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Can We See SPT Interactions in Coherent Pion Production.

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Snnalen der Physik. 7. Folgc, Rand 45, Heft 4, 1988, S.303-310
VEB J. A. Barth, Leipzig
Can We See SPT Interactions in Coherent Pion Production?
n. R E I N
IIT. Physikalisches Institut der Rheinisch-Westfalischen Technischen Hochschule, Aachen
A b s t r a c t . The possibility t o detect nonconventional scalar, pseudoscalar or tensor interactions
(SPT) in the angular distribution of pions produced coherently in neutrino nucleus reactions is reexamined. 1 t is found t h a t the angular distribution does not differ qualitatively from a corresponding
distribution arising from conventional VA interactions unless the energy of the outgoing pion is
restricted. Even then SPT interactions are likely t o be overshadowed by transverse VA interactions
which can mimic the former at finite although small momentum transfer Qz.
Uber den EinfluB von SPT-Wechselwirkungen auf den ProzeS
der kohgrenten Pionproduktion
I n h e l t s u b e r s i c h t . Es wird diskutiert, ob unkonventionelle skalare (S), pseudoskalare (P) oder
tensorielle (T) Wechselwirkungen in der Winkelverteilung von Pionen aus koharenten NeutrinoKern-StolJprozessen studiert werden konnen. Dabei zeigt sich, daB die Pion-Winkelverteilung in
eiriem solchen Balle nicht wet.entlich von der entsprecbenden Winkelverteilung der konventionellen
VA-Theorie verschieden ist, solange keine - einen SPT-Anteil begunstigenden - Einschrankungen
fur die Pionenergie bestehen. Selbst dann jedoch ersrheint die Entdeckung einer moglichen kleinen
SPT-Komponente unwahrscheinlich, da die neben den dominanten longitudinalen VA-Anteilen auch
vorhandenen transversalen VA-Komponentcn zii gleichen Formen der Winkelverteilung wie im
SPT-Falle fuhrcn.
The general current x current structure of weak interactions not only allows ,for
an effective V A behaviour of charged and neutral currents but also leaves room for
additional scalar (S),pseudoscalar ( P )or tensor ( T )interactions. Although such unconventional pieces are experimentally ruled out for charged current reactions the case is
not so clearcut in the neutral current sector, in particular if one encounters the possibility of more than one mediator of “neutral current” interactions. (One had of course
to go beyond the standard model with its single intermediate neutral vector boson 2,
in order to meet this situation.) The matter, however, is complicated by the so called
confusion theorem [ 11 which states that, given scale invariance, any y-distribution of
a n inclusive neutrino cross section compatible with V A is also compatible with SPT.
S o in order to escape the confusion theorem and to distinguish SPT interactions from
VA interactions one has t o look for exclusive reactions.
The obvious candidate for such an exclusive reaction, as pointed out by Lackner
[a] seemed t o be v-induced coherent no production off nuclear targets. Since the target
nucleus remains in its ground state it can neither change its internal quantum numbers
nor accept angular momentum transfer. Thus the neutrino helicity incident on the nucleus has to be carried off by the outgoing neutrino and pion. With the spinless pion
and no orbital angular momentum being involved in the parallel configuration (i.e. a t
304
Ann. Physik Leipzig 46 (1988) 4
Q2 = 0) this is possible if the interaction has VA character which preserves the neutrino's
helicity. I n the SPT case, however, the interaction forces the neutrino to flip its helicity
which means that forward pion emission will be prohibited. Looking therefore a t coherent no production in forward direction one expects distinctly different pion angular
distributions according to the different type of interaction.
Experimentally the exact forward pion production has zero weight. Fortunately,
for nuclear targets the coherence condition restricts the available Q2-domain so as to
filter out the interesting forward production process with high efficiency. Coherent pion
production has recently been established [ 31 in various neutrino experiments investigating neutral as well as charged current channels. The results are in agreement with
predictions [4] derived under the assumption of a VA structure of both charged and neutral current interactions. More precisely, invoking the conserved vector current (CVC)
and partially conserved axial vector current (PCAC) hypotheses it is essentially the
axial vector part of the VA interaction which is probed by coherent pion production a t
small angles. I n particular the pion angular distribution do/d cos 8, decreases monotonically, and in fact rather steeply, as expected on the basis of a dominant axial vector
current interaction. Nevertheless the question can be asked whether some admixture
of SPT interaction is still admitted which may show up with improved angular resolution. It is the purpose of the following note to discuss the coherent pion angular distribution with respect to this question putting emphasis on features directly accessible
to experiments.
