STAR HardProbes PWG

[Nihar Sahoo <nihar AT rcf.rhic.bnl.gov>]

Hello Sooraj and Rongrong,

It would be good and helpful to discuss this topic at our Thursday 
HP-pwg meeting.

Best
Nihar

On 2024-09-18 13:09, Sooraj Radhakrishnan wrote:
> Dear All,
>     Rongrong raised a question on relating <px> and pT shift from
> energy loss, pointing to jets with the case where py = 0. His
> contention was since px = -px for the sample with py = 0 , the v1 (and
> thus px) should be relatable to the pT shift of the spectra
>
> However, this is a special subset of jets and the condition px = -px
> is coming from our selection of jet sample requiring a particular pT.
> This is a limitation of our selection, we impose no energy loss for
> these jets from our selection. This constraint exists only for a small
> fraction of jets which have py very close to 0. On average we are
> still measuring the asymmetry in px distribution of the jets and <px>
> gives the mean momentum loss per jet along the x direction
>
> The calculated v1 is a well defined and well behaved quantity as you
> can see in the slides attached below
>
> On the other hand, defining a v1 from the pT shift of spectra for the
> case with py = 0 does not give a well defined quantity and the value
> depends on the bin chosen, as shown in the slides below. This is not
> the quantity we measure
>
> Thoughts are welcome
>
> thanks,
> Sooraj
>
> On Thu, Sep 12, 2024 at 7:44 PM Sooraj Radhakrishnan
> <skradhakrishnan AT lbl.gov> wrote:
>
> > Hi Rongrong,
> > Its not clear to me what you are trying to say. By definition,
> > (N(pT+pT_+) + N(pT+pT_-))/2 is N(pT) we measure. So this gives the
> > asymmetry at the measured pT
> >
> > //<px> = pT(N(pT+dpT+pT_+) - N(pT+dpT+pT_-))/(N(pT+dpT+pT_+) +
> > N(pT+dpT+pT_-)). I think dpT does affect the measured <px> value.
> > But again, dpT would not matter if we select on jets based on their
> > pT before energy loss.//
> > ---- Its not that we take the difference and divide by a yield along
> > the spectra. N(pT+dpT) is what we measure N(pT) as. So other than a
> > shift on the x-axis, this shouldnt matter
> >
> > Let me know if I am missing something
> >
> > thanks,
> > Sooraj
> >
> > On Thu, Sep 12, 2024 at 5:42 PM Ma, Rongrong <marr AT bnl.gov> wrote:
> >
> > Hello Sooraj
> >
> > Thanks for the responses. However, it seems like we are viewing <px>
> > is a very different way.
> >
> > Let's say we can measure the true jet pT (no detector effects, no
> > background), and we measure <px> at a given pT. Further, let's
> > assume there are only jets along +x and -x directions (py = 0 for
> > all jets).
> >
> > <px> = <pTcos(dphi)> = pT<cos(dphi)> = pT(N_+ - N_-)/(N_+ + N_-),
> > where N_+ and N_- are the number of jets along +x and -x directions
> > with pT after energy loss.
> >
> > Then we can assume jets traveling along +x direction loss momentum
> > of dpT_+, and those traveling along -x lose dpT_-. Then <px>
> > becomes: <px> = pT(N(pT+pT_+) - N(pT+pT_-))/(N(pT+pT_+) +
> > N(pT+pT_-)), where N(pT+pT_+) and N(pT+pT_-) are the number of jets
> > at pT+pT_+ and pT+pT_- before energy loss.
> >
> > If I understand you correctly, you are saying <px> is directly
> > corrected to (pT_+ - pT_-). I agree there is a connection, but the
> > jet spectrum also plays a role here.
> >
> > If we could select jets of the same pT BEFORE they lose energy, then
> > <px> is a direct measure of (pT_+ - pT_-). Because in this case:
> > <px> = <pTcos(dphi)> = [(pT-pT_+)N - (pT-pT_-)N]/2N = (pT_- -
> > pT_+)/2 (because jets are produced without asymmetry, we can assume
> > N_+ = N_- = N)
> >
> > However, we are selecting jets of the same pT AFTER energy loss.
