Understanding Parton Shower: An Introduction to QCD Processes on Colliders

[Phiphy]

What is "parton shower"?

I only know that parton shower is an algorithm of calculating QCD processes on the collider. Can anyone give me a brief introduction on the purpose and basic ideas of parton shower?
Thanks.

 

[GreyBadger]

It is fairly easy to write process matrix elements at leading order (LO). Recently, it has become fairly standard to have next-to-leading order QCD (NLO), and for some processes NNLO and above, matrix elements.

What do these tell us? Well, for example in the production of a Z boson, the LO element describes the process $$q\bar{q}\to Z$$. The NLO matrix element describes two things. Firstly, the real corrections, where an extra strong object exists in the final state (e.g. $$qg\to Zq$$ or $$qq\to Zg$$), and secondly the virtual corrections, where, for example, a gluon is exchanged between initial state quarks, or the Z splits to a quark loop.

Clearly, the number of diagrams (and mathematical gymnastics) become more and more at each order in QCD. However, for collider experiments we are well aware that we 'always' get Z + n jets. How can we describe the n jets without explicit matrix element calculations?

Parton showers are how we accomplish this without having to write explicit matrix element calculations to arbitrary order. Of course, this means we lose something... Parton showers generally work at the leading log level (i.e. following the DGLAP QCD evolution - look it up!). Essentially, the DGLAP equations describe how quarks and gluons behave at a given momentum scale - how they split (and give extra strong object - which we see as jets - in the final state) and evolve.

You then enter the lovely realm of matching... If I have a NLO matrix element, and a leading log parton shower, how to I make sure I don't double-count the first jet? Does it come from the matrix element, or the parton shower? This stuff is for people braver than me...

 

[Phiphy]

Thank you for the explanation.

So if we want to go from SM theory to hadron collider phenomena, what is the commonly used strategy? As I understand it, we first need to know the PDF of the proton, then calculate parton collision cross-section, then use parton shower to calculate jet production probability, and finally use jet algorithm to get the jet structure which can be compared with experiments. Is that correct?

And what is the relation between parton shower and fixed order calculation, are they substitutions of each other or we use both in the same strategy.

 

[GreyBadger]

So if we want to go from SM theory to hadron collider phenomena, what is the commonly used strategy? As I understand it, we first need to know the PDF of the proton, then calculate parton collision cross-section, then use parton shower to calculate jet production probability, and finally use jet algorithm to get the jet structure which can be compared with experiments. Is that correct?

Yep, that's pretty spot on. Although, the parton shower doesn't give you get production probability - it just tells you how individual strong objects (quarks + gluons) will evolve. The Leading Log approximation isn't very good at hard (i.e. high momentum, high angle w.r.t. the emitting particle) radiation, and generally that is what gives strong distinct jets. However, it's not bad if you don't care about the tails of transverse momentum distributions etc. Things like MadGraph have explicit calculations of n jet final states at leading order, and there are some monte carlos that now do full QCD NNLO (FEWZ, for example) production, which are more likely to give you hard jets. Any way, back to my original point - there is another stage after the parton shower. When the PS is run, we are left with lots of individual quarks and gluons. These must be combined (we don't see bare quarks) into (semi)stable hadrons, which are what we see in our detectors. This step is called hadronisation.

And what is the relation between parton shower and fixed order calculation, are they substitutions of each other or we use both in the same strategy.

No, we need both. A fixed order calculation gives us a production cross section for some hard process. The parton shower tells us how the initial and final states evolve (i.e. say I have $$q\bar{q}\to Z\to q\bar{q}$$, both the initial and final quarks can radiate, and I'm not going to see bare quarks in the final state anyway). The difficulty is in higher order calculations matching the results of the two properly, such that we don't double-count jets (i.e. $$qg \to Zq,Z\to q\bar{q}$$ - I need to make sure the extra quark jet isn't overestimated as the parton shower can give me extra quark jets too).

 

[Phiphy]

That's a clear picture of the strategy. Thank you again, GreyBadger.