Studies of the improved antenna/dipole algorithms

as implemented in PHOTOS,
and in KoralZ, TAUOLA for exact Matrix Element calculation

Note: There are naming-convention clashes with literature.

There are three steps in this study: first, we concentrate on the single-dipole emission. PHOTOS is compared with the full matrix-element calculations in case of W, Z, tau and Higgs-boson decays. These comparisons are to quantify the numerical consequence of the approximations used in PHOTOS for convenience. In principle, these approximations are not needed and can be improved with the help of the weights which are process-dependent. As it can be seen from comparisons below, the numerical consequences of the approximations are insignificant for all practical applications of PHOTOS we are aware of.

Because in the first part of this study we have used single-dipole emission, we will continue to use test1 in the second part as well (see here for definition of tests). In cases of Z and W decays can see excellent performance of PHOTOS exponentiated version as well.

If one turns to test2 (see), PHOTOS compares very well with KKMC for Z decays. In KKMC, double-photon matrix-element is used.
In case of W decays (see), agreement is less good, possibly because only a single-photon matrix-element is used in WINHAC. This conclusion requires higher-statistics runs to confirm. This does not proove that PHOTOS is complete next-to-leading-log exponentiated matrix element.
To achieve such goal, not only process-dependent correcting weights would have to be installed, but also treatment of PHOTOS phase-space would have to be documented and its NLL-correctness has to be proven. Some phase-space correction weights may need to be installed.
At this point, such ambitious project doesn't seem to be phenomenologically interesting.

Table 1: Summary of test of antenna algorithms.

GENERATOR	Branching ratio		Maximum SDP		T1	T2	Booklet
(n photons) ->	0	1	0	1
Comparison no 1:     KoralZ vs PHOTOS, O(1)
E_test=1.0
Koral Z O(1)	82.514	17.486
PHOTOS O(1)	82.362	17.638	0	0.0053	0.303	0.092
Comparison no 2:     KKMC-PHOTOS
E_test=1.0
KKMC	83.918	16.082
PHOTOS O(4)	83.836	16.164	0	0.0039	0.163	0.064
Comparison no 3:     KoralZ-PHOTOS
E_test=1.0
Koral Z	83.984	16.016
PHOTOS O(4)	83.836	16.164	0	0.0097	0.296	0.155
Comparison no 4:     KKMC - Koral Z
E_test=1.0
KKMC	83.918	16.082
Koral Z	83.984	16.016	0	0.0021	0.133	0.033
Comparison no 5:     TAUOLA - PHOTOS (mu channel)
E_test=0.05
TAUOLA	98.916	1.084
PHOTOS O(1)	98.927	1.073	0	0.0044	0.021	0.0046
PHOTOS EXP	98.935	1.065	0	0.0047	0.038	0.0048
Comparison no 6:     TAUOLA - PHOTOS (e channel)
E_test=0.05
TAUOLA	94.51	5.49
PHOTOS O(1)	94.54	5.46	0	0.002	0.071	0.011
Comparison no 7:     WINHAC - PHOTOS
E_test=1.0
WINHAC (exp)	92.776	7.224
PHOTOS (EXP)	92.739	7.261	0	0.0002	0.073	0.0016
Comparison no 8:     Photos Exponentiated
E_test=1.0
PHOTOS EXP	83.839	16.161
PHOTOS O(4)	83.836	16.164	0	0	0.0069	0

PRELIMINARY: Comparison of Exponentiated PHOTOS and PHOTOS O(4) for 2-photon test

GENERATOR	Branching ratio			Maximum SDP			T1	T2	Booklet
(n photons) ->	0	1	2	0	1	2
Comparison no 8A:     PHOTOS O(4) and PHOTOS EXP
E_test=1.0
PHOTOS O(4)	83.78	14.92	1.30
PHOTOS EXP	83.77	14.92	1.31	0	0.005	0.0009	0.015	0.070

• Comparison 1: KORAL-Z O(1) and PHOTOS O(1)
Process: Z -> mu⁺ mu^-


The differences are due to some approximation in the kernel used by PHOTOS O(1).
This kernel is simplified with respect to complete O(1).

• Comparison 2: KKMC and PHOTOS O(4)

The differences are quite similar as in the previous case.
It shows that the dominant part of the difference is due to simplification of the kernel. It could be removed, however the price would be some loss of the PHOTOS algorithm universality; PHOTOS kernel would have to be process-dependent.

• Comparison 3: KORAL-Z and PHOTOS O(4)
Process: Z -> mu⁺ mu^-


This study presents comparisons of PHOTOS O(4) with KoralZ.
The differences are comparable to the case of KKMC, but somewhat larger.

• Comparison 4: KKMC and KORAL-Z
Process: Z -> mu⁺ mu^-


This study presents comparison of two matrix-element exponentiated algorithms.
As one can see, there are some differences as well. They are in fact not smaller than in case of comparison PHOTOS-KKMC.

• Comparison 5: TAUOLA and PHOTOS in muon-channel
Process: tau^- -> mu^- ~nu_mu nu_tau


This study presents comparison of TAUOLA decay channel tau->mu nu nu gamma and TAUOLA (tau->mu nu nu) + PHOTOS (gamma).

• Comparison 6: TAUOLA and PHOTOS in electron-channel
Process: tau^- -> e^- ~nu_e nu_tau


This study presents comparison of TAUOLA decay channel tau->e nu nu gamma and TAUOLA (tau->e nu nu) + PHOTOS (gamma).

• Comparison 7: WINHAC and PHOTOS: bremsstrahlung in W decays
Process: W⁺ -> mu⁺ nu_mu


This study compares bremsstrahlung as generated by WINHAC and exponentiated PHOTOS.

The following parameters have been used in WINHAC:

• For WINHAC-generated QED: KeyRad=1 (no electroweak corrections)
• For PHOTOS-generated QED: KeyRad=0 (WINHAC generating on Born-level only)


• Comparison 8: Exponentiated PHOTOS and PHOTOS O(4)
Process: Z -> mu⁺ mu^-


This study presents comparison of PHOTOS Exponentiated and PHOTOS O(4).
It shows that in case of decays to muons, exponentiation is not needed for Z decays.

• Studies of W decays in the first order

Reference: Acta Phys.Polon.B34:4561-4570,2003

• Studies of H decays in the first order

Reference: Acta Phys.Polon.B34:2665-2672,2003