Beutrino Interactions - an Experimental Surrey
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Beutrino Interactions - an Experimental Surrey S. SanerJee lata Institute of Fundamental Research, Bombay 1. Introduction In the past few, years, enormous progress has been made in experimental V physics. With new results coming in from the SPS and the Serpukhov machines in addition to the Fermilab X facility, the studies have produced breakthroughs in a number o f f ie ld s . Before going to the results let me mention a few points on the precisions in these measurements. The CERH SPS and the Fermilab groups now u se a dichrom atic narrowband beam In addition to the wideband beams. The purity of the beams has gone up; th e wrong type X con tent ( P in V beam or V in V beam) is typically 2-32 and Vfi( Ve) contaminations are 1-2/. Furthermore the beam energy is fairly well, determined from the d ista n ce o f th e in ter a c tio n v ertex from a cen tra l beam a x is (for V 's from K decays, the uncertainity in this determination is •>» &X). The narrow band beam spectrum is much broader than the wide band spectrum and consequently the average beam energy is higher 75 GeV c f <B>TO «v 30 GeV). However th e fluxes are reduced by an order of magnitude. The V -fluxes are determined by various techniques. The uncertainity in the absolute flux determination is 7? for V 's from n-decays and is 10-122 for V 's from E-decays. The detector systems used in the measurements can be broadly divided into two classes, the large bubble chambers and the electronic counter setups using huge hadron calorimeters and fx-spectrometers. The main features of these two detectors are summarised in table 1.1. The detector configuration in the * - 171- SPS beam line is shown in fig. 1.1. The kinematic variables used in the- subsequent sections are defined in figure 1.2. B = energy of the incoming V B = energy of the leading outgoing lepton {ji in th e case of charged.current interactions) V = E-E = energy transferred to the hadronic system q * 4—momentum transfer - at the leptonic vertex 2 2 Q = -q = mass squared of the off-shell VtUboson 'V A. y - B 9 0 dimensionless scaling variablfes _ Q2 X ' x M = nucleonic mass 2. Charged Current Interaction - Most of the recent results in charged current interaction come from deep inelastic scattering of with a nucleon target, i • 6# VN - p ~ jl . _ ■ + - 2.1 V N -* y. x There are also some new results in exclusive studies like quasi elastic process, single pion production etc. 2.1. Exclusive Studies A. Quasi elastic channel: Data on quasi elastic channels V n - u“p and V p - u+n have been used to study the axial vector r P ' form factor. All the analyses £2.13. assume CVC and dipole form factor for the vector component with = 0.84 GeV/c2. The axial - 72 coupling was taken to be 1.25' (froin p decay) and the axial form factor was also assumed to'be of dipole type. The: results'are summarised in figure 2.1. The reaction, v p--* ,A++ was also studied £2.2j in the frame work of Adler Model £2.3}. The value o f Ma is converging to a value slightly higher than M^. One should note that the current value of the coupling constant is slightly higher than ,1.23 and the dipole form of the vector component is known only within at low Q2 (even worse at large Q2). " . B. One nion prr-duction; The ANL groups £2.4] has studied single pion. production in deuterium from threshold to E = 15 GeV. The reactions looked at are V p - p~p 7t+ y n - ^"*n n + 2 .2 Vn - ^i-p n° All three final states show strong £ -production suggesting a dominant isovector current. The analysis leads that the inter ference of the I = 1/2 (A1) and.the I = 3/2 (A^) components is needed to explain the data. However the data are consistent with a zero isotensor component. Assuming a zero isotensor current | A. I they obtained | - 0.57+0.06 and the relative phase 0 = 89.2+8.7 degrees. _ 2.2 Inclusive Studies- In a *V-A theory,- the differential, cross- section can be written in the absence of AS / 0 and AC- / 0 c u r r e n t as where P^' s are the nucleonic structure, functions. The relation is very similar to that in. the deep inelastic scattering of e or jx with nucleons. The extra term F^ comes from V-A interference and it changes sign from to V . At high energy one neglects M . " ^ terms and rev/rites 2.3 as ■ „ * „ e <&*> - — RV& a‘> * FLV:1,cx,eL) v There are several simplifying ideas involved in the analysis of the data.