{"id":"f5fd15b7-cbeb-4fd6-b393-7e2d0aa5c667","arxiv_id":"hep-lat/0402025","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Two-flavor dynamical lattice QCD yields a continuum-extrapolated I=2 pi-pi S-wave phase shift of -3.5, -9.5, and -16.9 degrees at center-of-mass energies 0.4, 0.6, and 0.8 GeV, consistent with experiment within large errors.","lead":"The CP-PACS collaboration computes the I=2 S-wave pion-pion scattering phase shift from first-principles lattice QCD with two flavors of dynamical quarks, at three lattice spacings, and extrapolates to the continuum. It is the first full-QCD (not quenched) determination of this scattering observable with a continuum limit, and the result lands near the experimental phase shifts.","discovery_kind":"unclear","skeptic_critique":{"model":"selfhosted/deepseek-v4.1-flash","headline":"The final phase-shift values rest on a truncated polynomial chiral fit in m_π² that demonstrably fails at the finest lattice spacing (Table V, χ²/dof = 8.2 at β = 2.10) and requires a 1/m_π² term at 7.8σ (Table IV); the phase-shift fit (Eq. 40) may be absorbing the same physics into its m_π⁶ term.","rationale":"The reader's verdict of CONDITIONAL is well calibrated. This is a genuine first — the first continuum-extrapolated I=2 ππ phase shift in two-flavor dynamical QCD — and the finite-volume machinery is applied correctly: the CM-only scattering length (Eq. 38, −0.0558(56)) and the all-systems value (Eq. 41, −0.0484(49)) agree within errors, which independently cross-checks the lab-frame extension (Eq. 9) and the re-derived zeta function of Appendix A against the CM calculation that does not use them. The result is externally benchmarked against the ChPT/Roy curve and the Hoogland and Losty data (Fig. 15), so circularity is low. The one mildly self-referential step — dividing by f_π^lat to flatten the m_π² dependence before a constant fit — is not on the critical path, because the authors explicitly use the un-normalized A(m_π,p) for the final phase shift. The load-bearing soft spot is therefore the chiral extrapolation, and the reader names it correctly. My sharpening is that the paper's own Tables IV and V show the truncated polynomial failing at β = 2.10 (χ²/dof = 8.2) and requiring a 7.8σ 1/m_π² term, so the assumption 'chiral breaking is small' is contradicted by the authors' own fit at the finest lattice spacing rather than merely untested. The continuum extrapolation with three points and one degree of freedom is a secondary but real limitation, and the authors acknowledge both. None of this warrants rejection: the concern is a systematic that the authors flag as future work, the central numbers are internally consistent (the √s = 0.4 value reproduces the scattering length to within the quoted error), and the qualitative 'consistent with experiment' claim survives the error bars. CONDITIONAL is the right verdict, and the concrete test above would settle whether the chiral extrapolation is the dominant uncontrolled systematic or is under control.","tokens_in":32586,"tokens_out":7895,"duration_ms":141371,"concrete_test":"At β = 2.10 (the finest lattice, where Table V gives χ²/dof = 8.2), refit the phase-shift amplitude A(m_π,p) with Eq. 40 augmented by an A40 m_π⁸ term, or equivalently drop the heaviest κ (m_π² ≈ 1.33 GeV²) and refit with the existing six parameters. Re-evaluate at physical m_π, redo the linear-in-a continuum extrapolation, and compare δ at √s = 0.8 GeV with the quoted −16.9(64)°. If the value moves outside the ±6.4° error band, the chiral extrapolation dominates the error budget and the central values are not robust; if it stays within, the polynomial ansatz is adequate and the concern does not land.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The abstract values (abstract:s4) are obtained by fitting the amplitude A(m_π,p) with Eq. 40 — a polynomial in m_π² and p² up to m_π⁶ — to data spanning m_π² = 0.24–1.33 GeV², then evaluating at m_π = 0.14 GeV (m_π² = 0.0196), a factor ~65 below the lightest simulated point. The extrapolation is therefore the dominant uncontrolled step. Two pieces of the paper's own evidence show the truncated polynomial is inadequate at the finest lattice spacing, exactly where the continuum extrapolation is anchored. First, Table V: the three-parameter polynomial fit for a0/m_π at β = 2.10 gives χ²/dof = 8.2, i.e., the ansatz does not describe the data. Second, Table IV: fitting the divergent form a0/m_π = A00/m_π² + A10 + A20 m_π² yields A00 = −0.273(35) at β = 2.10, a 7.8σ nonzero Wilson chiral-breaking term that grows toward the continuum (−0.033, −0.184, −0.273), opposite to the expectation that it should vanish. The authors then state (Sec. IV B) 'We assume that the effect of chiral breaking is small in our simulation points,' but their own fit says it is not small at β = 2.10. The phase-shift fit Eq. 40 has six parameters and more data points, so it reports χ²/dof = 1.33 (Table IX) and appears healthy, but that extra freedom can absorb the same curvature into A30 m_π⁶. Because the final phase shift uses the un-normalized A(m_π,p) (the authors explicitly decline to use the f_π-normalized  for the final numbers), this concern sits directly on the critical path to abstract:s4. The reader's weakest_assumption identifies this correctly; my addition is that the failure is not merely 'untested' but quantitatively demonstrated at β = 2.10 by the paper's own Tables IV and V.","agreement_with_reader":"agree"},"referee_report":{"model":"selfhosted/deepseek-v4.1-flash","summary":"The manuscript reports a two-flavor dynamical lattice QCD calculation of the I=2 S-wave ππ scattering phase shift, using the Lüscher finite-volume method in the center-of-mass frame and the Rummukainen–Gottlieb extension for two moving frames (L1, L2). Configurations are the CP-PACS clover-improved ensembles at β = 1.80, 1.95, 2.10 with four quark masses each; two-pion energy eigenvalues are extracted via the Lüscher–Wolff diagonalization of the four-point correlator matrix, and the phase shift is obtained at several momenta from a single ensemble set. After a combined polynomial fit in m_π² and p² (Eq. 40) and a linear-in-a continuum extrapolation, the authors quote δ = −3.50(64)°, −9.5(30)°, −16.9(64)° at √s = 0.4, 0.6, 0.8 GeV, together with scattering lengths a₀m_π = −0.0558(56) and â₀m_π = −0.0413(29). Appendix A gives a reorganized and, the authors argue, simplified representation of the zeta function Z^d₀₀(1;m) suitable for numerical evaluation.","tokens_in":33035,"tokens_out":6120,"duration_ms":105593,"significance":"If the result holds, this is the first continuum-extrapolated, full-QCD determination of a hadronic scattering phase shift, and it is a genuine step beyond the quenched and single-lattice-spacing studies that preceded it. The methodological content is substantial and reusable: the demonstration that Lüscher–Wolff diagonalization is essential for excited states in all three momentum frames, the explicit two-state eigenvalue analysis of the near-degenerate L2 system (Eq. 29 and Fig. 9), and the zeta-function representation of Eq. (A8) are contributions in their own right and are likely to be cited independently of the final numbers. The paper is also commendably candid about its own weak points, flagging the failure of the polynomial scattering-length fit at β = 2.10 and the growth of the chiral-breaking coefficient toward the continuum. The main reservation is that the quoted errors on the headline numbers are statistical only, while the dominant uncertainty is the chiral extrapolation over roughly a factor of 65 in m_π².","major_comments":[{"comment":"The abstract values (abstract:s4) and Table XI carry statistical errors only, yet the dominant uncontrolled step is the chiral extrapolation from m_π² = 0.24–1.33 GeV² down to m_π² = 0.0196 GeV². The paper nowhere quotes a systematic uncertainty for this extrapolation, and the two independent determinations of the scattering length — Eqs. (38)/(39) from CM0 alone versus Eqs. (41)/(42) from all momentum systems — differ by about 13% (a₀m_π = −0.0558(56) versus −0.0484(49)), which the authors attribute to continuum-extrapolation ambiguity but do not propagate into any quoted error. Please provide an explicit systematic error budget for the chiral extrapolation, for example by quoting the spread of the physical-point result under the fit variants already in the paper (Eqs. 33, 34, 35, 40), under dropping the heaviest quark mass at each β, and under the CM0-only versus global-fit procedures, and state whether the errors in Table XI are statistical or combined.","section":"Sec. IV B and Table XI","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The paper states 'We assume that the effect of chiral breaking is small in our simulation points,' but the authors' own fits contradict this at the finest lattice spacing: Table IV gives A₀₀ = −0.273(35) at β = 2.10, a 7.8σ nonzero Wilson chiral-breaking term that grows toward the continuum (−0.033, −0.184, −0.273) rather than vanishing, and Table V gives