This paper reviews the current status of experimental measurements of
radiative kaon decays. Several experiments at BNL, CERN and FNAL have recently
or will soon complete data collection; as a result, several new results are
available.Comment: 11 pages, 2 figures, LaTeX, presented at the 3rd Workshop on Physics
  and Detectors for Dafne, Frascati, Italy, November 16-19, 199

Kettell, S.

English

arXiv

This paper reviews the current status of experimental results on radiative kaon decays. Several experiments at BNL, CERN and FNAL have recently or will soon complete data collection; as a result, there are several new results

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67140hep-ex/yymmnnnJanuary 6, 2000EXPERIMENTAL RESULTS ON RADIATIVE KAONDECAYSS. KettellBrookhaven National Laboratory( PHYSICS AND DETECTORS FOR DA@NE - Fh.scati, Nov. 16-19,1999Fh3cati Pbysic3 Sene9 Vol. XVI, 2000 )ABSTRACTThis paper reviews the current status of experimental results onradiative kaon decays. Several txpenments at BNL, CERN andFNAL have recently or will soon complete data colk!ction; as aresult, there are several new results.1 IntrodcutionRadiative kaon decays provide a testing ground for Chid Pertur-bation Theory (ChPT). ChPT provides a framework for calculat-ing the decay rates for several modes, either directly or relative-?$-“T-”””-””””::,...to other measured modes. The radiative modes are important fordetermining long distance contributions to other &cays of inter-est: the tw~photon contribution to & + p+p–, and the CP-conserving and indirect CP-violating contributions to K; + zOe+e-0 + – They are a!so important as backgrounds to oth-andK~+x p p .er modes (e.g. the K;+ e+e-yy background to K;+ r“e+e–).A number of recent results have been reported in the literature,as well as in several recent conferences 1––6).2 Radiative Kfl DecaysThe radiative K.z decays: K++ 7r+7r”7,K;+ x+7r-7 and K;+T+r-y have two contributions. One is inner bremsstrahlung (IB)radiation from one of the charged particles. The second is directemission (DE) horn the vertex. The branching ratio of the IBcontribution scales with the underlying Kr2 decay rate. Whereas,the rate for direct emission is expected to be roughly comparablefor all three modes.A new result 7, for K~ + 7r+7r-~ from ‘KTe-V-is shown inFig. 1. The ener~ of the photon is shown, along with the con-tributions from IB and DE. The DE component is modified by”a--v *996 u&— --4—--7-g ~: G1 L .+ A*00- Oe<eI~ ::: kE ‘*-+ ‘-:5Z:L’ Izso2001 50 [~ Im00so1 J-0 0.0== 0.OD 0-07= 0.1 O.-lz= O-*B O--a/s 0-=7 e-o --- <=0->Figure 1: Photon enerugywith jit to IB and DE (with p propagator)from KTe V.“propagator” that serves to soften the DE spectrum. The branch-ing ratio for the direct emission component (see eq.1) isBR(K~~7r+7r-7; DE) = (3.70& 0.10) x 10-5(E~ > 20MeV) (1)The ratio of direct emission to DE+IB is (see eq.2)DE/(DE -I-IB) = 0.685 ~ 0.009 * 0.017 (2)This result is based on IU5%of the total KTeV data for this mode.There are new results from E7878, in the charged decay mode(K+ ~x+n”~) as well. ‘This result is striking, in that the branchingratio is a factor of 4 lcwer than the previous vaiue. The data istraditionally expressed in terms of the variable W, which is definedas:W2 = (p” q)~m~+ x (p+” q)/mg+ (3)= E; x (E.+ – Pm+x cos 6.