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Study of T-odd asymmetry in backward elastic dp scattering as a method to identify the reaction mechanism
__ __ FB
s
ELSEVIER
24 August I995 PHYSICS
LETTERS
B
Physics Letters B 356 (1995) 434-438
Study of T-odd asymmetry in backward elastic dp scattering as a method to identify the reaction mechanism M.P. Rekalo a, I.M. Sitnik b a National Science Center - Kharkov Institute of Physics and Technology, 310108 Kharkov. Ukraine h Joint Institute for Nuclear Researches, 141980 Dubna, Russia
Received 28 April 1995; revised manuscript received 6 June 1995 Editor: G.F. Bertsch
Abstract Recent measurements of the polarization observables in the dp + pd reaction at Dubna and Saclay have shown that a consideration of this reaction in the framework of the one nucleon exchange mechanism is inadequate. The T-odd effects due
to the polarization of both colliding particles are considered. It is shown that the new polarization observable is especially sensitive to the mechanism of the reaction. The paper is inspired by the fact that a polarized proton target, which can provide a polarized deuteron beam, is now installed at the Dubna synchrophasotron. Such measurements are feasible also at COSY.
1. Introduction
A study of polarization effects in backward elastic dp scattering at the maximal available energy is a very effective method for obtaining information about the deuteron structure in the region of large internal momenta. This is done in the framework of the Impulse Approximation (IA), there is a one-to-one connection between the only kinematical parameter of the reaction, the total energy in the CM system, and the deuteron wave function (DWF) argument in momentum space, when the deuteron is implied as a two nucleon system. That is a serious advantage of this reaction (and of the deuteron electrodisintegration also) in comparison with ed elastic scattering, where observables are connected with the DWF argument through an integral. Usually this reaction is interpreted in the framework of the one nucleon exchange (ONE) mechanism. That is a particular case of the IA.
Up to now, apart from cross sections [ 11, only the analyzing power T2o , induced by the initial deuteron tensor polarization [2-41, and the polarization transfer coefficient from the deuteron to the proton (~0) [4], have been investigated. The obtained experimental data, as is shown in Ref. [4], are in principal contradictions with such a simplified mechanism as the ONE. But this discrepancy does not mean that the IA is not valid in principle. For instance, one can try to correct the situation by taking into account the multitude of NN*-configurations, arising in the deuteron in the framework of the quark count [ 51, that lead to additional IA diagrams, where the neutron is replaced by NX. To distinguish whether the observed effects are induced by the more complicated deuteron structure or a more complicated reaction mechanism, it is necessary to measure new polarization observables. In particu-
0370-2693/9.5/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0370-2693(95)00754-7
M.P. Rekalo. I.M. Sitnik/
Physics L&ten B 356 (1995) 434-438
lar. it would be important to find such polarization observables that are especially sensitive to details of the reaction mechanism. As will be shown below, these are experiments that deal with T-odd observables of this process. The investigation of T-odd effects is of great interest because in any kind of the IA they are equal to zero. Therefore, the detection of nonzero values of T-odd polarization characteristics will indicate the necessity of a radical revision of the mechanism of the reaction considered. We discuss here the simplest T-odd observable of backward elastic dp scattering, namely the analyzing power, induced by a specific choice of polarization axes of the interacting particles relative to each other and to the beam direction. In Section 2 we analyze polarization effects in general form, using the parametrization of the full d+p -+ p + d amplitude in terms of four independent complex scalar amplitudes. Such a formalism is not connected directly either with the deuteron model or the reaction mechanism. In Section 3, we discuss shortly feasible mechanisms that lead to nonzero T-odd effects. In Section 4, we consider briefly how to measure the discussed analyzing power.
