Review of Beauty Production at HERA and elsewhere Review of Beauty Production at HERA Achim Geiser, DESY Hamburg XV International Workshop on Deep Inelastic Scattering and Related Subjects Munich, Germany, 19 April 2007 Achim.Geiser@desy.de The views expressed in this talk do not (necessarily) reflect those of the ZEUS or H1 collaborations Introduction Beauty tags at HERA and photoproduction cross section Theoretical considerations and cross checks with data: Plea for a change of default QCD scale for NLO calculations Speculation on photon-quark coupling Beauty production in DIS/F2b -> see talks B. Kahle, W.-K. Tung Conclusions 19. 4. 07 DIS07 workshop, Munich

Open Heavy Flavour production in ep scattering , mc ~ 1.5 GeV ,c ,c multiscale problem -> terms [as ln (Q2/mQ2)]n, [as ln (pT2/mQ2)]n, etc. in perturbative expansion -> potentially large th. errors 19. 4. 07 DIS07 workshop, Munich

pQCD approximations assume one dominant hard scale: NLO NLL pT2 pT2 NLO NLL =FFNS FONLL =ZM-VFNS (GM)-VFNS pT pT alternative: kt-factorization (see talk N. Zotov) 19. 4. 07 DIS07 workshop, Munich

Beauty tags with m+jets use m from semileptonic decay, separate b and c (can also use hadrons) 19. 4. 07 DIS07 workshop, Munich

Inclusive lifetime tags most significant impact parameter S1 2nd most S2 inclusive DIS charm beauty 19. 4. 07 DIS07 workshop, Munich

Double tagging of bb pair two direct flavour tags, e.g. D*+m or m+m -> large bg reduction (~50% beauty) , do not need jets -> access low pT and forward regions (proton direction) -> measure total beauty production cross section at HERA: B hadron m (same plot also exists for different b’s) s(ep -> bb + anything) = 16.1 +- 1.8stat +5.3-4.8,sys nb sNLO = 6.8 +3.0-1.7 nb (FMNR+HVQDIS) 19. 4. 07 DIS07 workshop, Munich

Beauty in photoproduction: summary b quark data/QCD: reasonable agreement, but tendency data > QCD at low pT kT factoriz. and NLO predictions agree mb = 4.75±0.25 GeV, m02 = mb2 + pT2 mr = mf = m, m0/2 < m < 2m0, fragmentation new/updated w.r.t. DIS06 theory uncert. underestimated? FONLL (VFNS) prediction not yet available, should it help? 19. 4. 07 DIS07 workshop, Munich

famous b cross sections at the Tevatron combination of appropriate fragmentation, NLL corrections, + many smaller experimental and theoretical issues (a bit of history) (Cacciari et al.) problem also for HERA? could one have done better? 19. 4. 07 DIS07 workshop, Munich

b cross sections at UA1 (630 GeV pp) NLO (1992) and FONLL (2004) agree with each other and with data (1991/94) (fragm. and decay spectra, br. ratios, ... were all consistently tuned in MC to measured data) FONLL (2004) agrees with data (1991) at b quark, B hadron, and muon level b data (1991/94) NLO (MNR) (1992) UA1, PLB 256 (1991) 112 UA1, Z.Phys.C 61 (1994) 41 MNR, Nucl.Phys.B 373 (1992) 295 Cacciari et al., JHEP 0407 (2004) 33 b quark data (1991) B hadron data (1991) FONLL (2004) (Cacciari et al., preliminary) FONLL (2004) (Cacciari et al., preliminary) 1 mu data (1991) FONLL (2004) very preliminary 19. 4. 07 DIS07 workshop, Munich

