1. 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
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
DIS07 workshop, Munich

2. 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
DIS07 workshop, Munich

3. 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)
DIS07 workshop, Munich

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

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

6. 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) = stat ,sys nb
sNLO = nb (FMNR+HVQDIS)
DIS07 workshop, Munich

7. 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?
DIS07 workshop, Munich

8. 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?
DIS07 workshop, Munich

9. 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
DIS07 workshop, Munich

10. Charm in photoproduction at HERA
QCD calculations using
CTEQ5M1 + AFG structure functions
mc = GeV, m02 = mc2 + pT2,
mr = mf = m, m0/2 < m < 2m0
f(c->D*) = 0.235
ePeterson = (FO NLO), (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
DIS07 workshop, Munich

11. 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
DIS07 workshop, Munich

12. 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 ?
DIS07 workshop, Munich

13. 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 ?
DIS07 workshop, Munich

14. “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
DIS07 workshop, Munich

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

16. 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
DIS07 workshop, Munich

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

18. 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
DIS07 workshop, Munich

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

20. 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
DIS07 workshop, Munich

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

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

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

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

25. 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
DIS07 workshop, Munich

26. 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)
DIS07 workshop, Munich

27. 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.)
DIS07 workshop, Munich

28. 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)
DIS07 workshop, Munich

29. 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
DIS07 workshop, Munich

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

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

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

33. 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 ? ! !
DIS07 workshop, Munich

34. 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)
DIS07 workshop, Munich

35. 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).
DIS07 workshop, Munich

36. Backup slides
DIS07 workshop, Munich

37. 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)
DIS07 workshop, Munich

38. 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
DIS07 workshop, Munich

39. 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
DIS07 workshop, Munich

40. 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/
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
DIS07 workshop, Munich

41. 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/
DIS07 workshop, Munich

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

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

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

45. 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
DIS07 workshop, Munich

46. 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
DIS07 workshop, Munich

47. 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
DIS07 workshop, Munich

48. 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
DIS07 workshop, Munich

49. 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
DIS07 workshop, Munich

50. 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
DIS07 workshop, Munich

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

52. 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
DIS07 workshop, Munich

53. 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
DIS07 workshop, Munich

54. Probe b PDF with Z+b-jet at Tevatron
talk K. Hatekayama, ICHEP06 b b b b
CDF
Z+b-jet/Z+jet :
CDF: (stat) +-0.5(sys) %
D0: (stat) (sys) %
NLO: % (CTEQ6) OK
DIS07 workshop, Munich