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iblep-disc-burgerlong

graph LR
  %%%%%%%%%%%%%%%%%%%%%%%
  %% Highlight definition
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  classDef highlight fill:#083008,stroke:#20B030,stroke-width:4px
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  %% Graph
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  iblep-disc-loops -->|Propagators| iblep-disc-burgershort;
  iblep-disc-loops -.->|Tadpoles| iblep-conn-lep;
  iblep-disc-loops -.->|Tadpoles| iblep-conn-omega;
  iblep-disc-burgerlong;
  iblep-conn-emfieldft;
  iblep-real-fixgauge -->|Gauge field| iblep-real-props;
  iblep-real-props -->|Propagators| iblep-real-threept;


class iblep-disc-burgerlong highlight
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  %% Interaction
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  click iblep-disc-loops "../../../workflows/disc/iblep-disc-loops/";
  click iblep-disc-burgershort "../../../workflows/disc/iblep-disc-burgershort/";
  click iblep-disc-burgerlong "../../../workflows/disc/iblep-disc-burgerlong/";
  click iblep-conn-lep "../../../workflows/conn/iblep-conn-lep/";
  click iblep-conn-omega "../../../workflows/conn/iblep-conn-omega/";
  click iblep-conn-emfieldft "../../../workflows/conn/iblep-conn-emfieldft/";
  click iblep-real-fixgauge "../../../workflows/real/iblep-real-fixgauge/";
  click iblep-real-props "../../../workflows/real/iblep-real-props/";
  click iblep-real-threept "../../../workflows/real/iblep-real-threept/";

iblep-disc-burgerlong computes the long-distance contribution to the burger diagram. For each stochastic hit it chooses a random space-time source position, solves a selected sea-quark propagator, shifts the source to the origin, and contracts it with each requested position-space photon propagator. The calculation is repeated for every short-distance cut from no cut through the configured maximum radius-squared.

Inputs and outputs

Inputs

  • A gauge configuration, or the deterministic random gauge field used by the debug setup.
  • An optional gauge transformation and light-quark eigenpack, where required by the selected solver setup.
  • The sea-quark flavour to solve: l, s, or c.
  • One or both supported photon discretisations: L (QED_L) and r (QED_r).

Outputs

  • File: A Hadrons result group with the Burger-long contraction datasets, written from the stem results/<trajectory>/<AMAstage>/burgerlong.hit<hit-start>.
  • File: A companion result group with the randomly selected source positions, from the stem results/<trajectory>/<AMAstage>/burgerlong.srcs.hit<hit-start>.
  • Database: Rows in the result database that map every contraction dataset to its trajectory-specific HDF5 result file.
  • An optional XML module graph at paths.xml/<runId>.xml.

The random positions are deterministic in debug and unit-test setups, so that these modes can be used for numerical regression testing.

Workflow

The executable loads or creates the gauge field, creates the sea solver selected by setup and AMAstage, and builds position-space photon propagators for the entries in qed.

For every hit in the half-open range [hits.start, hits.start + hits.step), it then:

  1. Generates one random source position and a point source at that position.
  2. Solves the requested light, strange, or charm propagator.
  3. Shifts the propagator so that the random source position becomes the origin.
  4. Performs the burger contraction, and slices off the short-distance contribution for every rSq in [-1, rSq].

rSq = -1 means that no short-distance points are removed. rSq = 0 removes the origin, and larger values apply progressively larger short-distance cuts. This convention means that the definition of rSq is consistent between the short- and long-distance workflows: to reconstruct the full diagram, sum the short- and long-distance results for a specified rSq.

This should generate results with compatible central values, and a decreasing error as rSq increases.

From datasets to physics

The contraction stored in each dataset is defined by QEDBurgerLong in the Hadrons documentation. After shifting source hit \(i\) to the origin, the module returns

\[ B_{f,i,\mathrm{long}}^{(a)}(R) =-\sum_{r^2>R^2}G_{\mu\mu,a}(r)\sum_\mu \operatorname{tr}_{s,c}\!\left[ \gamma_\mu S_f(r,0)\gamma_\mu S_f(0,r) \right], \]

for the photon prescription \(a\). For rSq = -1, the restriction is absent. The minus sign is the implemented \(i^2=-1\). Unlike Burger-short, this is a point-source contraction and does not use a two-noise estimator, so there is no same-noise bias subtraction.

