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Charge-symmetry-breaking effects from phase-shift analysis of elastic π± He scattering
Volume !75, number 3
PHYSICS LETTERS B
7 August 1986
CHARGE=SYMMETRYoBREAK~NG E F F E C T S F R O M P H A S E - S H W T ANALYS~S OF E L A S T I C ~ ± 4He S C A T T E R I N G M.Kho K H A N K H A S A Y E V , F~ N I C H I T I U : and M.G. S A P O Z H N I K O V Joint Ins~#uge for Nuclear Research, Dubna, Head Post Offie< P.O. Box 79, lOlO00 Moscow, USSR
Received t3 January i986; revised manuscript received 30 April 1986 A phase-shiP, analysis of e~astic ~ ± SHe scattering at energies 20-160 MeV was performed to determine pure hadronic phase shifts. No statistically significam difference be:ween *..he hadronic phase shifts deduced from ,v ~ SHe and ~ - 4 H e scattering was observed.
One interesting consequence of the difference between the a- and d-quark masses is that there must exist a difference between the pure hadronic cross sections of ~r+ and ~r scattering on nuclei with zero isospin. The authors of refs. [ i - 3 i claim ~o have discovered such a charge-symmetry-breaking (CSB) effec~ in ~r ± d scattering. CSB was also found in vr +- 3He, ~H elastic scattering [4]. The observed differences between the Co@omb corrected cross sections of ~r÷ and rr- nuclei scatr.ering were interpreted as a manifestation of different masses and widths of the 2,33-isobar states excited in ~r+- and r r - - n u d e i scattering [1-3}. Obtained estimates of the splitfings of the ~33states are in suitabie agreement with predictions of the models which take into account the differe m quark composition of 2~33-resormnces [5]. Nevertheless, there remain some doubts concerning the cor~ciusion on CSB [6,71. These doubts arise from the fact that for any firm conclusion about CSB one must not only calculate properly C o u ' o m b corrections but the pion-nucLear amplitude with very high precision, unattainable at this moment. So it wou~d be better to search for CSB in an as .modeI independent way as possible. The phase-shift analysis (PSA) is a rather convenient method for that purpose, tt is easier to perform a PSA of eiasfic 7raHe scattering
than one of r,, ;aC or ~r 460 scattering because the spin-isospin structure of 4He is simple and fewer free parameters are needed because only a few partial amplitudes take part in rr t h e scattering. An indication of CSB in that case wii~. be ~he discovery of a significant difference between the pure hadronic phases extracted from ~r+ t H e and ~r 4He scattering. The amplitude of rr 4He scattering was parame~trized as usual:
here fc(O) is the Coulomb amplitude where the non-point charge distributions in ~He and the pion were taken into account as in refs. [8,9]. The main difficulty in the search for CSB effects in PSA is to determine pure hadronic phase shifts. We used the formalism of approximative treating for external Coulomb corrections which had been developed in refs. [I0-13,3]. This approach allows a rather good simukaneous description of ~r+A and ~r-A elastic scattering both in the case of heavy nuclei [!i-13], and for v ± d scattering [31. According to ref. [10] the total phase shift A{..~:.) in the nuclear an',pIitude feN(O) ,±,o,
i i(2t+
)
1
O:~ leave of absence from Cemra! InstRute of Physics, W~N, Bucharest, Romania.
0370-2693/86/$03.50 ~> EIsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
×
exD(2i a{ ± ''~ - I 2i
p,(co e)
(2) 26i
Volume 175, number 3
PHYSICS LETTERSB
is
""'~+> ~a to~ ./
8 . ~. + ~ * >R,/ +i(~.~
(3)
~' - . ~ . ~ .
