Search for new Physics in rare B Decays

A search for the decay B+- to K+-K+-pi-+ was performed using data collected by the OPAL detector at LEP. These decays are strongly suppressed in the Standard Model but could occur with a higher branching ratio in supersymmetric models, especially in those with R-parity violating couplings. No evidence for a signal was observed and a 90% confidence level upper limit of 1.29x10^-4 was set for the branching ratio.

Enri co Ferm iInsti tute and D epartm ent ofPhysi cs,U ni versi ty ofC hi cago,C hi cago IL 60637, U SA 10 Fakul t at f ur Physi k,A l bert Ludw i gs U ni versi t at,D -79104 Frei burg,G erm any 11 Physi kal i sches Insti tut,U ni versi t at H ei del berg,D -69120 H ei del berg,G erm any 12   Typi calexcl usi ve processes ofb! ssd i ncl ude B ! K K 0 ;w hi ch are di cul t to separate from the standard pengui n process b! dss. A l though the i nterference ofthese two sources of the nalstate i s cruci ali n the study ofphenom ena such as C P vi ol ati on,thi s channeli s not sui tabl e for a di rect search for new physi cs. H owever the decay B ! K K + 1 , ei ther as a di rect three-body decay or through a K ? -l i ke resonance, i s a cl ear si gnature of thi s process. T hi s docum ent descri bes the rst search for the decay B ! K K + .

H adronic E vent Selection and Sim ulation
W e used data col l ected at LEP by the O PA L detector [ 11]between 1990 and 1995 runni ng at center-of-m ass energi es i n the vi ci ni ty ofthe Z 0 peak. H adroni c Z 0 decays were sel ected usi ng the num ber ofcharged tracks and the vi si bl e energy i n each event as i n R eference [ 12] . T hi s sel ecti on yi el ded 4. 41 m i l l i on hadroni c events. M onte C arl o events were used to determ i ne the sel ecti on e ci ency,for trai ni ng ofan artici alneuralnetwork (A N N ) used i n sel ecti ng the nalevent sam pl e (Secti on 3),and for the determ i nati on ofsom e ofthe system ati c uncertai nti es (Secti on 4). To determ i ne the sel ecti on e ci ency we generated 100000 M onte C arl o events ofthe process Z 0 ! bb w here one ofthe b quarks hadroni sed i nto a B m eson w hi ch subsequentl y decayed to K K + . O ne sam pl e was generated accordi ng to three-body decay phase space,w hi l e anothersam pl e wasgenerated w i th angul ardi stri buti on asexpected from a weak decay m atri x el em ent. In addi ti on,we generated sam pl es i n w hi ch the B m eson decayed vi a an i nterm edi ate K ? resonance. K ? (892),K ? (1680) and K ? (2045)resonanceswerechosen asthey al ldecay i nto K + and covertheenti respectrum ofK ? resonances.
For opti m i sati on ofthe sel ecti on ofevents and for som e ofthe studi es ofsystem ati c uncertai nti es,we generated 4 m i l l i on 5-avour hadroni c Z 0 decays (referred to as qq M onte C arl o). A l lthese sam pl eswere generated w i th the JET SET 7. 4 M onte C arl o program [ 13]w i th parameters tuned to the O PA L data [ 14] . T he heavy quark fragm entati on was param eteri sed by the fragm entati on functi on ofPeterson etal . [ 15] ,and al lsam pl es were processed w i th the O PA L detector si m ul ati on package [ 16] .

