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#  $Z^{\prime}$ search in non-minimal Universal Extra Dimensions: two bumps
and interference

AseshKrishna Datta†, Kenji Nishiwaki‡111This poster presentation was given by
Kenji Nishiwaki in the conference HPNP2015., Saurabh Niyogi¶ †Harish-Chandra
Research Institute, Allahabad 211-019, India
‡School of Physics, Korea Institute for Advanced Study, Seoul 130-722,
Republic of Korea
¶Institute of Mathematical Sciences, Chennai 600-113, India

###### Abstract

We discuss prospects of the $Z^{\prime}$ search at the LHC in non-minimal
Universal Extra Dimensions with tree-level brane-local terms in five
dimensions. In this scenario, we find two major differences from the usual
$Z^{\prime}$ physics: (i) two $Z^{\prime}$ candidates close-by in mass exist;
(ii) the effective couplings to the SM fermions could be very large due to
drastic overlapping of their profiles along the extra dimension. To evaluate
the actual situation precisely, we reconsider the important issues of resonant
processes, i.e., treatment of resonant propagators and including interference
effects. (This talk is based on tentative results of an ongoing project.)

##  I Introduction

Appearance of new heavy vector bosons is common to many physics scenarios
beyond the Standard Model (SM). Thus, search for these states is a standard
program in the hunt for new physics at colliders. Especially, signals of the
resonant production of electromagnetically neutral ones ($Z^{\prime}$
candidates) leading to a pair of leptons are very clean and hence very useful.
These neutral bosons are associated with a new gauge group which is
spontaneously broken at the scale of new physics, e.g., the Grand Unified
theories, the left-right symmetric models or the $U(1)$ extensions of the SM
around the electroweak scale. Another origin of new vector bosons is
(compactified) extra dimensions. When a higher-dimensional gauge boson lives
in the bulk space, various massive copies of the lightest mode knows as
Kaluza-Klein (KK) particles appear in four-dimensional compactified theories.
Well-known possibilities in this class of theories with five-dimensional (5D)
spacetime are the bulk SM in the Randall-Sundrum warped background or the
Universal Extra Dimension (UED) scenarios Appelquist:2000nn  (mainly) in the
flat space. In such cases, 5D bulk $SU(2)_{W}$ and $U(1)_{Y}$ gauge bosons are
found, where there are two types of $Z^{\prime}$ candidates. Note that when an
accidental $Z_{2}$ parity originating from a reflection in the extra space
ensures the existence of a dark matter candidate in the system, level-1
massive bosons cannot decay into a pair of SM particles, while the level-2
gauge bosons could do. Therefore, typically level-2 gauge boson resonances in
UED are sensitive to such Drell-Yan type search.

In the minimal UED case without tree-level brane-local terms, interactions
between level-2 gauge bosons and the SM fermions are generated at the one-loop
level Cheng:2002iz . Hence, two sharp nearby resonances are predicted, which
can be the ‘smoking gun’ signals for the UED type scenarios Datta:2005zs . On
the other hand, the expected production cross section is not large since this
process is a loop-induced one. Also, to evade the recent bound on level-1
colored particles at $7$ and $8$ TeV runs of the Large Hadron Collider (LHC),
the typical scale of (level-1) KK particles, which is the inverse of the
radius of the extra dimension, should be roughly larger than $1\sim 1.5$ TeV.
Thereby, it is not so easy to probe the minimal UED scenario through this
channel via level-2 states of such a kind.

When we introduce (tree-level) brane-local terms in the minimal scenario,
situations can be drastically changed Carena:2002me ; delAguila:2003bh ;
Flacke:2008ne ; Datta:2013yaa . Thanks to brane-local kinetic terms (BLKTs),
we can have situations where interactions between the level-2 gauge bosons and
the SM fermions are present at the tree level and relatively light
$Z^{\prime}$ candidates $(B_{(2)},W^{3}_{(2)})$ are possible. Interestingly,
at least a part of the parameter space in which the above properties are
realized, the effective gauge interaction is enhanced via a large overlapping
of wave functions of the particles along the extra direction. Thus,
$Z^{\prime}$ resonant production becomes a viable channel for probing such a
non-minimal UED (nmUED) scenario at the LHC.

Here, a nontrivial feature is expected. When effective gauge couplings between
a $Z^{\prime}$ candidate and the SM fermions take large values, the
$Z^{\prime}$ resonance becomes broad. In such a situation, a fresh look into
the validity of the narrow-width approximation, which is commonly used in
studies of (narrow) resonances, is needed.