Here. the o~± are ~he Coulomb phase shifts ~± = ,~g:, {l+ i + i~)l, ~ is the Coulomb parameter ~= ±~/fi, where e<= ,~, fl=@!'/c, Pz(cos 8) are ~,,~ Legendre ~olynomials., The phases 8"a.~ ±) a n d w (a.z ± ) are reduced phases w[hich represent the Coulomb distortion of the nuclear potential By ~;heir physical meaning 8~,~ ~ and ,~+t correspond to external Coulomb corrections [2]. The purely hadronic phase shifts 8.~.~ and ¢0~,~ must be equa! for rr+A and rr A scattering if charge symmetry exists. As was shown in ref. [7], ~<±;=a,(~:)
( dSq" , + sin 28~ , cosh 2~o~,, ) dk
:R,~
2k
a/~;=&,(k}(d~°~,, aj
~
+
7 August 1986
shifts which were analysed only one physica! set t~rned out to be satisfactory. The rejected sets had greater x 2 / N D F (two or more times greater than for the basic set) or violated unitarky ( ~ : , ~ exp(-2,~,0m/) > ".:). ~n tame 1 we collect the phase shifts obtained and the values of e~o~ and %. In rig. 1 the angular dependence of the asymmetry parameter
,4(e) : (d~ / d ~ - d , + / d ~ ) / ( d o - / i S + d~+/dO) is shown, it must be stressed that despite the fact that ~he magnitude of 3la.~ ~ ) and oaR, t'± ~ is not large (about 10% of 8u,/, ~u./) the role of these phases is rather [mportant [f the reduced phases x(:~) "JR, I a¢~ ~ are tur~ed off' the auality of the fit finis '~' drastically and x2/NDF increases 1.5-2 times (see fig. 1). "
'
c°s 28v,, sixth 2~°H,,) 2k '
(4)
.
05 A~ ~ 0':
0.3
where
0.2
2>Z~Z~H~ee~ ,~ dk' a~(k)
-
×f~
~ I ]
"~;
k~_ k,~
e,(cos ~ ) ~ " : ~ ( q ~ ) ~ ( ' ~ ) d cos e, (5) @2
here y is the reduced mass of ~ 4He, @2 = ,~2 _/~,2 2kk' cos #, . ~ ( q a ) and ,~,(q2) are the form facCors of 4He and of the pion. We calculate the derivatives d 3 ~ , y d k and dw:.
262
75 MeV
k '2 0.5 04 03 0.2 t
b
'
e
i
51MeV
1
01 ]
::'2i
T ,--,~ / _\
O&~
0~
-06t t
,]
',
',,~ '
l
t
20 gO 60 80 100 !20 ~ 0 1608.
Fig. l. Angular dependence of the asymme:ry parameter A ( # ) in ~r* 4He elastic scattering at (a) % = 24 MeV, (b) 51 MeV and (e) 75 MeV. Conth~uous lines represent PSA resN~s, dot-dashed lines represem the cMcu]afion in the CCE mode! [!5]. The dashed !ine at 51 MeV corresponds to a PSA fit when 8
.E
o)
Table 1 Pure hadronic phase shifts 3H. t and ~nelasticity parameters ~ . . t = e x p ( - 2 ~ H j ) from PSA of ~r ± 4He elastic seaueNng. The errors were determined in ~he ~ense of X2+1. Y 8s (MeV) (deg)
r~s
8 t, (deg)
~p
3])
;/D
(deg) ~.0020
3F
;IF
(deg)
%~
(~,ot
(rob)
(rob)
NDF
X2
Ref.