A nalysis P rocedure
In each event,charged tracks and el ectrom agneti c cl usters not associ ated to a charged track were com bi ned i nto jets,usi ng the JA D E al gori thm w i th the E0 recom bi nati on schem e [ 17] . W i thi n thi s al gori thm jets are de ned by y cut = 0: 04;w here y cut i s de ned i n R eference [ 17] .
T he pri m ary vertex ofthe event was reconstructed usi ng the charged tracks i n the event and the know l edge ofthe posi ti on and spread ofthe e + e col l i si on poi nt.
W e searched the hadroni c event sam pl e for the decay B ! K K + by com bi ni ng three charged tracksto form a B m eson candi date. A l lthree track com bi nati onswere consi dered. A l l trackswere requi red to have a m om entum ofatl east2 G eV=cand to be i n the sam e jet.T wo of the trackswere requi red to have the sam e charge and were assi gned the m assofa kaon.A thi rd track,w i th an opposi te charge,was assum ed to be the pi on. Tracks were requi red to sati sfy sel ecti on cri teri a based on the m easured rate ofenergy l oss due to i oni sati on (dE =dx) [ 18]as l i sted i n Tabl e 1. T hese dE =dx sel ecti on cri teri a are 44% e ci ent w hi l e rejecti ng 98. 5% ofthe background.
T he three tracks were tted to a com m on vertex and the decay l ength,the di stance from the e + e i nteracti on poi nt to the reconstructed secondary vertex,was cal cul ated. C andi dates w here the secondary vertex i s i n the hem i sphere opposi te to the candi date' s jet were rejected. T hi s cri teri on l eft 55% ofthe rem ai ni ng background events,but kept 96% ofthe si gnalevents.
Si nce the hadroni c data sam pl e consi sted m ostl y of non-bb events, we suppressed these eventsby m eansofa b-taggi ng al gori thm ,based on reconstructed di spl aced secondary verti ces. A n arti ci alneuralnetwork w i th i nputsbased on decay l ength si gni cance,vertex m ul ti pl i ci ty and i nvari antm assi nform ati on [ 19]wasused to sel ectverti cesw i th a hi gh probabi l i ty ofcom i ng from b hadron decays.Eventswereaccepted i fany ofthejetsweretagged by theneuralnetwork.
Sel ecti on Tabl e 1: Sum m ary ofdE =dx sel ecti on cri teri a: dE =dx (K ) i s the di erence between the m easured val ue ofthe i oni sati on energy l oss i n the jet cham ber and the expected val ue for (K ) and represents the expected standard devi ati on ofthe di stri buti on. N dE =dx i s the num ber of jet cham ber hi ts used for dE =dx. T he dE =dx cuts were chosen based on probabi l i ty val ues.
T he b-taggi ng sel ecti on was found to be 79% e ci ent, w hi l e rejecti ng 80% of the rem ai ni ng background.
T he nalsel ecti on wasbased on an arti ci alneuralnetwork desi gned to sel ectB ! K K + events w hi l e rejecti ng background events. W e used the JET N ET 3. 4 program [ 20]w i th a feedforward type net,trai ned w i th the back-propagati on al gori thm .T he neuralnetwork used seven i nputparam eters: the m om enta ofthe three tracks (p ,p K );the B candi date m om entum (p B ); the rati o of B candi date energy to the jet energy (X jet ); the decay l ength; and the vertex probabi l i ty, the probabi l i ty of the three tracks to ori gi nate from a com m on vertex w hi ch i s cal cul ated usi ng the track param eters. T he neuralnetwork retai ns 74% of the si gnalevents and rejects 97% ofbackground events w hen sel ecti ng candi dates w i th an A N N output above 0. 9. Fi gure 2 show s the di stri buti ons ofthe arti ci alneuralnetwork i nput param eters and the A N N outputforcandi datespassi ng the above cri teri a. W hi l e the data and the qq M onte C arl o show good agreem ent,one can cl earl y observe the di erences between these di stri buti ons and those ofthe si gnalM onte C arl o.
C andi dateswere accepted i fthei ri nvari antm ass wasi n the regi on:5: 10 G eV=c 2 < M K K < 5: 46 G eV=c 2 ;w hi ch corresponds to tw i ce the m ass resol uti on around the nom i nalB m ass. O nl y one candi date per jet was accepted,based on the l argest neuralnetwork output for candi datesi n a jet.Fi gure 3 (a)show sthe i nvari antm assdi stri buti on ofthe K K + candi dates. N o enhancem ent i s seen i n the si gnal regi on, w here 17 events were observed. M onte C arl o studi es i ndi cated that 88% ofthe background at thi s stage consi sts ofbb events.
Ifthe decay chai n B ! K K + i s assum ed to be di rect (i . e. ,w i thout an i nterm edi ate K ? resonance),then the m ass ofthe K + system can be expl oi ted to further reduce background w here the pi on and one ofthe kaons are from the decay ofa K ? resonance. T he m ass ofthe K + system was added as an i nput to the neural network, and the trai ni ng procedure of the A N N was repeated. Fi gure 3 (b) show s the i nvari ant m ass di stri buti on of the K K + candi datespassi ng the sel ecti on. H ere too,no enhancem enti sseen i n the si gnalregi on and the observed 14 events are used to determ i ne an upper l i m i t on the branchi ng rati o.

