Breakdown of CD factorization in hard diffraction Boris Koeliovich Valaraiso
CD factorization in diffraction e Ingelman-Schlein icture of diffraction h X It looks natural that DIS on the Pomeron robes its PDFs. Once the arton densities in the Pomeron are known, one can redict any hard diffractive hadronic reaction. G.Ingelman & P.Schlein 985 e P e X In the Good-Walker mechanism the diffractive amlitude is given h h by the difference between the elastic amlitudes of different Fock comonents in the rojectile article. In diffractive DIS A di / q q (r) / r / Hard diffraction of a hadron comes from difference of elastic amlitudes of hadronic states with and without a hard fluctuation A h di / q q (R + r) q q (R) / rr / Diffractive factorization also breaks down due to the comositeness of the Pomeron J.Collins, L.Frankfurt & M.Strikman 99; G.Alves, E.Levin, A.Santoro 997 B.#Koeliovich,#ISMD#05
Drell-Yan reaction: annihilation or bremsstrahlung? Parton model is not Lorentz invariant, interretation of hard reactions varies with reference frame. E.g. DIS looks like a robe for the roton structure in the Bjorken frame, but looks differently in the target rest frame, as interaction of hadronic comonents of the hoton. Only observables are Lorentz invariant. Similarly, in the target rest frame the Drell-Yan reaction looks like radiation of a heavy hoton (or Z, W), rather than q-qbar annihilation. g *,, W q q q q q q g a g b The cross section is exressed via the dioles looks similar to DIS d DY inc (q X) d dm = Z d r q ( r, ) ( r, x ) B.K. 994 A.Tarasov, A.Schäfer & B.K. 999 = + / + q B.#Koeliovich,#ISMD#05
Diffractive Drell-Yan In DY diffraction the Ingelman-Schlein factorization is broken * * * * q q q q q q q q g a b c Diffractive radiation of a heavy hoton by a quark vanishes in the forward direction [A.Schäfer, A.Tarasov & B.K. 998] d DY inc (q! q) = 0!!! d dm d T T =0 In both Fock comonents of the quark, q and qγ* only quark interacts, so they interact equally (b-integrated). This conclusion holds for any abelian diffractive radiation of γ, W, Z bosons, Higgs. 4 B.#Koeliovich,#ISMD#05
Diffractive Drell-Yan Diffractive DIS is dominated by soft interactions. On the contrary, diffractive Drell-Yan gets the main contribution from the interlay of soft and hard scales I.Potashnikova, I.Schmidt, A.Tarasov & B.K. 006 R.Pasechnik & B.K. 0 The Good-Walker form of the diffractive amlitudeand the saturated shae of the diole cross section, (R) / ex( R /R 0) leads to the unusual features of diffractive Drell-Yan, DY sd / DY inc 0 - S=40 GeV S=500 GeV DY sd DY incl / [ (R + r) (R)] / ex( R /R 0) R 0 0 - S=4 TeV The fraction of diffractive Drell-Yan cross section is steely falling with energy, but rises with the scale, because of saturation, which scale rises with energy. 0-4... x =0.5 x =0.9 0 0 0 0 4 M (GeV ) 5 B.#Koeliovich,#ISMD#05
Diffractive Z and W roduction Abelian diffractive radiation of any article is described by the same Feynman grahs, only coulings and sin structure may vary. R.Pasechnik, I.Potashnikova & B.K. 0 Σ X IP X G l l = IP IP, IR IP + IP IP, IR IP 000 00 E cms = 4 TeV 0. < x <.0, CTE0 Z boson DDY W + boson W - boson q T = 0, x = 0.5 Tevatron,.96 TeV CDF data d sd / dm (fb/gev ) 0 0. 0.0 diffractive / inclusive 0. 0.0 0.00 0.000 00 000 0000 M (GeV ) 0.00 00 000 0000 M (GeV ) 6 B.#Koeliovich,#ISMD#05
Diffractive heavy flavors I.Potashnikova, I.Schmidt, A.Tarasov & B.K. 006 Inclusive heavy flavors A Br = A + A + M + A Bremsstrahlung (like in DY) and roduction mechanisms A Pr = M M + A + A 4 + A 5 4 5 Diffractive heavy flavors m 4 ~ /m 4 Higher twist ~ /m Leading twist m Diffractive bremsstrahlung Higher twist bremsstrahlung 7 Leading twist bremsstrahlung B.#Koeliovich,#ISMD#05
Leading twist roduction mechanism in diffraction / m Numerically, the leading twist roduction mechanism is much larger comared with the bremsstrahlung mechanism 8 B.#Koeliovich,#ISMD#05
Diffractive heavy flavors I.Potashnikova, I.Schmidt, A.Tarasov & B.K. 006 0 charm 0 The leading twist behavior /m of the diffractive cross section is confirmed by CDF data. diff (µb) 0-0 - beauty 0-0 -4 0-5 to 0 0 0 4 9X s (GeV) B.#Koeliovich,#ISMD#05