+ ~)/(rn~+ x m:+)The new result from E787, shown in Figure 2, has about 8 timesFigure 2: (left) W spdrum of the signal events and best fits toIB+DE [solid curve] and IB alone [dashed curve]; (right) W spec-trum normalized to the IB spectrum.higherstatistics than the old one. The branching ratio for the directemission component, horn a fit to IB and DE (see eq.4) isBR(K++7r+7r07; DE) = (4.72& 0.77) x 10-6 (55 <TW+< 90MeV)(4)This represents half of the E787 data that is currently on tape. Theinterference term is small, (—0.44Z1.6)% and the direct emission is(1.85 t 0.30)%. The decay rate, corrected to full phase space’, isnow measured to be similar to that for KL: I’(K+ ~7r+7r07; DE) =808 & 132s-1 vs. I’(&+n+n-~; DE) = 617A 18s-1.KTeV also has new results on K; + x+n--e+e-, where thephoton has internally converted to two electrons. In addition to‘), a T-odd observable in the augularmesxxn-ingthe branching ratiodistribution of the plane of the r-pair vs. the plane of the electronpair is observed 10). This data represents one quarter of. the finalKTeV sample.A summary of the current experimental status of radiative K=2decays is shown in Table 1.Table 1: Summary of Radiative Kxz results.Decay Mode Branching Ratio CitationK;+ 7r+7r-7(DE) (3.70 & 0.10) x 10-5 KTeV-99 7,K++ T+TO-Y(DE) (4.72 & 0.77) X 10-6 E787-998,K~ + r+n–e+e- (3.63 5 .11& .14)X 10-7 KTeV-99 ‘)K;+ n0T07 <5.6 X 10–6 NA31-94 11)K:~7r+7r-7 (1.78 * 0.05) X 10-3 E731-93 12)I T~ ~~ion ~umes that the form factor has no mew depend-e.3 K+ 7r77 DecaysThe decay & - 7r077 is very interesting, since to 0@4) of Ch-PT the decay rate and spectral shape are completely determined,14). The prediction of the spectralwithout any free parametersshape is a striking success of ChPT; however, the decay rate is afactor of 3 too small. To match the experimental number a mod-el depe~dent contribution horn 0(p6) is needed, which is usually15). The CP-conserving con-parameterized with a constant avtnbution to K; ~ rOe’+e– depends on the value of av. Basedon half of the total da,ta sample, KTeV has recently measuredav = –0.72*0.05&0.06 16), implying a contribution of 1–2x 10-12.The charged mode K+ ~ 7r+77Jis more complicated, requiringan unknown parameter, t, even at 0(p4). Both the decay rate andspectral shape are predicted with this single parameter. E787 hasmeasured 2 = 1.8 * 0.6 17).The experimental measurements of K + 7r77 are summarizedin Table 2. The KTeV measurement of K; ~ x“e+e–~ shouldimprove by x 3; the meas&ements of K; -+ m“~l– are backgroundlimited, and will improve by W.4 KO to Two Real or Off-shell PhotonsThe decay & ~ 77 is predicted in 0@4) of ChPT, without anyhe parameters, to occumwith BR(& ~ 77) = 2.0 x 10-6 14). Thisis in good agreement with the ~erimental value 25) (see Table 3),although the experimental errors need to be reduced.The decay Ki ~ 77 is of interest for its importance in inter-preting the measurement of& ~ P+P-. The decay K;+ P+P- issensitive to internal top quark loops, that would allow a determi-Table2: Summa.~of K+~y7 resulti.‘ Decay Mode Branching Ratio CitationK;. + 7r0’y7 [1.68 & 0.07& 0.08)X 10-6 KT’eJ/-99 16)K++ 7r+77 (6.0 & 1.5* 0.7)X 10-7 E787-97 17)~%+~077 no limit (N~&02?)K~,~7r0e+e- <5.6 X 10–10 KTeV-99 18)I W+n”u+fl- !1<3.4 x 10-10 I KTeV-99 19) IK++7r+e+e- (2.94 * 0.05& 0.13)X 1C:7 E865-99 20)K++~+/L+p- (9.22 & 0.60& 0.49)X 10-8 E865-99 21)& ~ 7r0e+e– <1.1 x 10-6 NA31-93 22)K~+nOe+e-7 (2.20 & 0.48& 0.11)X 10-8 KTeV-99 23)K+ ~ ~+e+e-7 w30 events E865-99 24)riation of the fundamental SM parameter p. The decay is, “however,dominated by the decay K;+ ~~ with the photons converting toa p+ pair. For this reason a precise measure of K;+ 77 is need-ed. With the improved prectilon on K;+ p+p- horn E871, theW+”%’uncertainties on K; + 77 and ~~~+%. are now contributing sig-nificantly 26 – ’28) to the uncertainty on the ratior(K; + /.L+/L-)[B(K; + /J+/J-)r(K; +77) = 1B(K;+7r+7r”)x (5)[q+- B(K~+n+r-) 1[xB(K: +z”T”)%0 B(K; +x”x”) l?