Relating D0-anti-D0 Mixing and D0 -> l l- with New Physics Page: 4 of 25
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degrees of freedom associated with new interactions at a heavy scale M, we obtain an
effective hamiltonian written in the form of a series of operators of increasing dimension.
Here, we restrict our attention to the leading order operators, of dimension D = 6. For both
D - D0 mixing and D0 -> f+f- decays, the complete basis of effective operators is known
and is expressed most conveniently in terms of chiral quark fields,
(f 'HNP I1) = G Ci(p) (f lQzIl)(p) ,(3)
where the prefactor G has the dimension of inverse-squared mass, the C are dimensionless
Wilson coefficients, and the QZ are the effective operators of dimension six. Throughout, our
convention for defining chiral projections for a field q(x) will be qL,R(x) (1 + 'y5)q(x)/2.
For AC = 2 processes, there are eight effective operators that can contribute [14, 21],
61 = (TL2PCL) (TIL2"CL) , 65= (rRovCL) (rRPv CL)
Q2 = (rL2'pCL) (rR2"CR) , Q6 = (rzR2CR) (uR CR (4)
Q3 = (LCR) (RCL) , Q7 = (rLCR) (LCR) ,
64 = (uRCL) (TRCL) , 8= (TLo7vCR) (TLa7 vCR)
These operators are generated at the scale M where the NP is integrated out. A non-trivial
operator mixing then occurs via renormalization group running of these operators between
the heavy scale M and the light scale at which hadronic matrix elements are computed.
All possible NP contributions to c - f+f- can be similarly summarized. In this case,
however, there are now ten operators,
Q1 = (TL2ptL) (TIL2"CL) , 4= (CRL) (TRCL)
Q2 = (TL2ptL) (rR2"CR) , Q5 = (tRaJL) (TIRUPUCL) , (5)
Q3 = (CLCR) (RCL)
with five additional operators 06, ..., Q'o being obtained respectively from those in Eq. (5)
by the substitutions L -> R and R -> L. The corresponding Wilson coefficients will be
denoted as Ci(p). It is worth noting that only eight operators contribute to Do -> +t, as
(V+t --Q5D0) = (i+t Q10D0) = 0.
To obtain a general expression for XD as implied by the effective Hamiltonian of Eq. (3),
we evaluate the D0-to-D0 matrix element in the modified vacuum saturation approximation
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Golowich, Eugene; /Massachusetts U., Amherst; Hewett, JoAnne; /SLAC; Pakvasa, Sandip; U., /Hawaii et al. Relating D0-anti-D0 Mixing and D0 -> l l- with New Physics, article, March 31, 2009; United States. (https://digital.library.unt.edu/ark:/67531/metadc925940/m1/4/: accessed April 22, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.