- The most important-ones'are listed below (1) Charge Symmetry: For inclusive processes, this leads (for. h S = 0,Zk c = 0 c u r r e n t) F / P = F ^ n and F .5 ? = F^v n - 2 .5 ■ For isoscalar target this is simply ?? = F ^ • (2) Callan-Gross relation: Assuming th i spin-structure of the constituents, this relation gives 2xF1 .= F2 2.6 These two relations simplify 2.3 as d ^ VlV a V it d x d > - ~TT Ck {1+ a - » zj F^><iL) 411 - a -y /j iffe,a1-)] 2, ? ^ 74 - \ In quark-parton model, the structure functiofi are related to the' parton distribution functions. (F2J^F^) gives the scatter ing of V on -quark (or V on q). ^(FgTxF^H 1-y)2 gives'the . scattering of V on q (or i> on q). F2(x,Q2) signifies the momentum distribution of all quarks and antiquarks in the nucleon and xF^(x,Q2) Signifies the momentum distribution of the valence q u a rk s . Thus ^ ==5S [Q(X,Q2, *5U,Q2)(1-y)2:l ^ - 5 ^ I8(i,a2)«X«.ii2)(i-7)2J. One other important notion Is the Bjorken scaling. This 2 V states that in the lim it of E — °°, Q — 00 and —* — finite, the . Q hadronic structure functions are only functions of x. The scaling leads that the total V (orP) cross section on nucleons would have a linear energy dependence like the V -lepton scattering. Now reverting to the experimental data, one can broadly classify the results into two categories (1) integrated quantities (e.g. total cross section,<Q2> etc.), (2) differential distribu tions (e.g. x,y distributibn). A. Total cross-section: New data [2.5] come from (1 ) SPS narrow b an d beam ex p e rim e n ts (2 0 -1 9 0 GeV) by CBHS and BE3C, (2 ) FNAL narrow band beam ex p erim en t (2 0 -1 9 0 GeV) by CITiFR, ( 3 ) Serpukhov wideband beam experiment (8-30 GeV) by SKAT and IHEP-ITEP, (4) AN! 12' bubble chamber experiment. The D-data (fig .2.3) siqgsst a constant slope ((T/E) over the entire energy region. BEBC and CITFR data may suggest a slight increase above E = 80 GeV. The - 75 y-data at energy above 50 GeV have a constant slope. But lo.wer energy data indicate a decrease in slope, from 10 to 50 GeV. Fig. 2.4 shows the ratio of v to V cross section as a function of energy. The HPWP points show a systematic increase with, energy which is present on a much reduced scale in BEBC and CITFR data whereas it. is absent in the CDHS data. This discrepancy could be due to the different acceptance cuts in the different experi ments and the model dependent corrections to take into .account this effect. Gargamelle propane group (PS energies) and FNAL Michigan group (j2.6j studied the ratio ^ for P'~ At energies below one pion threshold, this ratio should be zero. Valence quark contri- bution.leads to a value 1/2. Correction from sea shifts the ratio to 0.6. It is difficult to'choose between the two with the present data (fig.2,2). B. Mean Squared Momentum; <Q^>/E data (fig .2.5) show a fall-o ff with energy upto E = 50 GeV. Above 50 GeV,'' the variation is rather small. 0 . Mean y -V a lu e : The mean y -v a lu e <y> has "oeen shown as a fu n c tio n of energy on fig .2.6. v-data show no energy dependence. For v , the CITFR data show a 10/ increase from low to high, energies whereas the CDHS data have no -energy dependence. It is to be noted that the old HPWF data showed, a substantially larger energy dependence. This discrepancy could be attributed to the acceptance problems in the various detectors. Shape parameter B: Experimental situation of B is rather complex since various groups employ different approaches in extracting - 76 - th is parameter aiid the value depends on the method _employed. The ,~.v,v - CDHS group [~2.7] has filled the y-distribution ^ -------1-( 17-BV’ )y *(1+B^,5 )y^ assuming a constant B. The BEBC collaboration /x F * d x v obtains B = jygg- = ' ~ i • This method takes into account 2 6" ^ ^ y-dependence of B but assumes B = B (i.e. charge symmetry). The CITFR group [2.83 fits both zero and first moments of y to obtain B. The data are shown on.figure 2.7 for V .