Unitarity Bounds for New Physcis from Axial Coupling at LHC Jing Shu Argonne / University of Chicago Based on the work: Jing Shu, arXiv: 0711.2516 [hep-ph] Pheno 2008 April 28, 2008 1 / 17
Outline • Motivation • Unitarity bound from an axial coupling • Two two-site moose UV completions • A stronger bound from 2 to n. • Experimental discovery and applications • Summary Pheno 2008 April 28, 2008 2 / 18
Motivation In QFT, if the tree level unitarity is violated in the scattering ampiltude, we know it must come from • Our theory becomes strongly coupled M.S. Chanowitz and M.K. Gaillard, Nucl. Phys. B 261, 379 (1985) • There is no gauge symmetry assciated with the massive spin one particles J.M. Cornwall, D.N. Levin, and G.Tiktopoulos, Phys. Rev. D 10, 1145 (1974) B.W. Lee, C. Quigg, H.B. Thacker, Phys. Rev. Lett. 38, 883 (1977); Phys. Rev. D 16, 1519 (1977) Applying to SM, and considering we haven’t discovered higgs yet, we know that SM higgs mass must be light, or ............... Pheno 2008 April 28, 2008 3 / 18
Motivation At the LHC, if there are new physics beyond SM, very probabally we won’t see the full sector of new physics. New particle spectrum Then perhaps the gauge symmetry in beyond SM the underlying theory is apparantly violated in the incomplete theory LHC energy that we can recontruct from LHC observables. SM particle spectrum A new spin one particle with a nonzero G 1 ψ 0 axial coupling to fermions is such a case. Pheno 2008 April 28, 2008 4 / 18
Motivation G n Then tree-level unitarity is violated New in , and we can ψ 0 ψ 0 → G 1 G 1 ¯ particle G 2 spectrum predict the scale of new physics beyond SM beyond the reach of LHC in a model- G 1 independent way! ψ 0 LHC energy SM t particle spectrum Perhaps one of the first scientific W, Z reasons to build the next generation colliders (VLHC, muon collider, etc). Pheno 2008 April 28, 2008 5 / 18
Unitarity bounds ? Suppose we observe a new spin one particle G 1 G 2 with mass at LHC, and decays into some G 1 M G ? ? fermion with mass . ψ 0 m 0 ψ 1 ψ 1 R L We can measure the couplings to the left and G 1 G 1 M G right components of and we find the axial ψ 0 LHC energy coupling is nonzero. g A ≡ ( g 1 L − g 1 R ) / 2 g 1 R g 1 L ψ 0 ψ 0 L R If , the leading order bad behaved processes are g A � = 0 m 0 coming from chirality-nonconserving channels such as √ s and it is ∝ m 0 ψ 0 ¯ L ψ 0 L → G 1 G 1 Here we focus on the J=0 partial wave amplitude and drop out the irevelant pieces that are related to G^1 self- interaction that perhaps could be measured at LHC. Pheno 2008 April 28, 2008 6 / 18
Unitarity bounds m 0 M = 4 g 2 √ s s ≫ m 2 0 M 2 A M 2 G G 0 L 0 R G 1 G 1 G 1 0 0 m L L 0 L 0 m 0 R L 0 R m G 1 G 1 G 1 0 0 L 0 0 R (c) (a) (b) R R � 1 d cos θ M = Cg 2 √ s A m 0 1 � 1 a 0 = 4 π M 2 32 π 2 − 1 G √ 2 π M 2 assume we define the spin-singlet G √ s � E U = combination for the inital states Cg 2 A m 0 C represents the color factor where C=1 is for the Abelian case and is for the SU(N) case. C = ( N 2 − 1) / 2 N Pheno 2008 April 28, 2008 7 / 18
Two-site UV completion (A) Could be viewed as a two ¯ ¯ site deconstructed “KK ψ A ψ B L L gluon” (N=3) and top quark After the link field gets a vev . y Σ � Σ i ¯ k � = u δ i ¯ k M SU(N) A the mass eigenstates of the gauge bosons SU(N) B and left-handed fermions become mixture of their gauge eigenstate. ψ A ψ B � G 0 � � � � � c g s g A µ R R µ = G 1 s g − c g B µ µ � ψ 0 � � � � ψ A � − c f s f The “0-mode” fermion is massless, we L L = ψ 1 ψ B s f c f can introduce a gauge invaraint mass L L M ′ ¯ term to give the mass. We ψ A ψ A could come from another SGSB work in the limit aaaaaaaaaaaaaaaaaaa M ′ ≪ yu, M M ′ sector like y ′ ¯ ψ A ψ A φ Pheno 2008 April 28, 2008 8 / 18
Two-site UV completion (A) In this limit, the “KK-modes” gain their G 1 , ψ 1 mass from the link field condensation ψ 1 ψ 1 (compactification in 5D case). The “0- R L σ mode” , on the other hand, gains their mass ψ 0 G 1 differently (like top quark from EWSB) and LHC energy does not couple to the link field. g 1 R g 1 L ψ 0 ψ 0 L R The tree level unitarity in a ψ 0 ψ 0 → G 1 G 1 ¯ m 0 scattering is recovered if one consider in ψ 1 G 0 the t, u-channel. The full results for maintainning tree-level unitarity is shown based on mass insertion techniques. Pheno 2008 April 28, 2008 9 / 18