2. Spin structure
of the d + p ----)p + d reaction
The process of elastic dp scattering at an arbitrary angle in the general case is defined by 12 independent complex amplitudes [6] and so, at least 23 polarization observables must be measured in the complete experiment. The problem of the complete experiment is much simpler in the case of forward (0 = 0”) and backward (0 = 180”) scattering, when the total helicity 01’ the interacting particles is conserved. In this case the spin structure of the full amplitude is defined by only four amplitudes (which are different for the two abovementioned kinematical conditions). There are some equivalent sets of amplitudes, suitable for the description of the discussed process. We use here the method of the so called scalar amplitudes g,(s), related with the helicity ones F~,,,+,+A,,A,, in the following way: Fo+-o+
=92(s),
F o+--*+- = -v%w,
435
F++,++ =a(~) +a(~), =gl(s) -g4(s)v
F-+++
(1)
where Ad ( AP) corresponds to the deuteron (proton) spin projection onto the beam direction (+ 1,0, - 1 for deuterons and Z!L~ for protons). It is easy to see from (1) that gr(s), g2(s) and g4(s) do not change the transversal (gt (s) and g4 (s) ) or longitudinal (g2( s) ) polarization of the initial deuteron, and gs (s) describes the transition between the transversally (longitudinally) polarized initial deuteron and longitudinally (transversally) polarized final one. In the latter case the proton spin must be reversed. In terms of scalar amplitudes the full amplitude F has the following form:
M = p&y,,
F=A+ia.B,
(2)
- (nU~)(nU;)l
A=gl(s)lU~U;
B=g3(s)[U1
x U;
+g4(s)n(nUl
x
-n(nUl
x
U;)l
q>,
where Ur ( UZ) is the spin vector of the initial (final) deuteron, XI (~2) is the two-component spinor of the initial (final) proton, u are the Pauli matrices, s is the Mandelstam variable (squared total energy), n is the unit vector along the beam direction. That is the most suitable formalism to analyze the problem of the complete experiment in backward dp scattering. We accept the following parametrization of the initial polarization states. These are p= ;(l
faP)
(3)
for protons, where P is the 3-vector of proton polarization, and lJiUT =
i(8ij
+
~iei,j~S[- Qi,j)
(4)
for deuterons, where the pseudovector S and the symmetrical tensor Qij characterize the vector and tensor deuteron polarization. We have Qij = Qji,
Qii = 0.
(5)
Here we consider the most simple polarization effects induced by the polarization of initial particles
436
M.P. Rekalo, I&f. Sitnik/
(analyzing powers). Substituting the relations into the following expression for cross sections:
g
= ;Ns~F(I
N= -!-
+uP)F+,
64~~s ’
Physics Letters B 356 (1995) 434-438
(2)
(6)
one obtains du
dR--
dd”
-
dR
transformation in the T-invariant theory. The important property of T-odd observables is their sensitivity to small phase diffferences of scalar amplitudes. Indeed, we have Im(gid)
[I + Al (Qi,jnini)
+Aj(Pn>(Sn)
+A4n.Q
PI,
MM sin(W) 11lgillgkl(~~)~
in difference with T-even observables, such combinations as
+ A2SP x
=
(7)
expressed
via
(W2
Wg&) = ldlgkIc0@#4N IgiIIgk((l - -+.
where the vector Q is defined as
Q; = Qijr1.jt and dcr(“)/dSL is the differential cross section when both the initial proton and deuteron are unpolarized. The cross section and the coefficients Al-A4 are related to the scalar amplitudes by the following expressions:
(9)
A2N-’
du”’ df2
(A2 + A3)N-‘~
3A4,$l--’!$?!
=Ret(gl
+g2-gd&lv = -Re[(gs
=2Im[(-gl
+g2
(10)
-g4)&1,
(11)
-g4)&1.
