G.D.Aiekвeev, L.G. Тkachev

MONTE..CARLO SIMULATI6N

Об11ВАИНВННЬ11 ИНСТИТУТ

, RAB РНЬI Х исс1едовани1

дУби а

El3-84~40

FOR ТНЕ SHOWERS IN ТНЕ DELPHI (LEP)

HADRON CALORIМETER

1984

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INТRODUCTION

Тhе modern theory .and existent exper imental data about the electromagnetic and hadron shower formation i n calorimeters are descr ibed in the detailed recent r eviews 111• In this paper pro­perties of а hadron calorimeter with streamer tubes · as sensitive elements are considered, because а calorimeter of this type i s under construction for DELPHI 121.5 cm thick layers of an iron yoke of the superconductive solenoid creating а magnetic f ield of 1.2 tesla will Ье used in this calorimeter as an absorber. Plastic streamer tubes 131 with cathode read-out performing in the self-quenching streamer mode 141 will Ье used as а detector. In this mode no formation of additional streamers on an anode wire piece is possiЬle, if there already exists а streamer in this r egion. Тhis phenomenon is known as the dead zone effect, and was observed in studies of both the streamer tubes 131 and drift chamЬers 141 • The dead zome value estimated in s.treamer tubes Ьу different methods varies from 1. 7 to 4.5 mm 131• In­vestigation of the hadron calorimeter character i stics dependin~ ~n the dead zone value, taking 'into ' account the strength and direction of the magnetic field is the aim of the present paper.

In the presented calculation the TATINA/5/ package was uti­lized as the main tool for generating hadronic showers in the 23 modules that constitute the bulk of the calorimeter wi th 1-xl m 2 cross section. Each module includes 5 cm of iron absor­ber; 0.1 cm of plastic (the front tube wall); 1 cm of argon (the gas filling of the tubes with а cross section of lxl cm2); 0.35 cm of plastic (the back tube wall, the read-out pads and the wall of the. air pressure bag); and, at last, 0.65 cm of air.

The badron beam was assumed to consist of "+ mesons wi th energi es of 5, 10, 20 or 40 GeV, travel l ing along the Z-axi s. The sensitive planes of streamer tubes were -t aken to Ье paral­lel to the xy-plane, the tubes were directed along t he y - axis. Тhе results were obtained for а zero magnetic f ield , and for three homo geneous field. values: Hi= 10 kp,aus s , Ну = Hz = 0; Ну = 10 kG, Нх =Hz = 0 and Hz = 10 kG, Их = Ну = 0. · I n the zer o-order appr,9ximat ion the las t t wo ·s ituat ions correspond t o t he barrel part of t he hadron calori me t er DELPHI ( Н = 10 kG) , and to the end сар ( H:z: = 10 kG), re spec tively. У

Bef ore starting the discuss i on on the influence of the dead zone e ff ect on the hadr on cal or imeter response it is necessary to no te tha t t he details .2!.. !=he strearoer f ormation process in

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the streamer tubes still remain inclear. Therefore а simple mode l of this process was adopted as in paper161.For each coun­ter the effective projection of track segments onto the anode wire, i.e., the projections corresponding to the segments of the tracks (hits) within the counter volume, were determined for all the tracks traversing the counter. It was also as sumed that the energy deposition has no influence on the streamer formation. The number of streamers within each ~ounter is de­termined Ьу the number, sizes, and mutual disposition of the track projections on the anode wire. The distance between ad­jacent streamers for each track projections cannot Ье less than the dead zone length DZ, and so the total number of streamers in the counters is simply the total number of dead zones that can Ье packed into the full track projection length, taking into account its position on the wire. The size of the dead zone is determined Ьу several factors, such as the gas mixture in the tubes, the gas pressure, the high voltage on the anode wire, etc. Here the inte~val DZ was taken as а parameter vary­ing from 3 to 7 mm . А reasonaЬle value for the DZ interval is 3-4 тm1З1 •

RESULTS

In ТаЬlе 1 some parameters of showers are listed both for the hit mode and for the streamer one with DZ = 3 mm: Nev is the number of generated showers, Nыte/ ev (Nstr/ev ) is the ave­r age numЬer of hits (streamers) registered in the calorimeter per shower, ohits / Nhits · (ostr / N str ) represents а quantity that characterizes the energy resolution for the sampling under con­sideration.

ln Fig.l the ener·gy dependence of the calorimeter response for different magnetic fields is presented in units of hits. The energy dependence turns out to Ье linear. In the presence of а magnetic field all track lengths are extended. Тhis may Ье the reason for the obtained increase in the numЬer of hits, which amounts to about 25%. А clear dependence of the hit res­ponse on the orientation of the magnetic field is not evident.

ln Figs.2a-2b the energy dependence of the calorimeter res­ponse is shown to vary with the orientation of the homogeneous magnetic field vector, and with the dead zone interval DZ which was taken as а parameter. Th make comparison easier the energy dependence is also given in terms of the hit response. А more or less universal behaviour of the calorimeter response as

2

а function qf the dead zone interval can Ье seen:

N str/ ev(DZ'"' 3) :N str / ev (DZ"" 5) :N вtr/ ev (DZ"' 7) = 1.30: 1.15: 1.0 1 (1}

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Fig.2. The energy dependenae variation of the calori­meter response for different dead zone effective va­lues: (а) Ну= 10 kG; (Ь) Hz = 10 kG.

