Beam-Energy Dependence of Directed Flow of Protons, Antiprotons and Pions in Au+Au Collisions

   arXiv: 1401.3043

Phys. Rev. Lett 112, 162301 (2014)

Fig 1 : Proton and Pion directed flow for central(0-10%), midcentral(10-40%) and peripheral(40-80%)collisions 


Proton v1 data: 
        const int N=8;
        double Rapidity[N]= {-0.7,-0.5,-0.3,-0.1,0.1,0.3,0.5,0.7};
        double Rapidity_Error[N]={0.0,};


//39 GeV(Proton)

//0-10%
double y1[N]={-0.00183177,-0.00105792,0.000280686,-0.0028787,-0.00219433,-0.00176371,-0.00150138,-0.000493285};
double ey1[N]={0.00275267,0.00178284,0.00157452,0.00163993,0.00160559,0.00155009,0.00177913,0.00287951};

//10-40%
 double y2[N]={0.002344038,0.002130304,0.00114654,0.000421975,-0.000262472,-0.0010985719,-0.002153078,-0.002369088};
 double ey2[N]={0.00074042,0.000468515,0.000415773,0.000429756,0.000421074,0.000406862,0.000461853,0.000748355};

//40-80%
double y3[N]={0.0244764,0.0160109,0.0121881,0.00421506,-0.00479728,-0.00427418,-0.00796883,-0.0225719};
double ey3[N]={0.00627613,0.00382401,0.00329252,0.00342734,0.00337589,0.00323828,0.00378072,0.0062885};

//27 GeV(Proton)

//0-10%
 double y1[N]={0.00168005,-0.00150845,-0.00156276,0.00259781,-0.000360093,0.0015301,0.00371383,-0.00199935};
 double ey1[N]={0.00254682,0.00163458,0.00143469,0.00150111,0.00151564,0.00146465,0.00167236,0.00264126};

//10-40%
 double y2[N]={0.00292014,0.00286089,0.001646253,0.0006686182,-0.00066452, -0.001286651,-0.002649415,-0.002530913};
 double ey2[N]={0.000577999,0.000362818,0.000317247,0.000331598,0.000334624,0.000322936,0.00036911,0.000592481};

//40-80%
double y3[N]={0.0251595,0.0131012,0.0103181,0.00144097,-0.00319432,-0.00579788,-0.0119397,-0.0234346};
double ey3[N]={0.00295614,0.00178624,0.00152316,0.00159332,0.0016066,0.00154545,0.00181006,0.00298887};

//19 GeV(Proton)

//0-10%
double y1[N]={-0.00134383,-0.00122819,0.000236273,0.00048833,0.00207413,0.000990917,-0.000575657,0.00380029};
double ey1[N]={0.00279075,0.00173766,0.00150895,0.00157073,0.00156014,0.00149642,0.00172419,0.00281888};

//10-40%
 double y2[N]={0.00243672,0.002730385,0.001762032,0.000570904,-0.00059197,-0.0016587906,-0.0024915741,-0.0024739075};
 double ey2[N]={0.000604527,0.000367083,0.000315311,0.000328544,0.000327017,0.000312082,0.000361421,0.000596174};

//40-80 %
double y3[N]={0.0284544,0.0164774,0.00854596,0.00414253,-0.00381164,-0.00952719,-0.0191047,-0.0268929};
double ey3[N]={0.00256019,0.00148724,0.0012488,0.00130395,0.00129844,0.00123402,0.00145718,0.00249369};

//11.5 GeV Proton
//0-10% 
 double y1[N]={-0.0129386,-0.00227438,0.00295323,-0.00056542,0.00234785,0.000163196,0.00632508,0.0132673};
 double ey1[N]={0.00296635,0.00183477,0.00159732,0.00166788,0.00165045,0.00158545,0.00183829,0.00304869};

//10-40%
double y2[N] = {-0.00341595,0.0009747036,0.001212443,0.0007160479,-0.0006701253,-0.00119874,-0.001219269,0.003111589};
double ey2[N]={0.000953644,0.000578296,0.000499372,0.00052311,0.000518108,0.000494702,0.000575027,0.00096231};

