Schubert, K R

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NEU TRAL P ION PRODUCTION AT THE I SR Klaus R .  SCHUBERT At the CERN Intersect ing Storage Rings ( I SR) we have measured angu­l ar and energy d i s t r ibut ions  of s ing l e  pho tons produced in pro ton-proton co l l i s ions at IS =  30 to  53 GeV . The exper imental  technique us ing a � l ead glass  total  absorpt ion Cerenkov counter  and two large area tr igger counters  has been descr ibed i.n two papers by Neuhofer et a i . 1  • 2 ) . ln thi s r epor t we reproduce in F i g . 1 the s ummary o f  all data obta ined , and then we want to concentrate  on the conclus ions which  may be drawn for TIO product ion and on the compar i son with  the  data on TI± product ion obta ined by o ther group s .  F i gure 1 shows the invar i an t  d i f f eren t i a l  cross-sec tion FY Ey d 3 o1 / d 3 p1 as a funct ion of x = 2Ey cos  Oy/ IS for d i ff erent values o f  the transver se  momentum Pt = Ey sin Oy and for  three primary energies  Is . To obtain these c r o s s-sect ions , the  mea sured energy spec tra  at four  f ixed angles  have been  d ivided by the calculated  e f f i c i ency o f  the y teles cope , corrected for y conver s ion in the l SR vacuum tube , trans­formed into  the proper centre-of-ma s s  system and abso lut ely normalized . The r e  are two bas i ca l ly  d i f ferent normal izat ion procedur es for par­t i c le prod uct ion data a t  the I SR ;  therefore we want t o  d i scuss  aga i n  0 11r pruccdure i n  some d e  ta i 1 .  S ing le-arm te l escope s , r equir ing the pro­d uc t  i P n  of  one par t i c le c and no o ther information on the event , measure dNc /dpd l l  = L diJ c /dpd�L Having mea sured the I SR lumino s ity  L, one can deduce p roduc t i on c ro s s - s e c t ions , independent of  the total  pp cro s s-sect ion . 305 The drawbacks of this method are contaminat ions due to beam-gas events and the precision l imitations given by the measurement of L (actual ly ±10%) .  The second procedure , adopted for our data , uses a "three-arm" set-up with one telescope in coincidence with two large area trigger counters about 3 m downstream from the interaction centre around each ISR beam tube . Thi s  method determines the ratio d (Ny•Hl •HZ) /dpd� Hl " HZ dNy/dpdn N .  . interact ion ( 1 ) where Hl · HZ are the coincidence counts from the two trigger counters  Hl and HZ with the correct time of  fl ight to  accept beam-beam events and to rej ect beam-gas events . If one subtracts the e lastic pp counts from Hl • HZ and if the remaining event s form a random sample of all in-elastic pp events , the ratio in Eq . ( 1 ) is equal to (day/dpdm /a .  , in el the product ion rate per inelastic interact ion . This ratio is independent of the knowledge of L and ainel " Do our detected Hl " HZ events form a random sample of all inelastic events? Using 3 ) a. 1 = (3Z ± Z ) mb and calculating L with an effective ine beam height4 ) heff = ( 6  ± 1 ) mm ,  we can estimate the observed fract ion R of detected events . With the trigger condi t ions in which most of the data have been taken , we f ind R = 0 . 54 ± 0 . 09 at IS = 30 GeV , R = 0 . 63 ± 0 . 11  at IS =  45  GeV and R = 0 . 66  ± 0 . 1 1 at IS = 53  GeV . Taking data with a fract ion R varying from 0 . 09 ± O . OZ to 0 . 79  ± 0 . 15 we find that the product ion rates and spectrum slopes are independent of R within ±5% . A further support for the randomness assumption is given by the ISR exper iment of Breidenbach et al . 