> >
> > Now, if we assume there is a shift in pT between true and
> > reconstructed jets. Then:
> > <px> = pT(N(pT+dpT+pT_+) - N(pT+dpT+pT_-))/(N(pT+dpT+pT_+) +
> > N(pT+dpT+pT_-)). I think dpT does affect the measured <px> value.
> > But again, dpT would not matter if we select on jets based on their
> > pT before energy loss.
> >
> > Best
> > Rongrong
> >
> > On Sep 12, 2024, at 7:09 PM, Sooraj Radhakrishnan
> > <skradhakrishnan AT lbl.gov> wrote:
> >
> > Hi Rongrong,
> > Thanks for follow up thoughts and comments. Please find my
> > responses below
> >
> > //If the centroid of the medium is offset by <x>, then the jets
> > traveling along +x direction will see a medium length of R+<x>,
> > while jets traveling along -x direction will see R-<x>. The
> > different is 2<x>. Do I miss something?//
> > ---- But the average difference a jet sees is still <x>. We are also
> > comparing to <px>, a jet along +x will have px - delta px and along
> > -x will have px + delta px, and per jet average would be delta px.
> > This is from the convention how we define flow amplitudes
> >
> > //I think I now understand your argument of very narrow pT range,
> > but I still think shifting and smearing in jet pT matter.
> >
> > Let's say there are 10 jets with pT = 10 GeV/c, and 6 of them go
> > along +x direction and 4 of them go along -x direction. Then <px> =
> > 20/10 = 2 GeV/c, due to that there are 2 more jets along +x than
> > alone -x direction. Here, <px> reflects the asymmetry of jet yields
> > along +x and -x directions.
> > - If all jet pT is shifted by 10%, <px> will also shift by 10%.
> > - If there is only smearing in jet pT (no shifting), <px> does not
> > change if we can collect all the jets after smearing. However, what
> > smearing does in real data analysis is to move jets in and out of 10
> > GeV/c bin, so it is not clear that <px> should stay the same.//
> >
> > ---- 'If all jet pT is shifted by 10%, <px> will also shift by 10%.'
> > --> This is not true. <px> from this will be zero as there is no
> > azimuthal preference for the shift. Lets say the true jet pT gets
> > shifted by delta pT. The physics is driven by the true jet pT, <px>
> > could have a dependence on true jet pT (not necessarily a scale
> > factor). The delta pT would be azimuthally symmetric and delta px
> > will average to zero. As long as the x-axis (pT axis) is corrected,
> > we are still measuring the <px> from the underlying physics
> >
> > //I think whether we need to correct for <px> depends on how we
> > interpret it. We can view it as a reflection of jet yield asymmetry
> > at a given pT (<px> = pT*v1?), then it is OK not to correct it. But
> > we already have v1 for that. If we want to connect it to energy
> > loss, then I think shifting and smearing matter. //
> >
> > --- The bin migration will matter and this is what we have been
> > evaluating with the pT smearing studies. The impact is small, as the
> > pT dependence of v1 is weak. So we can quote an uncertainty on the
> > measurement from this, or correct for the impact, mainly feed-in
> > from low jet pT and quote a systematic uncertainty on it. The
> > current uncertainties evaluate the impact of both detector effect
> > and background fluctuations. But it is using raw jet spectra and not
> > the unfolded one. We will evaluate with the unfolded jet spectra for
> > the paper
> >
> > //Thinking more on this, it is actually not clear if we can
> > interpret <px> as the energy loss difference. As the example above
> > shows, <px> is generated by jet yield asymmetry at a given jet pT
> > bin. It means there are more jets along +x than -x direction. Given
> > that jets traveling along +x direction lose less energy (smaller
> > pathlength) than those along -x direction, so they come from jets
> > with smaller initial energies which naturally have larger yield due
> > to steeply falling jet spectrum. So <px> should also depend on jet
> > spectrum shape. Furthermore, what we measure is <px> for jets in a
> > given pT bin AFTER energy loss. <px> might be related to the energy
> > loss those jets experienced, but the relation is not straightforward
> > to me. Smearing in jet pT moves jets in and out of the bin, making
> > the interpretation even more complicated, I think. //
> >
> > ----- 'Given that jets traveling along +x direction lose less energy
> > (smaller pathlength) than those along -x direction, so they come
> > from jets with smaller initial energies which naturally have larger
> > yield due to steeply falling jet spectrum' -- why do you say so?