##  II Properties of $Z^{\prime}$ candidates in non-minimal UED models

Figure 1:  Left: The generic profile of the variation of $M_{F_{(n)}}/R^{-1}$
as a function of $r^{\prime}_{F}\,(=r_{F}R^{-1})$ for the cases $n=1$ and
$n=2$ Datta:2013yaa . Right: Contours of deviation for the generic couplings
$V^{(2)}$-$F^{(0)}_{L}$-$F^{(0)}_{L}$ (or
$V^{(2)}$-$f^{(0)}_{R}$-$f^{(0)}_{R}$) from the corresponding SM values in the
$r^{\prime}_{V}-r^{\prime}_{Q/T/L}$ plane. $V$, $F$ and $f$ stand for generic
gauge boson, $SU(2)_{W}$ doublet and singlet fermion fields (with
corresponding chiralities), respectively. Note that when $V$ is the (KK) $W$
boson, types of the two fermions involved at a given vertex are different
Datta:2013yaa .

In the non-minimal UED scenarios with BLKTs, the effective KK mass of a
level-$n$ KK state $F_{(n)}$ is different from the corresponding value in the
minimal case (at the tree level), $M_{F_{(n)}}=n/R\,(n=1,2,3,\cdots)$, where
$R$ is the radius of the extra dimension. $r^{\prime}_{F}(\equiv r_{F}R^{-1})$
is the dimensionless coefficient corresponding to the brane-local kinetic term
$r_{F}$ for 5D field $F$. It plays an important role in phenomenology of the
non-minimal scenarios. As shown in the left panel of Fig. 1, KK masses
different from these in the minimal scenario can be obtained with varying
$r^{\prime}_{F}$, where each 5D field can take an individual coefficient
leading to wide varieties of mass spectra.

In general, $r_{F}$ also affects the strengths of the effective gauge
interactions involving KK particles $F_{(n)}$. In particular, the case of
$V^{(2)}$-$F^{(0)}_{L}$-$F^{(0)}_{L}$ (or
$V^{(2)}$-$f^{(0)}_{R}$-$f^{(0)}_{R}$) is interesting, where $V$, $F$ and $f$
stand for generic gauge boson, $SU(2)_{W}$ doublet and singlet fermion fields
(with corresponding chiralities), respectively. The right panel of Fig. 1
indicates the region where significant coupling enhancement is found when the
dimensionless coefficients of BLKTs for 5D fermions ($r^{\prime}_{Q/T/L}$) are
negative. With suitable coefficients for the electroweak gauge bosons, two
relatively lighter $Z^{\prime}$ candidates are realized with large effective
couplings to the SM fermions. Therefore, the $Z^{\prime}$ search at the LHC
can probe a favorable region of the nmUED parameter space.

##  III Propagator schemes

Usually in studies of resonant production of a particle with a narrow width,
one adopts the narrow-width approximation. This means that we use the simple
form of a resonant propagator generating the Breit-Wigner (BW) shape in the
resonant mass distribution

$\displaystyle\frac{1}{(\hat{s}-m_{R}^{2})+im_{R}\Gamma_{R}},$ (1)

where $\hat{s}$ indicates the total energy at the parton level, $m_{R}$ and
$\Gamma_{R}$ represent the mass and the total width of the resonant state,
respectively. A more precise form adopted in a widely used event generator
like Pythia 6 Sjostrand:2006za  is as follows:

$\displaystyle\frac{1}{(\hat{s}-m_{R}^{2})+i\sqrt{\hat{s}}\Gamma_{R}(\hat{s})},$
(2)

where the total width is replaced to energy-dependent one and the imaginary
part of the two-point function of the resonant particle is correctly
described. The full form of the propagator is

$\displaystyle\frac{1}{\left(1-\mathcal{R}\left[\Pi^{\prime}_{T}(m^{2})\right]\right)\left(\hat{s}-m^{2}\right)+\Pi_{T}(\hat{s})-\mathcal{R}\left[\Pi_{T}(m^{2})\right]},$
(3)

where $\mathcal{R}$ stands for the real part, $\Pi_{T}(\hat{s})$ is the
renormalized (transverse part) two-point function (of the gauge boson) in the
on-shell scheme and $m$ stands for the (renormalized) pole mass. In this way,
not only the imaginary part but also the real part are fully included.

Generally for large widths $(\Gamma/M>10\sim 15\%)$, it is nontrivial to
estimate the resulting effects and hence to work out at the colliders. Our
interest is just in such scenarios and we carefully treat this issue in our
analysis.

##  IV Tentative results

In this section, we present our tentative results on future LHC reach at
$\sqrt{s}=13\,\text{TeV}$ for the non-minimal UED scenarios with/without
$Z^{\prime}$ coupling enhancement. We work with four benchmark points of the
universal BLKTs for 5D quarks and leptons
$r^{\prime}_{Q}=r^{\prime}_{L}=-1.0,\,-0.5,\,0.0,\,+0.5$ with
$R^{-1}=3\,\text{TeV}$ and $r^{\prime}_{SU(2)_{L}}=r^{\prime}_{U(1)_{Y}}=1.3$.
Here, we assume two things: (i) the Weinberg angle between the two states are
exactly zero, which would be realized after considering one-loop corrections
Cheng:2002iz ; (ii) there is a $150\,\text{GeV}$ mass-split between the two
massive gauge bosons $B_{(2)}$ and $W^{3}_{(2)}$ like in the corresponding
minimal UED case, consequently the masses of the two level-2 states are

