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34 particle masses, 8 decay widths, 11 cross-sections, 8 trigger thresholds, 8 calibration constants — all encoded as Q16_16 integers. BRAM layout: 4 banks × 256 entries × 32-bit Bank 0: particle_masses (electron → upsilon_3S) Bank 1: decay_widths (W, Z, Higgs, top, J/ψ, ϒ) Bank 2: cross_sections (ttbar, W, Z, Higgs, jets at 13 TeV) Bank 3: triggers_calibration (LHC HLT + ECAL/HCAL constants) Cross-section interpolation: log-log between 7/8/13/14 TeV. Export: Verilog initial blocks for FPGA BRAM loading. The LHC trigger system processes 40M events/second using hardware LUTs. These tables are the same lookup operations — just in Q16_16 fixed-point.
323 lines
12 KiB
Python
323 lines
12 KiB
Python
"""Particle Physics LUT — Q16_16 lookup tables from 50 years of PDG data.
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The LHC trigger system classifies billions of events/second using hardware LUTs.
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The Particle Data Group (PDG) maintains precision measurements of every known
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particle property. This module encodes the most useful tables as Q16_16 values
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suitable for FPGA BRAM storage.
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Key insight: particle physics has been doing "computation via lookup tables"
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since the 1970s. The PDG tables ARE a LUT for the Standard Model.
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Tables encoded:
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1. Particle masses (Q16_16 in MeV)
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2. Decay widths (Q16_16 in GeV)
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3. Cross-sections (Q16_16 in pb)
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4. Trigger thresholds (Q16_16 in GeV)
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5. Calorimeter calibration constants (Q16_16)
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All values are deterministic Q16_16 integers — no floats in compute paths.
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"""
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import struct
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from pathlib import Path
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# ── Q16_16 Constants ──────────────────────────────────────────────────
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Q16_SCALE = 65536
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Q16_MAX = 2147483647
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Q16_MIN = -2147483648
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def _q16(value: float) -> int:
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"""Convert float to Q16_16 integer with clamping."""
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raw = int(value * Q16_SCALE)
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return max(Q16_MIN, min(Q16_MAX, raw))
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def _q16_to_float(q: int) -> float:
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"""Convert Q16_16 integer to float."""
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return q / Q16_SCALE
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# ── Particle Mass Table (PDG 2024) ───────────────────────────────────
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# Values in MeV, encoded as Q16_16 (so 938.272 → 938.272 * 65536)
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# Source: Particle Data Group, https://pdg.lbl.gov
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PARTICLE_MASSES_MEV = {
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# Leptons
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'electron': 0.51099895, # ± 0.00000000015
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'muon': 105.6583755, # ± 0.0000023
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'tau': 1776.86, # ± 0.12
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# Light quarks (MSbar masses)
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'up': 2.16, # ± 0.26 (at 2 GeV)
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'down': 4.67, # ± 0.29 (at 2 GeV)
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'strange': 93.4, # ± 3.4 (at 2 GeV)
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# Heavy quarks
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'charm': 1270, # ± 20 (MSbar)
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'bottom': 4180, # ± 30 (MSbar)
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'top': 172690, # ± 300 (pole mass)
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# Gauge bosons
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'photon': 0, # massless
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'W': 80379, # ± 12
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'Z': 91187.6, # ± 2.1
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'gluon': 0, # massless (confined)
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# Higgs
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'higgs': 125250, # ± 110
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# Light mesons
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'pion_charged': 139.57039, # ± 0.00018
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'pion_neutral': 134.9768, # ± 0.0005
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'kaon_charged': 493.677, # ± 0.016
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'kaon_neutral': 497.611, # ± 0.013
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'eta': 547.862, # ± 0.017
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'eta_prime': 957.78, # ± 0.06
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# Light baryons
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'proton': 938.27208816, # ± 0.00000029
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'neutron': 939.56542052, # ± 0.00000054
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'lambda': 1115.683, # ± 0.006
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'sigma_plus': 1189.37, # ± 0.07
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'sigma_zero': 1192.642, # ± 0.024
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'sigma_minus': 1197.449, # ± 0.030
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'xi_zero': 1314.86, # ± 0.20
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'xi_minus': 1321.71, # ± 0.07
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'omega_minus': 1672.45, # ± 0.29
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# Charmonium
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'J_psi': 3096.900, # ± 0.006
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'psi_2S': 3686.097, # ± 0.010
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# Bottomonium
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'upsilon_1S': 9460.30, # ± 0.26
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'upsilon_2S': 10023.26, # ± 0.31
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'upsilon_3S': 10355.2, # ± 0.5
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}
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# Encode as Q16_16 integers
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PARTICLE_MASSES_Q16 = {
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name: _q16(mass) for name, mass in PARTICLE_MASSES_MEV.items()
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}
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# ── Decay Width Table (PDG 2024) ─────────────────────────────────────
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# Values in GeV, encoded as Q16_16
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DECAY_WIDTHS_GEV = {
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'W': 2.085, # ± 0.042
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'Z': 2.4952, # ± 0.0023
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'higgs': 0.00407, # ± 0.00010 (SM prediction)
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'top': 1.42, # ± 0.51 (approximate)
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'J_psi': 0.0000929, # ± 0.0000017 (keV → GeV: 92.9 keV)
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'upsilon_1S': 0.00005402, # ± 0.00000125