(12)
As is evident from (9)-( 12), all four sources of asymmetry of the first interaction are independent. The coefficient Al determines the effect induced by the tensor polarization of the initial deuteron, firstly considered in Ref. [ 71. The coefficients AZ, A3 determine the effects induced by the vector polarization of both the initial deuteron and proton. The latter source of polarization effects is considered in detail in Ref. [ 81. All abovementioned asymmetries are T-even. And finally, the collision of tensor polarized deuterons with polarized protons is characterized by the coefficient A.+ This asymmetry is T-odd. Not only the mentioned ones, but all T-odd observables are related with amplitudes via expressions like Im( gig; ) . The appearance of imaginary parts of bilinear combinations is the direct consequence of complex conjugation as the necessary attribute of a T-
3. The analyses of sources of the T-odd asymmetry The T-odd asymmetry for the total cross section of dp scattering characterizes the T-violation and must be small (so called “null’‘-test [ 91) , But in the case of elastic dp scattering the coefficient A4 can be large enough due to nonzero relative phases of different amplitudes. As far as the interaction constant remains real in any kind of the IA (relativistic or nonrelativistic), such complications of the deuteron model as increasing the number of arguments (up to 6 [ lo] ), taking into account such vertexes as d + NN* I.51 or the relativistic one d -+ pE [ 111, does not lead to complexity of amplitudes. Only additional ones to the IA mechanisms of the reaction can provide such a property of amplitudes. These are - excitation of the A-isobar and so on in the intermediate state; - excitation of three-nucleon resonances in the direct channel of pd collisions; - exchange by fermion Regge poles. The complexity of amplitudes is also the inevitable outcome of the unitarity conditions. Such effects as excitation of the A-isobar in the intermediate state are considered, for example, in Ref. [ 121. The amplitude, responsible for this subprocess, can be expressed through the parameters of the NN + NA interaction and some integral over the definite combinations of the S- and D-components of the DWF. It demonstrates quasiresonance behaviour in the of Td z 0.75 GeV region. The resulting behaviour of the full amplitude in this region depends essentially on the formfactors of NN?r- and NNP-vertexes. The physical reasons for the appearance of such objects as three-baryon resonances are different. It is
M.P. Rekalo, 1.M. Sitnik/ Physics Letters B 356 f 1995) 434-438
enough to mention the possibility of the existence of the ANN-resonance, if the anomalous AN interaction (different from one-pion exchange) exists. The appearance of 3-baryon resonances seems absolutely natural in different versions of quark bag model [ 13 1. The reaction d + p -+ p + d seems to be most suitable for studying this problem due to the following circumstances: - the smallness and relatively simple spin structure of the main background amplitude (one-nucleon exchange) ; - the sensitivity of the differential cross section energy dependence to the values of the spin and space parity of 3-baryon resonances. The most probable interval of 3-baryon resonance masses is 3-3.5 GeV/c. So, a primary beam with energy Td 5 1 GeV is needed to investigate this problem. At higher energies a possible source of complexity of scalar amplitudes is a fermion Regge poles [ 141 (FRP) exchange. In quark language it can be interpreted as a more general three quark exchange in the u-channel, than in the case of the ONE. Such an exchange is equivalent to a new effective d -+ NR vertex (R is a reggeon), which allows one to take into account in some sense the quark degrees of freedom in the deuteron. The most interesting peculiarity of FRP is “self-conjugation”. That means the existence of two complex-conjugate trajectories with a special kind of argument for each Regge poie, namely a( fi> and cy* ( J;;) , where u is the Mandelstam variable. At u < 0 a number of reasons lead to the complex contribution of FRP to the amplitudes. At u > 0 only one of them survives, namely, that connected with signature factors [ 151 1 *exp[i7rcr(--fi)]
i *exp[ircu(JEI)],
At B = 180’ u is always positive:
11 =
(m; - rn;>2 s ’
It changes its sign at an angle defined by the following condition: I fcos(O())
=
cm;-m;>*
or, approximately,
2rnipz
’
(13)
431
(14) where pd is the initial deuteron 3-momentum in the Lab system. The phenomenology of FRP was very effective for the description of the m + N + rr + N, r + N --t v + N, 7~+ N ---t p f N reactions [ 161. It is interesting to note that the asymptotic Regge regime in reactions with participation of the deuteron is achieved earlier in comparison with TN and yN reactions. For instance, the Regge picture y + d -+ n + p commenced at an anomalously small energy, namely, Ey > 400 MeV. We mention here that the contribution of single bosonic Regge poles does not lead to nonzero phases between different amplitudes.
