arXiv subjects
Publications and source records attributed to Stéphane Peigné.
We present an elementary recursive construction of Hermitian projectors on multi-quark ${\rm SU}(N)$ color states, based on the characterization of these states by their quadratic Casimir, and using the birdtrack pictorial technique.
High-energy proton-nucleus (pA) collisions offer valuable insight into the role of cold nuclear matter effects in hadron production. In particular, multiple rescatterings of an incoming parton by the nuclear target are known to induce the radiation of many soft gluons. Hadron production is affected by fully coherent energy loss (FCEL), owing to those radiated gluons with a long formation time. Here we present a recently derived formula for the induced single soft gluon radiation spectrum beyond leading logarithmic accuracy, whose main features are demonstrated with the example of $q\, g \to q\, g$ scattering.
We study the decomposition into $SU(N)$ irreducible representations (irreps) of the tensor product $27 \otimes 27$, where $27$ is the highest-dimensional $SU(N)$ irrep present in a two-gluon system, and explicitly construct all Hermitian projectors on these irreps, as well as transition operators between them. This yields an explicit basis of the complete $27\otimes 27$ color space (defined as the space of $27\otimes 27\to 27 \otimes 27$ color maps) in terms of orthogonal multiplets. This study shows that even complex color structures can be addressed, with the help of the birdtrack pictorial technique, using only elementary tools. In particular, we highlight the usefulness of the quadratic Casimir operator, whose eigenspaces allow efficient filtering of all projectors and transition operators, and of the permutation operators that further improve this filtering. The product $27\otimes 27$ also has an interesting feature: three equivalent irreps $27$ appear in the decomposition, two of which are symmetric and can therefore be distinguished neither by the quadratic Casimir operator nor by their symmetry under permutation. In this case, it is convenient to use Clebsch-Gordan coefficients to derive the two associated, symmetric projectors. The latter are not uniquely determined (only their sum is), and we give the set of all solutions. Finally, we explicitly derive the soft anomalous dimension matrix associated with $27\otimes 27\to 27\otimes 27$, whose block-diagonal main structure is easy to understand, but whose detailed spectrum properties remain intriguing. The approach presented for $27 \otimes 27 \to 27 \otimes 27$ could in principle be applied to any product of $SU(N)$ irreps, and eventually automated.
Results are presented for the medium-induced, soft coherent radiation spectrum for all $2\to 2$ partonic channels in QCD, at leading-order in $α_s$ but beyond leading logarithmic accuracy. The general formula is valid in the full kinematic range of the underlying process, and reduces to previous results in special cases. The soft gluon radiation spectrum is expressed in terms of the color density matrix specific to each channel, quantifying the entanglement between the color components of the $2 \to 2$ production amplitude. Beyond the leading logarithm, the spectrum depends explicitly on the off-diagonal elements of this matrix, owing to the soft gluon's ability to probe the internal color structure of the parton pair.
These lectures are an elementary introduction to the "birdtrack" color pictorial technique, a useful tool in QCD. We review the basic rules, discuss color conservation and infinitesimal color rotations, learn how to project on partonic color states, how to derive their Casimir charges... and at the same time learn a little bit of representation theory.
The phenomenon of fully coherent energy loss (FCEL) in the collisions of protons on light ions affects the physics of cosmic ray air showers. As an illustration, we address two closely related observables: hadron production in forthcoming proton-oxygen collisions at the LHC, and the atmospheric neutrino fluxes induced by the semileptonic decays of hadrons produced in proton-air collisions. In both cases, a significant nuclear suppression due to FCEL is predicted. The conventional and prompt neutrino fluxes are suppressed by $\sim 10...25\%$ in their relevant neutrino energy ranges. Previous estimates of atmospheric neutrino fluxes should be scaled down accordingly to account for FCEL.
Hadron production in proton-nucleus (pA) collisions was previously shown to be suppressed by medium-induced fully coherent energy loss (FCEL). We show that the quenching of $D$ and $B$ mesons in pPb collisions at the LHC due solely to FCEL is, at least, on par with other nuclear effects such as gluon shadowing or saturation. This is consistent with previous findings for both quarkonium and light hadron production in pA collisions, emphasising that FCEL effects need to be included for a reliable understanding of hadron production measurements in pA collisions.
I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.
We single out the role of fully coherent induced gluon radiation on light hadron production in pA collisions. The effect has the same general features as for quarkonium production, however with a richer color structure as the induced radiation depends on the global color charge of the partonic subprocess final state. Baseline predictions for light hadron nuclear suppression in pPb collisions at the LHC are provided, taking into account only the effect of fully coherent energy loss, which proves to be of the same order of magnitude as gluon shadowing or saturation. This underlines the need to include fully coherent energy loss in phenomenological studies of hadron production in pA collisions.
