HYPERON POLARIZATION AT HIGH ENERGY : A TOOL TO INVESTIGATE THE STRONG INTERACTION

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HYPERON POLARIZATION AT HIGH ENERGY : A TOOL TO INVESTIGATE THE STRONG

INTERACTION

K. Heller

To cite this version:

K. Heller. HYPERON POLARIZATION AT HIGH ENERGY : A TOOL TO INVESTIGATE THE STRONG INTERACTION. Journal de Physique Colloques, 1990, 51 (C6), pp.C6-163-C6-173.

�10.1051/jphyscol:1990613�. �jpa-00230876�

COLLOQUE DE PHYSIQUE

Colloque C 6 , suppl6ment au n022, Tome 51, 15 novembre 1990

HYPERON POLARIZATION AT HIGH ENERGY : A TOOL TO INVESTIGATE THE STRONG INTERACTION

K. HELLER

School of Physics and Astronomy. University of Mimeapolis, Minnesota 55455, U.S.A.

Abstract

-

The polarization of hyperons produced in high energy inclusive interactions is one of the most universal properties of the strong interaction. Measurements of polarization yield regular behavior which may help unravel the mechanisms of particle production. A review of the current status of such measurements will highlight this behavior and indicate how it fits into the quark picture of strong interactions. This review will include the latest surprising results from Fermilab on spin effects in the production of 5- and Q- and anti- E- hyperons.

Common sense tells us that particles produced in high energy interactions are not polarized. Polarization is the result of the interference of at least two amplitudes which characterize the interaction

where f is the sum of all spin independent amplitude; and g is the sum of all spin dependent amplitudes. Clearly, f and g must have a simple phase relationship in order for there to be a significantly non-zero polarization. At energies below a few GeV, phase space limits the interaction to a few dominant amplitudes. Sizable polarizations result which are used to determine the dynamics of the interaction process. The study of polarization in this energy domain is the primary subject of this conference. At higher energies, one expects f and g to be comprised of many different amplitudes of approximately equal strength with a large number of different relative phases. A priori, one expects no polarization to result from a high energy interaction of several hundred GeV. Suppose, for example, a strange baryon (hyperon), such as a A particle, is made in a collision between two unpolarized high energy protons as illustrated in Figure 1. No attempt is made to determine the many other particles which also emerge from the collision. Any measurement of the polarization of this hyperon sums over all possible distributions of these other particles. This is called an inclusive measurement.

proton proton

hyperon

Fig 1

-

A high energy collision producing a hyperon.

Using a thermodynamic picture to describe the phase space for making the hyperon, there should be many possible amplitudes and thus no polarization is expected. However, more *an 15 years ago, our group at Fermilab discovered that A's which have a significant fraction of the incident proton momentum are produced with a large polarization /l/.

Since then many experimental groups have verified that result in an energy range from about 10 to 2000 GeV B. The polarization is in the direction perpendicular to the production plane (

G;,

x

Go&,

the only direction allowed if the strong interaction respects parity. Hyperon polarization is typically from 10% to 40% and seems to have a regular and simple behavior depending on the identity of the hyperon and its kinematics.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990613

C6-164 COLLOQUE DE PHYSIQUE

The existence of polarization makes hyperon production an ideal diagnostic tool with which to investigate the strong interaction. In the first place, a hyperon contains at least one strange valence quark which was not present in the initial target or projectile. Clearly new quarks were produced in the interaction. The valence quark content of the

"stable" hyperons and the corresponding anti-hyperons is given in the table below.