To begin with let us recall the differential cross section formula [4] for inelastic
neutrino reactions as depicted in Fig. 1.
Xtp'l
Fig. 1. Inelastic neutrino-nucleus scattering
If the current has VA structure one obtains [2, 51
and the kinematical quantities
Q 2 = -a2 = -(k - k')'
=
2ME XZJ,
306
D. REIN,
Interactions in Coherent Pion Production ?
are chosen as usual. M is the nucleon mass and E the incident neutrino energy. Invoking
current polarisation vectors defined conventionally as
the cross section formula (1)is easily converted into
The helicity components of the lepton tensor
La, = ””
&9np& & 7
leaving
are conveniently used to pursue the limit Q2 = 0. It turns out that for coherent processes
where the nucleus can not absorb angular momentum the limit Q 2 + 0 requires only the
helicity zero components of the currents to contribute. I n this case ( 5 ) reduces to
Since
I,
= Q2-
2&
1-&
,
& =
(2E - v)’ - (Q2
( 2 E - v ) ~ (Q2
+
+ v’)
+ v2) ’
one finds immediately
With the aid of PCAC the hadronic cross section component o, can be calculated
explicitly
1
Q2a, = ,f2,
G Y ( W ) > ( f , = 0.93 & >
(10)
resulting in Adler’s famous cross section relation [6]
which laid ground to previous investigations on coherent pion production.
If the interaction has SPT structure instead of VA structure the differential cross
section can still be written in a form which parallels (5), namely [ 2 ]
306
Ann. Physik Leipzig 45 (1988) 4
+,
where now Lik and Zik(i,k =
-, 0 and s instead of d ) denote the leptonic and hadronic helicity tensors in the case of the SPT part of the interaction. The details need not
concern us here and may be found in Lackner's work (ref. [ 2 ] ) .The leptonic part of the
interaction, Lik, can be calculated directly, its vertex factor containing only the unit
matrix and combinations of Dirac matrices y5 and oyv. Again only those components
corresponding to zero helicity transfer do contribute in the limit Q2 + 0 which means
that we have
Inserting
, L , = Lao=4Q2
I-&
the anologon of (9) is easily found
L,
=
4Q2-
VE,
-
Lss= 4Q2,
+
The important point is now that Z, (Zo, Zs,)
and Z8,will be nonsingular a t Q 2 = 0
assuming [a] the hadron tensor for SPT interactions to be equally finite in this limit
as W::. Then, with no PCAC condition q%fW;&=+ 0 available - which gave rise to
the SPT cross section (15) is suppressed by a factor Q2 a t Q2 close to zero.
Our interest is in the angular distribution of pions produced coherently off nuclei.
Therefore we want to compare doSPT/dx dy d cos 8, with davA/dx dy d cos 8,. The
latter has been treated previously by L. M. Sehgal and the author [4]. The result may be
quoted, neglecting the small pion mass
The nucleon number is denoted by A , otZ,"? is the total no-nucleon cross section, r =
Ref,,(O)/Im f n N ( 0 ) corrects for the nondiffractive part of otot, the slope parameter b
of the nuclear form factor appearing in the arguments of the exponential and of the
Bessel function I, is given by 6 = 113 R2 with R representing the nuclear radius.
Extrapolation t o nonzero Q2-values is provided by a propagator term rn$/(mi
Q2)2
with m, chosen t o be 1GeV/c2. Pion absorption within the nucleus is accounted for by
an absorption factor Fa, = exp(-9A1/30inel/16 n R2) with oiine,
being the inelastic nN
cross section.