χ²/d.o.f. = 8.2 for the polynomial fit at β = 2.10. Since the final phase shift uses the un-normalized A(m_π,p) fitted with Eq. (40), whose six parameters include an m_π⁶ term that can absorb exactly this curvature, the assumption is load-bearing and untested. Please test it directly: repeat the phase-shift analysis with the divergent form of Eq. (34) included in the amplitude fit, or demonstrate that the physical-point δ is stable when the m_π⁶ term is removed and when the heaviest mass is dropped at β = 2.10.","section":"Sec. IV B, Table IV, Table V","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"At the physical pion mass the inelastic threshold is 4m_π ≈ 0.56 GeV, so the quoted points at √s = 0.6, 0.8 and 1.0 GeV lie above it, whereas the single-channel Lüscher relation of Eqs. (3) and (9) assumes elastic unitarity. The paper discusses the inelastic threshold only for the simulated (heavy) pion masses in Fig. 1 and does not address the extrapolated physical point. Please justify the applicability of the elastic formula at these energies — for example by arguing that I=2 inelasticity is negligible below 1 GeV, with a citation — or restrict the quoted range to √s below the four-pion threshold.","section":"Table XI and Fig. 15","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The continuum extrapolation is performed as a linear function of a (A + aB) for an action that is O(a) improved, so the leading residual cutoff dependence is expected at O(a²) or O(α_s a) rather than O(a). With three lattice spacings and two parameters there is a single degree of freedom, and the choice of linear rather than quadratic a-dependence materially affects the intercept. Please justify the linear ansatz and show the a² fit as a cross-check, quoting the shift in the continuum values of a₀m_π, â₀m_π and δ(p).","section":"Table VIII, Fig. 12, Fig. 14","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The entry A(m_π,p_n) = −7.04(30) is internally inconsistent with the same row: m_π² = 1.332(2) and A(m_π,p_n)/m_π² = −0.528(23) imply A = −0.703, and the ratio Â/A = −3.12/−0.704 = 4.43 agrees with (f_π^lat/f_π)² = (0.1959/0.093)² = 4.44, whereas −7.04 would give 0.44. This appears to be a factor-of-ten typographical error. Please correct the table and confirm that the global fit of Table IX used the corrected value, since this point is one of the inputs to the fit that produces the headline phase shifts.","section":"Table XII, β = 2.10, κ = 0.1357 row","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"Only N_R = 2 random noise sources are used for the source operator, which is a very small ensemble for estimating the off-diagonal correlators G_nm that the diagonalization depends on. The symmetry averaging described in Sec. IV A mitigates but does not remove the concern; please comment on whether the N_R = 2 estimator introduces a bias in the extracted eigenvalues, and whether any check with larger N_R was performed.","section":"Sec. II B, Eq. (15)","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The sentence 'higher statics calculations of the scattering length' should read 'higher statistics calculations'.","section":"Sec. IV B","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The affiliation for Hiroshima University is printed as 'Hisoshima University' and should be corrected.","section":"Author list","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"Reference [14] (Bernard and Golterman, Phys. Rev. D53 (1998) 476) appears to carry the wrong year; the quenched chiral perturbation theory paper is Phys. Rev. D53 (1996) 476. Please verify.","section":"References","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The figure caption should state explicitly whether the error band on the dashed curve represents statistical errors only or a combined error, so that the comparison with the Hoogland et al. and Losty et al. data can be read correctly.","section":"Fig. 15","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The √s = 1.00 GeV entry, δ = −25(10)°, has a 40% uncertainty and lies furthest from any simulated kinematics; consider whether it adds information beyond the three points quoted in the abstract.","section":"Table XI","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"major_revision"},"author_rebuttal":null,"desk_editor":{"model":"selfhosted/deepseek-v4.1-flash","letter":"Worth your time, but read it as a methods paper with a physics headline attached, not the other way around. The genuinely new thing is that this is the first I=2 