Full text of "Asymmetries in t tbar production: LHC versus Tevatron"

See other formats

Asymmetries in tt production: LHC versus Tevatron

J. A. Aguilar-Saavedra, M. Perez- Victoria
Departamento de Fisica Tedrica y del Cosmos and CAFPE,

The measurement of a charge asymmetry in tt production at LHC constitutes more than an
independent confirmation of the forward-backward asymmetry found at Tevatron. Indeed, both
measurements together can be used to identify the source of the asymmetry. This is demonstrated
for the case of new Z' , W' vector bosons and colour-sextet and triplet scalars, exchanged in t,
u channels respectively, and a very heavy axigluon in the s channel. In particular, current LHC
measurements disfavour Z' , W' models above the 2a level.

PACS numbers: 12.60.-i,14.65.Ha

o

O

Q

in

43 :

Oh-
i .

Or
<D ■
43 '

^1-

>

o

in
o

X

The top quark is singled out among the other quarks
by its large mass and short lifetime, making the study
of its production and decay properties specially clean.
Furthermore, thanks to these particular features, it can
be a sensitive probe of new physics beyond the Standard
Model (SM) . Actually, some observations at the Fermilab
Tevatron might already be a hint of new physics. The
CDF and DO Collaborations have measured the values
A FB = 0.158 ±0.075 [1], A FB = 0.196 ±0.065 0, respec-
tively, for the forward-backward (FB) asymmetry in top
quark pair production. Both are above the SM predic-
tions, e.g. Afg = 0.051 - 0.089 The CDF Col-
laboration also reports a clear enhancement of the asym-
metry at high tt invariant masses, A-p-Q — 0.475 ± 0.114
for m t i > 450 GeV (more than three standard deviations
above the SM prediction A F ^ = 0.088 - 0.12), whereas
DO does not find a statistically significant mass depen-
dence.

On the other hand, the CMS Collaboration has re-
cently presented a measurement of the charge asymme-
try in tt production at the CERN Large Hadron Collider
(LHC), using 1.09 ib -1 of data 0. The reported value,
A c = -0.016 ± 0.030 (stat)^;^ (syst), is still domi-
nated by the statistical uncertainty, and a much better
precision is expected in the near future. Systematic un-
certainties are also expected to improve with a better
knowledge of the detector. Clearly, the measurement of
the charge asymmetry at LHC provides an independent
test of the excess observed at Tevatron. We recall here
that the Tevatron asymmetry Ap B mentioned above is
defined as the relative difference (normalised to the total
number) between the number of events with cos 8 >
and cos 6* < 0, with 8 the angle between the top quark
and initial proton in the centre of mass frame. At LHC,
the charge asymmetry Ac measured by the CMS Col-
laboration is the relative difference between events with
\r) t \ > \rjt \ and \i] t \ < \ru\, with r\ t {r\A the pseudo-rapidity
of the top (anti)quark, rj = — logtan6*/2, in the labora-
tory frame. This definition takes advantage of the larger
average longitudinal boost of t quarks in pp collisions as-
sociated to a FB asymmetry at the parton level.

Many SM extensions have been proposed to accommo-
date the FB asymmetry measured by the CDF Collabora-
tion. These models introduce new particles which can be
exchanged in s, t or u channels in the processes qq tt,
with q = u,d. While the presence of narrow s-channel
resonances in tt production could be eventually spotted
by an examination of the tt invariant mass distribution
with sufficient statistics (perhaps also requiring a centre
of mass energy of 14 TeV), this is more difficult for new
particles exchanged in t or u channels, as for example
new Z' ', W' vector bosons (t channel), or colour-sextet
and triplet scalars (u channel).

In this paper we show that, combining the measure-
ments of the charge asymmetry at LHC and the FB asym-
metry at Tevatron, it is possible to discriminate among
the different models, already disfavouring some of them.
To arrive at this conclusion, it is necessary to go beyond
the usual analyses with a few selected benchmark points,
and instead scan over all the allowed values of the cou-
plings and masses. It is also crucial to impose existing
constraints from experimental data, in order to bound
their range of variation.