> >
> > Here we are measuring the asymmetry in energy loss from the path
> > length difference, not the overall energy loss. The measured pT is
> > reflecting the average suppression from energy loss from the medium
> > interactions and the v1 is measuring the asymmetry on this along +x
> > and -x. So this still gives access to energy loss from the path
> > length asymmetry. For <px> what we measure is the momentum loss in a
> > given pT bin from the asymmetry. This would have bin edge effects
> > and we would need a pT dependent v1 or <px> measurement to evaluate
> > the energy loss. But these do directly relate to the energy loss
> > induced by the path length asymmetry. We can say <px> is the
> > asymmetry in momentum loss in a given pT bin
> >
> > thanks,
> > Sooraj
> >
> > On Thu, Sep 12, 2024 at 11:32 AM Ma, Rongrong <marr AT bnl.gov>
> > wrote:
> >
> > Hello Sooraj
> >
> > I have some further comments and thoughts inline.
> >
> > On Sep 11, 2024, at 5:58 PM, Sooraj Radhakrishnan
> > <skradhakrishnan AT lbl.gov> wrote:
> >
> > Hi Rongrong,
> > Thanks for the follow up
> >
> > //If the centroid of the medium is offset by <x>, the average path
> > length difference along positive and negative x is 2*<x>, right?//
> > ---- But since we are comparing to <px>, this should cancel out,
> > right? We are looking at the average momentum difference along +x
> > and -x  If the centroid of the medium is offset by <x>, then the
> > jets traveling along +x direction will see a medium length of R+<x>,
> > while jets traveling along -x direction will see R-<x>. The
> > different is 2<x>. Do I miss something?
> >
> > //In the D0 v1 paper, it is argued that the large D0 v1 slope is
> > driven by the drag from the titled bulk. Would jets also experience
> > such a drag? If so, that should also contribute to v1, right? Are
> > there any other effects that would induce jet v1? //
> > ----- D0 we measured was at low pT where collisional energy loss is
> > dominant. So the drag from the bulk would be more important there.
> > For the jet pT we are looking at, this should be less important. But
> > is a quantitative question to be taken into account in a detailed
> > model calculation, including other aspects like expansion of medium
> > etc. Thats why we dont want to quote a dE/dL for energy loss in QGP.
> > But I believe the measurements offer an important quantity in
> > getting towards that
> > I agree that this is a quantitative question. I think it is
> > important to point out that there are other effects that could
> > contribute to jet v1.
> >
> > //Still, it is not clear to me how the reconstruction efficiency
> > cancels in <px>. What is the definition of <px>?//
> > ---- What is the efficiency effect you are referring to here? The
> > jet reconstruction efficiency should cancel out as this is averaged
> > over all jets in the pT bin. <px> is the the mean of pTcos(phi
> > -Psi).
> > I think I now understand your argument of very narrow pT range, but
> > I still think shifting and smearing in jet pT matter.
> >
> > Let's say there are 10 jets with pT = 10 GeV/c, and 6 of them go
> > along +x direction and 4 of them go along -x direction. Then <px> =
> > 20/10 = 2 GeV/c, due to that there are 2 more jets along +x than
> > alone -x direction. Here, <px> reflects the asymmetry of jet yields
> > along +x and -x directions.
> > - If all jet pT is shifted by 10%, <px> will also shift by 10%.
> > - If there is only smearing in jet pT (no shifting), <px> does not
> > change if we can collect all the jets after smearing. However, what
> > smearing does in real data analysis is to move jets in and out of 10
> > GeV/c bin, so it is not clear that <px> should stay the same.
> >
> > I think whether we need to correct for <px> depends on how we
> > interpret it. We can view it as a reflection of jet yield asymmetry
> > at a given pT (<px> = pT*v1?), then it is OK not to correct it. But
> > we already have v1 for that. If we want to connect it to energy
> > loss, then I think shifting and smearing matter.
> >
> > Thinking more on this, it is actually not clear if we can interpret
> > <px> as the energy loss difference. As the example above shows, <px>
> > is generated by jet yield asymmetry at a given jet pT bin. It means
> > there are more jets along +x than -x direction. Given that jets
> > traveling along +x direction lose less energy (smaller pathlength)
> > than those along -x direction, so they come from jets with smaller
> > initial energies which naturally have larger yield due to steeply
> > falling jet spectrum. So <px> should also depend on jet spectrum
> > shape. Furthermore, what we measure is <px> for jets in a given pT
> > bin AFTER energy loss. <px> might be related to the energy loss
> > those jets experienced, but the relation is not straightforward to
> > me. Smearing in jet pT moves jets in and out of the bin, making the
> > interpretation even more complicated, I think.
