Study of incoherent pair generation in the beam-beam interaction simulation program Guinea-Pig

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Study of incoherent pair generation in the beam-beam

interaction simulation program Guinea-Pig

Cécile Rimbault, P. Bambade, K. Mönig, D. Schulte

To cite this version:

September2005

Study of in oherent pair generation in the

beam-beam intera tion simulation

program Guinea-Pig C. Rimbault  , P. Bambade  , K. Monig y , D. S hulte z 

LAL, IN2P3-CNRS et Univ. de Paris-Sud, BP 34 91898 Orsay Cedex, Fran e

y

DESY, Zeuthen, Germany

z

CERN, Geneva, Switzerland

Abstra t

Thispaperdealswithtwotopi s: thegenerationofin oherentpairsintwo

beam-beam simulation programs, Guinea-Pig and CAIN,and the in uen e of the ILC

beam parameter hoi es on the ba kground in the mi ro-vertex dete tor (VD)

indu edbydire t hits. One of the pro esses involved in in oherent pair reation

(IPC) is equivalent to a four fermions intera tion and its ross se tion an be

al ulatedexa tlywithadedi adedgenerator,BDK.A omparisonofGuinea-Pig

and CAIN resultswith BDKallows to identifyand quantifythe un ertaintieson

IPCba kgroundpredi tionsandtoben hmarktheGuinea-Pig al ulation. Based

onthissimulationanddierentVDdesigns,theve urrentlysuggestedILCbeam

parametersetshave been omparedregardingIPCba kgroundindu edintheVD

by dire t IPChits. We emphasize that thehigh luminosity set, as it is urrently

dened, would onstrain both the hoi es of magneti eld and VD inner layer

Guinea-Pig 1

[1℄ and CAIN [2℄ are programs dedi ated to simulating the beam-beam

intera tion in high-energy e

+

e linear olliders su h as ILC

2

and CLIC

3

. Reliable and

eÆ ient omputingtoolsareimportanttopredi tthe luminosityandtostudy the

ba k-grounds from se ondary parti les produ ed in the ollisions, in order to optimize the

design of both the ma hine and dete tors. In the framework of the EuroTeV Design

Study 4

, a omplete study,ben hmarking and improvement of Guinea-Pigisunder way,

in ollaborationwith the team working on CAIN.

In this note, a study of the produ tion of se ondary e

+

e pairs reated through the

in oherent s attering of syn hrotron radiation indu ed in the beam-beam intera tion,

so alled beamstrahlung, is presented. An important obje tive is to probe the realism

of the predi tions for the smallfra tion of su h pairs whi h an rea h the mi ro-vertex

dete tor(VD).Forlargeenoughrates,theindu edba kgrounds ansigni antly onfuse

thepatternre ognitionforasso iatinghitsinthe VD,andhen eleadtoredu ed impa t

parameter resolution for the tra ks involved. The aims of the study are to identify and

assess:

 the intrinsi theory un ertainty in the predi tion; for this, the three physi al

pro- esseswhi h ontributetoe

+

e pairprodu tionareinvestigatedand omparedfor

the dierent settings available inGuinea-Pigand CAIN. An additionaldedi ated

four-fermionevent generator, BDK [3℄, based on a dierent theoreti al approa h,

has alsobeen used forone of the physi alpro esses,

 the hangesinratesrea hing theVDforthedierentILCbeamparametersets [4℄

proposedasalternativestothenominalreferen e, andforthemostrelevantdesign

parametersof the threedete tor on epts presently under study [5, 6,7℄.

2 In oherent Pair Creation Pro esses

Following the emission of beamstrahlung photons, e

+

e pairs are produ ed both by

oherent(CPC)andin oherentpair reation(IPC) pro esses. TheCPCpro ess onsists

oftheintera tion ofthebeamstrahlungphotonswiththe olle tiveele tromagneti eld

of the opposite beam, while the IPC pairs arise from the intera tion of both real or

virtual photons from ea h beam with individual parti les of the other beam. For ILC

runningenergies up to1 TeV inthe enter of mass, the oherent produ tion pro ess is

negligible ompared tothe in oherent one.

