1/m<sub>c</sub> Terms in lambda<sup>+</sup><sub>c</sub> Semileptonic Decays Page: 3 of 6
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In addition, spin symmetry allows us to relate the form factors for C = 7, to
those for C = ygy,, with the result that the electroweak transition current is
purely left handed at the baryon level. Note that in contrast to the case when
both hadrons are heavy, we do not know the normalization of either of these form
factors. Nevertheless, in terms of these form factors we find that
fr = gi =Fi Fr, fz = -92 = -f3 = 93 = F. , (8)
so that GA = -Gy, regardless of the unknown normalisations of Fr and F2.
In addition, if we assume that the amplitude for the decay A+ -. Art+ fac-
torises, we may write it as
M +-- = froap)(A+ iBs)u(v), (9)
A = Fl(mAn - mA) + FJ(mA. + mA - 2EA)
8 = Ft(m + m nA) - F_(mn+ - mA - 24).
In terms of these, we Find that
-J AB P
(En + mA)A - (En - mA)B
D (En + ma)A + (En - mA)B8.
value of r = F/Fr. The complete picture reveals itself when one looks at tir
full forms for A and B, eqn. (10). Then we see that A and B have district
series, occuring at Ft(mn+ - mA) A -F,(mat + mA - 2E:), F(mA: + mA) _
F2(mA. -ma-2EA), respectively. This means that there are two possible seroes
in a, both occuring at values of r = F,/Fr very close to -mn+ /mA. The effect
of these heroes on a and y is shown in fig. 1. Thus, given a curious accident in
the ratio r, oue could, in principle, obtain any value for a For these decays. It is
perhaps somewhat fortituous that the measured values are close to the originally
predicted values. On the other hand, the range of values of r within which one
could obtain a value of a significantly different from - I is so snall, that one would
have to have been extremely unlucky for this prediction not to have worked.
What this means is that for other heavy -- light transitions, such as At -"
nat+ and As -+ pan, one can obtain any value of a, but a -1 would occur for all
but a very narrow range of values of the ratio r. Put another way, a measurement
of a much different from -- I for any of these decays would give a very precise
handle on the ratio r, provided that one believes that the factorisation assumption
is valid, and that the leading order terms in the HQET expansion are sufficient
for description of the decay.
l[l. g CORRECTIONS
In the notation of ref. [4, the order l/mr part of the heavy quark Lagrangian
SI 2m h f[DP(9v - uMu)D" + - -""F,, fhtc
If we ignore the pion's mass, we obtain
"*tf - "(
mA + m(
giving automatically a = - I, y = 0, c
sizes of the form factors Ft and F . lien
heavy -. light transitions, such as At -
Eperimentally measured values appear
howeverr, from egu. (12), note that
of the relative
be valid for all
Yen A6 -. p-".
es at F3/F, =
t, .thuigih tihe vtiues of both a r--- , -. --..amainate at this
where the coefficients of the various terms are obtained from tree-level matching
to the full QCD Lagrangian. In addition, tree-level matching of the local operator
Ch; to order 1/m, leads to
ih -- f - 2t rtI) 14. (14)
We thus have many possible additional contibutious to this order. We begin by
examining the local term
_ _ A
- i < A(p)jl't D 1h; IAt >= r(p)(ni + $aJ)'u(')M5. (15}
where Ms is the most general vector that can be constructed, and we have
absorbed factors of 1/m. into the dlfinitjons of the form factors at and ui.. t'
may be expressed in terms o[ two for m factors as
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Roberts, Winston. 1/m<sub>c</sub> Terms in lambda<sup>+</sup><sub>c</sub> Semileptonic Decays, article, February 1, 1992; [Newport News, Virginia]. (https://digital.library.unt.edu/ark:/67531/metadc931989/m1/3/: accessed August 14, 2020), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.