c

Volume 70B, number 3

PHYSICS LETTERS

10 October 1977

A M P L I T U D E S A N D E X C H A N G E M E C H A N I S M S F O R K* R E S O N A N C E S PRODUCED

BY T H E R E A C T I O N S K-+p ~ K* ±p A T 10 G e V / c

R. BALDI, T. BOHRINGER, P.A. DORSAZ, V. HUNGERBOHLER, M.N. KIENZLE-FOCACCI, M. MARTIN, A. MERMOUD, C. NEF and P. SIEGRIST

University of Geneva, Switzerland A.D. MARTIN

University of Durham, Durham Oty, U.K. Received 25 July 1977 We compare production of the low mass Kn-resonances by K÷ and K- beams in the non-charge-exchange reactions K±p --+K°rr±p at 10 GeV/c. High statistics data, obtained with the same apparatus, allow extraction of the K*(890) and K*(1420) production amplitudes corresponding to unnatural and natural parity exchange in the t-channel. The NPE-part dominates in both charge states. Its t-dependence shows a strong crossover at t ~- -0.3 (GeV/c) 2 for the K*(1420). For the K*(890) the crossover is weaker but it occurs at the same value of t. This behaviour can be explained by pomeron, f and to Regge exchange contributions to the NPE amplitude. The UPE amplitudes agree, both in normalisation and t-dependence, with the expectations of 7r and B exchange as isolated from data for the charge exchange reaction K-p --, (K-~r+)n. We determine the amplitudes for production of the K*(890) and K*(1420) in the non-charge-exchange reaction K±p --~ Ks07r±p at I0 GeV/c incident momentum. Previous amplitude analyses of the Kzr-system have been limited to K*-production in charge-exchange reactions. These reactions are dominated, at small values of momentum-transfer I tl, by ~r-B exchange, with a contribution from p-A 2 exchange, becoming increasingly important at larger t-values [ 1]. Th~ non-charge-exchange-reactions are complementary from the point of view of production mechanism: They are dominated by natural-parity, isoscalar, exchanges [2], and they provide therefore an interesting possibility for studying pomeron-exchange, in addition to w-f Regge exchanges. In this paper, we extract the amplitudes corresponding to natural and unnatural-parity-exchange in the t-channel frame, from the moments of the Kndecay angular distribution. We study, in particular, crossover effects in the NPE-amplitudes, by comparing the K + and K - induced reactions. Moments o f the Kn-decay angular distribution. The data have been taken with the two-arm spectrometer of the University of Geneva, at the CERN PS. The apparatus, data reconstruction and selection procedures, and the method of acceptance correction, are described

in detail elsewhere [3]. We calculate the acceptance corrected spherical harmonics moments of the angular distribution of the K 0 in the t-channel helicity frame. Fig. 1 shows the unnormalised moments (Re yjM) da/dt as function of t in the mass region of the K*(890) (0.84
K*(890} and K*(1420} amplitudes and amplitude bounds. To extract the Kp ~ (Krr)p amplitudes from the experimental moments it is convenient to use combinations of helicity amplitudes with definite asymptotic exchange naturality. We use L 0, L± to describe spin L KTr production, where L 0 describes helicity-zero production and, to leading order in the energy, L_+ - (Lx= 1 + Lx=_I)/X/-2 describe helicityone production by NPE and UPE respectively. In the K*(890) region an inspection of the moments shows that S and P waves suffice to describe the K~r system and that the NPE amplitude, P+, is dominant. The J = 3,4 moments show that the D wave is small. In our analysis we use only the J = 0, 2 moments in which no interference with D+ occurs, and which only contain small second order contributions, such as 377

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Yy) da/dt in the mass region of the K*(890)

and K*(1420) as a function of t. T h e normalisation is such

Volume 70B, number 3

PHYSICS LETTERS

Re(SD~). We therefore neglect the D wave. We note that the D wave cannot be neglected in {Y~I) since it contains a contribution Re(P+D~.) comparable to Re(SP~). Following ref. [1] we normalize the amplitudes so that

10 October 1977 i

IP°I

i

i

K"(890)

