{"arxiv_id":"2603.21775","incoming":{"papers":2,"sentences":4,"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2605.27857","title":"Multiplicity distributions in DIS for heavy nucleus","url":"/paper/2605.27857","section":"Introduction","sentence":"In this talk and these proceedings, based mainly on [ref] , we use this equivalence to replace the AGK cutting rules by the evolution equations.","intent_p":0.9,"contests_p":null}]}],"unlabelled_sentences":3},"outgoing":{"papers":43,"sentences":71,"groups":[{"kind":"extends","label":"Builds on","papers":2,"sentences":2,"quotes":[{"arxiv_id":"2302.10497","title":"Homotopy solution to non-linear evolution for heavy nuclei","url":"/paper/2302.10497","section":"Introduction","sentence":"We continue [ref] to develop the approach for the solution of the non-linear evolution equations that govern the deep inelastic processes (DIS) in QCD.","intent_p":0.99,"contests_p":null},{"arxiv_id":"2406.11673","title":"Modified homotopy approach for diffractive production in the saturation region","url":"/paper/2406.11673","section":"Introduction","sentence":"We continue [ref] to develop the approach for the solution of the non-linear evolution equations that govern the deep inelastic processes (DIS) in QCD.","intent_p":0.99,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses the method or tool of","papers":5,"sentences":5,"quotes":[{"arxiv_id":"2406.11673","title":"Modified homotopy approach for diffractive production in the saturation region","url":"/paper/2406.11673","section":"Leading twist BFKL kernel: homotopy approach for the solutions","sentence":"Introducing $ΔY,r⃗_ik,b⃗= 1 - 𝒩Y,r⃗_ik,b⃗$ we rewrite ME7 as follows: ∂/∂Y σ_nY,r⃗_01,b⃗ = /2 π∫d^2 r_2 Kr⃗_01| r⃗_12, r⃗_02 × [ - σ_nY,r⃗_01,b⃗ + σ_nY,r⃗_12,b⃗ ΔY,r⃗_02,b⃗ + ΔY,r⃗_12,b⃗ σ_nY,r⃗_02,b⃗ + ∑_k=1^n-1 σ_n - kY,r⃗_02,b⃗ σ_kY,r⃗_12,b⃗ ] The homotopy approach for finding $ΔY,r⃗_ik,b⃗$ has been developed in our previous paper (see Ref. [ref] ).","intent_p":0.91,"contests_p":null},{"arxiv_id":"hep-ph/9908317","title":"Solution to the evolution equation for high parton density QCD","url":"/paper/hep-ph/9908317","section":"Leading twist BFKL kernel: homotopy approach for the solutions","sentence":"To find solutions of EQXS00 we use the simplified BFKL kernel suggested in Ref. [ref] .","intent_p":0.96,"contests_p":null},{"arxiv_id":"2302.10497","title":"Homotopy solution to non-linear evolution for heavy nuclei","url":"/paper/2302.10497","section":"Leading twist BFKL kernel: homotopy approach for the solutions","sentence":"The equations $σ_n$ of EQXS00 for the leading twist BFKL kernel K2 take the form: ∂/∂Y σ_nY,r⃗_01,b⃗ = - 2 lnr_01 Q_s(Y,b⃗) σ_nY,r⃗_01,b⃗ + σ_nY,r⃗_01,b⃗ _lnQ_s^-2(Y,b⃗)^lnr_01^2dlnr_02^2 ΔY,r⃗_02,b⃗ + ΔY,r⃗_01,b⃗ _lnQ_s^-2(Y,b⃗)^lnr_01^2dlnr_02^2σ_nY,r⃗_02,b⃗ + ∑_k=1^n-1 _lnQ_s^-2(Y,b⃗)^lnr_01^2dlnr_02^2σ_n - kY,r⃗_02,b⃗ σ_kY,r⃗_01,b⃗ Introducing $z = lnr^2_01 Q^2_sY,b⃗$ ($z' = lnr^2_02 Q^2_sY,b⃗$ and $= Y - Y_A$ we rewrite EQXS01 as follows: ∂/∂ σ_n,z + κ ∂/∂z σ_n,z = - z σ_n,z + σ_n,z _ξ_0^A^z dz' Δ,z' + Δ,z _ξ_0^A^zdz' σ_n,z' + ∑_k=1^n-1 _ξ_0^A^zdz' σ_n - k,z' σ_k,zIn the following subsections we develop the homotopy approach [ref] for solving EQXS02 for small $n$.","intent_p":0.95,"contests_p":null},{"arxiv_id":"hep-ph/9807513","title":"Saturation Effects in Deep Inelastic Scattering at low $Q^2$ and its Implications on Diffraction","url":"/paper/hep-ph/9807513","section":"Introduction","sentence":"For $ξ> ξ^A_0$ we use the McLerran-Venugopalan formula for the initial condition at $Y=Y_A$ for DIS with nuclei[ We use the simplified form of McLerran-Venugopalan formula given in Ref. [ref] .","intent_p":0.87,"contests_p":null},{"arxiv_id":"2209.11940","title":null,"url":"/paper/2209.11940","section":"Conclusions","sentence":"Having these cross sections we can calculate the moments of our multiplicity distributions [ref] and obtain the multiplicity distribution $P_nz$ since P_nz = ∮d