11.1+0.4
76.4+19.5
1.9
[1Z191
3.5
[18,19]
24
+0.08 -4"51-0.11
0.913 +0.010 -0.003
+0.08 2.77 _0.06
1.0_
51
-8.6_+0.1
0.837_+0.013
8 . 3 4 - +0.08 0.06
+0.0 0"996-0.015
0.96_+0.04 0.973+_0.008
60
-10,0_+0.4
0.832 +- 0.03~
10.6_+0.2
0,940+_0.019
1.0+_0.06
0.985+-0,006
-0.05-/_-0.04
0.977+_0°004 35.5+_0.2
I09.2_+9.1
5.7
[181
68
-9,7+1.t
0.937 +0.005 - 0,003
12,5 +0.3 -0.6
0.830_+0.034
1.8+0.3
0.988_+0013
-0.15+0.12
0,983_+0,006
39.6+-0.4
120.6_+7.5
3,0
[181
75
+ 0.9 -14.6 -0.8
+ 0.064 0.665 - 0 , 0 6 7
+ 0.7 t2.7 - 0 . 8
+ 0.032 0"953-0.036
1.8 -+0.t
0.927+_0.016
-0.003-+0.06
0.975-+0.007
45.9±0/7
142.0±&5
2.9
[18]
0.875 +- 0~022
0.t5_+0.27
0,977 _+0.013 61.3_+2.5
199.5+22.9
3.3
[201
0.26+0.01 .
0.983+0.009 .
.
.
29,0+_0.4 79.1+8.7
rJ~ r0el
t20
+ l 1,9 - - - 3 K 7 - 1 9 , 8 0.380_+0.105
135
- 65.5 +6.4 _ 7.5
145 156
+ 3.7 24.2-5.l
+ 0.067 0.715_0.082
7.4+_1.1
0,739+_0.041
0.22_+0.41
0,897_+0.028
97.2+4.8
2"/2.3_+11.4
0.5
[201
0.380 +0.039 - 0.044 20,37+2.48 -
0.526+0.026 -
7.0+0.9 -
0.684+_0,012
1.95_+1.0
0,775_+0.018
105.1_+3.1 321,1_+7.7
1.4
[201
-46,8+3.1
0.568_+0.040
16.1_+Z3
0.431_+0.025
9,6_+0,9
0, 563 _+0.02"7
2.0_+0.6
0.753+_0,020
103.4-+2.7 324.2_+6,9
2.8
I20]
- 5 4 . 0 -+2.8 3.0
0.573+_0.040
21.4 +3.2
0255+0.026
8/7+0.9
0.552±0.032
1.0±0.6
0.755±0.026
114.1_+3.1 3232_+72
2.5
[201
- 4.1
-
-
p.
t-) G', 0",
Volume i 7 5 , number 3
PHYSICS LETTERS B
1 b 3i
-]
ill'
~S
i
+
Ep
i
f
1{
20 40 60 80 t00
~t
~1.' I
'
31
% E
i
T(McV) 2 0 - Z b 60 8"0 f{b4-e~
Fig. 2. {a) .-C~,e ~ , / ; between pure ... difference ~ = ~ ,~/ ( + } - ~.{ hadronic phases ~:.e obtained separately from ~r+ 4He and re 4He differential cross sections for S- and P-waves. (b) The corresponding difference %,z = zT~~ - r~ ) for the indasticity parameters rh = e x p ( - 2 ~ q , z ) is shown. The smali crosses at 51 MeV and 75 MeV correspond to the pion-helit~m phase difference induced by mass and width splittiags of the ~ :~3-resonances ( A m = 6 MeV, A E = 8 MeV) in the P~3-wave.