> >
> > Best
> > Rongrong
> >
> > //Regarding the smearing, I am not sure the leading pT bias would
> > reduce the smearing since the smearing is driven by background
> > fluctuation, not jets. //
> > --- This is what I am confused about a bit. If you look at the rho
> > distributions (Fig 1.10 in the note above), the rms is about 3 - 4
> > GeV/(c sr). With a jet area of 0.5 for R = 0.4 jets, the background
> > smearing should be around 2 GeV/c, isnt? But the rms of the delta pt
> > distributions for R = 0.4 jets from background smearing (Fig. 1.16)
> > is closer to 6 - 7 GeV/c. What causes this enhanced smearing?
> >
> > //When you perform smearing, do you take all the jets with a leading
> > track above 4 GeV/c?//
> > --- We apply the smearing to all the jets
> >
> > //Also, for the detector effects, this is a significant tail in the
> > response, which I assume is not included in the smearing. With this
> > exercise, is the intent to say that the v1 signal is not induced by
> > smearing or that our v1 results can be directly compared to
> > theoretical calculations?//
> > ---- The impact of smearing is small from the checks we have done.
> > We will check with the increased smearing from background
> > fluctuations and can also directly use the delta pT distribution
> > with the tails to see the impact. If the impact is small, the
> > measurements, with the uncertainties, can be compared to model
> > calculations. Its not just the smearing, but the pT dependence of
> > the signal also what decides the impact here. With the data driven
> > check we could evaluate this and if it is small, can have as part of
> > uncertainties. Else can have as a correction and quote systematics
> > on it
> >
> > //In any case, I think it is important to stress that these results
> > are not corrected for detector response and background fluctuation,
> > and a biased jet population is used. //
> > --- We will quote the jet pT as jet pT^raw to state it is
> > uncorrected jet pT. But the detector response and background
> > fluctuations shouldn't be a major factor here, from the checks so
> > far. Also, we see the significant signal after these smearing in the
> > data, they are not washed out. In the final results we might have to
> > quote a correction to account for these effects
> >
> > thanks,
> > Sooraj
> >
> > On Wed, Sep 11, 2024 at 12:09 PM Ma, Rongrong <marr AT bnl.gov>
> > wrote:
> >
> > Hello Sooraj
> >
> > Thanks for the explanation. I understand much better now.
> >
> > If the centroid of the medium is offset by <x>, the average path
> > length difference along positive and negative x is 2*<x>, right?
> >
> > In the D0 v1 paper, it is argued that the large D0 v1 slope is
> > driven by the drag from the titled bulk. Would jets also experience
> > such a drag? If so, that should also contribute to v1, right? Are
> > there any other effects that would induce jet v1?
> >
> > Still, it is not clear to me how the reconstruction efficiency
> > cancels in <px>. What is the definition of <px>?
> >
> > Regarding the smearing, I am not sure the leading pT bias would
> > reduce the smearing since the smearing is driven by background
> > fluctuation, not jets. When you perform smearing, do you take all
> > the jets with a leading track above 4 GeV/c? Also, for the detector
> > effects, this is a significant tail in the response, which I assume
> > is not included in the smearing. With this exercise, is the intent
> > to say that the v1 signal is not induced by smearing or that our v1
> > results can be directly compared to theoretical calculations?
> >
> > In any case, I think it is important to stress that these results
> > are not corrected for detector response and background fluctuation,
> > and a biased jet population is used.
> >
> > Thanks.
> >
> > Best
> > Rongrong
> >
> > On Sep 10, 2024, at 5:51 PM, Sooraj Radhakrishnan
> > <skradhakrishnan AT lbl.gov> wrote:
> >
> > Hi Rongrong,
> > Thanks for the email and the questions. Please find my responses
> > below
> >
> > //"Mean momentum loss = 0.232 +/- 0.068 +/- 0.03 for R = 0.2 jets
> > with 10 < pT,jet < 12 GeV/c ... for an estimated initial part length
> > asymmetry of 0.2 fm".
