PARTON ENERGY LOSS & GENERALIZED JET TRANSPORT …€¦ · PARTON ENERGY LOSS & GENERALIZED JET...

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PARTON ENERGY LOSS & GENERALIZED JET TRANSPORT COEFFICIENT Yuan-Yuan Zhang (CCNU, LBNL) Collaborators: Guang-You Qin, Xin-Nian Wang

Transcript of PARTON ENERGY LOSS & GENERALIZED JET TRANSPORT …€¦ · PARTON ENERGY LOSS & GENERALIZED JET...

Page 1: PARTON ENERGY LOSS & GENERALIZED JET TRANSPORT …€¦ · PARTON ENERGY LOSS & GENERALIZED JET TRANSPORT COEFFICIENT Yuan-Yuan Zhang (CCNU, LBNL) Collaborators: Guang-You Qin, Xin-Nian

PARTON ENERGY LOSS & GENERALIZED JET TRANSPORT COEFFICIENT

Yuan-Yuan Zhang (CCNU, LBNL) Collaborators: Guang-You Qin, Xin-Nian Wang

Page 2: PARTON ENERGY LOSS & GENERALIZED JET TRANSPORT …€¦ · PARTON ENERGY LOSS & GENERALIZED JET TRANSPORT COEFFICIENT Yuan-Yuan Zhang (CCNU, LBNL) Collaborators: Guang-You Qin, Xin-Nian

Improved High Twist approach

Improved approach

Go beyond collinear approximation

High-Twist approach

• Collinear approximation

l1

l2

lh

Z

q

Ap

x1p xpx2p + k⊥ x3p + k⊥

lq

lq q

yy1y20

lh

Ap Ap

X

S

eA DIS

~k? ⌧ ~l?<latexit sha1_base64="YZEVjdSai9dOBz5hJa1GMnQcz2c=">AAACDXicbZDLSsNAFIYn9VbrLerSzWAVXJWkCrosunFZwV6gCWEyPW2HTi7MTAol5AXc+CpuXCji1r0738ZpGlBbfxj4+c45nDm/H3MmlWV9GaWV1bX1jfJmZWt7Z3fP3D9oyygRFFo04pHo+kQCZyG0FFMcurEAEvgcOv74ZlbvTEBIFoX3ahqDG5BhyAaMEqWRZ544E6DpOPNSJwYRZ9jhHOeM/zDPrFo1KxdeNnZhqqhQ0zM/nX5EkwBCRTmRsmdbsXJTIhSjHLKKk0iICR2TIfS0DUkA0k3zazJ8qkkfDyKhX6hwTn9PpCSQchr4ujMgaiQXazP4X62XqMGVm7IwThSEdL5okHCsIjyLBveZAKr4VBtCBdN/xXREBKFKB1jRIdiLJy+bdr1mn9fqdxfVxnURRxkdoWN0hmx0iRroFjVRC1H0gJ7QC3o1Ho1n4814n7eWjGLmEP2R8fENinGceg==</latexit>

twist expansion for hard scattering part of Wµ⌫

<latexit sha1_base64="o5yDZWWeBlvh7jk/FLllX9JE/uc=">AAAB8XicbVDLSgNBEOz1GeMr6tHLYBA8hd0o6DHoxWME88DsGmYnk2TIzOwyDyEs+QsvHhTx6t9482+cJHvQxIKGoqqb7q445Uwb3//2VlbX1jc2C1vF7Z3dvf3SwWFTJ1YR2iAJT1Q7xppyJmnDMMNpO1UUi5jTVjy6mfqtJ6o0S+S9Gac0EnggWZ8RbJz00HrMQmFDaSfdUtmv+DOgZRLkpAw56t3SV9hLiBVUGsKx1p3AT02UYWUY4XRSDK2mKSYjPKAdRyUWVEfZ7OIJOnVKD/UT5UoaNFN/T2RYaD0WsesU2Az1ojcV//M61vSvoozJ1BoqyXxR33JkEjR9H/WYosTwsSOYKOZuRWSIFSbGhVR0IQSLLy+TZrUSnFeqdxfl2nUeRwGO4QTOIIBLqMEt1KEBBCQ8wyu8edp78d69j3nripfPHMEfeJ8/3+KRDA==</latexit>

medium induced radiation

radiative parton energy loss in cold nuclei

Page 3: PARTON ENERGY LOSS & GENERALIZED JET TRANSPORT …€¦ · PARTON ENERGY LOSS & GENERALIZED JET TRANSPORT COEFFICIENT Yuan-Yuan Zhang (CCNU, LBNL) Collaborators: Guang-You Qin, Xin-Nian

