Higgs LHC: the diffractive opportunity 1/ 26. Higgs LHC. the diffractive opportunity. M.B. Gay Ducati.

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1 Higgs LHC: the diffractive opportunity 1/ 6 Higgs LHC the diffractive opportunity M.B. Gay Ducati beatriz.gay@ufrgs.br High Energy Physics Phenomenology Group Physics Institute Universidade Federal do Rio Grande do Sul Porto Alegre, Brazil work with G.G. Silveira arxiv: [hep-ph]

2 Higgs LHC: the diffractive opportunity / 6 Outline Motivation Diffractive Higgs production γγ annihilation Double Pomeron Exchange (DPE) Deeply Virtual Compton Scattering (DVCS) Peripheral Collisions The KMR model Photoproduction approach: DPE in DVCS Results Summary

3 Higgs LHC: the diffractive opportunity 3/ 6 Motivation The existence of the Higgs boson is an open question in Particle Physics. LHC will allow to study a new kinematic region: Center-of-mass energy: s pp = 14 TeV and s AA = 5.5 TeV/A. Rapidity (CMS): η jets < 6.6, η γ,e ± < 3 and η µ <.5. Luminosity : L pp fb 1 and L AA 10 6 fb 1. Bjorken-x: x Higgs physics: it is expected that the pp collisions will be able to produce the Higgs boson. Some hadron-hadron collisions will occur with no strong interaction. The peripheral collisions are a new way to study the Higgs boson production in pp(aa) collisions. Other processes of Higgs production are under study to allow its detection in hadron colliders. DPE allows the Higgs boson production through the leading ggh vertex mainly in the mass range M H GeV.

4 Higgs LHC: the diffractive opportunity 4/ 6 Electromagnetic Higgs production 1990: Cahn and Jackson PRD 4 (1990) 3690 Müller and Schramm PRD 4 (1990) 3699 Peripheral heavy-ion collision γγ annihilation 007: Miller arxiv: [hep-ph] Contribution from Electroweak boson loops to the γγ H. p, A γ γ H p, A { M H = 150 GeV CJ: σpbpb = 7.0 pb s = 3.5 TeV/A MS:σ AA 100 pb M H = 10 GeV s = 14 TeV { M: σ pp = 0.1 fb p, A p, A

5 Higgs LHC: the diffractive opportunity 5/ 6 Diffractive Higgs production in pp and AA collisions p p 1991: Bialas and Landshoff PLB 56 (1991) 540 Regge Theory non-perturbative gluons 1997: Khoze, Martin and Ryskin PLB 401 (1997) : Levin and Miller arxiv: [hep-ph] QCD Pomeron hard-gluon exchange IP IP H { M H = 150 GeV BL : σ pp = 0.1 pb s = 16 TeV p p p, A p, A p, A H p, A { M H = 10 GeV KMR : σ exc/inc pp 1 fb/300 fb s = 14 / 5.5 (8.8) TeV/A LM : σ pa(aa) = 100 (3.9) pb

6 Higgs LHC: the diffractive opportunity 6/ 6 Diffractive processes within Dipole picture Deeply Virtual Compton Scattering 1997: Ji PRD 55 (1997) 7114 γ p γp by Pomeron exchange in ep collisions. Vector meson production 001: Munier, Staśto and Mueller NPB 603 (001) 47 γ p Vp with GBW model. γ γ, V (Υ,ω, J/ψ, ρ 0 ) t = 0 Q = 7 GeV x 10 3 { ρ 0 -meson at HERA MSM : dσ L dt t=0 = 0 nb/gev p p

7 Higgs LHC: the diffractive opportunity 7/ 6 Diffractive Higgs photoproduction Proposal: γp process by DPE in pp collision. q γ χ L t = 0 q χ R γ EFFECTIVE VERTEX SCREENING GLUON H p f g (x,k ) p The loop is treated in impact factor formalism at t = 0. Hγ final state: study the b-quark density in the proton. Gabrielli, Mele and Rathsman, PRD 77 (008)

8 Higgs LHC: the diffractive opportunity 8/ 6 Higgs production in Peripheral Collisions The γp process is a subprocess in peripheral pp collisions C.A. Bertulani Heavy Ion Phys. 14 (001) 51 b H Impact parameter: b > R NO STRONG INTERACTION! Only EM force acts in the second proton REAL PHOTONS

9 Higgs LHC: the diffractive opportunity 9/ 6 Peripheral photons Baur, Hencken and Trautman J. Phys. G4 (1998) 1657 A γ γ A X A γ A X A γ γ A X B B B B The photon virtuality is related to the nucleus radius: coherent action of the charged particles Q 1/R COHERENCE CONDITION In the proton case: Q 10 GeV. Uncertainty principle: upper limit to the photon transverse momentum Q 1 R j 8 MeV, Pb beam 330 MeV, proton beam

10 Higgs LHC: the diffractive opportunity 10/ 6 Photon spectra Hencken et al, PRept. 458 (008) 1 The energy fraction of the photon related to the incident nucleus obey the coherence condition photon energy x γ = beam energy = ω j xγ 10 3,Ca E x γ 10 4,Pb Z E ω L AA dl γγ /dw γγ [cm s 1 GeV 1 ] LHC Pb+Pb Ar+Ar p p e + e L AA dl γγ /dw γγ [cm s 1 GeV 1 ] RHIC Au+Au Cu+Cu p p e + e W γγ [GeV/c ] W γγ [GeV/c ] The photon distribution is strongly suppressed at high energies.

