Comment on "A sensitivity study of the primary correlators used to characterize chiral-magnetically-driven charge separation'' by Magdy, Nie, Ma, and Lacey
CComment on “A sensitivity study of the primary correlators used to characterizechiral-magnetically-driven charge separation” by Magdy, Nie, Ma, and Lacey
Yicheng Feng, Fuqiang Wang, ∗ and Jie Zhao Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA (Dated: September 22, 2020)This note points out an apparent error in the publication Phys. Lett. B (2020) 135771 byMagdy, Nie, Ma, and Lacey.
This note concerns an apparent error in the statisticaluncertainties in “A sensitivity study of the primary cor-relators used to characterize chiral-magnetically-drivencharge separation” by Magdy, Nie, Ma, and Lacey, pub-lished in Phys. Lett. B (2020) 135771 (MNML).Table I lists the data points read off from Fig. 2(∆ γ (Ψ SP ), ∆ γ (Ψ PP )) and Fig. 3 ( f , f , f CME ) ofMNML by a digital ruler ( https://apps.automeris.io/wpd/ ). The quantities ∆ γ (Ψ SP ) and ∆ γ (Ψ PP ) arethe charge-dependent azimuthal correlators [1] with re-spect to the spectator plane (SP) and the participantplane (PP), respectively, in 10-50% centrality Au+Aucollisions simulated by the AMPT (A Multi-Phase Trans-port) model in MNML. Using conventions in MNML, r = ∆ γ (Ψ SP ) / ∆ γ (Ψ PP ), r = v (Ψ SP ) /v (Ψ PP ) (where v (Ψ SP ) and v (Ψ PP ) are the elliptic flow parameterswith respect to SP and PP, respectively), f = r /r − f = 1 /r −
1, the chiral magnetic effect (CME)signal fraction in the ∆ γ (Ψ PP ) measurement is given by f CME = f /f [2]. The SP and RP (reaction plane) wereinterchangeable in those formulas, and SP was used in thecalculations as stated in MNML. From the read-off datapoints, we compute r , assuming uncorrelated ∆ γ (Ψ SP )and ∆ γ (Ψ PP ) errors; since r is not readily accessiblefrom MNML, we compute it by r = 1 / √ f + 1; from r and r we compute f , and then f CME using our com-puted f . These quantities are also listed in Table I.Our computed errors on f and f CME are many timeslarger than those in MNML, depending on the valuesof f . The absolute error on f is of course equal tothe absolute error on r /r . Since f can be zero, therelative error on f can blow up (cf. Table I). It appears,however, that the relative error on f in MNML equalsapproximately to the relative error on r in Table I. (Notethat the digital ruler could introduce some imprecision inthe read-out numbers. Also note that the error on r isnegligible compared to that on r ; whether or not the r error was properly propagated to f in MNML, whichin turn affects our calculated r , is of no significance.) Ifthe relative error on r /r was mistaken as the f relativeerror in MNML, then the f absolute error could be verysmall when f ∼
0; our digital ruler failed to read theerrors of the two f ∼ ) when the preprint ver-sion (arXiv:2002.07934v1) of MNML appeared. It wasalso pointed out at the meeting, by examining the rele-vant analysis code, that there was a double counting ofparticle pairs, artificially reducing the statistical errorsby a factor of √
2; this was acknowledged by the authorsat the STAR discussion meeting. Since this cannot beverified with the information available in MNML, we donot consider it here; considering it would increase all theerrors by factor √
2. When a newer preprint (Lacey andMagdy, arXiv:2006.04132v2) later appeared, which hadthe same f CME data points, we pointed out the issue tothe authors again, also at a STAR meeting. Despite ofthe multiple remonstrations, the issue was not fixed; thedata points published in MNML are identical to those inthe arXiv preprints.Figure 1 depicts our computed f and f CME in solidmarkers, compared to those from MNML in hollow mark-ers. With our correctly propagated errors, the datapoints (solid markers) appear to be too smooth, relativeto the error bars. Fitting a quadratic function to ourcomputed f gives a χ / NDF = 0 . / .