//40-80%
 double y3[N]={0.0305119,0.0239105,0.0162317,0.00540334,-0.00330357,-0.0149603,-0.0209334,-0.0318336};
 double ey3[N]={0.00206919,0.00121088,0.00102956,0.00108504,0.00107436,0.00101757,0.00119847,0.00207222};

//7.7 GeV Proton 
//0-10%
double y1[N]={-0.0203452,-0.00738625,-0.00433286,-0.00195176,0.000685336,0.00694344,0.00878699,0.0283179};
double ey1[N]={0.00543306,0.00321989,0.00273916,0.00281952,0.0027888,0.00270132,0.00320329,0.00545943};

//10-40%
double y2[N]={-0.0218351,-0.00944496,-0.00447499,-0.00132103,0.001304121,0.004387375,0.0093865102,0.02143059};
double ey2[N]={0.0006705,0.0006228,0.0005701,0.0005629,0.0005672,0.000569,0.0005728, 0.0006806};

//40-80%
double y3[N]={0.0246792,0.0240645,0.0134543,0.00284927,-0.00644522,-0.0140354,-0.0192329,-0.0228843};
double ey3[N]={0.00328052,0.00187255,0.00156262,0.0016295,0.00161519,0.00152971,0.00182294,0.00319493};

Pion v1 data:  

        const int N2=10;
        double Rapidity[N2]= {-0.9,-0.7,-0.5,-0.3,-0.1,0.1,0.3,0.5,0.7,0.9};
        double Rapidity_Error[N2]={0.0,};

//39 GeV
//0-10%
double y11[N2]={0.00418019,0.00455485,0.00221147,0.00190326,0.000687622,2.62369e-05,-0.002069,-0.00288105,-0.00438558,-0.0054163};
 double ey11[N2]={0.00118434,0.000674411,0.000634629,0.000629249,0.000653153,0.00064592,0.000626797,0.000633985,0.000686472,0.00133703};

//10-40%
double y21[N2]={0.0106218,0.00779001,0.00526938,0.00327819,0.0012148,-0.00100591,-0.00307684,-0.00500015,-0.00717131,-0.0103756};
double ey21[N2]={0.000454181,0.000256502,0.000240557,0.000238824,0.000247346,0.000245246,0.00023766,0.000239787,0.000258563,0.000486166};

//40-80%
double y31[N2]={0.0188297,0.0118609,0.00818098,0.00459556,0.00329827,-0.00226344,-0.00301623,-0.00717489,-0.0127507,-0.0225615};
double ey31[N2]={0.00253854,0.00141978,0.00132712,0.00131708,0.00136191,0.00135126,0.00130798,0.00131876,0.0014198,0.00261972};
  
//27 GeV 

//0-10%
double y11[N2]={0.00801762,0.00348652,0.00301775,0.00129137,-0.000247755,9.60463e-05,-0.000745626,-0.00250023,-0.00371171,-0.00737118};
double ey11[N2]={0.00122567,0.000698683,0.000649853,0.000645264,0.000674138,0.000675962,0.0006521,0.000658061,0.000711945,0.00128381};

 
//10-40%
double y21[N2]={0.0124658,0.00872285,0.00645321,0.00349878,0.00105076,-0.00108581,-0.00346087,-0.00624446,-0.00902525,-0.0129533};
double ey21[N2]={0.000424852,0.000240696,0.000223816,0.000222748,0.00023244,0.00023307,0.000224652,0.00022611,0.000243932,0.000435739};

   
//40-80%
double y31[N2]={0.0209678,0.0138602,0.0106669,0.006948,0.00180456,-0.00171034,-0.00643908,-0.0109785,-0.0171965,-0.0250005};
double ey31[N2]={0.00129285,0.00072834,0.000676335,0.000672978,0.000701464,0.000702805,0.000676854,0.000681152,0.000734832,0.00130763};

 
//19.6 GeV

//0-10 %
double y11[N2]={0.0056813,0.00429788,0.00288784,0.000135476,-0.000652433,0.000565074,-0.00216235,-0.00363369,-0.00392289,-0.00695512};
double ey11[N2]={0.00147488,0.000824887,0.000762077,0.000750962,0.000785803,0.000782604,0.000749137,0.000757518,0.00082704,0.00153486};