5 ) , where the angular distribution of all  charged particles has been measured . The shapes of thi s angular d i str ibution , obtained with the "three-arm" method us ing our trigger counter s and obtained wi th the single-arm method , agree wi thin ±3% .  With these justificat ions we have quoted our results a s  Fy/ainel . The errors in Fig . 1 are the quadratic sum of the statist ical error s and the normalization errors due to our method which we have estimated to be ±10% . 306 The conjecture of limit ing distributions 6 • 7 ) predict s that Fy/CT . 1 1ne reaches an s-independent limit if s + 00• Within the experimental errors ,  our data in the range IS = 30 to 53 GeV are in agreement with this pre­diction , even at x = O .  The photon production data of Fidecaro et al . 8 ) , obtained with a simi lar technique at the CERN-PS ,  indicate that at IS = 6 .  8 GeV the limit of FY/a . 1 has not yet been reached . At small 1ne values of pt and x their data are below the limit (at x = 0 a factor of about 1 . 6 ) . For p > 0 . 1  GeV and x > 0 . 05 the scal ing prediction t seems to be already fulfil led at IS =  6 . 8  GeV . Thi s observation is  in agreement with the data on TI± production9 • 1 0 ) at the !SR . The solid lines in Fig .  1 represent the function 1 Fy (pt ,x) CTinel 1 . 48 1 r -Pt x ) -- - exp - ---GeV pt , 162  MeV 0 . 083 ' (2) which is a satisfactory and very useful interpolation formula for our data points . With the restriction Py > ffin/2 ,  it wil l  be used in this report to derive TIO spectra and a TI0 angular distribution . The main source of photon production is  TIO decay . The next source is probably the decay K� + Tio Tio + 4y ,  which is estimated*) to contribute 7% ; thus N (y) ::::< 2 . 14 N (TI0 ) .  A rigorous deduction of TI0  spectra from the measured y spectra has not yet been made . The amount of Monte Carlo calculation work necessary has led us to look for approximative ways to solve this ques t ion . A first-order approximation1 ) i s  given by the method of Sternheimer 1 1 ) ; wi th pTI = p and Py = k :  1 d dNY - 2 p dp dkdfJ (p k, 8) • ( 3 )  This  is  valid for p > >  mTI/2 . The second approximation , also already discussed by Sternheimer , is a strict relation in the case of isotropic TI0 production in the centre-of-mass system1 2 ) : *) The aS!lllmptions are : TI0 / (TI+ + TI-) = 0 . 5 ,  (K+ + K-) / (TI+ + TI-) =  0 . 1 ,  (Ko + Ko ) / (K+ + K-) = 1 ,  al l K� decay (the branching ratio into TIO TIO is 0 .  33) . 307 I k-m2 ; 1, k l 1T 1 d Nll ( p ) p d pd�2 dp m�J·, k - 4k ( 4 )  ( 4 I ) A c c o r d i n g  t o  E q .  ( 4 ) , a s p e c t r um o f  p h o t o n s  p ro d u c e d  b y  t h e  d ec ay o f  i so t r o p i c  n eu t r a l  p io n s  mu s t  h a v e  t he f o l l owing two p ro p e r t i e s : a )  ny = d Ny /dk has a maximum q t  k = mn / 2 ;  b )  t h e  s p e c t rum p a r t  w i t h  k < m n / 2  i s  r i go r ou s ly r e l a t ed t o  t h e  par t w i t h  k > m,r / 2 ,  ny ( k )  = ny ( m�/ 4k The a s s ump t i on o f  i so t r o p i c  11° p r o du c t i o n  i s  b e s t  f ul f i l l ed f o r  B ern = 9 0 ° , i . e .  x = O ;  t h e r e f o r e ,  w e  wan t t o  s ta r t  w i t h  s o m e  conc l u s i o n s  f o r  t h e s e  da t a . A c c o r d i n g  t o  Eq . ( 4 ) , t he y s p e c t r a  a t  f ixed ang l e  canno t b e  pur e l y  e x p o n e n t i a l . B e c a u s e  we f ound e xpone n t i a l  beha v i o r 1 ) f o r  k � 1 5 0  MeV , we have r e f i t t e d  t he 9 0 °  p ho t on s p e c t r a  und e r  t he a s s ump­t i on of i so t r o p i c  11 °  s p e c t r a  of "Co c c o n i  s h a pe " : d N  ( 90 ° )  1T d N  ( 9 0 ° )  _Y __ _ dkdD 2A exp P o dN ( 90 ° )  1T dD F i gu r e  2 s hows t he 9 0 ° p h o t o n  da t a  for IS A ' ( 5 )  2 A • ( S ' ) 5 2 . 