S-wave ππ phase shift computed with dynamical quarks and extrapolated to the continuum, and the machinery is standard and correctly applied: Lüscher's finite-volume formula in the CM frame, Rummukainen-Gottlieb in the moving frames, Lüscher-Wolff diagonalization to separate the multi-exponential contamination. Appendix A's rewritten zeta function is a real, if unglamorous, contribution — they claim a simpler and more numerically efficient expression than Ref. [17] and flag typographical errors there. That appendix will get used by other people regardless of what happens to the phase-shift numbers. The demonstration that moving-frame plus diagonalization actually works in full QCD, with the L2 two-state mixing behaving as a simple 2×2 eigenvalue problem (their Eq. 29), is the part I'd point a student at first. The abstract values [abstract:s4] are consistent with experiment, but the error bars are large enough that 'consistent' is doing qualitative work, and the authors say so. The soft spot is exactly where the stress-test puts it: the chiral extrapolation runs from m_π ≈ 0.5–1.1 GeV down to 0.14 GeV, and the paper's own Table IV shows the Wilson chiral-breaking coefficient A00 growing toward the continuum (−0.033, −0.184, −0.273), opposite to what you'd want. Table V's χ²/dof = 8.2 at β = 2.10 says the three-term polynomial doesn't describe the finest-lattice data. The authors state the assumption plainly ('We assume that the effect of chiral breaking is small') and don't test it. The phase-shift fit Eq. 40 has enough freedom (m_π⁶ term) to absorb the same curvature and reports χ²/dof = 1.33, so the stress-test's worry that the healthy fit is hiding the problem is fair, not proven. Two things temper it: the authors present two continuum estimates (Eqs. 38/39 vs 41/42) whose spread they explicitly call the extrapolation uncertainty, and the f_π-normalized version lands closer to ChPT. The f_π^lat normalization is mildly circular — it uses a lattice decay constant with a perturbative renormalization factor the authors admit is inconsistent with experiment — but they decline to use it for the final numbers, which is the right call. Three lattice spacings is one degree of freedom; they say so. My read: the central claim holds as far as the data go, the systematics are named rather than buried, and the paper is more honest about its weaknesses than most. Send it out. A referee should push hard on the chiral fit and on whether the m_π⁶ term is doing real work, but this deserves referee time.","headline":"A real milestone — first continuum-extrapolated I=2 ππ phase shift in two-flavor QCD — with the chiral extrapolation as the acknowledged soft underbelly.","tokens_in":33777,"tokens_out":1133,"duration_ms":20077},"pith_extraction":{"msc":[],"pacs":["12.38.Gc","11.15.Ha"],"model":"selfhosted/deepseek-v4.1-flash","headline":"The CP-PACS collaboration reports a first-principles lattice determination of the I=2 pion-pion scattering phase shift in two-flavor QCD, extrapolated to the continuum and consistent with experiment.","keywords":["lattice QCD","pion-pion scattering","scattering phase shift","finite volume method","two-flavor dynamical quarks","chiral extrapolation","continuum limit","clover fermions"],"falsifier":"A repeat of the same analysis at a fourth, finer lattice spacing, or at substantially lighter pion masses, would settle it: if the $1/m_/pi^2$ coefficient $A_{00}$ in the authors' Eq. 34 does not shrink toward zero, the polynomial chiral fit underlying the quoted scattering length and phase shift is not under control, and the continuum numbers would move.","tokens_in":33946,"feed_emoji":"⚛️","tokens_out":2427,"duration_ms":41504,"temperature":0.7,"pith_summary":"The paper sets out to compute a real scattering observable — the $I=2$ $S$-wave pion-pion phase shift — directly from lattice QCD with dynamical up and down quarks, and to carry the result all the way to physical quark mass and zero lattice spacing. That is a step beyond the hadron mass spectrum: scattering quantities probe how hadrons interact, and in the quenched approximation they are known to suffer unphysical chiral divergences, so a full-QCD treatment matters. The authors work at three lattice spacings, use two different total-momentum frames to reach several energies from one set of configurations, and quote continuum values $(-3.50, -9.5, -16.9)$ degrees at $0.4$, $0.6$ and $0.8$ GeV, which sit on the experimentally determined curve. If the result holds up, it shows that the finite-volume