Summary of ATLAS problems with recoil (Marco Vanadia)

• In recent years, ATLAS top precision measurements (especially mass measurements) have incorporated an uncertainty related to the modeling secondary emissions.
  • This uncertainty relates to how recoil from secondary emissions is handled in double shower simulations.
  • It is becoming a limiting factor for current precision and future improvements in top quark measurements
• Goal of the workshop:
  • Investigate how to better understand this uncertainty and potentially reduce or mitigate its impact
  • Focus on short-term strategies for ongoing analyses (with VINCIA considered a longer-term solution)
    
    

Discussion:

• Q (Simon Plätzer): Generally in top-decays, there is always an ambiguity in how you set-up recoil transformations, Why is there no ambiguity in Vincia?
  • A (Peter skands): The question is that there are consistent and inconsistent choices, so there is an ambiguity in Vincia. Vincia has a family of maps, which are all consistent.
    • Just like when we do dipole recoil maps, We do have an ambiguity that we can make choices. But, for instance, if you had a dipole and you gave all of the recoil to a non-color-connected pattern, that would be inconsistent. So you can choose to have global recoil, or local recoil, or whatever. There's a whole family of consistent recoil schemes, where the ambiguities are higher order, But you could also make up recoil schemes that would just be wrong, and that's where Pythia sits.
  • S. Platzer: I am wondering how do you measure consistency, there must be a benchmark which we should be formulating?
  • P. Skands: We show it mathematically in the resonance final recoil paper in VINCIA, that if we only give recoil to one parton, whether it be the W or the B, then we violate a mathematical consistency constraint.

Pythia8: Introduction of the problem and recommendation (Peter Skands)

• In Pythia <= 8.313
  • Default: recoil-to-b (RTB) via recoilToColoured = on.
• Compare to the physical structure of t->wbg:
  • at Leading colour you have colour connections between the top and the gluon, and the gluon and the b.
  •  The connection between the top and the gluon is what is called "Resonance Final (RF)" dipole, in the context of vincia showers and thats allowed to radiate coherently.
  • However, thats in VINCIA and thats a longer time scale.
  • Pythia doesnt have the concept of RF dipole, so you dont have the option of connecting it to the top.
• Comment from S. Plätzer: the Herwig dipole shower is exactly doing what VINCIA is doing with collective recoils
  
  
• In Pythia <=8.309,
  
  • Option for recoil-to-top (RTT),  recoil-to-W via recoilToColoured = off + a dedicated user hook
  • In RTW, the W is forced to take the recoil. That is different from a true resonance final treatement, because its not a collective recoil and only the W that is recoiliing. The b, does not give any recoil.
  • The user hook, applies a correction factor to suppress radiation in the W hemishphere
• From Pythia >= 8.314
  
  • recoilStrategyRF replaces old settings, and the default is no longer RTB
  • Default: recoil-to-W + correction factor (weightRF = 1.0)

• Recommendations, for Pythia>= 8.314: 
  • Vary the weightRF (default 1.0), This option is quiet new and its important to determine a reasonable range.
  • weightRF = 0.0 is too extreme as this choice is equivelant to the old RTW, and this generate too much radiation in the W-hemishpere
  • instead Peter recommends a "max radiation"-variation which is in between of 0 and 1.
    • To set a good value for that, compare to higher order MEs and to VINCIA and other MCs. A complete guess is 0.5.
  • Also have a variation on the other side, "min radiation" variation:
    • Supresses the radiation even more.
    • This can be achived by forcing this weightRF factor to be > 1.
    • Pythia will complain but if you force the paramete, it will allow you to do that
    • Complete guess would be 1.5 or 2. The negative weight will be set to zeros, so you will not get any negative weights.
  • RTB is theoretically inconsistent (no recommendations for recoilStrategyRF=1)
    • because it messes up the b-quark fragementation in a theoretically inconssistent. It messes up the logarethmig resummation of the b-quark fragmentation
• In recent Pythia versions, Splitting-kernel variations were added with more options without destroying leading-order accuarecy. Ideally one would vary those.
• Finite width effects, on the total cross-section they are expected to be very very small, per mile effects. The effects can be larger in the lineshapes.
  