$\displaystyle m_{B_{(2)}}\simeq 4.0\,\text{TeV},\quad m_{W^{3}_{(2)}}\simeq
4.15\,\text{TeV}.$ (4)

For collider simulations, we use Pythia 6.4 Sjostrand:2006za  with our
modifications for implementing the BW and the “full” propagators shown in Eqs.
(1) and (3), respectively. CTEQ6L parton distribution function Pumplin:2002vw
is adopted and the factorization and renormalization scales are set at
$m_{B_{(2)}}$. We only focus on the signal process with dimuon final state,
$pp\to B_{(2)}/W^{3}_{(2)}\to\mu^{+}\mu^{-}$, while the major background
process within the SM, $pp\to\gamma^{\ast}/Z\to\mu^{+}\mu^{-}$ is considered.
The following kinematic cuts are imposed:

  * •

$p_{T}^{\mu}>30\,\text{GeV}$,

  * •

$\eta^{\mu}<2.5$,

  * •

$M_{\mu^{+}\mu^{-}}>2\,\text{TeV}$: the flat cut on the invariant mass on the
muon pair. This choice may not be optimal, and can be improved for specific
masses of the resonances being probed.

Note that we ignore detector effects for simplicity. To estimate the reach, we
adopt a rather strict set of criteria: we require a minimum of five events
with a significance $S\geq 5\sigma$. We use the following Poisson significance
estimator formula in Ref. Cowan:2010js

$\displaystyle
S=\sqrt{2\left[\left(s+b\right)\log\left(1+\frac{s}{b}\right)-s\right]},$ (5)

where $b$ and $s$ are the expected numbers of background and (background-
subtracted) signal events after the cuts, respectively.

Results are summarized in table 1, where “scale factors” represent effective
$Z^{\prime}$ coupling deviations from the SM $Z$ (sequential $Z^{\prime}$)
ones defined as ratios and the total widths of $B_{(2)}$ and $W^{3}_{(2)}$ are
calculated by Madgraph 5 Alwall:2011uj  with our own model file generated via
FeynRules Alloul:2013bka . Note that in the “full” propagator scheme, we
consider the complete treatment only for the SM fermions. For other KK
particles, we simply adopt the BW treatment. Also, we analyze the process with
and without interference effects between two nearby resonances. Here, in the
“large” coupling cases ($r^{\prime}_{Q}=r^{\prime}_{L}=-1.0,\,-0.5$), we can
see that propagator treatments and interference affect the required
luminosities for discovery ($10-20\%$). It is equally relevant to express this
effect in terms of the “degraded” reach in $m_{Z^{\prime}}$ for a given
luminosity.

Table 1: Integrated luminosities (in fb-1) required for the discovery of level-2 $Z^{\prime}$ candidates evaluated both in the cases of the BW propagator and propagators with full one-loop corrections of the SM fermions. “w int” and “wo int” stand for “with interference” and “without interference” of the two resonant states, respectively. $r^{\prime}_{Q},\,r^{\prime}_{L}$ (scale factor) | full, w int | BW w int | full wo int | BW wo int |  $B_{(2)}$ Width (GeV) |  $W_{(2)}^{3}$ Width (GeV)
---|---|---|---|---|---|---
$-1.0$ ($-3.5$) | $0.352$ | $0.411$ | $0.368$ | $0.43$ | $826$ | $1805$
$-0.5$ ($-1.46$) | $5.32$ | $5.46$ | $6.22$ | $6.38$ | $154$ | $397$
$0.0$ ($-0.72$) | $108$ | $109.5$ | $109.7$ | $115.7$ | $47$ | $173$
$0.5$ ($-0.34$) | $8516$ | $8601$ | $8611$ | $8765$ | $20$ | $116$

##  V Summary

We have discussed the $Z^{\prime}$-like physics of the non-minimal UED model
with tree-level brane-local terms, where the masses of the two $Z^{\prime}$
candidates can get to be relatively light compared to the typical value of
$2R^{-1}$ in the minimal case, and large enhancements could take place in the
effective couplings to the SM fermions in a part of the parameter space.
Another significant feature is that the two resonant peaks are close to each
other. In such a situation, correct treatments of the resonant propagators and
interference effects among the two nearby states could generate sizable
effects ($10\sim 20\%$ deviations) in required luminosities for the discovery
at the LHC.

## Acknowledgement

KN would like to thank Shinya Kanemura and all the other members of the
organizing committee of HPNP2015 for the stimulating opportunity and their
kind hospitality. KN and SN were partially supported by funding available from
the Department of Atomic Energy, Government of India for the Regional Centre
for Accelerator-based Particle Physics (RECAPP), Harish-Chandra Research
Institute. KN would like to thank Geneviève Bélanger, Giacomo Cacciapaglia,
Aldo Deandrea and Tetiana Berger-Hryn’ova for useful discussions. KN also
thank Laboratoire d’Annecy-le-Vieux de Physique Théorique and Université de
Lyon for the kind hospitality.

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