Hyperons Anti-Hyperons

110 U d s Z 0 u d s

2' U U S

C' d d s

'= 0 U S S

- - -

_{d s s}

Q- s s s

- ---

A0 --m u d s

g

⁰ u d s

-- -

F' ---

d d s

C O

W U S S

- ---

-

W d S s

The seven hyperons (and seven anti-hyperons) are made of only three different quarks which are all in the ground state of the quark configuration. They give us the opportunity to unravel the dynamics of quark production and

recombination. It is like having seven different cases of the three nucleon system instead of just mtium and 3 ~ e . The "stable" hyperons decay via the weak interaction and typically have lifetimes of about 10-10 seconds. This means that ultra-relativistic hyperons, produced with an energy of several hundred GeV, live long enough to travel meters through a spectrometer before decaying. Because the weak decay does not respect parity, the hyperon's decay distribution indicates its polarization. If a spin ID hyperon decays into a baryon and a meson such as

A0

-+

p

+

^{~ - 1}

the distribution of the direction of daughter baryon momenta with respect to the spin direction of the parent hyperon in the rest frame of the parent hyperon (Figure 2a),

-

dN - 1 + a P c o s 9 , d(cos 8)

can be used to determine the hyperon polarization, P. For each event identified as a hyperon decay, one need only transform into the hyperon rest frame and add that event to a histogram bin determined by the cosine of the angle between the spin direction and the daughter baryon momentum. The slope of that distribution is OP (Figure 2b)

.

Fig. 2a

-

Hyperon (A) rest frame defining 9, the angle between the daughter baryon momentum (proton, p) and the hyperon (A) spin, G.

Fig. 2b

-

A histogram of the daughter proton distribution as a function of cos9 for a perfect spectrometer acceptance.

The slope of the line is aP.

If one reverses the production angle, the direction of the normal to the production plane is reversed and so is the polarization. This gives a powerful tool for distinguishing a distribution caused by a polarization from that which is an artifact of apparatus acceptance. The slope of the distribution must change sign when the production angle changes sign. If the apparatus acceptance does not change as the production angle is reversed and equal amounts of positive and negative production angle data are taken, the effect of the apparatus acceptance cancels out and following ratio for each bin in cos 8 will yield the polarization.

N+(cos 0)

-

N-(cos 0)

= a P cos 0, N+(cos 0)

+

N-(cos 0)

where N+(cos 0) is the number of daughter baryons for a positive production angle in a given cos 0 bin. Of course, we use a much more sophisticated analysis scheme which corrects for the acceptance of the apparatus /3/ but the results always agree with this simple technique. For the spin 3/2 Q- , the vector polarization is transferred to the spin 112 daughter A in the decay $2 4 A K 141. The polarization of the daughter A can then be analyzed as outlined above.

The apparatus used for the detection of hyperons and the measurement of their polarization can be quite simple as shown in Figure 3.

Typical Experiment

side view

Neutral Hyperons

tracking

target

\ l

. . . ... . . . . . . . . . . . . . . .... . . .

.

^{. . . .} . . . . . . . . . . . . . .

1

^A

selection magnet

* 7 m M

Charged Hyperons

spectrometer

selection tracking

magnet P

chambers tracking chambers

Fig. 3

-

Two generic high energy hyperon spectrometers suitable for measuring the polarization of several hundred GeV hyperons. The selection magnet selects the charge, and in the case of charged hyperons, the momentum range of the hyperons. The tracking chambers deternine the bend of the charged particles through the spectrometer magnet, and thus their momentum. This bend is in the plane perpendicular to the one shown and therefore not visible in the figure. Typical distances between spectrometer elements are also given.

A hyperon polarization allowed by parity must be either into or out of the page at the target. This polarization can precess to a different direction depending on the magnetic field of the selection magnet and the magnetic moment of the hyperon. Typically, no particle identification is needed since the kinematic reconstruction of the daughter particles under all possible mass hypotheses is sufficient to identify the parent hyperon mass with negligible background.

Hyperons produced with a significant fraction of the momentum of the incident proton can be thought of as fragments of the initial proton with one, two, or three quarks produced in the interaction as s h ~ w n in Figure 4.

COLLOQUE DE PHYSIQUE

New Quarks Produced

m

- ^-

^m

-

p c + p - - - - + = p - =

U

U

:lJ=l ~ ~ ~ F l ,,

^U

" J = ^-

^S

l

d - s

Fig. 4

-

Schematic diagrams of valence quark production for hyperons considered as fragments of an incident proton.

J denotes the angular momentum the designated diquark.

