An arXiv preprint reports a speed comparison in partial-wave analysis (PWA), a likelihood-based fit of particle-decay data. In a synthetic benchmark, conventional per-iteration time rose from about 2 milliseconds at roughly 100 events to about 400 milliseconds at one million events, while the precomputed pipeline stayed between about 0.4 and 2.8 milliseconds. Including the one-time precomputation, the reported acceleration grew from about fivefold at roughly 100 events to more than 100-fold at one million, for a complete fit of 1,000 iterations.
At the largest benchmark size, the conventional pipeline exhausted device memory. The precomputed representation completed without difficulty in that comparison, so the test involved both runtime and whether the calculation could complete.
The calculation is reorganized before fitting
The framework, called CTPWA, is built on covariant tensor formalism, extensive precomputation and caching, and fully GPU-based likelihood computation and minimization. It casts the likelihood into a compact matrix form, with the gradient—the slope of the likelihood as parameters change—and the Hessian—a matrix describing how that slope changes—following analytically.
The benchmark used synthetic PWA samples with 10 decay channels, three polarization configurations and a phase-space sample equal to 10 times the number of data events, all in double precision.
The biggest gap appeared in derivative calculations
For one million events, the optimized formulas evaluated the negative log-likelihood, or NLL, and its gradient in about 2 milliseconds, compared with 23 milliseconds for GPU autograd and 2.3 seconds for CPU autograd. For a full 20-by-20 Hessian, analytic evaluation took about 6 milliseconds, versus 0.75 seconds with GPU autograd and 75 seconds with CPU autograd. The reported comparisons were about 122-fold and 12,000-fold, respectively.
A toy decay fit
The paper then tested a toy J/ψ → K+ K− η fit using one million toy Monte Carlo events. Its model included 16 intermediate resonances and 33 complex couplings, with phase-space integration based on 5 × 10^6 uniformly distributed Monte Carlo events.
With resonance parameters fixed, the complete toy fit took about 7 seconds across about 500 iterations. When those parameters were allowed to vary, the reported per-iteration cost was about 100 milliseconds and the complete fit took about 100 seconds across about 1,000 iterations. Hessian time was about 0.35 seconds in the fixed-parameter scenario and about 1.6 seconds in the floating-parameter scenario. The reported device-memory figures for the two scenarios were approximately 20 gigabytes and 32 gigabytes.
The toy model reproduced resonant structures across the full kinematic range. Its residuals were consistent with statistical fluctuations, and the fitted parameters agreed with the generated inputs.
A result bounded by synthetic data
Those results show what the framework did in the reported synthetic tests, not what it will necessarily do on every experiment. The benchmark used synthetic samples and the demonstration used toy Monte Carlo events, so the article provides no real experimental-data performance result to compare.
Availability and support
The document is identified as arXiv:2608.25963v1 [hep-ex] and dated 26 August 2026. The CTPWA framework is publicly available at https://github.com/BHXiang/ctpwa. The work received support from the National Key R&D Program of China, the National Natural Science Foundation of China and the Strategic Priority Research Program of the Chinese Academy of Sciences.
Paper data and sources
Original title: A High Performance Partial Wave Analysis Framework for Hadron Spectroscopy
Authors: Benhou Xiang, Shuangshi Fang, Beijiang Liu
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text