For a more detaiIed search for CSB we performed the PSA for ~+ 4He and rr- 4He scattering data separately. Parametrization of f,:N(9) and Couiomb corrections (3)-(5) were the same as before, and the ambiguities were re-analysed for control. Due to large errors of the phase shifts at T, > 100 MeV (see tabte 1) we performed the CSB anaIysis only for good-accuracy low-e!~ergy data, The vaiues of the phases obtained from this kind of anaiysis are prac~icaliy the same as before (see tabie i), but the errors became larger due to decreasing of the number of experimental points. Fig. 2 shows the difference e t between pure hadronic phases obtained from ¢r+ SHe and 0r-4He scattering separately. It is clear that no significant difference exists~ This indicates the vaIidity of charge symmetry in the energy interval considered at the present accuracy of the available experimental data~ We estimated the possiMe CSB effect in the v ~ 4 H e phase shifts due to the mass spli~ting of 2~3.~-resonances. For that purpose we calculated phase shifts of rr4He eiastic scattering in the framework of the CCE modal when the input rcN p~3-wave was slightly distorted to imitate the mass dif%rence of k33-resonances. For the imita.'.ion of/a~ 3 or k33 we siighfly shifted the parameters of the mass and width from the standard one° 264
7 August 1986
We have used the energy dependence of the P~3 phase shift from Rowe et aio [21], where the A-resonance parameters are as follows: m = 1233 MeV, i ' 0 = 116 MeV. For simuiation of the z~3+3+ W e ~sed m = !23i MeV, I ~ , = t 1 2 MeV, and for Af3 we used m = 1237 MeV, I}~ = t20 MeV~ This procedure did not distort the whole energy dependence of P.~3 phase sNftSo Deviation of the simulated P.~3 phase shifts from the standard ones does not exceed 1° for T ~ i00 MeV. i'~ is instructive that the calculations show that the difference in the P33-wave is amphfied in ~r 4He phase shifts. For example, at T = 75 MeV the difference between P33 phases is £~P~3 = 0"350" This indaces a twice as ~arge difference in "~r4He hadronic phases % =~(+~ ~,~ - ~(~,~ ~ in ';he P wave, The value of ~e is e e = 0.72 ° at T = 75 MeV. (]t is shown in fig° 2 by crosses.) It is also important to note that such an a.mp~ificadon of CSB rrN effects in pion-nuclear scattering must increase in the k 3 s e s o n a n c e energy region. So, precision measurements of elastic rr + and ~' scattering on a light nucleus are greatly appreciated, in principle, such a difference between hadronic phases may be detected in the PSA if the differentia1 cross sections of elastic scattering wiii be measured with I - 2 % precision. in conclusion, we have performed a simahaneous PSA of elastic rr + 4He and rr- 4He scattering with ailowanee for external Coulomb corrections. We have obtained quite a good description of the angular dependence of the asymmetry parameter A(8). No significant differences between pure hadronic phase shifts deduced separately from rr + 4He and rr SHe scattering have been found. ~t is atso shown that possible CSB effects in ~r N phases must be amplified in rrA phase shifts.
Re&fences [!1 [2I [3i {4I [5]
T.G. Masterson etal., Phys. Rev. C 26 (1982) 2091. T . G Masterson et al., Phys. Rev. C30 (1984) 2010. E. Pedroni et ai,, NucL Phys. A300 (1978) 321. B.M. Nee
Votume i75, number 3
PHYSICS LETTERS B
[7] J. ~-:rohlic~ et aL, Nucl. Phys. A435 (1985) 738. [8] K.M. Das and B.B. Deo, Phys. Rev. C26 (1982) 2ii. [9] M.D. Cooper, M.B. Johnson and GoB. West, Nucl. Phys. A292 (!977) 350. [t01 J. Fr~hlich et aL, J. Phys. 0 6 (1980) 84R [H t A Fr~h~icln et a~., Z. Phys. A302 (1981) 89. [12] J. Fr~3h}ich, H. Pilkuhn and H.G. Schiaiie, Phys. Le~.t. B12t (1983) 235. [I3} O. Dumbrajs et al., Phys. Rev. C29 (1984) 581. [14t M.Kg. Khankhasayev, Yad. Fiz. 36 (1982) 633. [t5} V.B. Belayaev and M.Kh. Khankhasayev, Phys. Left B~37 (t984) 299.
7 August 1986
[16I [17] [18} [19] [20]
E. Barrelet, Nuovo Cimento 8A (1972) 33I. M. Nordberg and K. 2~nsey, Phys. Left 20 (1966) 962. K. Crowe et al., Phys. Rev, 180 (1969) 1349. G. Fournier e~ aL, Nucl. Phys. A426 (1984) 54Z M. Albu et ak, preprin~ LNF-g2/27(R)(Fraseati, !982); Yu.A. Shcherbakov et aL, Nuovo Cimento 31A (i976) 249. [21] G. Rowe~ M. Salomon and R.H. Landm:, ?bys. Rev. CI8 (1978) 584.
