arXiv subjects

Cédric Lorcé

Publications and source records attributed to Cédric Lorcé.

At least 37 records · Page 2Linked to original sources

arXiv2022

Kinematical higher-twist corrections in $γ^* γ\to M \bar M $

We estimate kinematical higher-twist (up to twist 4) corrections to the $γ^*(q_1) γ(q_2) \to M(p_1) \bar{M}(p_2)$ amplitudes at large $Q^2=-q_1^2$ and small $s=(q_1+q_2)^2$, where $M$ is a scalar or pseudoscalar meson. This process is known to factorize at leading twist into a perturbatively calculable coefficient function and generalized distribution amplitudes (GDAs). The kinematical higher-twist contributions of order $s/Q^2$ and $m^2/Q^2$ turn out to be important in the cross section, considering the kinematics accessible at Belle and Belle II. We present numerical estimates for the cross section for $γ^* γ\to π^0 π^0$ with the $ππ$ GDA extracted from Belle measurements and with the asymptotic $ππ$ GDA as inputs to study the magnitude of the kinematical corrections. To see how the target mass corrections of order $m^2/Q^2$ affect the cross section, we also perform the calculation for $γ^* γ\to ηη$ by using a model $ηη$ GDA.In the range $s> 1$ GeV$^2$, the kinematical higher-twist corrections account for $\sim 15 \%$ of the total cross section, an effect which is not negligible. Since $ππ$ GDAs are the best way to access the pion energy-momentum tensor (EMT), our study demonstrates that an accurate evaluation of EMT form factors requires the inclusion of kinematical higher-twist contributions.

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arXiv2022

Kinematical higher-twist corrections in $γ^* γ\to ππ$

We apply the Braun-Manashov technique to improve the description of $γ^*(q_1) γ(q_2) \to M(p_1) M(p_2)$ amplitudes at large $Q^2=-q_1^2$ and small $s=(q_1+q_2)^2$. We derive the kinematical higher-twist contributions of order $s/Q^2$ and $m^2/Q^2$ to the helicity amplitudes and estimate their sizes in the kinematics accessible at Belle and Belle II.Since pion GPDs cannot be directly measured by experiment, $ππ$ GDAs are the best way to investigate the energy-momentum tensor form factors for pions.

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arXiv2022

2D energy-momentum tensor distributions of nucleon in a large-$N_c$ quark model from ultra-relativistic to non-relativistic limit

Form factors of the energy-momentum tensor (EMT) can be interpreted in certain frames in terms of spatial distributions of energy, stress, linear and angular momentum, based on 2D or 3D Fourier transforms. This interpretation is in general subject to "relativistic recoil corrections", except when the nucleon moves at the speed of light like e.g. in the infinite-momentum frame. We show that it is possible to formulate a large-$N_c$ limit in which the probabilistic interpretation of the nucleon EMT distributions holds also in other frames. We use the bag model formulated in the large-$N_c$ limit as an internally consistent quark model framework to visualize the information content associated with the 2D EMT distributions. In order to provide more intuition, we present results in the physical situation and in three different limits: by considering a heavy-quark limit, a large system-size limit and a constituent-quark limit. The visualizations of the distributions in these extreme limits will help to interpret the results from experiments, lattice QCD, and other models or effective theories.

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arXiv2022

On the deuteron relativistic charge distributions

We study the relativistic 2D charge distributions in the case of a spin-$1$ target. These charge distributions are based on a phase-space approach allowing one to study their frame dependence, and hence to relate the familiar rest-frame picture with the light-front picture developed in the last two decades. Like in the spin-$1/2$ case, we show that relativistic kinematical effects associated with spin are responsible for the distortions of the charge distributions seen in a moving frame. Applying our results to the deuteron, we observe a mild frame dependence compared to the nucleon case.

