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Results for “Odderon”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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18 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Spin-dependent Pomeron and Odderon in elastic proton–proton scattering

We introduce a new model of near-forward elastic proton-(anti)proton scattering at high energy based on the modern formulation of Pomeron and Odderon in terms of Wilson lines and generalized TMDs (GTMDs). We compute the helicity-dependent elastic amplitudes $\phi$1,2,3,4,5 in this model and study their energy dependence from the nonlinear small-x evolution equations. While both Pomeron and Odderon contribute to helicity-flip processes in general, in the forward limit t = 0 only the double helicity-flip amplitude $\phi$2, dominated by the spin-dependent Odderon, survives. This may effect the extraction of the ρ parameter as well as the total cross section in the LHC energy domain and beyond

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

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↗
DOE OSTI2024

Holographic odderon at TOTEM?

We consider the contribution of the Odderon to diffractive p p and p p ¯ elastic scattering at large center of mass energy. We identify the Odderon and Pomeron with the Reggeized 1 ± − and 2 + + glueballs in the bulk, respectively. We use for the gravity dual description the repulsive wall model, to account for the proper Gribov diffusion for off-forward scattering. The eikonalized and unitarized amplitudes exhibit a vanishingly small rho-parameter, and a slope parameter fixed by twice the closed string slope. The results for the differential and total cross sections are compared to the empirical results reported recently by the TOTEM collaboration. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2024

Photon-odderon interference in exclusive χ c charmonium production at the Electron-Ion Collider

Exclusive C = + 1 scalar, axial-vector, and tensor quarkonium production in high-energy electron-proton scattering requires a C -odd t -channel exchange of a photon or a three-gluon ladder. We derive the expressions for the corresponding amplitudes. The relative phase of the photon vs three-gluon exchange amplitudes is determined by the sign of the light-front matrix element of the eikonal color current operator d a b c J + a J + b J + c at moderate x , and is not affected by small- x QCD evolution. Model calculations predict constructive interference, which is particularly strong for momentum transfer | t | ∼ 1 GeV 2 where the cross section for χ c J production exceeds that for pure photon exchange by up to a factor of 4. Exclusive χ c J electroproduction at the high luminosity Electron-Ion Collider occurs with well measurable rates and measurements of these processes should find evidence for the perturbative odderon exchange. We also compute the total electroproduction cross section as a function of energy and provide first estimates of the number of χ c J events per month at the Electron-Ion Collider design luminosity. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Single spin asymmetry in forward p A collisions from the Pomeron-odderon interference

Working in the hybrid framework of the high energy p A collisions we identify a new contribution to transverse single spin asymmetry (SSA). The phase necessary for the SSA is provided by the Pomeron-odderon interference in the dense nuclear target. The complete formula for the p A → h X polarized cross section also contains the transversity distribution for the polarized projectile as well as the real part of the twist-three fragmentation function. We numerically estimate the asymmetry A N and its nuclear dependence. Based on a model computation we find that A N can be a percent level in the forward and low- P h ⊥ region. For large nuclei we find significant suppression, with A N ∝ A − 7 / 6 parametrically. As a notable feature we find a node of A N as a function of the P h ⊥ around the values of the initial saturation scale that could be used to test this mechanism experimentally. Published by the American Physical Society 2025

Benić, Sanjin↗
DOE OSTI2026

Eikonal spin-dependent odderon and gluon Sivers function of a proton and its small-𝑥 evolution

The matrix element in the proton of the eikonal Odderon operator, with a helicity flip, has been shown to correspond to the dipole gluon Sivers function. We employ a three quark light-front model of the proton to determine the Sivers function at moderately small 𝑥 0 ∼ 0.1 and transverse momentum 𝑘 ⊥ ≲ 1 GeV. The model light-cone (LC) wave function predicts the properties of 𝑥⁢𝑓$^{⊥⁢𝑔}_{1⁢𝑇⁡}$(𝑥,𝑘 ⊥ ) such as its overall magnitude, the position of its peak in 𝑘 ⊥ , and its behavior at small 𝑘 ⊥ . We then compute numerically the Balitsky-Fadin-Kuraev-Lipatov anomalous dimension characterizing the power-law tail at 𝑘 ⊥ ≳ 1.5 GeV of the gluon Sivers function at small (but preasymptotic) LC momentum fractions 𝑥 ∼ 𝑥 0 ⁢𝑒 −1/𝛼 𝑠 : 𝑥⁢𝑓$^{⊥⁢𝑔}_{1⁢𝑇⁡}$⁡(𝑥,𝑘 ⊥ ) ∼ 𝑘$^{−3.3}_{⊥}$.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Quark Sivers Function at Small-$x$: Leading contribution from the Spin-Dependent Odderon