  
• Peter wonders, based on Marcos talk, how RTB can be in better agreement with NLO+NLL, thats not understandable and expected to be the worst option.
  • Its important to follow up and attempt to understand.
  • This option is the least favourite and its theoretically inconsestint.
    
    

Discussion:

• Q (Lucio Cerrito):  We should not be too surprised that some of the things you might regard theoretically less consistent, are actually more in agreement with data, if the data, has produced a tune or some sort of consistent set of parameters, just because the numbers of parameters that control any of this phenomenology is so much larger than the few setups, theoretically. I think we should keep in mind that there is an enormous degree of freedom with the parameters within the simulation itself, that overwrite theoretical consistency that you have designed.
  
  • P. Skands: I am not comfortable with confusing theoretical consistency with tunning. It can happen accidentally, but its something we should not try to do.
  • P. Skands: Regarding why RTB misses b-ragmentation?
    • b-quark fragmentation usually re-tuned at LEP and there we have z->bbar and there is no resonance final dipols.
    • In top-quark decay, if the gluon radiates and generate further recoils, which is the RTB, the b-quark experience a very different energy loss, it gets twice as much recoil from that gluon as it would have gotten at LEP.
      
      
• Josh: do you think its a reasonable approach if we move to RTT and weightRF as an uncertainties?
  • P. Skands: I would consider it a reasonable approach if data didnt tell me that RTB does a better job.
  • I would love to have a consistent picture, where the things that expected to look right, also look right. That doesnt seems to be the case yet, which is not understandable. If its a result of accedantial consequence of cycles of tunning.
• Josh:  To understand the impact of tuning, would it be a useful exercise to take a bunch of top data that are sensitive to b-fragmentation and jet shapes and FSR and just tune twice, switching the nominal model and see what happens?
  • P. Skands: You can certainly change the effective alpha-S values, how much radiation you are generating off the B, how much radiation gluon is generating, And of course, if you move that up and down, you will change the energy distribution of the B quark after the shower. Comparing, a change in alpha S, with a change in how much recoil the B is taking from a fixed alpha S, I would hope that there are ways to disentangle that.
  • P. Skands: I mean, we could give you a stochastic selection between RTT and RTB, and just randomly choose between 0 and 1. You could also generate two samples and choose events stochastically in those two samples, with some weight.
• Marcos Vanadia:  I dont want to conclude the RTB is better copmared to theory predictions, because if you do a chi² and of the theory prediction, comparing it with RTT, RTB, they will both have a cascade probability of zero in the end. What we found is that if you look at the average of the distribution, the average of the distribution of the theory prediction and the 1 of 10 with RTB are in better agreement. And since top mass measurement, basically only depends on the average of the fragmentation, this was what better. If this is closer by accident, or there is some reason why RTB is in better agreement with the average of the prediction for RTB, or the average, I don't know. But I want to stress that the shapes are still not in agreement in any of the cases.
• Marcos Vanadia: I can tell you from experience, that finding an observable to disentangle alpha's effect from RTT effects is very, very complicated, so it's very hard to do it.
• Peter Skands: I think also theory-to-theory comparisons could play a role
  • Monte Carlo-level studies, one could sort of try and at least Understand  questions of tuning. Is there a consistent theoretical picture of Or is it more complicated than that?
  • One could also imagine, this is the second emission, so we're talking about second-order corrections. in principle, there is a virtual correction to the first emission an NNLO effect. which we're not accessing, because we're just using POWHEG, so we only have leading order precision on the first omission, that could go in any direction. The second emission, we are not matrix element correcting that yet. It may be through some accident. that the RTB Somehow manages to approximate those things better. 

Herwig 7.3: Recommendation (Simon Platzer)

• Overview of Herwig parton showers:
  • Angular-ordered shower and Dipole shower
  • The recoils in the angular-ordered shower recoils are constructed a posteriori, in a theoritically consistent way.
  • The dipole shower is doing what Vincia doing in Pythis
  • Non-of the shower option have the problem that the default Pythia has.
• Top decays in both shower types
• Recommendations

  • Both Herwig shower schemes (angular-ordered and dipole) are well motivated and can serve as a baseline to evaluate differences between showers within the same environment.