4. How to measure the T-odd effect The vector product near the coefficient expressed as follows: 3 n.QxP=--QzzPYsin(2P), 4
A4 can be
(15)
where z is the axis of the initial deuteron tensor polarization, n lies in the xz-plane and p is an angle between n and the x-axis, cv is a projection of P onto the y-axis. As is easy to see from ( 15), this vector product is equal to zero until the angle between the deuteron polarization axis and the beam direction remains 90”, independently of the choice of the initial proton polarization axis. If we deal with a polarized deuteron beam and a polarized proton target (PPT), the vertical polarization axis of the extracted beam is assumed. If one rotates the deuteron spin with the help of a solenoid (90”)) then a spin rotation, respectively, a beam direction can be achieved due to the anomalous part of the particle magnetic moment while the beam is deflected by dipoles. The target polarization axis must be vertical in this case. The connection between the summary bending angle of a beam line (~0 ) and spin rotation, respectively the beam direction (in the current deuteron rest frame) is expressed by the simple formula
pm =
4ooY$ - l),
where y = E/m, g = 1.716.
(16)
438
M. P. Rekalo. I. M. Sihik / Physics Letters B 356 (I 99.5) 434-438
One can see that it is not possible to provide an optimal spin rotation in a wide energy region of the beam having a fixed beam line. Now the existing beam line upstream the PPT at Dubna [ 171 (with the summary beam bending angle in dipoles of 27”) provides values of sin( 2p) increasing from 0.25 up to 0.49 while one changes the primary beam momentum from 3 up to 7 GeV/c. The need for the largest energy magnetic field integral in a solenoid (about 40 Tm) is, maybe, not realistic. Nevertheless, performing the experiment in this case is also possible. For example, in the case of a fixed magnetic field integral of about 10 Tm (decreasing with energy spin rotation in a solenoid), sin( 2p) remains on the level of N 0.2 in the mentioned range of primary beam energies. In the latter case a thin alignment of the PPT polarization axis is necessary for each energy of the primary beam. Maybe, it is more convenient to investigate this problem using a polarized proton beam and a polarized deuteron target. Such an experiment is feasible at the zero degree facility of COSY [ 181. Keeping in mind that the primary beam polarization is vertical, in order to have sin(2P) = 1 one has to orient the deuteron target polarization axis in the horizontal plane at an angle of 45” to the beam direction.
5. Conclusion We demonstrated here the importance of the study of T-odd polarization effects in backward elastic dp scattering as an effective tool of the determination of the reaction mechanism. A nonzero T-odd asymmetry arises only in the case that the mechanisms additional to the Impulse Approximation are essential. Revealing a nonzero T-odd asymmetry will lead to a radical revision of the mechanism of this reaction. Only one from four possible asymmetries (for the first interaction) is T-odd. Such measurements are realistic.
Acknowledgements This work is supported in part by the Russian Foundation for Fundamental researches, grants No. 93-023961 and No. 95-02-05043.
The authors thank A.M. Baldin, F. Lehar, N.M. Piskunov for strong support of this activity. They are also grateful to J. Arvieux, V.V. Fimushkin, M.V. Kulikov, VP Ladygin, A.A. Lukhanin, A. de Lesquen and Yu.A. Plis for fruitful discussion.
References I I ] I? Berthet et al., J. Phys. G: Nucl.Phys.
8 ( 1982) LI
11.