Three main physi alpro esses are responsible for IPC, refered to respe tively as

Breit-Wheeler(BW),Bethe-Heitler(BH)andLandau-Lifshitz(LL).Tworealphotonsintera t

inthe BWpro ess,arealandavirtualintheBHpro ess andtwovirtualonesintheLL

pro ess. The real photons are fromthe beamstrahlungandvirtual ones anbepi tured

asan o-shell photon loud a ompanyingea h high-energy beam ele tron orpositron.

1

Generator of Unwanted Intera tions for Numeri al Experiment Analysis-Program Interfa ed to

GEANT

2

fortheBWpro ess,anapproximationisusedforthepro essesinvolvingvirtualphotons,

alledthe EquivalentPhoton Approximation (EPA). This approximation treats virtual

photonsasreal onesby onvolutinganequivalent spe trumforthevirtualphotons with

the rossse tionforthereal-real ase. Thesephotonsaretreatedasbeingrealaslongas

theirvirtualityremainsbelowanupperlimit,abovewhi hthey are ignored. This upper

limit, Q

2

max

, is xed to the ele tron mass squared, m

2

e

, in CAIN whereas Guinea-Pig

oers the hoi e between m

2 e , m 2 e +p 2 ?

, the transverse mass squared of the nal state

ands=4,halfof theinvariantmass squared. The latest hoi e isre ommended andused

by default inGuinea-Pig. More details an be found in[1, 8℄.

Two important phenomena must betaken intoa ount in the produ tionof se ondary

pairs from the beam-beam intera tion: de e tions due to the ele tromagneti eld of

the opposite beam and the so- alled \beam-sizeee t".

 Ele tromagneti de e tions: Mostpairs areprodu edwithverysmallanglesalong

the beam axis. Half of them are emitted in the dire tion opposite to the beam

ofsame hargeand are onsequently defo usedwhile thosefollowingthe dire tion

of the beam of same harge are fo used. The resulting ee t is shown both in

gures 1 and 2. A lear a umulation at large transverse momenta an be seen.

Ele tromagneti de e tionshoweverdon'tae ttheenergyspe trumortheoverall

produ tion ross se tion. An additional ee t whi h arises from ele tromagneti

de e tionsis a suppression of virtual photonemissions atsmall angles.

 Suppressionfromnitebeamsize: Thevirtualityofthequasi-realphotonsinvolved

intwo of the IPC pro esses implies some spatial indetermina y. For the smallest

virtualphotontransverse momenta,thisquantumun ertaintyontheirlo alization

anex eedthe physi alsizesofthe tightlyfo used ollidingbeams. Asuppression

of the ross se tion for small transverse momentum virtual photons is expe ted

fromthis and onsequently a redu tion in pair produ tion rates [9℄.

2.1 Comparison of Guinea-Pig and CAIN

Input parameters and options

Table 1 gives the values of the beam parameters for several ILC design optimisations

under onsideration[4℄. TheAmeri anversionofthe olda eleratordesign(USSC)has

been used to ompare Guinea-Pigand CAIN. A ut of 5MeV isapplied on the energy

oftheprodu edIPC ele tronorpositron. The defaultsettingsofGuinea-PigandCAIN

are rstly used:

 the suppression ee t from the nite beam size is a tivatedin both programs.

 The virtual-photon suppression ee t due to the eld of the opposite beam is

turnedo.

 The maximum virtuality s ale allowed in pair produ tion pro esses is set to the

ele tron mass and tohalf the enter of mass energy ofthe s attering,respe tively

log(Pt) (GeV/c)

0

5000

10000

15000

-6

-4

-2

0

distribution of the pairs before (empty histogram) and after (solid

his-togram) ele tromagneti de e tions fromthe opposite beam.