7  GeV t o ge t h e r  w i t h  t h e  b e s t  two-par ame t e r  f i t  i n  A and p 0 • Tab l e  1 s h ows t h e  o b t a i n ed f i t  v a l u e s  f o r  a l l  IS i n c l u d i n g  t h o s e  f r o m  t h e  P S .  The e r r o r s  i n c l u d e  t h e  e s t ima t e d  sy s t ema t i c s  d u e  t o  norma l i za t i on a n d  ab s o l u t e  e n e r gy c a l i­b r a t i o n .  [The va l ue s  and e r r o r s  o b t a i ned a r e  i n  very good agre ement wi t h  t h e  r e s u l t s  of o u r  f i r s t  ana l y s i s 1 l . J T h e  a v e rage t rans v e r s e  moment um i s  ( p  ( ;r 0 ) )  = 2 p 0 , t h e  average y t ran s v e r s e  mome n t um app r o x ima-t t e l y  ( Pt (y )) '°"' /p � + ( m./ 2 ) ? .  308 I Table 1 Results of  the f i t s  for the 90° data -dcry I drl rs 2 A = Po (GeV) 0inel (MeV) 6. sa) 0 . 15 ± 0 . 02 152 ± 30 . 2 0 . 205 ± 0 . 021 162 ± 44. 7  I 0 . 2 13 + 0 . 021 156 ± I 5 2 . 7  I 0 . 209 ± 0 . 021  157 ± I __  .._____ - �  a) Ref erence 8 .  1 0  8 10 8 { p tTI ) (MeV) 304 ± 324 ± 3 12  ± 314 ± ·---20 12  20 12  . -�---I The obtained values of  [dcr (90°)/drl]/cr . 1 agree well with the data on y i.ne charged particles obtained at the ISR by Breidenbach et al . 5) and Barbi ellini et al . 1 3) . Thus Ny = Nall charged ± 15% in the x = 0 region . At forward angles  the as sumption of i sotropic TI 0 production i s  certainly not valid .  Nevertheless  we  pref er E q .  (4) to  Eq . ( 3 )  for est imating the TI O product ion rates, because i t  takes the " o  mas s into account . We have applied it with 8 = 8 to the interpolation TI y formula in Eq . (2) and mult iplied 3) the result s with crinel = 32 mb in order to get absolute TI O  cro s s-sections . They are shown in Fig. 3 for pt = 0 . 2  and 0 . 4  GeV , together wi th the medium angle TI+ data obtained by Ratner et al . 9 ) and the TI- data of Bertin et a1 . 1 0 ) . For the small pt value , N (n+) = N( TI-) = N(n °)  is well fulfilled . For the b igger p t value , where N(�+) > N('  ) , the ·rr 0 rates are more on the side o f  the negat ive piou s ,  The invariant differential cro ss-section E d 3 0  /d 3 p, a s  obtained 11 TI in the way described , may be integrated over all momenta for f ixed centre-of-mass  angle e cm to get an angular d i stribut ion doy/drl .  The result of this integrat ion is s hown in F i g .  4. Because of the good agreement between 2o(n °)  and o ( TI+) + cr ( TI ), we may integra te our resul ts  one s tep further and give an est imat ion 309 for the average charged multiplicity in proton·-proton collisions . As many authors  have shown: 1T �J doc s in e d6 " 0inel drl ( 6 )  We set  (n  ') = (n  ) = 2 (n1T o )  + 1 . 5 ,  where n1To contains the al-e all charwed ready mentioned K� + 1To1T decays and therefore takes into account K± production, and 1 . 5  i s  the average charge of the two leading baryons . The results are given in Table 2 and shown in Fig . 5 ,  together with directly obtained values for ( nc) in bubble chamber and cosmic-ray experiments .  Unfortunately, the estimated errors of ±15% are too big to be able to reach some definite conclus ions on the logarithmic or power law increase of ( Ile ) ·  Table 2 Deduced average charged multiplicities rs 30 . 2  GeV (nc) 9 . 3  ± 1 . 4 44 . 7 GeV 10 . 5  ± 1 . 6  52 . 10 . 9  �""l � Because of the present special interest in particle production at x = O, we sunnnarize in Fig .  