[2 ( J. Arvieux et al.. Nucl. Phys. A431 ( 1984) 6132. 131 L.S. Azhgirey et al., “Measurements of Tzti in Backward Elastic dp Scattering at Deuteron Momenta 3.5-6 GeV/c”, in: Abstracts of 14.th Int. IUPAP Conf. on Few Body Problems in Physics, Williamsburg, USA, May 26-3 I, 1994. pp. 22-25. [4) V. Punjabi et al., Phys. Lett. B350 (1995) 178. L.Ya. Glozman, V.G. Neudatchin and I.T. Obukhovsky. Phys. Rev. C48 ( 1993) 389. 16 V. Ghazikhanian et al., Phys. Rev. C43 ( 1991) 1532. r7 S.S. Vasan, Phys. Rev. D8 (1973) 4092. 18 I.M. Sitnik, VP Ladygin and M.P Rekalo, Yad. Fiz. 57 ( 1994) 1270. 19 E. Conzett, Phys. Rev. C48 ( 1993) 423. 110 V.A. Karmanov, Fiz. Elem. Chastits At. Yadra 19 ( 1988) 525 [transl.: Sov. 1. Part. Nucl. I9 (1988) 228 I. 1 I I ] W.W. Buck and F. Gross, Phys. Rev. D20 (1979) 2361. [ 121 L.A. Kondratyuk, FM. Lev and L.V. Schevchenko, Yad. Fiz. 29 (1979) 1081. I I3 I L.A. Kondratyuk and M.Zh. Schmatikov, Yad. Fiz. 4 I ( 1985) 222. I I41 V.N. Gribov, JETP 43 (1962) 1529. 1151 M.P. Rekalo, JETP 45 (1963) 595; V.N. Gribov, L. Okun and 1. Pomeranchuk, JETP 45 (1963) I 114. I 161 MP Rekalo, V.G. Gorshkov and G.V. Frolov, JETP 45 ( 1963) 285 and 672. [ 171 E Lehar et al., NIM A356 (1995) 58. [ I81 S.V. Dzhemuchadze et al., in: Proc. of hit. Symp. “Dubna Deuteron-93” Dubna, Russia, Sept. 14-18, JINR E2-94-9.5 ( 1994) p. 61; S.V. Dzhemuchadze et al., COSY Proposal No. 20 , IKP KFA, Julich, 1992.
s
ELSEVIER
24 August I995 PHYSICS
LETTERS
B
Physics Letters B 356 (1995) 434-438
Study of T-odd asymmetry in backward elastic dp scattering as a method to identify the reaction mechanism M.P. Rekalo a, I.M. Sitnik b a National Science Center - Kharkov Institute of Physics and Technology, 310108 Kharkov. Ukraine h Joint Institute for Nuclear Researches, 141980 Dubna, Russia
Received 28 April 1995; revised manuscript received 6 June 1995 Editor: G.F. Bertsch
Abstract Recent measurements of the polarization observables in the dp + pd reaction at Dubna and Saclay have shown that a consideration of this reaction in the framework of the one nucleon exchange mechanism is inadequate. The T-odd effects due
to the polarization of both colliding particles are considered. It is shown that the new polarization observable is especially sensitive to the mechanism of the reaction. The paper is inspired by the fact that a polarized proton target, which can provide a polarized deuteron beam, is now installed at the Dubna synchrophasotron. Such measurements are feasible also at COSY.
1. Introduction
A study of polarization effects in backward elastic dp scattering at the maximal available energy is a very effective method for obtaining information about the deuteron structure in the region of large internal momenta. This is done in the framework of the Impulse Approximation (IA), there is a one-to-one connection between the only kinematical parameter of the reaction, the total energy in the CM system, and the deuteron wave function (DWF) argument in momentum space, when the deuteron is implied as a two nucleon system. That is a serious advantage of this reaction (and of the deuteron electrodisintegration also) in comparison with ed elastic scattering, where observables are connected with the DWF argument through an integral. Usually this reaction is interpreted in the framework of the one nucleon exchange (ONE) mechanism. That is a particular case of the IA.
Up to now, apart from cross sections [ 11, only the analyzing power T2o , induced by the initial deuteron tensor polarization [2-41, and the polarization transfer coefficient from the deuteron to the proton (~0) [4], have been investigated. The obtained experimental data, as is shown in Ref. [4], are in principal contradictions with such a simplified mechanism as the ONE. But this discrepancy does not mean that the IA is not valid in principle. For instance, one can try to correct the situation by taking into account the multitude of NN*-configurations, arising in the deuteron in the framework of the quark count [ 51, that lead to additional IA diagrams, where the neutron is replaced by NX. To distinguish whether the observed effects are induced by the more complicated deuteron structure or a more complicated reaction mechanism, it is necessary to measure new polarization observables. In particu-
0370-2693/9.5/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0370-2693(95)00754-7
M.P. Rekalo. I.M. Sitnik/
Physics L&ten B 356 (1995) 434-438
lar. it would be important to find such polarization observables that are especially sensitive to details of the reaction mechanism. As will be shown below, these are experiments that deal with T-odd observables of this process. The investigation of T-odd effects is of great interest because in any kind of the IA they are equal to zero. Therefore, the detection of nonzero values of T-odd polarization characteristics will indicate the necessity of a radical revision of the mechanism of the reaction considered. We discuss here the simplest T-odd observable of backward elastic dp scattering, namely the analyzing power, induced by a specific choice of polarization axes of the interacting particles relative to each other and to the beam direction. In Section 2 we analyze polarization effects in general form, using the parametrization of the full d+p -+ p + d amplitude in terms of four independent complex scalar amplitudes. Such a formalism is not connected directly either with the deuteron model or the reaction mechanism. In Section 3, we discuss shortly feasible mechanisms that lead to nonzero T-odd effects. In Section 4, we consider briefly how to measure the discussed analyzing power.