GuineaPig - IPC Particles - E

>

5 MeV

θ

(rad)

Pt (GeV/c)

10

-3

10

-2

10

-1

10

-2

10

-1

1

GuineaPig - IPC Particles - E

>

5 MeV

θ

(rad)

Pt (GeV/c)

10

-3

10

-2

10

-1

10

-2

10

-1

1

versus  distributions for IPC parti les before (left-hand plot) and after

E m [GeV℄ 500 500 500 500 500 500 500 N [10 10 ℄ 2 2 2 1 2 2 2 Nb 2820 2820 2820 5640 2820 1330 2820  x [mm℄ 15.0 15.0 21.0 12.0 10.0 10.0 10.0  y [mm℄ 0.4 0.4 0.4 0.2 0.4 0.2 0.2  x [10 6 mrad℄ 10.0 9.6 10.0 10.0 12.0 10.0 10.0  y [10 6 mrad℄ 0.030 0.040 0.040 0.030 0.080 0.035 0.030  x [nm℄ 554 543 655 495 495 452 452  y [nm℄ 5.0 5.7 5.7 3.5 8.1 3.8 3.5  z [m℄ 300 300 300 150 500 200 150

Table 1:Beam parametersfor dierentILC design optimisations under onsideration.

Allthe resultsare given for one bun h rossing.

Qualitativelyspeaking, CAIN and Guinea-Piggivevery similarresults. Energy spe tra

are shown in gure 3 for BW, BH and LL pro esses, and show a very good agreement

between the two simulations. One notes that the mixed pro ess is largely dominant

whereas the real-real pro ess represents only a few per ent of the total produ tion.

Similar on lusionsholdforthe(P

t

;)spe traobtainedwithbothprograms(seegure4

and the plot on the left-handside of gure2).

The ross se tions

5

and the orresponding numbers of se ondary ele trons produ ed

per bun h rossing for ea h IPC pro ess are given in table 2 in the ase of the USSC

parameters. CAIN predi ts about 12% less parti les than Guinea-Pig. This omes

entirelyfrom the pro esses whi h involve virtual photons, espe iallythe virtual-virtual

one for whi h one nds a 20% dieren e.

2.2 Comparison with BDK for the Landau-Lifshitz pro ess

BDK is a Monte-Carlo event generator for four fermion pro esses in e

+

e intera tions

whi h is based on omplete al ulations with leading-order massive matrix elements

for all relevant ele troweak diagrams involved. The results for the e

+ e ! e + e e + e

pro ess obtained in Guinea-Pigand CAIN an be ompared with BDK as atest of the

Equivalent Photon Approximationused in the two beam-beam simulations.

To perform this test, one has to turn o the ross se tion suppression from the nite

beamsize,used bydefaultinGuinea-PigandCAINandlookatthedistributionsofpair

spa e variables before their de e tion. In BDK, in order to generate the same phase

spa e as in Guinea-Pig and CAIN, the square of the invariant mass of the produ ed

pairs is lowered down to 10

6 GeV

2

, orresponding to the threshold for ele tron-pair

produ tion.

5

For the two pro esses involving real photons, BW and BH, the quoted ross se tions should be

GuineaPig - IPC Particles - E

>

5 MeV

log(E) (GeV)

0

500

1000

1500

-2

-1

0

1

2

CAIN - IPC Particles - E

>

5 MeV

log(E) (GeV)

0

500

1000

1500

-2

-1

0

1

2

Figure3:Log-energyspe trafor thethreein oherentpair reationpro essesmodeledin

Guinea-Pig(left plot) and CAIN (right plot).

CAIN - IPC Particles - E

>

5 MeV

θ

(rad)

Pt (GeV/c)

10

-3

10

-2

10

-1

10

-2

10

-1

1

Figure4:Transverse momentum, Pt, versus polar angle, , for e



from IPC pro esses

Cross Se tion(mb)

All pro esses 58:0 50:7

Breit-Wheeler 1:05 1:04

Bethe-Heitler 37:7 34:5

Landau-Lifshitz 19:2 15:2

Totalnumberof ele trons and positronsperbun h rossing with L= 1.82 b

1

All pro esses 105500 92300

Breit-Wheeler 1900 1900

Bethe-Heitler 68600 62800

Landau-Lifshitz 35000 27700

Table 2:Number of parti les and (ee tive) ross se tions for ea h IPC pro ess in

Guinea-Pigand CAIN.

