ktht
commented
1 year ago TLDR is given at the very end.
I reran the analysis for the following three cases, where the tau decays are delegated to
Pythia 8.306(in Belle II conditions);Tauola++ 1.1.8out-of-the-box;Tauola++ 1.1.8with theSANClibrary.
All results are extracted from generator-level $\tau\to\pi+\nu$ decays, so to rule out any diluting effects caused by kinematic fit. In all cases, the tau decays are inclusive, meaning that about 110k events survives the requirement that both taus (which are produced in DY events) decay to single pions. Here are the results presented in beam coordinate axis, where the 3rd axis ($\mathbf{k}$) is along tau momentum, the 2nd axis ($\mathbf{r}$) lies on the plane spanned by tau and electron momenta, and the 1st axis ($\mathbf{n}$) orthogonal to the other two, all in c.o.m. frame:
PYTHIA (114631 events)
==================================
Asymmetry:
[ -0.245623 0.00659507 0.00603676
0.00401288 0.146801 -0.285333
0.00464098 0.237178 0.871981 ]
Summation:
[ -0.249686 0.00508408 0.00391348
0.00653464 0.138683 -0.276996
-0.00186421 0.243658 0.885224 ]
ML fit:
[ -0.249671 0.00921341 0.000212506
0.00753089 0.139364 -0.276324
-0.00312754 0.23755 0.886287 ]
1D diff XS:
[ -0.249255 0.00454215 0.00443124
0.00593798 0.138174 -0.276008
-0.00217371 0.244018 0.887989 ]
2D diff XS:
[ -0.24979 0.00523523 0.00417337
0.00672311 0.13868 -0.277246
-0.00190086 0.24378 0.88803 ]
TAUOLA++ (125591 events)
==================================
Asymmetry:
[ 0.0111791 -0.0478697 0.0527108
-0.0635396 -0.0205429 0.0736677
0.0388244 -0.0267217 0.842576 ]
Summation:
Matrix C:
[ 0.015075 -0.0591435 0.0364924
-0.0281235 -0.0268309 0.0240461
0.0477844-0.000387594 0.848719 ]
ML fit:
[ 0.0155621 -0.0607487 0.0326157
-0.0233263 -0.0256499 0.026586
0.0424554 0.00254594 0.852014 ]
1D diff XS:
[ 0.0152708 -0.0572985 0.0382227
-0.0298607 -0.0268092 0.0243901
0.0476596 0.000498932 0.849958 ]
2D diff XS:
[ 0.0145587 -0.0598416 0.0367065
-0.0284408 -0.0269722 0.0240464
0.0479108 0.000526788 0.852377 ]
TAUOLA++ with SANC (125285 events)
==================================
Asymmetry:
Matrix C:
[ -0.353658 -0.0329808 0.0666959
-0.0337471 0.446566 0.0746139
0.0401325 -0.00239454 0.736337 ]
Summation:
[ -0.340833 -0.0454045 0.0333969
-0.00858326 0.444391 0.0194261
0.0354548 -0.0014837 0.744016 ]
ML fit:
[ -0.343539 -0.0384257 0.0292925
-0.0120163 0.449523 0.0277464
0.0359525 -0.00182352 0.75129 ]
1D diff XS:
[ -0.344145 -0.0433198 0.0348278
-0.0104284 0.445861 0.0210741
0.0351133-0.000915811 0.744652 ]
2D diff XS:
[ -0.34602 -0.0457655 0.0330568
-0.00811796 0.446457 0.0196809
0.0361367 -0.00180716 0.74659 ]For context, the SM expectation for the spin correlation matrix in Belle II conditions is $\mathrm{diag}(-0.42, 0.53, 0.89)$:
The elements of matrix R are taken from Eq. 16 of this paper.