995 (i.e. the probability for a lower χ / NDF valueis 0.5%; if the errors were already artifically reduced byfactor √ f CME givessimilar result, as expected, because f CME is f scaled bythe essentially error-free f . (Incidentally, a quadratic fitto the f from MNML, with the incorrect errors, gives anumerically reasonable χ / NDF and p-value.) The errorwe computed for f is predominately determined by theerror on r . As expected, a quadratic fit to r gives a χ / NDF = 0 . / f . However, quadratic fits to the indi-vidual ∆ γ (Ψ SP ) and ∆ γ (Ψ PP ) give reasonable χ / NDF(p-value) of 5.22/3 (0.157) and 0.90/3 (0.825), respec-tively. Since r is the ratio of ∆ γ (Ψ SP ) over ∆ γ (Ψ PP ),one is forced to conclude that either the two ∆ γ quanti-ties are strongly correlated so standard error propagationdoes not apply or something is unnatural with the AMPT∆ γ data points in MNML. For the former, in order forthe r error to be inflated by a factor of ∼ χ / NDF ∼
1) from simple error propagation, the∆ γ (Ψ SP ) and ∆ γ (Ψ PP ) need to be (cid:112) − (1 / ) = 98%correlated if they have the same relative errors; sincethe error on ∆ γ (Ψ PP ) is significantly larger than that a r X i v : . [ nu c l - e x ] S e p % a - x f (read from MNML Fig.3) f (computed by us from data points in MNML) f (read from MNML Fig.3) cme f (computed by us from data points in MNML) cme f FIG. 1. The f and f CME as functions of a , the CME signalinput to AMPT in MNML. The hollow markers are those readfrom MNML Fig. 3. The solid markers are those computedby us with proper error propagation. on ∆ γ (Ψ SP ), even if they were 100% correlated, the r error would not be factor 5 smaller than that from sim-ple error propagation. Therefore, we conclude that theAMPT ∆ γ data points in MNML are unnatural.A few remarks are in order: • The authors of MNML make the point of a turn-onthreshold effect in f CME , obtained from the methodutilizing the SP and PP first proposed in Ref. [2].With the correctly propagated errors, this point be-comes moot. • Fig.4(a) of MNML shows a convex R Ψ distributionfrom AMPT with no input CME signal ( a = 0).This is contrary to other background studies us-ing hydrodynamics [3], toy model resonance simu-lations [4], and AMPT of multiple versions [5]. • A non-flat R Ψ distribution, either convex or con-cave, means that R Ψ is sensitive to background.The convexity of the AMPT result with a = 0 is comparable to the concavity of the a = 2% resultin MNML. Omitting the a = 0 point from MNMLFig.4(f), extrapolating only the a > R Ψ , is improper.In conclusion, there is an apparent error in the statis-tical uncertainties in “A sensitivity study of the primarycorrelators used to characterize chiral-magnetically-driven charge separation” by Magdy, Nie, Ma, and Lacey,published in Phys. Lett. B (2020) 135771. Thiswas pointed out by us to Magdy and Lacey, two ofthe authors, at an internal STAR meeting when thepreprint version (arXiv:2002.07934v1) of the said publi-cation appeared, and also later when another preprint(arXiv:2006.04132v2) using the same data points wasposted. The apparent error was not fixed–the relevantdata points published in MNML are identical to those inthe arXiv preprints. Tracing this error reveals that theAMPT data points in MNML are statistically unnatural.This work was supported by the U.S. Department ofEnergy under Grant No. DE-SC0012910. ∗ All correspondence should be addressed to F.W. < [email protected] > .[1] Sergei A. Voloshin, Phys. Rev. C 70 (2004) 057901,arXiv:hep-ph/0406311 [hep-ph].[2] Hao-jie Xu, Jie Zhao, Xiaobao Wang, Hanlin Li, Zi-WeiLin, Caiwan Shen, and Fuqiang Wang, Chin. Phys. C (2018) 084103, arXiv:1710.07265 [nucl-th].[3] Piotr Bo˙zek, Phys. Rev. C (2018) 034907,arXiv:1711.02563 [nucl-th].[4] Yicheng Feng, Jie Zhao, and Fuqiang Wang, Phys. Rev. C (2018) 034904, arXiv:1803.02860 [nucl-th].[5] Yicheng Feng, Jie Zhao, and Fuqiang Wang, AMPT sim-ulation results, in preparation. Those AMPT simulationresults have been extensively discussed in internal STARmeetings. T A B L E I . T h e a v a l u e s p l o tt e d i n M N M L F i g s . nd r e s li g h t l y o ff s e t c o m p a r e d t o t h e t e x t s w r i tt e n i n M N M L F i g . , e x c e p t o n e p l o tt e d a t a = . % . T h e ∆ γ ( Ψ S P ) , ∆ γ ( Ψ PP ) , f , f , a nd f C M E v a l u e s ( m i dd l e b l a c k ) a r e r e a d f r o m M N M L F i g s . nd b y a d i g i t a l r u l e r ( https://apps.automeris.io/wpd/ ) . T h e r , r , f , a nd f C M E ( l o w e r b l o c k ) a r e c o m pu t e db y u s w i t hp r o p e r e rr o r p r o p aga t i o n . T h e nu m b e r s i np a r e n t h e s e s a r e r e l a t i v ee rr o r s f o r e a s y c o m p a r i s o n . a % % % . % % % R e a d f r o m F i g s . nd f M N M L ∆ γ ( Ψ S P ) × . ± . ( . % ) . ± . ( . % ) . ± . ( . % ) . ± . ( . % ) . ± . ( . % ) . ± . ( . % ) ∆ γ ( Ψ PP ) × . ± . ( . % ) . ± . ( . % ) . ± . ( . % ) . ± . ( % ) . ± . ( . % ) . ± . ( . % ) f ( M N M L ) − . ± . ( % ) − . ± . ( . % ) − . ( e rr o r un r e a d a b l e ) . ( e rr o r un r e a d a b l e ) . ± . ( . % ) . ± . ( . % ) f . ± . ( . % ) . ± . ( . % ) . ± . ( . % ) . ± . ( . % ) . ± . ( . % ) . ± . ( . % ) f C M E ( M N M L ) − . ± . ( % ) − . ± . ( % ) − . ( e rr o r un r e a d a b l e ) . ± . ( % ) . ± . ( . % ) . ± . ( . % ) C o m pu t e db y u s r = ∆ γ ( Ψ S P ) / ∆ γ ( Ψ PP ) . ± . ( . % ) . ± . ( % ) . ± . ( . % ) . ± . ( % ) . ± . ( . % ) . ± . ( . % ) r = / √ f + . ± . ( . % ) . ± . ( . % ) . ± . ( . % ) . ± . ( . % ) . ± . ( . % ) . ± . ( . % ) f = r / r − − . ± . ( % ) − . ± . ( % ) − . ± . ( % ) . ± . ( % ) . ± . ( % ) . ± . ( % ) f C M E = f / f − . ± . ( % ) − . ± . ( % ) − . ± . ( % ) . ± . ( % ) . ± . ( % ) . ± . ( %%