The most obvious and robust constraints on the tt
asymmetries result from tt production itself. At Teva-
tron, the total cross section has been precisely measured,
a = 7.50 ± 0.48 pb {H, which limits the possible size
of new physics contributions. Total cross section mea-
surements at LHC will not be so restrictive because tt
production is dominated by gg fusion and the systematic
and theoretical uncertainties leave more room for possi-
ble departures in qq — > tt. On the other hand, the tt
cross section at high invariant masses is sensitive to new
physics and sets constraints on the masses and couplings
of any new particles giving rise to the tt asymmetry [9j .
Of course, there are additional restrictions on the extra
particles, as for example the production of like-sign top
pairs and dijets. They are not considered here because
they can be evaded in specific models I3~12|- Further-
more, we do not attempt to reproduce the tt invariant
mass distribution at Tevatron for the models considered,
as this distribution is reasonably similar to the measured

2

one [l| for most of the parameter space allowed by other
constraints, nor we consider the tij cross section at LHC,
which can be restrictive in certain parameter space re-
gions of t-channel models (l3| . The simplified analysis
presented here suffices for our purpose. Taking into ac-
count only the constraints from the Tevatron cross sec-
tion and the LHC tail, we find that different SM exten-
sions give predictions for the asymmetries corresponding
to different, often disjoint regions in the (Afb, Ac) plane,
rendering model discrimination feasible. The inclusion of
additional constraints will only shrink the allowed regions
and strengthen our conclusions.

We are also conservative in the interpretation of the ti
production limits. There are some discrepancies between
different state-of-the-art predictions for the SM ti total
cross section at Tevatron, with some results quite close to
the measured one. for example a = 7.46±g'jo pb but
also significantly smaller ones, a — 6.30 ± 0.191q23 [l5| .
While the former value requires small new physics con-
tributions or large new amplitudes A ncw ~ —2 Asm,
the latter allows for moderate contributions to both the
cross section and the asymmetry. Thus, when requir-
ing agreement with the Tevatron ti cross section we let
the SM contribution be anywhere between these two val-
ues, which makes our constraints much looser (and hence
the allowed regions larger) than if we stick to one of ei-
ther predictions. Taking into account the uncertainties
in these theoretical predictions as well as in the experi-
mental measurement, we require in our analysis that new
physics contributions to ti production lie inside the inter-
val [—0.8, 1.7] pb. For the LHC cross section at the high-
mass tail, no dedicated analysis is available yet. Still, an
examination of the invariant mass distributions that have
been released [16] shows that large excesses over the SM
prediction are already excluded. Following Refs. 0, [ItJ
we take the cross section for m t i > 1 TeV as a constraint,
requiring that its value is at most three times the SM pre-
diction.

All possible vector bosons and scalars contributing to
qq — > ti have been classified in Ref. [9j according to their
transformation properties under the SM gauge group
SU(3) C x SU(2) L x U(l)y. There are ten possible new
vector bosons and eight types of scalars, but perhaps
the most interesting extensions are new colour-singlet or
octet vector bosons, and colour-triplet or sextet scalars.
Their transformation properties and general interaction
Lagrangians with the quarks are collected in Table [Jj We
use standard notation with left-handed doublets qn and
right-handed singlets um, dm; t 1 are the Pauli matrices,
A a the Gell-Mann matrices normalised to tr(A a A & ) = 26 a b
and ip c = C-tp 7 ', with C the charge conjugation matrix.
The subindices a, 6, c denote colour, and e a bc is the totally
antisymmetric tensor.

In our analysis we take five illustrative examples rep-
resenting a large fraction of the models proposed in the
literature to explain the ti asymmetry, which also involve

TABLE I. Some vector bosons and scalar representations me-
diating qq — i> ti.

Label Rep.

Interaction Lagrangian

+gt j d m ^d R] ) B M
B\ (1,1)! -9ijdm^u Rj Bl? +h.c.
e M (8, 1) - [g^qu^^-qLj + gijUR^^-URj

+gt J d Ra ^d Rj ) Ql

^ 4 (3, 1)_4 -gijEabcURAbURjc + n - c -

Q 4 (6, 1)_4 [u R i a U Rjb + U R ibU Rja ] fi 4ai>t + h.c.

the three possibilities of new particle exchange in the s,
t or u channels.

Flavour-violating Z' boson If], 18- 2^1: A neutral vec-

tor boson £> M exchanged in the t channel in uu — > ti. We
take its Z'tu couplings to be right-handed, g™ 3 ^ 0, as
preferred by B physics constraints. Our results are in-
dependent of this choice, however. For a real Z' boson
the contribution to the FB and charge asymmetries is
strongly constrained by the absence of like-sign top pair
production [23]. However, the relation between tt and ti
production can be evaded by placing the new boson in a
complex representation of a flavour group [10|.

