Search for “Large” Spatial Extra Dimensions at the Tevatron Tom Ferbel University of Rochester Cairo - 2001 January 9-14 This was stolen from Greg by Tom, and edited for a 25 minute talk at Cairo
Dec 31, 2015
Search for “Large” Spatial Extra Dimensions at the Tevatron
Tom FerbelUniversity of
Rochester
Cairo - 2001January 9-14
This was stolen from Greg by Tom, and
edited for a 25 minute talk at Cairo
Is There Life Beyond the Standard Model ?The Standard Model is recognized as a low-energy approximation to a more complete theoryThis new theory supposedly takes over at some scale , comparable to the Higgs mass, i.e., 1 TeVAt one time, there were two serious candidates for such a theory:
SUSY Strong Dynamics
But more recently, it has been suggested that there may be no other scale, and that the SM model is fine up to some effective “Planck” scale of ~ 1 TeV
[ Arkani-Hamed, Dimopoulos, Dvali (1998) ]
How Does This Work?
Change in Newton’s law:
Ruled out for huge extra dimensions, but not for sufficiently small n compactified extra dimensions of size R:
1
2123
212
11
nnn
PlPl r
mm
Mr
mm
MrV
= the effective Planck Scale, MS
Rr
rR
mm
MrV
nnnPl
for
1 2123
Effectively Makes Gravity Strong
G’N = 1/MS2 GF MS 1 TeV
More precisely, from Gauss’s Law:
There are very few tests of Newton’s Law at distances smaller than 1 mm
Consequently, large spatial extra dimensions compactified at sub-millimeter scales cannot be excluded!
nPl
nS RMM 22
4 106
3 3
2 7.0
1 108
2
1
12
12
2
n,m
n,nm
n,mm
n,m
M
M
MR
n/
S
Pl
S
Kaluza-Klein Gravitons
Compactified dimensions greatly increase the strength of gravitational interactions through Kaluza-Klein “winding” modes or GKK gravitons
From the point of view of a (3+1) space-time, the Kaluza-Klein graviton modes are massive, with the mass excitation spaced 1/RBecause the mass per excitation mode is small (e.g. 400 eV for n = 3, or 0.2 MeV for n = 4), a very large number of modes can be excited at high energies
Compactified dimension
R
GKK
Flat
dimension
Each Kaluza-Klein graviton mode couples with gravitational strength For the large number of modes, accessible at high energies, gravitational coupling is therefore greatly enhancedLow energy precision measurements are not sensitive to ADD effects
Signatures for Large Extra Dimensions at the Tevatron
Kaluza-Klein gravitons couple to the energy-momentum tensor, and therefore contribute to most SM processes
Since gravitons can propagate in the bulk, from our perspective in (3+1) space-time, energy and momentum will appear not to be conserved in GKK emission
Since the spin-2 graviton, in general, has a momentum component in the bulk, its spin from the point of view of our brane can appear to be 0, 1, or 2
Depending on whether the GKK leaves our brane or remains virtual, collider
signatures can include single photons/Zs/jets with missing ET,, or pair produced objects
Real Gravitons Monojets at hadron colliders
GKK
gq
q GKK
gg
g
Single VB at hadron or e+e- colliders
GKK
GKK
GKK
GKK
V
VV V
Virtual Gravitons Fermion or VB pairs at hadron or e+e- colliders
V
V
GKKGKK
f
ff
f
Virtual Gravitons For the case of pair production, amplitude for gravity contribution interferes with the SM (e.g., l+l- production):
Production cross section has three terms: SM, interference, and direct gravity The sum in KK states is divergent in the effective theory, so calculation of cross sections, requires explicit cutoff Expected value of the cutoff is MS (the scale at which effective theory breaks down, and string theory must be used)
Three different conventions used for writing an effective Lagrangian:
Hewett, Phys. Rev. Lett. 82, 4765 (1999)Giudice, Rattazzi, Wells, Nucl. Phys. B544, 3 (1999); revised version, hep-ph/9811291Han, Lykken, Zhang, Phys. Rev. D59, 105006 (1999); revised version, hep-ph/9811350
All are completely equivalent, and only the definitions of MS differ:
M,cosfM
nbM,cosf
M
nadMcosd
d
dMcosd
d
*
S
*
S
*SM
*
2814
22
Hewett, GRW, and HLZ Formalisms
Hewett: neither sign of the interference nor the dependence on the number of extra dimensions is specified; hence, for the interference term use ~/MS
4(Hewett), where is of order 1, and ±1
GRW: sign of the interference is fixed, but the dependence on number of extra dimensions not
specified; therefore, interference term is ~/T
4 (where T is notation for MS)
HLZ: sign of interference and the n-dependence calculated in effective theory; with interference term ~F/MS
4(HLZ), and F containing explicit dependence on n:
Correspondence between formalisms:
Rule of thumb:
GRWHewett TSM
41
2
2 2
22 , log
2
n,n
nsM S
F
HLZHewett 44 2 SS MM
F
HLZGRW 44
1
ST M
F
51
nSS MM HLZHewett
4
nST M HLZGRW
Dilepton and diphoton production via virtual gravitonMass spectrum has been looked at [Gupta, Mondal, Raychaudhuri, hep-ph/9904234; Cheung, Phys. Rev. D61, 015005 (2000), Phys. Lett. B460, 383 (1999),…]Improvement [Cheung, Landsberg, PRD 62, 076003 (2000)]: simultaneous analysis of mass and angular distributions (J=2 graviton different angular distributions from SM )There are three terms: SM, interference, and direct graviton contributionUse Han/Lykken/Zhang formalism:
Virtual Graviton Exchange at the Tevatron
*
4cos, z
M S
HLZ
F
Dileptons: Diphotons:
2 2
22 , log
2
n,n
nsM S
F
822
42
2121
8222
4222
44
2
2
2121
2
512
61
12
21
2
96
1
MM
zzKxfxfdxdx
MzMQez
Qe
M
zKxfxfdxdx
dzdM
d
qg
q
GKK termSM
interference term
GKK term
NLO corrections accounted for via a constant K-factor
Search at DØ
First search for large extra dimensions at Tevatron
Based on Cheung/Landsberg, with following modifications:
DØ detector does not have a central magnetic field, hence cannot measure electric charge of electrons use |cos*|
Dimuon mass resolution at high mass is poor do not use dimuons
Dielectron and diphoton efficiencies are only moderate (~50%) due to tracking inefficiency (for electrons) and conversions or overlap of photons with random tracks maximize DØ discovery potential by combining dielectrons and diphotons (essentially ignore tracking information), i.e., use di-EM signature!
Instrumental background is not expected to be important at high mass,
hence, release strict EM-ID requirements to maximize efficiency
Mulitjet and Direct Photon Background
SM vs. instrumental backgrounds
[Landsberg & Matchev, PRD 62, 035004 (2000)]
Data Selection and Efficiency
Use entire Run-1st luminosity, low-threshold, di-EM triggers: Ldt = 127 6 pb-1
Offline criteria: Exactly 2 EM clusters, ET >5 GeV, ||<1.1 or 1.5<||<2.5, passing basic EM ID criteria:
EMF > 0.95ISO < 0.102 < 100
MET < 25 GeV No other kinematic restrictions in the analysis, since (M,cos*) define the process completely
Resulting data sample contains 1250 eventsEfficiency of the ID is determined from Z events obtained with same triggers, but lower ET(EM) threshold
Criterion # of events
Starting sample 87,542
Quality criteria 82,947
2 EM 82.927
=2 EM 82,425
ET > 25 GeV 36,409
Acceptance 30,585
EM ID 10,711
ET > 45 GeV 1,250
Criterion Signal Efficiency
EM ID (87 2)%
MET < 25 GeV (98 1)%
Event quality (99.8 0.1)%
Overall, per event
(79 2)%
Monte Carlo for Signal and Background
Based on Cheung/Landsberg LO parton level generator that produces weighted events
Augmented with fast parametrized DØ detector simulation that models:
DØ detector acceptance and resolutions
Primary vertex smearing and resolution
Effects of additional vertices from multiple interactions in the event
Transverse kick of the di-EM system to account for ISR effects
Integration over parton distribution functions (CTEQ4LO and other PDFs)
K-factor correction to cross sections
Both SM and gravity effects
Summary of BackgroundsSM backgrounds in the MC:
Drell-Yan (e-pairs)(gg is negligible not included)
Other SM backgrounds are mostly at low mass, and negligible:
W+j/< 0.4%WW < 0.1%top < 0.1%Z < 0.1%Z+ < 0.01%Other < 0.01%
Instrumental background from jj/j “” from jet fragmenting to leading 0
Determined from data with single-EM triggers (40 GeV threshold) & applying probability of (0.18 0.04)%, for a jet to mimic photon - independent of (ET,Instrumental background (mostly jj)~7%
Ignore smaller backgrounds
, f
b/b
in
M(di-EM), GeV
Total SM
backgroundqq
gg
At high mass, SM background
dominated by qq
MC Description of Data and Systematics
Kinematic distributions are well described by the sum of SM and instrumental backgrounds
Following systematic uncertainties on differential cross sections were taken into account:
Instrumental background (uncertain to 25%)
Source Uncertainty
K-factor 10%
Choice of PDF 5%
Ldt 4%
Efficiency 3%
Overall 12%
Observe good agreement in
Mass cutoff N B P
> 100 GeV 687 682 0.43
> 150 GeV 134 138 0.63
> 200 GeV 53 52.2 0.47
> 250 GeV 18 23.5 0.90
> 300 GeV 10 11.4 0.70
> 350 GeV 5 5.8 0.69
> 400 GeV 3 3.0 0.58
> 450 GeV 2 1.5 0.44
> 500 GeV 2 0.67 0.15
> 550 GeV 1 0.23 0.21
> 600 GeV 0 <0.1 1.00
Instrumentalbackground
Monte Carlo for Signal and Background
SM 4
8 MS = 1 TeVn=4
Fit MC & Data to Extract Effects of Gravity Bin the events in a M|cos*| grid (up to 4010 bins; M[0,2 TeV], |cos*|[0,1])Parameterize cross section in each bin as simple form in : = SM+4+28
Use Bayesian fit with flat prior (in ) to extract the best value of and 95% C.L. intervals:
Cross-check using maximum likelihood
950
22
1
95
0
2
20
2
20
.|;|maxˆ
,|expexp|
,!