> > - 0.232 is the slope of <px> vs. eta. Why is it related to energy
> > loss? Should I think of 0.232 as the average energy loss within the
> > eta range of the measurement (|eta| < 1-R) or at a given eta?
> > - Does the initial length asymmetry of 0.2 fm correspond to the
> > slope of <x> vs. eta or <x> at a given eta? //
> >
> > --- The <px> would be zero if jets along positive and negative
> > impact parameter direction (x) see the same amount of medium. But at
> > finite rapidity, the centroid of the medium along the impact
> > parameter direction is offset, leading to different path lengths for
> > jets along +x and -x. This results in more energy loss in one
> > direction vs the other and <px> reflects this difference in energy
> > loss
> >
> > We use slope to quantify the eta dependence as we see the
> > dependence is linear. Alternatively, we could quote the measured
> > value in the rapidity bin at |eta| = 0.6. That would then give the
> > <px> at a given eta, which could then be related to <x> in the same
> > bin. Taking the slope, with the observed linear dependence, gives
> > these values at eta = 1.0. <x> of 0.2 is also the slope or value at
> > eta = 1.0
> >
> > //- If both 0.232 GeV/c and 0.2 fm are slopes, do you implicitly
> > assume that energy loss does not depend on eta?//
> >
> > ----- No, this has an eta dependence as we see, largely
> > proportional to <x> at a given eta. In the region we measure, the
> > dependence is linear. But with more precision for differential
> > measurements along eta we could check if this is strictly linear or
> > not.
> >
> > //- You mentioned that "The impact of efficiency correction on <px>
> > is also small like in the case of v1 as it is self normalized". What
> > do you mean by self-normalized? I usually think of v1 as the
> > modulation of jet yield w.r.t. the first-order even plane, so it is
> > dimensionless and self-normalized. Should one think of <px> that
> > way? It is not clear to me since <px> is not dimensionless.//
> >
> > ---- Yes, <px> is also modulation relative to the first order event
> > plane. Since its the mean each jet comes in both the numerator and
> > denominator and the reconstruction efficiency cancels out.
> >
> > //- You also mentioned "The pT windows are narrow, so the impact
> > from pT dependence should also be small". There is a large smearing
> > in jet pT due to background fluctuation. So it is not clear to me
> > why a narrow selection in jet pT would help. I would think the other
> > way around. While it is probably true that the impact of tracking
> > efficiency on <px> is small due to survival bias (it is easier to
> > find jets whose leading particles are not missing), the effect of
> > background smearing is still there, right?//
> >
> > ----- For R=0.2 jets in particular, the background smearing is not
> > so large. You could see for example here
> (https://drupal.star.bnl.gov/STAR/system/files/STAR_InclJet_AN_Master_v5-5_0.pdf),
> > Fig 1.16. For 0-10% centrality, the width is about 15% for 11 GeV
> > jets. This should be smaller for 10-40% centrality. These are also
> > jets without leading pT selection. We did a smearing with 6%
> > resolution and didnt see impact on the results. We can try
> > increasing this by a factor of 2 to include impact of background
> > smearing as well.
> >
> > //- If there is an asymmetry in pathlength, does one need to take
> > into account possible background variation due to the asymmetry? I
> > kind of remember this was looked into for the jet v2 measurement in
> > Isobar.//
> >
> > ----- The bulk v1 is very small, at sub-percent level. For hard
> > probes, it is an offset of the hard production profile and bulk
> > distribution than variation of bulk density in azimuth. This also
> > means that expansion from bulk v1 is also very small, unlike the
> > case of v2. This should make it easier to evaluate the impact of
> > medium expansion on path length and interactions as well
> >
> > Let me know if you have further questions or comments
> >
> > thanks,
> > Sooraj
> >
> > On Tue, Sep 10, 2024 at 1:37 PM Ma, Rongrong <marr AT bnl.gov> wrote:
> >
> > Hello Sooraj
> >
> > I still have a few questions regarding to this statement "Mean
> > momentum loss = 0.232 +/- 0.068 +/- 0.03 for R = 0.2 jets with 10 <
> > pT,jet < 12 GeV/c ... for an estimated initial part length asymmetry
> > of 0.2 fm".