//10-40 %
double y21[N2]={0.0149177,0.0102598,0.00712506,0.00426143,0.00157739,-0.00174864,-0.00476216,-0.0071855,-0.0103166,-0.0146511};
double ey21[N2]={0.00050449,0.000279234,0.000257495,0.000254466,0.000265987,0.000265595,0.000253858,0.000255613,0.000277676,0.000503772};


//40-80 %
double y31[N2]={0.0250677,0.0176948,0.0129391,0.00710066,0.0015361,-0.00205885,-0.00695383,-0.0124711,-0.0184275,-0.025623};
double ey31[N2]={0.00118942,0.000653419,0.000601866,0.000596252,0.000622625,0.000621772,0.000593723,0.000596263,0.000646154,0.0011618};



//11.5 GeV

//0-10%
double y11[N2]={0.00916816,0.00508237,0.00269664,0.00194594,0.000126252,-0.00273391,-0.0004427,-0.00433598,-0.00213611,-0.00493046};
double ey11[N2]={0.00194924,0.00112243,0.00101313,0.000995277,0.00102804,0.00102633,0.000999545,0.00101835,0.00114069,0.0020668};

//10-40%
double y11[N2]={0.0181201,0.013824,0.00859977,0.00512448,0.00230668,-0.00191981,-0.00558514,-0.00975232,-0.0137853,-0.0176957};
double ey11[N2]={0.000599337,0.000344096,0.000310679,0.000306777,0.000316692,0.000316232,0.00030756,0.000311395,0.000346585,0.000616744};

//40-80%
double y31[N2]={0.0403169,0.0282246,0.0196425,0.0111353,0.00281105,-0.00397749,-0.011127,-0.0202217,-0.0284867,-0.0389162};
double ey31[N2]={0.00116482,0.000669188,0.000606475,0.000601291,0.000620558,0.000619358,0.000601131,0.000605408,0.000670804,0.00118378};

//7.7 GeV 
//0-10%
double y11[N2]={0.000441316,0.00182928,-0.000142038,-0.00089236,0.000221004,-0.00526669,-0.00246784,-0.00131499,0.000838314,-0.00750076};
double
ey11[N2]={0.00435667,0.00256068,0.00221022,0.00216492,0.00218349,0.00217873,0.00215614,0.00220043,0.00258115,0.00451173};

//10-40%
double y21[N2]={0.0180309,0.0146537,0.00902703,0.00496062,0.00290686,-0.00131913,-0.00603065,-0.00875126,-0.0123064,-0.0198444};
double
ey21[N2]={0.00121468,0.000716108,0.000617812,0.000609072,0.000614311,0.000612473,0.000605817,0.000612917,0.000710979,0.00121395};

//40-80% 
double y31[N2]={0.051107,0.0363774,0.0267159,0.0184652,0.00620654,-0.0041068,-0.0167095,-0.0267019,-0.0376915,-0.0526559};
double ey31[N2]={0.00227639,0.00134638,0.0011662,0.00115529,0.0011687,0.00116132,0.00114483,0.00115022,0.00132452,0.0022337};

Fig 2 : Proton-Antiproton and π+ - π− directed flow in mid-cental(10-40%) collisions 



//Proton  and Antiproton 

        const int N=8;
        double Rapidity[N]= {-0.7,-0.5,-0.3,-0.1,0.1,0.3,0.5,0.7};
        double Rap_Error[N]={0.0,};

//200 GeV

//Proton 

 double y1[N]={0.0002465769, 0.000215012, 0.0005242742, -0.0001312073, -0.0003756894, -0.0001796291, -0.0006640261,-0.000479241};
 double ey1[N]={0.0003378735, 0.0002293871, 0.0002100936, 0.0002169594, 0.0002093606, 0.0002037714, 0.0002239161, 0.0003344763};


//Antiproton

 double y2[N]={0.003234542, 0.001976365, 0.001949272,0.0005272557, -0.0003475102,-0.001055847, -0.002645546,-0.003739852};
 double ey2[N]={0.0004046012, 0.0002722523, 0.0002487879, 0.0002576158,0.0002516982,0.0002442893, 0.0002675602,0.0003997298};



//62.4 GeV

//Proton 

 double y1[N]={0.000177405, 0.005546418, -0.0001330919, -0.00549923, 0.0005598268, -0.002047904, 0.002002556, -0.004764448};
 double ey1[N]={0.003456989, 0.002107922, 0.001862863, 0.001934451, 0.00182623, 0.001731094, 0.00195932, 0.00324174};


