[PWGLF] Add alt. rotational BG and fix correction factors calculation

[vbarbaso]

• Add an alternative rotational background method using rotations around the mother-particle momentum axis.
• Fix and merge histograms for event and signal-loss factor calculation into the true and generated MC processes.
• Rework and expand the QA histograms and their organisation.
• general clean up

[github-actions]

O2 linter results: ❌ 0 errors, ⚠️ 0 warnings, 🔕 0 disabled

[alibuild]

Error while checking build/O2Physics/code-check for 18ca30f at 2026-09-03 13:56:

## sw/BUILD/O2Physics-code-check-latest/log
--
========== List of issues found ==========
++ echo 'Found 14 errors and 136 warnings.'
Found 14 errors and 136 warnings.
++ [[ 14 -gt 0 ]]
++ cat /sw/BUILD/7c8d9ca82fe918c5b84e0db1ea0caaac792b52fa/O2Physics-code-check/errors.txt
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:46:1: error: included header Vector4D.h is not used directly [misc-include-cleaner,-warnings-as-errors]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:62:8: error: constructor does not initialize these fields: pdg [cppcoreguidelines-pro-type-member-init,-warnings-as-errors]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:171:15: error: no header providing "ROOT::Math::PxPyPzMVector" is directly included [misc-include-cleaner,-warnings-as-errors]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:289:40: error: no header providing "Form" is directly included [misc-include-cleaner,-warnings-as-errors]
PWGLF/Utils/rsnOutput.h:85:39: error: the parameter 'name' is copied for each invocation but only used as a const reference; consider making it a const reference [performance-unnecessary-value-param,-warnings-as-errors]
PWGLF/Utils/rsnOutput.h:101:26: error: variable 'names' is non-const and globally accessible, consider making it const [cppcoreguidelines-avoid-non-const-global-variables,-warnings-as-errors]
PWGLF/Utils/rsnOutput.h:106:26: error: variable 'names' is non-const and globally accessible, consider making it const [cppcoreguidelines-avoid-non-const-global-variables,-warnings-as-errors]
PWGLF/Utils/rsnOutput.h:114:16: error: default arguments on virtual or override methods are prohibited [google-default-arguments,-warnings-as-errors]
PWGLF/Utils/rsnOutput.h:129:18: error: variable 'currentType' is not initialized [cppcoreguidelines-init-variables,-warnings-as-errors]
PWGLF/Utils/rsnOutput.h:157:25: error: variable 'currentTypeSys' is not initialized [cppcoreguidelines-init-variables,-warnings-as-errors]
PWGLF/Utils/rsnOutput.h:224:33: error: the parameter 'name' is copied for each invocation but only used as a const reference; consider making it a const reference [performance-unnecessary-value-param,-warnings-as-errors]
PWGLF/Utils/rsnOutput.h:233:43: error: the parameter 'name' is copied for each invocation but only used as a const reference; consider making it a const reference [performance-unnecessary-value-param,-warnings-as-errors]
PWGLF/Utils/rsnOutput.h:256:14: error: constness of 'unknownAxis' prevents automatic move [performance-no-automatic-move,-warnings-as-errors]
PWGLF/Utils/rsnOutput.h:275:16: error: default arguments on virtual or override methods are prohibited [google-default-arguments,-warnings-as-errors]
++ [[ 136 -gt 0 ]]
++ cat /sw/BUILD/7c8d9ca82fe918c5b84e0db1ea0caaac792b52fa/O2Physics-code-check/warnings.txt
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:457:16: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:460:106: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:462:16: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:465:116: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:467:16: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:470:118: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:472:16: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:475:64: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:477:16: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:480:110: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:482:16: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:485:116: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:487:16: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:490:116: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:492:16: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:495:74: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:497:16: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:500:16: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:503:72: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:505:16: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:522:30: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:524:35: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:526:37: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:536:30: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:538:35: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:540:37: warning: statement should be inside braces [readability-braces-around-statements]
[0 more errors; see full log]

Full log here.

[alibuild]

Error while checking build/O2Physics/staging for e160f98 at 2026-09-03 15:19:

## sw/BUILD/O2Physics-latest/log
/sw/SOURCES/O2Physics/slc9_x86-64-slc9_x86-64/0/PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:749:76: error: unused parameter 'tracks' [-Werror=unused-parameter]
ninja: build stopped: subcommand failed.

Full log here.

[alibuild]

Error while checking build/O2Physics/code-check for 053772e at 2026-09-03 15:36:

## sw/BUILD/O2Physics-code-check-latest/log
--
========== List of issues found ==========
++ echo 'Found 1 errors and 10 warnings.'
Found 1 errors and 10 warnings.
++ [[ 1 -gt 0 ]]
++ cat /sw/BUILD/b85bb4b67c6e7df2e403103393a4ecc1302fe2bc/O2Physics-code-check/errors.txt
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:64:8: error: constructor does not initialize these fields: pdg [cppcoreguidelines-pro-type-member-init,-warnings-as-errors]
++ [[ 10 -gt 0 ]]
++ cat /sw/BUILD/b85bb4b67c6e7df2e403103393a4ecc1302fe2bc/O2Physics-code-check/warnings.txt
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:556:30: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:558:35: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Tasks/Resonances/phianalysisTHnSparse.cxx:560:37: warning: statement should be inside braces [readability-braces-around-statements]
PWGLF/Utils/rsnOutput.h:31:1: warning: nested namespaces can be concatenated [modernize-concat-nested-namespaces]
PWGLF/Utils/rsnOutput.h:127:37: warning: redundant explicit casting to the same type 'int' as the sub-expression, remove this casting [readability-redundant-casting]
PWGLF/Utils/rsnOutput.h:144:5: warning: 'if' statement is unnecessary; deleting null pointer has no effect [readability-delete-null-pointer]
PWGLF/Utils/rsnOutput.h:156:43: warning: redundant explicit casting to the same type 'int' as the sub-expression, remove this casting [readability-redundant-casting]
PWGLF/Utils/rsnOutput.h:173:5: warning: 'if' statement is unnecessary; deleting null pointer has no effect [readability-delete-null-pointer]
PWGLF/Utils/rsnOutput.h:183:39: warning: pointer parameter 'point' can be pointer to const [readability-non-const-parameter]
PWGLF/Utils/rsnOutput.h:193:42: warning: pointer parameter 'point' can be pointer to const [readability-non-const-parameter]
++ [[ 1 -gt 0 ]]
++ exit 1
--

Full log here.