For a set \(\mathcal H\) of \(N_{\rm src}\) random source hits, first average the datasets at fixed trajectory, flavour, photon, AMA stage and cut:

\[ \overline B_{f,\mathrm{long}}^{(a)}(R) =\frac{1}{N_{\rm src}} \sum_{i\in\mathcal H}B_{f,i,\mathrm{long}}^{(a)}(R). \]

QEDBurgerLong fixes one current position at the point source, whereas the Burger-short estimator contains the sum over that position. Translational averaging over random point sources estimates the fixed-source average, so the matching long-distance contribution is

\[ B_{f,\mathrm{long}}^{(a)}(R) =V\,\overline B_{f,\mathrm{long}}^{(a)}(R), \qquad V=L_xL_yL_zL_t. \]

The bare full Burger contraction at cut \(R^2\) is therefore

\[ B_f^{(a)}(R) =B_{f,\mathrm{short}}^{(a)}(R) +V\,\overline B_{f,\mathrm{long}}^{(a)}(R), \]

using \(r^2\leq R^2\) in Burger-short and the complementary \(r^2>R^2\) dataset here. The same flavour, photon prescription and AMA definition must be used on both sides. The result should be independent of \(R\) within statistical and discretisation effects; this is an important analysis check.

This contains neither the electromagnetic coupling, the quark charge, nor local vector-current renormalisation. The physical same-flavour Burger contribution is

\[ B_{f,\mathrm{phys}}^{(a)} =e^2Q_f^2\left(Z_V^f\right)^2 B_f^{(a)}. \]

Apply the AMA combination separately to the short- and long-distance bare estimators before combining them. Average over gauge configurations only after the per-configuration source average and short/long reconstruction have been performed.

Run

iblep-disc-burgerlong <parameter-file.json> [Grid options]

The executable initializes Grid before parsing the workflow and uses Hadrons' naive scheduler. traj.start, traj.end, and traj.step are passed directly to the Hadrons trajectory counter.

Set dryRun to true to construct the workflow and generate result-database metadata without executing the module graph.

Input JSON

The following is an example input JSON copied from iblep/parameters/iblep-disc/debug/burgerlong.debug.json:

{
  "setup": "debug",
  "runId": "ibdisc",
  "AMAstage": "inexact",
  "flavour": "l",
  "dryRun": false,
  "traj": { "start": 0, "step": 20, "end": 20 },
  "hits": { "start": 0, "step": 4 },
  "rSq": 9,
  "paths": {
    "results": "data/results",
    "statDb": "db/ibdisc-burgerlong-debug.0",
    "appDb": "db/ibdisc-burgerlong-debug.0",
    "resultDb": "data/result.db",
    "xml": "log/loops.0",
    "gauge": "",
    "gaugeTransform": "",
    "eigenpack": ""
  },
  "charm": {
    "mc": 0.663,
    "residual": 1.0e-8
  },
  "qed": ["L", "r"]
}
Field Type Required Meaning and constraints
setup string Yes Solver and gauge setup. This example uses debug; production setups use a RBC/UKQCD gauge ensemble name.
AMAstage string Yes AMA solver stage supported by setup: inexact or exact.
runId string Yes Hadrons run identifier and XML filename component.
flavour string Yes Sea flavour: l, s, or c. Charm enables the charm solver.
dryRun boolean Yes Build XML without executing when true.
traj.start, traj.end, traj.step unsigned integer Yes Inclusive trajectory range and increment passed to Hadrons.
hits.start, hits.step unsigned integer Yes First stochastic hit and number of hits to process.
rSq integer Yes Largest short-distance cut. The workflow also includes the no-cut value -1.
qed string array Yes Photon discretisations: L, r, or both.
paths.results path Yes Root directory for burger-long result-group output stems.
paths.appDb, paths.statDb, paths.resultDb path Yes Hadrons application, statistics, and result-database paths.
paths.gauge path Setup-dependent NERSC gauge input for non-debug setups.
paths.gaugeTransform path Optional Gauge-transformation field used by supported deflated light solvers.
paths.eigenpack path Setup-dependent Light-quark eigenpack for supported deflated solver setups.
paths.xml path Optional Directory for the saved Hadrons module graph. An empty value disables XML output.
charm.mc, charm.residual number Yes Charm mass and solver residual, used when flavour is c.

The available setups are:

Key Meaning
debug A debug configuration .
unit-test A debug configuration.
RBCUKQCD-C0ZMobiusLCD RBC/UKQCD C0 ensemble with ZMobius light quarks with Local Coherence deflation.
RBCUKQCD-C0MADWFLCD RBC/UKQCD C0 ensemble with Mobius light quarks with Local Coherence deflation via MADWF solves.
RBCUKQCD-C0LLCD RBC/UKQCD C0L ensemble with light quarks with Local Coherence deflation.
RBCUKQCD-M0LCD RBC/UKQCD M0 ensemble with light quarks with Local Coherence deflation.
RBCUKQCD-C1MIRL RBC/UKQCD C1M ensemble with online deflation of light quarks.
RBCUKQCD-C1M16IRL RBC/UKQCD C1M16 ensemble with online deflation of light quarks.
RBCUKQCD-C1M20IRL RBC/UKQCD C1M20 ensemble with online deflation of light quarks.
RBCUKQCD-C1M32IRL RBC/UKQCD C1M32 ensemble with online deflation of light quarks.
JLQCD-fUd3Sa JLQCD fUd3Sa ensemble with a fine lattice spacing.
JLQCD-fUd3Sa JLQCD mUd3Sa ensemble with a medium lattice spacing.
JLQCD-fUd3Sa JLQCD mUd3Sb ensemble with a medium lattice spacing.
JLQCD-fUd3Sa JLQCD cUd2Sa ensemble with a coarse lattice spacing.
JLQCD-fUd3Sa JLQCD cUd2SaL ensemble with a coarse lattice spacing.
JLQCD-fUd3Sa JLQCD cUd3Sa ensemble with a coarse lattice spacing.
JLQCD-fUd3Sa JLQCD cUd3Sb ensemble with a coarse lattice spacing.

Output and data format

Files and HDF5 result groups

For a trajectory T, AMA stage A, and first hit H, the workflow supplies the following result-group output stems:

<paths.results>/<T>/<A>/burgerlong.hit<H>
<paths.results>/<T>/<A>/burgerlong.srcs.hit<H>

The first group contains one real, unnormalised QEDBurgerLong result for every Cartesian product of hit, photon prescription, and short-distance cut. It is a single-source value and has not been averaged over hits or multiplied by the lattice volume, charge, \(e^2\), or \(Z_V^2\). Dataset module names have the form:

burgerlong_<flavour>_<photon>_rSq<rSq>_hit<hit>

The second group records the random source-position fields used for the same hit range. The Hadrons result writer applies its normal trajectory-specific result-file naming; the direct database catalogue stores this resolved filename alongside each dataset name.

Result database

paths.resultDb is used for two related catalogues:

  • burgerlong_data is created directly by this executable and maps every contraction to its result file and dataset.
  • burgerlong_files is Hadrons result metadata attached to the output result group. It records the flavour, hit range, and companion source-position output stem.

burgerlong_data

Column Type Meaning
flavour text, not null Selected sea flavour.
photon text, not null Photon discretisation module name.
AMAstage text, not null AMA stage from the input.
hit unsigned integer, not null Stochastic hit index.
rSq integer, not null Short-distance cut used for this contraction.
filename text, not null Resolved trajectory-specific HDF5 result filename.
dataset text, not null QEDBurgerLong dataset/module name in that file.

The primary key is (flavour, photon, AMAstage, hit, rSq). Inserts use the Hadrons overwrite mode, so rerunning the same key refreshes its catalogue row.

burgerlong_files

The result-group metadata entry has the following fields:

Column Type Meaning
flavour text, not null Selected sea flavour.
sourcesFilename text, not null Output stem of the companion random-position result group.
hitStart unsigned integer, not null First processed hit.
hitEnd unsigned integer, not null One past the last processed hit.