Diffractive Higgsstrahlung Light quark do not radiate Higgs directly, only via roduction of heavy flavors. Therefore the mechanism is the same as for non-abelian diffractive quark roduction. R.Pasechnik, I.Potashnikova & B.K. 04 0 B.#Koeliovich,#ISMD#05
Diffractive Higgs from heavy flavored sea Diffractive Higgsstrahlung is similar to diffractive DY. Z, W, since in all cases the radiated article does not articiate in the interaction. However, the Higgs decoules from light quarks, so the cross section of (R,r, ;z) c c k H( r q ) ( ) H higgsstrahlung by light hadrons is small. A larger cross section may emerge due to intrinsic heavy flavors in light hadrons. Exclusive Higgs roduction, H, via coalescence of heavy quarks,! H S.Brodsky, I.Schmidt, J.Soffer & B.K. 006; S.Brodsky, A.Goldhaber, I.Schmidt & B.K. 009 The cross section of Higgs roduction was evaluated assuming % of intrinsic charm, and that heavier flavors scale as /m [M.Franz, M.Polyakov, K.Goeke 000]. At the Higgs mass 5 GeV intrinsic bottom and to give comarable contributions. B.#Koeliovich,#ISMD#05
Summarizing, Forward diffractive radiation of direct hotons, Drell-Yan diletons, and gauge bosons Z, W, by a arton is forbidden. A hadron can diffractively radiate in the forward direction due to ossibility of soft interaction with the sectators. This breaks down diffractive factorization resulting in a leading twist deendence on the boson mass, /M Non-abelian forward diffractive radiation of heavy flavors is ermitted even for an isolated arton. Moreover, this contribution turns out to be a leading twist /m and dominates the cross section. It comes from the interference between large and small distances. Diffractive higgsstrahlung at forward raidities is much suressed, and a larger contribution is exected from the coalescence of intrinsic heavy quarks in the roton. For M H=5 GeV dominance of intrinsic bottom and to is exected. B.#Koeliovich,#ISMD#05
B.#Koeliovich,#ISMD#05 Leading twist Bremsstrahlung mechanism: Leading twist ~ /m Production mechanism in diffraction: / /m Leading twist BACKUPS
Diffractive heavy flavors: data Measurements at ISR led to an amazingly large (robably incorrect) cross section of diffractive charm roduction (K.L.Giboni et al. 979), σ 0 60 µb. This exeriment was order of magnitude above the subsequent data for inclusive charm roduction. The E65 exeriment found no diffractive charm in Si collisions at 800 GeV. There is almost no A-deendence between hydrogen and silicon, so σ 6 µb The E690 exeriment reorted the diffractive charm cross section at σ = 0.6 ± 0. ± 0. µb at 800 GeV. Agrees well with our calculations. The CDF exeriment measured the fraction of diffractively roduced beauty, R bb di /tot =(0.6 ± 9 ± 6)%, at s =.8 TeV. The total cross section of beauty roduction at this energy has not been measured so far. If to rely on the theoretical bb bb rediction (J.Raufeisen & J.C.Peng) = 00 mb, then. mb. tot di 4 B.#Koeliovich,#ISMD#05
M d /dx F dm (nb GeV / Nucleon) 0 0 0 0 0 0 9 0 8 0 7 0 6 0 5 0 4 0 0 +d µ + µ - X s = 8.8 GeV M=4.5 GeV (x0 9 ) M=4.75 GeV (x0 8 ) M=5.5 GeV (x0 7 ) M=5.75 GeV (x0 6 ) M=6.5 GeV (x0 5 ) M=6.75 GeV (x0 4 ) E77 diole CTE5M modified diole M d /dx F dm (nb GeV ) 0 4 0 0 0 0 0 0 9 0 8 0 7 0 6 0 5 0 4 0 0 + µ + µ - X s = 500 GeV M=4.5 GeV (x0 9 ) M=4.75 GeV (x0 8 ) M=5.5 GeV (x0 7 ) M=5.75 GeV (x0 6 ) M=6.5 GeV (x0 5 ) M=6.75 GeV (x0 4 ) M=7.5 GeV (x0 ) diole CTE5M modified diole 0 M=7.5 GeV (x0 ) 0 M=7.75 GeV (x0 ) 0 0 0-0 - M=7.75 GeV (x0 ) M=8.5 GeV (x0) M=8.75 GeV 0.0 0. x 0 0 0-0 - M=8.5 GeV (x0) M=8.75 GeV e-05 0.000 0.00 0.0 0. x 5 B.#Koeliovich,#ISMD#05
Color diole descrition of diffraction Dioles are the eigenstates of interaction at high energies The total and single diffractive cross sections read [L.Laidus, A.Zamolodchikov & B.K. 98]. Z h tot = d r T h(r T ) (r T ) 6 X h 0 6=h d h!h0 sd dt t=0 = h (r T )i h (r T )i 6 B.#Koeliovich,#ISMD#05
More of diffractive Z and W x = 0.5 x = 0.9 q T = 0, M = M Z RHIC II, 500 GeV LHC, 4 TeV diffractive / inclusive 0. 0.0 q T = 0, M = M Z diffractive / inclusive 0. 0.0 0.00 0. 0.4 0.5 0.6 0.7 0.8 0.9 x 0.00 000 0000 E cms (GeV) 0.5 energy indeendent 5 < M < 0 5 GeV, CTE0 A W (x )= d W+ sd /dx d W sd /dx d W+ sd /dx + d W sd /dx A W (x ) 0-0.5 7-0. 0.4 0.5 0.6 0.7 0.8 0.9 x B.#Koeliovich,#ISMD#05