{"id":"780b3196-9b02-429e-a323-8d8394a1ec0f","arxiv_id":"2505.02711","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"The transverse spin asymmetry for isolated-photon SIDIS at EIC energies is estimated to reach 10% or more in specific kinematics, offering a path to constrain the quark-gluon-quark correlators F_FT(x,x') and G_FT(x,x') point by point.","lead":"This paper computes how large a spin-dependent asymmetry could be when an electron hits a sideways-spinning proton and produces an isolated photon, using two models of quark-gluon-quark correlations. It finds the asymmetry can reach 10 percent or more at low-energy Electron-Ion Collider kinematics, which would make the measurement a new window into multi-parton proton structure.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 10% asymmetry appears at Q^2 values that violate the paper's own stated factorization conditions; stricter cuts may erase the high-asymmetry region.","rationale":"The reader's weakest-assumption analysis identifies the same soft spot: the numerical scan keeps Q^2, ~Q^2, and Q^2 - ~Q^2 above 1 GeV^2 while the analytic formalism requires each to be much larger than M^2 ~ 0.88 GeV^2, and the largest asymmetries occur in the low-Q^2 part of the surviving phase space. I considered whether the more fundamental issue is instead the model dependence of FFT and GFT: Scenario 1 uses hand-chosen Fourier coefficients, and the SFP contribution is comparable to or larger than the HP contribution, so a single measurement does not by itself give point-by-point access to FFT(x_B,~x_B) and GFT(x_B,~x_B). Those are real limitations, but the paper is candid about them, varies some inputs, and provides a public notebook for exploration. The factorization violation, by contrast, is a correctness risk for the entire numerical estimate in the very bins that motivate the headline claim. It is testable with a straightforward cut-and-recompute exercise, and the outcome determines whether the 10% signal should be interpreted as a prediction of the collinear twist-3 framework or as an uncontrolled power-correction artifact. The reader's CONDITIONAL verdict already captures the need for such a check, so no verdict change is needed; the paper's phase-space guidance remains valuable, but the quantitative measurability claim should be read as contingent on a successful test of factorization in the high-asymmetry region.","tokens_in":18259,"tokens_out":4185,"duration_ms":50673,"concrete_test":"Recompute the Scenario 0 and Scenario 1 heat maps at sqrt(s)=29 GeV with phi'=phi_gamma=0 using the public Colab code, but impose the additional cuts Q^2 > 4 GeV^2, ~Q^2 > 4 GeV^2, and Q^2 - ~Q^2 > 4 GeV^2, so that all three quantities are at least several times M^2. If bins with |A_UT| of 10% or more survive these cuts, the factorization concern is numerically not decisive; if the surviving maxima drop to a few percent or the high-asymmetry region disappears, then the quantitative 'measurable 10%' claim rests on kinematics outside the stated domain of validity of the twist-3 collinear computation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 2 states that a partonic description is valid only if Q^2 >> M^2, ~Q^2 >> M^2, and Q^2 - ~Q^2 >> M^2, with M^2 approximately 0.88 GeV^2. Section 4 retains points satisfying only Q^2 > 1 GeV^2, ~Q^2 > 1 GeV^2, and Q^2 - ~Q^2 > 1 GeV^2. In exactly the region highlighted as producing |A_UT| of 10% or more at sqrt(s)=29 GeV (electron at mid or backward rapidity, low electron p_T, photon p_T above about 3 GeV, and aligned azimuthal angles), Q^2 can be only a few GeV^2 or less, so M^2/Q^2 is of order 0.3-1 and Q^2 - ~Q^2 can be comparable to M^2. This is precisely where target-mass, higher-twist, and other power corrections not present in Eqs. (3)-(6) can shift a twist-3 asymmetry of nominal size 10% by an order-one factor. The paper warns about the edges of phase space and about |A_UT|>1, but it does not mention the mismatch between its own factorization condition and the cuts used in the most optimistic panels. Because the central claim is that A_UT^gammaSIDIS will be measurable at the EIC, an O(1) uncertainty in those panels is load-bearing: it determines whether the headline 10% estimate is a reliable guide to the EIC or an artifact of kinematics outside the regime where the calculation is controlled.