The angular distribution in case of a SPT interaction may be obtained along the
ZOs,
Z8,
and ZSs
to be similarly proportional t o a pionsame lines if one assumes Zoo,
nucleus forward scattering amplitude leaving open only a n unknown constant of pro-
+
307
D. REIX,Interactions in Coherent Pion Production ?
portionality [2], i.e. a n effective coupling constant qii (i,j = 0, s). This is not completely
unrealistic because the Regge parametrization, which we know to work quite well even
a t niotlerate energies (see e.g. ref. [4]), treats the pion nucleon cross section anyway
as a quantity only mildly dependent on y, and once the pion is created inside the nucleus
the niiclear environment does not care about its creation mechanism. Thus we expect
a sensible SPT angular distribution - u p to a n unknown scale factor - if we replace
the '"LAC"-factor (1 - y) = fvA(!y) in equ. (17) by Q 2 . f"z'T(y) where, according t o
( 1 5), fqfJ7'(y) can be either
p ( y ) = (2 - ?/)2, f?FrP'(y) = y(2
IVc have evaluated
0
u Y
z
--
y) or f?&T(y) = y2.
(18)
SPT 111
SPT I1
,A[Y
/--.YJl&p-
I
I
,
I
Fig. 3. Pion angular distribntion dald cos 0 2 b for $2,. = 7 GeV and AIz7target nucleus
a ) based on VA interaction
h-d) arising from SPT interactions using different kinematical factors fI(y),frr(y),frrI(~)(see text).
Clnrves corresponding t o y = E,/E, < 0.5 (>O.b) are dashed (dashed-dotted); solid lines refer to
the full y-interval
Ann. Physik Leipzig 45 (1988) 4
308
is a reasonable representative for any average target nucleus of previous neutrino
20)
experiments: neither Neon ( A = 20) nor Freon (A=30) or even marble
differ much from A12' in their effective nuclear mass number 2 (and anyway the A
dependence of coherent pion production is weak). The integration of (19) has been done
for a fixed neutrino energy E = 7 GeV corresponding roughly to the average energy of
neutrinos incident on the SKAT bubble chamber a t Serpukhov. The results are shown
in Pig. 2. Subsidiary information is given by Fig. 3 where a selection of VA and SPT
angular distributions is displayed for incident energies of 2 and 20 GeV.
(A=
I
I
VA
-
SPTI
0.99 0.97 0.95 0.93 0.91 0.99 0.97 0.95 093 0.91
E = 20 G eV
h
?ally
099
a98
cos en--
099
098
Fig. 3. Same as Fig. 2 (VA and SPT-I) but for incident energy E,, = 2 GeV (a-b) and 20 GcV (c- rl)
One remarkable feature immediately obvious from Figs. 2 and 3 is the monotonic
decrease of do/d cos O,, even in the case of SPT interactions. It is the property of nuclear
coherence, i.e. the strongly collimating effect of the nuclear form factor which forces
the pion angle to peak in forward direction. Only a t lower pion energies, say E , =
E y < E/2 or y < 112, the extra factor Q2 in the integral (19) can make its printmark
on the angular distribution - a t the expense of a strong reduction of the rate. Thus it
does not seem impossible a t first sight t o distinguish VA and SPT interactions by their
influence on the coherent pion angular distribution.
One must, however, be cautious in drawing ones ultimate conclusions. Away from
Q2 = 0 the condition that only helicitp zero components of the hadronic tensors G , ~ ,
ant1 Zik may contribute, no longer applies. Quite differently, a t Q2
0 also transverse
+
:HI9
D. RE", Interactions in Coherent Pion Production ?
vector and axial vector current components give their contributions. They, too, are
suppressed by a factor Q2 relative t o the leading PCAC part, but in comparison with
8PT terms they should not be overlooked.
Let us consider, for the sake of definiteness, the differential cross section for the transverse vector part of a VA interaction. This is given, in the vector dominance (V1)M)
approach (71, by
doVector
trails ( V N
-+
YJr/^TGO)
d x dy dQn,
where
E"
denotes the neutral current vector coupling constant and g,,
n 0 ) c- 1 do(yJr/^-+ f ino)
- doT(poJ + M
&o
dQn,
4na
dQ,
the right hand side being parameterized according to [S]
is determined
(21)
d ' ( ~ J r / ^-+ Jtr7c0) = ~ 2 ~7( ysin2
) 8, I ~~t (0,) 12,
dQ,
with the help of some factors including the nuclear form factor PM(en)already implicit
i n (17). The quantity C(y)varies roughly as y2, a t least for small y. The pion angular
distribution, extracted therefrom, reads
dovector
trans
-
G2ME A2v
sin2 0, J dx dy y2Q2[ 1
47La
-p-- 2 n 2
d cos 13,
+ (1- y)2]
( z = cos e,).