• MCnet short term studentships are encoureged
  
  

Discussion:

• Josh: The idea behind the recommendation is to define a consistent baseline and then vary only the shower algorithm. But wouldn’t that probe much more than just recoil effects when estimating uncertainties?
  • S. Plätzer: Yes, but we think that the showers in this case would otherwise have comparable properties. But,it's still something to be worked out in detail. I mean, we could vary things within these showers, but we have no idea on how well motivated, how reliable such an uncertainty is. 
    • Josh: we already did made studies comparing the shower algorithms, and we saw some non-negligible differences in observables that one would naively not be expected to be affected by the recoil.
    • S. Plätzer:
      • there had been choices in the Angular ordered shower of how to do this interpretation of the branching variables, one of which we had advocated, which was actually giving a much better description of data.  But this was completely destroying the logarithmic accuracy of the shower, and hence it's not available as an option anymore.
      • in the dipole shower, you could use a scheme where basically, after the very first emission, you would not distribute recoil to anything else than the inside the b-jet. Which is also not a well-motivated choice. I can't prove that it's wrong or right, but it will have a next-to-leading logarithmic issue by a very similar pattern of how we understand logarithmic accuracy  In the PT spectrum of Trelyon. It will have a further logarithmic ambiguity due to the underlying structure of the massless dipole shower, like along the lines we see in event shapes. But this is in the process of being fixed. So, I suspect that once we have the remaining modifications available to the dipole shower, the final dipoles will be okay, and we're not offering that possibility of not recoiling the second emission against anything in the W, because we don't believe it could be right.
      • I'm very hesitant to offer switches just to see, we can test what the impact is, knowing very well that I would trust certain schemes much more than the other ones, but, of course, I still can't prove which one is the right and the wrong one, so for this, I think more theoretical work is still needed.
      • I think we just need to compare these two showers, and then we can look how we can proceed on the theory side
        
        

• Dominic: When evaluating systematic uncertainties, we compare pythia with Herwig, what would be the closest setting using the angular ordered shower to what we have in Pythia to basically remove artificial differences and to get as close as possible. In term of recoil scheme.
  • S. Plätzer:  This is the point where I absolutely disagree. The recoil scheme is an integral part of the parton shower. A consistent pattern shower construction is involving, a set of a recoil scheme, splitting kernels, an ordering variable, and a set of initial conditions. And you can't completely just modify one of them just independently of anything else. So, they all talk to each other. They even talk to hydronization in very detail. We should all understand these showers as entities in that thing.

Sherpa: Recommendations (Marek Schönherr)

• The first emission in top decay is briefly outlined:
  • Dominated by gluon radiation from the b-quark, with the top as spectator.
• The second emission and subsequent emissions are discussed:
  • After the first emission, standard QCD evolution takes over.
  • Most later splittings behave like ordinary QCD splittings without memory of the top decay origin.
• Recoil strategy:
  • Recoil follows the colour flow (dipole structure).
  • When the top acts as spectator, recoil is effectively transferred to the W boson.
• Settings / uncertainties:
  • Only global parton shower settings are available.
  • No dedicated or tunable top-decay-specific parameters in Sherpa.

Discussion

• P. SKands: comments on neglecting the top as an emitter, and think that it is consistent, within that language, to neglect the t as an active emitter. Within Vincia, we have to have it, since we don’t partition the radiation into two separate ends. But if we did, the top end would basically be inert. So it should amount to the same thing.
  • S. Plätzer: I disagree. Soft radiation is crucial, in particular also towards questions about the top mass. Both Herwig showers include the full radiation pattern of the decay (though, in algorithmic/event generator language, there might not be a ‘top’ splitting visible)
  • P. Skansa: I assume they partition the soft radiation in a consistent way
  • M. Schoenherr:
    • we studied that in quite a lot of detail for the W, and for the W, where basically you have a W decay into lepton neutrino, it's not exactly the same situation, because the neutrino is massless, which the W here isn't, but other than that, mass width ratios are very similar, and so on.
    • So what happens there is that essentially the Part of the dipole that is contributed by the W is, in the radiation spectrum, entirely in the per mil range. 
    • So. With the top, we haven't studied it in quite that detail, but for the W, that's the case, and that sort of leads to basically this negligibility statement.
    •  Now, for soft gluons, sometimes funny things happen. I completely realize that, and maybe one should have a bit of a closer look.
    • In the future developments, in the complete resonance aware shower, the radiation off the resonance itself will be included.

