93 research outputs found
Tree-level contribution to \bar{B} -> X_d gamma using fragmentation functions
We evaluate the most important tree-level contributions connected with the
b-> u \bar{u} d gamma transition to the inclusive radiative decay \bar{B}-> X_d
gamma using fragmentation functions. In this framework the singularities
arising from collinear photon emission from the light quarks (u, \bar{u} and d)
can be absorbed into the (bare) quark-to-photon fragmentation function. We use
as input the fragmentation function extracted by the ALEPH group from the
two-jet cross section measured at LEP, where one of the jets is required to
contain a photon. To get the quark-to-photon fragmentation function at the
fragmentation scale \mu_F \sim m_b, we use the evolution equation, which we
solve numerically. We then calculate the (integrated) photon energy spectrum
for b-> u \bar{u} d gamma related to the operators P^u_{1,2}. For comparison,
we also give the corresponding results when using nonzero (constituent) masses
for the light quarks.Comment: 13 pages, 4 figure
Towards next-to-next-to-leading-log accuracy for the width difference in the system: fermionic contributions to order and
We calculate a class of three-loop Feynman diagrams which contribute to the
next-to-next-to-leading logarithmic approximation for the width difference
in the system. The considered diagrams
contain a closed fermion loop in a gluon propagator and constitute the order
, where is the number of light quarks. Our results entail
a considerable correction in that order, if is expressed in
terms of the pole mass of the bottom quark. If the scheme is
used instead, the correction is much smaller. As a result, we find a decrease
of the scheme dependence. Our result also indicates that the usually quoted
value of the NLO renormalization scale dependence underestimates the
perturbative error.Comment: We corrected a typographical mistake in Eq. (4.18), made larger axis
labels in Fig.2. Version accepted by JHE
NLL QCD contribution of the electromagnetic dipole operator to B -> X_s gamma gamma with a massive strange quark
We calculate the O(alpha_s) corrections to the double differential decay
width dGamma_{77}/(ds_1 ds_2) for the process B -> X_s gamma gamma originating
from diagrams involving the electromagnetic dipole operator O_7. The
kinematical variables s_1 and s_2 are defined as s_i=(p_b - q_i)^2/m_b^2, where
p_b, q_1, q_2 are the momenta of b-quark and two photons. We introduce a
nonzero mass m_s for the strange quark to regulate configurations where the
gluon or one of the photons become collinear with the strange quark and retain
terms which are logarithmic in m_s, while discarding terms which go to zero in
the limit m_s -> 0. When combining virtual- and bremsstrahlung corrections, the
infrared and collinear singularities induced by soft and/or collinear gluons
drop out. By our cuts the photons do not become soft, but one of them can
become collinear with the strange quark. This implies that in the final result
a single logarithms of m_s survives. In principle the configurations with
collinear photon emission could be treated using fragmentation functions. In a
related work we found that similar results can be obtained when simply
interpreting m_s appearing in the final result as a constituent mass. We do so
in the present paper and vary m_s between 400 MeV and 600 MeV in the numerics.
This work extends a previous paper of us, where only the leading power terms
w.r.t. the (normalized) hadronic mass s_3=(p_b-q_1-q_2)^2/m_b^2 were taken into
account in the underlying triple differential decay width dGamma_{77}/(ds_1
ds_2 ds_3).Comment: arXiv admin note: substantial text overlap with arXiv:1110.125
Reduction of Charm Quark Mass Scheme Dependence in at the NNLL Level
The uncertainty of the theoretical prediction of the
branching ratio at NLL level is dominated by the charm mass renormalization
scheme ambiguity. In this paper we calculate those NNLL terms which are related
to the renormalization of , in order to get an estimate of the
corresponding uncertainty at the NNLL level. We find that these terms
significantly reduce (by typically a factor of two) the error on induced by the definition of . Taking into account the
experimental accuracy of around 10% and the future prospects of the
factories, we conclude that a NNLL calculation would increase the sensitivity
of the observable to possible new degrees of freedom
beyond the SM significantly.Comment: 13 pages including 3 figure
Complete (O_7,O_8) contribution to B -> X_s gamma at order alpha_s^2
We calculate the set of O(alpha_s^2) corrections to the branching ratio and
to the photon energy spectrum of the decay process B -> X_s gamma originating
from the interference of diagrams involving the electromagnetic dipole operator
O_7 with diagrams involving the chromomagnetic dipole operator O_8. The
corrections evaluated here are one of the elements needed to complete the
calculations of the B -> X_s gamma branching ratio at next-to-next-to-leading
order in QCD. We conclude that this set of corrections does not change the
central value of the Standard Model prediction for Br(B -> X_s gamma) by more
than 1 %.Comment: 19 pages, 8 figure
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