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					 Detailed comparison of the pp → π +pn and
pp → π +d reactions: deuteron D-state effects

                                The GEM collaboration
       M. Abdel-Bary a , A. Budzanowski b , A. Chatterjee c , J. Ernst d ,
   P. Hawranek a,e , F. Hinterberger d , V. Jha c , K. Kilian a , S. Kliczewski b ,
    D. Kirillov f , D. Kolev g , M. Kravcikova h , T. Kutsarova i , M. Lesiak e ,
J. Lieb j , H. Machner a , A. Magiera e , R. Maier a , G. Martinska k , S. Nedev l ,
  J. Niskanen m , N. Piskunov f , D. Prasuhn a , D. Proti´ a , P. von Rossen a ,
                                                            c
                a, c         f              b
     B. J. Roy , I. Sitnik , R. Siudak , M. Smiechowicz e , R. Tsenov g ,
         M. Ulicny a,k , J. Urbana, d , G. Vankova a,g , and C. Wilkin n,1
            a
                            u                                      u       u
               Institut f¨r Kernphysik, Forschungszentrum J¨lich, J¨lich, Germany
                             b
                               Institute of Nuclear Physics, Krakow, Poland
                          c
                             Nuclear Physics Division, BARC, Bombay, India
      d
                      u                                              a
          Institut f¨r Strahlen- und Kernphysik der Universit¨t Bonn, Bonn, Germany
                  e
                     Institute of Physics, Jagellonian University, Krakow, Poland
                        f
                          Laboratory for High Energies, JINR Dubna, Russia
                        g
                           Physics Faculty, University of Sofia, Sofia, Bulgaria
                            h
                               Technical University, Kosice, Kosice, Slovakia
               i
                 Institute of Nuclear Physics and Nuclear Energy, Sofia, Bulgaria
           j
             Physics Department, George Mason University, Fairfax, Virginia, USA
                                k
                                  P. J. Safarik University, Kosice, Slovakia
             l
                University of Chemical Technology and Metallurgy, Sofia, Bulgaria
               m
                 Department of Physical Sciences, University of Helsinki, Finland
                    n
                      Department of Physics & Astronomy, UCL, London, U.K.


                                      Abstract
    An extension of the high precision measurement of inclusive π + produc-
tion in proton–proton collisions at COSY using the Big Karl spectrograph is
proposed. The existing results on the forward cross sections for pp → π + d
and pp → π + np reactions at 951 MeV will be supplemented by similar data
taken around and below the peak of ∆ resonance production. The analysis
of such data will provide a quantitative test of the hypothesis of the import-
ance of the deuteron D–state in pion production as well as providing more
information on the production of singlet np final states. These experiments
are only possible at COSY, where there is currently a unique combination
of cooled proton beam and high resolution spectrograph that can together
deliver a resolution in np excitation energy of better than 100 keV.


——————————
1
    Email: cw@hep.ucl.ac.uk


                                            1
1    Overview
In 2005 the GEM collaboration published two important letters describing
high precision experiments carried out at COSY. One of these reported a
new measurement of the mass of the η meson which yielded mη = 547.311 ±
0.028 (stat.) ± 0.040 (syst.) MeV/c2 [1]. The error bars are here so small
that the GEM value should dominate the next compilation of the Particle
Data Group. The result, though consistent with values obtained in other
electronic experiments, is in contradiction with that presented by the CERN
NA48 experiment and, according to both referees on the GEM publication,
this brings into question the NA48 measurement of CP violation [2].
     The second experiment involved the measurement of inclusive pion pro-
duction in pp → π + X (X = d or pn) in the forward direction at a proton
beam energy of Tp = 951 MeV [3]. The mass resolution of σX = 97 keV
in the deuteron region was almost four times better than that achieved in
any previous experiment [4] and was such that events corresponding to the
π + d two–body final state could be unambiguously separated from those of
the π + pn continuum. Moreover, this high resolution was sufficient to put
very stringent limits on the production of spin–singlet np final states in the
pp → π + {pn}s reaction, showing that it was vanishingly small compared to
triplet production.
     By measuring the π + d and π + pn final states simultaneously it was pos-
sible to deduce the ratio
                        d2 σ                     dσ
             Rpn/d =         (pp → π + {pn}t )      (pp → π + d)          (1)
                       dΩ dx                     dΩ

with few systematic errors, being untroubled by questions of relative norm-
alisation of different experiments. Here x denotes the excitation energy ε in
the np system in units of the deuteron binding energy.
    Now if the pion production operator is of short range and one neglects
the coupling between the S and D states in the triplet np system through
the tensor force, then it can be shown that [5]
                                             √
                                     p(x)       x
                         Rpn/d ≈ N                  ,                    (2)
                                    p(−1) 2π(x + 1)

where p(x) and p(−1) are the pion cm momenta for the pn continuum or
deuteron respectively and N is a normalisation factor that should be unity.
Though our published results at 951 MeV [3] are consistent with the shape of
the x–dependence shown in Eq. (2), we were surprised to find that the overall
strength of Rpn/d was about a factor of N = 2.2 larger than that predicted