B ackground E stim ation
T he background to the process B ! K K + was esti m ated by tti ng a second-order pol ynom i alto the i nvari ant m ass ofa com bi natori albackground,obtai ned by rel easi ng the A N N cut,and then norm al i si ng the shape to the m ass si de-bands ofFi gure 3 (4{5 G eV=c 2 and 5. 6{ 6 G eV=c 2 ). M onte C arl o studi es i ndi cated that the background shape i s not al tered by thi s Fi gure 3:Invari antm assdi stri buti on ofthe K K + candi datesafteral lsel ecti on cri teri a were appl i ed a) vi a i nterm edi ate K ? resonance and b) w i th di rect producti on. T he dots represent the data,the sol i d l i ne show s the expected si gnalshape from M onte C arl o events after al lthe sel ecti on cri teri a were appl i ed w i th arbi trary norm al i sati on,and the dashed l i ne i sthe expected background. procedure. A l ternati vel y,we repeated thi s procedure by rel easi ng each ofthe sel ecti on cri teri a separatel y and by obtai ni ng the shape from M onte C arl o. A l lthe al ternati ve ts gave a consi stent resul t. W e al so took the num ber ofevents w i thi n the si gnalregi on i n each ofthe above cases and scal ed i t to the appropri ate sam pl e si ze. H ere too,al lesti m ates were consi stent. A swearesetti ng upperl i m i ts,theconservati ve approach i sto esti m ate thenum berofsi gnal events usi ng the l owest background esti m ate. W hi l e the tted background show n i n Fi gure 3 (a) gave 18. 8 events i n the si gnalregi on,the l owest esti m ate was 17. 5 events. T he respecti ve num bers for the di rect producti on case were 14. 8 and 14. 1 events.

System atic U ncertainties
System ati c uncertai nti es m ay ari se from the l i m i ted accuracy w i th w hi ch N B i s know n,from the uncertai nty i n the si m ul ati on used to determ i ne the e ci ency and from the background esti m ati on.

