Universal Extra-Dimension at LHC

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1 Universal Extra-Dimension at LHC Swarup Kumar Majee National Taiwan University S. K. Majee NCTS-NTHU, 17-May-2011 p.1

2 Plan Hierarchy problem Extra-dimensions Flat extra-dimension (ADD and UED model) Warped extra-dimension (RS-model) Universal Extra Dimension (UED) The Scalar, Fermion, and Gauge particles in the UED model Evolution of Gauge Couplings Tree level and Radiative Corrected KK-Mass spectra Decay modes and Branching ratios of KK-particle Collider Signature of UED at LHC Conclusion S. K. Majee NCTS-NTHU, 17-May-2011 p.2

3 Standard Model Higgs SM: SU(3) }{{ C SU(2) } L U(1) }{{ Y } Strong(g) E W(W ±,Z and γ) UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.3

4 Standard Model Higgs SM: SU(3) }{{ C SU(2) } L U(1) }{{ Y } Strong(g) E W(W ±,Z and γ) Higgs: Φ (1,2,1) ( φ + φ 0 ) V = m 2 Φ Φ+λ(Φ Φ) 2 λ > 0 UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.3

5 Standard Model Higgs SM: SU(3) }{{ C SU(2) } L U(1) }{{ Y } Strong(g) E W(W ±,Z and γ) Higgs: Φ (1,2,1) ( φ + φ 0 ) V = m 2 Φ Φ+λ(Φ Φ) 2 λ > 0 m 2 > 0 UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.3

6 Standard Model Higgs SM: SU(3) }{{ C SU(2) } L U(1) }{{ Y } Strong(g) E W(W ±,Z and γ) Higgs: Φ (1,2,1) ( φ + φ 0 ) V = m 2 Φ Φ+λ(Φ Φ) 2 λ > 0 m 2 > 0 m H = 2m 2, v = m 2 < 0 0 φ 0 0 = v m 2 λ = 246 GeV Other components of Φ Goldstone bosons UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.3

7 Hierarchy problem Due to femion loop Π f hh = ( 1) Λ 0 d 4 k (2π) 4 Tr = λ2 f 8π 2 Λ m 2 H = m2 H 0 +δm 2 H { ( iλ f 2 ) i k m f ( iλ f } i 2 ) p k m f If GeV, required fine-tuning to 1 part in UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.4

8 Hierarchy problem and SUSY Due to femion loop Π f hh = ( 1) Λ 0 d 4 k (2π) 4 Tr = λ2 f 8π 2 Λ m 2 H = m2 H 0 +δm 2 H { ( iλ f 2 ) i k m f ( iλ f } i 2 ) p k m f If GeV, required fine-tuning to 1 part in Due to scalar loop : δm 2 H = λ S 16π Λ λ S = λ f 2 Supersymmetry UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.4

9 Extra Dimensions Consider, a massless particle in 5D Cartesian co-ordinate system, and assume that the Lorentz invariance holds. p 2 = 0 = g AB p A p B = p 0 2 p 2 ±p 5 2, with g AB = diag(1, 1 1 1,±1) So, p 0 2 p 2 = p µ p µ = m 2 = p 5 2 = time-like ED: m 2 = ve tachyon We consider only one space-type extra dimension(y) UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.5

10 Extra Dimensions Consider, a massless particle in 5D Cartesian co-ordinate system, and assume that the Lorentz invariance holds. p 2 = 0 = g AB p A p B = p 0 2 p 2 ±p 5 2, with g AB = diag(1, 1 1 1,±1) So, p 0 2 p 2 = p µ p µ = m 2 = p 5 2 = time-like ED: m 2 = ve tachyon We consider only one space-type extra dimension(y) free particle moving along x-direction = non-compact ψ = Ae ipx +Be ipx, momentum p is not quantized particle in a box = so V(x) = 0, 0 < x < L = infinite elsewhere = compact quantized momenta p = nπ L UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.5