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"Summary: This paper proposes the transverse single-spin asymmetry A_UT^{\\gamma SIDIS} in semi-inclusive deep-inelastic production of isolated photons as an observable that accesses the quark-gluon-quark correlators F_FT(x,x') and G_FT(x,x') point-by-point over their full support. Building on the analytic cross section of Ref. [34], the authors rewrite the polarized cross section in a compact form using two azimuthal spin structures and the combinations F_n\\pm = F_FT \\pm G_FT (Eqs. (5)-(6)), and tabulate all 16 hard-scattering coefficients in Appendix A. They construct models for F_FT and G_FT from the JAM3D-22 Sivers first moment f_1T^{\\perp(1)} and the lattice d2 matrix element, using a Fourier expansion in polar coordinates (Eqs. (12)-(14)) with two parameter scenarios. Numerical results at \\sqrt{s} = 29, 63, and 141 GeV are presented as heat maps, with the finding that |A_UT| can reach 10% or more for \\sqrt{s} = 29 GeV at mid-to-backward electron rapidity, mid-to-forward photon rapidity, low electron p_T, high photon p_T, and aligned azimuthal angles. The paper also discusses the relative importance of hard-pole and soft-fermion-pole contributions and the possibility of a beam-charge asymmetry to separate the Compton and Interference channels.","tokens_in":18721,"tokens_out":12863,"duration_ms":136358,"significance":"The conceptual proposal is attractive and timely: a new EIC observable that encodes pointwise information on quark-gluon-quark correlations would be genuinely unprecedented, and the compressed analytic form plus the full Appendix A listing of hard coefficients is a service to the community. The accompanying Colab notebook is a constructive resource that allows independent exploration. These are real strengths. However, the status of the numerical estimates is limited by three coupled issues: the 10% result is produced in kinematic regions where the paper's own factorization conditions are not satisfied; the Scenario 1 Fourier coefficients are essentially unconstrained and no sensitivity range is given; and the conclusion that the asymmetry 'will be measurable' is not backed by a statistical significance estimate. If the first issue is resolved by stricter cuts and the model uncertainty is quantified, the paper would provide a useful and falsifiable benchmark. As it stands, the central claim is defensible in outline but requires revision.","major_comments":[{"comment":"Equation (3) is stated to be valid when Q^2 >> M^2, \\tilde{Q}^2 >> M^2, and Q^2 - \\tilde{Q}^2 >> M^2, while Sec. 4 retains points with only Q^2 > 1 GeV^2, \\tilde{Q}^2 > 1 GeV^2, and Q^2 - \\tilde{Q}^2 > 1 GeV^2 with M^2 \\approx 0.88 GeV^2. The high-asymmetry regions of Figs. 3 and 4 (\\eta' \\approx 0 or -1, p'_T \\lesssim 3 GeV, \\eta_\\gamma \\gtrsim 0, p_{\\gamma T} \\gtrsim 3 GeV at \\sqrt{s} = 29 GeV) can have Q^2 of only a few GeV^2, so M^2/Q^2 is of order 0.2-0.4 and power corrections absent from Eqs. (3)-(6) can change a nominal 10% asymmetry by an order-one factor. Please demonstrate that the 10% result survives under cuts that actually enforce the stated hierarchy (e.g., Q^2, \\tilde{Q}^2, |Q^2 - \\tilde{Q}^2| > 4 GeV^2 or > 4 M^2), or otherwise quantify the size of target-mass and higher-twist corrections in the published plots; without this, the headline claim is not established in the regime where the calculation is controlled.","section":"§2 and §4"},{"comment":"The '10% or larger' numerical result is driven by Scenario 1, whose coefficients a^q_3...a^q_7 and b^q_1...b^q_6 are chosen by hand as 'arbitrary values between -1 and 1' (Sec. 3), with only a^q_2 fixed by the lattice d2 constraint through Eq. (17). Because F_FT and G_FT are otherwise unconstrained, the quoted 10% is an output of a single ad-hoc parameter choice, not a bound or a scan; no uncertainties from JAM3D-22 or the lattice d2 values are propagated. Please add a sensitivity study over the coefficient space (the Colab notebook could serve this purpose) reporting the range of |A_UT| in the highlighted kinematic region, or explicitly downgrade the 10% statement to 'an illustrative model scenario' in the abstract and conclusions.","section":"§3, Scenario 1 (Eqs. (12)-(15))"},{"comment":"The