[CTP] Apply the ZNC cross-section ratio after the pile-up correction

DataFormats/Detectors/CTP/CTPRateFetcher.md

@@ -0,0 +1,42 @@
+# CTPRateFetcher
+
+## The ZDC cross-section ratio and the pile-up correction
+
+`CTPRateFetcher::fetch(..., "ZNC hadronic")` gives the PbPb hadronic interaction rate. Two things
+happen to the raw ZNC counting rate `R` on the way there: the Poisson inversion in
+`pileUpCorrection`, and the division by `sigma_ZNC / sigma_had = 28`. The order matters.
+
+Write `mu` for a mean number of interactions per colliding crossing, `N` for the number of
+colliding bunch pairs and `f` for the revolution frequency. Then
+
+    mu_ZNC = 28 * mu_had                 exact: the ZDC sees hadronic and EMD, and means add
+    R      = N f (1 - exp(-mu_ZNC))      a crossing is counted once, however many interactions
+    mu_ZNC = -ln(1 - R/(N f))            which is what pileUpCorrection computes
+
+and therefore
+
+    hadronic rate = N f mu_had = pileUpCorrection(R) / 28
+
+Invert first, divide second. `pileUpCorrection(R/28)` inverts the saturation of a rate that never
+saturated - the saturation is in `R` - and comes out low by
+
+    [-ln(1 - x/28)] / [(-ln(1 - x)) / 28] ,     x = R/(N f)
+
+The two agree to first order in `x` and drift apart with pile-up. Measured on three 2024 PbPb runs
+at 10 %, 50 % and 90 % of the run:
+
+    run    N_bc   R_ZNC [Hz]  x=R/(Nf)   mu_ZNC   divide first   divide last   ratio
+    544490 1088    1238358.4   0.10121  0.10671        44307.2       46628.8  0.9502
+    544490 1088    1158151.9   0.09466  0.09944        41432.6       43453.3  0.9535
+    544490 1088    1086013.1   0.08876  0.09295        38847.8       40616.7  0.9564
+    559856 1032    1268830.4   0.10933  0.11578        45404.1       47989.4  0.9461
+    559856 1032     959082.2   0.08264  0.08626        34303.6       35751.4  0.9595
+    559856 1032     756641.1   0.06520  0.06742        27054.4       27944.1  0.9682
+    568721 1032     633548.4   0.05459  0.05614        22648.8       23267.8  0.9734
+    568721 1032     623888.1   0.05376  0.05526        22303.1       22903.0  0.9738
+    568721 1032     635486.5   0.05476  0.05631        22718.2       23341.0  0.9733
+
+Both columns come from an unpatched build: `fetch(..., "ZNC")`, without `"hadronic"`, returns
+`pileUpCorrection(R)` already, so the second column is `fetch(..., "ZNC") / 28`.
+
+`getLumi` divides after `pileUpCorrection` and needs no change.

DataFormats/Detectors/CTP/src/CTPRateFetcher.cxx

@@ -17,13 +17,28 @@
 #include "CommonConstants/LHCConstants.h"
 
 using namespace o2::ctp;
+
+namespace
+{
+// sigma_ZNC / sigma_hadronic. Being a ratio of cross sections it belongs on mu and not on a
+// counting rate that has already saturated; see CTPRateFetcher.md in the parent directory.
+double zncHadronicRatio(const std::string& sourceName)
+{
+  const bool isZNChadronic = sourceName.find("ZNC") != std::string::npos &&
+                             sourceName.find("hadronic") != std::string::npos;
+  return isZNChadronic ? 28. : 1.;
+}
+} // namespace
+
 double CTPRateFetcher::fetch(o2::ccdb::BasicCCDBManager* ccdb, uint64_t timeStamp, int runNumber, std::string sourceName)
 {
   auto triggerRate = fetchNoPuCorr(ccdb, timeStamp, runNumber, sourceName);
-  if (triggerRate >= 0) {
-    return pileUpCorrection(triggerRate);
+  if (triggerRate < 0) {
+    return -1;
   }
-  return -1;
+  // fetchNoPuCorr has already divided by the ratio; put it back, invert the Poisson, divide again
+  const double ratio = zncHadronicRatio(sourceName);
+  return pileUpCorrection(triggerRate * ratio) / ratio;
 }
 double CTPRateFetcher::fetchNoPuCorr(o2::ccdb::BasicCCDBManager* ccdb, uint64_t timeStamp, int runNumber, std::string sourceName)
 {