11 Higgs LHC: the diffractive opportunity 11/ 6 Scattering amplitude Partonic process: γq γ + H + q q(l µ ) γ(q µ ) γ(q µ ) q(q µ l µ ) g(k µ ) g(k µ ) g(k µ ) H(q H ) q(p µ ) q(p µ ) HIGGS VERTEX GLUON-GLUON FUSION The scattering amplitude is obtained by the Cutkosky Rules Im A = 1 Z d(ps) 3 A (left) A (right)

12 Higgs LHC: the diffractive opportunity 1/ 6 Photon impact factor The color dipole is composed of two effective vertices to the γg coupling j»» ff l1 q l1 k χ µν L = ig s ee q t a γ µ γ ν γ ν γ µ (l 1 q) (l 1 k) j» χ λη R = ig s ee q t b γ λ k l (k l ) Photon polarization vectors for t = 0: γ η γ η» ff q l γ λ (q l ) ǫ L µǫ L ν = 4Q s p µp ν s q and X ǫ T µ ǫ T ν = g µν + 4Q s q p µp ν s l 1 l + l l l 1 l k k

13 Higgs LHC: the diffractive opportunity 13/ 6 Applying the rules Performing the product of the two sides of the cut one gets ggh A L A R = (4π) 3 α s α X! z} { ǫµǫ «eq λ V ba eikonal ση t b t a z } { 4p νp σ k 6 N c q ( Tr ˆ( q l)γµ lγ ν ( k+ l)γ η lγ λ + Tr ˆ( q l)γ ν ( k+ l q)γ µ ( k+ l)γ η lγ λ ) l 4 l (k + l + q) OTHER POSSIBILITIES For a non-heavy Higgs (M H 00 GeV), the ggh vertex reads quark top loop H Vµν ab «MHα s g µν kµk1ν δ ab 3 4πv k 1 k Forshaw, hep-ph/050874

14 Higgs LHC: the diffractive opportunity 14/ 6 The amplitude in parton level The imaginary part of the amplitude has the form Im A s = 4 9 «! M H α sα X αsc «Z eq F dk N cv π k 6 X(k,Q ) q First remark: dependence on k 6 due to the presence of the color dipole. Only the quark contribution extension to the hadron coupling. The dependence on the photon virtuality reads X(k,Q ) 1 + k Q 0 Q Computing the event rate in central rapidity dσ = 1 dy H dp dt yh,t=0 «α s αmh! X» Z e αsc F dk 9π q X(k,Q ). N cv π k 6 q

15 Higgs LHC: the diffractive opportunity 15/ 6 Parton Hadron The hadron coupling is represented by a non-diagonal PDF «α sc F Khoze, Martin and Ryskin f g(x,k [xg(x, k )] ) = K π lnk PLB 401 (1997) 330 The non-diagonality is approximated by a multiplicative factor K = (1.) exp( Bp /) Shuvaev et al PRD 60 (1999) where B = 5.5 GeV is the slope of the gluon-proton form factor. To correctly compute the pomeron coupling to the proton: x 0.01.

16 Higgs LHC: the diffractive opportunity 16/ 6 Phenomenology inside Gluon Radiation Forshaw, hep-ph/ The real gluon emission from the ggh vertex needs to be suppressed. Sum the virtual graphs that include terms like ln (M H /k). The emission probability of 1-gluon is computed by Sudakov form factors S(k,M H) = Nc π Z M H /4 k α s(ˆp ) ˆp dˆp Z MH / p T «dê Ê = 3αs M H 4π ln 4k Real emissions are not suppressed if the gluon color neutralization fails. Suppressing many gluons emission: It is included a factor e S to the cross section. Emissions below k are forbidden. As k 0 the non-emission probability goes to zero faster than any power of k, like k 6. Ê,ˆp H Higgs rest frame

17 Higgs LHC: the diffractive opportunity 17/ 6 Phenomenology inside Rapidity Gaps KMR, EPJC 18 (000) 167; Gotsman, Levin, Maor, arxiv: [hep-ph] The Rapidity Gap Survival Probability is calculated by R A(s, b) Sgap e Ω(b) d j b 5% Tevatron = R = A(s, b) N d b.7 3% LHC where N = e Ω 0 is the relevant opacity at Ω = 0. S gap depends on the spatial distribution of the proton. It is controlled by the B-slope of the gluon-proton form factor. γ p γ p H } } Gap Gap