Two-site UV completion (A) If we miss , which is not a gauge ψ 1 Apprent explicit eigenstate, its mass term and interactions violation of gauge are also not in a gauge invariant form. invariance! Violation of Goldstone equivalence Violation of principle, Wald Identity. ψ 0 does not couple to , as it doesn’t π Without , ψ 1 couple to Σ G 1 0 0 =0 � = Violation of tree- G 1 level unitaity. 0 0 Pheno 2008 April 28, 2008 10 / 18
Two-site UV completion (B) y ′ → ∞ Sending * **, with a WZW term ¯ ¯ ψ A ψ B L L left to cancel the gauge anomaly. No Dirac mass term in moose A and B. y � Σ † y Σ For fermions, the mass eigenstate is the SU(N) A SU(N) B gauge eigenstate. No mixing! Like the case in SM, no violation of gauge invaraince. σ ψ A ψ B G 1 R R LHC energy The tree level unitaity in a ψ 0 ψ 0 → G 1 G 1 ¯ g 1 R g 1 L scattering is recovered from the s-channel s σ ψ 0 ψ 0 exchange, or our symmetry breaking is L R m 0 triggered by strong dynamics. G 0 Very similar to in SM. ¯ tt → ZZ Pheno 2008 April 28, 2008 11 / 18
A stronger bound from 2-->n It is discovered that unitarity bounds from 2 to n process will give a stronger than the 2 to 2 process because of the growing of the phase space in the final state. F. Maltoni, J.M. Niczyporuk and S. Willenbrock, Phys. Rev. D 65, 033004 (2002) D. A. Dicus and H.J. He, Phys. Rev. Lett. 94, 221802 (2005); Phys. Rev. D 71, 093009 (2005). For a 2 to n inelastic collision, the total cross section is bounded by σ inel [2 → n ] � 4 π We assume that the corresponding 2 to 2 elastic channel is dominated by s-partial wave. s Pheno 2008 April 28, 2008 12 / 18
A stronger bound from 2-->n We can derive a unitarity bound from scattering. ψ 0 ψ 0 → nG 1 ¯ 2 n − 1 ( n 2 !) 2 1 �� M G � 2 1 � R = 2( n − 1) 2 π M G ( n !) 2 ( n − 1)!( n − 2)! E U = Cg A 2 g A m 0 R C = ( C F ) n/ 2( n − 1) We can double check the unitaity bound here by comparing with the true new physics scale in model A ( mass) and B ( mass) ψ 1 σ respectively. We find that the unitarity bound here is always higher than true new physics scale as long as all couplings are weakly coupled. Pheno 2008 April 28, 2008 13 / 18
Experimental discovery In order to know and , we have to measure chirality, so ψ 0 g 1 L g 1 R ψ 0 must decay before it hadronize if it is colored. top quark Γ ψ 0 > Λ QCD t’ quark (top partner) if it is colored chiral 4th generation The axial coupling could be measured by looking at the angular g A ψ 0 distribution of leptons from decay in the rest frame. ψ 0 One can even define variables like “polarization asymmetry” to directly measure such , which is just like A F B g A K. Agashe, A. Belyaev, T. Krupovnickas G. Perez and J. Virzi Phys. Rev. D 65, 033004 (2007) Perhaps our methods can’t apply to the models with discret parity as the pair produced missing will make it very difficult E T ψ 0 to reconstruct Pheno 2008 April 28, 2008 14 / 18
Applications 100 M G = 3TeV 90 Precise Unitarity Bound (TeV) (a) RS1 with SM in the bulk. 80 1st KK gluon top quark G 1 ψ 0 70 (b) RS1 with O(3) extended 60 custodial symmetry. 50 (a) 1st KK gluon top quark G 1 ψ 0 40 (b) (c) The same as (b) but with 30 (c) 1st KK gluon t’ quark G 1 ψ 0 (d) 20 (d) Top quark seesaw. 10 coloron top quark G 1 ψ 0 0 2 4 6 8 10 12 14 16 18 20 n We choose the typical parameters in the above models. Unitarity bounds very LOW! Pheno 2008 April 28, 2008 15 / 18
Applications Really apply to any model without discrete parity with a large axial coupling. Warped extra dimension models We really need the Higgsless models next generation etc! Little higgs models withour T -parity. colliders (VLHC?)to distinguish and study deconstructed moose models those posibilities in models with gauge extension detail. Generally speaking, if M G /g A < 3 TeV ψ 0 is the top quark, E U < 78 TeV Pheno 2008 April 28, 2008 16 / 18
Road map 0 We can measure aa M G , m 0 and find is spin one. G 1 G 1 0 Maybe colored or not? G 1 G 1 0 From decay, in the rest ψ 0 ψ 0 Imgine frame, the is measured through g A G 1 the angular distribution of leptons G 1 0 G 1 Build the next E U < ? TeV generation colliders? Pheno 2008 April 28, 2008 17 / 18
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