M odelling of dE =dx
To esti m ate the uncertai nty ari si ng from the m odel l i ng ofthe dE =dx sel ecti on cri teri a,we compared the e ci ency ofthe dE =dx cuts i n M onte C arl o si m ul ated events and i n data. W e took advantage ofthe abundance and rel ati ve ease ofreconstructi on ofD ?+ m esons,and expl oi ted them fortesti ng the system ati c uncertai nti es associ ated w i th the dE =dx sel ecti on cri teri a. W e searched forD ?+ m esons vi a thei r decay i nto a D 0 and a + ,w here the D 0 decays vi a a K + . To enhance the si gnalto background rati o we requi red the m om entum ofthe D ?+ candi date to be l arger than 15 G eV=c;the D ?+ decay vertex to be atl east 50 m away from the i nteracti on poi nt;and the hel i ci ty angl e, ,between the kaon m om entum i n the D rest fram e and the D di recti on i n the l aboratory fram e to sati sfy cos < 0: 7.Background esti m ati on,afterappl yi ng these sel ecti on cri teri a,wasdone asi n [ 23] . To avoi d possi bl e uncertai nty due to the di erence i n the m om entum spectrum ofthe D ?+ products w i th respect to the m om entum spectrum of tracksfrom the processB ! K K + ,we rewei ghted the dE =dx sel ecti on e ci ency asa functi on ofthe track m om enta. By appl yi ng the dE =dx cri teri a used to sel ectthe kaon we obtai ned an e ci ency of56. 2% i n data and 57. 0% i n M onte C arl o. T he respecti ve val ues for the pi on sel ecti on e ci ency are 75. 0% and 76. 8% . C om bi ni ng al lnum bers,the rel ati ve uncertai nty on the si gnale ci ency associ ated w i th the dE =dx cuts i s esti m ated at 3. 7% .
A rti cialneuralnetw ork uncertainty T he agreem enti sgood between thedata and theqq M onteC arl o,i n al lofthei nputvari abl esto the A N N (Fi gure 2). H owever,the M onte C arl o si m ul ati on com pared i n that gure represents the background and i s not used i n setti ng the upper l i m i t. T he si m ul ati on used to set the l i m i t i s that ofsi gnalevents and thus,si gnali nput vari abl es shoul d be com pared. T hi s i s not possi bl e for the decay B ! K K + . T herefore,once agai n we m ade use ofthe D ?+ si gnal . W e com pared the kaon and pi on m om entum di stri buti on,the D ?+ m om entum and fracti on of energy from the jet' senergy,the decay l ength and the vertex probabi l i ty. G ood agreem entwas achi eved between the data and M onte C arl o as show n i n Fi gure 4. Events were rewei ghted as a functi on ofthe track m om enta to re ect the si gnalspectrum as i n the dE =dx uncertai nty secti on,and the A N N outputwaseval uated. In orderto assi gn a system ati c uncertai nty to the e ci ency ofthe A N N ,we took the di erence between the fracti on ofD ?+ events passi ng the A N N cut i n the data to that i n the qq M onte C arl o. W e obtai ned an uncertai nty of4. 1% . In addi ti on,we took the di erence i n the A N N e ci ency obtai ned forthe si gnali nvol vi ng di erent K ? resonances. T hi s di erence was found to be 2. 1% and the overal luncertai nty assi gned for thi s source was 4. 6% B hadron lifetim e and decay m ultiplicity T he probabi l i ty to reconstruct the si gnal B m eson from al so depends on the e ci ency to reconstruct secondary verti ces i n both hem i spheres. T hi s i n turn i s sensi ti ve to the charged decay m ul ti pl i ci ty and l i feti m eoftheB hadrons.T heM onte C arl o wasrewei ghted to re ectthe m easured m ul ti pl i ci ti esand l i feti m es [ 22] .T he uncertai nty on these guresgave an uncertai nty of1. 1% and 1. 3% ,respecti vel y,on the sel ecti on e ci ency.

D etector m odelling
T he resol uti on ofthe tracki ng devi ces hasan e ecton the e ci ency. T he si m ul ated resol uti ons were vari ed by 10% rel ati ve to the val ues that opti m al l y descri be the data fol l ow i ng the studi es i n [ 24] . T he anal ysi s was repeated and the e ci ency esti m ati on was recal cul ated. T hi s source contri buted an uncertai nty of1. 2% .

Fragm entation m odelling
T he heavy-quark fragm entati on was si m ul ated usi ng the functi on ofPeterson etal . [ 15] . T he heavy-quark fragm entati on m odel param eter was vari ed to change the m ean scal ed energy of weakl y-decayi ng bottom hadrons w i thi n the experi m ental range: hx E i b = 0: 702 0: 008 [ 22] . T hi s change resul ted i n a 2% change i n the e ci ency. In addi ti on, the heavy-quark fragm entati on m odelwas changed to that suggested by C ol l i ns and Spi l l er [ 25]and to that ofK artvel i shvi l ietal . [ 26] ,w i th param eters tuned accordi ng to R eference [ 27] . N o si gni cant change i n the resul ti ng e ci ency was observed.

B ackground estim ation uncertainty
T he uncertai nty on the tted shape param eters and on the norm al i sati on gave an uncertai nty on the background esti m ate.T he di erenttechni quesused to esti m ate the background resul ted i n consi stentesti m atesw i th a sm al lstandard devi ati on (about1 event). H owever,si nce weused the l owest background esti m ate,these uncertai nti es were not taken i nto account as they were sm al l er than the di erence between the m ean background esti m ate and the one used.