abstract and Sec. 5 state that A_UT^{\\gamma SIDIS} 'will be measurable at the EIC', but the paper provides no estimate of the expected statistical uncertainty: no integrated luminosity, no event rates, no acceptance or binning efficiency are used to convert the 10% asymmetry into a significance. Since the central conclusion is measurability, a rough projection (even order-of-magnitude, using typical EIC luminosities and the cross sections in Eqs. (3) and (5)) is needed to support the claim; otherwise the conclusion should be softened to 'potentially observable'.","section":"§4 and §5"},{"comment":"The model evolution is 'inherited' from the Sivers-function DGLAP evolution, and the full twist-3 evolution including mixing with trigluon correlators (available via the code of Ref. [61]) is not used. The argument that such evolution effects cancel in asymmetries is standard for TMD ratio observables, but it is not automatic here because the numerator is a twist-3 collinear cross section involving F_FT and G_FT at several (x,x') pairs, while the denominator uses f_1 at scales Q, \\tilde{Q}, and \\sqrt{Q\\tilde{Q}}. Please quantify the impact of the full twist-3 evolution, or state explicitly why it is negligible at the scales of Figs. 3-6; otherwise the kinematic pattern of the 10% regions carries an unquantified dependence on this approximation.","section":"§3, model evolution (paragraph after Eq. (14))"}],"minor_comments":[{"comment":"The symbols '\\epsilon Pll^\\prime S' and '\\epsilon PlP_\\gamma S' are used in Eq. (5) but defined only later in Eq. (A.3); please define them at first use in Sec. 2.","section":"§2, Eq. (5)"},{"comment":"The color scale in Figs. 3-6 saturates at |A_UT| = 0.10, so '10% or larger' indicates only the saturation of the scale; please report the actual maximum value of |A_UT| found in each scenario, and whether any points exceed 0.10 after the |A_UT| > 1 rejection.","section":"§4, Figs. 3-6"},{"comment":"The sentence 'We must use caution when large asymmetries arise at the periphery of the subgraphs' is not quantitative; please define what fraction of the phase space is considered periphery and how many points are rejected by the |A_UT| \\le 1 cut.","section":"§4, after Eq. (7)"},{"comment":"There is a typographical artifact 'su fficient' in the sentence following Eq. (14); please correct the spacing and punctuation.","section":"§3, Eq. (14)"},{"comment":"The reflection of points across the x_B = \\tilde{x}_B line in Fig. 5 exploits Eq. (8), but the caption should clarify that the plotted asymmetry at reflected points is the same because the observable is evaluated at F_FT(x_B,\\tilde{x}_B) and the symmetry (8) relates this to the reflected point; as written, 'experimental coverage only explicitly gives points below the line' is not immediately clear.","section":"§4, Fig. 5 caption"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within the scope of a phenomenological journal and the authors are transparent about many caveats. My main editorial concern is that the abstract and conclusions state the 10% result and the measurability claim more strongly than the model freedom and kinematic cuts warrant; the requested revisions (stricter cuts or power-correction estimate, sensitivity scan, statistical projection) should be doable within the scope of the paper. There are no concerns about citation practice or novelty."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a useful paper, worth refereeing, but the headline 10% claim should be read as a model-dependent estimate, not a prediction. The new content is real: first EIC phase-space scan for A_UT^γSIDIS, a compact rewrite of the cross section, all 16 hard-scattering coefficients in an appendix, and a public Colab notebook. They lean on the analytic result in Ref. [34] and the FFT/GFT ansatz from Ref. [27]; both are published and the overlap is acknowledged. No circularity: the models are constrained by the Sivers first moment and lattice d2, not tuned to reproduce this asymmetry.\n\nWhat they do well: the derivation is transparent, the coefficients are all written out, and the paper is unusually honest about its own caveats—points with |A_UT|>1 are excluded, evolution is simplified, and the soft-fermion-pole dilution is discussed. The phase-space guidance (low CM energy, mid/backward electron, forward photon, aligned azimuths) is sensible and likely robust. The Colab notebook is a real asset.