Single Color-Octet Scalar Production at the LHC

Transcription

1 ingle Color-Octet calar Production at the LHC : Factorization and Resummation A. Idilbi, C. Kim and T. Mehen, ArXiv: [hep-ph] Chul Kim Duke University

2 Motivation calar ector in tandard Model (M) All the matter fields discovered so far are fermions. Hidden local symmetry in Nature requires pontaneous ymmetry Breaking Mechanism - Usually the potential is expressed in terms of scalar fields. The calar ector has not been tested experimentally. V ( φ) λ φ 4 = m λ Why not colored scalar particles?

3 Various NP Models predicting Color-Octet calar Color-octet scalar fields arose in GUTs. Model Hidden color symmetry breaking U(3) U(3) U(3) 1 C - Chiral Color Model Frampton and Glashow, Top Color Hill, 1991 Leptoquark Model U(5) Adjoint Perez et al., 008 Popov et al., 005, based on Pati-alam Unification U(4) U() U(1) U (3) U () U(1) V L c L U(5)-Type II eesaw Dorsner and Mocioiu, 008 Upper mass bound 440 TeV 50 TeV - Compared to GUT scale, surprisingly light Color-Octet calars UY - calar gluon (MRM) Plehn and Tait, 008

4 Manohar-Wise Model Manohar and Wise, Generic NP model satisfying the constraints of MFV Minimal Flavor Violation (MFV) Hypothesis If we expect new physics at a few TeV scale, - Generic flavor-violating interactions (Ex: FCNC) at a few TeV scale are not supported by experiments. - M Yukawa couplings should be only sources for quark flavor symmetry breaking. U, D U, D λij gij - Allowed U(3) c U() W U(1) Y representations for scalar fields with Yukawa couplings to M fermions consistent with MFV are 1) (1, ) 1/ : M Higgs doublet ) (8, ) 1/ : Another possible representation in quark Yukawa sector. - Yukawa ector for Color-Octet calar L Yukawa = η g + = U U D A A ij UR iqlj ηdgij DRi QLj H.C., T The same coupling as M

5 Color-Octet calar Production at the LHC Gluon fusion process gives a dominant contribution ( s = 14 TeV) - ingle Production : loop induced processes, depends on new physics parameters - Pair Production : Tree level process, Model-independent QCD Lagrangian for color-octet scalar fields LQCD, = ( D ) m a* ab b a* a

6 Constraints from Tevatron experiments ( s = 1.96 TeV) are weak. - Quark-antiquark initial state contributions are dominant. - From the comparison of measurement of 4b-jets, m 00 GeV suggested. Gerbush et al., (Under the assumption bb is a dominant decay channel) As mass increases, the single production becomes dominant. gg X gg X m < 1 TeV : Pair production > ingle production m > 1 TeV : Pair production < ingle production Gresham and Wise, 007

7 Factorization for the single production Kinematics Approximation to the partonic threshold region ( z= 1 ) ŝ - Gluon PDF is dominant in small x region ( ). m τ= m / s 1 - Color-octet scalar field can be described as a heavy field to do only soft interactions ( ). Three eparate cales m (1- z) μ m μ m (1 z) Λ m H QCD P Virtual Real & Virtual PDFs

8 Description of the factorization theorem τ σ( pp X ) τh ( m, μ ) ( m (1 z), μ ) F(, μ ) z F F F H( m, μ ) H τ F(, μf ) z μ H m ( (1 z), μ ) μf μ - Resummation of large logarithms such as ln μ H is necessary. μ

9 Factorization formula can be applicable to any other new physics model = Cm (, μ ) All the information on short distance interactions including EW/new physics interactions. - Long distance strong interactions like collinear or soft interactions. Precise Results enable us to extract correct information on unknown parameters. - New physics parameters - Better mass bounds if we do not see

10 Large K-factor for the single production Production Mechanism is similar to Higgs - Factorization formalism is similar - A difference is a strong interaction of color-octet scalar particle. trong Corrections to Higgs production are Huge Catani et. al, 003

11 Where do large color corrections come from? - Large log resummed effects at the threshold region ln(1 z) Ex) α..., 1 z As mass increases, the corrections become larger. - π -enhancement in timelike process (1) μ μ Ex) C ( Q, μ) α ln α ln + π Q iε Q π - Higgs production : -enhancement contribution is dominant. Ahrens, Becher, Neubert, and Yang, Color-Octet Production : more complicated. Timelike and spacelike processes are mixed. Resummation effects are larger than Higgs ( m m ) H

12 CET Operator for Color-Octet Production Collinear gauge-invariant building block - Describes two incoming gluons from protons B = in g G W, B = in g G W. a, μ ρ μν b ba a, μ ρ μν b ba n n, ρν n n n, ρν n Lightcone vectors n n n n = = 0, =. Gluon PDF in CET 1 n P f ( x) = p B δ x B p xn ( P) n P a, μ a g / p n n n μ n Heavy calar Effective Theory : analogous to HQET - After integrating out heavy mass, describes soft interactions. L HET 1 = v id D ac ( ) ( ) a* c a* ac c v v v v m 1 ( x) = e + e m imv x + imv x * ( v v ) a a a Bauer, Fleming, Pirjol, Rothstein, and tewart, 00,

13 Decoupling soft-interactions B Y B B B Y a, μ ab b, μ a, μ ab b, μ a ab b n n n, n Yn n, v v v - oft Wilson lines x a μ a Yk( x) = P exp ig dsk A( sk ) t, k = v, n, n. No more strong interaction like Higgs Bauer, Pirjol, and tewart, 001 B n tructure of CET Operators * v Yn, Yn, Yv ( ) oft gluon Wilson lines B n

14 Effective Theory Lagrangian for single color-octet production L EFT - Generic CET Operators O 1 ( ) 1 = Cf ( μ) Of ( μ ) + Cd( μ) Od( μ ) + O m m abc abc ( if, d ) = Y Y B YB m * μ ( ) ( ) ( μ) a b c ( f, d) v v n n n n - In case of Pseudoscalar color-octet abc abc p ( if, d ) * a μ b ν c 1 ρ σ O( f, d) = εμ ν ( Yvv) ( YB n n ) ( YB n n ), ε μν = εμν ρσn n. m Coloron (Axigluon) ( if, d ) O v A m abc abc X σ ρ a μ b ν c ( f, d) = εμνρσ Yv Xv YnBn YB n n * ( ) ( ) ( ) - Factorization and Resummation formulae are independent of the Lorentz tructure. - There is no mixing between O and O. f d.

15 Factorization Theorem 1 dz τ σ( pp X ) =τ Hi( m, μf) i( m(1 z), μf) F(, μf) τ z z i= f, d π dy x H ( m, μ ) =, C ( m μ), F( x, μ F) = fg/ p( y, μf) fg/ p(, μf), x y y ( f, d ) (, ), m f d f f 3d d i m z z abc def abc def ak bl cm 0 kd le mf { f, d} ( (1 )) =, 0Yv Yn Yn δ 1 + Yv Yn Yn m caling evolution dc f, d( m, μ ) =γ H( μ ) Cf, d( m, μ ), d ln μ 1 d f, d( m(1 z), μ) dz dln μ [ ] = γ (, ) Re ( ) (1 ) g z μ γh μ δ z f, d( m(1 z), μ), z x

16 Anomalous Dimensions for NLL Resummation 1 μ μ Γ cusp H cusp g ε (1 ) g γ ( μ ) = Γ ln + ln + B, γ ( z, μ ) = + B δ(1 z). m m i z + ln k k α (, g) (, g) α cusp Ak, B Bk. k= 1 4π k= 1 4π Γ = = μ m iε n n Timelike v ln μ m n n pacelike v oft function at NLO m z m z f ( (1 ), μ ) = d( (1 ), μ) α π μ μ α μ 1 ln(1 z) =δ(1 z) 1+ CA 1 + ln + ln CA 4 ln 4. 4 m m + + π π m (1 z) + 1 z +

17 Resummation Resummation in Moments pace : N ( τ&z 1) ( ) 1 N 1 N N d pp X H( m, 0 H, F) N(, F) fg/ p( F) σ = ττ σ μ μ μ μ μ [ G m ] N = σ0 exp (, μ ) F fg/ p( μf) m m -The scales are chosen as μ H = m, μ = = γe Ne N (0) (1) ( ) G ( m, μ ) = g ln N + g ( m, μ ) + g ( m, μ ) α ( m ) +... F F F LL NLL NNLL α λ= β0 ln N, α ln (1) 4 π O