Thelog-energy,transversemomentumandpolarangledistributionsofthe IPCparti les

produ edthroughtheLandau-Lifshitzpro essareshowningures5and 6,respe tively.

Table 3 gives the ross se tions for the pairs produ ed through all pro esses, without

the suppression from the nite beam size. Comparing with the results in table 2, for

whi hthisee t wasin luded,one ansee thatthe redu tionindu edamountstoabout

40% and that it of ourse only is present for pro esses involving virtual photons. Both

Guinea-Pigand CAIN predi t Landau-Lifshitz ross se tions in broad agreement with

BDK, with Guinea-Pigbeing the losest.

 (mb) Guinea-Pig CAIN BDK

Allpro esses 101 89:5

-Breit-Wheeler 1:01 1:11

-Bethe-Heitler 66:3 61:7

-Landau-Lifshitz 33:9 26:7 31:8

Table 3:Cross se tionsfor in oherent pairprodu tionwithoutnite beam-size

suppres-sion ee ts inGuinea-Pig, CAIN and BDK

2.3 Event rates in the Mi ro-Vertex Dete tor

Asmallfra tionoftheele tronsandpositronsprodu edthroughIPCpro esses anrea h

the mi ro-vertex dete tor (VD). The orresponding rates are omputed for a dete tor

onsisting of ve ylindri al layers [5℄, L

i

, i = 1 5, with the following lengths, ` and

LL process

log(E) (GeV)

0

1000

2000

-2

-1

0

1

2

Figure5:Log-energy spe trum for the Landau-Lifshitz pro ess in Guinea-Pig (upper

line), CAIN (lowerthin line) and BDK (dashed line).

LL process

log(Pt) (GeV/c)

0

2000

4000

6000

-5

-4

-3

-2

-1

LL process

θ

(rad)

10

10

2

10

3

10

4

0

0.5

1

1.5

Figure6:Log-Pt (left plot) and polar angle (right plot) distributions for the

t 0

ellingin amagneti eld B rea hes the VD,the helixequation isused:

r(z)=r 0 p 2(1 os(z)); (z)= z r 0 tan 0 ; with r 0 [m℄=3:33Pt[GeV= ℄=B[T℄;

where r(z) is the distan e in meters to the beam axis at the abs issa z. The magneti

eld isset to4Tand the USSC parameters are stillused.

Figure7 highlightsthe region in the two-dimensional (P

t

;) distribution orresponding

topairs whi h an rea h the VD.The minimum transverse momentum and polarangle

involved is found to be Pt>5MeV and  >10

Æ .

This region is fortunately outside of the beam-beam de e tion indu ed a umulation

zone,for thebeamparameters onsidered. The orrespondingP

t

and are not a

onse-quen e of the ele tromagneti de e tions, but arise intrinsi ally in the IPC pro ess, as

shown ingure 8.

It is important to note that the ranges in P

t

and  shown in gure 7, orresponding

to pairs whi h an rea h the VD, depend both on the VD geometri al design (for )

and on the dete tor magneti eld (for P

t

). On the other hand, the exa t lo ation of

thebeam-beam de e tion indu ed a umulationzone dependsonthe hosenILC beam

parameters. These onsiderationswill bedeveloped further inse tion 3.

θ

(rad)

Pt (GeV/c)

10

-3

10

-2

10

-1

10

-2

10

-1

1

versus  for ele trons from IPC pro esses. The region

or-responding to parti les rea hing the VD ( ir les) is indi ated with the two

dashed lines for the dete tor ongurationdes ribed inthe text. A thi k

dot-ted linehighlightstheedgeofthe beam-beamde e tionindu eda umulation

GuineaPig - Particles reaching VD

θ

(rad)

Pt (GeV/c)

0.02

0.04

0.06

0.08

0

0.5

1

1.5

2

versus  forele trons fromIPC pro esses rea hing the VD,

beforeele tromagneti de e tions (triangles) and after( ir les).