\n\nWhere it gets soft. The 10% numbers come from hand-chosen Fourier coefficients for correlators that are essentially unknown; Scenario 1 is built to make the asymmetry large. There are no propagated uncertainties and no variation over coefficient choices beyond two scenarios. That alone would make me say 'encouraging, not quantitative.' More important is the factorization mismatch the stress test flagged: Sec. 2 states the partonic description requires Q² >> M², ~Q² >> M², and Q²−~Q² >> M², but the numerical cuts only enforce >1 GeV² with M² ≈ 0.88 GeV². The high-asymmetry region sits at low electron p_T and mid/backward rapidity, where Q² can be a few GeV², so M²/Q² is of order 0.3–1. The paper does not flag that its own most optimistic panels sit at the edge of its stated domain. That is a genuine soft spot, and it is load-bearing for the 'measurable at the EIC' sentence. The physics could survive—power corrections might not kill a 10% twist-3 asymmetry—but we don't know until someone checks.\n\nBottom line: this deserves a serious referee. I would send it to peer review and expect revision: add a Q²-dependent version of the key panels or state the Q² distribution in the red regions, do a sensitivity scan over the unknown coefficients, and reframe the 10% as a model-dependent estimate. The analysis and code are solid enough to be useful immediately; the claim needs to be brought in line with the kinematics.","headline":"A careful, transparent first numerical look at a new twist-3 observable, worth refereeing, but the 10% headline panels sit at Q² values where the paper's own factorization condition is not comfortably met.","tokens_in":19246,"tokens_out":2322,"would_cite":true,"duration_ms":26207,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Transverse single-spin asymmetries in photon-tagged deep-inelastic scattering can map the proton's quark-gluon-quark correlators point-by-point across their full momentum-fraction support, with the paper's numerical estimates reaching 10…","keywords":["transverse single-spin asymmetries","quark-gluon-quark correlators","twist-3 factorization","semi-inclusive deep-inelastic scattering","isolated photon production","Electron-Ion Collider","Sivers function","d2 matrix element"],"falsifier":"Measure $A_{UT}^{\\gamma\\mathrm{SIDIS}}$ at the Electron-Ion Collider at $\\sqrt{s}=29$ GeV in the phase-space region identified as largest (mid or backward electron rapidity, forward photon rapidity, electron $p_T$ below about 3 GeV, photon $p_T$ above about 3 GeV, and $\\phi'=\\phi_\\gamma=0$); if the asymmetry is consistent with zero at few-percent precision across that region, the claim that this observable is a practical pointwise probe of $F_{FT}$ and $G_{FT}$ would be falsified for these models. A second check is to test whether the asymmetry in that region follows the $Q^2$ dependence implied by factorization; strong violations at low $Q^2$ would indicate power corrections dominate.","tokens_in":18004,"feed_emoji":"⚛️","tokens_out":9902,"duration_ms":101291,"temperature":0.7,"pith_summary":"This paper argues that a transverse single-spin asymmetry measured in the semi-inclusive deep-inelastic production of isolated photons (γSIDIS) would give the first direct, point-by-point view of the proton's quark-gluon-quark correlations, the twist-3 functions $F_{FT}(x,x')$ and $G_{FT}(x,x')$. Earlier observables only saw these functions under integrals over $x$ or $x'$, or along the diagonal $x=x'$. The authors rewrite the analytic cross section in a compact form in which the polarized numerator depends on $F_{FT}$ and $G_{FT}$ evaluated at the distinct momentum fractions $(x_B,\\tilde x_B)$ and $(x_B,0)$. Using models anchored to the Sivers function and to a lattice-QCD value for the $d_2$ matrix element, they scan the Electron-Ion Collider phase space and find the asymmetry can reach 10% or more at $\\sqrt{s}=29$ GeV. If the measurement works, it would supply information about multi-parton correlations in the nucleon that no earlier observable could provide.","feed_headline":"10% spin asymmetry could expose hidden quark-gluon structure","feed_subtitle":"At the Electron-Ion Collider, this