Apparently this form resembles closely the expression (17), apart from the replacement
of the PCAC-factor (1 - y) by Q2[l
( I - Y ) ~ ] . Just such a replacement, however,
has been required for a VA interaction away from Q2 = 0. (The correspondence would
almost be perfect if the relations Zoo=
and ,Yso ,Yo, = 0 happened to hold.)
This means, the shape of an SPT-induced pion angular distribution is not principally
different from the shape of the angular distribution originating from the transverse vector part of conventional VA interaction, and this holds independently of any y-cut.
The transverse vector contribution t o coherent pion production processes is of course
only a small correction, a few percent compared to the leading PCAC term. This is
mainly due t o the suppression factor Q2 - and even further suppression would occur
if' cuts in y were imposed. But a similar suppression applies also to the presumptive
+
+
310
Ann. Physik Leipzig 45 (1988) 4
SPT contributions which therefore should be buried among VA background terms (from
transverse current components) unless their couplings are unduely large. This, however,
is unlikely granting the impressive successes of the standard model of electroweali interactions [9].
Away from Q2 = 0 still other SPT helicitp components Zll, Zol,2-11etc. maj7 also
contribute - if they exist. They are, however, not expected to change the main conclusions phrased in the following way:
(i) The shape of coherent pion angular distribution is not sensitive to admixtures of
SPT interactions as long as no cut on the pion energy is applied.
(ii) The leading SPT contribution, on grounds of helicity conservation suppressed by a
factor Q 2 relative to the leading VA (in fact longitudinal axial vector-) contribution,
have t o compete with the nonleading - transverse - VA contributions producing
essentially the same shape of the angular distribution. Consequently neutrino-induced no-production does not seem to be suitable for pursuing SPT interactions - if
they exist a t all.
This note grew out of simulating questions of experimental colleagues a t BerlinZeuthen, in particular of R. Nahnhauer whom I want to thank. Likewise I am grateful
to L. M. Sehgal a t Aachen for illuminating remarks on the subject and to the German
Bundesministerium fur Forschung und Technologie for support.
References
[I] KAYSER,
B.; GARVEY,
G. T.; FISHBACH,
E.; ROSEN,S. P.: Phys. Lett. 52 B (1974) 38.5; KINGSLEY, R. I,.; WILCZEK,
F.; ZEE, A.: Phys. Rev. D 10 (1974) 2216.
[2] LACKNER,
K. S.: Nucl. Phys. B 163 (1979) 505, 527.
[3] FAISSNBR,
H. e t al.: Phys. Lett. 126 R (1983) 230; ISIKSAL,
E.; REIN,
D.; MORFIN,J.: Phys. Rev.
Lett. 52 (1984) 1006; BERGSMB,
F. et al.: Phys. Lett. 157 R (198,j) 469; RIARAGE, P. et al.: phys.
Lett. 140R (1984) 137; GRABOSCH,
H. J. et al.; Z. Phys. C. 31 (1986) 203.
[4] REIN,D.; SEHGAL,
L. M.: pu’ucl. Phys. I3 223 (1983) 29.
[6] NACHTMANN,
0.:
In: Textbook on Elementary Particle Physics - Weak Interactions (Ed. by
M. K. GAILLARLIand M. NIKOLIC)(Basko Polje Lectures 1077), Paris 1977.
[GI ADLER,8. L.: Phys. Rev. R 135 (1964) 963.
[7] PIKETTY,C.; STODOLSKY,
L.: Nurl. Phys. R 16 (1070) 571.
[81 BELLETINI,
C. et a].: Nuovo Cim. 66 A (1970) “13.
[9] see e.g. RunnrA, C.: Nobel Lecture 1984, Rev. Mod. Phys. 57 (1983) 6%.
Bei der Redaktion cingegangen am 20. Juli 1986.
Anschr. d. Verf.: Dr. I). REIN
111. Physikalisches Institut
der Rheinisch-Westfalischen Tcchnisclien
Horhschule
D-6100 Aachen
Physikzentrum
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