 (b) Guinea-Pig CAIN BDK All pro esses 64:15:9 37:44:5 -60.5  6.0 36.5  4.5 -Breit-Wheeler 8:22:1 6:41:9 -10.3  2.4 7.0  2.0 -Bethe-Heitler 26:63:8 20:93:3 -20.5  3.3 16.6  3.0 -Landau-Lifshitz 29:34:0 10:22:3 -29.7  4.0 13.4  2.7 37:55:3

Table 4:Cross se tions for the pair ba kground rea hing the VD predi ted by

Guinea-Pig, CAIN and BDK, with (upper lines) and without (lower lines) the \beam

Guinea-Pigand CAIN, with (upper lines) and without (lower lines) the expe ted

sup-pression from the nite beam size. It an be seen that the beam size ee t has little

in uen eonthe ba kgroundratesintheVD(withinstatisti al u tuations). A tivating

the virtual-photonsuppression ee t due to the oppositebeam eld has alsobeen tried

(insteadof the beam size ee t, to avoid potentialdouble ounting) and leads to a VD

ba kground redu tion of the order of 10%.

There is at least a 40% dieren ebetween CAIN and Guinea-Pigfor the total number

of IPC parti les rea hing the VD. A omparison with BDK for the Landau-Lifshitz

pro ess indi atesthat CAIN seemsto underestimate the orrespondingrate by afa tor

3,whereas Guinea-Pigisin good agreement.

2.4 Origin of the dieren e between CAIN and Guinea-Pig

This dieren e between CAIN and Guinea-Pig an be tra ed to the dierent hoi es

made in the two programs for the maximum virtuality, Q

max

, used in the equivalent

photonspe trum(see se tion2). Table 5shows this: if Q

max

isset tom

e

inGuinea-Pig

instead of the default value, one obtains 

al l

= 32:0 b and 

LL

=9:7 b for the

ba k-ground rea hing the VD, whi h is indeed onsistent with the results from CAIN (see

tables2 and 4). Guinea-Pig  e + e (mb)  VD (b) All pro esses 51:8 32:04:3 Breit-Wheeler 1:09 5:71:8 Bethe-Heitler 35:2 16:53:1 Landau-Lifshitz 15:6 9:72:4

Table 5:Cross se tions for in oherent pair produ tion, 

e +

e

, and for the pair

ba k-ground rea hing the VD, 

VD

, predi ted by Guinea-Pig, with the \beam size

ee t" a tivatedand usingQ

max

=m

e

for themaximum virtualityinthe

equi-valentphoton spe truminstead of the default value.

In order to assess the importan e of utting events with photon virtualities beyond a

ertain value as part of the equivalent photon approximation, the virtuality spe trum

generatedinGuinea-Pig,usingthe defaultrunningoptionQ

2

max

=s=4andnobeamsize

ee t, was extra ted and ompared with that whi h an be re onstru ted from BDK

events using the followingequation:

Q 2 =(P i P s ) 2 'm 2 e (2 (E i =E s +E s =E i ) os) 2E i E s (1 os); with << 1; whereP i;s =(E i;s ;p~ i;s

)are thefour-momentaof thein identands attered ele tronsand

 the s attering angle. The omparison is shown in gure 9, where the position of the

ele tron mass is alsoindi ated.

A mu h better agreement between the spe tra in Guinea-Pig and BDK an be seen

with the Guinea-Pigdefault hoi e for the maximum photon virtuality ut, at half the

invariantmass of the pro ess, than whensetting it tom

e

LL process

log(Q)

0

500

1000

1500

-10

-5

0

Figure9:Comparison of Guinea-Pig and BDK (dashed thi k line) photon virtuality

spe tra. The verti al dashedline indi atesthe positionof the ele tron mass.

LL process

log(Q2) (GeV)

log(Q1) (GeV)

-10

-5

0

-10

-5

0

in BDK simulation. The highlighted points orrespond to

events with pair parti les rea hing the VD. The dashed lines indi ate the

stru ted from the BDK events. The highlighted squares orrespond to the events for

whi hapair parti lerea hes the VD.Thedashedlines orrespond totheele tron mass.