spin asymmetry could map quark-gluon-quark structure.","key_machinery":"The object that carries the argument is the pair of twist-3 quark-gluon-quark correlators $F_{FT}(x,x')$ and $G_{FT}(x,x')$, which are light-cone matrix elements of a quark-antiquark pair joined by a gluon field strength, encoding the longitudinal momentum sharing among two quarks and a gluon in the polarized proton. The essential mechanism is the kinematic structure of Eq. (6): the polarized cross section is built from the linear combinations $F_\\pm = F_{FT} \\pm G_{FT}$ evaluated at exactly two points, the off-diagonal hard-pole point $(x_B,\\tilde x_B)$ and the soft-fermion-pole point $(x_B,0)$, rather than integrated over a momentum fraction. A second piece of machinery is the model that makes numerics possible: a Fourier expansion of $F_{FT}$ and $G_{FT}$ in polar coordinates adjusted to the support region, normalized by the first transverse moment of the Sivers function, with one Fourier coefficient fixed by the lattice-QCD value of the $d_2$ matrix element.","core_discovery":"The central claim is that $A_{UT}^{\\gamma\\mathrm{SIDIS}}$ is a direct probe of the dynamical twist-3 quark-gluon-quark correlators $F_{FT}$ and $G_{FT}$ in their full two-dimensional support. The numerator of the asymmetry reduces, after combining the two correlators into $F_\\pm = F_{FT} \\pm G_{FT}$ and compressing four azimuthal spin structures into two, to a sum over Compton and interference channels of hard coefficients times $F_\\pm(x_B,\\tilde x_B)$ plus soft-fermion-pole coefficients times $F_\\pm(x_B,0)$. The hard-pole term samples the off-diagonal point $(x_B,\\tilde x_B)$ and the soft-fermion-pole term samples $(x_B,0)$; the Bethe-Heitler and soft-gluon-pole contributions cancel. With a model built from the first transverse moment of the Sivers function and a lattice constraint for $d_2$, the authors find $|A_{UT}|$ around 3–5% in a minimal scenario and 10% or more in a fuller scenario, concentrated at low electron $p_T$, high photon $p_T$, mid or backward electron rapidity, mid or forward photon rapidity, and aligned azimuthal angles at $\\sqrt{s}=29$ GeV. They conclude the asymmetry will likely be measurable at the EIC and would provide unprecedented information on $F_{FT}$ and $G_{FT}$ across their full support.","pith_inferences":["Because the numerator is a sum of hard-pole and soft-fermion-pole terms, a single asymmetry measurement cannot separate $F_\\pm(x_B,\\tilde x_B)$ from $F_\\pm(x_B,0)$; combining electron and positron beam measurements may help disentangle the two kinematic slices by weighting charge combinations differently.","If the predicted 10% asymmetries are confirmed, the same experiment would provide an indirect check of the relation between $F_{FT}(x,x)$ and the Sivers first moment, and of the lattice $d_2$ constraint, at momentum fractions not accessible before.","The strong energy dependence suggests that EIC running at the lowest collision energy gives the best discovery window; a dedicated low-energy run may be worth more than high-luminosity high-energy running for this observable.","A null result in the predicted high-asymmetry region would be informative either way: it would either rule out the Sivers-normalized model of the correlators or signal that twist-3 collinear factorization needs higher-twist corrections at $Q^2$ of a few GeV$^2$."],"forward_implications":["If $A_{UT}^{\\gamma\\mathrm{SIDIS}}$ is measured, $F_{FT}(x,x')$ and $G_{FT}(x,x')$ can be extracted point-by-point over their entire support, replacing earlier observables that only sense integrals or the diagonal $x=x'$.","In most of the phase space where the asymmetry is large, the soft-fermion-pole terms $F_\\pm(x_B,0)$ are comparable to or larger than the hard-pole terms, so the same measurement also constrains the previously unmeasured functions $F_{FT}(x,0)$ and $G_{FT}(x,0)$.","At $\\sqrt{s}=29$ GeV with the electron at mid or backward rapidity, the photon at mid to forward rapidity, small electron transverse momentum, large photon transverse momentum, and azimuthal angles aligned, $|A_{UT}|$ is predicted to be 10% or more under the full model.","Raising the center-of-mass energy suppresses the asymmetry strongly: at $\\sqrt{s}=63$ GeV most of the phase space drops to near zero and