Slide 1: Title

Slide 2: reminder on charged Higgs in the MSSM: couplings, mass constraints, 
         current bound from LEP and Tevatron

Slide 3: production processes at the LHC: top decay into charged Higgs + bottom for 
         charged Higgs with m_H < m_top; associate production with top and bottom 
         quarks for m_H > m_top. Actually, in the transition region m_H \approx m_top
         one needs to combine the two in a consistent way, see e.g. hep-ph/0312286. 
         There are other production modes, which are however suppressed, see hep-ph/0503173
         for a review. This talk will focus on heavy charged Higgs production pp -> tbH.   
    
Slide 4: compilation of MSSM Higgs cross sections from hep-ph/0503173. Charged Higgs 
         production at the LHC has a cross section of O(1pb)-O(100fb) for large tan(beta). 

Slide 5: There are two ways to calculate charged Higgs production with top and bottom quarks:
         Only include light u,d,c,s quarks in the proton and calculate the gluon -> b bbar   
         splitting from pQCD order by order (4 flavour scheme), or treat the bottom as part 
         of the proton (5 flavour scheme). The 4 flavour schemes includes the full gluon ->
         b bbar splitting with all its kinematics, but may suffer from large log(m_b/m_H)  
         which appear order by order in perturbation theory. The 5 flavour scheme sum these
         logs through the AP evolution of the pdfs, but treats the gluon -> b bbar splitting 
         only in the leading log approximation. Both schemes are theoretically consistent, 
         but order the perturbation theory in a different way. They should agree if one 
         could take into account all orders, but will differ at any finite order. 
 
Slide 6: Here is a comparison of the 4FS and 5FS scheme calculations at LO taken from 
         hep-ph/0503173. One can see that the two calculations lead to quite different 
         predictions. 

Slide 7: A comparison between 4FS and 5FS has been done in the case of neutral MSSM Higgs 
         production with b-quarks, see hep-ph/0405302. We see that both calculations agree 
         at NLO within their respective error estimates (obtained through scale variation). 
         The comparison is not even fully consistent, since the 4FS calculation displayed 
         in the plot has been obtained with a 5FS pdf. A 4FS pdf, which was not available 
         at the time, would have a larger gluon contribution and would thus increase the 
         4FS calculation. Also, the 4FS calculation includes Higgs radiation off top quarks 
         not included in the 5FS. This contribution becomes negligible at large tan(beta), 
         but contributes with approx. -10% to the 4FS calculation with the parameters used 
         in the plot. 

Slide 8: Kinematical distributions, in particular of the bottom quark, are better described 
         in the 4FS, which includes the full kinematical information already at LO. This is 
         important since in 20% of the events, the bottom quarks in the production process 
         have a larger pt than the bottom from the top decay and thus contaminate the event 
         reconstruction. (The plot has been obtained with MadGraph). 

Slide 9: Some keywords to describe the NLO calculation in the 4FS. Note that there are two
         calculations, hep-ph/0601069 (Peng et al.) and arXiv:0906.2648 (Dittmaier, Kraemer, 
         Spira and Walser). All results shown in this talk are from the arXiv:0906.2648.
         A detailed comparison of the two calculations is in progress.

Slide 10: The scale dependence of the 4FS scheme calculation in LO and NLO. Looks good.

Slide 11: The scale dependence of the 4FS at LO and NLO with a pt-cut on the bottom quark.
          Looks even better...

Slide 12: The total cross section and the K-factor. Note that the K-factor is strongly 
          dependent on the way the LO cross section is defined. There is a considerable amount 
          of ambiguity in the definition of the LO, see arXiv:0906.2648 for our choice.
          What is relevant though is that the K-factor is rather independent of the Higgs 
          mass and that the reduction of the error from scale dependence at NLO works 
          for small and large Higgs masses.

Slide 13: Same as slide 12 for cross section with pt-cut. Same conclusions as for slide 12. 

Slide 14: Individual contributions to the NLO cross section: Large positive QCD and large 
          negative SUSY-QCD corrections which partially compensate each other. The dominant 
          SUSY QCD corrections come from tan(beta)-enhanced terms and can be resummed by 
          rescaling the coupling. (Note that we numbers have been obtained in SUSY point 
          SPS1b which has tan(beta)=30. That's good because to good approximation one can 
          study alternative SUSY scenarios by modifying Delta_b accordingly.

Slide 15: The NLO distributions: pt(higgs) and pt(top) are similar, pt(bottom) is much softer.

Slide 16: The shape of pt(bottom) is affected by NLO corrections: the distribution becomes 
          softer at NLO. This effect might be reduced by defining bottom-jets (instead of 
          looking at bottom quarks as is done in the current calculation). Only with the 
          4FS calculation do we have a NLO prediction of the pt(bottom) distribution.

Slide 17/18: Discovery contours have a large QCD uncertainty at LO. Only with the NLO 
             calculation can one get a meaningful estimate of the discovery prospects 
             of the LHC.

Slide 19: The scale dependence of the 5FS calculation at LO and NLO. (Obtained with a private 
          copy of Tilman Plehn's code, see hep-ph/0206121. Thanks, Tilman...) NLO looks 
          a little strange at low scales; where one in most calculations sees a turn-over 
          of NLO towards smaller cross sections, in this case it rises further. See 
          hep-ph/0312286 for a discussion of the scale dependence in the 5FS. 

Slide 20: Comparison of 4FS and 5FS calculation at NLO. Unfortunately, the two calculations 
          do not overlap, not even when a large scale variation is taken into account. 
          Too bad... 

Slide 21: Same is true for all Higgs masses...

Slide 22: Summary. Note that I did not discuss EWK corrections; see arXiv:0908.1332 and 
          references therein.

Slide 23: What one should do: the impact of NLO corrections on the shape of the pt(bottom) 
          distribution should be reduced when one defines a b-jet (i.e. a collinear safe 
          observable). Worth a try, but I'm not sure we will get around to doing this...
 	  It is not clear to me why the 4FS and 5FS calculations to not agree any better 
          at NLO. Needs further systematic study to understand the quality of the various 
          approximations involved in the two schemes. Comparison should also be done for 
          distributions. One can combine the two calculations ACOT style, but I am not 
          sure that makes much sense unless one better understands the source of the 
          discrepancy that we still observe at NLO.