REVIEW
Forward dijets in proton-nucleus collisions at next-to-leading order: the real corrections
High Energy Physics - Phenomenology · Submitted 24 Sep 2020 · 79 references
Pith's verdict: A careful real-emission NLO calculation for forward dijets that passes non-trivial soft and collinear limit checks, but is explicitly incomplete without its promised virtual companion.
T0 · AI review
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Referee report
The paper
The paper claims
The real NLO corrections to forward dijet production in proton–nucleus collisions reproduce the expected high-energy evolution for soft unmeasured gluons and the expected collinear evolution for collinear splittings.
The reading
What carries the argument
The load-bearing object is the three-parton component of the outgoing quark light-cone wavefunction, expanded to second order in the QCD interaction Hamiltonian with the nuclear shockwave inserted before, between, or after the emissions. The organising identity is Eq. (3.3), which rewrites the mixed initial/final-state energy denominator as two negative terms, turning the initial-state scattering into a subtraction that removes unphysical radiation in the no-scattering limit. This reshuffling produces compact expressions whose numerators vanish when daughter-parton transverse separations shrink, allowing cross-section formulae that reduce, upon integrating out one parton, to the known evolution kernels in the soft and collinear limits. At large $N_c$, the only surviving colour structures are dipole and quadrupole S-matrices, and in each limit only four of the sixteen emission topologies survive.
Extended reading notes
Core claim
The paper establishes that the real part of the NLO dijet cross-section for forward quark-channel production is contained in the newly reorganised tree-level trijet cross-sections for the $q\bar q q$ and $qgg$ final states. When any one of the three final partons is integrated out, the colour structure collapses at large $N_c$ into products of dipole and quadrupole S-matrices, and the remaining expressions yield the real terms of the B-JIMWLK evolution in the soft-gluon limit and the first DGLAP step for the initial quark, the final quark, and the final gluon (both $g\to gg$ and $g\to q\bar q$) in the collinear limit. The paper therefore claims to have the real NLO corrections to forward dijet production under control, with the matching virtual corrections promised in a companion publication.
Load-bearing premise
The load-bearing premise is that the virtual corrections, deferred to a later paper, will cancel the leftover soft and collinear divergences of these real terms exactly as sketched; if that cancellation is not realised, the real terms alone are not a physical NLO cross-section.
Editorial extensions
If this is right
- The real terms, once combined with the deferred virtual terms, should give the first complete NLO impact factor for forward quark-channel dijets in this formalism.
- The soft-gluon limit confirms that the B-JIMWLK evolution of the leading-order cross-section is generated by the real corrections alone; the hard NLO impact factor is only the part where the unmeasured gluon carries a momentum fraction of order one.
- The collinear limits identify which DGLAP splitting functions enter with which arguments, making the scale-dependence of the incoming quark distribution and of the quark and gluon fragmentation functions explicit.
- The corrected trijet cross-sections in Sections 3.2.1 and 3.2.2 supersede the earlier ones and should serve as the starting point for any further NLO calculation in this framework.
Reading between the lines
- A natural next step, the gluon-initiated channel, can likely be built from the same four-topology pattern in the soft and collinear limits; the main new inputs would be colour factors and symmetry factors.
- Because the final expressions still contain undone Fourier transforms over transverse coordinates, the practical accuracy of a phenomenological implementation will hinge on the quality of the S-matrix input, such as numerical solutions or mean-field approximations, rather than on the perturbative derivation itself.
- The fact that both limits select the same four of sixteen topologies suggests a useful consistency rule for future NLO impact factors in this framework: after integrating out an unmeasured parton, only graphs with no intermediate emission vertex between the shockwave and the soft or collinear parton should survive.
