## February 2025. Results for F-tilde in the physical continuum limit after fitting lattice QCD data to spline functions from
## from 'Constraints on axion-like particles using lattice QCD calculations of the rate for J/psi to gamma + axion'
## Authors: B. Colquhoun, C. T. H. Davies, G. P. Lepage & S. Renner 
## See the paper for a definition of F-tilde and how to include it in a calculation of the branching fraction for this decay mode.
##
## Columns are: (m_a/M_Jpsi)^2,  F-tilde,  sigma_F-tilde 
0.00 0.20169282187050766 0.003182843431246471
0.01 0.20195024113346283 0.00318059805797447
0.02 0.2022190449769858 0.0031783786320318513
0.03 0.2024992334010766 0.0031761857737023307
0.04 0.20279080640573519 0.0031740204324483064
0.05 0.20309376399096157 0.0031718838879672903
0.06 0.20340810615675575 0.003169777751205521
0.07 0.20373383290311775 0.0031677039653236778
0.08 0.20407094423004757 0.003165664806608368
0.09 0.20441944013754518 0.0031636628853217944
0.10 0.20477932062561058 0.003161701146480722
0.11 0.2051505856942438 0.0031597828705545706
0.12 0.20553323534344484 0.003157911674071155
0.13 0.20592726957321364 0.003156091510117281
0.14 0.2063326883835503 0.0031543266687201195
0.15 0.20674949177445473 0.0031526217770939426
0.16 0.20717767974592696 0.003150981799735542
0.17 0.20761725229796701 0.0031494120383503566
0.18 0.20806820943057486 0.0031479181315900856
0.19 0.2085305511437505 0.0031465060545813454
0.20 0.20900427743749395 0.0031451821182237535
0.21 0.20948938831180522 0.0031439529682346836
0.22 0.20998588376668428 0.0031428255839168907
0.23 0.21049376380213114 0.0031418072766242044
0.24 0.21101302841814581 0.003140905687899608
0.25 0.2115436776147283 0.0031401287872592216
0.26 0.2120857113918786 0.0031394848695950432
0.27 0.21263912974959667 0.00313898255216877
0.28 0.21320393268788257 0.0031386307711686514
0.29 0.21378012020673626 0.00313843877780112
0.30 0.21436769230615776 0.003138416133888939
0.31 0.2149666489861471 0.0031385727069478094
0.32 0.21557699024670418 0.0031389186647138192
0.33 0.2161987160878291 0.003139464469094796
0.34 0.21683182650952182 0.003140220869519577
0.35 0.21747632151178234 0.0031411988956604633
0.36 0.21813220109461068 0.0031424098495056525
0.37 0.2187994652580068 0.003143865296760325
0.38 0.21947811400197073 0.0031455770575572308
0.39 0.22016814732650247 0.003147557196460181
0.40 0.22086956523160203 0.0031498180117467095
0.41 0.22158242124293645 0.003152306303345354
0.42 0.22233661872861385 0.003153640748605949
0.43 0.22315624321043098 0.0031551936278804015
0.44 0.224039653200582 0.0031569121001925513
0.45 0.224985207211261 0.003158753584309838
0.46 0.22599126375466205 0.003160684564474222
0.47 0.22705618134297928 0.0031626794848548987
0.48 0.2281783184884068 0.003164719736392877
0.49 0.2293560337031387 0.0031667927383411264
0.50 0.23058768549936906 0.0031688911158095487
0.51 0.23187163238929198 0.0031710119739213416
0.52 0.23320623288510162 0.0031731562687067985
0.53 0.234589845498992 0.003175328274544011
0.54 0.23602082874315727 0.00317753514775497
0.55 0.23749754112979155 0.003179786585841208
0.56 0.2390183411710889 0.0031820945817641498
0.57 0.2405815873792434 0.003184473272616927
0.58 0.2421856382664492 0.0031869388819769167
0.59 0.24382885234490037 0.0031895097551557635
0.60 0.24550958812679105 0.0031922064864624835
0.61 0.24722620412431534 0.003195052137453215
0.62 0.24897705884966728 0.0031980725449457484
0.63 0.250760510815041 0.00320129671731485
0.64 0.25257491853263064 0.0032047573172400423
0.65 0.25441864051463026 0.003208491228632758
0.66 0.25629003527323396 0.003212540204903
0.67 0.25818746132063586 0.0032169515950116103
0.68 0.2601092771690301 0.0032217791428641633
0.69 0.2620538413306106 0.0032270838545046887
0.70 0.2640195123175717 0.0032329349262285034
0.71 0.2660046486421074 0.0032394107251204896
0.72 0.2680076088164118 0.003246599811608795
0.73 0.27002675135267895 0.0032546019913827825
0.74 0.272060434763103 0.0032635293814500393
0.75 0.2741070175598781 0.0032735074722135215
0.76 0.27616485825519826 0.003284676164278253
0.77 0.27823231536125764 0.00329719075532864
0.78 0.28030774739025033 0.0033112228489819134
0.79 0.28238951285437036 0.003326961154208065
0.80 0.28447597026581195 0.0033446121409639825
0.81 0.28656547813676914 0.0033644005154374614
0.82 0.288656394979436 0.0033865694771139537
0.83 0.29074707930600674 0.0034113807201874738
0.84 0.29283588962867535 0.0034391141440726467
0.85 0.29492118445963594 0.0034700672423416175
0.86 0.29700132231108267 0.0035045541466204575
0.87 0.29907466169520963 0.0035429043119866253
0.88 0.30113956112421086 0.003585460843130214
0.89 0.3031943791102805 0.003632578475598525
0.90 0.3052374741656127 0.0036846212431227245
0.91 0.3072672048024015 0.0037419598792819307
0.92 0.30928192953284095 0.00380496901827382
0.93 0.3112800068691253 0.0038740242738517314
0.94 0.3132597953234485 0.003949499286083399
0.95 0.31521965340800473 0.004031762831218638
0.96 0.3171579396349881 0.004121176089758023
0.97 0.3190730125165927 0.004218090161487994
0.98 0.32096323056501264 0.004322843904129047
0.99 0.32282695229244196 0.004435762155300463
1.00 0.3246625362110748 0.004557154377217224