,|,
NPdNP
BNPSS
dSbb
dbA
NP
LdtSn
BSenBSBNP
Sb
ijijji ij
ijijijijij
MS extraction
input
n=4MS = 1.3 TeV
expected limits: < 0.44 TeV-4
@ 95% C.L.
DØ Results in Di-EM Channels
High mass and small |cos| are characteristic signatures of LED
2-dimensional analysis resolves LED from high-mass and large |cos| tail from QCD diphotons
No excess seen at high mass and large scattering angles, where LED signal is expected
Limit found: 0.46 TeV-4
Expected limit: 0.44 TeV-4
DØ Limits on Large Extra DimensionsFor n > 2, MS limits can be obtained directly from limits on For n = 2, use average s for gravity contribution ( s = 0.36 TeV2)
Translate limits in the Hewett and GRW frameworks for ease of comparison with other experiments:
MS(Hewett) > 1.1 TeV and 1.0 TeV ()T(GRW) > 1.2 TeV
These limits are similar to most recent preliminary results from LEP2Complementary to those from LEP2, probing different range of energiesLooking forward to limits from CDF DY analysis (MS ~ 0.9-1.0 TeV), utilizing the same technique
Sensitivity is limited by statistics; reach in terms of MS will double in Run-2a (2 fb-1) and triple in Run-2b (20 fb-1)
^
^hep-ex/0008065,to appear in PRL
Highest-Mass Candidates
Parameters of the two candidate events of highest mass:
Run Event
Zvtx MET Type
ET1 ET
2 1 2 M cos*
Nje
t
PT-kick
90578
27506
3.6 cm
15 GeV
81 GeV 81 GeV 1.98
-1.91
575 GeV
0.86 0 11.7 GeV
84582
11674
-34 cm
15 GeV
ee 134 GeV
132 GeV
0.99
-1.59
520 GeV
0.84 0 18.8 GeV
Event with highest mass observed in Run-1
M() = 574 GeVcos* = 0.86
Summary
DO has searched for contributions from virtual graviton exchange in a context motivated by the possibility of there being only one scale for particle physics, and “large” extra spatial dimensions. On the basis of the production of massive e-pairs and di-photons, such a scale, must be higher than ~ 1 TeV
More studies are being pursued at both DO and CDF, and can be expected to start converging in winter 2001. These will be both on virtual-graviton exchange as well as real graviton (mono-jet) production.
Run-2 will (eventually) be sensitive to scales of 3-4 TeV
The LHC will be able to access effective “Planck” scales of > 10 TeV
And now back to musing on Flatland (such stuff as dreams are made on)
Next-to-Leading Order Corrections
Angle * in the parton-level cross section is defined as the angle between the incoming parton from p and the l+, i.e. in the Gottfried-Jackson frameIn the presence of ISR this frame is no longer viable, and we use instead the helicity frame, defining * as angle between the direction of the di-EM system (boost) and the direction of EM object in that frame.ISR-induced “smearing”, i.e. the difference between cos* in the GJ and helicity frame is small (~0.05)ISR effect is modeled in the signal MCSince NLO corrections for diphoton and dielectron production cross section are close, there is no theoretical “overhead” related to adding two channels; we use K = 1.3 ± 0.1No FSR for true di-EM final states
Boost of EM-pair
z
ISR
helicity angle
*
q
q
EM
EM
*
z
helicity angle= GJ angle
q q
EM
EM