We single out the role of fully coherent induced gluon radiation on light hadron production in pA collisions. The effect has an interesting color structure, as the induced radiation depends on the global color charge of the partonic subprocess final state. Baseline predictions for light hadron nuclear suppression in pPb collisions at the LHC are provided, taking into account only the effect of fully coherent energy loss, which proves of the same order of magnitude as gluon shadowing or saturation. This underlines the need to include fully coherent energy loss in phenomenological studies of hadron production in pA collisions.
We revisit the transverse momentum broadening of a fast parton pair crossing a nuclear medium, putting emphasis on the pair global color state, for any number of colors $N$ and within the eikonal limit for parton propagation and the Gaussian approximation for the gluon field of the target. This study should provide the necessary tools to address nuclear broadening of $n$-parton systems in phenomenology while highlighting the color structure of the process.
We derive the medium-induced, coherent gluon radiation spectrum associated with the hard forward scattering of an energetic parton off a nucleus, in the saturation formalism and within the Gaussian approximation for the relevant correlators of Wilson lines. The calculation reproduces the simple expression for the spectrum previously obtained in the opacity expansion formalism, and rigorously specifies its validity range. The connection between the calculations in the opacity expansion and saturation formalisms is made apparent. This study may serve as a first step in order to implement consistently induced coherent energy loss and gluon shadowing in `saturation-based models' of hadron nuclear suppression in proton-nucleus collisions.
The current status of coherent energy loss is reviewed, both in theory and in its phenomenological applications to p-A collisions.
We revisit the medium-induced coherent radiation associated to hard and forward (small angle) scattering of an energetic parton through a nuclear medium. We consider all $1\to 1$ hard forward processes ($g \to g$, $q \to q$, $q \to g$ and $g \to q$), and derive the energy spectrum of induced coherent radiation rigorously to all orders in the opacity expansion and for the specific case of a Coulomb scattering potential. We obtain a simple general formula for the induced coherent spectrum, which encompasses the results corresponding to previously known special cases.
We suggest the measurement of Drell-Yan (DY) lepton pairs in p-Pb collisions at the LHC (sqrt(s)=5.02 TeV) in order to disentangle the relative contributions of shadowing and coherent energy loss in quarkonium production off nuclei. The nuclear modification of low mass DY production is computed at NLO using various sets of nuclear parton densities. It is then observed that shadowing effects strongly cancel out in the J/psi over DY suppression ratio R_{pA}^{J/psi}(y) / R_{pA}^{DY}(y), unlike the effect of coherent energy loss. Such a measurement could be performed at forward rapidity by the ALICE and LHCb collaborations at the LHC.
Quarkonium production in proton-nucleus collisions is a powerful tool to disentangle cold nuclear matter effects. A model based on coherent energy loss is able to explain the available quarkonium suppression data in a broad range of rapidities, from fixed-target to collider energies, suggesting cold energy loss to be the dominant effect in quarkonium suppression in p-A collisions. This could be further tested in a high-energy fixed-target experiment using a proton or nucleus beam. The nuclear modification factors of J/$ψ$ and $Υ$ as a function of rapidity are computed in p-A collisions at $\sqrt{s}=114.6$ GeV, and in p-Pb and Pb-Pb collisions at $\sqrt{s}=72$ GeV. These center-of-mass energies correspond to the collision on fixed-target nuclei of 7 TeV protons and 2.76 TeV lead nuclei available at the LHC.
The effect of parton energy loss in cold nuclear matter on the suppression of quarkonia (J/psi, Upsilon) in heavy-ion collisions is investigated, by extrapolating a model based on coherent radiative energy loss recently shown to describe successfully J/psi and Upsilon suppression in proton-nucleus collisions. Model predictions in heavy-ion collisions at RHIC (Au-Au, Cu-Cu, and Cu-Au) and LHC (Pb-Pb) show a sizable suppression arising from the sole effect of energy loss in cold matter. This effect should thus be considered in order to get a reliable baseline for cold nuclear matter effects in quarkonium suppression in heavy-ion collisions, in view of disentangling hot from cold nuclear effects.
Considering forward dijet production in the $q\to qg$ partonic process, we derive the spectrum of accompanying soft gluon radiation induced by rescatterings in a nuclear target. The spectrum is obtained to logarithmic accuracy for an arbitrary energy sharing between the final quark and gluon, and for final transverse momenta as well as momentum imbalance being large as compared to transverse momentum nuclear broadening. In the case of equal energy sharing and for approximately back-to-back quark and gluon transverse momenta, we reproduce a previous result of Liou and Mueller. Interpreting our result, we conjecture a simple formula for the medium-induced radiation spectrum associated to hard forward $1 \to n$ processes, which we explicitly check in the case of the $g \to gg$ process.