2. Spin structure
of the d + p ----)p + d reaction
The process of elastic dp scattering at an arbitrary angle in the general case is defined by 12 independent complex amplitudes [6] and so, at least 23 polarization observables must be measured in the complete experiment. The problem of the complete experiment is much simpler in the case of forward (0 = 0”) and backward (0 = 180”) scattering, when the total helicity 01’ the interacting particles is conserved. In this case the spin structure of the full amplitude is defined by only four amplitudes (which are different for the two abovementioned kinematical conditions). There are some equivalent sets of amplitudes, suitable for the description of the discussed process. We use here the method of the so called scalar amplitudes g,(s), related with the helicity ones F~,,,+,+A,,A,, in the following way: Fo+-o+
=92(s),
F o+--*+- = -v%w,
435
F++,++ =a(~) +a(~), =gl(s) -g4(s)v
F-+++
(1)
where Ad ( AP) corresponds to the deuteron (proton) spin projection onto the beam direction (+ 1,0, - 1 for deuterons and Z!L~ for protons). It is easy to see from (1) that gr(s), g2(s) and g4(s) do not change the transversal (gt (s) and g4 (s) ) or longitudinal (g2( s) ) polarization of the initial deuteron, and gs (s) describes the transition between the transversally (longitudinally) polarized initial deuteron and longitudinally (transversally) polarized final one. In the latter case the proton spin must be reversed. In terms of scalar amplitudes the full amplitude F has the following form:
M = p&y,,
F=A+ia.B,
(2)
- (nU~)(nU;)l
A=gl(s)lU~U;
B=g3(s)[U1
x U;
+g4(s)n(nUl
x
-n(nUl
x
U;)l
q>,
where Ur ( UZ) is the spin vector of the initial (final) deuteron, XI (~2) is the two-component spinor of the initial (final) proton, u are the Pauli matrices, s is the Mandelstam variable (squared total energy), n is the unit vector along the beam direction. That is the most suitable formalism to analyze the problem of the complete experiment in backward dp scattering. We accept the following parametrization of the initial polarization states. These are p= ;(l
faP)
(3)
for protons, where P is the 3-vector of proton polarization, and lJiUT =
i(8ij
+
~iei,j~S[- Qi,j)
(4)
for deuterons, where the pseudovector S and the symmetrical tensor Qij characterize the vector and tensor deuteron polarization. We have Qij = Qji,
Qii = 0.
(5)
Here we consider the most simple polarization effects induced by the polarization of initial particles
436
M.P. Rekalo, I&f. Sitnik/
(analyzing powers). Substituting the relations into the following expression for cross sections:
g
= ;Ns~F(I
N= -!-
+uP)F+,
64~~s ’
Physics Letters B 356 (1995) 434-438
(2)
(6)
one obtains du
dR--
dd”
-
dR
transformation in the T-invariant theory. The important property of T-odd observables is their sensitivity to small phase diffferences of scalar amplitudes. Indeed, we have Im(gid)
[I + Al (Qi,jnini)
+Aj(Pn>(Sn)
+A4n.Q
PI,
MM sin(W) 11lgillgkl(~~)~
in difference with T-even observables, such combinations as
+ A2SP x
=
(7)
expressed
via
(W2
Wg&) = ldlgkIc0@#4N IgiIIgk((l - -+.
where the vector Q is defined as
Q; = Qijr1.jt and dcr(“)/dSL is the differential cross section when both the initial proton and deuteron are unpolarized. The cross section and the coefficients Al-A4 are related to the scalar amplitudes by the following expressions:
(9)
A2N-’
du”’ df2
(A2 + A3)N-‘~
3A4,$l--’!$?!