18 Resummation in Momentum pace Becher and Neubert, 006 Becher, Neubert, and Xu, dz τ σ( pp X ) =σ0τ V (, z m, μf) F,, z μf z z η γeη (,, ) ˆ z e V z m μ = H( m, μ ) U ( μ, μ, μ ) (, μ ). F H H F 1 η η (1 z) Γ( η) L d e / (, ) s ω γ E + μ = ω ( ω, μ), ( ω ) = ( ω)/ m, ( 1 ), 1/( L ) 0 ω = m z s = e μ Up to NLL ( H = = 1) ˆ, α ( μ ) B α ( μ ) g 1 1 F ln U( μh, μ, μ F) = 4 UNLL ( μh, μ ) + ln + ln, β0 α( μh) β0 α( μ) B A 4π 1 A β β U r r r r NLL ( μh, μ ) = 1 ln (1 ln ) ln β0 α( μh) r A1 β0 β0 1 A α ( μ ) <η μ μ = < ( ) 1 F (, F) ln 0 β0 α μ Hˆ = H / σ α( μ) r = α ( μ ) : In the integral, we subtract the singular values at z=1, and then add the same quantity keeping the analytic continuation in η. Ex) x η = 0. x 0 H 0

19 Exponentiation of the large π corrections In case of Higgs, Ahrens, Becher, Neubert, and Yang, 009 (0) A CH( μ ) = CH ( μ ) Re 1+ ln π mh iε (0) CH ( μ ) 1+ μ (0) CH ( ) : μ = mh παc mh - Exponentiation of π -enhancement A μ = α C U ( μ = im, μ, μ ) = U ( im, m ) U ( m, μ, μ ) H H H F π H H H H F μ Choice of the hard scale to minimize the perturbative corrections παca π( H, H) 1 U im m e + π i / Evoulution from μ= mhe to m παc H A mh μ =

20 Complicated ituation of the Color-Octet calar Production (0) αc A 1 μ 1 μ Cf, d( μ ) = Cf, d( μ ) Re 1+ ln ln π m iε m πα C πα C C ( μ ) 1 + or C ( μ ) 1 +. (0) A (0) A f, d f, d 4 μ = 4 μ = m m - We cannot eliminate the large term with the choice of i μ = me α (- π/ α 0) /4 π μ=me π i - Minimizing the corrections : π παca παca 8 παca Uπ = 1+ e Reflecting π -corrections fully, μ = μ = U ( μ, μ, μ ) = U U ( m, μ, μ ) H F π F 4 4 m m π i /4 Evoulution from μ= mhe to m H ~ 0% enhancement

21 K-factors UP to NLL frequency, K-factor is universal. 1 dz τ τ Km (, τ ) = Vzm (,, μf) F, μf / FLO, μ z F z z z - At = 500 GeV, m K =.4. - At = 3 TeV, m K = 3.6.

22 cale Dependence - Choice of the soft scale I μ +μ μ = II [ μ μ μ I (1) I (0) I : ( m(1 z), ) 0.15 ( m(1 z), ) μ μ μ II (1) II (1) : ( m(1 z), ) Min ( m(1 z), ) - Default choice of the factorization scale : μ F = m -Uncertainty(500 GeV m 3 TeV) i 15% variance for the choice of μ i 5% variance for the choice of μ F

23 Application to Manohar-Wise Model i At m = 1 TeV, σ ( pp X ) = 57fb, σ ( pp X ) = 73fb NLL 0 0 R NLL I σ ( pp X ) = 1 fb, σ ( pp X ) = 6 fb LO 0 0 R LO I Gresham and Wise, 007

24 Conclusion The single color-octet production at the LHC can be factorized and described successfully when CET applied. ystematic resummation enables us to calculate universal K factor with NLL accuracy, which increases the cross section -4 times. The large corrections arising from the timelike process gives an additional 0% enhancement. caling dependences up to NLL accuracy are not small, but they can be reduced significantly with the higher order corrections.