> > - 0.232 is the slope of <px> vs. eta. Why is it related to energy
> > loss? Should I think of 0.232 as the average energy loss within the
> > eta range of the measurement (|eta| < 1-R) or at a given eta?
> > - Does the initial length asymmetry of 0.2 fm correspond to the
> > slope of <x> vs. eta or <x> at a given eta?
> > - If both 0.232 GeV/c and 0.2 fm are slopes, do you implicitly
> > assume that energy loss does not depend on eta?
> > - You mentioned that "The impact of efficiency correction on <px>
> > is also small like in the case of v1 as it is self normalized". What
> > do you mean by self-normalized? I usually think of v1 as the
> > modulation of jet yield w.r.t. the first-order even plane, so it is
> > dimensionless and self-normalized. Should one think of <px> that
> > way? It is not clear to me since <px> is not dimensionless.
> > - You also mentioned "The pT windows are narrow, so the impact from
> > pT dependence should also be small". There is a large smearing in
> > jet pT due to background fluctuation. So it is not clear to me why a
> > narrow selection in jet pT would help. I would think the other way
> > around. While it is probably true that the impact of tracking
> > efficiency on <px> is small due to survival bias (it is easier to
> > find jets whose leading particles are not missing), the effect of
> > background smearing is still there, right?
> > - If there is an asymmetry in pathlength, does one need to take
> > into account possible background variation due to the asymmetry? I
> > kind of remember this was looked into for the jet v2 measurement in
> > Isobar.
> >
> > Best
> > Rongrong
> >
> > On Sep 9, 2024, at 3:04 AM, Sooraj Radhakrishnan
> > <skradhakrishnan AT lbl.gov> wrote:
> >
> > Dear All,
> > Please find the Preliminary request slides for the jet v1, <px>
> > measurements here
> https://drupal.star.bnl.gov/STAR/system/files/JetV1PreliminaryRequest.pdf
> > thanks,
> > Sooraj
>
>  --
>
> Sooraj Radhakrishnan
>
> Research Scientist,
> Department of Physics
>
> Kent State University
> Kent, OH 44242
>
> Physicist Postdoctoral Affiliate Nuclear Science Division
> Lawrence Berkeley National Lab
> MS70R0319, One Cyclotron Road
>  Berkeley, CA 94720
>  Ph: 510-495-2473 [1]
>
> Email: skradhakrishnan AT lbl.gov
>
>  --
>
> Sooraj Radhakrishnan
>
> Research Scientist,
> Department of Physics
>
> Kent State University
> Kent, OH 44242
>
> Physicist Postdoctoral Affiliate Nuclear Science Division
> Lawrence Berkeley National Lab
> MS70R0319, One Cyclotron Road
>  Berkeley, CA 94720
>  Ph: 510-495-2473 [1]
>
> Email: skradhakrishnan AT lbl.gov
>
>  --
>
> Sooraj Radhakrishnan
>
> Research Scientist,
> Department of Physics
>
> Kent State University
> Kent, OH 44242
>
> Physicist Postdoctoral Affiliate Nuclear Science Division
> Lawrence Berkeley National Lab
> MS70R0319, One Cyclotron Road
>  Berkeley, CA 94720
>  Ph: 510-495-2473 [1]
>
> Email: skradhakrishnan AT lbl.gov
>
> --
>
> Sooraj Radhakrishnan
>
> Research Scientist,
> Department of Physics
>
> Kent State University
>  Kent, OH 44242
>
> Physicist Postdoctoral AffiliateNuclear Science Division
> Lawrence Berkeley National Lab
> MS70R0319, One Cyclotron Road
> Berkeley, CA 94720
> Ph: 510-495-2473 [1]
>
> Email: skradhakrishnan AT lbl.gov
>
> --
>
> Sooraj Radhakrishnan
>
> Research Scientist,
> Department of Physics
>
> Kent State University
>  Kent, OH 44242
>
> Physicist Postdoctoral AffiliateNuclear Science Division
> Lawrence Berkeley National Lab
> MS70R0319, One Cyclotron Road
> Berkeley, CA 94720
> Ph: 510-495-2473 [1]
>
> Email: skradhakrishnan AT lbl.gov
>
>
> Links:
> ------
> [1] tel:%28510%29%20495-2473

Attachment: check.pdf
Description: Adobe PDF document