24% of the produ ed pairs arise through an intera tion where atleast one of the

quasi-real photons involved has a virtuality larger than m

e

. Removing these events redu es

the ross se tion by about 24 mb, whi h orresponds to the CAIN result (see table 3).

Moreover,only33%oftheVDba kground omesfromtwolowvirtualityphotons,whi h

orresponds toa ross se tion of 12b, again ina ordan e with CAIN (see table4).

BDKbeingagenuinematrixelement al ulation,itshouldgivethemorereliable

predi -tionatlargevirtuality. Onthe otherhand,the equivalentphotonapproximation should

bebest inthe quasi-reallimit. Sin e the twospe tra haveverysimilarshapesand sin e

theadditional rossse tion predi tedby BDK, as omparedwith the equivalent photon

approximation using a ut on photonvirtualites atm

e

, isin the large virtuality part of

the spe trum, it an be argued that the Guinea-Pigpredi tion, with the ut set at its

default value of half the invariant mass of the produ ed nal state, is the better one.

Howmu hthis predi tion anbetrustedishoweverlimitedby thefa tthat thisdefault

ut, although it seems a rather natural hoi e, is ad ho , while the matrix elements

usedinBDKare onlyleadingorder ones. Nonetheless,what doesseem learisthat the

ross se tion predi ted by the equivalent photon approximation with a ut on photon

virtualitiesatm

e

is too small.

3 Impa t of ILC beam parameter sets on pair

ba kground rates in the VD

Lookingatgure7,tworegionsareinterestingtohighlight: that orrespondingtoevents

whi h an rea hthe VD,represented by there tangle, andthe stripewheremostevents

a umulateafterbeing de e tedby the ele tromagneti eldofthe oppositebeam. The

edge of this stripeis represented by the thi k dashedline.

The a eptan e re tangle depends onthe hara teristi s of the VD (lengthand radius)

and on the magneti eld, B, while the a umulation stripe depends on the beam

pa-rameters (

x

, 

z

, N). One has to be sure that the hosen beam parameters and VD

designallowstheVDa eptan ere tangletostay learothe paira umulationstripe,

alledin the following\in ationary ase".

We have tested the ve oÆ ial sets of beam parameters: nominal, low Q, large Y, low

Pand high luminosity, for three values of the magneti eld, 3T [7℄, 4T [5℄ and 5T [6℄,

and fourdierent inner VDlayer radii,10mm, 15mm, 20mmand 25mm. Results using

the TESLA TDR onguration are also given for referen e and omparison, sin e it

orresponds toa ase whi hwas studiedindetailwith fullGEANT-based dete tor

sim-ulations. Guinea-Pigwas used with itsdefault settings aspreviously des ribed.

Table6givesthe rossse tionsforthe IPCparti lesrea hingthe VDforallthe studied

ases. The underlinednumbers orrespond toin ationary ases. For allsu h ases, the

smallestVD inner layer radii are probably ex luded.

In reasing the magneti eld by 1T for a given VD design (15 or 20 mm) suppresses

on average 38% of the onsidered ba kground. One an also noti e an approximate

1 1  (r 1 =20mm; B =3T)and (r 1 =15mm; B =4T),  (r 1 =15mm; B =3T)and (r 1

=10mm; B =5T)ex ept forin ationary ases.

Figure11showsthe (P

t

;)planeforIPCele tronsrea hingtheVDforr

1

=15mmand

B = 3;4;5 T and the evolution of the a umulation limit ompared to the ase with

nominal parameters (illustrated by the thi k line). One an see that the nominal and

low Q designs lead to the same results, both for the ross se tion and for the distan e

between theVDa eptan eandthe paira umulationregion. Thelarge Ydesignoers

thesafest distan e tothe a umulationregionwhile forthe low Pand highlum designs,

thea eptan e ofthe VD at3and 4T istoo lose tothe a umulationzone, not tosay

inside, as it is learly shown in the last pi ture of gure 11. For this last design, the

hoi e of B=3T is probablyex luded if aninnermost VDlayerof 15 mmis desired.

