# YaJEM

## Overview

YaJEM (Yet another Jet Energy-Loss Model) is a Monte Carlo (MC) code based on PYSHOW and reduces to PYSHOW in the case of no medium. Essentially, it computes radiative medium modification of a shower based on the schematic assumption that the virtuality of each parton in the shower traversing the medium is increased by where ζ is the parton trajectory in space and time. This modification leads to additional medium-induced radiation. The code, the resulting modified fragmentation function, applications and comparison plots with R_{AA} are described in arXiv:0806.0305 [1] and arXiv:0808.1803 [2].

## The brick problem

While in the realistic case, is given by a 3d hydro model for each trajectory, for the brick can be (and has been) enforced in PYSHOW. However, apart from this, the model is not really suited for the brick, as its output is a medium-modified parton shower, which must be compared with an unmodified parton shower. The way I have applied the code to the brick problem is as follows:

- Compute parton showers both in vacuum and in medium using the brick settings fm and

- No fragmentation (usually, the code would use the Lund scheme of PYTHIA)

- Take the distribution of leading partons from the showers (Here is the first caveat - a shower initialized with a quark might have a gluon as leading parton in the end, both in vacuum and in medium, and the probability is not the same. As for now, I ignored the conversion reactions just asking for the distribution of any leading parton, even if it is a gluon)

- Assume that the two distributions and are related by

- discretize this expression and solve for subject to conditions which guarantee that the result is a probability distribution (cf. the description in Phys.Rev.C77:017901,2008, I use the same code here) (Here is the second caveat - this procedure might not give the desired result - at least in Phys.Rev.C77:017901,2008 it did not, but the problem may be better posed here).

There are yet more caveats to consider, having to do with how PYSHOW works.

- There is a minimum virtuality scale in PYSHOW (default 1 GeV) below which a parton is no longer branched. Estimating the evolution time of the shower given an initial parton energy of E as
**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau \sim E/Q_{min}^2}**one finds for the 10 GeV shower**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau \sim 2}**fm. This means that the shower from a 10 GeV quark doesn't usually see any distance scale greater than 2 fm. To be fully consistent, the code should allow for partons below the scale**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Q_{min}}**to be 'resurrected' to larger virtualities by the medium. Technically, this is not quite easy, as it requires restructuring PYSHOW. In the realistic case, it is also unnecessary, as the medium density drops strongly, so late time evolution doesn't have much effect. Only for the brick this becomes an issue. So any pathlength dependence is best studied for the 100 GeV quark case.

- The peak of the leading parton momentum distribution for the vacuum situation is roughly at 0.5 E. This means that an energy loss of 40% in medium is about the asymptotic value of the distribution and probes a rather extreme regime of the code in which no parton contains any sizeable part of the energy flux. Thus, only plots for 5%, 10% and 20% energy loss are shown.

- Due to the discretization in the inversion, the result comes in rather coarse bins and may not be sensitive to smaller structures in the distribution.

## Results

Extracted energy loss probability distributions for a 100 GeV down quark as shower initiator:

Extracted energy loss probability distribution for a 10 GeV down quark shower initiator:

Extracted longitudinal momentum distribution of the leading shower parton - note that the vacuum distribution peaks at **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z\approx 0.45}**
, hardly leaving any room for 40% energy loss.

## The revised brick problem

The above treatment cannot readily be compared with energy loss calculations assuming an infinite energy parent parton. The reason is that in the latter case it is always clear what the propagating parton is and what the gluon radiation is, whereas in the framework above a branching with the gluon taking 70% of the energy of a propagating quark would not be counted as 70% energy loss but as 30% energy loss with a conversion of the leading parton in the shower from a quark to a gluon.

It has been suggested to address this by

- computing with a charm quark as shower initiator and

- extract the distribution of the leading charm quark in the shower which, if gluon branching into charm pairs is small, should to a good approximation track the original quark

One immediate difference is that the vacuum fragmentation of charm is much harder than that of light quarks, the distribution peaks about . This allows more room for medium induced energy loss before finite energy corrections affect the simulation and allows to compute 40% energy loss as well.

## Results for the revised brick problem

Extracted energy loss probability distributions for a 100 GeV charm quark as shower initiator:

Extracted longitudinal momentum distribution of the leading shower parton - note that the vacuum distribution is much harder than above and peaks at **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z\approx 0.9}**
, allowing for 40% energy loss.

## Relation to medium temperature

The model does not assume any particular relation between **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \hat{q}}**
and the medium temperature **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T}**
, this requires an extra model of the medium degrees of freedom which can be chosen independently.

## Discussion

The model shows changes of the energy loss probability distributions with , the initial energy scale **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E}**
and the pathlength **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle L}**
. In particular, the extracted **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \hat{q}}**
depends in a non-trivial way on both external parameters.

Most of these features can be understood by realizing that the model assumes finite parton energy and explicitly enforces energy momentum conservation at each vertex, and by realizing that the shower evolution happens in a limited spacetime region.

The 'true' effect of the medium on the hadron spectrum is much more pronounced than the brick treatment here would suggest. This is because of the medium effects on subleading partons in the shower which translates to more than a shift of the final fragmentation function by **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Delta E}**
as extracted here.

However, I thought it more useful to address the brick problem *as posed* instead of solving it *as it suits the model* (which seems to be more popular at the moment).

The results of the revised brick problem are somewhat different, they show a rather flat energy loss distribution with (at least for small fractional energy loss) a large contribution close to zero. This may indicate a discrete escape probability without energy loss or just small energy loss, the inversion procedure cannot discriminate here.

## References

[1] Jet modification in 200 AGeV Au-Au collisions T.~Renk, 0808.1803 [hep-ph].

[2] Parton shower evolution in a 3-d hydrodynamical medium T.~Renk, 0806.0305 [hep-ph].