6 all pertinent ISR results obtained so far . The experiments  of  Ref s .  5 and 1 3  do not determine momenta of the particles produced ; thus the only compa�able quantity is do/drl . The scaling conjecture of s-independent invariant cros s-sections leads to a constant do/drl : do (90°) drl ( 7 )  Also shown in F ig .  6 are the P S  results  on  y production8 ) and those on (TI± + K±) production obtained in the CERN 2 m bubble chamber by Muck 1 4 )  r- r et al .  at Plab = 12 GeV/c ,  v s  = 4 . 9  GeV and plab = 24 GeV/c ,  v s  = 6 . 9  Ge1 310 Our conclusions are the following : a) The y data agree well with the charged particle data . b) The one-arm measurement of Ref . 5 agrees well with the three-arm measurements 1 • 1 3 ) . c ) In contrast to data in the fragmentation region there i s  a pronounced increase of rate between PS energies and ! SR energies . d) A Mueller-Regge ansatz of the form do/d� = A + B s- l / 4 gives a good fit to all data , though B is negative and rather large compared to A .  I wish t o  thank K .  Winter and all my co l leagues i n  the CERN-Hamburg­Vienna Collaboration for their help in preparing this talk . 311  REFERENCES 1 )  G .  Neuhofer , F .  Niebergal l ,  J .  Penz ias , M. Regler , K . R . Schubert ,  P . E .  Schumacher , W .  Schmidt-Parzefall and K .  Winter , Phys . Let ter s }.!_ B ,  438  ( 197 1 ) . 2) G. Neuho fer , F .  Ni eberga ll ,  J .  Penz ias , M. Reg ler , W. Schmidt-Parzefall K . R .  Schubert ,  P . E .  Schumacher , M. Steuer and K .  Winter , Phys . Letter s 38 B ,  5 1  ( 19 72 ) . 3) G .  Barbiellini , M. Bozzo ,  P .  Darriulat , G .  Diambr ini-Pa lazzi , G .  de Zorz i ,  A. Fainberg ,  M. I .  Ferrero , M .  Ho lder , A .  McFarland , G .  Maderni , S .  Orito , J .  P ilcher , C .  Rubbia ,  A .  Santroni , G .  Sette, A. Stande , P. Strolin ar.d K .  Tittel , to be submit ted to Phys . Letters (April 1 97 2 ) . 4 )  Thanks are due to M. Bot t-Bodenhausen, C . J .  Fabj an , C .  Gruhn , L. S .  Peak and B .  Winstein , who shared the I SR interact ion region 4 with us , for this communicat ion .  5 )  M. Breidenbach , G .  Charpak , G .  Coignet , D .  Drij ard , G .  F i scher , G .  Fliigge , Ch . Gottfried , H .  Grote , A .  Minten , F .  Saul i ,  M. Szeptyc1 and E . G . H .  Wi lliams , Angular d i stribut ions of charged part icles between 30° and 90° produced in pp co l l is ions at ISR energ ies , submi tted to Phys .  Letters (March 1 9 72 )  .. 6 )  R . P .  Feynman , Phys . Rev . Letters � .  1 4 1 5  ( 1969 ) . 7 )  J .  Benecke , T . T .  Chou , C . N .  Yang and E .  Yen , Phys . Rev . �. 2 159 ( 1969 ) . 8) M. Fidecaro , G .  Finocchiaro , C .  Gatt i ,  G .  Giacomel l i , W . C .  Midde lkoop and T. Yamagata, Nuovo Cimento �. 7 3  ( 1962) . 9) L . G .  Ratner , R. J .  E l l i s ,  G .  Vannini , B . A .  Babcock , A . D .  Kr isch and J . B .  Roberts , Phys . Rev . Letters '}}__, 68 ( 19 7 1 ) . 10)  A .  Bertin ,  P .  Capi luppi , A .  Cr i stal l ini , M. D ' Ago st ino-Bruno , R . J .  E l li s ,  G .  Giacomell i ,  C .  Maroni , F .  Mercatal i ,  A .M .  Ros s i  and G .  Vannini , Phys . Letters � B ,  260 ( 1 9 7 2 ) . 1 1 )  R .M .  Sternheimer , Phys .  Rev . �. 277 ( 19 55 ) . 1 2 )  R. Hagedorn , Relat ivistic k i nema t i c s  (W. A .  Benj amin Inc . ,  New York and Ams t erdam, 1964 ) , chap ter 7-6 B .  13 )  G .  Barbiel l in i ,  B .  Bozzo , P .  D a r r i u l a t ,  G .  D i ambr i n i -P a l a z z i ,  G .  De Zorzi , M .  Holder , A .  McFar land , G .  Maderni , P .  Mery , 312 S. Drito , J .  