Finally, table 7 summarises the main results on erning the IPC and the ba kground

in the VD. The integrated luminosities, L, are extrapolated from the luminosities per

bun h rossing,L

b

,givenby Guinea-Pig. N

IPCe

=b isthenumberofparti lesgenerated

bytheIPCpro essesanditdependsbothontheluminosityperbun h rossing,L

b

,and

thebeamstrahlungradiation,quantiedintable7byN

,theaveragenumberofemitted

photons per beam parti le. One sees that the virtual-virtualpro ess is independant of

the hoi e of beam parameters. The last part of table 7 gives an estimation of the

number ofIPC ba kground parti lesrea hing the VDfor dierent inner layerradii and

magneti elds. Considering for example the TESLA VD design, i.e. r

1

= 15mm and

B = 4T, with the nominal, low Q and large Y beam parameter sets, ' 1:2 million/s

IPC parti les are estimated to rea h the VD, while for the low P and high luminosity

TESLA TDR Nominal r 1 =10mm 1320 1719 907 1067 16611 928 r 1 =15mm 857 495 304 888 596 395 r 1 =20mm 465 274 173 586 365 214 r 1 =25mm 344 193 112 425 234 163 Low Q Large Y r 1 =10mm 600 14314 9011 35118 18913 12911 r 1 =15mm 9011 559 317 13211 798 547 r 1 =20mm 539 317 205 798 517 325 r 1 =25mm 387 246 175 658 386 245

Low P HighLum

r 1 =10mm 3527 1731 410 4460 2807 1523 r 1 =15mm 1457 775 504 490 705 403 r 1 =20mm 775 464 293 674 353 243 r 1 =25mm 595 333 203 484 283 182

Table 6:Cross se tions inb forthe pair ba kground rea hing the VD perbun h

ross-ing for dierent beam parameters sets. The TESLA TDR ase is shown for

Tesla - r = 15mm

θ

(rad)

Pt (GeV/c)

10

-3

10

-2

10

-1

10

-2

10

-1

1

Nominal - r = 15mm

θ

(rad)

Pt (GeV/c)

10

-3

10

-2

10

-1

10

-2

10

-1

1

Low Q - r = 15mm

θ

(rad)

Pt (GeV/c)

10

-3

10

-2

10

-1

10

-2

10

-1

1

Large Y - r = 15mm

θ

(rad)

Pt (GeV/c)

10

-3

10

-2

10

-1

10

-2

10

-1

1

Low P - r = 15mm

θ

(rad)

Pt (GeV/c)

10

-3

10

-2

10

-1

10

-2

10

-1

1

High Lum - r = 15mm

θ

(rad)

Pt (GeV/c)

10

-3

10

-2

10

-1

10

-2

10

-1

1

Figure11:Pt versus  plane for the ba kground ele trons rea hing the VD for r

1 =

Luminosities L b [b 1 ℄ 1.92 1.46 0.71 1.14 2.84 3.44 L[nb 1 :s 1 ℄ 27.0 20.6 20.0 16.1 18.9 48.5 IPC parti les N 1.66 1.35 0.86 2.00 1.97 1.89 N IPCe =b 135200 96600 38100 96800 219000 258600  BW =b [mb℄ 1.5 1.3 0.5 2.5 1.5 1.3  BH =b [mb℄ 41 36 26 51 48 47  LL =b [mb℄ 29 29 28 31 28 27

IPC parti lesrea hing the VD

r 1 =15mm B =3T N IPCe =b 16313 12811 648 15012 41220 1700 N IPCe =train[10 3 ℄ 460 362 360 424 548 4753 r 1 =15mm B =4T N IPCe =b 9410 869 396 909 22015 24015 N IPCe =train[10 3 ℄ 265 243 220 254 291 679 r 1 =15mm B =5T N IPCe =b 588 578 225 628 14212 13812 N IPCe =train[10 3 ℄ 162 161 124 174 189 388 r 1 =20mm B =3T N IPCe =b 889 859 386 909 21915 23015 N IPCe =train[10 3 ℄ 249 239 212 254 291 650 r 1 =20mm B =4T N IPCe =b 527 537 225 587 13111 12011 N IPCe =train[10 3 ℄ 146 148 124 164 174 340 r 1 =20mm B =5T N IPCe =b 336 316 144 366 829 839 N IPCe =train[10 3 ℄ 92 86 80 103 110 233

Table 7:Guinea-Pigsimulationresultsofba kgroundprodu tionfordierentILCdesign

The goals of this study were on the one hand to evaluate the un ertainty in the

ba k-groundfrom in oherent pair reation rea hing the VD dire tly, predi ted by the

beam-beam intera tion simulation programs, Guinea-Pig and CAIN, and on the other hand

toevaluate the impa t of the hoi e of beam parameters on this ba kground.