265
PHYSICS LETTERS B
7 August 1986
CHARGE=SYMMETRYoBREAK~NG E F F E C T S F R O M P H A S E - S H W T ANALYS~S OF E L A S T I C ~ ± 4He S C A T T E R I N G M.Kho K H A N K H A S A Y E V , F~ N I C H I T I U : and M.G. S A P O Z H N I K O V Joint Ins~#uge for Nuclear Research, Dubna, Head Post Offie< P.O. Box 79, lOlO00 Moscow, USSR
Received t3 January i986; revised manuscript received 30 April 1986 A phase-shiP, analysis of e~astic ~ ± SHe scattering at energies 20-160 MeV was performed to determine pure hadronic phase shifts. No statistically significam difference be:ween *..he hadronic phase shifts deduced from ,v ~ SHe and ~ - 4 H e scattering was observed.
One interesting consequence of the difference between the a- and d-quark masses is that there must exist a difference between the pure hadronic cross sections of ~r+ and ~r scattering on nuclei with zero isospin. The authors of refs. [ i - 3 i claim ~o have discovered such a charge-symmetry-breaking (CSB) effec~ in ~r ± d scattering. CSB was also found in vr +- 3He, ~H elastic scattering [4]. The observed differences between the Co@omb corrected cross sections of ~r÷ and rr- nuclei scatr.ering were interpreted as a manifestation of different masses and widths of the 2,33-isobar states excited in ~r+- and r r - - n u d e i scattering [1-3}. Obtained estimates of the splitfings of the ~33states are in suitabie agreement with predictions of the models which take into account the differe m quark composition of 2~33-resormnces [5]. Nevertheless, there remain some doubts concerning the cor~ciusion on CSB [6,71. These doubts arise from the fact that for any firm conclusion about CSB one must not only calculate properly C o u ' o m b corrections but the pion-nucLear amplitude with very high precision, unattainable at this moment. So it wou~d be better to search for CSB in an as .modeI independent way as possible. The phase-shift analysis (PSA) is a rather convenient method for that purpose, tt is easier to perform a PSA of eiasfic 7raHe scattering
than one of r,, ;aC or ~r 460 scattering because the spin-isospin structure of 4He is simple and fewer free parameters are needed because only a few partial amplitudes take part in rr t h e scattering. An indication of CSB in that case wii~. be ~he discovery of a significant difference between the pure hadronic phases extracted from ~r+ t H e and ~r 4He scattering. The amplitude of rr 4He scattering was parame~trized as usual:
here fc(O) is the Coulomb amplitude where the non-point charge distributions in ~He and the pion were taken into account as in refs. [8,9]. The main difficulty in the search for CSB effects in PSA is to determine pure hadronic phase shifts. We used the formalism of approximative treating for external Coulomb corrections which had been developed in refs. [I0-13,3]. This approach allows a rather good simukaneous description of ~r+A and ~r-A elastic scattering both in the case of heavy nuclei [!i-13], and for v ± d scattering [31. According to ref. [10] the total phase shift A{..~:.) in the nuclear an',pIitude feN(O) ,±,o,
i i(2t+
)
1
O:~ leave of absence from Cemra! InstRute of Physics, W~N, Bucharest, Romania.
0370-2693/86/$03.50 ~> EIsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
×
exD(2i a{ ± ''~ - I 2i
p,(co e)
(2) 26i
Volume 175, number 3
PHYSICS LETTERSB
is
""'~+> ~a to~ ./
8 . ~. + ~ * >R,/ +i(~.~
(3)
~' - . ~ . ~ .
