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--- advanced_tools:renormalization:bphz [2017/09/26 16:26]
jakobadmin [Why is it interesting?]
+++ advanced_tools:renormalization:bphz [2018/03/28 08:52]
184.22.176.169 ↷ Links adapted because of a move operation
@@ Line 3: / Line 3: @@
 <tabbox Why is it interesting?>
-The Bogoliubov-Parasiuk-Hepp-Zimmermann (BPHZ) renormalization scheme is an conceptually extremely interesting way to get rid of the infinities that arise in [[quantum_theory:quantum_field_theory]]. In contrast to other popular scheme, the BPHZ method to get rid of infinites involves no UV cutoff. This is interesting, for example if one considers the famous hierarchy problem. Usually it is argued that a small mass for the Higgs particle is unnatural, because it gets loop corrections that are proportional to the cutoff squared. For a large cutoff scale like, for example, the Planck scale, one would therefore suspect a large Higgs mass, unless these corrections somehow cancel with the bare Higgs mass parameter. In the BPHZ scheme there is no cutoff and therefore no fine-tuning problem:
+The Bogoliubov-Parasiuk-Hepp-Zimmermann (BPHZ) renormalization scheme is an conceptually extremely interesting way to get rid of the infinities that arise in [[theories:quantum_field_theory]]. In contrast to other popular scheme, the BPHZ method to get rid of infinites involves no UV cutoff. This is interesting, for example if one considers the famous hierarchy problem. Usually it is argued that a small mass for the Higgs particle is unnatural, because it gets loop corrections that are proportional to the cutoff $\Lambda$ squared
+$$m_H = m_0 + c \Lambda^2 + \ldots$$
+For a large cutoff scale like, for example, the Planck scale, one would therefore suspect a large Higgs mass, unless these corrections somehow cancel with the bare Higgs mass parameter $m_0$. In the BPHZ scheme there is no cutoff and therefore no fine-tuning problem:
 <blockquote>It has been shown [[https://inspirehep.net/record/12944?ln=en|5)]] that a different renormalization scheme (BPHZ) needs no fine tuning of the bare paramters.
@@ Line 64: / Line 68: @@
 </tabbox>
+{{tag>theories:quantum_theory:quantum_field_theory}}

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