Influence of Crystal Fiber Inhomogeneity on the Energy Resolution of a Sampling Electromagnetic Calorimeter

Sampling electromagnetic calorimeters (ECALs) are widely used in high-energy physics experiments thanks to their ability to efficiently measure electromagnetic particles' energy over a broad dynamic range while maintaining good energy resolution. These detectors alternate passive layers made of dense absorber materials, with active layers, like scintillators. Scintillating materials, such as inorganic garnets, are promising candidates for high-luminosity environments like the Large Hadron Collider (LHC) due to their high radiation hardness, ensuring longer operational lifetimes without compromising performance. However, fluctuations in light yield (LY) can lead to a degradation in energy resolution (ER). One concept of sampling calorimeter is the so called spaghetti calorimeter (SpaCaL), it relies on optimal scintillating fiber placement inserted in heavy absorber. Hence addressing possible LY variations is critical to guarantee that the detector meets the stringent requirements of future high-luminosity runs at the LHC. To maintain optimal ECAL performance, providing feedback to scintillator producers on the acceptable limits of LY variation is essential. For this purpose, a W-GAGG SpaCal was modeled using Monte Carlo methods. Electrons with energies ranging from 1 to 100 GeV were simulated through the SpaCal to study ER. We introduced artificial longitudinal variations of LY along the GAGG fibers with fixed values across a range of conditions to evaluate their impact on our modeled detector's performance. Our results indicate that, to preserve the ER and maintain an acceptable constant term c = 1%, the longitudinal variation of LY should not exceed 2%/cm. Additionally, we found the optimal fiber configuration to minimize performance degradation from LY fluctuations by testing different end orientations and placements relative to the reflector in both SpaCal sections.