Tools for Xtra Dimensions. GDR Bruxelles 12-14 novembre 2007 - Helenka Przysiezniak CNRS LAPP. Tools…meaning… Calculations Generators Generators + detector simulation Cosmological XtraD’s Accelerator XtraD’s … I will concentrate on Generators for accelerator searches of XtraD’s
GDR Bruxelles 12-14 novembre 2007 - Helenka Przysiezniak CNRS LAPP
I’ve never used:
We (ATLAS colleagues M.ElKacimi, D.Goudjdami, H.P.)
have played with
and have used
for the Universal Extra Dimensions model.
Which lead us to modify PYTHIA in order to generate “UED events”
We (ATLAS colleagues G.Azuelos etal.) had used
+an adapted HDECAY for the Randall Sundrum model with a radion
and in the meantime, the RS graviton has been implemented
thanks to some ATLAS collaborators.
Looking for the Randall Sundrum Model
A reminder of the Randall Sundrum Model
How can the weak scale be related to the Planck scale Mweak Mplanck ?
R&S were somehow inspired by the
Arkani-Hamed, Dimopoulos and Dvali (ADD) model :
Planck scale is « brought down » to the TeV scale
using 1 non factorisable xtraD
which doesn’t need to be 16 orders of magnitude large!
Universe made of two 4-dimensional branes
sandwiching a slice of 5-d spacetime.
SM fields live on the TeV brane (y=)
while gravity lives everywhere :
on the TeV and Planck (y=0) branes,
as well as in the bulkKK excitations of the graviton
5th dimension warped exponentially
ds2 = e -2krc|y|dx dx -r2c dy2
1/k ~ 1/1017-18GeV : curvature radius
rc : bulk radius
m=m0e-krc Mweak/ MPlanck~1 krc ~ 35
“y” is the massless graviscalar radion
while “” is the massless graviton
Randall Sundrum phenomenology in PYTHIA
Narrow massive graviton resonances in the TeV energy range
(4D KK excitations of Graviton)
First excited graviton has been implemented into Pythia.
Pythia production of
graviton state G* :
KF = 5000039
qq and gg intial states:
391 ffbar G*
392 gg G*
393 qqbar gG*
394 qg qG*
395 gg gG*
Universal decay modes:
ffbar, gg, , ZZ, WW
G* mass, k/MPlanck
So you see that the
CMS private Herwig
works as well
Universal Extra Dimensions (UEDs)
A review of the Universal Extra Dimensions (UEDs) model
“Universal” == ALL SM particles propagate into the XtraD(s)
n=1,2,3,… Kaluza Klein (KK) excitations for each SM particle of mass
mn2=n2/R2 + mSM2
n=0 corresponds to the SM particle
R : compactification scale ; Λ : cutoff scale above which the theory is no longer valid
Momentum is conserved in the extra dimensions.
In 3D (3D+t), this implies conservation of the KK number:
never a vertex with only one KK excitation hence KK particles are always produced in pairs
A bit of UED zoology
Q (Doublet), U and D (Singlets) fields describe the quarks in (4+) dimensions
e.g. for the 3rd generation first level particles
U(0)3tR and D(0)3bR
For each fermion 1 tower/chiral state ==
2 towers/quark flavor, 2 towers/lepton, 1 tower/neutrino
Bosons W3j and Bj mix within each level, as in the SM (level 0).
Each Higgs boson KK level is composed of:
1 charged Higgs, 1 scalar CP-odd Higgs of mass Mj and 1 scalar CP-even of mass (M2j+m2h)
The interactions between the Higgs field, the gauge bosons and the fermions
are described by the same couplings as those for the SM
“n=1” KK states – a very degenerate situation
All SM particles have practically the same mass == 1/R (compactification scale)
Below : 1/R = 500 GeV
Radiative Corrections – larger mass splittings
KK number is conserved at the tree level, but can be violated in first order loops
First order corrections can bring large contributions to the KK masses.
Tree level radiative corrections
~20% for strongly interacting particles (heaviest being the gluon)
<10% for leptons and EW bosons (lightest being the photon)
SM quark and gluon KK excitations will cascade decay to the
Lightest Kaluza Klein Particle (LKP) :*
Fermions and bosons live in a 4+δ ( R ~ TeV-1 ) dimensional “thick” brane
embedded in a larger 4+N ( size ~ eV-1 ; e.g. N=2 ) bulk where only gravitons propagate.
No a priori constraints on the number of UEDs.
Study the δ =1 case.
With radiative corrections to the masses
the KK excitations of SM quarks and gluons decay in a cascade
down to the Lightest KK Particle : the LKP *
The additional ingredient of gravity mediated decays (e.g. of the LKP)
KK excitations would also decay through KK number violating interactions mediated by gravity.
When decay widths of first level KK excitations due to mass splitting
gravity mediated decay widths,
gluon and quark excitations will decay in a cascade down to the * which in turn will decay as
Large density of states for the KK gravitons in the 5th D
the splitting between adjacent levels is of order eV
“Doing” Universal Extra Dimensions using :
CompHEP + PYTHIA
2005 : Generate events using CompHEP (CalcHEP).