                                      2
by the final state interaction theorem [5]. We concluded that this defect was
a consequence of the S      D coupling that was not included in the theorem.
    Unfortunately, there are no detailed estimations of the effects of the tensor
force on pion production to the π + {pn}t continuum. However, such ef-
fects have been studied for pp → π + d [6] where the calculations show dra-
matic changes when the S        D coupling is introduced. Since, on kinematic
grounds, the D–state amplitudes would be expected to change sign between
the deuteron bound state and the np continuum, the factor of 2.2 could be
explained, at least semi-quantitatively, as being due to S–D interference.
    It is important to note that our data were taken above the peak asso-
ciated with the production of the ∆ resonance and that this interference is
predicted to change sign below the resonance [3, 6]. We should therefore
like to repeat the experiment at two more energies, one below the ∆ peak
(Tp ≈ 450 MeV) and one close to it (Tp ≈ 600 MeV). Assuming that the
theoretical calculations of Ref. [6] are accurate, we would then expect Rnp/d
to be less than unity at the lower energy and roughly equal to one around
the ∆ peak. The experiment could therefore provide the first real evidence
of the great importance of deuteron D–state effects in pion production and
should be the stimulus for more detailed coupled–channel calculations for
pp → π + pn. Furthermore, on the basis of the pp → ppπ 0 data [7], one
might expect at these lower energies to be able to identify some singlet np
production through a detailed study of the fine structure of the spectrum.
    As one of the referees on the pion production paper stressed, These results
are new (in this quite old field) because of the unique capabilities of COSY.
For both this work and the η mass determination we have been very well
served by the excellent qualities of the Big Karl spectrometer coupled with
those of the cooled proton beam. Given that Big Karl will be retired at
the end of 2006 it is our desire to exploit its potential, hopefully to provide
confirmation on the importance of D–state effects in pion production.




                                       3
2    Details of the 951 MeV experiment
In our published experiment [3], pions were observed near the forward dir-
ection using Big Karl. Their position and track direction in the focal plane
were measured with two packs of multiwire drift chambers, each having six
layers. The chambers were followed by scintillator hodoscopes that determ-
ined the time of flight over a distance of 3.5 m. In order to optimise the
momentum resolution, a liquid hydrogen target of only 2 mm thickness was
used with windows made of 1 µm Mylar. The beam was electron cooled at
injection energy and, after acceleration, stochastically extracted, resulting in
the resolution in excitation energy of σ = 97 keV for the deuteron peak, as
shown in Fig. 1. This was much better than that without beam cooling and,
in particular, the background was considerably reduced.
                            4
                           10

                                     pp→πd



                            3
                           10
          counts/0.2 MeV




                                                 pp→πpn



                            2
                           10




                            1
                           10
                                -5    0      5        10   15        20
                                                 ε (MeV)



Figure 1: The results from our previous experiment (histogram) [3] compared
with the prediction (curve) of the purely S-wave fsi theory of Eq. (2) [5].

    Though corrections for acceptance etc. have been included in the figure,
these are slowly varying for ε ≤ 20 MeV. Given the logarithmic scale, it
is clear that there is an excellent separation of the pp → π + pn from the
pp → π + d reaction. Hence, since the luminosity and detection efficiencies
largely cancel out between the reactions, this means that we had a very good
determination of Rpn/d .

                                             4
                           400




                           300
          counts/0.2 MeV




                           200




                           100




                            0
                                 -2   0   2   4   6   8      10 12   14   16   18   20   22
                                                          ε (MeV)


Figure 2: Comparison of the measured pn excitation energy spectrum on a
linear scale with the prediction for the shape of the singlet cross section.