Charm in photoproduction at HERA QCD calculations using CTEQ5M1 + AFG structure functions mc = 1.5 +- 0.2 GeV, m02 = mc2 + pT2, mr = mf = m, m0/2 < m < 2m0 f(c->D*) = 0.235 ePeterson = 0.035 (FO NLO), 0.02 (FONLL) NLO (FMNR) reasonable agreement some differences at forward h FONNL (Cacciari et al.) similar, not better at large pT update? => Do not expect major change for b at HERA from NLO (no resummation) -> FONLL (with resummation) but would be nice to have 19. 4. 07 DIS07 workshop, Munich

remarks on QCD scale dependence Ideally (calculation to all orders) QCD predictions should not depend on the choice of renormalization and factorization scales mr, mf => not physical parameters => can not be determined from data In practice, finite order calculations do depend on the choice of these scales = reference points for perturbative expansion (Taylor expansion) => 1. choose “natural” scale of process involved (common sense) but subscales (e.g. initial state gluon radiation) often lower “optimal” choice of scales such that, ideally, cross sections will not change when higher order corrections are included => 2. best bet: NLO = LO => hope: NNLO = NLO sensitivity to scale variations indicates sensitivity to higher order corr. => 3. best bet: ds/dm = 0 => hope: minimize corrections range of variation of scale is supposed to reflect theoretical error for uncalculated higher orders use all three criteria to determine a “reasonable” choice 19. 4. 07 DIS07 workshop, Munich

example: total b cross section at HERA-B Bonciani, Catani, Mangano, Nason Nucl. Phys. B 529 (1998) 424 NLO stability: NLO = LO dsNLO/dm = 0 NLO+NLL stability: NLO+NLL = LO NLO+NLL = NLO dsNLO+NLL/dm = 0 “natural” scale in many cases, such solutions do not exist => consider only those cases where they do ? 19. 4. 07 DIS07 workshop, Munich

example: Higgs production at LHC plenary talk. A. Vogt NNLO stability: NNLO = NLO dsNNLO/dm = 0 N3LO = NLO N3LO = NNLO dsNLO+NLL/dm = 0 N3LO stability: “natural” scale NNLO/N3LO calculations, where available, support validity of scheme ? 19. 4. 07 DIS07 workshop, Munich

“optimal” ren./fact. scale from theory m0/2 < m < 2m0 “standard” scale range proposed new default NLO (NNLO) QCD literature survey of: - beauty at SppS, Tevatron, HERA-B - top at Tevatron - Z, H at LHC m02 = m2 (+ pT2) - jets in gp and at Tevatron m02 = ET2 m0/4 < m < m0 1/4 1/2 1 2 19. 4. 07 DIS07 workshop, Munich

cross check with data: c and b at Tevatron standard scale 19. 4. 07 DIS07 workshop, Munich

cross check with data: c and b at Tevatron new scale very preliminary approximate estimate (A.G.), to be calculated exactly very preliminary approximate estimate (A.G.), to be calculated exactly 19. 4. 07 DIS07 workshop, Munich

beauty at SppS, b+c at RHIC standard scale FONLL b+c -> e 19. 4. 07 DIS07 workshop, Munich

beauty at SppS, b+c at RHIC new scale FONLL b+c -> e very preliminary approximate estimate (A.G.), to be calculated exactly very preliminary approximate estimate (A.G.), to be calculated exactly 19. 4. 07 DIS07 workshop, Munich

top at Tevatron, charm at HERA standard scale 19. 4. 07 DIS07 workshop, Munich

top at Tevatron, charm at HERA new scale approximate estimate (A.G.), mt=172 GeV to be calculated exactly very preliminary approximate estimate (A.G.), to be calculated exactly 19. 4. 07 DIS07 workshop, Munich

Incl. Jets at HERA PHP DIS standard scale 19. 4. 07 DIS07 workshop, Munich

Incl. Jets at HERA PHP DIS new scale approximate estimate (A.G.), to be calculated exactly 19. 4. 07 DIS07 workshop, Munich

Beauty in photoproduction: standard standard scale m02 = m2 + pT2 19. 4. 07 DIS07 workshop, Munich

Beauty in PHP: new reference scale new scale m0 -> m0/2 thanks to E. Nuncio- Quiroz m0/2 < m < 2m0 (preliminary) 19. 4. 07 DIS07 workshop, Munich

Conclusion/Plea: propose, from now on, to use default QCD scale m0/2 for all heavy flavour (and other?) NLO cross section predictions at HERA and elsewhere, including LHC scale variation by factor 2 seems reasonable some people are doing this already: inclusive jets b jets 19. 4. 07 DIS07 workshop, Munich