Generalized Jet transport coefficient q̂(~k?)<latexit sha1_base64="D26God0PCgZBJwPyUwc51FYksiE=">AAACAXicbVBNS8NAEN3Ur1q/ol4EL8Ei1EtJqqDHohePFewHNCFsttN26SZZdzeFEuLFv+LFgyJe/Rfe/Ddu2xy09cHA470ZZuYFnFGpbPvbKKysrq1vFDdLW9s7u3vm/kFLxokg0CQxi0UnwBIYjaCpqGLQ4QJwGDBoB6Obqd8eg5A0ju7VhIMX4kFE+5RgpSXfPHKHWKUPWcUdA0lHmZ+6HATPznyzbFftGaxl4uSkjHI0fPPL7cUkCSFShGEpu47NlZdioShhkJXcRALHZIQH0NU0wiFIL519kFmnWulZ/VjoipQ1U39PpDiUchIGujPEaigXvan4n9dNVP/KS2nEEwURmS/qJ8xSsTWNw+pRAUSxiSaYCKpvtcgQC0yUDq2kQ3AWX14mrVrVOa/W7i7K9es8jiI6Rieoghx0ieroFjVQExH0iJ7RK3oznowX4934mLcWjHzmEP2B8fkDLHSXWQ==</latexit>

p′ p′

l l′ l′ l

xp + k⊥ xp + k⊥

0 X y

q̂ = ⇢

Zdk2?

hd�idk2?

k2?<latexit sha1_base64="k8am2UDX/tBmgivavQoRdU8VlFE=">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</latexit>

one nucleon

q̂ ⌘Z

d2k?(2⇡)2

q̂(~k?)

=

Zd2k?(2⇡)2

Zdx�(x� k2?

2p+l�)4⇡↵sC2(R)

N2c � 1

⇢(y)�(x,~k?)<latexit sha1_base64="MSEuaM/gmmNNEgokw9TjV8dBJek=">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</latexit>

q̂(~k?)<latexit sha1_base64="ZiPxEDzS7KKvJOHwaVJvJOaUBnI=">AAACAnicdVDLSgNBEJyN7/iKehIvg0HQS9iJYuIt6MVjBKNCdllmJ51kyOzDmdlAWBYv/ooXD4p49Su8+TfOJhFUtKChqOqmu8uPBVfatj+swszs3PzC4lJxeWV1bb20sXmlokQyaLFIRPLGpwoED6GluRZwE0uggS/g2h+c5f71EKTiUXipRzG4Ae2FvMsZ1UbyStvY6VOd3mb7zhBYOsi81IlBxtmBVyrbFdu2CSE4J6R2bBtyclKvkjomuWVQRlM0vdK704lYEkComaBKtYkdazelUnMmICs6iYKYsgHtQdvQkAag3HT8Qob3jNLB3UiaCjUeq98nUhooNQp80xlQ3Ve/vVz8y2snult3Ux7GiYaQTRZ1E4F1hPM8cIdLYFqMDKFMcnMrZn0qKdMmtaIJ4etT/D+5qlbIYaV6cVRunE7jWEQ7aBftI4JqqIHOURO1EEN36AE9oWfr3nq0XqzXSWvBms5soR+w3j4B0huXuQ==</latexit>

�(x,~k?)<latexit sha1_base64="LZn61LgEWwtJF5GX6vQs8m9NQmE=">AAACAXicdVBNSwMxEM36WetX1YvgJVgEBSmbKlpvRS8eK1gVusuSTac2NLsbkmyxLPXiX/HiQRGv/gtv/huztYKKPhh4vDfDzLxQCq6N6747E5NT0zOzhbni/MLi0nJpZfVCJ6li0GSJSNRVSDUIHkPTcCPgSiqgUSjgMuyd5P5lH5TmSXxuBhL8iF7HvMMZNVYKSuvYk12+fbPr9YFlvWGQeRKUHO4EpbJbcV2XEIJzQg4PXEuOjmpVUsMktyzKaIxGUHrz2glLI4gNE1TrFnGl8TOqDGcChkUv1SAp69FraFka0wi0n40+GOItq7RxJ1G2YoNH6veJjEZaD6LQdkbUdPVvLxf/8lqp6dT8jMcyNRCzz0WdVGCT4DwO3OYKmBEDSyhT3N6KWZcqyowNrWhD+PoU/08uqhWyV6me7Zfrx+M4CmgDbaJtRNAhqqNT1EBNxNAtukeP6Mm5cx6cZ+fls3XCGc+soR9wXj8AeKmW7g==</latexit>