(K~ -+77) 1[1.55% ][(0.23%)(1.28%)][1.42%]= (1.213* 0.030)X 10-5KLOE should be able to contribute to improving both of these mea-surements. Finally there is a long distance dispersive contribution,from two off-shell photcms, for which additional input from ChPTand measurements of”the decays Ki ~ e+e–-y, K; a p+p– e+e– andK; ~e+e-e+e- are needed 29).Results of kaon decays to two real or off-shell photons are sum-nmrized in Table 3. The KTeV measurements of & —}e+e–e+e–Table 3: Summary of results of decays to two photons.rDecay Mode Branching Ratio CitationF&+ ‘y’y (2.4 + 0.9) x 10-6 NA31-95 25)I K;,+-y~ II (5.92* 0.15) X 10-4EK;+ p+p- (7.24 + ().17)x 10-9K;+ e+e- 8.7tj:; X 10-12K; + e+e-7 (1.C16&.023z.02 &.04)X 10-5K~-+p+/J-7 (3.:23* 0.23* 0.19)x 1o-TK;, + e+e–e+e– (4.:14* 0.27 =t 0.31) X J.0-8%%%=3E871-98 30NA48-99 31E79!3-9532KTeV-98 3BK;+ e+e-p+p- ~40 events ! KTeV-99 ‘~K; +p+p-p+p- no limitK;+ p+p- < 3.2x 10-7 CERN-73 35)K:+ e+e- <1..4 x 10–7 CPLEAR 36)K~,+ e+e-~~ (6.:31& 0.14& 0.42) X 10-7 KTeV_99 37). . , 1K; +p+/.J-77 II(1.42t& + 0.14) i 10-9 ~KTeV-99 38)and K;+ p+p-e+e– should improve by x4 and the modes K; +e+e–y7 and K; + p+p-77 should improve by x 3 with the finalKTeV data set. The K; ~ e+e-v should improve by x20 andK~ + p+p-7 should improve by x30. The Ks modes may beimproved by NA48 in a,special run, after d/c. The K; -+77 andK;+ 77 as well as several other modes will be improved by KLOE.There is no improvement in the forseeable future for Kg ~ e+e– orK;+ p+p-.5 Radiative Kn DecaysThe form factors in the decays K++ /+vg7, A and V, and, R, inthe decays K++ /+v&’+/’–, are predicted by ChPT. Recent mea-surements should allow precise experimental determinations of allthree parameters. The most recent determination of l~v + ~’ [ =0.165 & 0.007 & 0.011 horn the E787 measurement of the direc-t emission component of K+ ~ p+v7, ususally called StructureDependent (SD+) radiation, is consistent with the previous deter--:-.+:-- -r 1P-- J D I nlAf2Lnnln L.- 77+ \ -+. 4A, A 1;-;+AUIUaIJIUUL [Iv T I’AI= u.L-tu-1-U.UJ. U lIUMJ Al 7G V~. - ZULUIJof –0.25 < Fv – ~A <0.07 is derived from the K++ p+v~(Sl?+).An improved messure of Fv – ~A along with a measure OfR *oulda.. -.-:1 .1.1- ---- a-— moecUfs dvauaule auuLl 11 UMI J.2oud.A summary of the recent radiative K@ results is presented inTable 4.Table 4: %mrnary of Radiative Ka nxults.Decay Mode Branching Ratio CitationK+ -+ p+zq (5.50 * 0.28)X 10-3 KEK-85 39)~q+J ..+. .={nm-P v 1(~~)[1 2QL 10L lQ\”ln–5(’”’J’J L “’a A “’u] A ‘w~~~~.g~ 40)K++ e+zq(DE) (1.52 & 0.23) X 10-5 CERN-79 41)K++ #.L+V/$+~- <4.1 x 10–7 E787-89 42)I -.,I K“ + e+vu+b- ii <5.0 x 10-7I — ---- /421I E787-98 ‘“~ i6 Other Radiative Kaon DecaysThe experimental sensitivity for the other radiative kaon decaysK.fi, KW and ~~ are such as to only be sensitive to IB contn-butions. All of these measurements are consistent with theoreticalpredictions. A summary of the results is given in Table 5.Table 5: Summary of Radiative 3- and d-body decays.Decay Mode Branching Ratio CitationK++r+r+r-~ (1.04h 0.31) x 10-4 ITEP-89 45)K– + 7r-7r07r07 ~(7.53::) x 10-6 IHEP-95 46)K++ TO/J+Vp~ <6.1 X 10–5 ZGS-73 47)K;+ mpVPY (5.P$$) x 10-4 NA48-98 48)K+ -+~”e+v.-y ~(2.62 ~ 0.20) x 10-4 ITEP-91 ‘!9)K;+ rev.y (3.62~~) X 10-4 NA31-96 50).*K++ n“z”e+v,=y <5 x 10–6 ITEP-92 51)K++ n+fi-e+ve7 ~no limit (E86$97?)A couple of modes should be seen for the first time in existingdata, K++ 7r0p+vP7 (E787) and K++ r+x-e+v.7 (E865). Imp-rovements in other modes may be poss~bie, particularly at 1HJ5F.-----7 ConclusionsSeveral new results are expected from KTeV and NA48, as well asa few more horn E787,E865 and E871. With the turn on of Da@nesm~ KT.(31? which ic mall mninnwl f~~ tho radiativ~ mnck, we—- -.---, ..-. — . . . . . . . ..l-==. - .-. .—. -.. . . .- .-—can expect another round of new measurements. 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Eperimental Results on Radiative Kaon Decays

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