Maximum likelihood reconstruction for the Daya Bay experiment

Transcription

1 Maximum likelihoo econstuction fo the Daya Bay expeiment Dongmei Xia, Liangjian Wen Institute of High Enegy Physics, CAS, Beijing, , China Astact. The Daya Bay anti-neutino expeiment is esigne to pecisely etemine the neutino mixing angle 13. The Maximum likelihoo (ML) econstuction ase on the optical moel gives unifomity enegy econstuction an pecisely vetex econstuction fo the antineutino etecto (AD) of the Daya Bay expeiment. In this pape, we caliate the key paametes of the optical moel with Co 60 souce, making the peicte chages of the PMTs acco with the oseve chages. With the optimize paametes, the ML econstuction povies the enegy econstuction with non-unifomity less than 4%; an the ias of the vetex econstuction is less than 40cm. 1. Intouction to the optical moel. The Daya Bay antineutino expeiment ha pulishe a non-zeo sin 13 with a significance of 7.7 stana eviations[1]. The maximum likelihoo econstuction of the antineutino etecto fo the Daya Bay expeiment can povie unifomity enegy econstuction an pecisely vetex econstuction. Unifomity enegy econstuction help to select invese eta ecay (IBD) events though which to etect antineutinos, an the pecisely vetex econstuction helps to unestaning the ackgoun of the expeiment y povie vetex cuts. Fig. 1: An illustation of the optical moel of the ML econstuction of AD fo the Daya Bay expeiment.

2 The optical moel of the ML econstuction is ase on the constucto of the AD in the Daya Bay expeiment[]. The peicte chage of photo multiplie( PMT ) is efine as with two components, the iectly photo gaphs (p.e) efinition of an ae in equation 1. Fo an the eflecte p.e as shown in figue1. The f cos is, is a nomalization paamete; the PMT angula esponse cuve, in which is angle etween the PMT nomal iection an the vecto fom PMT position pointing to souce position.; R is the istance etween PMT an aioactive souce; is the aveage attenuation length of the liqui scintillate an (LS) the G-LS a [3]; is the PMT elative quantum efficiency(). Fo, the expecte chage is contiute y the sum of mio souces with the same fomula, the suscipts j, k enotes that light is the j-th oe eflecte y ottom eflecto an the k-th oe eflecte y the top eflecto; t ae the eflectivity fo the top an ottom eflecto espectively; R is the istance fom the mio souce to the PMT; jk is the angle etween the PMT nomal iection an the vecto fom the PMT position pointing to the mio souce position. A sum of an gives total expecte chage. f cos R exp R a f cos R j k jk, jk, t exp jk, R jk, a Paametes etemine the istiutions of the PMT chage ae the key paametes: The aveage attenuation length a. PMT angula esponse cuve f cos. The top an ottom eflectivity t. PMT elative quantum efficiency.. Caliate the key paametes The goal of caliates the paametes is to make the expecte chage of the PMTs accos to the oseve chage. We use the.5mev emitte y Co 60 fo caliating, which povie aout 5 p.e fo each PMT. The caliation souce is locate at the automatic caliation units(acu)[4] in AD an i the caliation evey week..1. PMT elative quantum efficiency The elative of the 4 PMTs locate at the same level can e etemine using the caliation souce at the cente of ACUA. The elative value of p.e otaine y PMTs on the same level with the same ing nume is the PMT elative quantum efficiency, fo the etecto is centosymmetical. To get the elative quantum efficiency () of the 19 PMTs, we use the low enegy caliation souce of Ge 68, who emits a few p.e makes sue each PMT otains one p.e at most. Hit times of each PMT of p.e is ecoe, an the atio of single PMT hits to all PMT hits etemines the elative... Attenuation length eflectivity PMT angula esponse cuve A function is uilt to caliate the attenuation length a the eflectivity t an the PMT f simultaneously, fo these paametes ae couple eeply. angula esponse cuve cos jk (1)

3 nij is the aveage oseve chage, n ij ij Num 19 () j i n ij ij is the expecte chage an is function aout the paametes to e caliate ij a, t,, f cos caliation souces that locate at Num iffeent position in the AD. f cos is efine as a. 19 is the nume PMTs quantity, Num is the total nume of as function of f cos p0 p1 cos p cos. Optimize paametes is etemine y minimize when scanning the value of the paametes..3. Pefomance of the paametes Figue shows the value of oseve chage to expecte chage as a function of the incient angle (left) an the istance (ight) fom the PMT to the aioactive souce. is the angle etween the PMT nomal iection an the vecto fom PMT position pointing to souce position. The pefomance of the optical moel with the optimize paametes is much ette than that with the ol paametes as figue inicates. Fig : Top: The value of oseve chage to expecte chage as a function of an istance fo the ol paametes; Bottom: The value of oseve chage to expecte chage as a function

4 of an istance fo the optimize paametes. 3. Pefomance of the Reconstuction The pefomance of the ML econstuction is stuie though neuton which is pouce y AmC aioactive souce, the souce scanne the etecto along vetical an aial iection. The enegy unifomity is significant fo neuton is also one pouction of IBD event Enegy econstuction The accuacy of the enegy econstuction is inicates y compaing the econstucte enegy an the tue enegy of neuton events. The econstucte enegy is etemine y fitting the enegy spectum with Doule Gaussian function as shown in figue 3. Fig.3.: Enegy istiution of the neuton events. Fig.4.: The non-unifomity of the enegy econstuction along vetical (left) an aial(ight) of the AD. Fom figue 4, we see the non-unifomity along vetical iection of the enegy econstuction is within 4%, an that long aial iection is within 1%. 3.. Vetex econstuction Bias of the vetex econstuction is efine as the mean value of vetical of aial iffeence etween the econstucte vetex an the tue vetex, while esolution of the vetex econstuction is efine as

5 the sigma of the vetex istiution. The ias of ML econstuction is within 0cm while the esolution is aout 5cm. The econstucte vetex stetches fathe fom the tue vetex along vetical iection as shown in the left sie of figue 5. The esolution is smalle as the event is fathe fom the cente of AD along aial iection as we see in the ight sie of figue 6. Fig.5.: Bias of the vetex econstuction along vetical an aial. Fig.6.: Resolution of the vetex econstuction along vetical an aial. Monte Calo stuy inicates the ispesion of the enegy eposition is aout 8cm fo neuton events. So the esolution of the ML econstuction is small enough. Bias long z iection might ecause of the eflective panel in the optical moel, an futhe stuy is neee to fix this phenomenon. 4. Conclusion With the caliation ata of Co 60, we optimize the key paametes of the optical moel of the ML econstuction of AD fo the Daya Bay expeiment. We can pecisely peict the chages collecte y the 19 PMTs with the caliate paametes. We pesent the unifomity of the enegy econstuction, an the ias an esolution of the vetex econstuction using neuton souce. The non-unifomity is within 4% along the etecto, an the ias an esolution is within 0cm an aout 5cm espectively. Refeences [1] An F P et al. (Daya Bay collaation), Phys.Rev.Lett,(01),108: [] Wen L J et al., Nucl.Inst.Meth.A, (011), 69: [3] Ding Y Y et al., Nucl.Inst.Meth.A, (008), 584: 38. [4] An F P et al. (Daya Bay collaation), Nucl.Inst.Meth.A, (01), 685, 78-97