We present the calculation of the leading contribution to the quark Sivers function at small-Bjorken x as in [1]. This calculation uses the high energy scattering approximation and operator formalism developed in [2,3] to obtain a dominant contribution to the quark Sivers function coming from the spin-dependent odderon, in agreement with the results of [4]. We then calculate this dominant contribution in the diquark model of the proton to obtain a small-x estimate for the Sivers function.

Santiago, M. Gabriel↗
DOE OSTI2022

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↗
DOE OSTI2025

Gluon Sivers function from forward exclusive χ c 1 photoproduction on unpolarized protons

Exclusive production of a χ c 1 axial vector quarkonia in photon-proton scattering at high energies requires a C -odd t -channel exchange. In the limit of vanishing momentum transfer this occurs either via the exchange of a photon, the Primakoff process, where the spin of the proton does not change. For axial-vector meson production, as a consequence of the Landau-Yang theorem, the Primakoff cross section is finite as t → 0 . Alternatively, a C -odd spin dependent Odderon can be exchanged, which involves a spin flip of the proton. The resulting cross section is related to the square of the collinear trigluon correlator or the k ⊥ -moment of the gluon Sivers function. Using two models for the gluon Sivers function from the literature we compute the ratio of Sivers to Primakoff cross sections and the angular coefficient λ θ governing the angular distribution of the χ c 1 → J / ψ + γ decay as functions of x . We point out that these observables constrain the magnitude of the gluon Sivers function at small x which could be accessed in electron-proton scattering and ultraperipheral proton-proton and nucleus-proton collisions. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Unpolarized GPDs at small x and non-zero skewness

We study the small-x asymptotics of unpolarized generalized parton distributions (GPDs) and generalized transverse momentum distributions (GTMDs). Unlike the previous works in the literature, we consider the case of non-zero (but small) skewness while allowing for non-linear contributions to the evolution equations. We first show that unpolarized GPDs and GTMDs at small x are related to the eikonal dipole amplitude N, whose small-x evolution is given by the BK/JIMWLK evolution equations, and to the odderon amplitude $\mathscr{O}$, whose evolution is also known in the literature. We then show that the effect of non-zero skewness ξ ≠ 0 is to modify the value of the evolution parameter (rapidity) in the arguments for the dipole amplitudes N and $\mathscr{O}$ from Y = ln(1/x) to Y = ln min{1/|x|, 1/|ξ|}.

Generalized parton distributions (GPDs)↗
DOE OSTI2026

Single spin asymmetry in e+p → e′ +B↑ +X

We study an exotic type of single spin asymmetry in unpolarized electron-proton scattering, in which the outgoing electron momentum exhibits a left-right asymmetry relative to the transverse spin of the leading baryon B in the target fragmentation region. We lay out two theoretical frameworks for describing this effect: The twist-three fracture function at high-Q2 and the spin-dependent odderon in the high energy limit.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Entanglement enabled intensity interferometry in ultrarelativistic ultraperipheral nuclear collisions