11 ADD-model Consider a D-dimensional spacetime D = 4+δ Space is factorised into R 4 M δ, where M δ is a δ-dimensional space with volume V δ R δ. This implies the four-dimensional effective M Pl is M 2 Pl = M2+δ Pl(4+δ) Rδ Assuming M Pl(4+δ) m EW, we get M 2 Pl = m2+δ EW Rδ implies, R δ cm ( ) 1TeV 1+ 2 δ m EW δ = 1 R = cm is excluded due to the deviation from Newtonian gravity. But, for δ = 2 it is in the mm range. ( N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali) UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.6

12 RS-model m IR = m UV exp( πkr) (pic from José Santiago s talk) for kr 12, a mass m UV O(M Pl ) on the UV-brane corresponds to a mass on the IR brane with a value m IR O(M EW ). (Randall, Sundrum) UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.7

13 UED at a glance In UED model each particle can access all dimensions. ( Appelquist, Cheng, Deobrescu) We consider only one space-type extra dimension(y) So our co-ordinate system : {x(t, x),y} Compactification : S 1 /Z 2 Z 2 symmetry : y y necessary to get the chiral fermions of the SM Translational symmetry breaks p 5, hence KK number (n) is not conserved. y y +πr symmetry preserve KK parity ( 1) n conserved. 0 πr UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.8

14 UED at a glance n = 1 states must be produced in pairs Lightest n = 1 state is stable LKP All heavier n = 1 states finally decay to LKP and corresponding SM (n = 0) states Collider signals are soft SM particles plus large E Limit on the R GeV from g µ 2, B 0 B 0 mixing, Z b b (Agashe, Deshpande, Wu; Chakraverty, Huitu, Kundu; Buras, Spranger, Weiler; Oliver, Papavassiliou, Santamaria) 300 GeV from oblique parameters (Gogoladze, Macesanu) 600 GeV from b sγ at NLO (Haisch, Weiler) LKP dark matter Upper bound 1 TeV from overclosure of the universe (Servant, Tait) UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.9

15 Scalar, Fermion, and Gauge boson Scalar : φ(x, y) = 2 2πR φ (0) (x)+ 2 2πR n=1 φ (n) (x)cos ny R. UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.10

16 Scalar, Fermion, and Gauge boson Fermions : Scalar : Q i (x,y) = U i (x,y) = D i (x,y) = φ(x, y) = 2 2πR φ (0) (x)+ 2 2πR [ (ui ) 2 (x)+ 2 2πR d i L 2 [u ir (x)+ 2 2πR 2 2πR [d ir (x)+ 2 n=1 n=1 n=1 [ [ [ n=1 Q (n) ny il (x)cos U (n) ny ir (x)cos D (n) ny ir (x)cos φ (n) (x)cos ny R. R +Q(n) ir R +U(n) il R +D(n) il (x)sin ny R (x)sin ny R (x)sin ny R ] ], ] ]. ] ], UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.10

17 Scalar, Fermion, and Gauge boson Fermions : Scalar : Q i (x,y) = U i (x,y) = D i (x,y) = φ(x, y) = 2 2πR φ (0) (x)+ 2 2πR [ (ui ) 2 (x)+ 2 2πR d i L 2 [u ir (x)+ 2 2πR 2 2πR [d ir (x)+ 2 n=1 n=1 n=1 [ [ [ n=1 Q (n) ny il (x)cos U (n) ny ir (x)cos D (n) ny ir (x)cos φ (n) (x)cos ny R. R +Q(n) ir R +U(n) il R +D(n) il (x)sin ny R (x)sin ny R (x)sin ny R ] ], ] ]. ] ], Gauge boson : A µ (x,y) = A 5 (x,y) = 2 2πR A (0) µ (x)+ 2 2πR 2 2πR n=1 n=1 A (n) ny 5 (x)sin R. A (n) µ (x)cos ny R, UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.10