Thein oherentpair reation ross se tionpredi ted inCAINis12%less thantheone in

Guinea-Pig. This omesfromthepro essesinvolvingvirtualphotons,Breit-Wheelerand

Landau-Lifshitzpro esses,and isexplainedby thedierent hoi es inthetwoprograms

forthe maximalvalue ofthe photonvirtuality (settothe ele tron massinCAIN and to

halfof the invariant mass of the produ ednal state inGuinea-Pig). These dieren es

are enhan ed for the fra tion of the events whi h produ e parti les rea hing the VD

dire tly, with CAIN predi ting a 40% lower rate than Guinea-Pig. A omparison with

an e

+

e ! 4f dedi ated generator, BDK, was made for the Landau-Lifshitz pro ess

andshowed averygoodagreementbetween itsresultsand thoseofGuinea-Pig. Forthe

VDba kground arising from this pro ess, CAIN predi ts a three times lower rate then

BDK. This dieren e omes indeed from the hoi e of virtuality limit sin e the three

simulationsleads toalmost exa tly the same results atlow virtualities.

ThesimilarityoftheGuinea-PigandBDKvirtualityspe trafound,addedtothealmost

equal rossse tionpredi tions,seemtojustify a hoi e ofvirtualitylimitlargerthanthe

ele tronmass,ashasbeen doneinGuinea-Pig. This givessome onden eintheresults

from that program, even if the parti ular value hosen does not have a rst prin iple

explanation and the BDK al ulation does not in lude any radiative orre tions.

Other potential un ertainties in the IPC rates predi ted may arise from the two

die-rent sour es of virtual photon suppression, whi h are modeled with ee tive methods

inGuinea-Pigand CAIN, be auseneither orresponds toafullywell-denedparameter

region where standard methods an be applied. However, for what on erns the

ba k-groundin the VD,these two ee ts donot produ e hanges in rates larger than about

10%, whi h issmallin the present ontext.

The design of the a elerator an on the other hand signi antly hange the rates of

dire t pair ba kgrounds in the VD, for a given magneti eld and inner layer radius.

Contrarytothenominal,lowQandlargeYbeamparametersets,whi hleavethe hoi es

of magneti eld and VD innermost layer radius rather open, the low P and high lum

designs would be more onstraining. For instan e, for the ase of the high lum design,

tohave similar ba kground rates as with the other designs, a magneti eld of 5T and

alarger inner layerradius would have tobeused.

A knowledgement

We would liketo thank Toshiaki Tau hi and Kaoru Yokoya forthe onstru tive

dis us-sions regarding the photonvirtualityquestion. This work issupported by the

Commis-sion of the European Communities under the 6

th

Framework Programme "Stru turing

[1℄ D. S hulte, Ph. D. Thesis,University of Hamburg 1996. TESLA-97-08.

[2℄ K.Yokoya, User's Manual of CAIN - Version 2.3, O t. 2001.

[3℄ F.A. Berends, P.H. Daverveldt and R. Kleiss, Comp.Phys.Common.40(1986)285.

[4℄ ILC Suggested Beam Parameters Range, feb. 2005, ILC WG1,

http://www-proje t.sla .stanford.edu/il /a eldev/beamparameters.html

[5℄ TESLA TDR, Mar h2001.

[6℄ http://www-sid.sla .stanford.edu/

[7℄ http://www-jl .kek.jp/

[8℄ K.Yokoya and P.Chen, KEK Preprint91-2, April 1991,pp. 1-38.