$<latexit sha1_base64="iQj0vZEfDr7aIcTn4dY9ASRFiAE=">AAAB+HicdVDLSgNBEJyNrxgfWfXoZTAInsJOFJPcgl48RjAPSJYwO5lNhsw+mOlV4pIv8eJBEa9+ijf/xtkkgooWNBRV3XR3ebEUGhznw8qtrK6tb+Q3C1vbO7tFe2+/raNEMd5ikYxU16OaSxHyFgiQvBsrTgNP8o43ucz8zi1XWkThDUxj7gZ0FApfMApGGtjFvuQ+KDEaA1UquhvYJafsOA4hBGeEVM8dQ+r1WoXUMMksgxJaojmw3/vDiCUBD4FJqnWPODG4KVUgmOSzQj/RPKZsQke8Z2hIA67ddH74DB8bZYj9SJkKAc/V7xMpDbSeBp7pDCiM9W8vE//yegn4NTcVYZwAD9likZ9IDBHOUsBDoTgDOTWEMiXMrZiNqaIMTFYFE8LXp/h/0q6UyWm5cn1Walws48ijQ3SEThBBVdRAV6iJWoihBD2gJ/Rs3VuP1ov1umjNWcuZA/QD1tsnuJqTyw==</latexit>

non-perturbative quantity (what we want to probe!)special case calculated by static potential model �(0,~k?)

<latexit sha1_base64="LDKLCPS0bx8/bOCrBCQ7mXbcw9M=">AAACAHicbVBNS8NAEN34WetX1IMHL8EiVJCSVEGPRS8eK9gPaELYbCft0k2y7G4KJeTiX/HiQRGv/gxv/hu3bQ7a+mDg8d4MM/MCzqhUtv1trKyurW9slrbK2zu7e/vmwWFbJqkg0CIJS0Q3wBIYjaGlqGLQ5QJwFDDoBKO7qd8Zg5A0iR/VhIMX4UFMQ0qw0pJvHrt8SKv2hTsGko1yP3M5CJ6f+2bFrtkzWMvEKUgFFWj65pfbT0gaQawIw1L2HJsrL8NCUcIgL7upBI7JCA+gp2mMI5BeNnsgt8600rfCROiKlTVTf09kOJJyEgW6M8JqKBe9qfif10tVeONlNOapgpjMF4Ups1RiTdOw+lQAUWyiCSaC6lstMsQCE6UzK+sQnMWXl0m7XnMua/WHq0rjtoijhE7QKaoiB12jBrpHTdRCBOXoGb2iN+PJeDHejY9564pRzByhPzA+fwBhLZZG</latexit>

TAqg (x, x1, x2) ⇡ C ⇤ ⇢(y�1 , y?)⌦ fA

q (x)⌦ �(x2,~k?)

k2?<latexit sha1_base64="CP2s6EYy4vv7YfeWI7qg5dHthbo=">AAACenicbVFdb9MwFHXC1yhfBR4RkrUKSFmpkjAJHjf2wuOQ1m1S3Uau6zRWndiznSmR5R/BX+ONX8ILD7hdQLBxJctH59wjX5+7kJxpE8ffg/DW7Tt37+3c7z14+Ojxk/7TZ6da1IrQCRFcqPMF1pSzik4MM5yeS0VxueD0bLE+2uhnl1RpJqoT00o6K/GqYjkj2Hgq6389yewFXLm5PXSI09xEzQg2mU3c9kodUmxVmCFEWEolGgjh0VuIVCGiNkvm70ZtZpGkSrohEoaVVMM8u5gfRo23dATKFSa+q2BRk6UjdEmJXbs/PmfXv/E8dTDrD+JxvC14EyQdGICujrP+N7QUpC5pZQjHWk+TWJqZxcowwqnroVpTickar+jUwwr7mWZ2G52DrzyzhLlQ/lQGbtm/HRaXWrflwneW2BT6urYh/6dNa5N/nFlWydrQilw9lNccGgE3e4BLpigxvPUAE8X8rJAU2Adl/LZ6PoTk+pdvgtN0nLwfp1/2Bwefujh2wAuwCyKQgA/gAHwGx2ACCPgRvAxeB2+Cn+FuOAz3rlrDoPM8B/9UuP8L+Ti/6A==</latexit>

�(0,~k?)

k2?= C2(T )

4↵s

(k2? + µ2D)

2<latexit sha1_base64="fbbRbbNa0o3O75TAk8JStgiLDNw=">AAACYHicbZFPT9swGMadMEbXwSjstl2sVZNagaqkILELEoIddmQSBaS6RI77prHqJJbtMFWWvyQ3Dlz2SeamnTRgr2T5p+f14z+PUym4NlH0GIQbbzbfbrXetd9v73zY7eztX+uqVgxGrBKVuk2pBsFLGBluBNxKBbRIBdyk84tl/+YelOZVeWUWEiYFnZU844waLyWdXyRTlFkic96LDjG5B2bnLvECKOn6zs7/8p0dOnd6kfipd9XHK98xJlTInCZWO2eJgMz0njkOSFEn9nvDRPFZbvrNRkmnGw2ipvBriNfQReu6TDoPZFqxuoDSMEG1HseRNBNLleFMgGuTWoOkbE5nMPZY0gL0xDYBOfzVK1OcVcqP0uBG/ddhaaH1okj9yoKaXL/sLcX/9ca1yb5NLC9lbaBkq4OyWmBT4WXaeMoVMCMWHihT3N8Vs5z65Iz/k7YPIX755NdwPRzER4Phz+Pu2fk6jhb6jL6gHorRCTpDP9AlGiGGnoKNYDvYCX6HrXA33FstDYO15yN6VuGnP4Cvt+s=</latexit>