Original abstract
Using the CGC effective theory together with the hybrid factorisation, we study forward dijet production in proton-nucleus collisions beyond leading order. In this paper, we compute the "real" next-to-leading order (NLO) corrections, i.e. the radiative corrections associated with a three-parton final state, out of which only two are being measured. To that aim, we start by revisiting our previous results for the three-parton cross-section presented in our previous paper. After some reshuffling of terms, we deduce new expressions for these results, which not only look considerably simpler, but are also physically more transparent. We also correct several errors in this process. The real NLO corrections to inclusive dijet production are then obtained by integrating out the kinematics of any of the three final partons. We explicitly work out the interesting limits where the unmeasured parton is either a soft gluon, or the product of a collinear splitting. We find the expected results in both limits: the B-JIMWLK evolution of the leading-order dijet cross-section in the first case (soft gluon) and, respectively, the DGLAP evolution of the initial and final states in the second case (collinear splitting). The "virtual" NLO corrections to dijet production will be presented in a subsequent publication.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
Using the CGC effective theory together with the hybrid factorisation, we study forward dijet production in proton-nucleus collisions beyond leading order. In this paper, we compute the "real" next-to-leading order (NLO) corrections, i.e. the radiative corrections associated with a three-parton final state, out of which only two are being measured. To that aim, we start by revisiting our previous results for the three-parton cross-section presented in our previous paper. After some reshuffling of terms, we deduce new expressions for these results, which not only look considerably simpler, but are also physically more transparent. We also correct several errors in this process. The real NLO corrections to inclusive dijet production are then obtained by integrating out the kinematics of any of the three final partons. We explicitly work out the interesting limits where the unmeasured parton is either a soft gluon, or the product of a collinear splitting. We find the expected results in both limits: the B-JIMWLK evolution of the leading-order dijet cross-section in the first case (soft gluon) and, respectively, the DGLAP evolution of the initial and final states in the second case (collinear splitting). The "virtual" NLO corrections to dijet production will be presented in a subsequent publication.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Using the CGC effective theory together with the hybrid factorisation, we study forward dijet production in proton-nucleus collisions beyond leading order. | contribution 0.94 | 0.89 | 0.06 | asserted 0.96 |
| s1 | In this paper, we compute the "real" next-to-leading order (NLO) corrections, i.e. the radiative corrections associated with a three-parton final state, out of which only two are being measured. | contribution 1.00 | 0.95 | 0.15 | asserted 1.00 |
| s2 | To that aim, we start by revisiting our previous results for the three-parton cross-section presented in our previous paper. | method 0.82 | 0.64 | 0.02 | asserted 0.92 |
| s3 | After some reshuffling of terms, we deduce new expressions for these results, which not only look considerably simpler, but are also physically more transparent. | contribution 0.45 | 0.94 | 0.10 | asserted 1.00 |
| s4 | We also correct several errors in this process. | contribution 0.87 | 0.92 | 0.02 | asserted 1.00 |
| s5 | The real NLO corrections to inclusive dijet production are then obtained by integrating out the kinematics of any of the three final partons. | method 0.91 | 0.91 | 0.11 | asserted 1.00 |
| s6 | We explicitly work out the interesting limits where the unmeasured parton is either a soft gluon, or the product of a collinear splitting. | method 0.79 | 0.95 | 0.07 | asserted 0.97 |
| s7 | We find the expected results in both limits: the B-JIMWLK evolution of the leading-order dijet cross-section in the first case (soft gluon) and, respectively, the DGLAP evolution of the initial and final states in the second case (collinear splitting). | result 0.92 | 0.93 | 0.38 | asserted 1.00 |
| s8 | The "virtual" NLO corrections to dijet production will be presented in a subsequent publication. | future work 0.98 | 0.20 | 0.03 | asserted 0.99 |
What was examined, and what was not
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References
How the literature uses it
24 arXiv papers cite this in 44 sentences
Papers citing it · 26 sentences without a confident label
Builds on it 1 paper
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Combined with the real NLO correction to the dijet cross section in the quark-initiated channel computed in [ref] , this work thus completes the calculation of the full trijet cross section in pA collisions.
Forward trijet production in proton-nucleus collisions: gluon initiated channel · Conclusions · 0.92
Uses its method or tool 1 paper
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Using the factorized notation eq:splitforsubtr, the procedure of Ref. [ref] for obtaining amplitudes for the emission-after-the-shock contributions in [ref] is the following.
Diffractive deep inelastic scattering at NLO in the dipole picture: the $q \bar q g$ contribution · Radiative corrections · 0.95
Compares with it 1 paper
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The connection is easiest to see in terms of the diagrams for the amplitude, which are the same in both approaches and lead to the same expressions[Note however that Refs. [ref] use a different normalization for single particle states and for phase space integrals.].