An important tool in studying the subfemtoscale spacetime structure of matter in ultrarelativistic heavy-ion collisions is Hanbury Brown–Twiss (HBT) intensity interferometry of identical particles in the final state of the collisions. We propose that a variant of the entanglement enabled intensity interferometry (𝐸 2 ⁢𝐼 2 ) framework introduced by Cotler and Wilczek can provide a powerful alternative to HBT interferometry in extracting fundamental nonperturbative features of quantum chromodynamics at high energies. We apply this framework to demonstrate that the spatial distributions of color singlet (pomeron) configurations in nuclei are sensitive to measurements of exclusive resonant decays of 𝜌 mesons into 𝜋 ± pairs in ultrarelativistic ultraperipheral nuclear collisions (UPCs) at the Relativistic Heavy Ion Collider and the Large Hadron Collider. A preliminary analysis suggests that the model-independent extraction of pomeron distributions will require careful treatment of the interplay of 𝐸 2 ⁢𝐼 2 in the vector meson exclusive decay with the incoherent cross section for exclusive vector meson production. The 𝐸 2 ⁢𝐼 2 framework developed here is quite general. It can also be employed as a tool to extract information on the spin structure of pomeron couplings as well as enhance the discovery potential for rare odderon configurations from exclusive vector meson decays into few-particle final states both in UPCs and at the Electron-Ion Collider.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Proceedings of RIKEN BNL Research Center Workshop: Small-x Physics in the EIC Era [Slides]

Understanding the high energy limit of hadronic and nuclear collisions is at the forefront of nuclear and particle physics. When boosted to ultrahigh energies, all hadrons and nuclei eventually transform into a universal form of matter called the Color Glass Condensate (CGC). The CGC is characterized by the high density (saturation) of small-x gluons which leads to distinct experimental signatures. Tantalizing hints of the CGC have been observed at HERA, RHIC and the LHC, but the prospects for the discovery of the CGC are more promising at future experiments such as the Electron-Ion Collider (EIC) at BNL Indeed, according to the National Science Academy report published in 2019, one of the three major goals of the EIC is to address the nature of the gluon saturation. (The other two are the mass and spin structure of the nucleons.) With this in mind, the small-x community is gearing up to meet the challenges of the EIC era. Over the past several years, there has been impressive progress in the next-to-leading order (NLO) calculations in the CGC framework of various observables such as single hadron production in proton-nucleus collisions, inclusive and exclusive dijet and trijet production in Deep Inelastic Scattering (DIS), jet-plus-photon production in DIS, etc. We expect that NLO calculations will be the standard tool to confront future experimental data at the EIC. Another emerging trend of the community is the interplay between small-x physics and spin physics. The RHIC result for the gluon helicity ΔG has underscored the necessity to understand the longitudinal spin structure of the proton at small-x. There have been theoretical indications that a significant fraction of spin and orbital angular momentum is stored in the small-x region. As for the transversely polarized proton, a surprising new connection between the gluon Sivers function at small-x and the QCD Odderon has been pointed out and its implications at the EIC has been discussed. In view of these developments, we think it is timely to organize a dedicated workshop on small-x physics to summarize the present status of the field and to discuss future directions. A major focus of this workshop will be to identify outstanding problems that could significantly benefit from collaborative efforts amongst scientists working on formal, phenomenological, and computational aspects of small-x physics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Comparison of differential elastic cross sections in $pp$ and $p\bar{p}$ collisions as evidence of the existence of the colourless $C$-odd three-gluon state

We analyze the differences between the $pp$ and $p\bar{p}$ differential elastic cross section measurements by theD0 and TOTEM Collaborations at the Tevatron, Fermilab, and the LHC, CERN that lead to a significance larger than 3$\sigma$ of the existence of thecolourless $C$-odd three-gluon state, the odderon.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

SU(3) Gauge Symmetry: An Experimental Review of Diffractive Physics in e+p, p+p, p+ A, and A+A Collision Systems

This review focuses on diffractive physics, which involves the long-range interactions of strong nuclear force at high energies described by SU(3) gauge symmetry. It is expected that diffractive processes account for nearly 40% of the total cross-section at LHC energies. These processes consist of soft-scale physics where perturbation theory cannot be applied. Although highly successful and often described as a perfect theory, quantum chromodynamics relies heavily on perturbation theory, a model best suited for hard-scale physics. The study of pomerons could help bridge the soft and hard processes and provide a complete description of the theory of the strong interaction across the full momentum spectrum. Here, we will discuss some of the features of diffractive physics, experimental results from SPS, HERA, and the LHC, and where the field could potentially lead. With the recent publication of the odderon discovery in 2021 by the D0 and TOTEM collaborations and the new horizon of physics that lies ahead with the upcoming Electron-Ion Collider at Brookhaven National Laboratory, interest is seemingly piquing in high energy diffractive physics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