=Ret(gl
+g2-gd&lv = -Re[(gs
=2Im[(-gl
+g2
(10)
-g4)&1,
(11)
-g4)&1.
(12)
As is evident from (9)-( 12), all four sources of asymmetry of the first interaction are independent. The coefficient Al determines the effect induced by the tensor polarization of the initial deuteron, firstly considered in Ref. [ 71. The coefficients AZ, A3 determine the effects induced by the vector polarization of both the initial deuteron and proton. The latter source of polarization effects is considered in detail in Ref. [ 81. All abovementioned asymmetries are T-even. And finally, the collision of tensor polarized deuterons with polarized protons is characterized by the coefficient A.+ This asymmetry is T-odd. Not only the mentioned ones, but all T-odd observables are related with amplitudes via expressions like Im( gig; ) . The appearance of imaginary parts of bilinear combinations is the direct consequence of complex conjugation as the necessary attribute of a T-
3. The analyses of sources of the T-odd asymmetry The T-odd asymmetry for the total cross section of dp scattering characterizes the T-violation and must be small (so called “null’‘-test [ 91) , But in the case of elastic dp scattering the coefficient A4 can be large enough due to nonzero relative phases of different amplitudes. As far as the interaction constant remains real in any kind of the IA (relativistic or nonrelativistic), such complications of the deuteron model as increasing the number of arguments (up to 6 [ lo] ), taking into account such vertexes as d + NN* I.51 or the relativistic one d -+ pE [ 111, does not lead to complexity of amplitudes. Only additional ones to the IA mechanisms of the reaction can provide such a property of amplitudes. These are - excitation of the A-isobar and so on in the intermediate state; - excitation of three-nucleon resonances in the direct channel of pd collisions; - exchange by fermion Regge poles. The complexity of amplitudes is also the inevitable outcome of the unitarity conditions. Such effects as excitation of the A-isobar in the intermediate state are considered, for example, in Ref. [ 121. The amplitude, responsible for this subprocess, can be expressed through the parameters of the NN + NA interaction and some integral over the definite combinations of the S- and D-components of the DWF. It demonstrates quasiresonance behaviour in the of Td z 0.75 GeV region. The resulting behaviour of the full amplitude in this region depends essentially on the formfactors of NN?r- and NNP-vertexes. The physical reasons for the appearance of such objects as three-baryon resonances are different. It is
M.P. Rekalo, 1.M. Sitnik/ Physics Letters B 356 f 1995) 434-438
enough to mention the possibility of the existence of the ANN-resonance, if the anomalous AN interaction (different from one-pion exchange) exists. The appearance of 3-baryon resonances seems absolutely natural in different versions of quark bag model [ 13 1. The reaction d + p -+ p + d seems to be most suitable for studying this problem due to the following circumstances: - the smallness and relatively simple spin structure of the main background amplitude (one-nucleon exchange) ; - the sensitivity of the differential cross section energy dependence to the values of the spin and space parity of 3-baryon resonances. The most probable interval of 3-baryon resonance masses is 3-3.5 GeV/c. So, a primary beam with energy Td 5 1 GeV is needed to investigate this problem. At higher energies a possible source of complexity of scalar amplitudes is a fermion Regge poles [ 141 (FRP) exchange. In quark language it can be interpreted as a more general three quark exchange in the u-channel, than in the case of the ONE. Such an exchange is equivalent to a new effective d -+ NR vertex (R is a reggeon), which allows one to take into account in some sense the quark degrees of freedom in the deuteron. The most interesting peculiarity of FRP is “self-conjugation”. That means the existence of two complex-conjugate trajectories with a special kind of argument for each Regge poie, namely a( fi> and cy* ( J;;) , where u is the Mandelstam variable. At u < 0 a number of reasons lead to the complex contribution of FRP to the amplitudes. At u > 0 only one of them survives, namely, that connected with signature factors [ 151 1 *exp[i7rcr(--fi)]
i *exp[ircu(JEI)],
At B = 180’ u is always positive:
11 =
(m; - rn;>2 s ’
It changes its sign at an angle defined by the following condition: I fcos(O())
=
cm;-m;>*
or, approximately,
2rnipz
’
(13)
431
(14) where pd is the initial deuteron 3-momentum in the Lab system. The phenomenology of FRP was very effective for the description of the m + N + rr + N, r + N --t v + N, 7~+ N ---t p f N reactions [ 161. It is interesting to note that the asymptotic Regge regime in reactions with participation of the deuteron is achieved earlier in comparison with TN and yN reactions. For instance, the Regge picture y + d -+ n + p commenced at an anomalously small energy, namely, Ey > 400 MeV. We mention here that the contribution of single bosonic Regge poles does not lead to nonzero phases between different amplitudes.