If the quarks have no relative angular momentum in the ground state, the spin structure of the quarks in a baryon is given by constructing fermion wavefunctions which are symrnemc in spin and isospin (the color quantum number provides the antisymmetric form of the complete fermion wavefunction). Since spin and isospin have the same algebra, this can be achieved if the spin follows the isospin. Using this "naive quark model", one can identify the spin of diquarks within the baryon, indicated by J in Figure 4. The spin structure of the wavefunction each "stable"

barvon, B, is

d d s

U d S A

T

:

UT

&L - d d T

S S U 4'3-

The inclusive polarization of different hyperons produced by 400 GeV protons at a 5 rnilliradian production angle shows that the polarization of each is similar in magnitude and kinematic behavior. The most obvious qualitative feature of the data, shown in Figure 5, is that some hyperons are produced with negative polarization while others, the C's, are produced with positive polarization.

Fig. 5 - Inclusive polarization of different hyperons rroduced by 400 GeV protons at 5 rnrad as a function of hyperon momentum 0.3-

0.2 z 0 0.1-

!- Q

g

^{0 .}

4

0' ^-0.1

a

-

0.2

- 0.3 -0.4

-

^H p t N - H + X S + 4 0 0 GeV 2 - 5 rnrad

- A h 0 H'

H -

4 5 '

-

-

- * [ ! : 4 ? p $ f g

-

" l ' " " l ' l ' t '

i

60 100 140 180 2 2 0 260 300 M O M E N T U M in GeVlc

The different sign of polarization for different hyperons is in remarkable agreement with the predictions from the simple quark model outlined above. If we classify the production process by the sign of the hyperon polarization, as shown in Figure 6, it is apparent that the spin of the hyperon is in the same direction as the spin of strange quark for hyperons with negative polarization and is in the opposite direction for hyperons with positive polarization.

Hyperon Has

Negative Polarization Positive Polarization

-

d d

t

^d

U

S ,

J = l L

^U

U S U

3

^s-l

^J=17

Strange quark has Strange quark has negative polarization negative polarization

Fig. 6

-

Schematic diagrams of valence quark production for hyperons. The arrows represent the spin of the valence quarks and diquarks and the spin of the hyperon.

In other words, all of the inclusive hyperon polarization results are consistent with the hypothesis &at when a hyperon is a fragment of the incident proton, its strange quarks are always polarized in the negative (relative to the

perpendicular to the production plane) direction 151.

Both the relative signs of the hyperon polarization and the relative magnitudes of agree with a simple set of rules put forth by DeGrand and Miettinen /6/:

Use the valence quark picture and wavefunctions.

Quarks from the sea which must speed up to form the hyperon are negatively polarized.

Quarks from the projectile which must slow down to form the hyperon are positively polarized.

The strength of the quark polarization is the same whether the quark originates from the sea or the projectile.

A classical picture, in analogy to forces experienced by moving electric charges, is consistent with these rules. In this picture, the origin of the hyperon polarization is the process by which quarks are accelerated into the hyperon rest system by the wlor force. To be specific, consider that two of the quarks (diquark) which make up the hyperon were originally valence quarks of the proton. After the interaction, but before the quarks combine, that diquark is moving with a high velocity relative to the collision center of mass. The other valence quark of the hyperon comes from the sea and is essentially at rest relative to the center of mass. Both the quark and the diquark have a net color and they are attracted together by the color force to form the hyperon. If the quarks were static, the color field acting on each quark would be a color "electric" field. However, each quark is moving relative to the other quark. Because of the Lorentz transformation, the moving color "electric" field gives a color "magnetic" field in the rest frame of each quark. This

C6-168 COLLOQUE DE PHYSIQUE

color "magnetic" field is perpendicular to the production frame. In the quark rest frame, the quark sees a color

"electric" field and accelerates toward the diquark. It also sees a wlor "magnetic" field so that its magnetic moment aligns with it, polarizing the quark. Because the velocity of the diquark is opposite to the that of the quark, it sees an opposite color "magnetic" field and thus receives an opposite polarization. In this picture, the hyperon polarization comes from the soft combination process of the quarks and has nothing to do with the process of quark production in the interaction. There are, of course, other models which have the hyperon polarization arising from the quark production mechanism or the production together with the combination process h'/. The real test of all of these models is their ability to predict the simple kinematic behavior of hyperon polarization. So far none is satisfactory in that regard.