P i lcher , C. Rubb i a ,  G. Se t t e ,  A. Staude ,  P S t ro l i n  and K. Ti ttel , Experimental observat ion o f  tile angular distribut i on of charged particles around 90° in the centre o f  ma s s  produced by proton-proton collisions at very high energi e s , submit ted to Phys . Let ters (February 1 97 2) . 14)  H .J .  Muck , M. Schachter , F .  Selonke ,  B .  Wes sels ,  V .  Blobe l ,  A .  Brandt , G .  Drews , H .  Fesefeldt , B .  Hel lwig ,  D .  Monkerneyer , P .  Soding , G .W .  Brandenburg ,  H .  Franz , P .  Freund , D . Luer s ,  W. Richter and W. Schrankel ,  report DESY 7 2 / 9  ( 1 9 72 ) ,  submitted to Phys . Letters . 31 1 3 1 4  10 3 0.3 0.1 o. r - - - - - - -0 0 1L _ _ _  ___[ . 0 0.05 • 52.7 GeV e 44.7 GeV . 30.2 GeV o 6.8 GeV I I I .-�  x 0.10 0.15 Fig. l The (normalized ) s ingle photon distribution function 2) as function of x = 2 k cos0 I fS' for vairious values of the transverse momentum k.J. = k s in0 and of the centre-of-mass energy fS'. The solid l ines represent the interpolation for­mula of eq . 2 . The dashed lines connect the data 8) at VS' • 6 . 8  GeV to guide the eye . 0. 1 0.0 1  - 1  -1 ny ( GeV sterad ) - 1 - - --�- 1 ,-ny = 0inel do-y d p d o  vs =  52.7 GeV r 0 0. 2 0.6 0.8 1 .0 p y (GeV J Fig. 2 The 90° single photon spectrum at VS =  5 2 . 7  GeV . The solid line represents the b e s t  two parameter f i t  of the photon spectrum originating from the decay of isotro­pically produced ·rr0 of a "Cocconi type" spectrum , eqs . 5 .  3 1 5  100 10 10 '3 1 6  • Bert in  e t  a l  TT -o Ratner et al TT + T h i s  ana l y s i s  TTo p = 0.2 GeV/c t P. = 0.4 GeV/ c t �������������__L__����������-0.1 0. 2 0. 3 1 3 E.i&J. The neu tral p ion d :l s t ribut ion func tion End o"'ir /rl P Tr  in the y;' range from 30 to 5 3  GeV fo·r t ransverse tnomenta of 0 . 2  and 0 . 4  GeV/c . To compare it with the T/ and TI- rlata o f  refs . 9 and 10 in the same '(s' range , 6 inel = 1 2  mharn has been as sumed . x 10 5 2 0.5 0. 2 0.1 00 _1 _ cr. I me dcru d O  30° • 30.2  GeV e 44 . 7  G eV • 52 . /  r:� ev Fip; . 4  The neu traJ p ion angular d i s t rihu t ions . The rl a t a  poi n t s  a t  90° a r e  the resu l t s  o f  the reanalysis  a s  gi ven i n  t ah l e  1 ;  the points a t  10° to 2 4 °  are the values o f  ref . 2 wi t h  rl <"'" (A) /d r-t = 1 / 2  d F/8) /0 ;_. The solid  l ine represents  the d i s tri huti on ob t a ined hv anplying eq . 4 '  to eq . 2 ,  integra ted over a l l  momen ta , a t  y--;; = 44 . 7  GeV . w ...... 00 20 I< n,harged > I t 1 T T T 10 f-f t I 1 tt 1 I ! � I 2 T ! � 1 5 �  e l  0 , • t • Bubble chamber data • 0 �irab e l le , Serpukhov t CJ Emu l s i o n 7  S erpukhov A Cosmic Ray data of Jones e t  al • Cosmic Ray emulsion data 2 f- • d to ,  von Lindern et al A Thi s  report 1 _L_..J.._t \fS :�aV1 ' • l,. ...._,.. .... .. ' � 3 5 10 20 50 1 0 0  Fig. 5 The deduced values for the average charged mul tiplicity in pp col l is ions , together with o lder results .  w ..... "" C' . 3 �  0 . 2 --0 . 1  .:__ 0 �. ' '"' i riE" -1'.:� a o  � ( e  = 90� ) C M  C M  , f 10  2 0 30 40 I 1 T I lt ... ... • M u e c k  e t  a l .  n-+K -o F i d e c a r o  et a l .  y • B re ide n ba c h  et a l .  a l l  c h . !:,. N e u h c f e r  et a l .  y & B a r b i e l l i n i  et a l .  a l l  c h .  5 0  VS (GeV )  Fig. 6 The summary of par tic.le production data [ lT +K ,  't and all charged ] at x = 0 .  The solid l ine represents -1 / 4 an A +  B s least square f i t  to the data . The resul t s  are A • 0 . 274 i C . 012 , B .. -0 . 37 7  ± 0 . 03 1 . 

Neutral pion production at the ISR

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