18 Effects of KK-modes on RGE RGE in SM : 16π 2 E dg i de = b ig 3 = β SM (g) d dlne α i 1 (E) = b i 2π Solution : α i 1 (E) = α i 1 (M Z ) b i 2π ln E M Z with b Y b 2L b 3C = UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.11

19 Effects of KK-modes on RGE RGE in SM : 16π 2 E dg i de = b ig 3 = β SM (g) d dlne α i 1 (E) = b i 2π Solution : α i 1 (E) = α i 1 (M Z ) b i 2π ln E M Z with b Y b 2L b 3C = In UED, DDG-Nucl.Phys.B537:47-108, π 2 E dg i de = β SM(g)+(S 1)β UED (g) where, S = ER β UED = b i g i 3 with by b2l b3c = UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.11

20 Gauge Couplings U(1) α SU(2) SU(3) log 10 (E/GeV) UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.12

21 Gauge Couplings U(1) 60 U(1) 50 α SU(2) α -1 g SU(2) 1 TeV 5 TeV 20 TeV SU(3) 10 SU(3) log 10 (E/GeV) log 10 (E/GeV) (Bhattacharyya, Datta, Majee, Raychaudhuri) UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.12

22 Radiatvie Corrections Cheng, Matchev, Schmaltz S. K. Majee NCTS-NTHU, 17-May-2011 p.13

23 Radiative corrections Tree level n th mode KK-mass m n = m 2 0 +n2 /R 2 Consider the kinetic term of a scalar field as L kin = Z µ φ µ φ Z 5 5 φ 5 φ, Tree level KK masses originate from the kinetic term in the y-direction. If there is Lorentz invariance, then Z = Z 5, there is no correction to those masses. A direction is compactified Lorentz invariance breaks down. Then, Z Z 5, leading to m n (Z Z 5 ). UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.14

24 Radiative: Bulk Corrections These corrections are finite and nonzero only for bosons. These corrections, for a given field, are the same for any KK mode. For a KK boson mass m n (B), these corrections are given by δm 2 n(b) = κ ζ(3) 16π 4 ( 1R ) 2 κ = 39g 2 1 /2, 5g2 2 /2 and 3g2 3 /2 for Bn,W n and g n, respectively. UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.15

25 Radiative: Orbifold Corrections Orbifolding additionally breaks translational invariance in the y-direction. The corrections to the KK masses arising from interactions localized at the fixed points are logarithmically divergent. δm n (f) m n (f) ( δm 2 ) n (B) m 2 n(b) = ( a g2 3 16π 2 +b g2 2 ) 16π 2 +c g2 1 16π 2 ln Λ2 µ 2, The mass squared matrix of the neutral KK gauge boson sector in the B n, Wn 3 given by basis is n2 R 2 + ˆδm 2 B n g2 1 v2 1 4 g 1g 2 v g 1g 2 v 2 n2 R 2 + ˆδm 2 W n g2 2 v2 For n = 1 and R 1 = 500 GeV, it turns out that sin 2 θ 1 W 0.01 (<< sin2 θ W 0.23), i.e., γ 1 and Z 1 are primarily B 1 and W 1 3, respectively. UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.16

26 Mass Spectra S. K. Majee NCTS-NTHU, 17-May-2011 p.17

27 Mass Spectra S. K. Majee NCTS-NTHU, 17-May-2011 p.17

28 Allowed transitions S. K. Majee NCTS-NTHU, 17-May-2011 p.18

29 Branching ratios γ 1 is the LKP. It is neutral and stable. KK W - and Z-bosons Hadronic decays closed. Can not decay to their corresponding SM-mode and LKP, as kinematically not allowed. W ± 1 and Z 1 decay democratically to all lepton flavors: B(W ± 1 ν 1L ± 0 ) = B(W± 1 L± 1 ν 0) = 1 6 B(Z 1 ν 1 ν 0 ) = B(Z 1 L ± 1 L 0 ) 1 6 for each generation. Z 1 l ± 1 l 0 decays are suppressed by sin2 θ 1. UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.19