The behavior of the polarization is usually expressed in terms of three kinematic variables:

The energy of the interaction in the center of mass E* =-

6

2

The fraction of incident proton momentum can;ied by the hyperon in the initial direction of the proton (in the center of mass system)

The transverse momentum of the hyperon relative to the initial proton direction

= p sin Q,

If X is positive (negative) and greater in magnitude than about 0.2, the hyperon can be considered a fragment of the incident (target) proton.

Based primarily on A polarization data, which span the largest kinematic region of any of the hyperon measurements, the hyperon polarization is consistent with the kinematic behavior summarized below and illustrated in Figures 7, 8, and 9. A more complete summary and the references to the original experiments, can be found in reference /8/:

Energy independence between laboratory energies between about 10 and 2000 GeV.

A transverse momentum plateau. The polarization increzses linearly with ^{p ~ .} up to about 1 GeVIc.

Above 1 GeVlc, the polarization is constant.

The polarization increases linearly with X, Above

-

¹ GeVlc, it is independent of 6.

Fig. 7

-

Inclusive hyperon polarization magnitude as a function of collision energy for data with p

-

1 GeVIc and ^X

-

0.5. The dashed line is drawn to provide a reference.

E

Fig. 8

-

Polarization of A's produced by 400 GeV protons as a function of pr for fixed X for two different values of X

and a schematic consistent with all of the existing 400 GeV A data.

Fig. 9 - Polarization of h's produced by 400 GeV protons as a function of X for all pr > 1 GeV/c. Also shown is lower pr data (pr = 0.5 GeV/c ).

Not only should a model be able to account for the regular kinematic behavior of the hyperon polarization, it should also predict the polarization of anti-hyperons produced by protons. Of course, an anti-hyperon has no valence quarks in common with the incident proton. The anti-quarks presumedly come from the sea. To preserve parity in the strong interaction, the polarization of the anti-hyperon must be perpendicular to the production plane. However, if the anti-hyperon canies no information about the incident proton, the dynamics which produces a polarization has no obvious reference to determine the production plane. This symmetry argument, leads to the rule: If the hyperon has no valence quarks in common with the incident proton, the hyperon cannot be polarized. Anti-A data from proton

C6-170 COLLOQUE DE PHYSIQUE

production at Fennilab show no detectable polluization 191. In the figure below, the points are anti-h polarization measurements and the dashed line shows the A polarization for comparison.

0.10 r

Fig. 10

-

Polarization of anti

-

h's produced by 400 GeV protons as a function of pr. The dashed line represenls the polarization of h's produced by 400 GeV protons.

So far everything that we know about hyperon polarization gives a simple, consistent picture even if we don't understand the origin of that picture. Now I would like to report the results of the latest experiment of our group at Fermilab, the first measurement of the polarization of the Q- and the anti- 5 hyperons. Although one hyperon is made of quarks and the other of anti-quarks, neither has any valence quarks in common with the incident 800 GeV proton. The experiment was done by: J. Duryea, G. Guglielrno, K. Heller, K. Johnsl, and K. Thorne2 from Minnesota; K. B. ~ u k 3 , C. James, and R. Rameika from Fermilab; P. M. Ho, M. Longo, and ^{A. Nguyen} from Michigan; and H. T. Diehl, S. Teige, G. Thomson, and Y. Zou from Rutgers. The apparatus was similar to previous hyperon experiments and is shown in Figure 11. The reconstructed Cl- mass (Figure 12) demonstrates the

cleanliness of the data sample and resolution of the apparatus. The production angle was 2.5 mrad.

2 mm MWPC

/

2 m m MWPC4 2 m m MWPCr

Proton

vacuum

Mutllpllclly Counler

Momenlum

Annlyzlng

\

Fig. 11

-

Apparatus used in Fermilab E-756 to measure the polarization of

z-,

P, and anti- S- hyperons produced by 800 GeV protons at 2.5 mrad.