ID.i

I{*(1420}

J~

2

~ M ,02 -~-= do (sin28p> ([P012 + IP+[ 2 + IP 12)+ [SI 2 (1) where (sin28p) indicates an average over the Kn mass 1 interval &M. We assume that 8p, the I = ~ KTr phase shift is given by a K*(890) Brelt-Wigner form. The factor F / A M is included so that the normalization of ILi 2 does not depend on the size of the mass interval. In the case of the K*(1420) the significant amplitudes are D± and DO, together with S and P+. From the results in the K*(890) region we have anticipated that P+ is the P wave responsible for the P-D interference effects manifest in (y2), (y~3) and (Y~I). The {Y~) and (YI) moments are consistent with zero [3] indicating that P0 and P are indeed negligible. The moments with M = 3, 4 are also consistent with zero [3], indicating that K*(1420) production with t channel helicity-two is negligible. There is also no evidence for higher than D waves in the Krr mass region up to 1.5 GeV, as the higher order J > 4 moments are compatible with zero [3]. As before we normalize the amplitudes so that

p AM

p2L-~ =
+ IP+I 2 + IS] 2

(2)

wher} again we have included mass averaging to take account of the variation of the resonant amplitude across the mass interval. We list the explicit relations between these amplitudes and the experimentally non-zero moments in the Appendix. Even with the above simplifications there are more unknowns than independent observables; we need additional assumptions in order to solve for the amplitudes. Positivity constraints, however, impose bounds on the amplitude magnitudes and interference terms [4]. We use eqs. (A4) and (A5) to determine these bounds in the K*(890) and K*(1420) regions respectively, from the data for both the K + and K - reactions. In fig. 2 we show the results for the NPE amplitudes. These amplitudes are found to be dominant in all four reactions, except at the lowest t

°o

o'.,-t (GeV/c)t o'.,

0.8

%

0'.2 o'., o18 0.8 -t (s ev/c)=

Fig. 2. The bounds on the NPE amplitudes, obtained from applying the positivity constraints to the 10 GeV/c K-+p--+K%r-+p data, first in the K*(890) mass interval (0.84 < MKrr < 0.94 GeV) and, second, in the K*(1420) mass interval (1.34 < MKTr< 1.5 GeV). In the K*(890) region the positivity constraints were applied to the (Y~o),(y~,l,o) subset of observed moments, and in the K*(1420) region to the (Y~o),(Y~, (y42,I,o) subset of moments. The amplitudes are normalized as in eqs. (1) and (2) with i"(890) = 49.4 MeV and 1"(1420) = 108 MeV. values for K*(1420) production, where these bounds indicate that IDol ~ ID+I. We see that the positivity conditions constrain these dominant NPE amplitudes within narrow limits. The bounds on the UPE quantities show these amplitudes have the structure expected from rr and B exchange. For example, the coherence factors (~ cos O)popand (~ cos O)DoD - are bounded in the region of - 1 indicating that the helicity-zero and helicity-one UPE amplitudes are coherent. More important, the UPE amplitudes agree, in both normalization and t structure, with the rr and B exchange contribution as calculated from the CEX reaction K - p -+ (K-rr+)n. This will be demonstrated explicitly in the next section. Amplitude analysis. In order to solve for the amplitude components we need to make a simplifying assumption in the UPE sector. Motivated by the consistency of the amplitude bounds with the rr-B exchange model, we assume that helicity-zero and helicity-one tYPE amplitudes are coherent with a relative phase of 7r. That is (~ c o s 0 ) e o e - = (~ c o s O ) D o D _ = - 1

.

(3) 379

V o l u m e 70B, n u m b e r 3

PHYSICS L E T T E R S

K (8~lo) !

t

!

2

' " K~+{1420)

K•-(14201

t

t

!

2

)D. I

&

Kj -(890)

10 O c t o b e r 1977

t

P.

\ID*

It

1V P*

t D, t

taJ c~ i--

1

CD

~r0

o

02 0.4 06

0.2

0./*

I 0.8 '

o

'

,

,

We should add that since NPE is so dominant in these reactions, the NPE amplitudes are insensitive to the specific assumptions in the UPE sector. (i) K*(890) region. In principle, we could now solve eqs.. (A4) to find all the amplitude magnitudes. In practice, however, the determination of the small S wave from the data is unreliable. Therefore, we fix its magnitude with respect to IP01 to the value expected from n exchange, -

sin63 eias3I/~/3,

(4)

where 82I are the Klr phase shifts for spin L and isospin I. Note that the sin 6p1 factor of the P wave is already accounted for in eqs. (A4). We neglect 63, and we take 61 = 40 ° and 83 = - 1 5 ° [51. We then determine [P+[, [P0[ and ]P_[ by a least-squares fit to the moments. The results are shown in fig. 3. We see the dominance of NPE. The curves are the UPE amplitudes calculated from the CEX reaction, K - p -* K-Tr+n. Explicitly they are calculated from the 7r-B exchange parametrization of the 13 GeV/c data [1 ], multiplied by the isospin factor of ½. The difference in laboratory momentum, PL and mass interval, AM, 380