Output is « LesHouches » standard.
Use Pythia 6.2 for the hadronization and decay
while introducing UED particles into Pythia (PYTHIA_UED).
It’s possible but rather complicated…
N.B. It’s rather simple but somehow ATLAS software makes it rather complicated…
Production cross sections
pp g*g*,g*q*,q*q* KK + KK
From Macesanu, McMullen and Nandi
Phys.Rev.D62 (2002) 015009,hep-ph/0201300.
□ : final state KK quark pair
: final state KK quark-gluon
: final state KK gluon pair
+ : top production
: Solid line: sum of all
Initial state quark pair
Initial state quark-gluon
Initial state gluon pair
Sum of all
== 100 fb-1 @ LHC
1 evt == 1 fb-1 @ LHC
Decay widths for bosons and fermions
decay widths (N=2,6)
Dq q’ W*, qZ*
Mass splitting decay widths
Search for the radion using the ATLAS detector,EPJ C, 4, C16, 1-13(2002), Azuelos etal.
The Hierarchy Problem and New Dimensions at a Millimiter
Phys.Lett. B429 (1998) 263-272, Arkani-Hamed, Dimopoulos, Dvali.
A Large Mass Hierarchy from a Small Extra Dimension,
Phys.Rev.Lett. 83 (1999) 3370-3373,Randall and Sundrum.
Bulk Fields in the Randall-Sundrum Compactification Scenario,
hep-ph/9907218v2, hep-ph/9907447, hep-ph/9911457 (best one),
Goldberger and Wise.
Graviscalars from higher-dimensional metrics and curvature-Higgs mixing
Radion effects on unitarity in gauge-boson scattering,
Phys.Rev. D64 (2001) 076003, Han, Kribs,McElrath.
Shifts in the Properties of the Higgs Boson from Radion Mixing,
hep-ph/0202155, Hewett and Rizzo.
The Scalar-Sector of the Randall-Sundrum Model,
hep-ph/0206192, Dominici, Grzadkowski, Gunion, Toharia.
Randall Sundrum Model
The gravitational and gauge interactions become united at the weak scale, which we
take as the only fundamental short distance scale in nature.
n>=2 new compact spatial dimensions large compared to the weak scale. The
Planck scale M_PL~G_N^-1/2 is not a fundamental scale; its enormity is simply a
consequence of the large size of the new dimensions.
SM particles must be localized to a 4d submanifold. The only fields propagating in the 4+n-d
bulk are the 4+n-d graviton.
the large Planck scale (weakness of gravity) arises because of the small overlap of the
graviton wave function in the 5th dimension (which is the warp factor) with our brane.
This is the only small number produced. All other scales are set by the TeV scale.
KK gravitational modes in the RS spacetime have TeV scale mass splittings and couplings,
in sharp contrast to KK decomposition in product spacetimes (e.g.ADD) which or large
compactified dimensions gives rise to a high number of light modes with splittings of the
order of the compactification scale (very small).
Goldberger and Wise:
KK decomposition of a non-gravitational scalar bulk field propagating in the RS spacetime.
The mass spectrum of the 4d KK modes is suppressed by a factor exp(-kr_c) relative to the
5d scalar mass. If kr_c is around 12, the low-lying KK modes would be characterized by a
scale which is on the order of a TeV: SM particles could be low-lying KK excitations of bulk
fields. (voir suite)
Goldberger and Wise (suite):
In RS, r_c is associated with the vacuum expectation value of a massless 4d scalar field.
r_c is not determined by the dynamics of the model. For this scenario to be relevant,
it is necessary to find a mechanism for generating a potential to stabilize the value of r_c.
Such a potential can arise classically from the presence of a bulk scalar with interaction
terms that are localized to the 2 3-branes. The minimum of this potential can be arranged
to yield a value of kr_c~10 without fine tuning of parameters.
A bulk scalar with (5th dimension) dependent VEV can generate a potential to stabilize r_c
without having to fine tune the parameters of the model.
However, there is still one fine tuning associated with the 4d cosmological constant.
When the radion and higgs have about the same mass, they mix heavily.
For L=10TeV and =1/6 and for radion mass~higgs mass, (gg) falls rapidly. This is because
the trace anomaly contribution cancels the one-loop top quark contribution for this highly
mixed state at that mass.
When the radion is much heavier than the higgs and =1/6, radion->ww,zz become close to 0.
But the photon BR climbs since it also couples to the trace anomaly (as for BR(gg)).
For =0 there is no Higgs-radion mixing. For close to 1/6, tree level couplings of the radion
to fermions and weak gauge bosons are suppressed and gg branching fraction becomes
dominant even for a very heavy radion.
Therefore, for a generic not too close to 1/6 the radion branching fraction phenomenology
mostly follows what we find for =0, except for the region of large mixing (m_h~m_),
where our discussion of the =1/6 case applies.
Bounds on Universal Extra Dimensions, Appelquist, H.C.Cheng, B.A.Dobrescu
Bosonic Supersymmetry, Getting Fooled at the LHC, Cheng, Matchev, Schmaltz
New Signal for Universal Extra Dimensions, Macesanu, McMullen, Nandi
C.Macesanu private communication