W boson [H-[26||: A charged boson Bj\ with right-
handed couplings g\3 exchanged in the t channel in
dd — > ti. Charged bosons with left-handed couplings
can also appear in SU(2)^ triplets but this possibility is
again disfavoured by B physics constraints.

Axigluon 0, [27l - [29| : A colour octet vector with
axial couplings g\ = — g% = —gfi, produced in the s
channel, qq —> ti. We consider this new particle to be
heavy enough not to be produced on shell; otherwise its
presence would generally be noticed by a bump in the
ti invariant mass distribution [38| and the discrimination
from i-, u-channel resonances would be straightforward.
The exception to this rule is given by colour octets below
the ti production threshold [39j or very broad [39L |4(]1 | but
in those cases the predictions are very model-dependent
and deserve a separate study j^. We assume the ax-
igluon is only produced in uu and dd initial states, which
give the largest fraction of the ti cross section at the Teva-
tron and the LHC, and neglect additional contributions,
for example from ss annihilation. In any case, includ-
ing these small contributions hardly affects our results.
No assumptions are necessary about the relative size of
first- and third-generation couplings, since the axigluon
is taken heavy and the cross section is propo rtional to the
product of couplings. (Other models [30h33I | in which the
couplings of the new colour octet are not purely axial give
very similar results for the relation between Aq and ^4fb ,
but the asymmetries generated are smaller relative to the

3

increase in cross section.)

Colour-triplet scalar fill 34-3(|: A colour triplet w 4
with flavour- violating tu couplings 1713 , necessarily right-
handed, exchanged in the u channel in uu — > tt. Notice
that the antisymmetry in colour indices implies that di-
agonal couplings to uu, tt identically vanish.

Colour-sextet scalar [TU 12, 34-37 1: A colour sextet

O , also with right-handed flavour- violating tu couplings
f/13, and exchanged in the u channel. In contrast with
w 4 , for the sextet there may be diagonal uu, tt couplings,
albeit not related to the flavour-violating ones. They
can potentially give rise to large (unobserved) tt signals
unless suppressed by some flavour symmetry [llj, [l2 1 .

The predictions of these models for the asymmetries
Apb and Ac are found by performing a comprehen-
sive scan over the allowed parameter space, with par-
ticle masses between 100 GeV and 10 TeV, except for
the axigluon, which is assumed to be very heavy and
its amplitude replaced by a four-fermion interaction (4l| .
The interval of the scan is adjusted as necessary to ob-
tain a smooth variation of the predictions with the mass.
The couplings are scanned uniformly in the range al-
lowed by the Tevatron cross section limits, i.e. requir-
ing Act = [—0.8, 1.7] pb. This constraint fixes the maxi-
mum size of the coupling for each mass considered. (The
resulting allowed range for the coupling may be a sin-
gle interval or the union of two, due to the competition
between the interference and quadratic contributions to
the cross section.) The total number of parameter space
points sampled ranges between more than 2000 for the Z'
boson to almost 10000 for oj 4 . Our computations are per-
formed by including the new particles and four-fermion
interactions in the leading-order generator Protos [42j |.

The new physics contributions to A-p-Q (for m t j > 450
GeV) and Ac (inclusive) are presented in Fig. [T] (left),
for the five models studied, taking into account the con-
straints on the tt cross section and tail mentioned above.
We only show the regions where is positive, as is

the excess found by the CDF and DO Collaborations. To
a good approximation, the total asymmetries Afb, Ac
are obtained by summing the SM contributions, A|g =
0.088±0.013 (43, A C M = 0.0130±0.0011 Q, to A^ and
A c ew , respectively. This amounts to considering the dom-
inant contributions to the total asymmetry, which are: (i)
interference between new physics and tree-level SM con-
tributions, as well as purely new physics ones; (ii) the
interference between the next-to-leading order and tree-
level SM. As one can observe, current LHC data already
bring interesting implications for the models discussed.
A salient feature of our analysis is that for the Z' boson
the positive asymmetries (which require a large coupling)
have minimal values A£° B W > 0.32, A c cw > 0.04 allowed
by tt cross section constraints. Hence, the present LHC
measurement of Ac disfavours this model at 2.2tr (97%
confidence level) . The same measurement also disfavours
the W' at 2a (95% confidence level) if the new physics

contribution to the Tevatron asymmetry is moderate,
A^™ > 0.12, as it is preferred by the CDF measure-
ment, Af^ = 0.387 ±0.115, and also hinted by the more
recent one by the DO Collaboration. The rest of models
predict smaller asymmetries at LHC, and are less con-
strained by the present measurement of Ac . Notice that
the difference between a W boson and the scalar and ax-
igluon models stems from the different uu and dd parton
densities. At Tevatron (pp collider) both u, d from the
proton and u, d from the antiproton are valence quarks,
so that dd is roughly 1/4 smaller than uu. At LHC (pp)
both u, d are sea quarks and dd is only 1/2 smaller than
uu, resulting in a slope twice larger for the W allowed
region.