,

,

0

Itt' i

/

(~'sinBig°÷t 0 2! '{'01.2"$]$0,.&L(~si ],0,6nolel]*D.j,

= I s i n ~ 1 e i~'

,~L

0

Fig. 3. The 10 GeV/c K±p ~ K°n±p amplitudes in the K*(890) mass region (0.84 < MKTr< 0.94 GeV) normalized as in eq. (1). The curves represent the predictions for Po and P_ obtained from an analysis of 13 GeV/c K-p ~ K-~r+n data [1].

IsI/Ieol

,

li,,0.2 1,0.~ 0'8

4

.t

Fig. 4. The 10 GeV/c K+-p -* K°n+-p amplitudes in the K*(1420) mass region (1.34 < MK~r < 1.5 GeV) normalized as in eq. (2). The analysis was based on eqs. (A5-A7). The curves are the predictions for D o and D_ obtained from an analysis of 13 GeV/c K - p ~ K-~r+n data [1].

are accounted for by the normalization used in eq. (1). Our data agree well, both in normalization and t dependence, with these predictions. This justifies, a posteriori, our assumptions for UPE. Moreover it indicates that I = 0 UPE is small. (ii) K*(1420) region. In this case we use the data to solve eqs. ( A 5 - A 7 ) for the magnitudes of the five amplitudes (D+, P+; D 0, D_, S), the SD coherence for UPE, and the PD coherence for NPE. The results are shown in fig. 4. The SD coherence factor, ~SD sin 8 s of eq. (A6) is found to lie in the region 0.85 to 1. As for K*(890) production, the curves are calculated from the 7r-B exchange parametrization [1 ] of K*(1420) production in the 13 GeV/c CEX reaction. (sin28 D) was not included in ref. [1 ], but it is accounted for in

Volume 70B, number 3

PHYSICS LETTERS

the curves of fig. 4. Cross-over phenomena and exchange mechanisms. Comparison of K*+(1420) and K*-(1420) production by NPE shows a strikingly different t dependence: the K - induced reaction has a larger cross section at small t and a steeper slope than the K+ initiated reaction. The cross-over occurs at t c = -0.32 + 0.06 (GeV/c) 2. A similar, though less pronounced, behaviour occurs for the K+p ~ K*-+(890)p pair of reactions, with t c = -0.29 + 0.06 (GeV/c) 2. The error on t c includes a 10% uncertainty in the relative normalization between K + and K - data. The NPE amplitudes are dominated by t channel I = 0 exchanges, since the I = 1 (P-A2) exchanges are known from the analysis [ 1, 6] o f the CEX reaction data and found to be relatively small. Thus we conclude isoscalar exchanges (the pomeron, co and f) dominate the non-CEX processes, K-+p ~ K*-+p. Such exchanges are expected to couple dominantly to the single helicity flip amplitudes: the coupling to nucleons is predominantly non-flip, while the coupling at the meson vertdx is necessarily flip. The NPE amplitudes should therefore vanish as VrL-7', as observed. The difference of K - and K ÷ initiated resonance production indicates interference between exchanges with opposite C-parity. However, an exchange-degenerate paii of co, f trajectories gives equal differential cross section. The observed cross-over of the NPE cross sections can be explainedby a breaking of w, f exchange degeneracy, or by a pomeron contribution. Pomeron-exchange would also provide a natural explanation for the observation that the cross-over effect is stronger for the K*(1420) than for the K*(890). Indeed, if the pomeron were an SU(3) singlet, generalized C-parity would forbid it in K*(890) production, but allow it in K*(1420) production. A detailed study of these exchange mechanisms is in progress.