30 Branching ratios γ 1 is the LKP. It is neutral and stable. KK W - and Z-bosons Hadronic decays closed. Can not decay to their corresponding SM-mode and LKP, as kinematically not allowed. W ± 1 and Z 1 decay democratically to all lepton flavors: B(W ± 1 ν 1L ± 0 ) = B(W± 1 L± 1 ν 0) = 1 6 B(Z 1 ν 1 ν 0 ) = B(Z 1 L ± 1 L 0 ) 1 6 for each generation. Z 1 l ± 1 l 0 decays are suppressed by sin2 θ 1. KK leptons The level 1 KK modes of the charged leptons and neutrinos directly decay to γ 1 and corresponding zero mode states. UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.19

31 Branching ratios The heaviest KK particle at the 1st KK-level g 1. B(g 1 Q 1 Q 0 ) B(g 1 q 1 q 0 ) 0.5. UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.20

32 Branching ratios The heaviest KK particle at the 1st KK-level g 1. B(g 1 Q 1 Q 0 ) B(g 1 q 1 q 0 ) 0.5. KK quarks SU(2)-singlet quarks (q 1 ): B(q 1 Z 1 q 0 ) sin 2 θ B(q 1 γ 1 q 0 ) cos 2 θ 1 1 SU(2)-doublet quarks (Q 1 ): SU(2) W -symmetry B(Q 1 W ± 1 Q 0 ) 2B(Q 1 Z 1 Q 0 ) and furthermore for massless Q 0 we have B(Q 1 W ± 1 Q 0 ) 65%, B(Q 1 Z 1 Q 0 ) 33% and B(Q 1 γ 1 Q 0 ) 2%. UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.20

33 Collider Signature Bhattacharyya, Datta, Majee, Raychaudhuri S. K. Majee NCTS-NTHU, 17-May-2011 p.21

34 Production M{qg QV 1 } 2 = πα s (ŝ)(a 2 L +a2 R ) { 2ŝˆt+2ŝm 2 } { 2ŝˆt 4ˆtm 2 Q Q +2ŝm2 Q +4m2 V 6 ŝ m 2 } Q (ˆt m 2 Q )2 2{ 2ˆtm 2 +2(ŝ+ˆt)m 2 Q V m 2 V 1 m 2 Q 2m4 V 1 } ŝ(ˆt m 2 ) Q Excited quark SU(2) Doublet(Q) (a R = 0) SU(2) Singlet (q) (a L = 0) Excited boson a L a R W 1 2 g 0 Z 1 g ( T3 e Q sin 2 θw) 1 g ( eq sin 2 θw) 1 γ 1 2cosθ 1 W e Q cosθ W cosθ 1 W 2cosθ 1 W e q cosθ W cosθ 1 W UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.22

35 Production Crosssection Production cross section (fb) q 1 γ 1 Q 1 γ 1 q 1 Z 1 Q 1 W 1 Q 1 Z R -1 (GeV) - // _ s = 14 TeV q 1 γ 1 Q 1 γ 1 q 1 Z 1 Q 1 W 1 Q 1 Z 1 _ /s = 10 TeV R -1 (GeV) - / 1000 UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.23

36 Basic cuts and n l crosssection basic cuts p jet T > 20GeV p lepton T p miss T > 5GeV > 25GeV M li l j > 5GeV η < 2.5 for all leptons and jet lepton isolation : R > 0.7, (n l 2 cases) crosssection (fb) Channel 0l 1l 2l 3l 4l Signal (500 GeV) Signal (1 TeV) Background UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.24