Now there's also the SANC library, which lets users generate spin correlation matrices for a number of c.o.m. energies and scattering angles of taus that are produced in DY events. Each spin correlation matrix is given two event weights, one with EW corrections applied and the other without the said corrections. Additional NLO QED corrections can be applied as well. The spin correlation matrices are saved to a text file with some metadata like the SM parameters, which NLO corrections are applied and the author credits. AFAICT, the library generates the spin correlation matrices only for three initial states: $d\bar{d}$, $u\bar{u}$ and $e^+e^-$. If one wants to pass those tables to Tauola++, then the following conventions must be followed:
- for $d\bar{d}$, $u\bar{u}$ and $e^+e^-$ initial states, the text files must be named as
table1-1.txt,table2-2.txtandtable11-11.txt, respectively; - the files must be stored in the same directory where the events are generated;
- the user has to specify 3 ranges of c.o.m. energies (with the first range given in logarithmic scale);
- the user has to select 21 scan points for the scattering angle.
Tauola++ interpolates between the energies and scattering angles if a given event is generated at slightly different c.o.m. energies or scattering angles than those for which the spin correlation matrix is known. Official documentation of Tauola++ and SANC can be found here (*) (also published here). I used f95 compiler with -std=legacy -ffixed-line-length-132 options to build the auxiliary LoopTools libary. The C object files had to be compiled with -DHAVE_UNDERSCORE option because C functions called from Fortran need to end with an underscore (a detail that I had long forgotten).
As a cross-check, I generated the spin correlation matrices with SANC at c.o.m. energy of 10.58 GeV for 100 different scattering angles and computed their weighted average:
LO:
[[-0.41986834 -0.00002869 0.00000000]
[-0.00002869 0.52668345 -0.00264794]
[ 0.00000000 -0.00264794 0.89318489]]
With EW corrections:
[[-0.41986688 -0.00002869 0.00000001]
[-0.00002869 0.52668162 -0.00271822]
[ 0.00000001 -0.00271822 0.89318526]]
With QED corrections:
[[-0.41957273 0.00059840 0.00030224]
[ 0.00059840 0.52587721 -0.01316196]
[ 0.00030224 -0.01316196 0.89369552]]Here's my summary:
- simulation of tau decays is consistent on per-generator level, which is to say that the various methods of estimating the tau spin correlation matrix (asymmetry, ML fit etc) differ only so slightly;
- out-of-the-box
Tauola++models only longitudinal spin correlations. This shouldn't come as a surprise since this very fact is also stated inTauola++documentation (*); - correlation matrices directly produced by
SANCand those simulated byTauDecayare most consistent with the theory expectation; - all elements of the correlation matrices produced with
Tauola++in combination withSANCappear to be off by a constant factor of $1.20$ from the expectation; - in case of
Tauola++(with or withoutSANC), the off-diagonal elements of the spin correlation matrix appear quite large actually. The largest element (when accounting for the constant factor of $1.20$ from the previous point) is around $0.09$; - judging from the
SANCtables, NLO EW and QED corrections have negligible impact on spin correlations; Pythiahas the largest disagreement with the theory expectation. In particular, it appears to produce a spin correlation matrix that has large off-diagonal elements. The only diagonal element that is remotely close to the expectation is the longitudinal element.
What else can we do?
- instead of MadGraph try using
KKMCeefor generating the MEs, which is the standard MC generator at Belle. However, it probably means that we'd have to use LHE or HepMC format (either intermittently or as input to our FW); - use
TauSpinner(which is part ofTauola++) on top of the existing software and/or combine it withKKMCee(like how it's done at Belle) to produce new sample of events and see if the SM expectation can be reproduced with this configuration. This likely implies that the tau spins are generated as uncorrelated and correlations are recovered by reweighting the events using weights computed byTauSpinner. It does complicate some of the methods that we use to estimate the spin correlation matrices (in particular the ML fit, which does not handle event weights yet AFAICT); - follow up with the authors of
Pythiaon the discrepancies seen in tau spin correlation matrix.
Besides the last point I won't make any promises on whether or not I actually deliver them.
veelken
It turns out that depending on the software one uses to decay the tau pair -- Pythia8, Tauola or TauDecay --, the spin correlation matrix can vary quite a bit even if no event selection cuts are applied. Here are the matrices for the simplest tau decay mode (tau->pi+nu) computed by averaging over the scalar products of polarimetric vectors, but the results change very little when other methods for computing the spin correlation matrix are used: