On next to soft threshold corrections to DIS and SIA processes

A. Ajjath (The Institute of Mathematical Sciences, HBNI, Taramani, Chennai, 600113, India) ; Pooja Mukherjee (The Institute of Mathematical Sciences, HBNI, Taramani, Chennai, 600113, India) ; V. Ravindran (The Institute of Mathematical Sciences, HBNI, Taramani, Chennai, 600113, India) ; Aparna Sankar (The Institute of Mathematical Sciences, HBNI, Taramani, Chennai, 600113, India) ; Surabhi Tiwari (The Institute of Mathematical Sciences, HBNI, Taramani, Chennai, 600113, India)

We study the perturbative structure of threshold enhanced logarithms in the coefficient functions of deep inelastic scattering (DIS) and semi-inclusive e + e − annihilation (SIA) processes and setup a framework to sum them up to all orders in perturbation theory. Threshold logarithms show up as the distributions ((1−z) −1 log i (1−z))+ from the soft plus virtual (SV) and as logarithms log i (1−z) from next to SV (NSV) contributions. We use the Sudakov differential and the renormalisation group equations along with the factorisation properties of parton level cross sections to obtain the resummed result which predicts SV as well as next to SV contributions to all orders in strong coupling constant. In Mellin N space, we resum the large logarithms of the form log i (N) keeping 1/N corrections. In particular, the towers of logarithms, each of the form a s n / N α log 2 n α N , a s n / N α log 2 n 1 α N $$ {a}_s^n/{N}^{\alpha }{\log}^{2n-\alpha }(N),{a}_s^n/{N}^{\alpha }{\log}^{2n-1-\alpha }(N)\cdots $$ etc for α = 0, 1, are summed to all orders in a s .

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      "surname": "Mukherjee", 
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      "surname": "Ravindran", 
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      "surname": "Tiwari", 
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      "source": "Springer", 
      "value": "We study the perturbative structure of threshold enhanced logarithms in the coefficient functions of deep inelastic scattering (DIS) and semi-inclusive e + e  \u2212  annihilation (SIA) processes and setup a framework to sum them up to all orders in perturbation theory. Threshold logarithms show up as the distributions ((1\u2212z) \u22121 log i (1\u2212z))+ from the soft plus virtual (SV) and as logarithms log i (1\u2212z) from next to SV (NSV) contributions. We use the Sudakov differential and the renormalisation group equations along with the factorisation properties of parton level cross sections to obtain the resummed result which predicts SV as well as next to SV contributions to all orders in strong coupling constant. In Mellin N space, we resum the large logarithms of the form log i (N) keeping 1/N corrections. In particular, the towers of logarithms, each of the form   <math> <msubsup> <mi>a</mi> <mi>s</mi> <mi>n</mi> </msubsup> <mo>/</mo> <msup> <mi>N</mi> <mi>\u03b1</mi> </msup> <msup> <mo>log</mo> <mrow> <mn>2</mn> <mi>n</mi> <mo>\u2212</mo> <mi>\u03b1</mi> </mrow> </msup> <mfenced> <mi>N</mi> </mfenced> <mo>,</mo> <msubsup> <mi>a</mi> <mi>s</mi> <mi>n</mi> </msubsup> <mo>/</mo> <msup> <mi>N</mi> <mi>\u03b1</mi> </msup> <msup> <mo>log</mo> <mrow> <mn>2</mn> <mi>n</mi> <mo>\u2212</mo> <mn>1</mn> <mo>\u2212</mo> <mi>\u03b1</mi> </mrow> </msup> <mfenced> <mi>N</mi> </mfenced> <mo>\u22ef</mo> </math>  $$ {a}_s^n/{N}^{\\alpha }{\\log}^{2n-\\alpha }(N),{a}_s^n/{N}^{\\alpha }{\\log}^{2n-1-\\alpha }(N)\\cdots $$  etc for \u03b1 = 0, 1, are summed to all orders in a  s ."
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Published on:
14 April 2021
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2021 (2021)
Issue 4
Pages 1-41
DOI:
https://doi.org/10.1007/JHEP04(2021)131
arXiv:
2007.12214
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

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