In the streamer mode the effect of saturation is evident as the energy increases, while such an effect is absent in the hit-mode. This saturation effect is .most pronounced in the presence of а longitudinal magnetic field, Hz = 10 .kG, which acts as а focusing system on charged particles in the shower; owing to this phenonienon the overlapping effect of track pro­jections i.s extremely essential and must Ье taken into account~

In Fig . З the energy dependence of the calorimeter response for different magnetic fields is presented; the dead 'zoцe in­terval is set equal to PZ = 3 mm. As . in the case of the hit response (Fig.1), the magnetic field must lead to an increase of the hadron calorimeter response. But, contrary to the num­ber of hits, the enhancement of the number of streamers varies with the magnetic field orientation. :r"he increase is the high­est when the field is transversal, Н ж = 10 kG, Н1 = Hz =О,. since it makes the shower par-ticles turn and move along the axis of the streamer tubes, which are directed along the У­axis, thus increasing the projection of all track segments on the anode wires and, consequently, the number of streamers. It seems appropriate here to note that the average momentum of charged particles born in the shower and pa,ssing through the tubes is not small (ТаЬlе 2). The curvature radius of most tracks is much greater than the transversal size of streamer tubes -. Because of this in the case of Ну= 10 kG', Нж =Hz =О the increase in the numЬer:- of streamers is connected with the increase in the numЬer of tubes being crossed Ьу tra~ks when the magnetic field is directed along the tubes a~d comparaЬle with the effect in the hit mode. Тhе increase of the numЬer

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Fig.3. The calorimeteP responэe in the streamer mode (DZ = 3 mm) versus the energyJ value and direction of the magnitude fie~. ·

200

100

ТаЫе 2

The average momentum of charged particles in а .hadron shOыer (20% accuracy)

1!,kG н! о ~-10 ~-10 Н а10 10

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Pr .~v/c 1920 1440 1820 1510 1690 1540 1850 1510

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of streamers is the smallest in the longitudinal fiel~ Hz = = 10· kG, Нж =Ну =О, owing to the focusing action of such field ;

It is interesting, as one passes from the hit mode to the streamer mode, to compare such shower characteristics as the -transversal and longitudinal sizes of s1юw.ers. In Figs.4 and 5 examples are. presented of the energy .dependences in the field Ну = 10 kG of the values r and z which represent the ayerage­transversal and longitudinal sizes of showers respectively. An excess of about 20% is clearly visiЬle in the transversal size of the shower measured in the streamer mode over the size corresponding to the hit one. This is connected with а decrease of the relative contribution of the region i-n . the vicinity of the shower axis due to enhanced · overlapping of the tracks. No such difference can Ье seen in the z behaviour under the same condition. Similar dependences were observed for these values in the cases Н и о and 1 Hl · = 10 kG with other orien­tation. Dependence of parameters r and z on streng.th and di­rection of - the magnetic field in the streamer mode is shown in Figs46,7. As one should expect the largest transversal sho­wer size is obtained in transversal magnetic fields, and the

5

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Fig . 4. The average transversa Z size of the shoыer versus the energy at different r egistra­tion modes .

f,cm STRE AMERS, DZ •Зmm

10.0

!1.0 t t 8.D 1

7.0 • •- Н • О

•- kx•'ЮkG 15.0 • •- Hy•10kG

о- н1~10kG 5.0

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Fi g .5. The average Zongitudi­naZ si ze of t he shoыer versus t he _ener gy at different r e­gis t ration modes.

STREAMERS, OZ =Зmm Z, SдМPlES

10.0 • 9.0 • 1

8.0 t t •- Н • О

7.0 t • - Hx=101<G • - Hy • 1> kG

6.0 o-Hz =10kG

5.0

--'-11 20 E •• GeV <О

Fig . ?. The average Zongitu­dina Z size of the / hadron sho­ыer versus the ener gy at di fferent va Zues and direc­tions of the magneti c fieZd.

Fig. B. The energy resoZution of the hadron caZorimet er at di fferent r egistration modes.

smal lest one is obtained i n tЪе case of a · longitudinal fi~ld (focusing). No clear dependence on the magnetic field is obta i­ned f or the longi tudinal size of а shower.