But: Heavy Flavours in gg at LEP? at some point, pushing up sb(non-direct) might make sc(non-direct) too large changing scale m0 -> m0/2 does not really help (LO process is pure QED) 19. 4. 07 DIS07 workshop, Munich

investigate very tentative idea: Interference of QED with nonperturbative QCD?? Amplitudes (HERA): colourless system of 3 quasi-real gluons u d (+2/3-1/3)√a = 1/3√a -1/3√a (Q=b) +2/3√a (Q=c) (CFas(m2))3/2 quasi-real (Q2 ~ 10-3 GeV2) m2 ~ mQ2+pT2 mg2~Q2 Ο(1) (non- pert.) 19. 4. 07 DIS07 workshop, Munich

Interference of QED with nonperturbative QCD? amplitudes for effective photon coupling: b ~ -1/3 (1 + k (CF as(m2))3/2) m2 ~ mQ2+pT2 ~2mQ2 as(2mb2) ≈ 0.20 c ~ 2/3 (1 - ½k (CF as(m2))3/2) as(2mc2) ≈ 0.27 where k = unknown complex factor of non-perturbative origin (of order 1) example: arbitrarily assume k ≈ 2 (real) effective gb coupling enhanced by factor (1+2x0.14)2 = 1.64 effective gc coupling reduced by factor (1-½x2x0.22)2 = 0.61 cancellation ~ 0.14 ~ 0.22 (~0.15 for pTc ~ mb) 19. 4. 07 DIS07 workshop, Munich

Heavy Flavours in gg at LEP, revisited very preliminary scale and coupling changes cancel add charm mc = 1.5±0.25 GeV standard predictions (k=0) from Drees et al., PLB 306 (1993) 371 beauty mb = 4.75±0.25 GeV L3 DELPHI (prel.) OPAL (prel.) g PDF uncertainty not yet included m0 = √2 m / 2 k = 2 m0 = √2 m (default) k = 0 19. 4. 07 DIS07 workshop, Munich

Beauty in photoproduction: standard reminder: m02 = m2 + pT2 standard photon coupling 19. 4. 07 DIS07 workshop, Munich

Beauty in photoproduction: new scale m0 -> m0/2 standard photon coupling reminder: k=0 (preliminary) 19. 4. 07 DIS07 workshop, Munich

Beauty in photoproduction: non-standard m0 -> m0/2 non-standard photon coupling k=2 (very preliminary) still consistent -> not excluded 19. 4. 07 DIS07 workshop, Munich

compatibility with other measurements? purely hadronic processes (Tevatron, LHC) unaffected purely weak processes (W/Z at Tevatron, CC at HERA) unaffected change of coupling only relevant for (quasi-)real photons (Q2 > 1 GeV2-> perturbative -> k << 1 -> very small/negligible) no significant change for DIS at HERA, e+e- -> qqX reduction of charm photoproduction at HERA, qualitatively compensated by increase due to m -> m/2 (to be checked quantitatively) for hard scale m >> mq, modifications for up and down quark contributions cancel exactly in leading order => u,d; s,c cancel no net effect for 2,4,6 final state flavours (e.g. NF=4 gp fixed target) some increase (~4%) in PHP high ET jet production at HERA, high ET single photon production at Tevatron (5=3-2 flavours, b only) should affect e.m. branching ratios, e.g. D*->Dg (but not electroweak ones like b->sg, since Wg coupling unaffected) other processes ? ! ! 19. 4. 07 DIS07 workshop, Munich

beauty production in DIS at HERA plot to be updated see talk B. Kahle data: still large errors (only ~10-20% analyzed) theory: uncertainty of up to ~factor 2 due to - choice of QCD scale - treatment of flavour threshold (see backup slides) 19. 4. 07 DIS07 workshop, Munich