Further discrimination can be achieved by the mea-
surement of Ac at high invariant masses, for example
rriu > 600 GeV for which the SM cross section is only
six times smaller than the total rate and statistics will
be good. The result is shown in Fig. [T] (right). For a
Z' boson exchanged in the t channel the asymmetry en-
hancement is much more pronounced than for the rest
of models, and an unfolded measurement at high mass
can definitely probe this model. (The same comment ap-
plies to W bosons.) Moreover, although apparently the
scalars and the axigluon have similar predictions also for
high m t t, the fact is that model parameters giving close
(A^, A c cw ) points in the left-hand plot correspond to
different A c ew in the right-hand one. This can be under-
stood by recalling that for light oj 4 /£1 4 scalars exchanged
in it-channel the top quarks are preferrably produced in
the direction of the initial antiquark. A positive Afb at
Tevatron can only be generated for scalar masses above
few hundreds of GeV, so that the enhancement of the it-
channel propagator in the backward direction is less pro-
nounced. For this reason, Ac at LHC is small for large
m t i except when u 4 /tt 4 are heavy and it even decreases
with mtt f° r light scalars and/or high m t i-

These arguments provide a strong motivation for the
analysis of the m t j dependence of the charge asymmetry
at LHC. To demonstrate its relevance we select one point

from Fig. [T] (left), A™™

0.13, A c cw ~ 0.016 and three

models yielding these values: (i) a heavy axigluon
|29| (see Ref. [J for details on the effective operators); (ii)
a colour sextet [II HS-^; (iii) a colour triplet \x&\M-
[3^|. We plot in Fig.[2]the charge asymmetry as a function
of the cut to™ on the tt invariant mass. The differences
in the behaviour are striking and illustrate the general
trend. In order to reproduce the same values for Apg^,
A™™, the colour sextet and triplet must have different
mass and coupling, because the interference with the SM
has opposite sign [9j, [35 1 . But it is the mass that mainly
determines the variation of the asymmetry with to™ 11 .
As we have mentioned aboce, for a relatively light u-
channel particle (for instance the w 4 benchmark in Fig. [5])
the asymmetry does not grow with m t i due to the effect
of the it-channel propagator which prefers backward top

4

0.08

0.06

0.25

0.04

0.02

M B (m ;; >450GeV) A pB (m rr >450GeV)

FIG. 1. Left: allowed regions for the new physics contributions to the FB asymmetry at Tevatron and the inclusive charge
asymmetry at LHC. Right: the same, with the charge asymmetry for m t i > 600 GeV.

0.15

1 i«0.10

§„ : C/A~ = 0.33TeV"~
£2 4 : g 13 = 1.17 M= 950GeV
CO 4 : g n = 0.936 M= 340 GeV

400

500

600

700

800

900

1000

FIG. 2. Dependence of the charge asymmetry on the m t i cut,
for a point with A 1 ^ ~ 0.13, y4g cw ~ 0.016 (inclusive).

quarks, while the numerator prefers forward top quarks.
For a heavier it-channel particle (as for example the Q
benchmark in the same figure) the it-channel propagator
effect is attenuated and the asymmetry reaches higher
values. Thus, a more precise measurement of the inclu-
sive charge asymmetry and an unfolded measurement at
high mass will be of great help discriminating these mod-
els. Additional information can eventually be obtained
from more subtle observables, such as the polarisation of
the ti pair [44J. Besides, we have also checked that for
a central charge asymmetry with \r)tt\ < 1 S EH the
results are quite similar, while for a forward one some
discrimination power is lost.