machinery for extracting scattering amplitudes works in realistic QCD, not just in quenched toy settings, and it opens the door to the harder $I=0$ and $I=1$ channels.","feed_headline":"Pion scattering phase shift computed from full QCD","feed_subtitle":"A two-flavor lattice simulation at three spacings yields phase shifts that match experiment between 0.4 and 0.8 GeV.","key_machinery":"Two ingredients carry the argument. The first is Lüscher's finite-volume relation, which converts the energy of two pions in a periodic box into the infinite-volume phase shift through a zeta function, together with the Rummukainen-Gottlieb extension that boosts the relation to a frame with nonzero total momentum; the authors use the center-of-mass frame and two moving frames to sample several energies from one ensemble, and they re-derive a simplified, numerically efficient representation of the zeta function in an appendix. The second is the Lüscher-Wolff diagonalization: the pion four-point function is a sum of many exponentials because several two-pion states share the same quantum numbers, so the authors build the matrix $M(t,t_0) = G(t_0)^{-1/2} G(t) G(t_0)^{-1/2}$ and fit its eigenvalues, which behave as single exponentials. This is what makes the first excited state, and the nearly degenerate pair in the $(1,1,0)$ frame, extractable at all.","core_discovery":"The central claim is that the $I=2$ $S$-wave $pp$ phase shift can be obtained from two-flavor dynamical lattice QCD and extrapolated to the continuum, giving $/delta = -3.50(64)^/circ$, $-9.5(30)^/circ$ and $-16.9(64)^/circ$ at $/sqrt{s} = 0.4$, $0.6$ and $0.8$ GeV. The authors also quote a scattering length, $a_0 m_/pi = -0.0558(56)$ from the zero-momentum ground state alone and $-0.0484(49)$ when all momentum frames are fitted jointly, against a chiral-perturbation-theory prediction of $-0.0444(10)$; a decay-constant-normalized variant gives $-0.0413(29)$ and $-0.0404(24)$. The quoted phase shifts agree with the curve extracted from experiment via the Roy equations and with the experimental points themselves, within the still-large errors.","pith_inferences":["The gap between the two determinations of $a_0 m_\\pi$ quoted in the paper ($-0.0558$ versus $-0.0484$) is presented as an extrapolation ambiguity, and it is a useful reminder that with three lattice spacings the continuum fit has a single degree of freedom.","The observed correlation between the scattering length and the lattice decay constant suggests that quoting a decay-constant-normalized scattering length may partly absorb chiral-extrapolation error; a future calculation with a nonperturbative axial-current renormalization would test whether that correlation survives.","If the $I=2$ channel is this well behaved, the natural next stress test is $I=0$, where disconnected diagrams enter and where the same finite-volume machinery has not yet been validated in full QCD.","The authors' own table showing the Wilson chiral-breaking coefficient growing toward the continuum limit is a concrete handle: a simulation at a fourth, finer lattice spacing would show whether that coefficient actually vanishes as expected or persists."],"forward_implications":["Scattering amplitudes, not just masses, become accessible to full-QCD lattice calculations, which is the prerequisite for studying resonances and multi-hadron physics from first principles.","The moving-frame extension is shown to work in practice, so a single ensemble can supply several kinematic points rather than requiring a separate lattice volume for each energy.","The diagonalization of the four-point correlator is demonstrated to be necessary for excited states and for nearly degenerate levels, giving a template for future multi-state analyses.","Because the phase shift agrees with the experimentally determined curve, the finite-volume method passes a nontrivial check against data rather than only against itself.","The remaining bottleneck is identified as chiral and continuum extrapolation rather than the finite-volume formalism, which directs future effort toward lighter pions, finer lattices and higher statistics."],"supporting_citations":[{"why":"Supplies the finite-volume relation between the two-pion box energy and the infinite-volume phase shift, the method the whole calculation rests on.","marker":"[10,11]"},{"why":"Supplies the Lüscher-Wolff diagonalization of the correlator matrix, the technique used to separate the ground and excited two-pion states.","marker":"[12]"},{"why":"Supplies the extension