Summary and conclusions b production measured at HERA from variety of detection techniques. Beauty cross sections at HERA and elsewhere in reasonable agreement with perturbative QCD predictions (but often above central prediction). theory-inspired arguments suggest shift in choice of “optimal” renormalization/factorization scales to ~half their “standard” values good agreement with many different data sets, plea to make this the new default, also for LHC. up/down scale variation by factor 2 to be kept. b “excess” of gg at LEP => investigate modification of photon-quark coupling from interference with non-perturbative QCD? => compatible with HERA beauty data. Compatibility with other measurements and theoretical constraints to be checked Important e.g. for as from PHP jets at HERA -> hopefully exclude (confirm??) soon. first measurements of beauty contribution to proton structure function F2 available (more next talk). Starting to become useful to understand treatment of mb in different QCD schemes, reduce errors on gluon extraction from F2 and F2c, and cross check b PDF for LHC (see backup slides). 19. 4. 07 DIS07 workshop, Munich

Backup slides 19. 4. 07 DIS07 workshop, Munich

Unintegrated gluon density: approximation of higher orders based on CCFM evolution (contains BFKL) talk H. Jung heavy quarks at HERA Higgs at LHC heavy quarks at Tevatron LO matrix element kt factori- zation (CCFM) NLO collinear DGLAP factorization, kt = 0 kt = 0 kt = 0 Implementation in actual QCD calculations: NLO: FMNR (photoproduction), HVQDIS (Harris&Smith,DIS) FONLL/VFNS: Cacciari et al. (PHP), MRST/CTEQ (DIS, F2) kt-factorization: CASCADE (H. Jung), LP (Lipatov,Zotov) 19. 4. 07 DIS07 workshop, Munich

The structure of the proton special HERA run in 2007 small +-Y- to 0th order QCD (Quark Parton Model, Q2 >> mq2): "higher" order QCD corrections in general: F2 structure function is not PDF 19. 4. 07 DIS07 workshop, Munich

Heavy Flavour contributions to F2 mainly Boson Gluon Fusion, driven by gluons multiple hard scales: Q2, mb,c, pT -> F2 flavour tagging , c c QCD or c , c -> F2bb, F2cc 19. 4. 07 DIS07 workshop, Munich

F2bb at ZEUS and H1 why such a large theory spread? B. Kahle ZEUS data lie above H1 data but compatible within errors. HVQDIS+CTEQ5F4 agrees with similar predictions by H1 ZEUS: 39 pb-1 H1: 57.4 pb-1 Theory predictions except HVQDIS+CTEQ5F4 provided by P.D.Thompson, hep-ph/0703103 why such a large theory spread? ZEUS data point at Q2=200GeV2; x=0.13 is shifted to lower x value to be separated from the H1 point 19. 4. 07 DIS07 workshop, Munich

PDF Schemes and Parameters Order Scheme, Nf mM2 Mb(GeV) MRST04 as2 VFNS Q2 4.3 MRST NNLO as3 CTEQ6HQ 4.5 HVQDIS+CTEQ5F4 FFNS, 4 pt2+4M2 4.75 CTEQ5F3 FFNS, 3 MRST FF CTEQ6.5 Q2+M2 Theory predictions except HVQDIS+CTEQ5F4 provided by P.D.Thompson, hep-ph/0703103 19. 4. 07 DIS07 workshop, Munich

NNLO vs. NLO dependence? MRST NNLO close to MRST04 (NLO) (both VFNS, scale Q2) => differences NOT dominated by NNLO vs. NLO 19. 4. 07 DIS07 workshop, Munich

FFNS vs. VFNS scheme dependence? MRST FF close to MRST NNLO (VFNS) (both scale = Q2) => differences NOT dominated by FFNS vs. VFNS scheme 19. 4. 07 DIS07 workshop, Munich

MRST vs. CTEQ gluons? MRST FF very close to CTEQ5F3 (also FFNS) (both scale = Q2) => differences NOT dominated by MRST vs. CTEQ gluon 19. 4. 07 DIS07 workshop, Munich

scale Q2 vs. scale pT2+4m2 ? CTEQ5F3 (scale = Q2) noticably larger than HVQDIS+CTEQ5F4 (scale = pT2+4m2) at low Q2, similar at high Q2 (both FFNS) => scale choice makes important difference 19. 4. 07 DIS07 workshop, Munich