Now at University of Arizona 2 Now at Fennilab

3 Now at University of California, Berkeley

Fig. 12

-

A histogram of the Q- events as a function of the kinematic reconstruction of the pxK mass

.

The p~ has been constrained to give the A mass.

The results of the measurement, given in Figure 13 compared to the polarization measured at the same time, clearly show that the !Z polarization is consistent with zero. Since the Q- has no valence quarks in common with the incident proton, this is exactly the result expected. The S- polarization is consistent with that measured at 400 GeV.

-020 l

Z5D 300 1 5 C L O C 450 < D 3

MOMENTUM Ih' GEVIC

Fig. 13

-

Polarization of

E-

and Q- hyperons produced by 800 GeV protons at 2.5 mrad as a function of hyperon momentum. Note the suppressed zero on the momentum scale.

By simply reversing the magnetic field of the selection magnet and the spectrometer magnet, the same apparatus was used to measure the polarization of anti-S- hyperons which are positive particles. The reconstructed 2- and anti-=- mass (Figure 14) shows the consistency of the data sets.

COLLOQUE DE PHYSIQUE

Although one expects that the anti-=- will not be polarized, we were very surprised to find that its polarization is not zero but is, in fact, consistent with the E- polarization. The polarization of anti-S- compared to an equal size subsample of S- is shown in Figure 15 together with the polarization of the k

.

7000.

6000

MOMENTUM IN GEVlC

-

_F

z

4

4s:

.

; . _::

^sow

2: 4000

2 3 30W

B ]

'

Fig. 14

-

A histogram of the anti- Z events

'1 -

a m - - -

- -

- - - -

-

- 1

^{Fig. 15}

^-

Polarization of anti-=-, E-, and

Q- hyperons produced by 800 GeV

2

1

hyperon momentum Note the suppressed

X zero on the momentum scale.

C

E

^{4.10 0}

T

^l

i ^-

& m ?

l 1

protons at 2.5 mrad as a function of

4.36

compared to a histogram of a subsample of

- , -- ^-

0 X -

A

a-

020-

250 3 0 0 350 6 0 0 450 500

low the E- events as a function of the kinematic

o reconstruction of the

6

x+ a+ mass and the

1.29 1.30 1.31 1.32 1.33 1.34 1.35 (&V/=')

12000~ p sr n- mass respectively. The px ( px+)

10000-

- .

=soo0.

S

::

.

9 6OW:

- '

. _..

E 4000

W :

2000

0 C C

1.29 1.30 1.31 1.32 1.33 1.34 1.35

~ A C(CeVIZ)

has been constrained to give the A (X ) mass.

-- -

I

:

.

-

-

:

Combining all of the anti-=- data and comparing to an equal subsample of S- data, gives the following polarization results:

P( 2- ) =

-

0.10

+

^0.02

P(anti-S-) =

-

0.10 f 0.02

for production by 800 GeV protons at an angle of 2.5 rnilliradians with an average X = 0.4 and average ⁼ 0.77 GeVIc.

What does this unexpected anti-=- polarization mean? Maybe the non-valence part of the incident proton, the glue, is incorporated into the anti-E- hyperon and carries the directional information. If so, why isn't the anti-A polarized? It wasn't at 400 GeV but maybe it is at 800 GeV. But then why isn't the Q- polarized at 800 GeV?

Before this experiment, we were struggling to understand the beautiful consistency of hyperon polarization. Now that consistency has been destroyed. Within the framework of our models, we are left with a set of information which is seemingly in conflict. It is possible that the anti-=- experiment is wrong. We will try to repeat it during the 1991 part of the Fermilab fixed target run. It is also possible that something interesting happens between 400 and 800 GeV and the anti-A polarization should be measured at the higher energy. Perhaps hyperon polarization is not caused by a single mechanism but is very complex. The regularity we observe is only because we have been looking at a very narrow set of data. On the other hand, maybe more measurements will reveal how the new measurements fit into an even more elegant consistency. The polarizations of other anti-hyperons need to be measured.

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m,

2419 (1981)

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