4. How to measure the T-odd effect The vector product near the coefficient expressed as follows: 3 n.QxP=--QzzPYsin(2P), 4
A4 can be
(15)
where z is the axis of the initial deuteron tensor polarization, n lies in the xz-plane and p is an angle between n and the x-axis, cv is a projection of P onto the y-axis. As is easy to see from ( 15), this vector product is equal to zero until the angle between the deuteron polarization axis and the beam direction remains 90”, independently of the choice of the initial proton polarization axis. If we deal with a polarized deuteron beam and a polarized proton target (PPT), the vertical polarization axis of the extracted beam is assumed. If one rotates the deuteron spin with the help of a solenoid (90”)) then a spin rotation, respectively, a beam direction can be achieved due to the anomalous part of the particle magnetic moment while the beam is deflected by dipoles. The target polarization axis must be vertical in this case. The connection between the summary bending angle of a beam line (~0 ) and spin rotation, respectively the beam direction (in the current deuteron rest frame) is expressed by the simple formula
pm =
4ooY$ - l),
where y = E/m, g = 1.716.
(16)
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M. P. Rekalo. I. M. Sihik / Physics Letters B 356 (I 99.5) 434-438
One can see that it is not possible to provide an optimal spin rotation in a wide energy region of the beam having a fixed beam line. Now the existing beam line upstream the PPT at Dubna [ 171 (with the summary beam bending angle in dipoles of 27”) provides values of sin( 2p) increasing from 0.25 up to 0.49 while one changes the primary beam momentum from 3 up to 7 GeV/c. The need for the largest energy magnetic field integral in a solenoid (about 40 Tm) is, maybe, not realistic. Nevertheless, performing the experiment in this case is also possible. For example, in the case of a fixed magnetic field integral of about 10 Tm (decreasing with energy spin rotation in a solenoid), sin( 2p) remains on the level of N 0.2 in the mentioned range of primary beam energies. In the latter case a thin alignment of the PPT polarization axis is necessary for each energy of the primary beam. Maybe, it is more convenient to investigate this problem using a polarized proton beam and a polarized deuteron target. Such an experiment is feasible at the zero degree facility of COSY [ 181. Keeping in mind that the primary beam polarization is vertical, in order to have sin(2P) = 1 one has to orient the deuteron target polarization axis in the horizontal plane at an angle of 45” to the beam direction.
5. Conclusion We demonstrated here the importance of the study of T-odd polarization effects in backward elastic dp scattering as an effective tool of the determination of the reaction mechanism. A nonzero T-odd asymmetry arises only in the case that the mechanisms additional to the Impulse Approximation are essential. Revealing a nonzero T-odd asymmetry will lead to a radical revision of the mechanism of this reaction. Only one from four possible asymmetries (for the first interaction) is T-odd. Such measurements are realistic.
Acknowledgements This work is supported in part by the Russian Foundation for Fundamental researches, grants No. 93-023961 and No. 95-02-05043.
The authors thank A.M. Baldin, F. Lehar, N.M. Piskunov for strong support of this activity. They are also grateful to J. Arvieux, V.V. Fimushkin, M.V. Kulikov, VP Ladygin, A.A. Lukhanin, A. de Lesquen and Yu.A. Plis for fruitful discussion.
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