37 Two Leptons Signal Q 1 W 1 production followed by Q 1 Q W 1 Q 1 Z 1 production followed by Q 1 QZ 1 We separately consider like-flavor, i.e., e + e or µ + µ, as well as unlike-flavor, i.e., µ + e + e + µ, in our discussion. Background dominanat: t t and b b severely cut down: p jet T > 20GeV W pair production in association with a jet. Z pair (real or virtual) Zγ Additional Cuts: p T l 1 < 25 GeV, p T l 2 < 25 GeV, and M l1 l 2 M Z > 10 GeV UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.25

38 Two Leptons dσ/dp T l dσ/dp T l dσ/dm l1 l p T l 1 p T l 2 M l1 l 2 dσ/dp T l dσ/dp T l dσ/dm l1 l p T l 1 p T l 2 M l1 l 2 dσ/dp T l dσ/dp T l dσ/dm l1 l p T l 1 p T l 2 M l1 l 2 dσ/dp T l dσ/dp T l dσ/dm l1 l p T l 1 p T l 2 M l1 l 2 UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.26

39 Two Leptons s 14 TeV 10 TeV Cut used Signal Background Signal Background Basic cuts (43.10) ( ) 10.0 (14.6) ( ) Lepton isolation (35.24) (429.64) 8.28 (12.06) (212.78) p l 1 T < 25 GeV (30.88) (154.90) 7.52 (10.74) (80.70) p l 2 T < 25 GeV (18.00) 9.44 (18.40) 4.53 (6.52) 5.27 (10.22) M l1 l 2 M Z > (17.88) 9.18 (17.98) 4.51 (6.48) 5.17 (10.08) Cross section (in fb) at the LHC signal and background for the like-flavour(unlike-flavour) dilepton plus missing p T plus single jet for R 1 = 500GeV. UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.27

40 Three Leptons Signal Q 1 W 1 production followed by Q 1 Q 0 Z 1 Q 1 Z 1 production followed by Q 1 Q 0 W 1 Background t t production, WZ or Wγ production in association with a jet. Additional Cuts p T l 1 < 25 GeV, p T l 2 < 25 GeV, and M l1 l 2 M Z > 10 GeV. UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.28

41 Three Leptons s 14 TeV 10 TeV Cut used Signal Background Signal Background Basic cuts Lepton isolation p l 2 T < 25 GeV p l 3 T < 40 GeV M li l j M Z > 10 GeV Cross section (in fb) at the LHC of signal and background for the trilepton plus one jet and missing p T channel for R 1 = 500 GeV. UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.29

42 Four Leptons Signal Q 1 Z 1 production followed by Q 1 Q 0 Z 1 M li l j M Z > 10 GeV for i,j = 1,2,3,4, i j. s 14 TeV 10 TeV Cut used Signal Background Signal Background Basic cuts Lepton isolation M li l j M Z > 10 GeV Cross section (in fb) at the LHC of signal and background for the tetralepton plus one jet and missing p T channel for R 1 = 500 GeV. UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.30

43 Luminosity plot for a 5σ signal Lep 2-Lep(U) 2-Lep(U) 4-Lep 3-Lep 3-Lep 2-Lep(L) 2-Lep(L) _ s = 14 TeV / _ s = 10 TeV Integrated Luminosity (fb -1 ) - - // / R -1 (GeV) R -1 (GeV) UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.31

44 Conclusions we have focussed on the production of the n = 1 excitation of a EW gauge boson along with an n = 1 excited quark. First, we imposed some basic cuts to suit LHC observability: the leptons are required to satisfy p T > 5 GeV, the jet must have a p T not less than 20 GeV, the missing transverse momentum must be more than 25 GeV. R > 0.7 Single jet + p/ T + two leptons: Signal: f b, Background: 9.18 f b, Single jet + p/ T + three leptons: Signal: 5.00 f b, Background: 1.02 f b, Single jet + p/ T + four leptons: Signal: f b, Background: f b. The analysis performed here is based on a parton-level simulation and is of an exploratory nature. UED@LHC S. K. Majee NCTS-NTHU, 17-May-2011 p.32

45 S. K. Majee NCTS-NTHU, 17-May-2011 p.33

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