//Antiproton

 double y2[N]={0.01078279, 0.001898466, 0.004722212, 0.001765132, -0.003233805, -0.007092542, -0.009320073, -0.01453812};
 double ey2[N]={0.005562472, 0.003379211, 0.002987473, 0.003058372, 0.002667993, 0.002516108, 0.002860403, 0,0.004786215};


//39 GeV

//Proton 

 double y1[N]={0.002344038,0.002130304,0.00114654,0.000421975,-0.000262472,-0.0010985719,-0.002153078,-0.002369088};
 double ey1[N]={0.00074042,0.000468515,0.000415773,0.000429756,0.000421074,0.000406862,0.000461853,0.000748355};

 
//Antiproton

 double y2[N]={0.0173537,0.00916808,0.00616074,0.00164461,-0.00281191,-0.00480854,-0.00996457,-0.0186553};
 double
 ey2[N]={0.00203402,0.00121536,0.00105959,0.00108694,0.0010569,0.0010277,0.00118605,0.00201606};


//27 GeV
//Proton
double y1[N]={0.00292014,0.00286089,0.001646253,0.0006686182,-0.00066452, -0.001286651,-0.002649415,-0.002530913};
 double ey1[N]={0.000577999,0.000362818,0.000317247,0.000331598,0.000334624,0.000322936,0.00036911,0.000592481};


//Antiproton

double y2[N]={0.0175334,0.0145298,0.0072682518,0.002720407,-0.00277517,-0.007467592981,-0.01430623,-0.0185639};
double
ey2[N]={0.00201992,0.00120299,0.00104355,0.00107102,0.00107854,0.00105587,0.00122367,0.00206987};


//19.6 GeV Proton

 double y1[N]={0.00243672,0.002730385,0.001762032,0.000570904,-0.00059197,-0.0016587906,-0.0024915741,-0.0024739075};
 double ey1[N]={0.000604527,0.000367083,0.000315311,0.000328544,0.000327017,0.000312082,0.000361421,0.000596174};
 
  
//Antiproton

 double y2[N]={0.0176968,0.014685,0.00960508,0.00226171,-0.00408872,-0.00806293,-0.0160356,-0.0154424};
 double ey2[N]={0.0029639,0.00166103,0.00140058,0.00142061,0.00141965,0.00138892,0.00164573,0.00293298};

//11.5 GeV
//proton   
double y1[N] = {-0.00341595,0.0009747036,0.001212443,0.0007160479,-0.0006701253,-0.00119874,-0.001219269,0.003111589};
double ey1[N]={0.000953644,0.000578296,0.000499372,0.00052311,0.000518108,0.000494702,0.000575027,0.00096231};


//Antiproton

double y2[N]={0.0235744,0.016393,0.00912069,0.00487699,-0.00341544,-0.01011392,-0.013514,-0.0183287};
double ey2[N]={0.00580193,0.00310947,0.00253119,0.00252167,0.00248834,0.0024729,0.00303509,0.00569761};

//7.7 GeV

//proton
double y1[N]={-0.0218351,-0.00944496,-0.00447499,-0.00132103,0.001304121,0.004387375,0.0093865102,0.02143059};
double ey1[N]={0.0006705,0.0006228,0.0005701,0.0005629,0.0005672,0.000569,0.0005728, 0.0006806};

//Antiproton
        double y2[N]={0.01359597, 0.0129865, 0.01020059, 0.0036495, -0.00362359, -0.011925307, -0.02580274, -0.0208779};
        double ey2[N]={0.0216594,0.0109609,0.00797432,0.00732109,0.00726075,0.00781687,0.0106249,0.020885};

Positive and Negative charged Pion: 

        const int N2=10;
        double x2[N2]= {-0.9,-0.7,-0.5,-0.3,-0.1,0.1,0.3,0.5,0.7,0.9};
        double ex2[N2]={0.0,};

//200 GeV 

//pion plus 
        double y21[N2]={0.002495852, 0.001620547,0.000930214, 0.0006090426, 0.0003593528, -0.0001377286, -0.0006991617, -0.0010537, -0.001818681, -0.001875918};
        double ey21[N2]={0.0001289897, 7.748487e-05, 7.885012e-05, 7.873746e-05, 8.178383e-05, 8.016477e-05, 7.769842e-05, 7.802784e-05, 7.656267e-05, 0.0001314223};


