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Small Cosmological Constant from the QCD Trace Anomaly?
potential relevance of this effect.
mately described by the de Sitter metric (i) ÷ exp¦Hi¦.
scribed by Eq. (4) are conformally invariant (for m ÷ 0).
vanishing trace of the classical energy-momentum tensor.
logical constant ¬ in Eq. (3) as a bare quantity .
the conformal invariance of the classical theory in Eq. (4).
corresponds to the running of the renormalized mass.
) blatantly contravenes our observations.
tions (3) associated with a ﬂat space-time vanishes.
estimate of the expected order of magnitude of the effect.
duced by the cosmic expansion.
SS (see, e.g.,  for free ﬁelds).
leading order they effectively behave as massive free ﬁelds.
turbed time-dependent operator in the interaction picture.
order in 1¡N) long-range four-point interactions; cf. .
Eq. (5) gets diminished by an amount of ﬁrst order in H.
interpretation of the astrophysical data [1,2].
a similar nonanalytical dependence on the coupling g.
for the present epoch as well as for earlier stages; cf. .
example, quintessence (see, e.g., ).
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ÿgÿ1=2 A=g .00 The Callan-Symanzik or Gell-Mann–Low .g.s..
8 GN hT  i ÿ g ren .
function describes the scale dependence .
 and reﬂects the dynamical  2002 The American Physical Society 081302-1 .
3  — at least for m QCD . (5) represent the so-called gluonic and quark condensates.. respectively. see. ^  ^ a The expectation values hG a G  iren and h  ^ iren occurring in Eq. the m function corresponds to the running of the renormalized mass.
t ÿ t0  encodes the dynamics of an intermediate (interaction) degree of freedom which has been integrated out. next-to-leading order in 1=N) long-range four-point interactions.e.
%  pH. England. Aspects of Symmetry (Cambridge University Press. Martin. Birrell and P.. Eksp. Hu. i. Ellis. M. Reall. 70. 397 (1972). 042001 (2001). Wang. Schafer and E. 896 (1999).e. At least it indicates the potential relevance of the effect described in the present Letter with regard to the interpretation of the astrophysical data [1. P. L.ubc. quintessence (see. Lett.. E. V. 46 (2002). Rev. Phys. V. I. C. Chiba. W. J. P. ibid. 081302-4 . Rev. Dave. 204 (1986). Phys. 2302 (2001).. Phys. [JETP Lett. W. 536. L. 116. J. These investigations might perhaps lead to a better understanding of some of the problems in cosmology without necessarily invoking yet unknown low-energy ﬁelds. Novozhilov and D. the present Letter motivates a deeper examination of the vacuum of strongly interacting ﬁelds in the gravitational background of our expanding Universe — for the present epoch as well as for earlier stages. and B. 438 (1977). 507. Jaffe et al. Phys. 86. S. D 7. . Pryke et al. 1421 (1972). Phys. Mauskopf et al. I. 536. Astrophys. P. ˘  I. Duncan.. Hertog. 081302-4 The author is indebted to B. 063502 (1999)... R. Phys. 15 (1976). Quantum Fields in Curved Space (Cambridge University Press. Perlmutter et al. Copeland. and R. Nature (London) 391. In summary. Nature (London) 404. the general structure of all ^ ^ these terms is given by m2 h y  iren and according to the arguments after Eq. cf.  E.

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