Here. the o~± are ~he Coulomb phase shifts ~± = ,~g:, {l+ i + i~)l, ~ is the Coulomb parameter ~= ±~/fi, where e<= ,~, fl=@!'/c, Pz(cos 8) are ~,,~ Legendre ~olynomials., The phases 8"a.~ ±) a n d w (a.z ± ) are reduced phases w[hich represent the Coulomb distortion of the nuclear potential By ~;heir physical meaning 8~,~ ~ and ,~+t correspond to external Coulomb corrections [2]. The purely hadronic phase shifts 8.~.~ and ¢0~,~ must be equa! for rr+A and rr A scattering if charge symmetry exists. As was shown in ref. [7], ~<±;=a,(~:)
( dSq" , + sin 28~ , cosh 2~o~,, ) dk
:R,~
2k
a/~;=&,(k}(d~°~,, aj
~
+
7 August 1986
shifts which were analysed only one physica! set t~rned out to be satisfactory. The rejected sets had greater x 2 / N D F (two or more times greater than for the basic set) or violated unitarky ( ~ : , ~ exp(-2,~,0m/) > ".:). ~n tame 1 we collect the phase shifts obtained and the values of e~o~ and %. In rig. 1 the angular dependence of the asymmetry parameter
,4(e) : (d~ / d ~ - d , + / d ~ ) / ( d o - / i S + d~+/dO) is shown, it must be stressed that despite the fact that ~he magnitude of 3la.~ ~ ) and oaR, t'± ~ is not large (about 10% of 8u,/, ~u./) the role of these phases is rather [mportant [f the reduced phases x(:~) "JR, I a¢~ ~ are tur~ed off' the auality of the fit finis '~' drastically and x2/NDF increases 1.5-2 times (see fig. 1). "
'
c°s 28v,, sixth 2~°H,,) 2k '
(4)
.
05 A~ ~ 0':
0.3
where
0.2
2>Z~Z~H~ee~ ,~ dk' a~(k)
-
×f~
~ I ]
"~;
k~_ k,~
e,(cos ~ ) ~ " : ~ ( q ~ ) ~ ( ' ~ ) d cos e, (5) @2
here y is the reduced mass of ~ 4He, @2 = ,~2 _/~,2 2kk' cos #, . ~ ( q a ) and ,~,(q2) are the form facCors of 4He and of the pion. We calculate the derivatives d 3 ~ , y d k and dw:.
262
75 MeV
k '2 0.5 04 03 0.2 t
b
'
e
i
51MeV
1
01 ]
::'2i
T ,--,~ / _\
O&~
0~
-06t t
,]
',
',,~ '
l
t
20 gO 60 80 100 !20 ~ 0 1608.
Fig. l. Angular dependence of the asymme:ry parameter A ( # ) in ~r* 4He elastic scattering at (a) % = 24 MeV, (b) 51 MeV and (e) 75 MeV. Conth~uous lines represent PSA resN~s, dot-dashed lines represem the cMcu]afion in the CCE mode! [!5]. The dashed !ine at 51 MeV corresponds to a PSA fit when 8
.E
o)
Table 1 Pure hadronic phase shifts 3H. t and ~nelasticity parameters ~ . . t = e x p ( - 2 ~ H j ) from PSA of ~r ± 4He elastic seaueNng. The errors were determined in ~he ~ense of X2+1. Y 8s (MeV) (deg)
r~s
8 t, (deg)
~p
3])
;/D
(deg) ~.0020
3F
;IF
(deg)
%~
(~,ot
(rob)
(rob)
NDF
X2
Ref.
11.1+0.4
76.4+19.5
1.9
[1Z191
3.5
[18,19]
24
+0.08 -4"51-0.11
0.913 +0.010 -0.003
+0.08 2.77 _0.06
1.0_
51
-8.6_+0.1
0.837_+0.013
8 . 3 4 - +0.08 0.06
+0.0 0"996-0.015
0.96_+0.04 0.973+_0.008
60
-10,0_+0.4
0.832 +- 0.03~
10.6_+0.2
0,940+_0.019
1.0+_0.06
0.985+-0,006
-0.05-/_-0.04
0.977+_0°004 35.5+_0.2
I09.2_+9.1
5.7
[181
68
-9,7+1.t
0.937 +0.005 - 0,003
12,5 +0.3 -0.6
0.830_+0.034
1.8+0.3
0.988_+0013
-0.15+0.12
0,983_+0,006
39.6+-0.4
120.6_+7.5
3,0
[181
75
+ 0.9 -14.6 -0.8
+ 0.064 0.665 - 0 , 0 6 7
+ 0.7 t2.7 - 0 . 8
+ 0.032 0"953-0.036
1.8 -+0.t
0.927+_0.016
-0.003-+0.06
0.975-+0.007
45.9±0/7
142.0±&5
2.9
[18]
0.875 +- 0~022
0.t5_+0.27
0,977 _+0.013 61.3_+2.5
199.5+22.9
3.3
[201
0.26+0.01 .
