Falsifying Models of New Physics via
WW
Scattering
Jacques Distler,
1
Benjamin Grinstein,
2
Rafael A. Porto,
3
and Ira Z. Rothstein
3
1
University of Texas, Dept. of Physics, Austin, Texas 78712, USA
2
University of California, San Diego, Dept. of Physics, La Jolla, California 92093-0319, USA
3
Carnegie-Mellon University, Dept. of Physics, Pittsburgh, Pennsylvania 15213, USA
(Received 2 October 2006; published 22 January 2007)
We show that the coefFcients of operators in the electroweak chiral Lagrangian can be bounded if the
underlying theory obeys the usual assumptions of Lorentz invariance, analyticity, unitarity, and crossing to
arbitrarily short distances. Violations of these bounds can be explained by either the existence of new
physics below the naive cutoff of the effective theory, or by the breakdown of one of these assumptions in
the short distance theory. As a corollary, if no light resonances are found, then a measured violation of the
bound would falsify generic models of string theory.
DOI:
10.1103/PhysRevLett.98.041601
PACS numbers: 12.15.Ji, 11.25.Wx, 11.55.
ÿ
m, 12.60.±r
The standard model (SM) is only an effective Feld
theory, a good approximation only at energies below
some scale
±
. This scale, however, is still undetermined.
If, as naturalness arguments indicate, new physics is re-
quired to explain the relative smallness of the weak to
Planck scale ratio, then we would expect the theory to
break down at energies of about 1 TeV. However, even if
naturalness arguments fail, we still know that the SM,
augmented by Einstein gravity, must break down at the
scale of quantum gravity, where predictive power is lost.
In searching for low-energy effects of the physics which
underlies the SM, it is prudent to take the model indepen-
dent approach of adding operators of dimension higher
than four to the SM Lagrangian and parameterizing the
new physics by their coefFcients. Dimensional analysis
dictates that these coefFcients contain inverse powers of
±
, so the precision with which we must extract them grows
with the scale of new physics. This decoupling phenomena
makes falsifying theories of the underlying short distance
interactions [the ultraviolet (UV))] extremely difFcult.
Indeed, if the scale of quantum gravity is as high as the
Planck scale, it becomes interesting to ask the question as
to whether or not the theory is, even in principle, falsiFable.
One possibility is that the mathematical structure leads to
unique low-energy predictions. However, in the case of
string theory, recent progress seems to indicate that this is
not a likely scenario. Another possibility is that there are
low-energy, non-Planck suppressed, consequences of some
underlying symmetries. Symmetries link the UV and the
infrared (IR) by distinguishing between universality
classes. However, string theory does not seem to have
any problems generating the low-energy symmetries man-
ifested at energies presently explored. Indeed, given the
enormous number of string vacua, it may be that string
theory can accommodate whatever new physics is found at
the TeV scale by the Large Hadron Collider (LHC).