• Josh: What existing scheme ( in Herwig or Pythia) is Sherpa closest to?
  • M. Schoenherr:  it's closest to the W recoil scheme. It's not exactly that
    • because we take the top as recoil, but essentially the longitudinal recoil, is no problem, because that is entirely absorbed by the Gluon. But the transverse recoil is given to the top, but since the top is fixed, it's basically passed on to the W for us, We don't boost the entire final state, but we give it to the W.

Using theory predictions of fragmentation to constrain recoil-to-top uncertainty (Gennaro Corcella)

• The presentation revisits an older NLO+NLL calculation of B-quark fragmentation in top decays and compares it to modern MC predictions (e.g. Pythia).
• In ttbar production, the B-hadron spectrum factorizes into a perturbative b-quark production component convoluted with a non-perturbative fragmentation function. The key observable is the energy fraction xB of the b-quark in the top rest frame.
• At NLO, large logarithms appear, including collinear (mass) logarithms and soft logarithms. These require resummation to obtain reliable predictions.
• The resummation is performed using the perturbative fragmentation function formalism, where the result factorizes into a massless coefficient function and a perturbative fragmentation function, evolved via DGLAP equations. Both collinear and soft logarithms are resummed at next-to-leading logarithmic (NLL) accuracy.
• At the level of the B-quark energy spectrum, the fixed-order result diverges at large x, while the resummed prediction yields a finite, smooth Sudakov peak and improved stability.
• A comparison with Pythia recoil schemes for xB in ttbar events shows that, the NLO+NLL calculation appears to prefer the recoil-to-b option
  • This behaviour is not fully understood and requires further investigation.

NNLO B-fragmentation fits and their application to ttbar production (Terry Generet)

• Overview
  • NNLO QCD predictions for B-hadron production in top decays.
  • Not focused on recoil schemes; emphasis on capabilities, limitations, and possible applications.
• Framework
  • Applicable to:
    • Isolated top decay
    • ttbar production with B-hadrons
    • Includes B-hadron decays (e.g. to μ, J/ψ)
  • Based on QCD factorization (not parton showers)
  • Assumes massless b-quark / B-hadron → valid at high energies
  • Includes:
    • Collinear resummation (DGLAP)
    • Partial soft-gluon resummation
• Isolated top decay
  • Process: t→Wb with leptonic W decay
  • Observables:
    • mlb​, B-hadron energy
      
      • Good precision (few %) in bulk region
      • Large soft effects at high energy
      • Low-energy region unreliable (mass effects)
• Top pair production
  • Observables: mlb, B-hadron energy (lab frame)
  • Good NNLO convergence in bulk; energy observable particularly robust
• Other observables
  • Decay products (J/ψ, μ) also accessible
  • Similar behavior: reliable in inclusive energy-type observables
  • More differential observables (e.g. involving jets) suffer from large uncertainties

Rivet studies from ATLAS (Matilde Uboldi)

• Validation of smooth recoil variation (weightRF)
  • Studied interpolation between RTB and RTT.
  • RTW and RTT give very similar results.
  • Intermediate configurations (weightRF = 0.2, 0.4, 0.6, 0.8) largely overlap → limited sensitivity in many observables.
  • Switching recoil options (useParents) shows negligible impact.
• Search for recoil-sensitive observables (incl. FSR and fragmentation effects)

  • B-fragmentation observables:

    • Some sensitivity to recoil.

    • Not clearly discriminating given current experimental precision.

  • Jet shapes:

    • Show differences between recoil schemes.
    • Sensitivity present but not conclusive.

  • Jet substructure (CMS measurements):

    • Some observables exhibit potential discriminating power.
    • However, mismodelling and/or experimental uncertainties often limit usefulness.

  • Lund jet plane:

    • Studied but no Rivet routine available yet.
    • No strong sensitivity observed so far.

  • Top mass:

    • Directly affected by recoil choice.
    • Shape differences visible across generator setups.

  • Boosted top mass:

    • Clear separation between recoil schemes.
    • Demonstrated strong sensitivity.
    • Successfully used in ATLAS to constrain recoil uncertainty.