at $\\sqrt{s}=141$ GeV only extreme forward kinematics survive.","Comparing electron and positron beams produces a charge asymmetry that isolates the interference channel, giving access to valence-type $q-\\bar q$ combinations of the correlators."],"supporting_citations":[{"why":"Supplies the analytic leading-order result showing $F_{FT}$ and $G_{FT}$ enter point-by-point in $A_{UT}^{\\gamma\\mathrm{SIDIS}}$, the starting point of this paper.","marker":"[34]"},{"why":"Provides the operator definitions and symmetry relations for $F_{FT}$ and $G_{FT}$ used to build the model.","marker":"[23]"},{"why":"Gives the parton-model unpolarized cross section and the kinematic conditions $Q^2,\\tilde Q^2 \\gg M^2$ for a partonic description.","marker":"[48]"},{"why":"Provides the unpolarized PDFs used in the numerical denominator of the asymmetry.","marker":"[49]"},{"why":"Establishes the connection between $F_{FT}(x,x)$ and the first transverse moment of the Sivers function, the normalization input for the model.","marker":"[50]"},{"why":"Supplies the lattice QCD values of the $d_2$ matrix element that fix one Fourier coefficient in the $F_{FT}$ model.","marker":"[53]"},{"why":"Provides the Sivers first-moment extraction used to normalize the quark-gluon-quark correlators in both scenarios.","marker":"[59]"},{"why":"Contains the Fourier-series construction for $F_{FT}$ and $G_{FT}$ in polar coordinates that the model expands.","marker":"[27]"}],"fun_headline_variants":["10% spin asymmetry at EIC could map quark-gluon-quark","Direct probe: transverse spin asymmetry reveals quark-gluon-quark","Gamma SIDIS spin asymmetry: window into quark-gluon-quark","EIC spin asymmetry up to 10% probes multiparton correlations","Spin asymmetry could unlock quark-gluon-quark momentum structure"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that twist-3 collinear factorization applies at the kinematics scanned, where the cuts only impose $Q^2 > 1$ GeV$^2$ and $\\tilde Q^2 > 1$ GeV$^2$ with $M^2 \\approx 0.88$ GeV$^2$; the large-asymmetry region, with low electron transverse momentum and mid or backward electron rapidity, can sit at $Q^2$ of only a few GeV$^2$ where higher-twist corrections may be sizable.","fun_headline_variants_meta":{"raw":{"variants":["10% spin asymmetry at EIC could map quark-gluon-quark","Direct probe: transverse spin asymmetry reveals quark-gluon-quark","Gamma SIDIS spin asymmetry: window into quark-gluon-quark","EIC spin asymmetry up to 10% probes multiparton correlations","Spin asymmetry could unlock quark-gluon-quark momentum structure"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000239,"raw_usage":{"total_tokens":1586,"prompt_tokens":1090,"completion_tokens":496,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":706,"completion_tokens_details":{"reasoning_tokens":402}},"tokens_in":706,"tokens_out":496,"duration_ms":5840,"temperature":1.0,"reasoning_tokens":402,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T00:44:21.289595+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure $A_{UT}^{\\gamma\\mathrm{SIDIS}}$ at the Electron-Ion Collider at $\\sqrt{s}=29$ GeV in the phase-space region identified as largest (mid or backward electron rapidity, forward photon rapidity, electron $p_T$ below about 3 GeV, photon $p_T$ above about 3 GeV, and $\\phi'=\\phi_\\gamma=0$); if the asymmetry is consistent with zero at few-percent precision across that region, the claim that this observable is a practical pointwise probe of $F_{FT}$ and $G_{FT}$ would be falsified for these models. A second check is to test whether the asymmetry in that region follows the $Q^2$ dependence implied by factorization; strong violations at low $Q^2$ would indicate power corrections dominate.","supporting_citations":[{"cited_title":"The transverse nucleon single-spin asymmetry for the semi-inclusive production of photons in lepton-nucleon scattering","cited_arxiv_id":"1910.02883","evidence_quote":"Supplies the analytic leading-order result showing $F_{FT}$ and $G_{FT}$ enter point-by-point in $A_{UT}^{\\gamma\\mathrm{SIDIS}}$, the starting point of this paper."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the parton-model unpolarized cross section and the kinematic conditions $Q^2,\\tilde Q^2 \\gg M^2$ for a partonic description."}],"review_version":1}