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'tau': 2.267e-12, # lifetime → width (very small)
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'muon': 2.996e-19, # lifetime → width
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}
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DECAY_WIDTHS_Q16 = {
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name: _q16(width) for name, width in DECAY_WIDTHS_GEV.items()
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}
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# ── Cross-Section Table (representative, in pb) ──────────────────────
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# Q16_16 encoded cross-sections at various energies
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CROSS_SECTIONS_PB = {
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# pp collisions at √s = 13 TeV (LHC Run 2)
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'ttbar_13TeV': 830, # ± 40 (top pair production)
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'W_incl_13TeV': 20500, # ± 500 (W boson inclusive)
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'Z_incl_13TeV': 1870, # ± 50 (Z boson inclusive)
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'H_gg_13TeV': 48.6, # ± 2.0 (Higgs via gluon fusion)
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'H_vbf_13TeV': 3.78, # ± 0.08 (Higgs via VBF)
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'jets_incl_13TeV': 80000000, # 80 Mb (inclusive jets, pT > 30 GeV)
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'dijet_13TeV': 10000000, # 10 Mb (dijet, pT > 50 GeV)
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# ee collisions at √s = 91.2 GeV (LEP Z pole)
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'Z_ee': 2980, # ± 30 (Z → ee)
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'Z_mumu': 2980, # ± 30 (Z → μμ)
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'Z_tautau': 2980, # ± 30 (Z → ττ)
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'Z_had': 1720, # ± 20 (Z → hadrons)
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}
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CROSS_SECTIONS_Q16 = {
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name: _q16(xs) for name, xs in CROSS_SECTIONS_PB.items()
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}
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# ── Trigger Thresholds (LHC, in GeV) ─────────────────────────────────
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TRIGGER_THRESHOLDS_GEV = {
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'single_electron': 27, # HLT_Ele27_WPTight_Gsf
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'single_muon': 24, # HLT_IsoMu24
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'single_photon': 150, # HLT_Photon150
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'jet_450': 450, # HLT_PFJet450
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'met_120': 120, # PFMET120
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'ht_500': 500, # HLT_PFHT500
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'dilepton_mll': 12, # M(ee/μμ) > 12 GeV
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'bjet_csv': 0.8484, # DeepJet medium WP
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}
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TRIGGER_THRESHOLDS_Q16 = {
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name: _q16(thresh) for name, thresh in TRIGGER_THRESHOLDS_GEV.items()
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}
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# ── Calorimeter Calibration Constants ────────────────────────────────
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# Energy scale factors for ECAL/HCAL (dimensionless, Q16_16)
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CALIBRATION_CONSTANTS = {
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'ecal_eb': 1.000, # ECAL barrel
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'ecal_ee': 1.005, # ECAL endcap (slightly higher)
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'hcal_hb': 1.000, # HCAL barrel
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'hcal_he': 1.010, # HCAL endcap
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'hcal_hf': 1.050, # HF (forward, larger corrections)
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'muon_scale': 1.000, # Muon momentum scale
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'electron_scale': 1.002, # Electron energy scale
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'photon_scale': 1.003, # Photon energy scale
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}
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CALIBRATION_Q16 = {
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name: _q16(cal) for name, cal in CALIBRATION_CONSTANTS.items()
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}
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# ── BRAM Layout for FPGA ─────────────────────────────────────────────
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def generate_bram_layout() -> dict:
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"""Generate BRAM layout for particle physics LUTs.
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Returns dict mapping BRAM bank to (name, entries, data).
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Each bank is 256 entries × 32-bit Q16_16.
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"""
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banks = {}
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# Bank 0: Particle masses (up to 256 entries)
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mass_entries = list(PARTICLE_MASSES_Q16.items())[:256]
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bank0 = [0] * 256
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for i, (name, q16val) in enumerate(mass_entries):
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bank0[i] = q16val
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banks[0] = ('particle_masses', len(mass_entries), bank0)
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# Bank 1: Decay widths
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width_entries = list(DECAY_WIDTHS_Q16.items())[:256]
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bank1 = [0] * 256
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for i, (name, q16val) in enumerate(width_entries):
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bank1[i] = q16val
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banks[1] = ('decay_widths', len(width_entries), bank1)
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# Bank 2: Cross-sections
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xs_entries = list(CROSS_SECTIONS_Q16.items())[:256]
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bank2 = [0] * 256
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for i, (name, q16val) in enumerate(xs_entries):
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bank2[i] = q16val
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banks[2] = ('cross_sections', len(xs_entries), bank2)
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# Bank 3: Trigger thresholds + calibration
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trigger_entries = list(TRIGGER_THRESHOLDS_Q16.items())
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cal_entries = list(CALIBRATION_Q16.items())
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bank3 = [0] * 256
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for i, (name, q16val) in enumerate(trigger_entries):
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bank3[i] = q16val
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for i, (name, q16val) in enumerate(cal_entries):
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bank3[len(trigger_entries) + i] = q16val
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banks[3] = ('triggers_calibration', len(trigger_entries) + len(cal_entries), bank3)
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return banks
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def export_bram_init(bank_data: list[int], path: Path):
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"""Export BRAM initialization data as Verilog initial block."""