Diffractive deep inelastic scattering at NLO in the dipole picture: the $q \bar q g$ contribution · Initial and final Fock states · 0.91
Cites it as background 12 papers
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In the context of $pA$ collisions, this includes the single inclusive hadron (or jet) production in $pA$ collisions [ref] , photon production at central rapidities [ref] , and the “real” NLO corrections to dihadron production [ref] — i.e. the NLO effects associated with a 3-parton final state, out of which only 2 are measured.
Dihadron production in DIS at NLO: the real corrections · Introduction · 0.91
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Remarkable efforts to march toward NLO predictions are set out to compute the real corrections for dijet production [ref] and LO trijets [ref] in $pA$ collisions.
Single Inclusive Jet Production in $pA$ Collisions at NLO in the small-$x$ regime · Introduction · 0.84
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A class of observables that attracted much attention over the last years refers to the production of a pair of jets in “dilute-dense” collisions (electron-nucleus, proton-nucleus, ultraperipheral proton-nucleus and nucleus-nucleus) at high energy [ref] .
Probing parton saturation and the gluon dipole via diffractive jet production at the Electron-Ion Collider · Introduction · 1.00
What it cites · 90 sentences without a confident label
Compares with 8 papers
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As expected, qgg1-eik1 is the same as the result of acting with the “production” version of the JIMWLK Hamiltonian [ref] on the last term (the dipole $𝒮(w, w)$) in the LO $qg$ cross-section [ref].
One gluon, two gluon: multigluon production via high energy evolution · Direct emissions by the quark · 0.84
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As expected, qgg1-eik1 is the same as the result of acting with the “production” version of the JIMWLK Hamiltonian [ref] on the last term (the dipole $𝒮(w, w)$) in the LO $qg$ cross-section [ref].
JIMWLK evolution for multi-particle production in Langevin form · Direct emissions by the quark · 0.84
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As expected, qgg1-eik1 is the same as the result of acting with the “production” version of the JIMWLK Hamiltonian [ref] on the last term (the dipole $𝒮(w, w)$) in the LO $qg$ cross-section [ref].
Treading on the cut: Semi inclusive observables at high energy · Direct emissions by the quark · 0.84
Cites as background 46 papers
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Yet, via explicit calculations and tenuous efforts, one was able to build the NLO versions of the BK [ref] and B-JIMWLK [ref] equations, and also of the “'impact factors” (the scattering matrix elements void of evolution) for a few, relatively simple, processes, like single inclusive hadron production in $pA$ collisions [ref] , the structure functions for electron-proton ($ep$) or electron-nucleus ($eA$) deep inelastic scattering (DIS) at small Bjorken $x$ [ref] , exclusive diffractive vector-meson and dijet production in DIS at small $x$ [ref] , and inclusive photon + dijet production in $eA$ collisions at small $x$ [ref] .
Dipole factorization for DIS at NLO: Combining the $q\bar{q}$ and $q\bar{q}g$ contributions · Introduction · 0.90
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Yet, via explicit calculations and tenuous efforts, one was able to build the NLO versions of the BK [ref] and B-JIMWLK [ref] equations, and also of the “'impact factors” (the scattering matrix elements void of evolution) for a few, relatively simple, processes, like single inclusive hadron production in $pA$ collisions [ref] , the structure functions for electron-proton ($ep$) or electron-nucleus ($eA$) deep inelastic scattering (DIS) at small Bjorken $x$ [ref] , exclusive diffractive vector-meson and dijet production in DIS at small $x$ [ref] , and inclusive photon + dijet production in $eA$ collisions at small $x$ [ref] .
Paving the Way Towards Precision Physics in Saturation Studies Through Exclusive Diffractive Light Neutral Vector Meson Production · Introduction · 0.90
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Yet, via explicit calculations and tenuous efforts, one was able to build the NLO versions of the BK [ref] and B-JIMWLK [ref] equations, and also of the “'impact factors” (the scattering matrix elements void of evolution) for a few, relatively simple, processes, like single inclusive hadron production in $pA$ collisions [ref] , the structure functions for electron-proton ($ep$) or electron-nucleus ($eA$) deep inelastic scattering (DIS) at small Bjorken $x$ [ref] , exclusive diffractive vector-meson and dijet production in DIS at small $x$ [ref] , and inclusive photon + dijet production in $eA$ collisions at small $x$ [ref] .
High Energy QCD at NLO: from light-cone wave function to JIMWLK evolution · Introduction · 0.90
Discussion
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