10 October 1977

we expand the moments in terms of amplitudes for Kn-production in the reaction Kp -+ (Krr)p. The expansion involves squares of amplitudes for production of a Kn-state with angular momentum L, ILl 2, and interference terms between states with different L, of the form Re (L'L*). A summation of nucleon spinflip and non-flip terms is implicit in all such amplitude products, i.e. ILl2 = ILfl 2 + ILnfl 2 and

(AI)

Re(L,L*)= Re(LfLf , , + L n, f L n,f )

since in this experiment we have no information on nucleon polarisation. The interference terms can be rewritten in the form [4] Re(L'L*) = IL'I'ILI "~L,L'cosckL, L

(A2)

where 0 ~< ~ ~< 1 is the degree of nucleon spin coherence, and ¢ is the relative phase between amplitudes L and L'. It can be decomposed into (A3)

¢L'L = 8L' -- 8L + OL'L

where OL,L is the production (Regge) phase, and 8L is the decay (Breit-Wigner) phase of the spin L amplitude. Note that we cannot determine ~ and ¢ separately, since only the product occurs in the equations. In the K*(890) region, we use the set of moments N(Y~o> = ISI 2 + (sin260) (IP+l 2 + Ie012 + IP_I 2) ,

N(Y~2) =~55 (sin28p) [IP012 - ½(Ie+l 2 + IP_I2)]

N(Y~) =~56- (sin28p)IPoI" IP_ I (~ c o s

O)Pop -

N ( y 2 ) =-1/11~ (sin28p)(Ip+12 - 11°-12) '

We gratefully acknowledge the hospitality of CERN, and we thank the Fonds National Suisse for support of this work. One of us (A.D.M.) thanks Peter Collins and Chris Michael 'for useful discussions and thanks the Science Research Council for support.

Appendix

,

(A4)

to solve for the amplitude magnitudes. The normalisation, N, is specified in eq. (1). The factor (sin28p) accounts for the variation of the resonant P-wave within the mass interval. We fix the P0 - P - coherence factor to the value predicted by n-exchange (~ cos O)pop- = - 1 . In the K*(1420)-region, the amplitude expansion reads:

Relation between moments and amplitudes. Here

381

Volume 70B, number 3

PHYSICS LETTERS

10 October 1977

N(Y~0) = [SI2 + IP÷l 2 + (sin25D) (ID+I 2 + [D012 + ID_12),

follows that

N(Y~I) = 2 q~[-5 iP+I'ID+I ~P÷D÷(sin6o cos~e+o÷) ,

~SD0 (sin (~Dcos ¢SDo)

N(Y~2) = 2 ISI • ID01 ~SOo ( sin 6D cos g)SDo) -- X/q-~ Ie+l 2 + (2/7) X/rff(sin260) liD012 + ½(ID+I 2 + ID_I2)],

N(Y I) = x/2"l S I" ID_I ~SD_(sin/i D cos ¢SD_) + (x/if-O/7)(sin28 D) ID01" ID_I'(~ cos O)DoD-

g ( Y 2) = ~

,

= --~SD_gsin ~D cos dPSD) ~

(A6)

(~SD sin 5S) (sin26D).

The seven even J moments, (yM), determine the five amplitude magnitudes and (~SD sin 5s). The three odd J moments determine the NPE coherence, ~p÷D+(sin 5D cos ~P÷D+)~ (sin25D) (~ sin where 0 =

IP+I 2 - ( x / ~ / 1 4 ) (sin25 D )

O)p+D+, (h7)

01+l)+ + 6p.

× (ID+I2 - ID_I2), N(Y~3) = - ~ I P + I "

ID+l ~P+D+(sin 5D cos ~PP+D+),

N(Y23) = --V~/-~IP+I" ID+I ~P.D÷(sin 5D cos OP÷O÷), N(Y~4) = (6/7)(sin25 D) lID012- ~(ID+I 2 + ID_I2)] ,

N(Y~) = (x/-60/7) (sin25 D) ID01" ID_I (~ cos 0)OoD- , N(Y~) = -(Vq-0/7) (sin2~ O ) (ID+I2 - IO_12)

(m5)

where the normalisation, N, is given by eq. (2). Again, motivated b y n , B exchange for the UPE sector, we assume D O and D are coherent with a relative phase of 7r, (~ cos O)DoD- = --1, and that OSDo = 0. Then it

382

References [1] P. Estabrooks et al., Phys. Letters 60B (1976) 473. [2] C. Michael, Nucl. Phys. B57 (1973) 292. [3] R. Baldi et al., Systematic study of KTr-production in the reaction K-+p~ K°sn-+p. Technique and measurements at 10 GeV/c, submitted to the EPS-Conference, Budapest (1977). [4] P. Estabrooks et al., Nucl. Phys. B106 (1976) 61. [5] P. Estabrooks et al., Study of KTr-scatteringusing the reactions K+-p~ K+-~r+nat 13 GeV/c, submitted to the SVIII Int. Conf. on High Energy Physics, Tbilisi (1976); SLAC-PUB-1886. [6] P. Estabrooks and A.D. Martin, Nucl. Phys. B102 (1976) 537.