum region including novel (but small) effects that arise due to grooming. We derive a factorization theorem within SCET and resum any large logarithm in the measured transverse momentum up to NNLL accuracy using the ζ-prescription as implemented in the artemide package and provide a comparison with simulations.

Extraction of unpolarized quark transverse momentum dependent parton distributions from Drell-Yan/Z-boson production

We present the extraction of unpolarized quark transverse momentum dependent parton distribution functions (TMDPDFs) and the non-perturbative part of TMD evolution kernel from the global analysis of Drell-Yan and Z-boson production data. The analysis is performed at the next-to-next-to-leading order (NNLO) in perturbative QCD, using the ζ-prescription. The estimation of the error-propagation from the experimental uncertainties to non-perturbative function is made by the replica method. The importance of the inclusion of the precise LHC data and its influence on the determination of non-perturbative functions is discussed.

Linearized Boltzmann-Langevin model for heavy quark transport in hot and dense QCD matter

In relativistic heavy-ion collisions, the production of heavy quarks at large transverse momenta is strongly suppressed compared to proton-proton collisions. In addition an unexpectedly large azimuthal anisotropy was observed for the emission of charmed hadrons in non-central collisions. Both observations pose challenges to the theoretical understanding of the coupling between heavy quarks and the quark-gluon plasma produced in these collisions. Transport models for the evolution of heavy quarks in a QCD medium offer the opportunity to study these effects - two of the most successful approaches are based on the linearized Boltzmann transport equation and the Langevin equation. In this work, we develop a hybrid transport model that combines the strengths of both of these approaches: heavy quarks scatter with medium partons using matrix-elements calculated in perturbative QCD, while between these discrete hard scatterings they evolve using a Langevin equation with empirical transport coefficients to capture the non-perturbative soft part of the interaction. With the hybrid transport model coupled to a state-of-the-art event-by-event bulk evolution model based on 2+1D relativistic viscous fluid dynamics, we study the azimuthal anisotropy and nuclear modification factor of heavy quarks in Pb+Pb collisions at $\sqrt{s} = 5.02$ TeV. The parameters of our model are calibrated using a Bayesian analysis comparing to available $D$-meson and $B$-meson data at the LHC. Using the calibrated model, we study the implications on heavy-flavor transport properties and predict novel observables.