//pion minus 
double y22[N2] = {0.002607237, 0.001507207, 0.0007809651, 0.0005432609, 0.0003560829, -0.0001391768, -0.0007296598, -0.0009652907, -0.001882503, -0.002054314};
double ey22[N2]={0.0001285157, 7.700321e-05, 7.820331e-05, 7.80596e-05, 8.130248e-05, 8.059429e-05, 7.804403e-05, 7.821683e-05, 7.671306e-05, 0.0001317454};


//62 GeV

//pion plus 
        double y21[N2]={0.004287786,0.003236116, 0.002369577, 0.0009344104, 0.0007406681, 0.001672886, 0.0001653047, -0.0009801575, -0.004344014, -0.009773637 };
        double ey21[N2]={0.001631476,0.001069357, 0.001115082, 0.00110286, 0.001164732, 0.001220143, 0.00117198, 0.001178644, 0.001101794, 0.00132122};

//pion minus 

double y22[N2]={0.004382954,0.004117326,0.001229527,7.417232e-05,-0.002455201,-0.0005152861,-0.001928802,-0.003224193,-0.00226843,-0.005085041 };
double ey22[N2]={0.00141524, 0.001232294, 0.001335001, 0.001323657, 0.001336265, 0.001136895,0.001063003, 0.001070578,0.001004617, 0.001203547};


//39 GeV

//pion plus
        double y21[N2]={0.0109445,0.00773885,0.00524334,0.00343379,0.00160978,-0.000649723,-0.00300401,-0.00504323,-0.00798078,-0.011393};
        double ey21[N2]={0.000521105,0.000294292,0.000275742,0.000273563,0.000282915,0.000280367,0.000271706,0.000274338,0.000295833,0.000553013};

 // Pion minus 
        double y22[N2]={0.0110647,0.00828918,0.00590016,0.00377886,0.00161982,-0.000684347,-0.00256065,-0.00439674,-0.00683917,-0.00994148};
        double ey22[N2]={0.000518389,0.000292246,0.000273953,0.000271983,0.000281631,0.000279341,0.000270644,0.000273035,0.000294305,0.00055169};

//27 GeV 

//pion plus
  
        double y21[N2]={0.0135511,0.00969729,0.00667144,0.00335904,0.00101182,-0.00151049,-0.00453285,-0.00638047,-0.00927839,-0.0142414};
        double ey21[N2]={0.00057034,0.000324661,0.000301969,0.000300196,0.000313271,0.000314037,0.000303135,0.000305295,0.000329488,0.000587928};

 // Pion minus 
        double y22[N2]={0.0138726,0.008936,0.00671994,0.00378474,0.00131286,-0.00158854,-0.00378421,-0.00658994,-0.00914576,-0.0143495};
        double
        ey22[N2]={0.000565422,0.000320755,0.000298325,0.000296934,0.000309859,0.000310638,0.000299438,0.000301406,0.000325196,0.000581894};

//19.6 GeV 
//pion plus
 
        double y21[N2]={0.0160849,0.0123355,0.00807006,0.00494161,0.00122771,-0.00153803,-0.0050725,-0.00818653,-0.011541,-0.016216};
        double ey21[N2]={0.000556038,0.000308246,0.000284029,0.000280359,0.000292901,0.00029282,0.000280183,0.000282521,0.000306927,0.000554688};
        
  
 // Pion minus 
        double y22[N2]={0.0144346,0.0104764,0.00745356,0.0041527,0.00154976,-0.00114601,-0.00477961,-0.0074476,-0.0102069,-0.0151694};
        double
        ey22[N2]={0.000550993,0.0003045,0.000280704,0.000277313,0.000289836,0.000289477,0.000276695,0.000278627,0.000302665,0.000548912};


//11.5 GeV

//pion plus

        double y21[N2]={0.0233604,0.0165231,0.0116872,0.00788576,0.00194927,-0.00232941,-0.00652091,-0.0114557,-0.0166497,-0.0247683};
        double ey21[N2]={0.000998776,0.000575418,0.000519441,0.000512361,0.000528564,0.00052793,0.000513976,0.000521115,0.000579497,0.00102171};
        