0.983+0.009 .
.
.
29,0+_0.4 79.1+8.7
rJ~ r0el
t20
+ l 1,9 - - - 3 K 7 - 1 9 , 8 0.380_+0.105
135
- 65.5 +6.4 _ 7.5
145 156
+ 3.7 24.2-5.l
+ 0.067 0.715_0.082
7.4+_1.1
0,739+_0.041
0.22_+0.41
0,897_+0.028
97.2+4.8
2"/2.3_+11.4
0.5
[201
0.380 +0.039 - 0.044 20,37+2.48 -
0.526+0.026 -
7.0+0.9 -
0.684+_0,012
1.95_+1.0
0,775_+0.018
105.1_+3.1 321,1_+7.7
1.4
[201
-46,8+3.1
0.568_+0.040
16.1_+Z3
0.431_+0.025
9,6_+0,9
0, 563 _+0.02"7
2.0_+0.6
0.753+_0,020
103.4-+2.7 324.2_+6,9
2.8
I20]
- 5 4 . 0 -+2.8 3.0
0.573+_0.040
21.4 +3.2
0255+0.026
8/7+0.9
0.552±0.032
1.0±0.6
0.755±0.026
114.1_+3.1 3232_+72
2.5
[201
- 4.1
-
-
p.
t-) G', 0",
Volume i 7 5 , number 3
PHYSICS LETTERS B
1 b 3i
-]
ill'
~S
i
+
Ep
i
f
1{
20 40 60 80 t00
~t
~1.' I
'
31
% E
i
T(McV) 2 0 - Z b 60 8"0 f{b4-e~
Fig. 2. {a) .-C~,e ~ , / ; between pure ... difference ~ = ~ ,~/ ( + } - ~.{ hadronic phases ~:.e obtained separately from ~r+ 4He and re 4He differential cross sections for S- and P-waves. (b) The corresponding difference %,z = zT~~ - r~ ) for the indasticity parameters rh = e x p ( - 2 ~ q , z ) is shown. The smali crosses at 51 MeV and 75 MeV correspond to the pion-helit~m phase difference induced by mass and width splittiags of the ~ :~3-resonances ( A m = 6 MeV, A E = 8 MeV) in the P~3-wave.