MRST VFNS vs. CTEQ VFNS ? MRST04 much larger than CTEQ6HQ everywhere (both VFNS, scale = Q2) difference: treatment of flavour threshold within VFNS scheme => flavour threshold treatment within VFNS = source of large (largest?) uncertainties details see talk R. Thorne, HERA-LHC meeting 19. 4. 07 DIS07 workshop, Munich

MRST VFNS vs. CTEQ VFNS ? Conclusion on differences at HERA-LHC workshop: (talks M. Cacciari, R. Thorne, W-K. Tung + discussion with authors) prescription for threshold treatment is ambigous, and both schemes follow a reasonable prescription; both should be equally valid for inclusive F2 CTEQ prescription has the virtue of simplicity MRST prescription more complicated, but potentially more “physical” (no discontinuities at flavour threshold) => might be preferable if emphasis is placed on detailed description of threshold behaviour 19. 4. 07 DIS07 workshop, Munich

HVQDIS+CTEQ5F4 vs. CTEQ6HQ ? HVQDIS+CTEQ5F4 (FFNS, scale = pT2+4m2) very close to CTEQ6HQ everywhere (VFNS, scale = Q2) (+ reminder: MRST FF ~ MRST NNLO) => differences in flavour threshold treatment within VFNS can be partially mimicked by scale changes within FFNS scheme 19. 4. 07 DIS07 workshop, Munich

choice of mb ? mb(pole) = mb(mb) (1 + 4/3 as/p ) triggered by question at HERA-LHC workshop both FFNS and VFNS scheme use pole mass: mb(pole) = mb(mb) (1 + 4/3 as/p ) = mb(Q) (1 + as/p (4/3+ln(Q2/mb2)) (note: ln(1/4) ~ -4/3 => mb(pole) ~ mb(mb/2) ) so far, MRST use mb = 4.3 GeV so far, CTEQ use mb = 4.5 GeV HVQDIS uses mb = 4.75 ± 0.25 GeV recent measurement of pole mass (Kühn, HQET): mb ~ 4.8 GeV ± O(LQCD) agreement brokered by M. Cacciari: in future, everybody will use mb = 4.75 GeV leading order QCD 19. 4. 07 DIS07 workshop, Munich

consequences of change of mb ? MRST will somewhat come down at low Q2 CTEQ will slightly come down at low Q2 HVQDIS will stay as it is 19. 4. 07 DIS07 workshop, Munich

implications for F2c recompute predictions for F2c with QCD parameters optimized from investigations of F2b => apply to verify and/or constrain gluon PDF 19. 4. 07 DIS07 workshop, Munich

What will we learn from F2b? F2b sensitivity to gluon much smaller than other theoretical uncertainties => F2b will NOT yield a direct measurement of the gluon PDF F2b very useful to understand the effect of mb in different theoretical QCD approaches, in particular the VFNS scheme, which can not be studied (yet) with more differential b cross sections VFNS or FFNS scheme used in any (recent) inclusive F2 fit => study of F2b allows to quantify theoretical error on F2 due to nonzero mb, mc (expected to be small, to be verified) Study of mb scheme in F2b will help to optimize QCD treatment of mc in F2c without introducing a strong a priori bias on gluon => reduce theoretical error on gluon extraction from F2c Measurement of F2b at Q2 >> 4mb2 will allow validation of theoretical b PDF for Tevatron/LHC 19. 4. 07 DIS07 workshop, Munich

Beauty contribution to F2 first measurement of F2bb first NNLO calculation data in agreement with NLO and NNLO checks b PDF for LHC: HERA LHC, e.g. H,Z Q2 >> mb2 19. 4. 07 DIS07 workshop, Munich

Probe b PDF with Z+b-jet at Tevatron talk K. Hatekayama, ICHEP06 b b b b CDF Z+b-jet/Z+jet : CDF: 2.4+-0.7(stat) +-0.5(sys) % D0: 2.1+-0.4(stat) +0.3-0.2(sys) % NLO: 1.8+-0.4 % (CTEQ6) OK 19. 4. 07 DIS07 workshop, Munich