18 Higgs LHC: the diffractive opportunity 18/ 6 Cross section for central rapidity The cross section is calculated for central rapidity (y H = 0) dσ dy H dt yh,t=0 = S gap πb «α s αmh! " X Z # eq dk e S(k,M ) H f g(x,k ) X(k,Q ) 3N cπv q k k 6 0 Quark contribution 1 : α sc F /π f g(x,k ) = K (ln k ) xg(x, k ) Gap Survival Probability : Sgap 3% (5%) for LHC (Tevatron) Gluon radiation suppression 3 : Sudakov factor S(k,MH) ln `M H/4k Cutoff k 0: Necessary to avoid infrared divergencies :: k 0 = 1 GeV. Electroweak vacuum expectation value: v = 46 GeV gluon-proton form factor: B = 5.5 GeV 1 Khoze, Martin, Ryskin, EJPC 14 (000) 55 Khoze, Martin, Ryskin, EJPC 18 (000) Forshaw, hep-ph/050874

19 Higgs LHC: the diffractive opportunity 19/ 6 Results: pp vs. γp process Higher rate in the mass region expected for Higgs detection. dσ/dy H dt (t,y H =0) (pb/gev ) E LHC =14 TeV MRST001lo γp -> γ + H + p pp -> p + H + p 40 x Q =1.0 GeV 10 3 x Forshaw Q =0.04 GeV Higgs mass M H (GeV)

20 Higgs LHC: the diffractive opportunity 0/ 6 Results: Q -dependence Peripheral collisions: photon limit of Q = 0.04 GeV Divergent region: highest cross section for Higgs production Perturbative region: Q 1 GeV KMR, hep-ph/ Smaller event rate: range expected to its detection σ exc 3 fb. dσ/dy H dt (t,y H =0) (pb/gev ) CTEQ6 MRST001lo MRST004nlo (fb/gev ) E LHC =14 TeV k 0 =1.0 GeV M H =140 GeV Q (GeV ) Peripheral photons Perturbative region Q = 0.04 GeV

21 Higgs LHC: the diffractive opportunity 1/ 6 Results: Gluon distribution functions dσ/dy H dt (t,y H =0) (fb/gev ) E TEV =1.96 TeV CTEQ6 MRST001lo MRST004nlo Higgs mass M H (GeV) dσ/dy H dt (t,y H =0) (pb/gev ) CTEQ6 MRST001lo MRST004nlo E LHC =14 TeV Higgs mass M H (GeV) Tevatron: Distinct behaviors for the LO and NLO distributions; j NLO MH 00 GeV Leading contribution LO M H 400 GeV LHC: NLO distributions show a higher contribution than the LO ones.

22 Higgs LHC: the diffractive opportunity / 6 Results: Cutoff sensitivity dσ/dy H dt (t,y H =0) (fb/gev ) E TEV =1.96 TeV MRST001lo Q =0.04 GeV k 0 =1.00 GeV k 0 =1.5 GeV k 0 =1.50 GeV k 0 =.00 GeV Higgs mass M H (GeV) dσ/dy H dt (t,y H =0) (pb/gev ) E LHC =14 TeV MRST001lo Q =0.04 GeV E LHC =14 TeV Q =0.04 GeV k 0 =30.00 GeV k 0 =1.00 GeV k 0 =1.5 GeV k 0 =1.50 GeV k 0 =.00 GeV Higgs mass M H (GeV) The event rate is 5x less sensivite on the cut k 0 if compared to the previous approaches. The results for LHC vanishes as k 0 increases: dσ/dtdy H (30 GeV ) 0

23 Higgs LHC: the diffractive opportunity 3/ 6 Results: Energy dependence Higgs mass Non-uniform event-rate behavior at Tevatron. Uniform and Small dependence on Higgs mass at LHC. dσ/dy H dt (t,y H =0) (pb/gev ) TEVATRON LHC M H =10 GeV M H =140 GeV M H =180 GeV MRST001lo Q =0.04 GeV E CM (TeV)

24 Higgs LHC: the diffractive opportunity 4/ 6 Results: Energy dependence PDFs Significative distinction among the LO and NLO distributions: Same difference in the region s 1 TeV {z } includes LHC 500 dσ/dy H dt (t,y H =0) (fb/gev ) TEVATRON LHC CTEQ MRST001lo MRST004nlo Q =0.04 GeV M H =140 GeV E CM (TeV)

25 Higgs LHC: the diffractive opportunity 5/ 6 Summary We compute the event rate for Higgs boson production in γp process for Peripheral Collisions at LHC: dσ 600 fb/gev dtdy H The event rate is fifteen times higher than the rate predicted by previous results in pp collisions. To compare effectively we need to study this rate for pp(aa) collisions. A preliminary result for pp collision: dσ/dy H 15 fb (M H = 10 GeV). Previously: dσ/dy H 1 fb, σipip exc 3.0 fb and σexc γγ = 0.1 fb. It is shown a clear difference of 15% between LO and NLO distributions in the kinematic region of LHC: It assigns the importance of the gluon recombination effects (if the non-perturbative effects are small). The calculation is five times less sensitive to the integration cuts if compared to the KMR approach.

26 Higgs LHC: the diffractive opportunity 6/ 6 Perspectives Study this approach in hadron-hadron collsions: pp, pa and AA. Introduction of the photon distribution of the proton (or nucleus). To extend the phenomenology analysis: More precise predictions for the GSP;... Inclusion of QCD and Electroweak-theory corrections: Color dipole; Higgs vertex;... and more.