The allowed regions in Fig.[T]have been obtained, as ex-
plained above, by imposing a "minimal" set of constraints:

the ti cross section at the Tevatron and the high invari-
ant mass cross section at the LHC. Hence, these allowed
regions contain all the possible predictions for the asym-
metries in viable models^ Additional constraints could
be imposed, for example the tij cross section at the LHC,
which is important for a certain range of masses in Z' ,
W' models [j^ j. or the ti tail at the Tevatron. Doing
this is not necessary in our analysis, since the regions we
obtain with our minimal constraints are already disjoint,
as we have shown. At any rate, we expect that the range
of predictions for viable models will not be much smaller
than the allowed regions shown in Fig.Q] For example the
tij cross section constraint is important only for a nar-
row Z\ W mass range above the top quark mass, where
on-shell associated production, e.g. gu tZ 1 — > tiu,
is large. Also, the constraints on new physics from the
Tevatron tail are loosened by the smaller detection effi-
ciency for the new contributions (4(| . Though systematic
scans of the parameter space for viable models have not
been performed elsewhere, some sample points studied
in detail [ll|, [H, EH 0, Efi| suggest that most of the
parameter space allowed by our constraints gives viable
models.

In summary, in this paper we have investigated the re-
lation between the ti asymmetries at Tevatron and LHC.
If the excess found by the CDF and DO Collaborations

1 Notice that the bulk contribution to the total cross section at
Tevatron comes from the region with m t j ~ 400 — 500 GeV,
where detection efficiency of the new physics is not very different
from that of SM tt production. At LHC the efficiency lose at the
tail for light t-channel particles is not very pronounced Q], and
in any case the agreement between the SM prediction and the
experimental measurement suggests much more stringent limits
than the ones considered here.

5

corresponds to new physics, the most robust probe to in-
vestigate its origin is the study of tt production at LHC,
searching for a charge asymmetry and an enhanced tt tail.
We have shown how the measurements of the Tevatron
and LHC asymmetries can be used to identify the source
of these excesses. In particular, with present data the
models with Z' and W bosons are already disfavoured
at the 95% confidence level. The results presented here
also provide a strong motivation for the detailed study
of the mtt dependence of the charge asymmetry at LHC,
which will be possible thanks to the good statistics ex-
pected at this top quark factory.

This work has been partially supported by projects
FPA2010-17915 (MICINN), FQM 101 and FQM 437
(Junta de Andalucia) and CERN/FP/116397/2010
(FCT).

[1] T. Aaltonen et al. [CDF Collaboration], Phys. Rev. D
83, 112003 (2011).

[2] V. Abazov et al. [DO Collaboration], larXiv: 1107.49951
[hep-ex] .

[3] P. Ferrario and G. Rodrigo, Phys. Rev. D 78, 094018
(2008).

[4] W. Bernreuther and Z. G. Si, Nucl. Phys. B 837, 90
(2010).

[5] W. Hollik and D. Pagani, arXiv:1107.2606 [hep-ph].

[6] J. H. Kuhn and G. Rodrigo. larXiv :1109.6830 [hep-ph].

[7] CMS Collaboration, note CMS PAS TOP-11-014.

[8] T. Aaltonen et al. [CDF Collaboration], CDF note 9913.

[9] J. A. Aguilar-Saavedra and M. Perez- Victoria, JHEP
1105, 034 (2011).
[10] S. Jung, A. Pierce and J. D. Wells, Phys. Rev. D 83,
114039 (2011).

[11] Z. Ligeti, M. Schmaltz and G. M. Tavares, JHEP 1106,
109 (2011).

[12] B. Grinstein , A. L. Kagan, M. Trott and J. Zupan, Phys.

Rev. Lett. 107, 012002 (2011).
[13] M. I. Gresham , I. -W. Kim and K. M. Zurek,

larXiv: 1107.43641 [hep-ph].
[14] U. Langenfeld, S. Moch and P. Uwer, Phys. Rev. D 80,

054009 (2009).

[15] V. Ahrens, A. Ferroglia, M. Neubert, B. D. Pecjak and

L. L. Yang, JHEP 1009, 097 (2010).
[16] CMS Collaboration, note CMS PAS TOP-10-007.
[17] C. Delaunay, O. Gedalia, Y. Hochberg, G. Perez and

Y. Soreq, JHEP 1108, 031 (2011).
[18] S. Jung, H. Murayama, A. Pierce and J. D. Wells, Phys.

Rev. D 81, 015004 (2010).
[19] V. Barger, W. Y. Keung and C. T. Yu, Phys. Rev. D 81,

113009 (2010); V. Barger, W. Y. Keung and C. T. Yu,

Phys. Lett. B 698, 243 (2011).
[20] J. Cao, L. Wang, L. Wu and J. M. Yang, Phys. Rev.