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arXiv2021

Energy-momentum tensor in QCD: nucleon mass decomposition and mechanical equilibrium

We review and examine in detail recent developments regarding the question of the nucleon mass decomposition. We discuss in particular the virial theorem in quantum field theory and its implications for the nucleon mass decomposition and mechanical equilibrium. We reconsider the renormalization of the QCD energy-momentum tensor in minimal-subtraction-type schemes and the physical interpretation of its components, as well as the role played by the trace anomaly and Poincaré symmetry. We also study the concept of "quantum anomalous energy" proposed in some works as a new contribution to the nucleon mass. Examining the various arguments, we conclude that the quantum anomalous energy is not a genuine contribution to the mass sum rule, as a consequence of translation symmetry.

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arXiv2021

Relativistic spin sum rules and the role of the pivot

Spin sum rules depend on the choice of a pivot, i.e. the point about which the angular momentun is defined, usually identified with the center of the nucleon. The latter is however not unique in a relativistic theory and has led to apparently contradictory results in the literature. Using the recently developed phase-space approach, we compute for the first time the contribution associated with the motion of the center of the nucleon, and we derive a general spin sum rule which reduces to established results after appropriate choices for the pivot and the spin component.

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arXiv2020

Analytic constraints on the energy-momentum tensor in conformal field theories

In this work we investigate the matrix elements of the energy-momentum tensor for massless on-shell states in four-dimensional unitary, local, and Poincaré covariant quantum field theories. We demonstrate that these matrix elements can be parametrised in terms of covariant multipoles of the Lorentz generators, and that this gives rise to a form factor decomposition in which the helicity dependence of the states is factorised. Using this decomposition we go on to explore some of the consequences for conformal field theories, deriving the explicit analytic conditions imposed by conformal symmetry, and using examples to illustrate that they uniquely fix the form of the matrix elements. We also provide new insights into the constraints imposed by the existence of massless particles, showing in particular that massless free theories are necessarily conformal.

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arXiv2020

Potential linear and angular momentum in the scalar diquark model

We present an analytic two-loop calculation within the scalar diquark model of the potential linear and angular momenta, defined as the difference between the Jaffe-Manohar and Ji notions of linear and angular momenta. As expected by parity and time-reversal symmetries, a direct calculation confirms that the potential transverse momentum coincides with the Jaffe-Manohar (or canonical) definition of average quark transverse momentum, also known as the quark Sivers shift. We examine whether initial/final-state interactions at the origin of the Sivers asymmetry can also generate a potential angular momentum in the scalar diquark model.

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arXiv2020

Charge Distributions of Moving Nucleons

Relativistic charge distributions of targets with arbitrary average momentum are introduced. They provide an interpolation between the usual Breit frame and infinite-momentum frame distributions. We find that Breit frame distributions can be interpreted from a phase-space perspective as internal charge quasi-densities in the rest frame of a localized target, without any relativistic correction. We show also that the apparent discrepancies between Breit frame and infinite-momentum frame distributions simply result from kinematical artifacts associated with spin.

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arXiv2020

Study of the potential transverse momentum and potential angular momentum within the scalar diquark model

We make use of a simple scalar diquark model to study the potential transverse momentum and potential angular momentum, defined as the difference between the Jaffe-Manohar and Ji notions of transverse momentum and orbital angular momentum, respectively. A non-vanishing potential angular momentum has been previously found in lattice calculations and is believed to appear due to the effects of initial/final state interactions between the spectator system and the struck quark in high energy scattering processes. Such re-scattering phenomena are similar in nature to those who are responsible for generating the Sivers shift. This motivates us to search for an estimate of the potential angular momentum in terms of the expectation value of the transverse momentum of the struck quark.

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arXiv2020

Probing Nucleons and Nuclei in High Energy Collisions

This volume is a collection of contributions for the 7-week program "Probing Nucleons and Nuclei in High Energy Collisions" that was held at the Institute for Nuclear Theory in Seattle, WA, USA, from October 1 until November 16, 2018. The program was dedicated to the physics of the Electron Ion Collider (EIC), the world's first polarized electron-nucleon (ep) and electron-nucleus (eA) collider to be constructed in the USA. These proceedings are organized by chapters, corresponding to the weeks of the program: Week I, Generalized parton distributions; Week II, Transverse spin and TMDs; Week III, Longitudinal spin; Week IV, Symposium week; Weeks V & VI, eA collisions; Week VII, pA and AA collisions. We hope these proceedings will be useful to readers as a compilation of EIC-related science at the end of the second decade of the XXI century.