of the finite-volume formula to a frame with nonzero total momentum, which enables the L1 and L2 laboratory systems.","marker":"[17]"},{"why":"Supplies the two-flavor dynamical gauge configurations, the lattice scale, and the measured pseudoscalar decay constants used throughout.","marker":"[16]"},{"why":"Supplies the one-loop chiral perturbation theory expression for the pion mass dependence of the scattering length that the data are fitted against.","marker":"[26]"},{"why":"Supplies the Roy-equation determination of the phase shift from experimental input, the curve against which the continuum result is compared.","marker":"[28]"},{"why":"Supply the experimental phase-shift data points that the lattice result is plotted against.","marker":"[30,31]"},{"why":"Supplies the renormalization-group improved gauge action and the perturbative tadpole coefficient used in the simulation.","marker":"[24]"}],"fun_headline_variants":["Two-flavor lattice QCD yields I=2 pion scattering phase shifts","Pion phase shifts reach continuum limit in two-flavor QCD","Lattice QCD at three spacings computes I=2 pion phase shifts","Continuum-extrapolated pion phase shifts track experimental values","Two-flavor lattice QCD gives pion scattering length and phase shifts"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The chiral extrapolation assumes that the Wilson-type symmetry-breaking term scaling as $1/m_/pi^2$ is small at the simulated pion masses of 0.5 to 1.1 GeV, even though the authors' own fit shows that coefficient growing toward the continuum limit instead of shrinking.","fun_headline_variants_meta":{"raw":{"variants":["Two-flavor lattice QCD yields I=2 pion scattering phase shifts","Pion phase shifts reach continuum limit in two-flavor QCD","Lattice QCD at three spacings computes I=2 pion phase shifts","Continuum-extrapolated pion phase shifts track experimental values","Two-flavor lattice QCD gives pion scattering length and phase shifts"]},"model":"selfhosted/deepseek-v4.1-flash","effort":"low","attempts":1,"cost_usd":0.0,"raw_usage":{"total_tokens":1425,"prompt_tokens":978,"completion_tokens":447,"prompt_tokens_details":null,"completion_tokens_details":{"reasoning_tokens":367}},"tokens_in":978,"tokens_out":447,"duration_ms":7021,"image_pages":[],"temperature":1.0,"reasoning_budget":50,"reasoning_tokens":367,"transport_provider":"selfhosted","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-11-13T08:51:50.822615+00:00","model_set":{"reader":"selfhosted/deepseek-v4.1-flash"},"pipeline_version":"pith-pipeline@v1.5.0-archive-selfhost","input_kind":null,"input_chars":null,"input_total_chars":null,"passes_missing":null,"published_standing":null,"published_confidence":null,"objection_audit":null,"run_record":null,"basis":{"kind":"not_recorded","source":null,"chars_given":null,"chars_total":null},"receipt":null,"falsifier":"A repeat of the same analysis at a fourth, finer lattice spacing, or at substantially lighter pion masses, would settle it: if the $1/m_/pi^2$ coefficient $A_{00}$ in the authors' Eq. 34 does not shrink toward zero, the polynomial chiral fit underlying the quoted scattering length and phase shift is not under control, and the continuum numbers would move.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the Lüscher-Wolff diagonalization of the correlator matrix, the technique used to separate the ground and excited two-pion states."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the extension of the finite-volume formula to a frame with nonzero total momentum, which enables the L1 and L2 laboratory systems."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the two-flavor dynamical gauge configurations, the lattice scale, and the measured pseudoscalar decay constants used throughout."},{"cited_title":"Gasser and H","cited_arxiv_id":null,"evidence_quote":"Supplies the one-loop chiral perturbation theory expression for the pion mass dependence of the scattering length that the data are fitted against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the Roy-equation determination of the phase shift from experimental input, the curve against which the continuum result is compared."},{"cited_title":"Iwasaki, Nucl","cited_arxiv_id":null,"evidence_quote":"Supplies the renormalization-group improved gauge action and the perturbative tadpole coefficient used in the simulation."}],"lane_accuracy":{"status":"not yet measured","lane":{"model":"selfhosted/deepseek-v4.1-flash","input_kind":null},"url":"https://pith.science/accuracy"},"review_version":1}