Eur. Phys. J. C (2015) 75:385
DOI 10.1140/epjc/s10052-015-3611-6
Letter
Higgs pseudo observables and radiative corrections
Marzia Bordone
1
, Admir Greljo
1,3
, Gino Isidori
1,2,a
, David Marzocca
1
, Andrea Pattori
1
1
Physik-Institut, Universität Zürich, 8057 Zurich, Switzerland
2
INFN, Laboratori Nazionali di Frascati, 00044 Frascati, Italy
3
Faculty of Science, University of Sarajevo, Zmaja od Bosne 33-35, 71000 Sarajevo, Bosnia and Herzegovina
Received: 16 July 2015 / Accepted: 10 August 2015 / Published online: 25 August 2015
© The Author(s) 2015. This article is published with open access at Springerlink.com
Abstract We show how leading radiative corrections can
be implemented in the general description of h → 4 decays
by means of pseudo observables (PO). With the inclusion
of such corrections, the PO description of h → 4 decays
can be matched to next-to-leading-order electroweak calcu-
lations both within and beyond the Standard Model (SM).
In particular, we demonstrate that with the inclusion of such
corrections the complete next-to-leading-order SM predic-
tion for the h → 2e2μ dilepton mass spectrum is recovered
within 1 % accuracy. The impact of radiative corrections for
non-standard PO is also briefly discussed.
1 Introduction
The decays of the Higgs particle, h(125), can be charac-
terised by a set of pseudo observables (PO) that describes, in
great generality, possible deviations from the Standard Model
(SM) in the limit of heavy New Physics (NP) [1].
The Higgs PO are defined from a momentum expansion
of the on-shell electroweak Higgs decay amplitudes. More
precisely, the PO relevant to h → 4 are defined by the
momentum expansion around the physical poles (due to the
exchange of SM electroweak gauge bosons) of the following
three-point correlation function
0|T {J
μ
(x), J
ν
(y), h(0)}|0, (1)
where J
μ
(x) are generic leptonic currents. This expansion
encodes in full generality the short-distance contributions to
the decay amplitudes in extensions of the SM with no new
light states [1]. However, in order to compare this amplitude
decomposition with data, also the long-distance contribu-
tions due to soft and collinear photon emission (i.e. the lead-
ing QED radiative corrections) must be taken into account.
Soft and collinear photon emission represents a universal
correction factor [2,3] that can be implemented, by means of
a
e-mail: gino.isidori@lnf.infn.it
appropriate convolution functions (or, equivalently, show-
ering algorithms such as those adopted in PHOTOS [4],
PYTHIA [5], or SHERPA [6]) irrespective of the specific
short-distance structure of the amplitude.
1
In this paper we
illustrate how this works, in practice, in the h → 4 case.
We focus our analysis to the h → 2e2μ case, that is par-
ticularly interesting for illustrative purposes: the effect of
radiative corrections can be implemented by simple analytic
formulae, allowing a transparent comparison with numeri-
cal methods. As we will show, the inclusion of the universal
QED corrections is necessary and sufficient to reach an accu-
rate theoretical description of the Higgs decay spectrum, that
recovers the best up-to-date SM predictions in absence of NP.
2 QED corrections for the h → 4 dilepton spectrum
In this section we describe how leading QED radiative correc-
tions affect the dilepton spectrum of h → 4 decays assum-
ing a generic PO decomposition of the amplitude. As antici-
pated, we focus our discussion to the case of two lepton pairs
with different flavor (h → 2e2μ) and, more precisely, on the
double differential lepton-pair invariant-mass distribution
F(m
ee
, m
μμ
) =
d
2
(h → 2e2μ)
dm
ee
dm
μμ
. (2)
The emission of soft and collinear photons leads to
infrared (IR) divergences in the h → 4 spectrum. The full
structure of such divergences is rather complicated. How-
ever, as we have checked by means of an explicit calculation
at O(α), such divergences can be factorized in F(m
ee
, m
μμ
)
and can be analyzed separately for each dilepton system. This
happens because each fermion current in Eq. (1) carries an
overall neutral electric charge.
1
For a discussion about the implementation of universal QED correc-
tions in a general EFT context see also Ref. [7].
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