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arXiv2020

Covariant multipole expansion of local currents for massive states of any spin

We study the structure of scalar, vector, and tensor currents for on-shell massive particles of any spin. When considering higher values for the spin of the particle, the number of form factors (FFs) involved in the decomposition of the matrix elements associated with these local currents increases. We identify all the fundamental structures that give rise to the independent FFs, systematically for any spin value. These structures can be conveniently organised using an expansion in covariant multipoles, built solely from the Lorentz generators. This approach allows one to uniquely identify the terms which are universal and those that arise because of spin. We derive counting rules which relate the number of FFs to the total spin $j$ of the state, showing explicitly that these rules match all the well-known cases up to spin 2.

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arXiv2020

Universality of the Poincaré gravitational form factor constraints

Relativistic spin states are convention dependent. In this work we prove that the zero momentum-transfer limits of the leading two form factors in the decomposition of the energy-momentum tensor matrix elements are independent of this choice. In particular, we demonstrate that these constraints are insensitive to whether the corresponding states are massive or not, and that they arise purely due to the Poincaré covariance of the states.

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arXiv2020

Gravitational form factor constraints and their universality

By adopting a local QFT framework one can derive in a non-perturbative manner the constraints imposed by Poincaré symmetry on the form factors appearing in the Lorentz covariant decomposition of the energy-momentum tensor matrix elements. In particular, this approach enables one to prove that these constraints are in fact independent of the internal properties of the states appearing in the matrix elements. Here we outline the rationale behind this approach, and report on some of the implications of these findings.

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arXiv2019

Mass structure and pressure forces inside the nucleon

We summarize recent works on the question of the nucleon mass decomposition and the 2D relativistic distribution of pressure forces on the light front. All these mechanical properties are encoded in the energy-momentum tensor of the system which can be constrained using various types of high-energy lepton-nucleon scatterings. Some further developments for targets with spin $>1/2$ are also reported.

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arXiv2019

Energy, angular momentum and pressure force distributions inside nucleons

We review some of the recent developments regarding mass, angular momentum and pressure forces inside hadrons. These properties are all encoded in the energy-momentum tensor of the system, which is described at the non-perturbative level in terms of gravitational form factors. Similarly to electromagnetic form factors, Fourier transforms of gravitational form factors allow one to map out the distribution of the above mechanical properties in position space, providing a whole new way of studying in detail the internal structure of hadrons.

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arXiv2019

The energy-momentum tensor of spin-1 hadrons: formalism

We provide the complete decomposition of the local gauge-invariant energy-momentum tensor for spin-1 hadrons, including non-conserved terms for the individual parton flavors and antisymmetric contributions originating from intrinsic spin. We state sum rules for the gravitational form factors appearing in this decomposition and provide relations for the mass decomposition, work balance, total and orbital angular momentum, mass radius, and inertia tensor. Generalizing earlier work, we derive relations between the total and orbital angular momentum and the Mellin moments of twist-2 and 3 generalized parton distributions, accessible in hard exclusive processes with spin-1 targets. Throughout the work, we comment on the unique features in these relations originating from the spin-1 nature of the hadron, being absent in the lower spin cases.

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arXiv2019

Poincaré constraints on the gravitational form factors for massive states with arbitrary spin

In this work we analyse the constraints imposed by Poincaré symmetry on the gravitational form factors appearing in the Lorentz decomposition of the energy-momentum tensor matrix elements for massive states with arbitrary spin. By adopting a distributional approach, we prove for the first time non-perturbatively that the zero momentum transfer limit of the leading two form factors in the decomposition are completely independent of the spin of the states. It turns out that these constraints arise due to the general Poincaré transformation and on-shell properties of the states, as opposed to the specific characteristics of the individual Poincaré generators themselves. By expressing these leading form factors in terms of generalised parton distributions, we subsequently derive the linear and angular momentum sum rules for states with arbitrary spin.

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