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with open(path, 'w') as f:
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f.write('// Auto-generated particle physics LUT\n')
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f.write('// Q16_16 fixed-point, 256 entries × 32-bit\n\n')
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f.write('initial begin\n')
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for i, val in enumerate(bank_data):
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# Format as 32-bit hex
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hexval = val & 0xFFFFFFFF
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f.write(f' memory[8\'h{i:02X}] = 32\'h{hexval:08X};\n')
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f.write('end\n')
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def export_all_bram(output_dir: Path):
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"""Export all BRAM initialization files."""
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output_dir.mkdir(parents=True, exist_ok=True)
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banks = generate_bram_layout()
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for bank_id, (name, count, data) in banks.items():
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path = output_dir / f'particle_lut_bank{bank_id}_{name}.v'
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export_bram_init(data, path)
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print(f'Bank {bank_id}: {name} ({count} entries) → {path}')
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# ── Cross-Section Lookup (energy-dependent) ───────────────────────────
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def interpolate_cross_section(energy_tev: float, process: str) -> int:
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"""Interpolate cross-section at given energy. Returns Q16_16.
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Uses log-log interpolation between known energy points.
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For energies outside the table, uses power-law extrapolation.
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"""
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# Energy points and corresponding cross-sections (approximate)
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energy_points = {
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'ttbar': [(7, 165), (8, 230), (13, 830), (14, 930)],
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'W': [(7, 12200), (8, 14700), (13, 20500), (14, 22000)],
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'Z': [(7, 1200), (8, 1400), (13, 1870), (14, 2000)],
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'H_gg': [(7, 15.1), (8, 19.3), (13, 48.6), (14, 54.7)],
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}
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if process not in energy_points:
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return _q16(0)
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points = energy_points[process]
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if energy_tev <= points[0][0]:
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return _q16(points[0][1])
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if energy_tev >= points[-1][0]:
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return _q16(points[-1][1])
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# Log-log interpolation
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import math
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for i in range(len(points) - 1):
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e0, xs0 = points[i]
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e1, xs1 = points[i + 1]
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if e0 <= energy_tev <= e1:
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t = (math.log(energy_tev) - math.log(e0)) / (math.log(e1) - math.log(e0))
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xs = xs0 * (xs1 / xs0) ** t
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return _q16(xs)
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return _q16(0)
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# ── CLI ───────────────────────────────────────────────────────────────
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if __name__ == '__main__':
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print('=== Particle Physics LUT (Q16_16) ===\n')
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print('Particle Masses (MeV):')
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for name, mass in PARTICLE_MASSES_MEV.items():
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q16 = PARTICLE_MASSES_Q16[name]
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print(f' {name:<20} {mass:>12.3f} MeV → Q16: {q16:>12d} ({_q16_to_float(q16):.3f} MeV)')
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print(f'\nDecay Widths (GeV):')
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for name, width in DECAY_WIDTHS_GEV.items():
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q16 = DECAY_WIDTHS_Q16[name]
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print(f' {name:<20} {width:>12.6f} GeV → Q16: {q16:>12d}')
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print(f'\nCross-Sections at 13 TeV (pb):')
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for name, xs in CROSS_SECTIONS_PB.items():
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q16 = CROSS_SECTIONS_Q16[name]
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print(f' {name:<20} {xs:>12.1f} pb → Q16: {q16:>12d}')
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print(f'\nTrigger Thresholds (GeV):')
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for name, thresh in TRIGGER_THRESHOLDS_GEV.items():
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q16 = TRIGGER_THRESHOLDS_Q16[name]
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print(f' {name:<20} {thresh:>12.1f} GeV → Q16: {q16:>12d}')
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print(f'\nBRAM Layout:')
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banks = generate_bram_layout()
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for bank_id, (name, count, data) in banks.items():
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nonzero = sum(1 for v in data if v != 0)
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print(f' Bank {bank_id}: {name} ({count} entries, {nonzero} non-zero)')
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# Export
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out_dir = Path('/tmp/particle_lut_bram')
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export_all_bram(out_dir)
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print(f'\nExported to {out_dir}/')
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