Wµ⌫ =F(Nc,

~l?,~k?) ⇤ Pqg(z)⌦Hµ⌫(0)(x)

⌦ Dq!h

z(zh/z)⌦ T

Aqg (x, x1, x2)

<latexit sha1_base64="RD8qP3P71JAhLGD9j7FmwPGfK1E=">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</latexit>

approximately factorize

Generic factorized Wµ⌫<latexit sha1_base64="mI8H3gjSsvMi1NG52rXGZ1pZfh4=">AAAB8XicdVDLSsNAFJ34rPVVdelmsAiuQpKGtu6KblxWsA9sYplMp+3QySTMQyihf+HGhSJu/Rt3/o2TtoKKHrhwOOde7r0nShmVynE+rJXVtfWNzcJWcXtnd2+/dHDYlokWmLRwwhLRjZAkjHLSUlQx0k0FQXHESCeaXOZ+554ISRN+o6YpCWM04nRIMVJGuu3cZUGsA65n/VLZsc/rVc+vQsd2nJrruTnxan7Fh65RcpTBEs1+6T0YJFjHhCvMkJQ910lVmCGhKGZkVgy0JCnCEzQiPUM5iokMs/nFM3hqlAEcJsIUV3Cufp/IUCzlNI5MZ4zUWP72cvEvr6fVsB5mlKdaEY4Xi4aaQZXA/H04oIJgxaaGICyouRXiMRIIKxNS0YTw9Sn8n7Q9263Y3rVfblws4yiAY3ACzoALaqABrkATtAAGHDyAJ/BsSevRerFeF60r1nLmCPyA9fYJQACRTg==</latexit>

Page 4: PARTON ENERGY LOSS & GENERALIZED JET TRANSPORT …€¦ · PARTON ENERGY LOSS & GENERALIZED JET TRANSPORT COEFFICIENT Yuan-Yuan Zhang (CCNU, LBNL) Collaborators: Guang-You Qin, Xin-Nian

Gluon spectrum under approximations

Wµ⌫ ! dNg

dl2?dz<latexit sha1_base64="7M1UxQxTpQwmVikkll0plLguqOw=">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</latexit>

:radiated gluon spectrum {static scattering center (no energy transfer)

soft radiative gluon (z 0)!<latexit sha1_base64="cxWfgFGGW5x61BC31F0o7CjuqG0=">AAAB8nicbVBNS8NAEJ3Ur1q/qh69LBbBU0mqoMeiF48V7AekoWy2m3bpJht2J0op/RlePCji1V/jzX/jts1BWx8MPN6bYWZemEph0HW/ncLa+sbmVnG7tLO7t39QPjxqGZVpxptMSaU7ITVcioQ3UaDknVRzGoeSt8PR7cxvP3JthEoecJzyIKaDRESCUbSS39ViMESqtXrqlStu1Z2DrBIvJxXI0eiVv7p9xbKYJ8gkNcb33BSDCdUomOTTUjczPKVsRAfctzShMTfBZH7ylJxZpU8ipW0lSObq74kJjY0Zx6HtjCkOzbI3E//z/Ayj62AikjRDnrDFoiiTBBWZ/U/6QnOGcmwJZVrYWwkbUk0Z2pRKNgRv+eVV0qpVvYtq7f6yUr/J4yjCCZzCOXhwBXW4gwY0gYGCZ3iFNwedF+fd+Vi0Fpx85hj+wPn8AcQJkZE=</latexit>

agree with GLV result (same approximation)

dN static+softg

dl2?dz=8⇡↵3

sC2(T )CA

NcPqg(z)

Zd2k?(2⇡)2

Zdy�1 ⇢A(y

�1 , ~y?)

⇥~k? ·~l?

l2?(~l? � ~k?)2

✓1� cos[(xL +

xD

1� z)p+y�1 ]

◆1

(k2? + µ2D)2

<latexit sha1_base64="pY2pYLbj0wRNKX30mk4hTkmEZpw=">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</latexit>

Plot scaled gluon spectrum

N static+softg =

Zd'

2⇡

2~k? ·~l?(~l? � ~k?)2

✓1� cos[(xL +

xD

1� z)p+y�1 ]

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with at z=0.1,0.2,0.3N staticg

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