For a more detaiIed search for CSB we performed the PSA for ~+ 4He and rr- 4He scattering data separately. Parametrization of f,:N(9) and Couiomb corrections (3)-(5) were the same as before, and the ambiguities were re-analysed for control. Due to large errors of the phase shifts at T, > 100 MeV (see tabte 1) we performed the CSB anaIysis only for good-accuracy low-e!~ergy data, The vaiues of the phases obtained from this kind of anaiysis are prac~icaliy the same as before (see tabie i), but the errors became larger due to decreasing of the number of experimental points. Fig. 2 shows the difference e t between pure hadronic phases obtained from ¢r+ SHe and 0r-4He scattering separately. It is clear that no significant difference exists~ This indicates the vaIidity of charge symmetry in the energy interval considered at the present accuracy of the available experimental data~ We estimated the possiMe CSB effect in the v ~ 4 H e phase shifts due to the mass spli~ting of 2~3.~-resonances. For that purpose we calculated phase shifts of rr4He eiastic scattering in the framework of the CCE modal when the input rcN p~3-wave was slightly distorted to imitate the mass dif%rence of k33-resonances. For the imita.'.ion of/a~ 3 or k33 we siighfly shifted the parameters of the mass and width from the standard one° 264
7 August 1986
We have used the energy dependence of the P~3 phase shift from Rowe et aio [21], where the A-resonance parameters are as follows: m = 1233 MeV, i ' 0 = 116 MeV. For simuiation of the z~3+3+ W e ~sed m = !23i MeV, I ~ , = t 1 2 MeV, and for Af3 we used m = 1237 MeV, I}~ = t20 MeV~ This procedure did not distort the whole energy dependence of P.~3 phase sNftSo Deviation of the simulated P.~3 phase shifts from the standard ones does not exceed 1° for T ~ i00 MeV. i'~ is instructive that the calculations show that the difference in the P33-wave is amphfied in ~r 4He phase shifts. For example, at T = 75 MeV the difference between P33 phases is £~P~3 = 0"350" This indaces a twice as ~arge difference in "~r4He hadronic phases % =~(+~ ~,~ - ~(~,~ ~ in ';he P wave, The value of ~e is e e = 0.72 ° at T = 75 MeV. (]t is shown in fig° 2 by crosses.) It is also important to note that such an a.mp~ificadon of CSB rrN effects in pion-nuclear scattering must increase in the k 3 s e s o n a n c e energy region. So, precision measurements of elastic rr + and ~' scattering on a light nucleus are greatly appreciated, in principle, such a difference between hadronic phases may be detected in the PSA if the differentia1 cross sections of elastic scattering wiii be measured with I - 2 % precision. in conclusion, we have performed a simahaneous PSA of elastic rr + 4He and rr- 4He scattering with ailowanee for external Coulomb corrections. We have obtained quite a good description of the angular dependence of the asymmetry parameter A(8). No significant differences between pure hadronic phase shifts deduced separately from rr + 4He and rr SHe scattering have been found. ~t is atso shown that possible CSB effects in ~r N phases must be amplified in rrA phase shifts.
Re&fences [!1 [2I [3i {4I [5]
T.G. Masterson etal., Phys. Rev. C 26 (1982) 2091. T . G Masterson et al., Phys. Rev. C30 (1984) 2010. E. Pedroni et ai,, NucL Phys. A300 (1978) 321. B.M. Nee
Votume i75, number 3
PHYSICS LETTERS B
[7] J. ~-:rohlic~ et aL, Nucl. Phys. A435 (1985) 738. [8] K.M. Das and B.B. Deo, Phys. Rev. C26 (1982) 2ii. [9] M.D. Cooper, M.B. Johnson and GoB. West, Nucl. Phys. A292 (!977) 350. [t01 J. Fr~hlich et aL, J. Phys. 0 6 (1980) 84R [H t A Fr~h~icln et a~., Z. Phys. A302 (1981) 89. [12] J. Fr~3h}ich, H. Pilkuhn and H.G. Schiaiie, Phys. Le~.t. B12t (1983) 235. [I3} O. Dumbrajs et al., Phys. Rev. C29 (1984) 581. [14t M.Kg. Khankhasayev, Yad. Fiz. 36 (1982) 633. [t5} V.B. Belayaev and M.Kh. Khankhasayev, Phys. Left B~37 (t984) 299.
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[16I [17] [18} [19] [20]
E. Barrelet, Nuovo Cimento 8A (1972) 33I. M. Nordberg and K. 2~nsey, Phys. Left 20 (1966) 962. K. Crowe et al., Phys. Rev, 180 (1969) 1349. G. Fournier e~ aL, Nucl. Phys. A426 (1984) 54Z M. Albu et ak, preprin~ LNF-g2/27(R)(Fraseati, !982); Yu.A. Shcherbakov et aL, Nuovo Cimento 31A (i976) 249. [21] G. Rowe~ M. Salomon and R.H. Landm:, ?bys. Rev. CI8 (1978) 584.
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