In Fi g . 8 the energy dependence of the calorimeter resolution i s presented for the hit and streamer modes. As an example , t fie

6

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resul ts of simulation are given. for the case of Н= О , . but the same behaviour takes place for the energy reso l ution in t he pre­sence of а magnetic field . I n the streamer mode t he resolut i on becomes worse compared with hit mode. especially a t а l ow energy . This is due to · an additional ~;;ource of ·f luctuations connected with t he accidental character of the streamer formation on t rack segments. "

From t he existent theoretical concepts about hadron shower forma t ion in the sampling calorime ter the energA r esolution de­pendence is described Ьу t he following formula 1/

uE = [ ( 50% )2 + (R'Цt )2 ] у. ::::~% '

Е y' E (Gev) . . 3E(Gev) у'Е (2 )

here R' = 30-40%, t = х / Х 0 is t he thi ёkness of an iron l ayer in unit s of radiation l engths Х0 • Formul a (2 ) was 0btained assuming the s tatistical i ndependence of counts in d i fferen t l aye'r s of the calorime t er detector . The f i rs t term is connec t ed with fluc tuation of t he undetectaЬle par t of t he hadron energy and t he second one represents fl uc tuat ion of t he energy di ssi­pated in ioni za tions. Тhе energy r esolut i on curve accor di ng to (2 ) is pres ented i n Fi g . 8 . Correla tion of counts in di f ferent t ube l ayers dur ing t he shower forma t ion proces s axis ting in both modes (hit and s t reamer), a s wel l as coun t losses owing to track overlapp i ng (satura tion effec t in the ca lorime ter r esponse) l ead to noticeaЬl e devia tion from dependence (2), and this de­viation increases with energy.

CONCLUSION

The hadron calorime ter response and its other properties depend appreciaЬly on the mode (hit or streamer) of shower r e­gistration. In the st~eamer mode the significant dependence of shower parameters on the magnitude and orientation of .the mag­netic field vector is observed. Because of thi s it may .be ne­cessary to calibrate the prototype of the DELPHI hadron calori­meter in а magnetic f i eld. Description of the experimental data. obtained in this wa:y with simulation programs will give а possi­bility of better understanding the processes in the hadron calo­rimeter. This is necessary for adequate iнterpretation of infor­mation from а hadron calorimeter like DEL~HI.

ACКNOtVLEDGEМENТS

The authors would like to thank warmly Т. Baroncelli for the possibility of using TATINA program, G.V.Micelmacher and G.Pon-

7

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tecorvo for useful discussions and I.Farago f or the help in calculations.

REFERENCES

1. Amaldi U. Phys.Scr., 1981, 23, р.409; Iwata S. DPNU-3-79, 1979; FaЬian C.W. et al. NIM, 1977, 141, р.бl.

2. DELFHI, Technical Proposal. CERN/LEPS/83-3,17 Мау 1983. 3. Iarocci Е. NIМ, 1983, 217, р . 3о-. 4. Alekseev G.D. et al. Sov.Journ.of Part. and Nuclei, 1982,

13, р.293. 5. Baroncelli Т . TATINA Manual, CERN, Geneva, 1983. б . Arefiev А . et al. ITEP-150, Moscow, 1983.

(

Received Ьу PuЬlishing Department on SeptemЬer 18, 1984.

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Апехсеев r .д . , Ткачев Л . Г . Е I З-84-640 Модепированне nроцаесов • адрониом капориметре установки Д!ЛФИ (LEP)

Методом •юнте-Карпо модепируетс• обра:sование JtДерно­

зпектромагннтных пивней в адроином калориметре , состовщем нз

•епеза, nроспоенного nnocкocт.RNИ стримерных 'l'рубок. ПоказаJЮ,

что эффект мертвой зоны . пока.nизованной на аводиwх nравопоках в местах образования стрнмеров , СУi~'ествеино измеuет аепичкиу

сигнала с капориметра и $ффективныR nоnеречныА ра:sмер пива. .

Вариация сигнала в магнитных nonяx, соотаетс1'8уаurх qрокному

капориметру дЕЛФИ, достигает 20-30% , что nрмводкт к необхQАМ­мостн доnопнмтепьиой капибровкн кацориметра .

Работа выnопнеиа • Лаборатории ядерных nробnем оияи .

ПpenPiaC'I' 06ьеД1U18ИИоrо 101етаnтrа qepнwx исследовций . Jlубиа 1984

Alekaeev G,D. , Тkachev L.G. Мonte-carlo liaulation for tbe Sbovera in tbe DRLPКI (LEP) Нadron Caloriшeter

в t~s-.;в~ ..;;6lt0

МOQte-carlo siшulation for ahower foraation i1 perfo~d for а hadran caloriшeter conai•ting of iron layera vitb in­serted plastic atreaшer tubea . I t ia abovn tbat t~e dead zone effect locali•ed on anode vire• in the placea of atre ... r for88tion chanв•• esaentially Ьoth tbe calori .. ter relpoQae and the effective tranaver1al aiae of tbe ehover. Тhе reapon•• variation vitb the value and dir ection of tbe 111gnetic field coi'Papondlna to DILPIII had'&'on calori•t•r achiev•• 20%. wЫch cauaea tbe neceaaity of additional calo~i .. ter cali~'&'a­tion in the 118snetic field.

Тhе ~••tiaation Ьаа Ьееn performed at tba Laboratory of Nucleal' РrоЫ81118. Jtмa.

Pnprint of dut Joint Inatitute fol' Juclмl' •••eai'C!a. DuЪaa 198•