   
 // Pion minus 
        double y22[N2]={0.0190933,0.0151897,0.0096416,0.00550739,0.00200569,-0.00275592,-0.00552333,-0.0106062,-0.0152229,-0.0185007};
        double ey22[N2]={0.000981245,0.00056226,0.000507231,0.000500849,0.000517063,0.00051642,0.000502331,0.000508304,0.000565184,0.00100339};


//7.7 GeV

//pion plus

      double y21[N2]={0.0263428,0.0182313,0.0127261,0.00816863,0.0029451,-0.000838424,-0.00662795,-0.0121488,-0.0175733,-0.0242242};
        double ey21[N2]={0.00115879,0.000684898,0.000591136,0.000581837,0.000585772,0.00058431,0.000577756,0.000585429,0.00067869,0.00114976};
        
 // Pion minus 
        double y22[N2]={0.0177322,0.0148518,0.0097621,0.00484279,0.00296891,-0.000666419,-0.0057781,-0.00903913,-0.0132229,-0.0207987};
        double ey22[N2]={0.00112423,0.000661336,0.000570038,0.000561605,0.000566271,0.000564669,0.000558678,0.000565402,0.000656118,0.00111938};

Fig. 3 and 4

NA49 and E895 data points are from reference : C. Alt et al. (NA49 Collaboration), Phys. Rev. C 68, 034903 (2003) and H. Liu et al. (E895 Collaboration), Phys. Rev. Lett. 84, 5488 (2000).

v1(y) slope (dv1/dy) at midrapidity as a function of beam energy for mid-central collisions(10-40%).
Beam Energy Pion: π+ Stat. Error Syst. Error
7.7 -2.33159e-02 1.95083e-03 9.47368e-04
11.5 -2.38797e-02 1.73353e-03 4.72265e-04
19.6 -1.63150e-02 9.49440e-04 3.86864e-04
27.0 -1.30634e-02 1.02075e-03 3.38137e-04
39.0 -1.10353e-02 9.21438e-04 3.59618e-04
62.4 -5.87525e-03 6.96240e-04 4.46856e-04
200 -2.35619e-03 5.23337e-05 2.46856e-05

Beam Energy Pion: π− Stat. Error Syst. Error
7.7 -1.73067e-02 1.88481e-03 9.14410e-04
11.5 -1.86460e-02 1.69459e-03 4.61386e-04
19.6 -1.46003e-02 9.38462e-04 3.82357e-04
27.0 -1.26760e-02 1.00908e-03 3.34132e-04
39.0 -1.08669e-02 9.17088e-04 3.57570e-04
62.4 -4.8208e-03 6.76113e-04 4.46856e-04
200 -2.33137e-03 5.24990e-05 2.46856e-05

Beam Energy Antiproton Stat. Error Syst. Error
7.7 -3.58057e-02 2.164369e-02 1.9e-02
11.5 -3.51478e-02 8.47682e-03 7.1e-03
19.6 -2.93238e-02 4.73378e-03 4.0e-03
27.0 -2.32090e-02 3.56216e-03 3.0e-03
39.0 -1.86672e-02 3.54199e-03 3.0e-03
62.4 -1.65848e-02 2.97745e-03 6.104e-3
200 -4.89110e-03 2.5203e-04 2.86368e-04

Beam Energy Proton Stat. Error Syst. Error
7.7 1.25633e-02 1.10027e-03 0.0029
11.5 -5.44871e-03 1.11279e-03 0.0021
19.6 -5.94486e-03 7.77508e-04 0.0014
27.0 -4.97679e-03 7.61942e-04 0.0010
39.0 -3.42149e-03 9.27623e-04 0.0012
62.4 -2.67291e-03 1.95178e-3 3.17921e-3
200 -8.21396e-04 2.11236e-4 5.2713e-4

Beam Energy Net-proton Stat. Error Syst. Error
7.7 0.0131475 0.00110027 0.0029
11.5 -0.003985273 0.0011279 0.0021
19.6 -0.003697327 0.000567 0.0014
27.0 -0.000788 0.00067566 0.0010
39.0 0.00162967 0.0019 0.00096
62.4 0.00762832 0.00390818 0.0056
200 0.00852520 0.000901741 0.0024337

For any questions please contact STAR Physics Analysis Coordinator : Frank Geurts - geurts@rice.edu