λ/2 π i e^ fλ/λ^n + 1 where the contour of integration is the circle around the point $λ=0$ and $fλ$ is the cumulant generating function, which is defined as fλ = ∑^∞_n=1 C_n /n! λ- 1^n where $C_n$ are cumulants [ref] .","intent_p":0.87,"contests_p":null}]},{"kind":"comparison","label":"Compares with","papers":1,"sentences":1,"quotes":[{"arxiv_id":"hep-ph/9908317","title":"Solution to the evolution equation for high parton density QCD","url":"/paper/hep-ph/9908317","section":"Region I","sentence":"This asymptotic behaviour coincides with the solution with the general BFKL kernel [ref] .","intent_p":0.98,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites as support","papers":3,"sentences":3,"quotes":[{"arxiv_id":"2412.02504","title":"Particle production in the toy world: multiplicity distribution and entropy","url":"/paper/2412.02504","section":"AGK equations without AGK cutting rules","sentence":"Second, in the simple but instructive one dimensional models for $σ_n$, the evolution equation can be written for $σ_n$ which do not address the AGK cutting rules in an explicit way [ref] .","intent_p":0.97,"contests_p":null},{"arxiv_id":"1702.03489","title":"Deep inelastic scattering as a probe of entanglement","url":"/paper/1702.03489","section":"Introduction","sentence":"We calculate the entropy ($S_E$) of the produced gluons and show that $S_E = lnN_DIS$ where $N_DIS$ is the multiplicity in the deep inelastic scattering process, confirming the main ideas of Ref. [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"hep-ph/0007192","title":"Geometric scaling for the total gamma^* p cross section in the low x region","url":"/paper/hep-ph/0007192","section":"Introduction","sentence":"It is important to note, that this behaviour has been proven on general theoretical grounds [ref] and has been seen in the experimental data on DIS [ref] .","intent_p":0.99,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":21,"sentences":21,"quotes":[{"arxiv_id":"hep-ph/9812311","title":"Factorization and high-energy effective action","url":"/paper/hep-ph/9812311","section":"Introduction","sentence":"The scattering amplitude of the colourless dipole with the size $x_01$ which determines the DIS cross section, satisfies the Balitsky-Kovchegov (BK) non-linear equation [ref] : ∂/∂Y N_01Y = /2 π∫d^2x_2 x^2_01/x^2_02 x^2_12 [ N_02Y + N_12Y - N_01Y - N_02YN_12Y ] where $N_ikY=NY, x⃗_ik,b⃗$ is the scattering amplitude of the dipoles with size $x_ik = |x⃗_ik| = |x⃗_i - x⃗_k|$ and with rapidity $Y$ at the impact parameter $b⃗ = x⃗_0+x⃗_1/2$.","intent_p":0.89,"contests_p":null},{"arxiv_id":"1211.69111","title":null,"url":"/paper/1211.69111","section":"Introduction","sentence":"This distribution has become a hot subject during the past several years [ref] especially because of the new view on the entropy in DIS.","intent_p":0.86,"contests_p":null},{"arxiv_id":"1506.05394","title":"Entanglement entropy and entropy production in the Color Glass Condensate framework","url":"/paper/1506.05394","section":"Introduction","sentence":"This distribution has become a hot subject during the past several years [ref] especially because of the new view on the entropy in DIS.","intent_p":0.86,"contests_p":null},{"arxiv_id":"1602.00720","title":"Entanglement Entropy of Scattering Particles","url":"/paper/1602.00720","section":"Introduction","sentence":"This distribution has become a hot subject during the past several years [ref] especially because of the new view on the entropy in DIS.","intent_p":0.86,"contests_p":null},{"arxiv_id":"1702.03489","title":"Deep inelastic scattering as a probe of entanglement","url":"/paper/1702.03489","section":"Introduction","sentence":"This distribution has become a hot subject during the past several years [ref] especially because of the new view on the entropy in DIS.","intent_p":0.86,"contests_p":null}]}],"unlabelled_sentences":39},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/2603.21775"}}