D84, 074001 (2011).
[21] E. L. Berger, Q. H. Cao, C. R. Chen, C. S. Li and

H. Zhang, Phys. Rev. Lett. 106, 201801 (2011).
[22] B. Bhattacherjee, S. S. Biswal and D. Ghosh, Phys. Rev.

D 83, 091501 (2011).
[23] J. A. Aguilar-Saavedra and M. Perez- Victoria, Phys.

Lett. B 701, 93 (2011)
[24] K. Cheung, W. Y. Keung and T. C. Yuan, Phys. Lett. B

682, 287 (2009); K. Cheung and T. C. Yuan, Phys. Rev.

D 83, 074006 (2011).
[25] Q. H. Cao, D. McKeen, J. L. Rosner, G. Shaughnessy

and C. E. M. Wagner, Phys. Rev. D 81, 114004 (2010).
[26] J. Shelton and K. M. Zurek, Phys. Rev. D 83, 091701

(2011).

[27] P. Ferrario and G. Rodrigo, Phys. Rev. D 80, 051701

(2009) .

[28] P. H. Frampton, J. Shu and K. Wang, Phys. Lett. B 683,
294 (2010).

[29] Y. Bai, J. L. Hewett, J. Kaplan and T. G. Rizzo, JHEP
1103, 003 (2011).

[30] A. Djouadi, G. Moreau, F. Richard and R. K. Singh,
Phys. Rev. D 82, 071702 (2010); A. Djouadi, G. Moreau
and F. Richard, Phys. Lett. B701, 458-464 (2011).

[31] C. Delaunay, O. Gedalia, S. J. Lee, G. Perez and E. Pon-
ton, Phys. Rev. D 83, 115003 (2011); Phys. Lett. B703,
486-490 (2011).

[32] G. Burdman, L. de Lima and R. D. Matheus, Phys. Rev.
D 83, 035012 (2011).

[33] E. Alvarez, L. Da Rold and A. Szynkman, JHEP 1105,
070 (2011),

[34] J. Shu, T. M. P. Tait and K. Wang, Phys. Rev. D 81,
034012 (2010).

[35] A. Arhrib, R. Benbrik and C. H. Chen, Phys. Rev. D 82,
034034 (2010).

[36] I. Dorsner, S. Fajfer, J. F. Kamenik and N. Kosnik, Phys.
Rev. D 81, 055009 (2010); Phys. Rev. D 82, 094015

(2010) .

[37] K. M. Patel and P. Sharma, JHEP 1104, 085 (2011).
[38] R. Barcelo, A. Carmona, M. Masip and J. Santiago, Phys.

Rev. D 84, 014024 (2011).
[39] J. A. Aguilar-Saavedra and M. Perez- Victoria, Phys.

Lett. B 705, 228 (2011).
[40] R. Barcelo, A. Carmona, M. Masip and J. Santiago,

larXiv:1106.4054l [hep-ph].
[41] F. del Aguila, J. de Bias and M. Perez- Victoria, JHEP

1009, 033 (2010); J. A. Aguilar-Saavedra, Nucl. Phys. B

843, 638 (2011); C. Degrande, J. M. Gerard, C. Grojean,

F. Maltoni and G. Servant, JHEP 1103, 125 (2011).
[42] J. A. Aguilar-Saavedra, Nucl. Phys. B 804, 160 (2008).
[43] J. M. Campbell and R. K. Ellis, Phys. Rev. D 60 (1999)

113006.

[44] J. Cao, L. Wu and J. M. Yang, Phys. Rev. D 83, 034024

(2011) ; D. Choudhury, R. M. Godbole, S. D. Rindani
and P. Saha, Phys. Rev. D 84, 014 023 (2011); D. Krohn,
T. Liu, J. Shelton and L. T. Wang. larXiv: 1 105.37431 [hep-
ph[; D. W. Jung, P. Ko and J. S. Lee, Phys. Lett. B 701,
248 (2011).

[45] J. L. Hewett, J. Shelton, M. Spannowsky, T. M. P. Tait
and M. Takeuchi, Phys. Rev. D84, 054005 (2011).

[46] M. I. Gresham, I. W. Kim and K. M. Zurek, Phys. Rev.
D 83, 114027 (2011).
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8823804259300232, "perplexity": 7379.094175815272}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655896905.46/warc/CC-MAIN-20200708062424-20200708092424-00024.warc.gz"}