    The S–wave np continuum can be either spin–triplet (T = 0) or singlet
(T = 1) but, because of its large scattering length, the shape of the excitation
energy continuum is expected to be very different for singlet production, as
illustrated in Fig. 2 on a linear scale. The absence of any sharp peak at
ε ≈ 0.8MeV means that triplet final states completely dominate the reaction;
more quantitative conclusions are drawn in Ref. [3].
    Since the deviations between experiment and the predictions of the fsi
theorem [5] in Fig. 1 cannot be due to singlet production, the only plausible
explanation remaining at small ε is that it is due to the tensor force that
couples the spin–triplet S and D of the np system. It has been shown in
model calculations [6] that the D–state plays an important role in pp → π + d
but primarily through terms that are linear in the D-state amplitude. This
can be seen from Fig. 3 where the prediction with no D-state is roughly
the average of those with the standard D-state amplitude and one with the
reversed sign.
    Although the fsi theorem [5] is strictly valid only for a single uncoupled
partial wave, it is known that, unlike the case of an S–state, a D–wave
function changes sign between the bound state and scattering regions [9].
Thus it is to be expected that the S–D interference effects will change sign
when going from the pp → π + d to pp → π + {pn}t . Very naively one would
therefore expect that the discrepancy factor N in Eq. (2) should be roughly
equal to the ratio of the broken curve (reversed D–state) in Fig. 3 to that

                                                          5
Figure 3: D-state effects in the predicted excitation function [6] for the zero
degree pp → π + d differential cross section as a function of the η parameter.
The solid curve shows the results with the standard value [8], the broken
curve with the reversed sign, and the dots with no D-state at all. Our
951 MeV data correspond to the value of η = 2.6.


of the solid one (standard D–state form). Possibly entirely fortuitously, this
ratio is exactly equal to our measured value of N = 2.2!
    This semi-quantitative argument cannot be considered as an adequate re-
placement for a consistent coupled-channel calculation of pp      π+d    π + pn
with an np tensor force, which has still to be performed. However, the en-
ergy variation of the broken and solid curves in Fig. 3 suggests that N ≈ 1
in the region of η ≈ 1.6 (Tp ≈ 600 MeV). Hence close to or just below the
resonance we would expect to find much smaller deviations from the fsi the-
orem of Eq. (2). This seems to be consistent with existing experimental
data [4, 10, 11], though these were all taken with poorer experimental resolu-
tion that did not allow for the identification of the singlet contribution from
the shape of the excitation energy spectrum. Without such an identification
it would be possible to lay some of the deficiencies of the theorem at the door
of a possible singlet contribution, as was done in Ref. [5].




                                      6
3     Beam request
In order to identify the singlet contribution to pp → π + pn and hopefully
track the effects of the deuteron D–state on pion production, we should
like to repeat our experiment using Big Karl under conditions that were
identical to those published [3]. This programme would necessarily require
measurements at and below the ∆ resonance but extra confirmation of our
hypothesis will be provided by the study of a third energy between the ∆
peak and our previous 951 MeV run. We therefore ask for beam time for the
measurement of inclusive forward pion production in proton–proton collisions
at 400, 600, and 800 MeV.
    Our request is summarised in Table 1. The pion laboratory momenta
corresponding to the pp → π + d reaction and the consequent pion survival
probabilities for the Big Karl central trajectory length of 16 m are presented
for the three energies. Taking into account the acceptance of Big Karl, the
differential cross sections and a possible intensity of the electron–cooled beam
of 108 /s, this programme should be delivered within one week of beam time.

               Table 1: Summary of proposed measurements

     Beam   Pion lab   Survival               dσ/dΩcm         Acceptance
    energy momentum probability              (pp → dπ + )       in cm
    (MeV)   (MeV/c)  at 16 m (%)               (µb/sr)           (sr)
     400          220             27              146             0.043
     600          410             50              605             0.044
     800          590             61              275             0.049




                                       7
References
 [1] M. Abdel-Bary et al., Phys. Lett. B 619 (2005) 281.

 [2] A. Lai et al., Phys. Lett. B 533 (2002) 196.

 [3] M. Abdel-Bary et al., Phys. Lett. B 610 (2005) 31.

 [4] R.G. Pleydon et al., Phys. Rev. C 59 (1999) 3208.

                     a
 [5] A. Boudard, G. F¨ldt, and C. Wilkin, Phys. Lett. B 389 (1996) 440.

 [6] J. Niskanen, Nucl. Phys. A 298 (1978) 417;
     Phys. Rev. C 49 (1994) 1285.

 [7] See for example: R. Bilger et al., Nucl. Phys. A 663 (2001) 633.

 [8] R. Reid, Ann. Phys. (N.Y.) 50 (1968) 411.

         a
 [9] G. F¨ldt and C. Wilkin, Physica Scripta 56 (1997) 566.

[10] K. Gabathuler et al., Nucl. Phys. B 40 (1972) 32.

[11] W.R. Falk et al., Phy. Rev. C 32 (1985) 1972.




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